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Research ArticleAutomatic Modulation Classification Exploiting HybridMachine Learning Network
FengWang Shanshan Huang HaoWang and Chenlu Yang
Array and Information Processing Laboratory College of Computer and Information Hohai University West Focheng Road No8Jiangning District Nanjing 211100 China
Correspondence should be addressed to FengWang jihonghopealiyuncom
Received 2 September 2018 Revised 17 October 2018 Accepted 25 November 2018 Published 4 December 2018
Academic Editor Ibrahim Zeid
Copyright copy 2018 Feng Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
It is a research hot spot in cognitive electronic warfare systems to classify the electromagnetic signals of a radar or communicationsystem according to their modulation characteristics We construct a multilayer hybrid machine learning network for theclassification of seven types of signals in different modulation We extract the signal modulation features exploiting a setof algorithms such as time-frequency analysis discrete Fourier transform and instantaneous autocorrelation and accomplishautomatic modulation classification using naive Bayesian and support vector machine in a hybrid manner The parameters in thenetwork for classification are determined automatically in the training process The numerical simulation results indicate that theproposed network accomplishes the classification accurately
1 Introduction
The automatic modulation classification (AMC) of the elec-tromagnetic signals of radar and communication systems isan important function in modern electronic warfare systems[1ndash4] The AMC process in a cognitive electronic warfaresystem for radar and communication signal surveillance isshown in Figure 1 The AMC mainly consists of featureextraction and modulation classification [5ndash7] Modulationfeature extraction is composed of a series of transform andanalysis algorithms in time domain frequency domain ortime-frequency domain such as time-frequency analysis [8]cyclic cumulant [9ndash12] and radar ambiguity function [13]and so on The classification processing consists of variouspattern recognition andmachine learning algorithms such assupport vector machine (SVM) [14] deep learning [15] andclustering algorithms [16]
Pattern recognition has made a lot of progress and gainedextensive applications in the field of computer vision whereSVM artificial neural network and deep learning are widelyused to realize image classification [17ndash19] The AMC ofthe communication and radar signals can be regarded asan important branch of pattern recognition A series ofresults have been reported in a range of open literatures
To recognize the radar emitter signal in [20] the feature isextracted by signal fuzzy function slice and singular valuedecomposition and modulation classification is obtained bythe utilization of a kind of fuzzy clustering classificationapproach In [21] a combination of the ldquoRihaczek distributionand Hough transformrdquo algorithms is introduced to extractthe features of the signals in time-frequency domain andthe AMC of radar signals in quadrature amplitude modu-lation (QAM) and phased shift keying (PSK) modulationis achieved In [22] wavelet transform and manifold learn-ing are employed to realize feature extraction and high-dimensional data dimensionality reduction respectively andthe nearest neighbor algorithm is adopted to realize clas-sification of five types of signals (binary amplitude shiftkeying (2ASK) binary frequency shift keying (2FSK) binaryphase shift keying (BPSK) linear frequency modulation(LFM) and Clock Pulse (CP) A type of feature extractionmethod using blind channel estimation and cumulant isproposed in [23] and classification of the modulated signalsis realized by a type of multiclassification algorithm based onmaximum likelihood [24] accomplishes feature extractionandmodulation classification using high-order cumulant andbinary tree based SVM and verifies its performance usingvarious signals such as 2ASK 4ASK quadrature phase shift
HindawiMathematical Problems in EngineeringVolume 2018 Article ID 6152010 14 pageshttpsdoiorg10115520186152010
2 Mathematical Problems in Engineering
Received signals Signature of modulation Modulation classifier
Support vector machineDeep learning
Feature extraction
Time frequency analysisFourth order cumulant
Figure 1 The structure of an AMC system for radar and communication signal surveillance
keying (QPSK) 2FSK and 4-frequency shift keying (4FSK)[25] gives the modulation feature by the exploitation of atype of time-frequency image method based on local binarymode and identifies the radar signals by SVM algorithm In[26] genetic programming is carried out for extracting usefulfeatures and the nearest neighbor algorithm is selected forthe classification of certain types of radar signals
It can be seen from the above literatures and several otherrelated literatures [27ndash32] that there are several commonproblems in study of this field
(1) The articles usually focus on signals emitted fromeither radar or communication systems while electronicwarfare systems in application may receive signals from bothof these systems That is to say the current studied AMCalgorithms lack a universal study on the classification ofthe radar and communication signals simultaneously (2)The changes of the signal parameters are not considered inconstructing the data sample libraries for training and testthough it has been demonstrated that these changes have asignificant influence on the performance of the classificationalgorithms (3) Without exploring the different multifeaturesof the signal modulations the AMC approaches proposed inmany of the open literatures are based on only one featurewhich makes the classification more difficult to implement(4) Most studies overemphasize the use of advanced clas-sification algorithms while ignoring the study on signalfeature extraction techniques [33]The characteristics ofmosttypes of digital modulation used in modern communicationand radar systems have significant differences which can beobtained according to their definitions using certain featureextraction algorithms The lack of these features actuallyincreases the difficulties of the subsequent classificationalgorithms
Different from the above research works this paperemphasizes feature extraction and classification of the radarand communication signal simultaneously Multidimen-sional modulation features in time-frequency domain fre-quency domain and envelope domain and phase domain areextracted with the utilization of a set of feature extractionalgorithms so as to find the differences of signals in differentmodulation asmuch as possible It aims to reduce the pressureof the classification algorithm effectively and improve theclassification accuracy At the same time a multilayer hybrid
classification network is constructed for the classificationexploiting multiple features and its effectiveness to improvethe classification performance is tested by seven types of radarand communication signals commonly used in practicalsystems including BPSK QPSK 16-quadrature amplitudemodulation (16QAM) LFM single frequency (SF) 2FSK and4FSK
The rest of this paper is organized as follows Section 2gives the structure of the hybrid machine learning algorithmand describes the principle of the signal modulation featureextraction and classification network Section 3 analyzesthe feature extraction algorithms for the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK including time-frequency analysis instantaneous auto-correlation (IA) anddiscrete Fourier transform (DFT) Section 4 analyzes theidea of the dimension reduction of the modulation featureswhen using PCA and SVM for classification Performanceevaluation of the feature extraction and classification networkis discussed in Section 5 The Conclusions are drawn inSection 6
2 The Principle of the HybridClassification Network
Aiming at classifying the signal set BPSK QPSK 16QAMLFM SF 2FSK and 4FSK this paper proposes a hybridAMC network consisting of a variety of modulation featureextraction algorithms and machine learning classificationmethodsThe overall framework of the hybrid AMC networkis shown in Figure 2
(1) Classification of SF LFM and BPSK QPSK 16QAM2FSK and 4FSK According to Figure 2 short-time Fouriertransform (STFT) algorithm is used in the first-layer of thenetwork to extract the standard deviation of the first-orderdifference of the time-frequency spectrumpeaks (recorded as1205771) identifying SF LFM from BPSKQPSK 16QAM 2FSKand 4FSK
According to the signal definition of SF and LFM thefirst-order difference in time-frequency spectrum of thesetwo signals is a fixed constant Hence the values of 1205771for these two modulation types are approximately zeroeswhich is quite different from the large 1205771 values of the other
Mathematical Problems in Engineering 3
BPSK QPSK 16QAM LFM SF 2FSK 4FSK
Training set
Time-frequency analysis
SF LFM
Standard deviationof peak first-order
SF LFM BPSK QPSK 16QAM 2FSK 4FSK
Discrete Fourier transform
2FSKStandard deviation
BPSK QPSK 16QAM
4FSK
Instantaneous autocorrelation
Standard deviation of envelopeStandard deviation Zero-crossing ratio
PCA
Two dimensional feature construction
Test set reconfiguration
Projection matrix
Correct recognition rate
Test set
Instantaneous autocorrelation
Correct recognition rate
SVM Classifier
BPSK QPSK 16QAM
Correct recognition rate
Positive class QPSK
ClassifierSVM1
ClassifierSVM2
No
Negative class BPSK
Negative class 16QAM
Naive Bayes
Naive Bayes
Correct recognition rate
Second layer classification (left)
Second layer classification(right)
Third layer classification
First layer classification
Peak number3
difference1
3 = 2 3 = 4
2
lt
lt
gt
gt
Figure 2 Diagram of the classification network
signals According to the decision threshold 1205881 which canbe obtained through naive Bayes [34] during the trainingperiod the signal set SF LFM can be identified from theother signals
(2) Classification of SF and LFM The left branch of thesecond-layer of the network implements the classification ofthe signal set SF LFM According to the difference of SFand LFM the standard deviation feature based on the realpart of IA is extracted and recorded as 1205772 LFM and SF can
be classified in terms of the decision threshold 1205882 which canbe obtained by the naive Bayes training
(3) Classification of 2FSK 4FSK and BPSKQPSK16QAM The right branch of the second-layer implementsthe classification of the signal set BPSK QPSK 16QAM2FSK and 4FSK The frequency feature based on DFT isextracted for identification The numbers of frequency peaksof 2FSK and 4FSK are 2 and 4 respectively while the otherthree signals havemultiple frequency peaks in the bandwidth
4 Mathematical Problems in Engineering
The number of the frequency peaks is extracted and recordedas 1205773 According to the decision threshold 1205883 which can beobtained by training 2FSK4FSK can be identified from thesignal set BPSK QPSK and 16QAM(4) Classification of BPSK QPSK and 16QAM In thethird-layer of the network the remaining signal set BPSKQPSK 16QAM of the right branch is classified Threefeatures including standard deviation of envelope zero-crossing ratio and standard deviation of the real part of IAare extracted for classification By determining the principalcomponents with the contribution rate PCA algorithm isused to reduce the dimensionality of the features from 3-dimension to two-dimension making it suitable for theapplication of the one-to-one method of SVM RegardingQPSK as a positive class BPSK and 16QAM are sequentiallysubstituted into the SVM classifier as a negative class to findthe support vector Two optimal boundaries are determinedin light of the position of the support vector and theclassification of BPSK QPSK and 16QAM is accomplishedfinally
The classification structure can be regarded as a machinelearning network based on sample training and test It isnecessary to construct a large learning sample aggregate forextracting the modulation features of the above seven signalsand determine the multiple thresholds for the multilayerclassification during the training process In the test phasethe predetermined thresholds are used for different class andthe correct recognition rate of each class is achieved in theend
3 Feature Extraction Algorithms
The extracted modulation features are mainly based on thedifferences of radar and communication signals in time-frequency spectrum frequency spectrum and phase mod-ulation Different algorithms are used to extract differentfeatures for signals of different class The time-frequencyfeature is extracted by using STFT which identifies thesignal set SF LFM from the other signals SF and LFM arediscriminated by the feature of the real part of IA Accordingto the number of frequency peaks which obtained basedon DFT 2FSK and 4FSK are identified from the signal setBPSK QPSK and 16QAM The features based on the realpart of IA are used to distinguish between BPSK QPSKand 16QAM The following section will discuss the featureextraction algorithms including STFT IA and DFT
31 Feature Extraction Based on STFT Time-frequency fea-ture of the signals can be extracted by STFT For a discretesignal 119904(119899) at discrete time instant 119899 its STFT is given by
119904 (119899) ℎ (119899 minus 119898) 119890minus119895(2120587119873119904)119899119896119896 = 0 1 2 119873119904 minus 1
(1)
where 119896 represents the discrete frequency and 119873119904 is thetotal frequency number 119898 refers to time delay and ℎ(119899 minus
119898) denotes the Rectangular window function In (1) thenonstationary signal can be regarded as the superpositionof a series of short-time stationary signals which highlightsthe varying characteristics of the original signal frequencywith time delay The peak of the frequency along time delaydimension can be given by
where119873 denotes the total number of windows and 119875(119898) rep-resents the maximum frequency peak corresponding to the119898th window The frequency peak of each time window canbe extractedThe difference of frequency peak correspondingto two adjacent time windows can be given by
119882 (119898) = 119875 (119898 + 1) minus 119875 (119898) 119898 = 1 2 119873 minus 1 (3)
The standard deviation of the difference in (3) can begiven by
1205771 = radic 1119873 minus 1119873minus1sum119898=1
[119882 (119898) minus 119882]2 (4)
where 119882 refers to the mean of 119882 and 119882 = (1(119873 minus1)) sum119873minus1119898=1119882(119898) The STFT of the seven waveform types withSignal-to-Noise Ratio (SNR) equal to 20 dB are illustrated inFigure 3 As can be seen from Figure 3(a) the frequency ofSF is the same since it has only one frequency The differencebetween the adjacent frequencies for SF is constant so thestandard deviation is zero From Figure 3(b) we can see thatthe frequency of LFM changes linearly which leads to a con-stant difference between the two adjacent frequencies Hencethe standard deviation is also zero Figures 3(c) and 3(d) showthat the frequencies of 2FSK and 4FSK are variable whichmeans that the difference between the adjacent frequenciesis not constant Figures 3(e) 3(f) and 3(g) show that whenthere is a phase variation for BPSK QPSK or 16QAM signalthe instantaneous frequency has a large disturb which leadsto fluctuations between the adjacent frequencies Hence thestandard deviations of the signals such as BPSK QPSK16QAM 2FSK and 4FSK will be larger than those of the SFand LFM In this case SF and LFM can be identified from theother signals by setting the standard deviation threshold 120588132 Feature Extraction Using IA [35] Features based onIA can be extracted to distinguish between SF LFM andBPSK QPSK 16QAM respectively The IA of a discretesignal 119904(119899) is of the following form
where 119898 refers to time delay The difference between thedefinition of IA and auto-correlation function lies in thatthere is no time integration in the calculation of IA Theadvantage of using IA is that it retains the instantaneous phaseinformation of the signal The IA expressions of some of thesignals are analyzed below
where 119860 is the amplitude of the signal 1198910 refers to the carrierfrequency and 1205930 represents the initial phase of the signalThe real part of IA of SF can be given by
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)
where 119902 is the number of samples of the signal It can be seenfrom (7) that if 119898 is certain the IA of SF is related only to thecarrier frequency which is a constant Hence the output ofthe real part of IA is a direct-current (DC) signal as shown inFigure 4(a)
where 120583 is the slope of frequency modulation The real partof IA of LFM can be given by
119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)
It can be seen from (9) that the output of the real part of IA isan alternating current (AC) signal of frequency 120583119898 which isshown in Figure 4(b)
where 120593119894 denotes the discrete phase of a code group repre-senting BPSK or QPSK For BPSK the value of 120593119894 is 0 or 120587For QPSK the value of 120593119894 is 0 1205872 120587 or 31205872 The real partof IA of the PSK signal is of the following form
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119894119901 + 119898 lt 119899 le (119894 + 1) 119901119877 (119899 119898) = 1198602 cos (21205871198910119898 + 120593119894+1 minus 120593119894)
where119901 is the number of samples within one code and119898 lt 119901The real part of IA is DC within the same code period Indifferent code period it can be divided into two cases theadjacent code is the same (120593119894+1minus120593119894 = 0) or different (120593119894+1minus120593119894 =0) For BPSK shown in Figure 4(c) the real part of IA is atwo-value transition of which 120593119894+1 minus 120593119894 = 0 correspondsto a positive transitions and 120593119894+1 minus 120593119894 = plusmn120587 correspondsto a negative transition However there is a status of 120593119894+1 minus120593119894 = plusmn1205872 for QPSK for which the real part of IA is zero(the projection on the real axis) Therefore the real part ofIA for QPSK is a three-value output which is illustrated inFigure 4(d)
From (13) we can see that when 119898 is constant the outputof IA is DC in the same code period However it causesa phase jump 120593119894+1 minus 120593119894 and amplitude transition 119860 119894+1 sdot 119860 119894between different code period Hence the output of the IAfor 16QAM is a multivalue transition see Figure 4(e)
Two features are extracted based on the real part of theIA
where 119886(119894) is the value of the real part based on IA at timeinstant 119894 and 119886 = (1119873119904) sum119873119904119894=1 119886(119894) represents the mean of119886(119894) The standard deviation for SF signal will be small sincethe fluctuation of its IA is small However the IA of LFMfluctuates greatly ie the standard deviation is larger Underthis circumstance SF and LFM can be identified by settingthe standard deviation threshold 1205882 of the real part of IAFeature 2 Define zero-crossing ratio as
1205774 = Num 119886 (119894) isin 1205761 (15)
where Numsdot denotes a counter and 1205761 refers to a smallrange belonging to zero (such as minus0001 lt 1205761 lt 0001) Asshown in the Figure 4 a binary jump occurs for the IA ofBPSK meaning that there is no zero in the output Howeverthe IA of QPSK is of a three-value transition form with alarge number of zeroes in the output The IA of 16QAM issimilar to QPSK Therefore the difference of zero-crossingratio between BPSK and QPSK 16QAM signals can be usedas a classification feature
33 Feature Extraction Based on DFT For the remainingsignal set BPSKQPSK 16QAM 2FSK 4FSK the frequencyspectrum features of the signals are extracted using DFTAccording to the signal definitions the peaks of 2FSKand 4FSK are 2 and 4 within the bandwidth respectivelyHowever there are much more peaks for BPSK QPSK and16QAM
Since frequency peaks of the signal set BPSK QPSK16QAM 2FSK and 4FSK are different the number offrequency peaks based on DFT can be extracted as a typicalfeature For a discrete signal 119904(119899) its DFT can be given by
where 119896 represents the discrete frequency and 119873119904 is the totalfrequency number The number of peak can be defined as
1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)
where | sdot | refers to the modulo operation and 1205762 the thresholdof frequency peak taking 07 times of the maximum valueSince the number of peaks of 2FSK and 4FSK is smaller thanthe other three signals 2FSK and 4FSK can be identified fromother signals by setting the frequency peak threshold 1205883
Mathematical Problems in Engineering 7
0
02
04
06
08
1
12
14A
mpl
itude
1000 2000 3000 4000 50000Sample point
(a) SF
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(b) LFM
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(c) BPSK
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(d) QPSK
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Am
plitu
de
1000 2000 3000 4000 50000Sample point
(e) 16QAM
Figure 4 The real part of IA of the signals
34 Feature Extraction Based on Signal Envelope The mul-tilevel amplitude of the 16QAM signal is quite differentfrom the constant envelope BPSK and QPSK signal Henceenvelope features in time domain can be used to classifyBPSK QPSK and 16QAM For a discrete signal 119904(119899) the
standard deviation of the envelope can be defined as
where 119904 = (1119873119904) sum119873119904119894=1 |119904(119894)| represents the mean of theinstantaneous envelope
4 Analysis of SVM Based on PCADimensionality Reduction
Three features are extracted for the classification of BPSKQPSK and 16QAM so as to ensure the classification accuracyunder various conditions Due to the large number offeatures the classification tends to be complicated If thethree features can be replaced by the two features SVM canbe used to classify the three modulated signals in the Two-dimensional (2D) feature space Therefore PCA algorithm isused to perform principal component analysis on the Three-dimensional (3D) features extracting principal componentsin features and reducing the dimension of features
41 PCA Algorithm The PCA algorithm transforms theoriginal data with possible correlation into a set of newdata with linear independence of each dimension throughlinear transformation and it can be used to extract theprincipal feature components of the data thereby achievingthe purpose of dimensionality reduction [36] The main ideais to map the 1198961 dimensional features to 1198962 dimension (1198962 lt1198961) which is a completely new orthogonal feature called theprincipal component It can be easily understood that PCAcan be used to find the most useful linear combination iethose new features with relatively large discrimination toachieve the purpose of reducing the dimension
There are two basic requirements for PCA dimensionalityreduction First of all the projections of the samples in theprincipal component direction are required to be as dispersedas possible The more dispersed projections the larger thevariance of the samples ie more useful information iscarried in the reduced dimension projections Secondly thedistances from the sample points to the principal componentdirection are required to be as small as possible ie the errorscan be reduced as much as possible The steps of the PCAdimensionality reduction algorithm [37] for 1198961-dimensionalmodulation feature samples are summarized as follows
(1) Arrange the modulation feature samples into matrixX of 119872 (sample numbers) rows and 1198961 columns
(2) Process the sample data recorded as 119883 includingzero-meanization and normalization
(3) For the processed sample data its covariance matrixcan be given by
119877119909 = 1119872 (119883119879119883) (19)
where [sdot]119879 refers to transposition operation(4) According to
119877119909119906 = 120582119906 (20)
calculate the eigenvalue 120582119894 and the eigenvector 119906119894of 119877119909 Arrange the eigenvalues from large to small
Positive classQPSK
ClassifierSVM1
ClassifierSVM2
Negative classBPSK
Negative class16QAM
QPSK BPSK QPSK 16QAM
Figure 5 Three-class classification of SVM based on one-to-onemethod
and the corresponding eigenvectors are also arrangedfrom large to small
where 1198961 is the original sample data dimension and1198962 is the sample data dimension after dimensionalityreductionThe newmatrix 119861 (119861 = [1199061 sdot sdot sdot 1199061198962]) calledprojection matrix is composed of the feature vectorscorresponding to the first 1198962 eigenvalues
(6) Determine the projection data of the original featuredata in the projection matrix and then its principalcomponent can be given by
119909 = 119883119861 (22)
42 One-to-One Multiclassification Method Based on SVMSVM is originally an effective binary-class classificationmethod and its basic model is defined as a linear classifierwith largest interval in feature space For multiclassificationproblems SVM can also achieve classification in an one-to-many mode one-to-one mode etc In this paper the one-to-one mode of SVM is employed due to its simplicity Theflowchart for three-class classification using SVM based onone-to-one method is shown in Figure 5 and it will be usedto classify BPSK QPSK and 16QAM
The basic classification principle of SVM is summarizedbelow The discriminant function of implementing SVM isgiven by [38]
where 119909 is the training sample input after dimensionalityreduction using PCA 119908 refers to a weight vector 119910119894(plusmn1)denotes a category label and 119887 is an offset Its interval is givenby
The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into
120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)
where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get
where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples
The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification
5 Simulation Analysis
51 Performance Analysis without Fading Channel Effect
511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation
512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations
Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As
10 Mathematical Problems in Engineering
Table 1 Parameters for different types of modulated signals
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
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Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
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250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
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umbe
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Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
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200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
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Figure 11 Standard deviation of envelope
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05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
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2 Mathematical Problems in Engineering
Received signals Signature of modulation Modulation classifier
Support vector machineDeep learning
Feature extraction
Time frequency analysisFourth order cumulant
Figure 1 The structure of an AMC system for radar and communication signal surveillance
keying (QPSK) 2FSK and 4-frequency shift keying (4FSK)[25] gives the modulation feature by the exploitation of atype of time-frequency image method based on local binarymode and identifies the radar signals by SVM algorithm In[26] genetic programming is carried out for extracting usefulfeatures and the nearest neighbor algorithm is selected forthe classification of certain types of radar signals
It can be seen from the above literatures and several otherrelated literatures [27ndash32] that there are several commonproblems in study of this field
(1) The articles usually focus on signals emitted fromeither radar or communication systems while electronicwarfare systems in application may receive signals from bothof these systems That is to say the current studied AMCalgorithms lack a universal study on the classification ofthe radar and communication signals simultaneously (2)The changes of the signal parameters are not considered inconstructing the data sample libraries for training and testthough it has been demonstrated that these changes have asignificant influence on the performance of the classificationalgorithms (3) Without exploring the different multifeaturesof the signal modulations the AMC approaches proposed inmany of the open literatures are based on only one featurewhich makes the classification more difficult to implement(4) Most studies overemphasize the use of advanced clas-sification algorithms while ignoring the study on signalfeature extraction techniques [33]The characteristics ofmosttypes of digital modulation used in modern communicationand radar systems have significant differences which can beobtained according to their definitions using certain featureextraction algorithms The lack of these features actuallyincreases the difficulties of the subsequent classificationalgorithms
Different from the above research works this paperemphasizes feature extraction and classification of the radarand communication signal simultaneously Multidimen-sional modulation features in time-frequency domain fre-quency domain and envelope domain and phase domain areextracted with the utilization of a set of feature extractionalgorithms so as to find the differences of signals in differentmodulation asmuch as possible It aims to reduce the pressureof the classification algorithm effectively and improve theclassification accuracy At the same time a multilayer hybrid
classification network is constructed for the classificationexploiting multiple features and its effectiveness to improvethe classification performance is tested by seven types of radarand communication signals commonly used in practicalsystems including BPSK QPSK 16-quadrature amplitudemodulation (16QAM) LFM single frequency (SF) 2FSK and4FSK
The rest of this paper is organized as follows Section 2gives the structure of the hybrid machine learning algorithmand describes the principle of the signal modulation featureextraction and classification network Section 3 analyzesthe feature extraction algorithms for the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK including time-frequency analysis instantaneous auto-correlation (IA) anddiscrete Fourier transform (DFT) Section 4 analyzes theidea of the dimension reduction of the modulation featureswhen using PCA and SVM for classification Performanceevaluation of the feature extraction and classification networkis discussed in Section 5 The Conclusions are drawn inSection 6
2 The Principle of the HybridClassification Network
Aiming at classifying the signal set BPSK QPSK 16QAMLFM SF 2FSK and 4FSK this paper proposes a hybridAMC network consisting of a variety of modulation featureextraction algorithms and machine learning classificationmethodsThe overall framework of the hybrid AMC networkis shown in Figure 2
(1) Classification of SF LFM and BPSK QPSK 16QAM2FSK and 4FSK According to Figure 2 short-time Fouriertransform (STFT) algorithm is used in the first-layer of thenetwork to extract the standard deviation of the first-orderdifference of the time-frequency spectrumpeaks (recorded as1205771) identifying SF LFM from BPSKQPSK 16QAM 2FSKand 4FSK
According to the signal definition of SF and LFM thefirst-order difference in time-frequency spectrum of thesetwo signals is a fixed constant Hence the values of 1205771for these two modulation types are approximately zeroeswhich is quite different from the large 1205771 values of the other
Mathematical Problems in Engineering 3
BPSK QPSK 16QAM LFM SF 2FSK 4FSK
Training set
Time-frequency analysis
SF LFM
Standard deviationof peak first-order
SF LFM BPSK QPSK 16QAM 2FSK 4FSK
Discrete Fourier transform
2FSKStandard deviation
BPSK QPSK 16QAM
4FSK
Instantaneous autocorrelation
Standard deviation of envelopeStandard deviation Zero-crossing ratio
PCA
Two dimensional feature construction
Test set reconfiguration
Projection matrix
Correct recognition rate
Test set
Instantaneous autocorrelation
Correct recognition rate
SVM Classifier
BPSK QPSK 16QAM
Correct recognition rate
Positive class QPSK
ClassifierSVM1
ClassifierSVM2
No
Negative class BPSK
Negative class 16QAM
Naive Bayes
Naive Bayes
Correct recognition rate
Second layer classification (left)
Second layer classification(right)
Third layer classification
First layer classification
Peak number3
difference1
3 = 2 3 = 4
2
lt
lt
gt
gt
Figure 2 Diagram of the classification network
signals According to the decision threshold 1205881 which canbe obtained through naive Bayes [34] during the trainingperiod the signal set SF LFM can be identified from theother signals
(2) Classification of SF and LFM The left branch of thesecond-layer of the network implements the classification ofthe signal set SF LFM According to the difference of SFand LFM the standard deviation feature based on the realpart of IA is extracted and recorded as 1205772 LFM and SF can
be classified in terms of the decision threshold 1205882 which canbe obtained by the naive Bayes training
(3) Classification of 2FSK 4FSK and BPSKQPSK16QAM The right branch of the second-layer implementsthe classification of the signal set BPSK QPSK 16QAM2FSK and 4FSK The frequency feature based on DFT isextracted for identification The numbers of frequency peaksof 2FSK and 4FSK are 2 and 4 respectively while the otherthree signals havemultiple frequency peaks in the bandwidth
4 Mathematical Problems in Engineering
The number of the frequency peaks is extracted and recordedas 1205773 According to the decision threshold 1205883 which can beobtained by training 2FSK4FSK can be identified from thesignal set BPSK QPSK and 16QAM(4) Classification of BPSK QPSK and 16QAM In thethird-layer of the network the remaining signal set BPSKQPSK 16QAM of the right branch is classified Threefeatures including standard deviation of envelope zero-crossing ratio and standard deviation of the real part of IAare extracted for classification By determining the principalcomponents with the contribution rate PCA algorithm isused to reduce the dimensionality of the features from 3-dimension to two-dimension making it suitable for theapplication of the one-to-one method of SVM RegardingQPSK as a positive class BPSK and 16QAM are sequentiallysubstituted into the SVM classifier as a negative class to findthe support vector Two optimal boundaries are determinedin light of the position of the support vector and theclassification of BPSK QPSK and 16QAM is accomplishedfinally
The classification structure can be regarded as a machinelearning network based on sample training and test It isnecessary to construct a large learning sample aggregate forextracting the modulation features of the above seven signalsand determine the multiple thresholds for the multilayerclassification during the training process In the test phasethe predetermined thresholds are used for different class andthe correct recognition rate of each class is achieved in theend
3 Feature Extraction Algorithms
The extracted modulation features are mainly based on thedifferences of radar and communication signals in time-frequency spectrum frequency spectrum and phase mod-ulation Different algorithms are used to extract differentfeatures for signals of different class The time-frequencyfeature is extracted by using STFT which identifies thesignal set SF LFM from the other signals SF and LFM arediscriminated by the feature of the real part of IA Accordingto the number of frequency peaks which obtained basedon DFT 2FSK and 4FSK are identified from the signal setBPSK QPSK and 16QAM The features based on the realpart of IA are used to distinguish between BPSK QPSKand 16QAM The following section will discuss the featureextraction algorithms including STFT IA and DFT
31 Feature Extraction Based on STFT Time-frequency fea-ture of the signals can be extracted by STFT For a discretesignal 119904(119899) at discrete time instant 119899 its STFT is given by
119904 (119899) ℎ (119899 minus 119898) 119890minus119895(2120587119873119904)119899119896119896 = 0 1 2 119873119904 minus 1
(1)
where 119896 represents the discrete frequency and 119873119904 is thetotal frequency number 119898 refers to time delay and ℎ(119899 minus
119898) denotes the Rectangular window function In (1) thenonstationary signal can be regarded as the superpositionof a series of short-time stationary signals which highlightsthe varying characteristics of the original signal frequencywith time delay The peak of the frequency along time delaydimension can be given by
where119873 denotes the total number of windows and 119875(119898) rep-resents the maximum frequency peak corresponding to the119898th window The frequency peak of each time window canbe extractedThe difference of frequency peak correspondingto two adjacent time windows can be given by
119882 (119898) = 119875 (119898 + 1) minus 119875 (119898) 119898 = 1 2 119873 minus 1 (3)
The standard deviation of the difference in (3) can begiven by
1205771 = radic 1119873 minus 1119873minus1sum119898=1
[119882 (119898) minus 119882]2 (4)
where 119882 refers to the mean of 119882 and 119882 = (1(119873 minus1)) sum119873minus1119898=1119882(119898) The STFT of the seven waveform types withSignal-to-Noise Ratio (SNR) equal to 20 dB are illustrated inFigure 3 As can be seen from Figure 3(a) the frequency ofSF is the same since it has only one frequency The differencebetween the adjacent frequencies for SF is constant so thestandard deviation is zero From Figure 3(b) we can see thatthe frequency of LFM changes linearly which leads to a con-stant difference between the two adjacent frequencies Hencethe standard deviation is also zero Figures 3(c) and 3(d) showthat the frequencies of 2FSK and 4FSK are variable whichmeans that the difference between the adjacent frequenciesis not constant Figures 3(e) 3(f) and 3(g) show that whenthere is a phase variation for BPSK QPSK or 16QAM signalthe instantaneous frequency has a large disturb which leadsto fluctuations between the adjacent frequencies Hence thestandard deviations of the signals such as BPSK QPSK16QAM 2FSK and 4FSK will be larger than those of the SFand LFM In this case SF and LFM can be identified from theother signals by setting the standard deviation threshold 120588132 Feature Extraction Using IA [35] Features based onIA can be extracted to distinguish between SF LFM andBPSK QPSK 16QAM respectively The IA of a discretesignal 119904(119899) is of the following form
where 119898 refers to time delay The difference between thedefinition of IA and auto-correlation function lies in thatthere is no time integration in the calculation of IA Theadvantage of using IA is that it retains the instantaneous phaseinformation of the signal The IA expressions of some of thesignals are analyzed below
where 119860 is the amplitude of the signal 1198910 refers to the carrierfrequency and 1205930 represents the initial phase of the signalThe real part of IA of SF can be given by
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)
where 119902 is the number of samples of the signal It can be seenfrom (7) that if 119898 is certain the IA of SF is related only to thecarrier frequency which is a constant Hence the output ofthe real part of IA is a direct-current (DC) signal as shown inFigure 4(a)
where 120583 is the slope of frequency modulation The real partof IA of LFM can be given by
119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)
It can be seen from (9) that the output of the real part of IA isan alternating current (AC) signal of frequency 120583119898 which isshown in Figure 4(b)
where 120593119894 denotes the discrete phase of a code group repre-senting BPSK or QPSK For BPSK the value of 120593119894 is 0 or 120587For QPSK the value of 120593119894 is 0 1205872 120587 or 31205872 The real partof IA of the PSK signal is of the following form
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119894119901 + 119898 lt 119899 le (119894 + 1) 119901119877 (119899 119898) = 1198602 cos (21205871198910119898 + 120593119894+1 minus 120593119894)
where119901 is the number of samples within one code and119898 lt 119901The real part of IA is DC within the same code period Indifferent code period it can be divided into two cases theadjacent code is the same (120593119894+1minus120593119894 = 0) or different (120593119894+1minus120593119894 =0) For BPSK shown in Figure 4(c) the real part of IA is atwo-value transition of which 120593119894+1 minus 120593119894 = 0 correspondsto a positive transitions and 120593119894+1 minus 120593119894 = plusmn120587 correspondsto a negative transition However there is a status of 120593119894+1 minus120593119894 = plusmn1205872 for QPSK for which the real part of IA is zero(the projection on the real axis) Therefore the real part ofIA for QPSK is a three-value output which is illustrated inFigure 4(d)
From (13) we can see that when 119898 is constant the outputof IA is DC in the same code period However it causesa phase jump 120593119894+1 minus 120593119894 and amplitude transition 119860 119894+1 sdot 119860 119894between different code period Hence the output of the IAfor 16QAM is a multivalue transition see Figure 4(e)
Two features are extracted based on the real part of theIA
where 119886(119894) is the value of the real part based on IA at timeinstant 119894 and 119886 = (1119873119904) sum119873119904119894=1 119886(119894) represents the mean of119886(119894) The standard deviation for SF signal will be small sincethe fluctuation of its IA is small However the IA of LFMfluctuates greatly ie the standard deviation is larger Underthis circumstance SF and LFM can be identified by settingthe standard deviation threshold 1205882 of the real part of IAFeature 2 Define zero-crossing ratio as
1205774 = Num 119886 (119894) isin 1205761 (15)
where Numsdot denotes a counter and 1205761 refers to a smallrange belonging to zero (such as minus0001 lt 1205761 lt 0001) Asshown in the Figure 4 a binary jump occurs for the IA ofBPSK meaning that there is no zero in the output Howeverthe IA of QPSK is of a three-value transition form with alarge number of zeroes in the output The IA of 16QAM issimilar to QPSK Therefore the difference of zero-crossingratio between BPSK and QPSK 16QAM signals can be usedas a classification feature
33 Feature Extraction Based on DFT For the remainingsignal set BPSKQPSK 16QAM 2FSK 4FSK the frequencyspectrum features of the signals are extracted using DFTAccording to the signal definitions the peaks of 2FSKand 4FSK are 2 and 4 within the bandwidth respectivelyHowever there are much more peaks for BPSK QPSK and16QAM
Since frequency peaks of the signal set BPSK QPSK16QAM 2FSK and 4FSK are different the number offrequency peaks based on DFT can be extracted as a typicalfeature For a discrete signal 119904(119899) its DFT can be given by
where 119896 represents the discrete frequency and 119873119904 is the totalfrequency number The number of peak can be defined as
1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)
where | sdot | refers to the modulo operation and 1205762 the thresholdof frequency peak taking 07 times of the maximum valueSince the number of peaks of 2FSK and 4FSK is smaller thanthe other three signals 2FSK and 4FSK can be identified fromother signals by setting the frequency peak threshold 1205883
Mathematical Problems in Engineering 7
0
02
04
06
08
1
12
14A
mpl
itude
1000 2000 3000 4000 50000Sample point
(a) SF
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(b) LFM
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(c) BPSK
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(d) QPSK
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Am
plitu
de
1000 2000 3000 4000 50000Sample point
(e) 16QAM
Figure 4 The real part of IA of the signals
34 Feature Extraction Based on Signal Envelope The mul-tilevel amplitude of the 16QAM signal is quite differentfrom the constant envelope BPSK and QPSK signal Henceenvelope features in time domain can be used to classifyBPSK QPSK and 16QAM For a discrete signal 119904(119899) the
standard deviation of the envelope can be defined as
where 119904 = (1119873119904) sum119873119904119894=1 |119904(119894)| represents the mean of theinstantaneous envelope
4 Analysis of SVM Based on PCADimensionality Reduction
Three features are extracted for the classification of BPSKQPSK and 16QAM so as to ensure the classification accuracyunder various conditions Due to the large number offeatures the classification tends to be complicated If thethree features can be replaced by the two features SVM canbe used to classify the three modulated signals in the Two-dimensional (2D) feature space Therefore PCA algorithm isused to perform principal component analysis on the Three-dimensional (3D) features extracting principal componentsin features and reducing the dimension of features
41 PCA Algorithm The PCA algorithm transforms theoriginal data with possible correlation into a set of newdata with linear independence of each dimension throughlinear transformation and it can be used to extract theprincipal feature components of the data thereby achievingthe purpose of dimensionality reduction [36] The main ideais to map the 1198961 dimensional features to 1198962 dimension (1198962 lt1198961) which is a completely new orthogonal feature called theprincipal component It can be easily understood that PCAcan be used to find the most useful linear combination iethose new features with relatively large discrimination toachieve the purpose of reducing the dimension
There are two basic requirements for PCA dimensionalityreduction First of all the projections of the samples in theprincipal component direction are required to be as dispersedas possible The more dispersed projections the larger thevariance of the samples ie more useful information iscarried in the reduced dimension projections Secondly thedistances from the sample points to the principal componentdirection are required to be as small as possible ie the errorscan be reduced as much as possible The steps of the PCAdimensionality reduction algorithm [37] for 1198961-dimensionalmodulation feature samples are summarized as follows
(1) Arrange the modulation feature samples into matrixX of 119872 (sample numbers) rows and 1198961 columns
(2) Process the sample data recorded as 119883 includingzero-meanization and normalization
(3) For the processed sample data its covariance matrixcan be given by
119877119909 = 1119872 (119883119879119883) (19)
where [sdot]119879 refers to transposition operation(4) According to
119877119909119906 = 120582119906 (20)
calculate the eigenvalue 120582119894 and the eigenvector 119906119894of 119877119909 Arrange the eigenvalues from large to small
Positive classQPSK
ClassifierSVM1
ClassifierSVM2
Negative classBPSK
Negative class16QAM
QPSK BPSK QPSK 16QAM
Figure 5 Three-class classification of SVM based on one-to-onemethod
and the corresponding eigenvectors are also arrangedfrom large to small
where 1198961 is the original sample data dimension and1198962 is the sample data dimension after dimensionalityreductionThe newmatrix 119861 (119861 = [1199061 sdot sdot sdot 1199061198962]) calledprojection matrix is composed of the feature vectorscorresponding to the first 1198962 eigenvalues
(6) Determine the projection data of the original featuredata in the projection matrix and then its principalcomponent can be given by
119909 = 119883119861 (22)
42 One-to-One Multiclassification Method Based on SVMSVM is originally an effective binary-class classificationmethod and its basic model is defined as a linear classifierwith largest interval in feature space For multiclassificationproblems SVM can also achieve classification in an one-to-many mode one-to-one mode etc In this paper the one-to-one mode of SVM is employed due to its simplicity Theflowchart for three-class classification using SVM based onone-to-one method is shown in Figure 5 and it will be usedto classify BPSK QPSK and 16QAM
The basic classification principle of SVM is summarizedbelow The discriminant function of implementing SVM isgiven by [38]
where 119909 is the training sample input after dimensionalityreduction using PCA 119908 refers to a weight vector 119910119894(plusmn1)denotes a category label and 119887 is an offset Its interval is givenby
The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into
120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)
where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get
where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples
The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification
5 Simulation Analysis
51 Performance Analysis without Fading Channel Effect
511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation
512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations
Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As
10 Mathematical Problems in Engineering
Table 1 Parameters for different types of modulated signals
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
02
03
04
05
06
07
08
Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
50
100
150
200
250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
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Mathematical Problems in Engineering 3
BPSK QPSK 16QAM LFM SF 2FSK 4FSK
Training set
Time-frequency analysis
SF LFM
Standard deviationof peak first-order
SF LFM BPSK QPSK 16QAM 2FSK 4FSK
Discrete Fourier transform
2FSKStandard deviation
BPSK QPSK 16QAM
4FSK
Instantaneous autocorrelation
Standard deviation of envelopeStandard deviation Zero-crossing ratio
PCA
Two dimensional feature construction
Test set reconfiguration
Projection matrix
Correct recognition rate
Test set
Instantaneous autocorrelation
Correct recognition rate
SVM Classifier
BPSK QPSK 16QAM
Correct recognition rate
Positive class QPSK
ClassifierSVM1
ClassifierSVM2
No
Negative class BPSK
Negative class 16QAM
Naive Bayes
Naive Bayes
Correct recognition rate
Second layer classification (left)
Second layer classification(right)
Third layer classification
First layer classification
Peak number3
difference1
3 = 2 3 = 4
2
lt
lt
gt
gt
Figure 2 Diagram of the classification network
signals According to the decision threshold 1205881 which canbe obtained through naive Bayes [34] during the trainingperiod the signal set SF LFM can be identified from theother signals
(2) Classification of SF and LFM The left branch of thesecond-layer of the network implements the classification ofthe signal set SF LFM According to the difference of SFand LFM the standard deviation feature based on the realpart of IA is extracted and recorded as 1205772 LFM and SF can
be classified in terms of the decision threshold 1205882 which canbe obtained by the naive Bayes training
(3) Classification of 2FSK 4FSK and BPSKQPSK16QAM The right branch of the second-layer implementsthe classification of the signal set BPSK QPSK 16QAM2FSK and 4FSK The frequency feature based on DFT isextracted for identification The numbers of frequency peaksof 2FSK and 4FSK are 2 and 4 respectively while the otherthree signals havemultiple frequency peaks in the bandwidth
4 Mathematical Problems in Engineering
The number of the frequency peaks is extracted and recordedas 1205773 According to the decision threshold 1205883 which can beobtained by training 2FSK4FSK can be identified from thesignal set BPSK QPSK and 16QAM(4) Classification of BPSK QPSK and 16QAM In thethird-layer of the network the remaining signal set BPSKQPSK 16QAM of the right branch is classified Threefeatures including standard deviation of envelope zero-crossing ratio and standard deviation of the real part of IAare extracted for classification By determining the principalcomponents with the contribution rate PCA algorithm isused to reduce the dimensionality of the features from 3-dimension to two-dimension making it suitable for theapplication of the one-to-one method of SVM RegardingQPSK as a positive class BPSK and 16QAM are sequentiallysubstituted into the SVM classifier as a negative class to findthe support vector Two optimal boundaries are determinedin light of the position of the support vector and theclassification of BPSK QPSK and 16QAM is accomplishedfinally
The classification structure can be regarded as a machinelearning network based on sample training and test It isnecessary to construct a large learning sample aggregate forextracting the modulation features of the above seven signalsand determine the multiple thresholds for the multilayerclassification during the training process In the test phasethe predetermined thresholds are used for different class andthe correct recognition rate of each class is achieved in theend
3 Feature Extraction Algorithms
The extracted modulation features are mainly based on thedifferences of radar and communication signals in time-frequency spectrum frequency spectrum and phase mod-ulation Different algorithms are used to extract differentfeatures for signals of different class The time-frequencyfeature is extracted by using STFT which identifies thesignal set SF LFM from the other signals SF and LFM arediscriminated by the feature of the real part of IA Accordingto the number of frequency peaks which obtained basedon DFT 2FSK and 4FSK are identified from the signal setBPSK QPSK and 16QAM The features based on the realpart of IA are used to distinguish between BPSK QPSKand 16QAM The following section will discuss the featureextraction algorithms including STFT IA and DFT
31 Feature Extraction Based on STFT Time-frequency fea-ture of the signals can be extracted by STFT For a discretesignal 119904(119899) at discrete time instant 119899 its STFT is given by
119904 (119899) ℎ (119899 minus 119898) 119890minus119895(2120587119873119904)119899119896119896 = 0 1 2 119873119904 minus 1
(1)
where 119896 represents the discrete frequency and 119873119904 is thetotal frequency number 119898 refers to time delay and ℎ(119899 minus
119898) denotes the Rectangular window function In (1) thenonstationary signal can be regarded as the superpositionof a series of short-time stationary signals which highlightsthe varying characteristics of the original signal frequencywith time delay The peak of the frequency along time delaydimension can be given by
where119873 denotes the total number of windows and 119875(119898) rep-resents the maximum frequency peak corresponding to the119898th window The frequency peak of each time window canbe extractedThe difference of frequency peak correspondingto two adjacent time windows can be given by
119882 (119898) = 119875 (119898 + 1) minus 119875 (119898) 119898 = 1 2 119873 minus 1 (3)
The standard deviation of the difference in (3) can begiven by
1205771 = radic 1119873 minus 1119873minus1sum119898=1
[119882 (119898) minus 119882]2 (4)
where 119882 refers to the mean of 119882 and 119882 = (1(119873 minus1)) sum119873minus1119898=1119882(119898) The STFT of the seven waveform types withSignal-to-Noise Ratio (SNR) equal to 20 dB are illustrated inFigure 3 As can be seen from Figure 3(a) the frequency ofSF is the same since it has only one frequency The differencebetween the adjacent frequencies for SF is constant so thestandard deviation is zero From Figure 3(b) we can see thatthe frequency of LFM changes linearly which leads to a con-stant difference between the two adjacent frequencies Hencethe standard deviation is also zero Figures 3(c) and 3(d) showthat the frequencies of 2FSK and 4FSK are variable whichmeans that the difference between the adjacent frequenciesis not constant Figures 3(e) 3(f) and 3(g) show that whenthere is a phase variation for BPSK QPSK or 16QAM signalthe instantaneous frequency has a large disturb which leadsto fluctuations between the adjacent frequencies Hence thestandard deviations of the signals such as BPSK QPSK16QAM 2FSK and 4FSK will be larger than those of the SFand LFM In this case SF and LFM can be identified from theother signals by setting the standard deviation threshold 120588132 Feature Extraction Using IA [35] Features based onIA can be extracted to distinguish between SF LFM andBPSK QPSK 16QAM respectively The IA of a discretesignal 119904(119899) is of the following form
where 119898 refers to time delay The difference between thedefinition of IA and auto-correlation function lies in thatthere is no time integration in the calculation of IA Theadvantage of using IA is that it retains the instantaneous phaseinformation of the signal The IA expressions of some of thesignals are analyzed below
where 119860 is the amplitude of the signal 1198910 refers to the carrierfrequency and 1205930 represents the initial phase of the signalThe real part of IA of SF can be given by
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)
where 119902 is the number of samples of the signal It can be seenfrom (7) that if 119898 is certain the IA of SF is related only to thecarrier frequency which is a constant Hence the output ofthe real part of IA is a direct-current (DC) signal as shown inFigure 4(a)
where 120583 is the slope of frequency modulation The real partof IA of LFM can be given by
119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)
It can be seen from (9) that the output of the real part of IA isan alternating current (AC) signal of frequency 120583119898 which isshown in Figure 4(b)
where 120593119894 denotes the discrete phase of a code group repre-senting BPSK or QPSK For BPSK the value of 120593119894 is 0 or 120587For QPSK the value of 120593119894 is 0 1205872 120587 or 31205872 The real partof IA of the PSK signal is of the following form
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119894119901 + 119898 lt 119899 le (119894 + 1) 119901119877 (119899 119898) = 1198602 cos (21205871198910119898 + 120593119894+1 minus 120593119894)
where119901 is the number of samples within one code and119898 lt 119901The real part of IA is DC within the same code period Indifferent code period it can be divided into two cases theadjacent code is the same (120593119894+1minus120593119894 = 0) or different (120593119894+1minus120593119894 =0) For BPSK shown in Figure 4(c) the real part of IA is atwo-value transition of which 120593119894+1 minus 120593119894 = 0 correspondsto a positive transitions and 120593119894+1 minus 120593119894 = plusmn120587 correspondsto a negative transition However there is a status of 120593119894+1 minus120593119894 = plusmn1205872 for QPSK for which the real part of IA is zero(the projection on the real axis) Therefore the real part ofIA for QPSK is a three-value output which is illustrated inFigure 4(d)
From (13) we can see that when 119898 is constant the outputof IA is DC in the same code period However it causesa phase jump 120593119894+1 minus 120593119894 and amplitude transition 119860 119894+1 sdot 119860 119894between different code period Hence the output of the IAfor 16QAM is a multivalue transition see Figure 4(e)
Two features are extracted based on the real part of theIA
where 119886(119894) is the value of the real part based on IA at timeinstant 119894 and 119886 = (1119873119904) sum119873119904119894=1 119886(119894) represents the mean of119886(119894) The standard deviation for SF signal will be small sincethe fluctuation of its IA is small However the IA of LFMfluctuates greatly ie the standard deviation is larger Underthis circumstance SF and LFM can be identified by settingthe standard deviation threshold 1205882 of the real part of IAFeature 2 Define zero-crossing ratio as
1205774 = Num 119886 (119894) isin 1205761 (15)
where Numsdot denotes a counter and 1205761 refers to a smallrange belonging to zero (such as minus0001 lt 1205761 lt 0001) Asshown in the Figure 4 a binary jump occurs for the IA ofBPSK meaning that there is no zero in the output Howeverthe IA of QPSK is of a three-value transition form with alarge number of zeroes in the output The IA of 16QAM issimilar to QPSK Therefore the difference of zero-crossingratio between BPSK and QPSK 16QAM signals can be usedas a classification feature
33 Feature Extraction Based on DFT For the remainingsignal set BPSKQPSK 16QAM 2FSK 4FSK the frequencyspectrum features of the signals are extracted using DFTAccording to the signal definitions the peaks of 2FSKand 4FSK are 2 and 4 within the bandwidth respectivelyHowever there are much more peaks for BPSK QPSK and16QAM
Since frequency peaks of the signal set BPSK QPSK16QAM 2FSK and 4FSK are different the number offrequency peaks based on DFT can be extracted as a typicalfeature For a discrete signal 119904(119899) its DFT can be given by
where 119896 represents the discrete frequency and 119873119904 is the totalfrequency number The number of peak can be defined as
1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)
where | sdot | refers to the modulo operation and 1205762 the thresholdof frequency peak taking 07 times of the maximum valueSince the number of peaks of 2FSK and 4FSK is smaller thanthe other three signals 2FSK and 4FSK can be identified fromother signals by setting the frequency peak threshold 1205883
Mathematical Problems in Engineering 7
0
02
04
06
08
1
12
14A
mpl
itude
1000 2000 3000 4000 50000Sample point
(a) SF
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(b) LFM
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(c) BPSK
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(d) QPSK
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Am
plitu
de
1000 2000 3000 4000 50000Sample point
(e) 16QAM
Figure 4 The real part of IA of the signals
34 Feature Extraction Based on Signal Envelope The mul-tilevel amplitude of the 16QAM signal is quite differentfrom the constant envelope BPSK and QPSK signal Henceenvelope features in time domain can be used to classifyBPSK QPSK and 16QAM For a discrete signal 119904(119899) the
standard deviation of the envelope can be defined as
where 119904 = (1119873119904) sum119873119904119894=1 |119904(119894)| represents the mean of theinstantaneous envelope
4 Analysis of SVM Based on PCADimensionality Reduction
Three features are extracted for the classification of BPSKQPSK and 16QAM so as to ensure the classification accuracyunder various conditions Due to the large number offeatures the classification tends to be complicated If thethree features can be replaced by the two features SVM canbe used to classify the three modulated signals in the Two-dimensional (2D) feature space Therefore PCA algorithm isused to perform principal component analysis on the Three-dimensional (3D) features extracting principal componentsin features and reducing the dimension of features
41 PCA Algorithm The PCA algorithm transforms theoriginal data with possible correlation into a set of newdata with linear independence of each dimension throughlinear transformation and it can be used to extract theprincipal feature components of the data thereby achievingthe purpose of dimensionality reduction [36] The main ideais to map the 1198961 dimensional features to 1198962 dimension (1198962 lt1198961) which is a completely new orthogonal feature called theprincipal component It can be easily understood that PCAcan be used to find the most useful linear combination iethose new features with relatively large discrimination toachieve the purpose of reducing the dimension
There are two basic requirements for PCA dimensionalityreduction First of all the projections of the samples in theprincipal component direction are required to be as dispersedas possible The more dispersed projections the larger thevariance of the samples ie more useful information iscarried in the reduced dimension projections Secondly thedistances from the sample points to the principal componentdirection are required to be as small as possible ie the errorscan be reduced as much as possible The steps of the PCAdimensionality reduction algorithm [37] for 1198961-dimensionalmodulation feature samples are summarized as follows
(1) Arrange the modulation feature samples into matrixX of 119872 (sample numbers) rows and 1198961 columns
(2) Process the sample data recorded as 119883 includingzero-meanization and normalization
(3) For the processed sample data its covariance matrixcan be given by
119877119909 = 1119872 (119883119879119883) (19)
where [sdot]119879 refers to transposition operation(4) According to
119877119909119906 = 120582119906 (20)
calculate the eigenvalue 120582119894 and the eigenvector 119906119894of 119877119909 Arrange the eigenvalues from large to small
Positive classQPSK
ClassifierSVM1
ClassifierSVM2
Negative classBPSK
Negative class16QAM
QPSK BPSK QPSK 16QAM
Figure 5 Three-class classification of SVM based on one-to-onemethod
and the corresponding eigenvectors are also arrangedfrom large to small
where 1198961 is the original sample data dimension and1198962 is the sample data dimension after dimensionalityreductionThe newmatrix 119861 (119861 = [1199061 sdot sdot sdot 1199061198962]) calledprojection matrix is composed of the feature vectorscorresponding to the first 1198962 eigenvalues
(6) Determine the projection data of the original featuredata in the projection matrix and then its principalcomponent can be given by
119909 = 119883119861 (22)
42 One-to-One Multiclassification Method Based on SVMSVM is originally an effective binary-class classificationmethod and its basic model is defined as a linear classifierwith largest interval in feature space For multiclassificationproblems SVM can also achieve classification in an one-to-many mode one-to-one mode etc In this paper the one-to-one mode of SVM is employed due to its simplicity Theflowchart for three-class classification using SVM based onone-to-one method is shown in Figure 5 and it will be usedto classify BPSK QPSK and 16QAM
The basic classification principle of SVM is summarizedbelow The discriminant function of implementing SVM isgiven by [38]
where 119909 is the training sample input after dimensionalityreduction using PCA 119908 refers to a weight vector 119910119894(plusmn1)denotes a category label and 119887 is an offset Its interval is givenby
The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into
120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)
where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get
where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples
The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification
5 Simulation Analysis
51 Performance Analysis without Fading Channel Effect
511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation
512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations
Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As
10 Mathematical Problems in Engineering
Table 1 Parameters for different types of modulated signals
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
02
03
04
05
06
07
08
Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
50
100
150
200
250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
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4 Mathematical Problems in Engineering
The number of the frequency peaks is extracted and recordedas 1205773 According to the decision threshold 1205883 which can beobtained by training 2FSK4FSK can be identified from thesignal set BPSK QPSK and 16QAM(4) Classification of BPSK QPSK and 16QAM In thethird-layer of the network the remaining signal set BPSKQPSK 16QAM of the right branch is classified Threefeatures including standard deviation of envelope zero-crossing ratio and standard deviation of the real part of IAare extracted for classification By determining the principalcomponents with the contribution rate PCA algorithm isused to reduce the dimensionality of the features from 3-dimension to two-dimension making it suitable for theapplication of the one-to-one method of SVM RegardingQPSK as a positive class BPSK and 16QAM are sequentiallysubstituted into the SVM classifier as a negative class to findthe support vector Two optimal boundaries are determinedin light of the position of the support vector and theclassification of BPSK QPSK and 16QAM is accomplishedfinally
The classification structure can be regarded as a machinelearning network based on sample training and test It isnecessary to construct a large learning sample aggregate forextracting the modulation features of the above seven signalsand determine the multiple thresholds for the multilayerclassification during the training process In the test phasethe predetermined thresholds are used for different class andthe correct recognition rate of each class is achieved in theend
3 Feature Extraction Algorithms
The extracted modulation features are mainly based on thedifferences of radar and communication signals in time-frequency spectrum frequency spectrum and phase mod-ulation Different algorithms are used to extract differentfeatures for signals of different class The time-frequencyfeature is extracted by using STFT which identifies thesignal set SF LFM from the other signals SF and LFM arediscriminated by the feature of the real part of IA Accordingto the number of frequency peaks which obtained basedon DFT 2FSK and 4FSK are identified from the signal setBPSK QPSK and 16QAM The features based on the realpart of IA are used to distinguish between BPSK QPSKand 16QAM The following section will discuss the featureextraction algorithms including STFT IA and DFT
31 Feature Extraction Based on STFT Time-frequency fea-ture of the signals can be extracted by STFT For a discretesignal 119904(119899) at discrete time instant 119899 its STFT is given by
119904 (119899) ℎ (119899 minus 119898) 119890minus119895(2120587119873119904)119899119896119896 = 0 1 2 119873119904 minus 1
(1)
where 119896 represents the discrete frequency and 119873119904 is thetotal frequency number 119898 refers to time delay and ℎ(119899 minus
119898) denotes the Rectangular window function In (1) thenonstationary signal can be regarded as the superpositionof a series of short-time stationary signals which highlightsthe varying characteristics of the original signal frequencywith time delay The peak of the frequency along time delaydimension can be given by
where119873 denotes the total number of windows and 119875(119898) rep-resents the maximum frequency peak corresponding to the119898th window The frequency peak of each time window canbe extractedThe difference of frequency peak correspondingto two adjacent time windows can be given by
119882 (119898) = 119875 (119898 + 1) minus 119875 (119898) 119898 = 1 2 119873 minus 1 (3)
The standard deviation of the difference in (3) can begiven by
1205771 = radic 1119873 minus 1119873minus1sum119898=1
[119882 (119898) minus 119882]2 (4)
where 119882 refers to the mean of 119882 and 119882 = (1(119873 minus1)) sum119873minus1119898=1119882(119898) The STFT of the seven waveform types withSignal-to-Noise Ratio (SNR) equal to 20 dB are illustrated inFigure 3 As can be seen from Figure 3(a) the frequency ofSF is the same since it has only one frequency The differencebetween the adjacent frequencies for SF is constant so thestandard deviation is zero From Figure 3(b) we can see thatthe frequency of LFM changes linearly which leads to a con-stant difference between the two adjacent frequencies Hencethe standard deviation is also zero Figures 3(c) and 3(d) showthat the frequencies of 2FSK and 4FSK are variable whichmeans that the difference between the adjacent frequenciesis not constant Figures 3(e) 3(f) and 3(g) show that whenthere is a phase variation for BPSK QPSK or 16QAM signalthe instantaneous frequency has a large disturb which leadsto fluctuations between the adjacent frequencies Hence thestandard deviations of the signals such as BPSK QPSK16QAM 2FSK and 4FSK will be larger than those of the SFand LFM In this case SF and LFM can be identified from theother signals by setting the standard deviation threshold 120588132 Feature Extraction Using IA [35] Features based onIA can be extracted to distinguish between SF LFM andBPSK QPSK 16QAM respectively The IA of a discretesignal 119904(119899) is of the following form
where 119898 refers to time delay The difference between thedefinition of IA and auto-correlation function lies in thatthere is no time integration in the calculation of IA Theadvantage of using IA is that it retains the instantaneous phaseinformation of the signal The IA expressions of some of thesignals are analyzed below
where 119860 is the amplitude of the signal 1198910 refers to the carrierfrequency and 1205930 represents the initial phase of the signalThe real part of IA of SF can be given by
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)
where 119902 is the number of samples of the signal It can be seenfrom (7) that if 119898 is certain the IA of SF is related only to thecarrier frequency which is a constant Hence the output ofthe real part of IA is a direct-current (DC) signal as shown inFigure 4(a)
where 120583 is the slope of frequency modulation The real partof IA of LFM can be given by
119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)
It can be seen from (9) that the output of the real part of IA isan alternating current (AC) signal of frequency 120583119898 which isshown in Figure 4(b)
where 120593119894 denotes the discrete phase of a code group repre-senting BPSK or QPSK For BPSK the value of 120593119894 is 0 or 120587For QPSK the value of 120593119894 is 0 1205872 120587 or 31205872 The real partof IA of the PSK signal is of the following form
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119894119901 + 119898 lt 119899 le (119894 + 1) 119901119877 (119899 119898) = 1198602 cos (21205871198910119898 + 120593119894+1 minus 120593119894)
where119901 is the number of samples within one code and119898 lt 119901The real part of IA is DC within the same code period Indifferent code period it can be divided into two cases theadjacent code is the same (120593119894+1minus120593119894 = 0) or different (120593119894+1minus120593119894 =0) For BPSK shown in Figure 4(c) the real part of IA is atwo-value transition of which 120593119894+1 minus 120593119894 = 0 correspondsto a positive transitions and 120593119894+1 minus 120593119894 = plusmn120587 correspondsto a negative transition However there is a status of 120593119894+1 minus120593119894 = plusmn1205872 for QPSK for which the real part of IA is zero(the projection on the real axis) Therefore the real part ofIA for QPSK is a three-value output which is illustrated inFigure 4(d)
From (13) we can see that when 119898 is constant the outputof IA is DC in the same code period However it causesa phase jump 120593119894+1 minus 120593119894 and amplitude transition 119860 119894+1 sdot 119860 119894between different code period Hence the output of the IAfor 16QAM is a multivalue transition see Figure 4(e)
Two features are extracted based on the real part of theIA
where 119886(119894) is the value of the real part based on IA at timeinstant 119894 and 119886 = (1119873119904) sum119873119904119894=1 119886(119894) represents the mean of119886(119894) The standard deviation for SF signal will be small sincethe fluctuation of its IA is small However the IA of LFMfluctuates greatly ie the standard deviation is larger Underthis circumstance SF and LFM can be identified by settingthe standard deviation threshold 1205882 of the real part of IAFeature 2 Define zero-crossing ratio as
1205774 = Num 119886 (119894) isin 1205761 (15)
where Numsdot denotes a counter and 1205761 refers to a smallrange belonging to zero (such as minus0001 lt 1205761 lt 0001) Asshown in the Figure 4 a binary jump occurs for the IA ofBPSK meaning that there is no zero in the output Howeverthe IA of QPSK is of a three-value transition form with alarge number of zeroes in the output The IA of 16QAM issimilar to QPSK Therefore the difference of zero-crossingratio between BPSK and QPSK 16QAM signals can be usedas a classification feature
33 Feature Extraction Based on DFT For the remainingsignal set BPSKQPSK 16QAM 2FSK 4FSK the frequencyspectrum features of the signals are extracted using DFTAccording to the signal definitions the peaks of 2FSKand 4FSK are 2 and 4 within the bandwidth respectivelyHowever there are much more peaks for BPSK QPSK and16QAM
Since frequency peaks of the signal set BPSK QPSK16QAM 2FSK and 4FSK are different the number offrequency peaks based on DFT can be extracted as a typicalfeature For a discrete signal 119904(119899) its DFT can be given by
where 119896 represents the discrete frequency and 119873119904 is the totalfrequency number The number of peak can be defined as
1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)
where | sdot | refers to the modulo operation and 1205762 the thresholdof frequency peak taking 07 times of the maximum valueSince the number of peaks of 2FSK and 4FSK is smaller thanthe other three signals 2FSK and 4FSK can be identified fromother signals by setting the frequency peak threshold 1205883
Mathematical Problems in Engineering 7
0
02
04
06
08
1
12
14A
mpl
itude
1000 2000 3000 4000 50000Sample point
(a) SF
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(b) LFM
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(c) BPSK
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(d) QPSK
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Am
plitu
de
1000 2000 3000 4000 50000Sample point
(e) 16QAM
Figure 4 The real part of IA of the signals
34 Feature Extraction Based on Signal Envelope The mul-tilevel amplitude of the 16QAM signal is quite differentfrom the constant envelope BPSK and QPSK signal Henceenvelope features in time domain can be used to classifyBPSK QPSK and 16QAM For a discrete signal 119904(119899) the
standard deviation of the envelope can be defined as
where 119904 = (1119873119904) sum119873119904119894=1 |119904(119894)| represents the mean of theinstantaneous envelope
4 Analysis of SVM Based on PCADimensionality Reduction
Three features are extracted for the classification of BPSKQPSK and 16QAM so as to ensure the classification accuracyunder various conditions Due to the large number offeatures the classification tends to be complicated If thethree features can be replaced by the two features SVM canbe used to classify the three modulated signals in the Two-dimensional (2D) feature space Therefore PCA algorithm isused to perform principal component analysis on the Three-dimensional (3D) features extracting principal componentsin features and reducing the dimension of features
41 PCA Algorithm The PCA algorithm transforms theoriginal data with possible correlation into a set of newdata with linear independence of each dimension throughlinear transformation and it can be used to extract theprincipal feature components of the data thereby achievingthe purpose of dimensionality reduction [36] The main ideais to map the 1198961 dimensional features to 1198962 dimension (1198962 lt1198961) which is a completely new orthogonal feature called theprincipal component It can be easily understood that PCAcan be used to find the most useful linear combination iethose new features with relatively large discrimination toachieve the purpose of reducing the dimension
There are two basic requirements for PCA dimensionalityreduction First of all the projections of the samples in theprincipal component direction are required to be as dispersedas possible The more dispersed projections the larger thevariance of the samples ie more useful information iscarried in the reduced dimension projections Secondly thedistances from the sample points to the principal componentdirection are required to be as small as possible ie the errorscan be reduced as much as possible The steps of the PCAdimensionality reduction algorithm [37] for 1198961-dimensionalmodulation feature samples are summarized as follows
(1) Arrange the modulation feature samples into matrixX of 119872 (sample numbers) rows and 1198961 columns
(2) Process the sample data recorded as 119883 includingzero-meanization and normalization
(3) For the processed sample data its covariance matrixcan be given by
119877119909 = 1119872 (119883119879119883) (19)
where [sdot]119879 refers to transposition operation(4) According to
119877119909119906 = 120582119906 (20)
calculate the eigenvalue 120582119894 and the eigenvector 119906119894of 119877119909 Arrange the eigenvalues from large to small
Positive classQPSK
ClassifierSVM1
ClassifierSVM2
Negative classBPSK
Negative class16QAM
QPSK BPSK QPSK 16QAM
Figure 5 Three-class classification of SVM based on one-to-onemethod
and the corresponding eigenvectors are also arrangedfrom large to small
where 1198961 is the original sample data dimension and1198962 is the sample data dimension after dimensionalityreductionThe newmatrix 119861 (119861 = [1199061 sdot sdot sdot 1199061198962]) calledprojection matrix is composed of the feature vectorscorresponding to the first 1198962 eigenvalues
(6) Determine the projection data of the original featuredata in the projection matrix and then its principalcomponent can be given by
119909 = 119883119861 (22)
42 One-to-One Multiclassification Method Based on SVMSVM is originally an effective binary-class classificationmethod and its basic model is defined as a linear classifierwith largest interval in feature space For multiclassificationproblems SVM can also achieve classification in an one-to-many mode one-to-one mode etc In this paper the one-to-one mode of SVM is employed due to its simplicity Theflowchart for three-class classification using SVM based onone-to-one method is shown in Figure 5 and it will be usedto classify BPSK QPSK and 16QAM
The basic classification principle of SVM is summarizedbelow The discriminant function of implementing SVM isgiven by [38]
where 119909 is the training sample input after dimensionalityreduction using PCA 119908 refers to a weight vector 119910119894(plusmn1)denotes a category label and 119887 is an offset Its interval is givenby
The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into
120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)
where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get
where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples
The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification
5 Simulation Analysis
51 Performance Analysis without Fading Channel Effect
511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation
512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations
Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As
10 Mathematical Problems in Engineering
Table 1 Parameters for different types of modulated signals
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
02
03
04
05
06
07
08
Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
50
100
150
200
250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
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Mathematical Problems in Engineering 5
minus5
0
5
x 107
05
1015
20minus40minus20
02040
Frequency (Hz)DelaySample point
Am
plitu
de (d
B)
(a) SF
minus50
5
x 107
02
46
810
minus40minus20
02040
Frequency (Hz)DelaySample point
Am
plitu
de (d
B)
(b) LFM
minus5
0
5
x 107
010
2030
40minus50
0
50
Frequency (Hz)DelaySample point
Am
plitu
de (d
B)
(c) 2FSK
minus5
0
5
x 107
010
2030
40minus50
0
50
Frequency (Hz)DelaySample point
Am
plitu
de (d
B)
(d) 4FSK
minus3 minus2 minus1 0 1 2 3
x 107
05
1015
20minus40minus20
02040
Frequency (Hz)DelaySample point
Am
plitu
de (d
B)
(e) BPSK
minus3 minus2 minus1 0 1 2 3
x 107
05
1015
20minus40minus20
02040
Frequency (Hz)DelaySample point
Am
plitu
de (d
B)
(f) QPSK
minus3 minus2 minus1 0 1 2 3x 107
05
1015
20minus40minus20
0204060
Frequency (Hz)DelaySample point
Am
plitu
de (d
B)
(g) 16QAM
Figure 3 Time-frequency spectrum using STFT
where 119860 is the amplitude of the signal 1198910 refers to the carrierfrequency and 1205930 represents the initial phase of the signalThe real part of IA of SF can be given by
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)
where 119902 is the number of samples of the signal It can be seenfrom (7) that if 119898 is certain the IA of SF is related only to thecarrier frequency which is a constant Hence the output ofthe real part of IA is a direct-current (DC) signal as shown inFigure 4(a)
where 120583 is the slope of frequency modulation The real partof IA of LFM can be given by
119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)
It can be seen from (9) that the output of the real part of IA isan alternating current (AC) signal of frequency 120583119898 which isshown in Figure 4(b)
where 120593119894 denotes the discrete phase of a code group repre-senting BPSK or QPSK For BPSK the value of 120593119894 is 0 or 120587For QPSK the value of 120593119894 is 0 1205872 120587 or 31205872 The real partof IA of the PSK signal is of the following form
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119894119901 + 119898 lt 119899 le (119894 + 1) 119901119877 (119899 119898) = 1198602 cos (21205871198910119898 + 120593119894+1 minus 120593119894)
where119901 is the number of samples within one code and119898 lt 119901The real part of IA is DC within the same code period Indifferent code period it can be divided into two cases theadjacent code is the same (120593119894+1minus120593119894 = 0) or different (120593119894+1minus120593119894 =0) For BPSK shown in Figure 4(c) the real part of IA is atwo-value transition of which 120593119894+1 minus 120593119894 = 0 correspondsto a positive transitions and 120593119894+1 minus 120593119894 = plusmn120587 correspondsto a negative transition However there is a status of 120593119894+1 minus120593119894 = plusmn1205872 for QPSK for which the real part of IA is zero(the projection on the real axis) Therefore the real part ofIA for QPSK is a three-value output which is illustrated inFigure 4(d)
From (13) we can see that when 119898 is constant the outputof IA is DC in the same code period However it causesa phase jump 120593119894+1 minus 120593119894 and amplitude transition 119860 119894+1 sdot 119860 119894between different code period Hence the output of the IAfor 16QAM is a multivalue transition see Figure 4(e)
Two features are extracted based on the real part of theIA
where 119886(119894) is the value of the real part based on IA at timeinstant 119894 and 119886 = (1119873119904) sum119873119904119894=1 119886(119894) represents the mean of119886(119894) The standard deviation for SF signal will be small sincethe fluctuation of its IA is small However the IA of LFMfluctuates greatly ie the standard deviation is larger Underthis circumstance SF and LFM can be identified by settingthe standard deviation threshold 1205882 of the real part of IAFeature 2 Define zero-crossing ratio as
1205774 = Num 119886 (119894) isin 1205761 (15)
where Numsdot denotes a counter and 1205761 refers to a smallrange belonging to zero (such as minus0001 lt 1205761 lt 0001) Asshown in the Figure 4 a binary jump occurs for the IA ofBPSK meaning that there is no zero in the output Howeverthe IA of QPSK is of a three-value transition form with alarge number of zeroes in the output The IA of 16QAM issimilar to QPSK Therefore the difference of zero-crossingratio between BPSK and QPSK 16QAM signals can be usedas a classification feature
33 Feature Extraction Based on DFT For the remainingsignal set BPSKQPSK 16QAM 2FSK 4FSK the frequencyspectrum features of the signals are extracted using DFTAccording to the signal definitions the peaks of 2FSKand 4FSK are 2 and 4 within the bandwidth respectivelyHowever there are much more peaks for BPSK QPSK and16QAM
Since frequency peaks of the signal set BPSK QPSK16QAM 2FSK and 4FSK are different the number offrequency peaks based on DFT can be extracted as a typicalfeature For a discrete signal 119904(119899) its DFT can be given by
where 119896 represents the discrete frequency and 119873119904 is the totalfrequency number The number of peak can be defined as
1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)
where | sdot | refers to the modulo operation and 1205762 the thresholdof frequency peak taking 07 times of the maximum valueSince the number of peaks of 2FSK and 4FSK is smaller thanthe other three signals 2FSK and 4FSK can be identified fromother signals by setting the frequency peak threshold 1205883
Mathematical Problems in Engineering 7
0
02
04
06
08
1
12
14A
mpl
itude
1000 2000 3000 4000 50000Sample point
(a) SF
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(b) LFM
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(c) BPSK
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(d) QPSK
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Am
plitu
de
1000 2000 3000 4000 50000Sample point
(e) 16QAM
Figure 4 The real part of IA of the signals
34 Feature Extraction Based on Signal Envelope The mul-tilevel amplitude of the 16QAM signal is quite differentfrom the constant envelope BPSK and QPSK signal Henceenvelope features in time domain can be used to classifyBPSK QPSK and 16QAM For a discrete signal 119904(119899) the
standard deviation of the envelope can be defined as
where 119904 = (1119873119904) sum119873119904119894=1 |119904(119894)| represents the mean of theinstantaneous envelope
4 Analysis of SVM Based on PCADimensionality Reduction
Three features are extracted for the classification of BPSKQPSK and 16QAM so as to ensure the classification accuracyunder various conditions Due to the large number offeatures the classification tends to be complicated If thethree features can be replaced by the two features SVM canbe used to classify the three modulated signals in the Two-dimensional (2D) feature space Therefore PCA algorithm isused to perform principal component analysis on the Three-dimensional (3D) features extracting principal componentsin features and reducing the dimension of features
41 PCA Algorithm The PCA algorithm transforms theoriginal data with possible correlation into a set of newdata with linear independence of each dimension throughlinear transformation and it can be used to extract theprincipal feature components of the data thereby achievingthe purpose of dimensionality reduction [36] The main ideais to map the 1198961 dimensional features to 1198962 dimension (1198962 lt1198961) which is a completely new orthogonal feature called theprincipal component It can be easily understood that PCAcan be used to find the most useful linear combination iethose new features with relatively large discrimination toachieve the purpose of reducing the dimension
There are two basic requirements for PCA dimensionalityreduction First of all the projections of the samples in theprincipal component direction are required to be as dispersedas possible The more dispersed projections the larger thevariance of the samples ie more useful information iscarried in the reduced dimension projections Secondly thedistances from the sample points to the principal componentdirection are required to be as small as possible ie the errorscan be reduced as much as possible The steps of the PCAdimensionality reduction algorithm [37] for 1198961-dimensionalmodulation feature samples are summarized as follows
(1) Arrange the modulation feature samples into matrixX of 119872 (sample numbers) rows and 1198961 columns
(2) Process the sample data recorded as 119883 includingzero-meanization and normalization
(3) For the processed sample data its covariance matrixcan be given by
119877119909 = 1119872 (119883119879119883) (19)
where [sdot]119879 refers to transposition operation(4) According to
119877119909119906 = 120582119906 (20)
calculate the eigenvalue 120582119894 and the eigenvector 119906119894of 119877119909 Arrange the eigenvalues from large to small
Positive classQPSK
ClassifierSVM1
ClassifierSVM2
Negative classBPSK
Negative class16QAM
QPSK BPSK QPSK 16QAM
Figure 5 Three-class classification of SVM based on one-to-onemethod
and the corresponding eigenvectors are also arrangedfrom large to small
where 1198961 is the original sample data dimension and1198962 is the sample data dimension after dimensionalityreductionThe newmatrix 119861 (119861 = [1199061 sdot sdot sdot 1199061198962]) calledprojection matrix is composed of the feature vectorscorresponding to the first 1198962 eigenvalues
(6) Determine the projection data of the original featuredata in the projection matrix and then its principalcomponent can be given by
119909 = 119883119861 (22)
42 One-to-One Multiclassification Method Based on SVMSVM is originally an effective binary-class classificationmethod and its basic model is defined as a linear classifierwith largest interval in feature space For multiclassificationproblems SVM can also achieve classification in an one-to-many mode one-to-one mode etc In this paper the one-to-one mode of SVM is employed due to its simplicity Theflowchart for three-class classification using SVM based onone-to-one method is shown in Figure 5 and it will be usedto classify BPSK QPSK and 16QAM
The basic classification principle of SVM is summarizedbelow The discriminant function of implementing SVM isgiven by [38]
where 119909 is the training sample input after dimensionalityreduction using PCA 119908 refers to a weight vector 119910119894(plusmn1)denotes a category label and 119887 is an offset Its interval is givenby
The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into
120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)
where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get
where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples
The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification
5 Simulation Analysis
51 Performance Analysis without Fading Channel Effect
511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation
512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations
Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As
10 Mathematical Problems in Engineering
Table 1 Parameters for different types of modulated signals
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
02
03
04
05
06
07
08
Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
50
100
150
200
250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
where 120583 is the slope of frequency modulation The real partof IA of LFM can be given by
119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)
It can be seen from (9) that the output of the real part of IA isan alternating current (AC) signal of frequency 120583119898 which isshown in Figure 4(b)
where 120593119894 denotes the discrete phase of a code group repre-senting BPSK or QPSK For BPSK the value of 120593119894 is 0 or 120587For QPSK the value of 120593119894 is 0 1205872 120587 or 31205872 The real partof IA of the PSK signal is of the following form
119877 (119899 119898) = 1198602 cos (21205871198910119898) 119894119901 + 119898 lt 119899 le (119894 + 1) 119901119877 (119899 119898) = 1198602 cos (21205871198910119898 + 120593119894+1 minus 120593119894)
where119901 is the number of samples within one code and119898 lt 119901The real part of IA is DC within the same code period Indifferent code period it can be divided into two cases theadjacent code is the same (120593119894+1minus120593119894 = 0) or different (120593119894+1minus120593119894 =0) For BPSK shown in Figure 4(c) the real part of IA is atwo-value transition of which 120593119894+1 minus 120593119894 = 0 correspondsto a positive transitions and 120593119894+1 minus 120593119894 = plusmn120587 correspondsto a negative transition However there is a status of 120593119894+1 minus120593119894 = plusmn1205872 for QPSK for which the real part of IA is zero(the projection on the real axis) Therefore the real part ofIA for QPSK is a three-value output which is illustrated inFigure 4(d)
From (13) we can see that when 119898 is constant the outputof IA is DC in the same code period However it causesa phase jump 120593119894+1 minus 120593119894 and amplitude transition 119860 119894+1 sdot 119860 119894between different code period Hence the output of the IAfor 16QAM is a multivalue transition see Figure 4(e)
Two features are extracted based on the real part of theIA
where 119886(119894) is the value of the real part based on IA at timeinstant 119894 and 119886 = (1119873119904) sum119873119904119894=1 119886(119894) represents the mean of119886(119894) The standard deviation for SF signal will be small sincethe fluctuation of its IA is small However the IA of LFMfluctuates greatly ie the standard deviation is larger Underthis circumstance SF and LFM can be identified by settingthe standard deviation threshold 1205882 of the real part of IAFeature 2 Define zero-crossing ratio as
1205774 = Num 119886 (119894) isin 1205761 (15)
where Numsdot denotes a counter and 1205761 refers to a smallrange belonging to zero (such as minus0001 lt 1205761 lt 0001) Asshown in the Figure 4 a binary jump occurs for the IA ofBPSK meaning that there is no zero in the output Howeverthe IA of QPSK is of a three-value transition form with alarge number of zeroes in the output The IA of 16QAM issimilar to QPSK Therefore the difference of zero-crossingratio between BPSK and QPSK 16QAM signals can be usedas a classification feature
33 Feature Extraction Based on DFT For the remainingsignal set BPSKQPSK 16QAM 2FSK 4FSK the frequencyspectrum features of the signals are extracted using DFTAccording to the signal definitions the peaks of 2FSKand 4FSK are 2 and 4 within the bandwidth respectivelyHowever there are much more peaks for BPSK QPSK and16QAM
Since frequency peaks of the signal set BPSK QPSK16QAM 2FSK and 4FSK are different the number offrequency peaks based on DFT can be extracted as a typicalfeature For a discrete signal 119904(119899) its DFT can be given by
where 119896 represents the discrete frequency and 119873119904 is the totalfrequency number The number of peak can be defined as
1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)
where | sdot | refers to the modulo operation and 1205762 the thresholdof frequency peak taking 07 times of the maximum valueSince the number of peaks of 2FSK and 4FSK is smaller thanthe other three signals 2FSK and 4FSK can be identified fromother signals by setting the frequency peak threshold 1205883
Mathematical Problems in Engineering 7
0
02
04
06
08
1
12
14A
mpl
itude
1000 2000 3000 4000 50000Sample point
(a) SF
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(b) LFM
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(c) BPSK
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(d) QPSK
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Am
plitu
de
1000 2000 3000 4000 50000Sample point
(e) 16QAM
Figure 4 The real part of IA of the signals
34 Feature Extraction Based on Signal Envelope The mul-tilevel amplitude of the 16QAM signal is quite differentfrom the constant envelope BPSK and QPSK signal Henceenvelope features in time domain can be used to classifyBPSK QPSK and 16QAM For a discrete signal 119904(119899) the
standard deviation of the envelope can be defined as
where 119904 = (1119873119904) sum119873119904119894=1 |119904(119894)| represents the mean of theinstantaneous envelope
4 Analysis of SVM Based on PCADimensionality Reduction
Three features are extracted for the classification of BPSKQPSK and 16QAM so as to ensure the classification accuracyunder various conditions Due to the large number offeatures the classification tends to be complicated If thethree features can be replaced by the two features SVM canbe used to classify the three modulated signals in the Two-dimensional (2D) feature space Therefore PCA algorithm isused to perform principal component analysis on the Three-dimensional (3D) features extracting principal componentsin features and reducing the dimension of features
41 PCA Algorithm The PCA algorithm transforms theoriginal data with possible correlation into a set of newdata with linear independence of each dimension throughlinear transformation and it can be used to extract theprincipal feature components of the data thereby achievingthe purpose of dimensionality reduction [36] The main ideais to map the 1198961 dimensional features to 1198962 dimension (1198962 lt1198961) which is a completely new orthogonal feature called theprincipal component It can be easily understood that PCAcan be used to find the most useful linear combination iethose new features with relatively large discrimination toachieve the purpose of reducing the dimension
There are two basic requirements for PCA dimensionalityreduction First of all the projections of the samples in theprincipal component direction are required to be as dispersedas possible The more dispersed projections the larger thevariance of the samples ie more useful information iscarried in the reduced dimension projections Secondly thedistances from the sample points to the principal componentdirection are required to be as small as possible ie the errorscan be reduced as much as possible The steps of the PCAdimensionality reduction algorithm [37] for 1198961-dimensionalmodulation feature samples are summarized as follows
(1) Arrange the modulation feature samples into matrixX of 119872 (sample numbers) rows and 1198961 columns
(2) Process the sample data recorded as 119883 includingzero-meanization and normalization
(3) For the processed sample data its covariance matrixcan be given by
119877119909 = 1119872 (119883119879119883) (19)
where [sdot]119879 refers to transposition operation(4) According to
119877119909119906 = 120582119906 (20)
calculate the eigenvalue 120582119894 and the eigenvector 119906119894of 119877119909 Arrange the eigenvalues from large to small
Positive classQPSK
ClassifierSVM1
ClassifierSVM2
Negative classBPSK
Negative class16QAM
QPSK BPSK QPSK 16QAM
Figure 5 Three-class classification of SVM based on one-to-onemethod
and the corresponding eigenvectors are also arrangedfrom large to small
where 1198961 is the original sample data dimension and1198962 is the sample data dimension after dimensionalityreductionThe newmatrix 119861 (119861 = [1199061 sdot sdot sdot 1199061198962]) calledprojection matrix is composed of the feature vectorscorresponding to the first 1198962 eigenvalues
(6) Determine the projection data of the original featuredata in the projection matrix and then its principalcomponent can be given by
119909 = 119883119861 (22)
42 One-to-One Multiclassification Method Based on SVMSVM is originally an effective binary-class classificationmethod and its basic model is defined as a linear classifierwith largest interval in feature space For multiclassificationproblems SVM can also achieve classification in an one-to-many mode one-to-one mode etc In this paper the one-to-one mode of SVM is employed due to its simplicity Theflowchart for three-class classification using SVM based onone-to-one method is shown in Figure 5 and it will be usedto classify BPSK QPSK and 16QAM
The basic classification principle of SVM is summarizedbelow The discriminant function of implementing SVM isgiven by [38]
where 119909 is the training sample input after dimensionalityreduction using PCA 119908 refers to a weight vector 119910119894(plusmn1)denotes a category label and 119887 is an offset Its interval is givenby
The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into
120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)
where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get
where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples
The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification
5 Simulation Analysis
51 Performance Analysis without Fading Channel Effect
511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation
512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations
Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As
10 Mathematical Problems in Engineering
Table 1 Parameters for different types of modulated signals
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
02
03
04
05
06
07
08
Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
50
100
150
200
250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
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Mathematical Problems in Engineering 7
0
02
04
06
08
1
12
14A
mpl
itude
1000 2000 3000 4000 50000Sample point
(a) SF
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(b) LFM
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(c) BPSK
1000 2000 3000 4000 50000Sample point
minus15
minus1
minus05
0
05
1
15
Am
plitu
de
(d) QPSK
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Am
plitu
de
1000 2000 3000 4000 50000Sample point
(e) 16QAM
Figure 4 The real part of IA of the signals
34 Feature Extraction Based on Signal Envelope The mul-tilevel amplitude of the 16QAM signal is quite differentfrom the constant envelope BPSK and QPSK signal Henceenvelope features in time domain can be used to classifyBPSK QPSK and 16QAM For a discrete signal 119904(119899) the
standard deviation of the envelope can be defined as
where 119904 = (1119873119904) sum119873119904119894=1 |119904(119894)| represents the mean of theinstantaneous envelope
4 Analysis of SVM Based on PCADimensionality Reduction
Three features are extracted for the classification of BPSKQPSK and 16QAM so as to ensure the classification accuracyunder various conditions Due to the large number offeatures the classification tends to be complicated If thethree features can be replaced by the two features SVM canbe used to classify the three modulated signals in the Two-dimensional (2D) feature space Therefore PCA algorithm isused to perform principal component analysis on the Three-dimensional (3D) features extracting principal componentsin features and reducing the dimension of features
41 PCA Algorithm The PCA algorithm transforms theoriginal data with possible correlation into a set of newdata with linear independence of each dimension throughlinear transformation and it can be used to extract theprincipal feature components of the data thereby achievingthe purpose of dimensionality reduction [36] The main ideais to map the 1198961 dimensional features to 1198962 dimension (1198962 lt1198961) which is a completely new orthogonal feature called theprincipal component It can be easily understood that PCAcan be used to find the most useful linear combination iethose new features with relatively large discrimination toachieve the purpose of reducing the dimension
There are two basic requirements for PCA dimensionalityreduction First of all the projections of the samples in theprincipal component direction are required to be as dispersedas possible The more dispersed projections the larger thevariance of the samples ie more useful information iscarried in the reduced dimension projections Secondly thedistances from the sample points to the principal componentdirection are required to be as small as possible ie the errorscan be reduced as much as possible The steps of the PCAdimensionality reduction algorithm [37] for 1198961-dimensionalmodulation feature samples are summarized as follows
(1) Arrange the modulation feature samples into matrixX of 119872 (sample numbers) rows and 1198961 columns
(2) Process the sample data recorded as 119883 includingzero-meanization and normalization
(3) For the processed sample data its covariance matrixcan be given by
119877119909 = 1119872 (119883119879119883) (19)
where [sdot]119879 refers to transposition operation(4) According to
119877119909119906 = 120582119906 (20)
calculate the eigenvalue 120582119894 and the eigenvector 119906119894of 119877119909 Arrange the eigenvalues from large to small
Positive classQPSK
ClassifierSVM1
ClassifierSVM2
Negative classBPSK
Negative class16QAM
QPSK BPSK QPSK 16QAM
Figure 5 Three-class classification of SVM based on one-to-onemethod
and the corresponding eigenvectors are also arrangedfrom large to small
where 1198961 is the original sample data dimension and1198962 is the sample data dimension after dimensionalityreductionThe newmatrix 119861 (119861 = [1199061 sdot sdot sdot 1199061198962]) calledprojection matrix is composed of the feature vectorscorresponding to the first 1198962 eigenvalues
(6) Determine the projection data of the original featuredata in the projection matrix and then its principalcomponent can be given by
119909 = 119883119861 (22)
42 One-to-One Multiclassification Method Based on SVMSVM is originally an effective binary-class classificationmethod and its basic model is defined as a linear classifierwith largest interval in feature space For multiclassificationproblems SVM can also achieve classification in an one-to-many mode one-to-one mode etc In this paper the one-to-one mode of SVM is employed due to its simplicity Theflowchart for three-class classification using SVM based onone-to-one method is shown in Figure 5 and it will be usedto classify BPSK QPSK and 16QAM
The basic classification principle of SVM is summarizedbelow The discriminant function of implementing SVM isgiven by [38]
where 119909 is the training sample input after dimensionalityreduction using PCA 119908 refers to a weight vector 119910119894(plusmn1)denotes a category label and 119887 is an offset Its interval is givenby
The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into
120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)
where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get
where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples
The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification
5 Simulation Analysis
51 Performance Analysis without Fading Channel Effect
511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation
512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations
Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As
10 Mathematical Problems in Engineering
Table 1 Parameters for different types of modulated signals
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
02
03
04
05
06
07
08
Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
50
100
150
200
250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
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8 Mathematical Problems in Engineering
where 119904 = (1119873119904) sum119873119904119894=1 |119904(119894)| represents the mean of theinstantaneous envelope
4 Analysis of SVM Based on PCADimensionality Reduction
Three features are extracted for the classification of BPSKQPSK and 16QAM so as to ensure the classification accuracyunder various conditions Due to the large number offeatures the classification tends to be complicated If thethree features can be replaced by the two features SVM canbe used to classify the three modulated signals in the Two-dimensional (2D) feature space Therefore PCA algorithm isused to perform principal component analysis on the Three-dimensional (3D) features extracting principal componentsin features and reducing the dimension of features
41 PCA Algorithm The PCA algorithm transforms theoriginal data with possible correlation into a set of newdata with linear independence of each dimension throughlinear transformation and it can be used to extract theprincipal feature components of the data thereby achievingthe purpose of dimensionality reduction [36] The main ideais to map the 1198961 dimensional features to 1198962 dimension (1198962 lt1198961) which is a completely new orthogonal feature called theprincipal component It can be easily understood that PCAcan be used to find the most useful linear combination iethose new features with relatively large discrimination toachieve the purpose of reducing the dimension
There are two basic requirements for PCA dimensionalityreduction First of all the projections of the samples in theprincipal component direction are required to be as dispersedas possible The more dispersed projections the larger thevariance of the samples ie more useful information iscarried in the reduced dimension projections Secondly thedistances from the sample points to the principal componentdirection are required to be as small as possible ie the errorscan be reduced as much as possible The steps of the PCAdimensionality reduction algorithm [37] for 1198961-dimensionalmodulation feature samples are summarized as follows
(1) Arrange the modulation feature samples into matrixX of 119872 (sample numbers) rows and 1198961 columns
(2) Process the sample data recorded as 119883 includingzero-meanization and normalization
(3) For the processed sample data its covariance matrixcan be given by
119877119909 = 1119872 (119883119879119883) (19)
where [sdot]119879 refers to transposition operation(4) According to
119877119909119906 = 120582119906 (20)
calculate the eigenvalue 120582119894 and the eigenvector 119906119894of 119877119909 Arrange the eigenvalues from large to small
Positive classQPSK
ClassifierSVM1
ClassifierSVM2
Negative classBPSK
Negative class16QAM
QPSK BPSK QPSK 16QAM
Figure 5 Three-class classification of SVM based on one-to-onemethod
and the corresponding eigenvectors are also arrangedfrom large to small
where 1198961 is the original sample data dimension and1198962 is the sample data dimension after dimensionalityreductionThe newmatrix 119861 (119861 = [1199061 sdot sdot sdot 1199061198962]) calledprojection matrix is composed of the feature vectorscorresponding to the first 1198962 eigenvalues
(6) Determine the projection data of the original featuredata in the projection matrix and then its principalcomponent can be given by
119909 = 119883119861 (22)
42 One-to-One Multiclassification Method Based on SVMSVM is originally an effective binary-class classificationmethod and its basic model is defined as a linear classifierwith largest interval in feature space For multiclassificationproblems SVM can also achieve classification in an one-to-many mode one-to-one mode etc In this paper the one-to-one mode of SVM is employed due to its simplicity Theflowchart for three-class classification using SVM based onone-to-one method is shown in Figure 5 and it will be usedto classify BPSK QPSK and 16QAM
The basic classification principle of SVM is summarizedbelow The discriminant function of implementing SVM isgiven by [38]
where 119909 is the training sample input after dimensionalityreduction using PCA 119908 refers to a weight vector 119910119894(plusmn1)denotes a category label and 119887 is an offset Its interval is givenby
The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into
120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)
where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get
where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples
The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification
5 Simulation Analysis
51 Performance Analysis without Fading Channel Effect
511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation
512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations
Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As
10 Mathematical Problems in Engineering
Table 1 Parameters for different types of modulated signals
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
02
03
04
05
06
07
08
Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
50
100
150
200
250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into
120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)
where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get
where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples
The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification
5 Simulation Analysis
51 Performance Analysis without Fading Channel Effect
511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation
512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations
Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As
10 Mathematical Problems in Engineering
Table 1 Parameters for different types of modulated signals
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
02
03
04
05
06
07
08
Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
50
100
150
200
250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Figure 6 Standard deviation of the difference of the STFT peak
shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line
In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line
In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM
SFLFM
0
01
02
03
04
05
06
07
08
Stan
dard
dev
iatio
n of
enve
lope
100 200 300 400 500 600 700 800 9000Sample number
Figure 7 Standard deviation of real part of IA of SF and LFM
2FSK4FSKBPSK
QPSK16QAM
0
50
100
150
200
250
300
350
Peak
num
ber
500 1000 1500 2000 25000Sample number
Figure 8 Peak numbers of the signal classes
In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction
The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
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AnalysisInternational Journal of
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Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Mathematical Problems in Engineering 11
BPSKQPSK16QAM
QPSK 16QAM
BPSK
10dB
20dB
30dB
10dB10dB
20dB20dB
30dB
30dB0
005
01
015
02
025
03
035
04
045
05N
umbe
r rat
io o
ver z
ero
poin
t
200 400 600 800 1000 1200 14000Sample number
Figure 9 Zero-crossing ratio
BPSKQPSK16QAM
16QAM
BPSK
10dB
20dB
20dB
10dB
10dB
30dB
30dB 30dB
20dB
QPSK
01
02
03
04
05
06
07
08
09
Stan
dard
dev
iatio
n of
the r
eal p
art o
f IA
200 400 600 800 1000 1200 14000Sample number
Figure 10 Standard deviation of the real part of IA
deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss
The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of
BPSKQPSK16QAM
16QAM
QPSK
20dB
10dB 10dB
10dB
20dB
20dB 30dB
30dB 30dB
BPSK
0
005
01
015
02
025
Stan
dard
dev
iatio
n of
enve
lope
200 400 600 800 1000 1200 14000Sample number
Figure 11 Standard deviation of envelope
0
02
04
06
08
1
12C
ontr
ibut
ion
rate
05 1 15 2 25 30Characteristic number
Figure 12 Characteristic of the contribution rate
the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines
513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of
12 Mathematical Problems in Engineering
Table 2 Correct recognition rate at different SNRs
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper
52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as
119911 (119899) = 119871minus1sum119896=0
ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)
where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation
The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel
BPSKQPSK
16QAMSupport vector
16QAM
QPSK
BPSK
Optimum boundary 2
Support vector
Optimum boundary 1
minus2 minus1 0 1 2minus3First principal component characteristic
minus2
minus15
minus1
minus05
0
05
1
15
2
25
3
Seco
nd p
rinci
pal c
ompo
nent
char
acte
ristic
Figure 13 Three-class classification based on SVM
53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]
The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Mathematical Problems in Engineering 13
Algorithm in [9]Proposed algorithm
075
08
085
09
095
1C
orre
ct re
cogn
ition
rate
5 10 15 20 250SNR (dB)
Figure 14 Comparison of correct recognition
the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach
6 Conclusion
This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)
References
[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018
[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014
[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016
[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015
[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996
[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007
[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005
[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011
[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012
[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012
[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015
[12] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008
[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996
[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
14 Mathematical Problems in Engineering
SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014
[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017
[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017
[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018
[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016
[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018
[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015
[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012
[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014
[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017
[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009
[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013
[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012
[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015
[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011
[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018
[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010
[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016
[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016
[33] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009
[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018
[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003
[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013
[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences