Novel Time and Freq. Synch

Wireless Pers Commun (2015) 81:225238DOI 10.1007/s11277-014-2125-0

Novel Time and Frequency Synchronization Techniquesfor OFDM Systems in Double Selective Fading Channel

Hossam Asran Ehab F. Badran Amira I. Zaki

Published online: 18 October 2014 Springer Science+Business Media New York 2014

Abstract OFDM receiver performance is affected by the time offset and the carrier fre-quency offset, as these two parameters have sever effect on the signal reception quality. Inthis paper, two novel schemes for time estimation (TE) and frequency estimation (FE) areproposed to overcome the time and carrier frequency offset problem, and therefore improvethe performance of the OFDM reception. The proposed techniques are based on the fact that,using the correlation of constant amplitude zero auto correlation sequence with a unity peakto average power ratio gives a sharp time metric peak. The proposed timing symbol basedon this fact introduces a TE technique that has a sharp peak at the correct time instant andno side lobes. In addition, the proposed FE technique is based on the same training symboland it takes place in two steps. The first step is the fine FE technique, which depends oncalculating the phase difference between the cyclic prefix and the preamble tail. It is referredto as fractional FE. The second step is the coarse offset FE and it is referred to as integer FE.The coarse offset FE is based on FFT and it has less mean square error than other methods.

Keywords OFDM Frame synchronization Frequency offset compensation

1 Introduction

The developing of new services with promising high data rate and quality of service (QoS),like the 4G wireless networks, increased the demand on free frequency bands. Due to the

H. Asran E. F. Badran (B) A. I. ZakiDepartment of Electronics and Communication Engineering, Arab Academyfor Science, Technology and Maritime Transport, Alexandria,Egypte-mail: [email protected]

H. Asrane-mail: [email protected]

A. I. Zakie-mail: [email protected]

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scarcity of free bands in the spectrum, researches introduce advanced techniques to overcomethe problem of the spectrum scarcity, increase the system capacity and at the same timeprovide reasonable QoS. One of the most important techniques is the orthogonal frequencydivision multiplexing (OFDM) technique.

The OFDM has been widely used in different systems like digital audio/video broadcasting(DA/VB), it has been selected due to its high spectral efficiency and its ability to overcomethe multipath fading effect [1]. This made the OFDM the downlink technique used in themobile communication system long-term evolution (LTE) system.

The OFDM system transmits data as a set of low parallel data rate streams over orthogonalnarrowband subcarriers (100 Hz50 KHz) [2,3]. The OFDM transmission can be simplygenerated using inverse fast Fourier transform (IFFT) at the transmitter side, and receivedusing fast Fourier transform (FFT) at the receiver side. The OFDM can provide very highdata rate by using large number of carriers. The orthogonality of the OFDM subcarrierseliminates the possibility of the inter carrier interference (ICI) and inter symbol interference(ISI). The cyclic prefix insertion in the OFDM symbols, which implies that the last part ofthe OFDM symbol is copied and inserted at the beginning of the OFDM symbol, preservesthe subcarrier orthogonality in the case of a time dispersive channel, as long as the channeldispersion time is shorter than the cyclic prefix length [2].

The synchronization between the transmitter and the receiver is another important factorthat affects the system performance. However, loss of synchronization leads to time andfrequency shifts that will cause ISI and ICI. Thus, the loss of synchronization will degradethe performance of the system [2,3].

The OFDM frequency and time synchronization is divided into two main categories thedata-aided and non-data-aided categories ([410] and the references therein). The data-aidedmethod, which depends on a training sequence or pilot symbol for the estimation of bothof the time offset and the frequency offset. This method has the advantage of using simplecalculations and providing high accuracy, but it has the disadvantage of wasting the bandwidthand the data transmission rate.

The non-data-aided methods usually use the cyclic prefix for estimation. These methodsdo not waste the bandwidth or data speed, but the estimation range is limited.

In this paper, some of the previously mentioned time and frequency synchronizationschemes are discussed and compered to the two proposed techniques. The rest of the paperis organized as follows. Section 2 describes the OFDM system mathematical model. Section3 presents and compares the previous time synchronization schemes. Section 4 presents theproposed time offset estimation algorithm. Section 5 covers the proposed fine and coarsefrequency synchronization method. The computer simulation and results are carried out inSect. 6. Finally, Sect. 7 presents the conclusions.

2 OFDM System Model

The OFDM system is shown in Fig. 1. The OFDM data can be represented mathematical by

x (n) =M1

k=0S(k) e j2knN , N = 0, 1, 2, . . . , N 1 (1)

where S(k) is the complex modulated symbol modulating the kth subcarrier. The frequencyof the kth sub-carrier is given by fk = kn/N and n is the sample number. The transmittedsignal will be affected by multipath Rayleigh fading wireless channel which has an impulseresponse that is given by

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Double Selective Fading Channel 227

Fig. 1 OFDM system blockdiagram

s0, s1, sN-1

s0, s1, sN-1

s0s1

sN-1

S/P IFFT

Channel

P/S FFT

N-1

Time & Freq. Sync.

~ ~ ~

Fig. 2 Schmidl training symbol N/4 N/4

B B

I (n) =L1

l=0h (l) (n l), (2)

where L is the number of multipath component, l is the time delay and h (l) is the gain ofthe lth multipath component, which must not exceed the length of CP. Thus, the receivedsignal can be expressed as

r (n) =L1

l=0h (l) x(n l) e j2n/N , (3)

where is the carrier frequency offset due to the receiver oscillator mismatch and the Dopplershift of the moving mobile user.

3 OFDM Synchronization Schemes

This section introduces a brief description of the research work previously introduced forOFDM system synchronization. The time synchronization is essential in OFDM systems tokeep the orthogonality of the sub-carriers and to avoid the ICI and ISI. The target in timesynchronization is to estimate the time offset and to find the beginning of the OFDM frame.

3.1 Schmidl and Cox Method

In Schmidl and Cox [4] introduce a synchronization technique based on generating twoidentical parts of training symbols in the time domain each of length N/2 as shown in Fig. 2(where B an m-sequence).

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0 50 100 150 200 250 300 350 4000

0.2

0.4

0.6

0.8

1

Time (sample)

Tim

ing

Met

ric

schmidl

Fig. 3 Schmidl and Cox method timing metric in an ideal channel

The time metric introduced by Schmidl [4] can be computed by the correlation of thesetwo parts. In this technique the beginning of the symbol duration can be estimated at themaximum point of the time metric as follows [4]

M (m) = |P (m)|2

(R(m))2, (4)

where

P (m) =N2 1

n=0r (m + n) r

(m + n + N

2

), (5)

R (m) =N2 1

n=0

r(

m + n + N2

)2, (6)

where r () is training symbol. Thus the time offset will be as follows [4]

= arg max (M (m)) , (7)and the frequency offset will be

f = angle(P())

. (8)

However this time metric suffer from plateaus which mean uncertain estimation of thebeginning of the frame especially at low SNR. Figure 3 shows the timing metric in anideal channel (no noise) and Fig. 4 shows the timing metric in an AWGN channel with lowSNR=1 dB.3.2 Minns Method

Minns proposed a different training symbol in [5] as a modification to the Schmidl and CoxMethod [4]. Minns training symbol can be designed in time domain as shown in Fig. 5.As shown in the Figure, Minns symbol has four equal length parts of PN sequence each of

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0 50 100 150 200 250 300 350 4000

0.2

0.4

0.6

0.8

1

schmidl algorithm

Time (sample)

Tim

ing

Met

ric

SNR=1dB

Fig. 4 Schmidl and Cox method timing metric in an AWGN channel with SNR = 1 dB

Fig. 5 Minns training sysmbol N/4 N/4 N/4 N/4

B B -B -B

Fig. 6 Minns training symbol N/4 N/4 N/4 N/4

A B A B

length N/4. The first two parts are identical and the other two marts are the negative version ofthe first two parts. This negative sign is used to overcome the time metric plateau of Schmidlalgorithm, and gives a peak at the starting of the OFDM symbol.

Thus, the time metric can be computed using Eq. (4), Where

P (m) =1

l=0

N4 1

n=0r

(m + n + l N

2

) r

(m + n + l N

2+ N

4

)(9)

R (m) =1

l=0

N4 1

n=0

r(

m + n + l N2

+ N4

)2. (10)

Although, Minns method [5] overcomes the plateau problem it still suffers from large Meansquare error (MSE) due to the large variance of the time metric loops, which makes itunreliable to be used especially in a multipath Rayleigh fading environment.

3.3 Parks Method

In order to enhance the time offset estimation, Park [6] introduces a new symbol with fourportions. Every two closed symbols are of great difference. In Parkers method, the OFDMtraining symbol can be generated in time domain as shown in Fig. 6.

where A is an m-sequence with a length of N/4 passed throw IFFT, and B is the symmetrictime version of the conjugate of A. The time metric can be computed by Eq. (4), where

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0 50 100 150 200 250 300 350 4000

0.2

0.4

0.6

0.8

1

Time (sample)

Tim

ing

Me

tric

Park

Fig. 7 Parks method timing metric in an ideal channel

Fig. 8 Chois training symbol N/2 N/2

C DChois training symbol

P (m) =N4 1

n=0r

(m + N

2 n

) r

(m + n + N

2 1

)(11)

R (m) =N4 1

n=0|r(m + n 1)|2 , (12)

and the time offset will be calculated using Eq. (7). Due to the difference between the twoadjacent portions of the symbol, Park method gives a sharp peak at the correct time sampleas shown in Fig. 7, which illustrates the timing metric in an ideal channel. This peak has verysmall variance, which means a better estimation in the ISI environment when compared toboth methods of Minn and Schmidl.

Although the sharp peak of Parks scheme, the method suffers from large side lobes atN/4 samples around the main lobe due to the repetition of portion one in portion three, whichwill degrade the scheme performance at low SNR with frequency selective channel [6].

3.4 Chois Method

Choi has introduced a time domain training symbol using constant amplitude zero autocor-relation (CAZAC) sequence in [7]. Chois training symbol is generated in time domain asshown in Fig. 8.

where C is the IFFT output of N/2 (CAZAC) sequence and D is the complex conjugate ofthe time reversed version of C. Again time metric is defined using Eq. (4), using the followingP(m) and R(m) functions [7]

P (m) =N2 1

n=0r(m n) r(m + n + 1) (13)

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R (m) = 12

N2 1

n=0

r(

m + n N2

)2, (14)

The time offset will be calculated using Eq. (7). The Chois time metric gives a very sharppeak at the correct time symbol. However, a small minor loop which affects the estimationin the very low SNR. This can be concluded from Fig. 9, which illustrate timing metric ofChois scheme in an ideal channel.

4 Proposed Time Synchronization Scheme

Although the time synchronization scheme introduced by Choi [7] has a sharp peak at thecorrect time sample, it has a minor lobe which will affect the estimation performance at lowSNR. As a modification of Chois training symbol, this paper proposes a new training symbolwhich eliminates the minor lobes occurred in Chois symbol. The new symbol is generatedby multiplying the whole symbol of Choi with an m-sequence of length N. So that it can beconstructed as illustrated in Fig. 10 and will have the form shown in Fig. 11 in time domain.

c (k) = ejrk2

N2 , k = 1, 2, 3, . . . N

2, (15)

where CC is the IFFT of c (k) multiplied by the first N2 part of the m-sequence, and DD iscomplex conjugate of the time reversed version of c (k) after the IFFT multiplied by the last

Fig. 9 Chois method timingmetric in an ideal channel

400Time (sample)

Tim

ing

Met

ric

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1 Choi

Fig. 10 Proposed time offsetestimation method

Fig. 11 The proposed trainingsymbol N/2 N/2

CC DD

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0 50 100 150 200 250 300 350 4000

0.2

0.4

0.6

0.8

1

Time (sample)

Tim

ing

Met

ric

Proposed

Sharp peak at the beginning of the frame

Fig. 12 The timing metric of the proposed time offset technique

N2 part of the m-sequence. The time metric is defined using Eq. (4), using the following P(m)

and R(m) functions

P (m) =N2 1

n=0rr

(N2

n)

rr(

N2

+ n + 1)

(16)

R (m) = 12

N2 1

n=0

rr(

m + n N2

)2

(17)

Thus the time offset will be

= arg max(M (m))The proposed time metric outperforms the previous methods as it gives a very sharp peakat the starting instant of the frame, and at the same time eliminates the side lobe appearedin Parks and Chois methods. The timing metric of the proposed time offset estimationtechnique is shown in Fig. 12.

5 Proposed Frequency Synchronization Scheme

The carrier frequency offset (CFO) estimation is an important process in the OFDM systemas the time offset estimation, to ensure the high performance of the OFDM system. Carrierfrequency errors, which are created due to different factors such as differences in samplingclock frequencies of the transmitter and the receiver and clock jitter result in a shift of thereceived signal spectrum in the frequency domain. If the frequency error is an integer multipleof the subcarrier spacing, then the subcarriers are still mutually orthogonal, but the receiveddata symbols, which are mapped to the OFDM spectrum, are in the wrong position in thedemodulated spectrum, resulting in large bit error rate (BER). If the CFO is not an integermultiple of the subcarrier spacing, then energy spills over between the subcarriers, resultingin loss of their orthogonality causing ICI.

This section presents two techniques to perform the CFO estimation. The first one for thefractional part as in [4] in which the offset will be less than one cycle and the other is the

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X X FFT Max( + )

( ){ ( )}

G(k)

Fig. 13 Proposed coarse frequency offset estimation method

proposed technique for the integer part which can estimate frequency offset as wide as thewhole OFDM symbol.

5.1 Schmidl and Cox Method for Fine CFO Estimation

In fractional/fine CFO the frequency mismatch is less than one subcarrier spacing. Thissmall frequency error happens manly in slow varying environment, usually indoor. It thatcan be easily compensated by using non-data-aided methods in order not to lose the spectralefficiency. As the cyclic prefix contains redundant information that can be used to estimatethe fine frequency offset using:

f i =angle

{Ngk=1 r

( k) r ( k + N)

}

2(18)

To improve the overall performance, this method can be carried out on the next data OFDMframes then the average value is taken.

5.2 Proposed Coarse/Integer Frequency Estimation

After the fine frequency offset has been compensated, integer frequency estimation takesplace. The proposed system is shown in Fig. 13 and uses the proposed symbol as the trainingsymbol. Consider the received fine compensated symbol r

( + k) and k = 0, 1, 2, . . . , N 1

then multiply it by PN sequence pn(k)

r (k) = r ( + k) pn (k) , (19)As the transmitted training symbol is known to the receiver then

G (k) = r (k) Conj{Seq (k)} (20)where Seq(k) is the transmitted training symbol and G(k) will contain the phase difference.The difference between the transmitted training symbol Seq (k) and the received symbol islocated only in the phase so if G(k) is passed through FFT that means convolution betweenG (k)and Conj{Seq (k)} in the frequency domain, then the output will gives a peak at thecorrect shift. This shift happens due to the offset in the other domain. Then the Integerfrequency offset can be calculated by finding the maximum of the output of the FFT asfollows

fc = Max {F FT {G (k)}} (21)The output of the proposed coarse CFO estimation is shown in Fig. 14. It is concluded

from Fig. 14 that the proposed technique succeeded to define the correct CFO.

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Fig. 14 Proposed coarse CFO estimation at 100.35 Hz

Table 1 Simulation parametersNo. of subcarriers N = 256Length of CP Ng = N/4 = 32Modulation type Mod = QPSKChannel model AWGN + Rayleigh fadingChannel delays [0 1 2 3 4] sample timeChannel gains [1 0.8913 0.3548 0.3162 0.1000]

It is also worth to compare the proposed technique to the technique previously introducedby Wan [8] from the complexity side. The complexity of the CFO estimator is most probablydue to the computational complexity carried out by the calculations in the FFT phase. Asshown in Fig. 13, the proposed method uses only one FFT calculation per estimation andgives a sharp peak at the correct integer frequency shift. On the other hand, the methodproposed in [8] uses N number of FFT at least per estimation, which causes much highercomputational load and hardware power.

6 Simulation and Results

In this section, simulation results are carried out using MATLAB. The OFDM system para-meters are defined in Table 1.

The comparison between traditional estimation algorithms presented in Sect. 3 shows thatChois technique [7] outperforms the other techniques. The comparison shows the plateau ofSchmidl time metric [4] with width equal to the CP length. Park [5] and Choi [6] methodsgives a peak at the end of the CP. Moreover, Park and Choi methods give side lobes in thetiming metric pattern.

In this section, simulation of the proposed time estimation technique takes place andcompared to the Chois method one in a multipath Rayleigh fading channel. The simulationresults are demonstrated in Fig. 15. By comparing the results shown in Fig. 15, it is concludedthat, the proposed scheme has a low variance and a sharp peak at the correct sample whileChoi [7] has wider variance of the main lobe and a plateaus due to the channel dispersion. Itis also observed, that the time metric of the proposed technique suffers no side lobes.

This section also presents the simulation results of the proposed CFO estimation algorithm.Figures 16 and 17 compares the performance of the proposed Fine CFO estimation methodwith Chois method [7] in both AWGN and Rayleigh fading channel respectively. Figure 16shows that the proposed Fine estimation has less mean square error in AWGN channel then

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proposed

290 295 300 305 310 315 3200

0.1

0.2

0.3

0.4

Time (sample)

Tim

ing

Met

ric

290 295 300 305 310 315 3200

0.1

0.2

0.3

0.4 Choi

Time (sample)

Tim

ing

Met

ric

Fig. 15 Proposed and Choi [7] time metric at Rayleigh fading channel

0 5 10 15 20 25 3010 -7

10 -6

10 -5

10 -4

10 -3

10 -2

Mea

n Sq

uare

Err

or

ProposedSeungChoi

Fig. 16 Fine CFO estimation in a AWGN channel

0 5 10 15 20 25 3010 -6

10 -5

10 -4

10 -3

10 -2

SNR (db)

Mea

n Sq

uar

e Er

ror

ProposedChoi

Fig. 17 Fine CFO estimation in a multipath Rayleigh fading channel

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0 50 100 150 200 250 3000

100

200

300

Frequency Sample

FFT(

G(k))

0 50 100 150 200 250 3000

0.05

0.1

0.15

0.2

Frequency Sample

FFT(

G(k))

[8] Method

Proposed coarse CFO Estimation

Fig. 18 Coarse CFO estimation at SNR = 15 dB over AWGN channel

0 50 100 150 200 250 3000

50

100

150

200

Frequency Sample

FFT(

G(k))

Proposed coarse CFO Estimation

0 50 100 150 200 250 3000

0.2

0.4

0.6

0.8

Frequency Sample

FFT(

G(k)) [8] Method

Fig. 19 Coarse CFO estimation at SNR = 0 dB over Rayleigh fading channel

the Chois method in AWGN channel for different SNR. On the other hand, Fig. 17 indicatesthat proposed estimation algorithm has better mean square error performance in a multipathRayleigh fading channel for SNR up to 15 dB. This is in addition to the less complexity ofthe proposed technique when compared to the traditional ones as stated before.

Figure 18 shows that the proposed coarse estimation method has a sharp peak at the correctfrequency shift in AWGN channel. Although the method proposed in [8] also have a correctpeak, it has large ground noise which lead to miss estimation in the low SNR and in largeoffsets. In Fig. 19, the signal is passing through a Rayleigh fading channel which leads toside lobes in both methods. However, the proposed side lobes are small compared to the mainone.

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7 Conclusions

In order to improve the performance of the OFDM Synchronization method, this paperproposed time and CFO Synchronization schemes with a CAZAC sequence. The proposedschemes use the property that the IFFT CAZAC sequence is a CAZAC. Several time and CFOSynchronization schemes [48] have been presented and explained. Computer simulationresults show performance comparisons and show that the proposed methods achieve superiorperformance with simple and accurate computational load compared to the existing methodsin both AWGN and Rayleigh fading channels.

References

1. Schulze, H., & Lueders, C. (2005). Theory and applications of OFDM and CDMA: Wideband wirelesscommunications. New York: Wiley.

2. Ratasuk, R., Tolli, D., & Ghosh, A. (2010). Carrier aggregation in LTE-advanced. In Proceedings of IEEE71st vehicular technology conference VTC-2010 (pp. 15). Taipei.

3. Dahlman, E., Parkvall, S., & Skld, J. (2011). 4G LTE/LTE-advanced for mobile broadband. Amsterdam:Elsevier Ltd.

4. Schmidl, T., & Cox, D. (1997). Robust frequency and timing synchronization for OFDM. IEEE Trans-actions on Communications, 45(12), 16131621.

5. Minn, H., Zeng, M., & Bhargava, V. K. (2000). On timing offset estimation for OFDM systems. IEEECommunication Letters, 4(7), 242244.

6. Park, B., Cheon, H., & Kang, C. (2003). A novel timing estimation method for OFDM systems. IEEECommunications Letters, 7(5), 239241.

7. Choi, S. D., Choi, J., M., & Lee, J. H. (2006). An initial timing offset estimation method for OFDM systemsin Rayleigh fading channel. Proceedings of IEEE 64th vehicular technology conference VTC-2006.

8. Wang, H., et al. (2012). A novel synchronization algorithm for OFDM systems with weighted CAZACsequence. Journal of Computational Information Systems, 8(6), 22752283.

9. Boshehba, S. A., Badran E. F., & Mahmoud, M. (2013). A modified blind deterministic carrier frequencyoffset estimator for OFDM systems. Proceedings of the 2013 JapanEgypt conference on electronics,communications and computers (JEC-ECC2013) (pp. 1822). Cairo, Egypt, 1719.

10. Badran, E. F., Samara M., & Aly, M. H. (2013). A novel frame synchronization scheme via waveletpacket transform for OFDM systems. Proceedings of the 2013 JapanEgypt conference on electronics,communications and computers (JEC-ECC2013) (pp. 1217). Cairo, Egypt, 1719.

Hossam Asran received the B.Sc. degree (Honors) in electronicsand communications engineering from Arab Academy for Science andTechnology and Maritime Transport university, Alexandria, Egypt, inAugust 2008. Received the M.Sc. degree in August 2013.

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Ehab F. Badran received the B.Sc. degree with honors and M.Sc.degree in electrical engineering from Assiut university, Assiut, Egypt,in May 1995 and March 1998, respectively, and the M.Sc. and Ph.D.degrees in electrical engineering from Louisiana State University(LSU), Baton Rouge, USA, in May 2001 and May 2002, respectively.From 1995 to 1998, he was an instructor with the department of elec-trical engineering, Assiut university, where in May 1998, he was pro-moted to assistant lecturer. From January 2000 to May 2002, he wasa teaching and research assistant with the department of electricaland computer engineering, Louisiana State University during his Ph.D.studies. From September 2002 to August 2003, he was an assistant pro-fessor with the department of electrical engineering, Assiut University.From September 2003 to May 2007, he worked as an assistant profes-sor in the department of electronics and communication engineering,Arab Academy for Science and Technology and Maritime Transport,Alexandria, Egypt. From June 2007 to May 2011, he was an associate

professor in the same department. In June 2011, he was promoted to be a professor. His research and teachinginterests are in wireless communications, signal processing, MIMO systems, and image signal processing.Prof. Dr. Ehab Farouk Badran was the vice dean of college of engineering and technology for educationalaffairs from 12 January 2012 until 14 March 2014.

Amira I. Zaki received the B.Sc. degree (Honors) in electrical engi-neering from Arab Academy for Science and Technology and Mar-itime Transport university, Alexandria, Egypt, in August 2000. Workedas a GTA from 2000 till 2005 in the same university. Received theM.Sc. degree in June 2004. She was promoted in 2004 and worked as ateacher assistant in the department of electronics and communicationsin the Arab Academy for Science and Technology and Maritime Trans-port university. She received the ph.D. from the faculty of engineering,Alexandria University, Alexandria, Egypt in April 2004 and promotedto work as a teacher in the Arab Academy for Science and Technologyand Maritime Transport, Alexandria, Egypt. Her current research areasof interest include wave propagation in different media, smart antennaarrays, spacetime coding, communication systems, fractal antenna,wireless communications, signal processing, MIMO systems and UWBsystem.

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Novel Time and Freq. Synch

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