OFDM-Doppler Diversity

Doppler Diversity for OFDM High-SpeedMobile Communications

Mohamed Imran, Noor Mohamed

Telecommunication Lab,66123, Saarbrucken, Germany

http://www.nt.uni-saarland.de

Abstract. Doppler diversity technique for orthogonal frequency divi-sion multiplexing(OFDM) helps to improve the Doppler spread in high-speed mobile communications. Here we intend to study the working prin-ciple of original Doppler diversity with the simplified scheme to reducecomplexity calculation in the OFDM receivers. This paper tries to vali-date the research done by Wang et al.[1]. They found that comparing twoproposed diversity techniques will help us to pursue novel Doppler diver-sity research to find new methods for efficient high data transmission.They believed that simplified Doppler diversity based on the originaldiversity approach can reduce complexity and increase OFDM systemefficiency by 60%. Also, this paper suggests new methods for optimalreceiver configuration, thereby improving the system performance. Sim-ulation results indicate that OFDM with optimal configuration has lessinterference compared to non-optimal receivers. Finally, project resultsverify the need to combat Doppler spread in high-speed mobile commu-nications.

Keywords: Orthogonal frequency Division Multiplexing Doppler Di-versity, simplified Doppler Diversity, Complexity Reduction

1 Introduction

Efficient high data rate transmission over a given channel is the core aim ofany telecommunication system. However, in wireless channels the bandwidth isinversely proportional to the symbol duration. Therefore, shorter symbol dura-tion increase the data rate. Yet, in wireless channels the effect of fading severelycausing Inter Symbol Interference (ISI) if single-carrier modulation such as Time-Division Multiple Access (TDMA) is used. To combat ISI Orthogonal FrequencyDivision multiplexing (OFDM) systems are popular, as the OFDM increasesthe symbol duration much larger than the delay spread in wireless channels.In OFDM, the entire channel is divided into many narrow-band sub-channels,which are transmitted in parallel to maintain high data-rate transmission andat the same time increase the symbol duration to combat ISI. However, whenthe receiver moves, the performance of the system will degrade. This is due toDoppler spread in the channel which destroys orthogonality between the sub-carriers resulting Inter Carrier Interference (ICI).

2 Doppler Diversity for OFDM High-Speed Mobile Communications

Past studies show that introducing Doppler diversity in the receiver can re-duce the Doppler spread effectively[2]. Several other studies [3, 4] primarily fo-cused on developing multi-path Doppler diversity for single carrier systems. Spe-cially, Kim et al. [5] introduced Doppler diversity for OFDM systems. However,these approaches add huge calculation efforts on the receivers, as it increasesthe complexity. Also, there is no study conducted to investigate the optimalconfiguration in the receivers and without such configuration, a receiver is hardto implement. Wang et al.[1] asked whether there is better way to simplify theapproach, to reduce the complexity of calculations and to optimally configure atreceivers.

Aim of this research was to develop a simplified Doppler diversity based onthe original diversity approach which can reduce complexity heavily. This createsa new dimension to effectively reduce calculation and also to optimally config-ure them at the receivers. We tested our hypothesis by conducting a study tocompare the performance between the original diversity and simplified Dopplerdiversity. We claim that our approach to develop new simplify Doppler approachis far efficient than other research works conducted [3, 4] and a novel way to em-ploy Doppler Diversity for High-speed mobile communications.

This paper is structured as following chapters: 1. OFDM: an Overview 2.Doppler Diversity 3. Simplified Doppler Diversity 4. Results and discussion.

2 Orthogonal Frequency Division Multiplexing: anOverview

The idea of OFDM is to divide the available spectrum into several sub carriers.To obtain high spectral efficiency, the frequency response of the carriers areorthogonal, narrower and overlapping, hence the name Orthogonal FrequencyDivision Multiplexing. However, this orthogonality is destroyed when the channelis time variant, and its characteristics change over the duration of one OFDMsymbol duration. These changes can be modeled by a Doppler spread : it is thedifference in Doppler frequencies affecting different channel paths which leads toloss of orthogonality.

The following sections cover detailed descriptions of the Channel models,Doppler diversity and the simplified Doppler diversity approaches:

2.1 Doppler Effect

The Doppler effect is the change of frequency and wavelength when the trans-mitting and receiving points are moving with respect to each other. A classicalexample is the situation when we stand in a train station and a whistling trainpasses. We hear the whistle tone change and it is higher when the train ap-proaches, then changes to lower when the train leaves the station. For a passen-ger in a train the whistle tone remains same. Thus, the Doppler effect may resultfrom motion of either the source or the receiver where the frequency change isgiven by:

OFDM 3

f = f0 + fd ∗ cosΘ (1)

where the f0 is the original frequency, fd is the Maximum Doppler shiftedfrequency with the incident angle Θ between the transmitter and receiver.

2.2 Channel models

A channel model is designed to validate the performance of a communicationsystems in various conditions. It is important to model the influence of channelon the complex envelope, because the complex envelope is what will be decodedat the receiver. For a time dependent signal x(t), the output of the channel s(t) iscomputed by convolution of the time dependent signal with the impulse responseof the channel h(t) as given below:

s(t) = h(t) ∗ x(t) (2)

From the Eqn.2 it is clear that modeling impulse response of a channel iscrucial to estimate the channel influence under fading conditions. A selectivefading channel in wireless communications is often modeled by WSSUS[6]. Themodel defines the output of the attenuated signal with respect to the input signalin a multi path environment as:

Attenuated Output Signal = Time Dependent Attenuation * Phase rotation in all paths

Impulse response of channel = Attenuated Output Signal * Delays in all the paths

It is clear from the above expressions that a channel which has been affectedby Doppler is considered as a Frequency Selective channel which is composed ofdifferent delays on various paths. The impulse response will be dependent on thedelay of all the paths shifted by Doppler. We can now define the Doppler spreadfunction with impulse response of the channel as:

h(ν, τ) =

M∑p=0

K∑k=−K

α(k, p).δ(ν − νk).δ(τ − τk) (3)

In Eqn.3, the impulse response h depends on the speed of the receiver ν andDoppler delay τ where K will be the parameter dependent on the maximumDoppler shifts fd, and α is the fading amplitude of the signal dependent onmaximum Doppler shifts and paths p.

3 Doppler Diversity

Doppler diversity is defined as the squared ratio of the trace of a received signalto its absolute value as explained in [7]. To understand the complexity in thedemodulation, let us analyze Doppler diversity in the original proposed method.


Let us take the receiver which employs Doppler diversity as it contains an OFDMsignal which is the combination of different sub carriers N with the BPSK-modulated sub-symbols for the entire symbol duration.

Received Signal = Impulse response of the channel * OFDM Transmitted signal + Noise

From the above expression it is relatively straight forward that the convolu-tion of the OFDM signals with the impulse response of the channel is what willbe received. We define the received signal:

X(t) =

M∑p=0

K∑k=−K

α(k, p).s(τ − τP ). exp(j2πνt) +W (4)

where s(τ − τP ) is the shifted signal at the receiver with the noise consideredas additive noise.

Fig. 1. Receiver with original Doppler Diversity

In Fig.1 the input signal is shifted to different branches, the branches aredenoted as Q. For each Doppler branch the received signal is shifted by a pre-determined frequency. This shifting of the signal is done to implement matchedfiltering, as it increases the SNR (Signal-to-Noise ratio). Matched filtering is usedfor signal analysis to determine the unknown signal by correlation with a pre-determined signal. Every branch has a different matched output with differentlyshifted signals and all branches are uncorrelated. The cross-correlation betweenthe branches is shown in [5] with respect to the frequency shifts for the Diversitybranches. Selection of these frequencies is important since the statistical proper-ties of Doppler branches depend on different frequencies. During the frequency

OFDM 5

selection the interference scale factor is calculated, this factor explains the inter-ference suppression. Also, the correlation coefficient is determined for the bestvalue during frequency shifts as explained in [5].

After shifting, serial-to-parallel conversion and FFT (Fast Fourier Trans-form) is done on each Doppler diversity branch. To compensate Doppler spreadcombining techniques play a major role. In maximum ratio combining [8] eachbranch is multiplied by the complex conjugate of its corresponding channel gainas the channel information is assumed to be known with the interference factor.As an example, we can consider three branches where the signal in each path isrotated and weighted according to the phase and strength of the channel, suchthat signals from all paths are combined to yield the maximum ratio betweensignal and noise terms. Hence, the phases of signal components are corrected andsignals at different branches are combined coherently. For the different branchthe output is given as expression:

Output of Combiner = Sum(Interference Factor * Channel gain * Signal in the branch)

Here the channel gain will be the linear combination of the shifted frequencieswith the Doppler frequencies. The channel gain, which is required in this scheme,can be estimated using pilot sub-symbols or symbols in practice. Thus the outputof the combiner z(i) with ith branch can be represented by notations:

z(i) =

Q∑q=1

ηqH∗(i, Fx)X(i) (5)

where ηq is the interference factor with the different frequencies Fx in allbranches i.

Now, the signal after demodulation is:

X(i, Fx) =

N−1∑m=0

z(m). exp(−j2π · m · iN

) (6)

where m is the diversity paths. From above, we can observe that after de-modulation branch outputs are individually weighted and added together.

We can observe that the Doppler compensation works fine but the complexityof the decoding gets higher as each branch has the serial-to-parallel converterand FFT demodulation. So the overall complexity of the received branches willbe 4QN +QNlogN −N as explained in Wang et al.[1]. Hence, there is need tosimplify and propose a new approach.

4 Simplified Doppler Diversity

To reduce the complexity of the Doppler diversity technique the new simpli-fied approach is proposed with the same characteristics but with the additionaloptimal configuration at the receivers. To understand the simplification better,


Fig. 2. Receiver with simplified Doppler Diversity

let us analyze the similarities between the original approach and the simplifiedapproach.

In Fig.2, the Doppler compensation is done before the FFT. Each branch isthe sum of the desired signal, Interference and the noise:

Carrier output of branch1 = Desired signal + Interference + Noise

On comparing the above expression with the original Doppler diversity withEqn.5 nothing has changed so the simplification does the same as the origi-nal diversity approach. Instead of maximum ratio combining, simplified Dopplerdiversity uses the equal gain combining on the received paths. Thus, the equal-ization is performed at the receiver by dividing the received symbol with theoutput Yi by the apriori known phase of the signal. Thus, the decoded symbolis the sum of the phase compensated channel from all the receive paths:

X(i, Fx) =

N−1∑m=0

yq(m). exp(−j2π ·m · i/N) (7)

where yq is the new diversity branch with different weights w1, w2, w3 asshown in Fig.2.

5 Results

5.1 Complexity Reduction

Fig.2 shows that simplified Doppler diversity shifts the received signal and com-bines them before the FFT demodulation. The entire structure is kept simplewithout including FFT in the diversity branches as compared to original Dopplerdiversity. This architecture reduces the complexity of the simplified Dopplerdiversity. We found that the complexity of the original Doppler diversity was4QN + QNlogN − N where Q times NlogN arises from the FFT demodula-tion as included in the diversity scheme. As the new simplified Doppler diversity

OFDM 7

without FFT has the complexity reduced to NlogN without the Q branches in-cluded in the diversity schemes. As an example, let the number of sub-carriersbe 256 and the receiver has the Doppler diversity branches as Q=3. With thisconfiguration the complexity calculation for the original Doppler diversity willbe 35 · 256 but using simplified model complexity is 14 ·256. This reduces ourlinear calculation by 60%.

Fig. 3. Comparison of the amount of linear calculation for OFDM receiver

As shown in the Fig.3, the complexity is correlated to the number of Dopplerdiversity branches. Hence, there is a linear increase in the calculation as thenumber of diversity branches increases. Yet, in the simplified Doppler diversitythe calculation rate is decreased so it is not linear. This result is beneficial forhardware implementations, as the operations done on the chip will be minimized.

5.2 Error rate in simplified scheme

Number of Sub-carriers 256Bandwidth 2MhzMaximum Doppler 1111Hz

Above table shows the parameters used for the simulation. The whole appli-cation was developed for the High-speed mobile communications, the speed ofthe vehicle was considered 500 km/h.

As we can interpret from the Fig.4, the SIR(Signal-Interference-Ratio) for thereceivers without Doppler diversity is quite low initially but as speed increases


Fig. 4. Comparison of SIR for OFDM receiver

the SIR decrease is not so significant. To compare with non-optimal diversityresults let the SNR be fixed at 20db. If we observe at lower maximal Dopplershifts [e.g. 0.06] the Signal-to-Interference Ratio(SIR) is 20db. When the sameconfiguration is applied for the non-optimal receivers the SIR is 20db at 0.4,which creates a gain in SIR of 26db. As the receiver moves faster the actualconfiguration suffers hugely as the curves does not decrease as expected. For anon-optimal receiver this shows a decrease in SIR. For the optimal configura-tion the gain is larger compared to the non-optimal and configuration withoutDoppler diversity. To illustrate, we could observe the gain about 300db wherethe optimal configuration has the number of branches Q as:

Q = 2K + 1 (8)

Here K will be the doppler spread. From Eqn.8 it is obvious that for high-speed mobile communications the characteristics of the channel is representedby the Doppler spread. Hence, if the Doppler spread is estimated accurately,then the configuration at the receiver is set according to the above equation tocombat Doppler spread effectively.

5.3 OFDM Simulation Project

To understand the research paper better, OFDM simulation was done to confirmthe theoretical aspects of the paper. The simulation parameters are the same asin the paper. The results are shown in the table, with three diversity branches inthe Rayleigh fading environment. The DPSK modulation was used in the simu-lation. As we could observe in Fig.5 , the theoretical Bit Error Rate (BER) was

OFDM 9

computed for the DPSK modulation without any Doppler spread in the Rayleighchannel. Theoretical results confirm BER for DPSK modulation scheme usingMATLAB R© BER-tool. We find that as the SNR increases the BER decreasesin theoretical results. However, this will change in the same DPSK modulationwith Doppler spread.

Fig. 5. BER vs. SNR curve(Doppler Shift=1111 Hz)

With Doppler spread of Fd = 1111Hz, the maximal Doppler spread, theBER does not decrease as the SNR increases. Thus the Doppler spread causesthe increase in BER as compared to Doppler free channel. Fig.6 proves that theBER increases as the vehicle moves as the Doppler spread increases. Hence, theabove simulation verifies the need to combat Doppler spread in the High-speedmobile communications.

6 Discussion

We found that simplifying Doppler Diversity can reduce the complexity of cal-culations effectively as it can be implemented for High-speed mobile communi-cations. Experimental results prove that reducing complexity calculations leadsto a better way to find the optimal configuration at the receivers. As claimed,the paper suggests that simplifying Doppler diversity approach is a novel wayto reduce calculation efforts and also to apply them on real time devices movingat high speeds.

Results show that the receiver with simplification of the optimal DopplerDiversity is not affected by the Doppler spread, the signal interference ratio isfar better than the original Doppler diversity. It creates a new technology to


Fig. 6. BER vs, Dopler Shifts at SNR=15db

implement Doppler diversity on hardware devices. It bridges research to realtime implementation.

Thus to conclude, for high-speed railway mobile communication, with thenew simplified scheme, the calculation time of signal processing can be reducedgreatly with an efficiency increase of about 60%. Hence, with accurate Dopplerspread estimation the receiver could be configured to have the Best performance,thus reducing Doppler spread interference in OFDM.

References

1. Xin, Wang, et al. ”Doppler diversity for OFDM high-speed mobile communications.”Communications, 2006. ICC’06. IEEE International Conference on. Vol. 10. IEEE,2006.

2. Sayeed, Akbar M., and Behnaam Aazhang. ”Joint multipath-Doppler diversity inmobile wireless communications.” Communications, IEEE Transactions on 47.1(1999): 123-132.

3. Thomas, Timothy A., and Frederick W. Vook. ”Multi-user frequency-domain chan-nel identification, interference suppression, and equalization for time-varying broad-band wireless communications.” Sensor Array and Multichannel Signal ProcessingWorkshop. 2000. Proceedings of the 2000 IEEE. IEEE, 2000.

4. Boudreau, Richard, J-Y. Chouinard, and A. Yongacoglu. ”Exploiting Doppler-diversity in flat, fast fading channels.” Electrical and Computer Engineering, 2000Canadian Conference on. Vol. 1. IEEE, 2000.

5. Kim, Byung-Chul, and I-Tai Lu. ”Doppler diversity for OFDM wireless mobile com-munications. part I: frequency domain approach.” Vehicular Technology Conference,2003. VTC 2003-Spring. The 57th IEEE Semiannual. Vol. 4. IEEE, 2003.

6. Kurth, R. R., D. L. Snyder, and E. V. Hoversten. Detection and Estimation The-ory. Research Laboratory of Electronics (RLE) at the Massachusetts Institute ofTechnology (MIT), 1969.

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7. Zemen, Thomas, and Christoph F. Mecklenbruker. ”Doppler diversity in MC-CDMAusing the Slepian basis expansion model.” 12th European Signal Processing Con-ference (EUSIPCO). 2004.

8. Molisch, Andreas F. Wireless communications. Vol. 15. John Wiley and Sons, 2010

OFDM-Doppler Diversity

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