A Robust Algorithm for OFDM Synchronizationwith Modified Polyphase Training Sequences

Gaurav PotnisDepartment of Electrical Engineering

Indian Institute of Technology, MadrasChennai - 600036, India.

Email: ee05s050@iitm.ac.in

Abstract— Orthogonal Frequency Division Multiplexing(OFDM) systems are sensitive to timing and frequency estimationerrors, which causes inter-symbol-interference (ISI) and inter-carrier-interference (ICI), leading to degradation in the systemperformance. An algorithm is presented in this paper, based onmodified polyphase sequences; proposed for timing and frequencysynchronization of OFDM system which is robust, efficient andcomputationally less complex. The proposed algorithm gives100% success of timing index acquisition at 10 dB SNR whichis at least 5 dB less compared to all existing algorithms.The algorithm is also compatible with IEEE 802.16e wirelessMetropolitan Area Network (MAN) standard. This approach isbased on modification of polyphase sequences by taking FFT ofit.

I. INTRODUCTION

Orthogonal frequency division multiplexing (OFDM) [1]system is the heart of the existing technologies, such asIEEE 802.11a, IEEE 802.16, IEEE 802.22 and 3GPP-LTE [2].OFDM is used in the European digital Audio/Video broadcast(DAB/DVB) system and is being investigated for other mobilecommunication systems, as well as for broadband digitalcommunication on existing copper networks [3].Synchronization has been one of the crucial research topicsin OFDM system [4] because of its sensitivity to timing andfrequency errors [5]. The OFDM receiver is realized in threestages like Synchronization, Channel Estimation (CE) and For-ward Error Correction (FEC) decoder. There are two problemsfrom the design point of view for OFDM receiver before CEstage i.e., timing offset occurs because of multipath fading andfrequency offset arises from the frequency mismatch betweentransmitter and receiver oscillators. The frequency offset alsooccurs due to the existence of doppler shift in channel [7] -[8].In OFDM, ISI caused by multipath fading, can be avoidedby inserting Cyclic Prefix (CP) with length greater than thechannel impulse response. The ICI caused my mismatch inoscillators, can be eliminated by maintaining the orthogonalityof carriers under the condition that the transmitter and thereceiver have the exact same carrier frequency. Therefore, itis important to estimate the timing offset to identify the starttime of each frame and the FFT window position for eachOFDM symbol. The demodulation of a signal with an offsetin the carrier frequency causes a high bit error rate and maydegrade the performance.

The timing and frequency estimates can be obtained with theaid of training sequence. The preamble is first symbol of theframe and a training sequence is inserted in the preamble ofOFDM frame. All the previous work on preamble design andsynchronization refers to the classical paper of Schmidl andCox [10]. However, the timing metric suffers from a plateau,which leads to some uncertainty in determining the start ofthe frame. So the correlation is followed by averaging methodto finalize the start time. To avoid the ambiguity caused byplateau of timing metric, Minn et al [13] modified Schmidland Cox’s [10] method and proposed two new methods. Parket al [14] presented a training symbol consisting of four parts:first two are symmetric and last two are conjugate of first tworespectively, so his method produces even sharper timing met-ric and has significant smaller MSE than [10] and [13]. Kanshi et al [15] proposed a scheme that exploited the repetitivestructure of a training symbol for carrier synchronization andpresented superior performance with respect to the approachpresented in [10] in terms of better detection properties withaccuracy and larger estimation range.The methods proposed in [9] - [15] were not very effective intime varying channel conditions with multipath environment.Seung’s [16] method is robust for multipath fading environ-ment. Polyphase codes used by Sueng [16] that have beenproposed by Frank and Zadoff [17] has limitation that thelengths of such sequences are restricted to perfect squares.Hence, Frank and Zadoff sequence fails while trying to pro-duce a sequence of any length other than perfect squares. Thislimitation is overcome by Chu [18] in which he modifies [17]to produce sequences of any length. Thus use of polyphasesequence is not new in literature, infact it is also proposedto be used for IEEE 802.11n, IEEE 802.16m and 3GPP-LTE.But, they use polyphase sequence in its raw form.Recently, polyphase preambles (Frank and Chu sequences)[18] belonging to the class of Constant Amplitude ZeroAuto-Correlation (CAZAC) sequences are adopted in IEEE802.16 and IEEE 802.15.3, due to their perfect autocorrelationproperty [19]. But sequences produced by (Frank and Chusequences) [18] have larger alphabet size, Y. Liu and P. Fan[20] proposed modified Chu sequences with smaller Alphabetsize.In this paper a new algorithm is proposed by considering[20] as seed sequence and further processing it in order

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to get a perfect training sequence for a preamble which isrobust in multipath fading environment. The novelty standsin the processing of small alphabet sized polyphase sequencewhich increases the robustness and reduces complexity. Thefurther paper is arranged in this manner, section II of thispaper presents the properties of polyphase training sequence,the proposed preamble structure and superiority of polyphaseover Pseudo Noise (PN) sequences. Section III talks aboutthe OFDM system equation and synchronization estimators.Simulation results are discussed in section IV and finallysection V, gives the conclusion.

II. TRAINING SEQUENCES

A. Properties of Training Sequences

Training sequences used in a preamble need to satisfyfollowing properties:

• These sequences should zero autocorrelation for any lag.• These sequences should have sharp autocorrelation peak

with negligible amount of side lobes.• These can be generated for any length.• These sequences have very low Peak to Average Power

ratio (PAPR).• These sequence have very low alphabet size [20].

High PAPR preambles should be clipped by the power ampli-fier, resulting in lower synchronization and channel estimationaccuracy and hence degraded in detection performance. Theperformance is further improved by boosting up the transmis-sion power of preambles relative to that of the data signals.Furthermore, to reduce the adverse effect of adjacent cellinterference on the synchronization and channel estimationaccuracy, a set of low PAPR preambles with low cross-correlation energy should be used.

B. Proposed Preamble Structure

One training symbol is placed at the beginning of eachframe as preamble symbol. The frame structure is shown in fig.1. Here, the sequence used to generate the training sequence

Fig. 1. Frame structure of OFDM system with insertion of modifiedpolyphase training sequence.

should be chosen on basis of having a low PAPR so that thereis little distortion in the transmitter amplifier. The preamble hasa repeating pattern, from which a subscriber station acquiresthe frame timing and the carrier frequency offset.Here, a new preamble structure is proposed with modifiedConstant Amplitude Zero Autocorrelation (CAZA) sequences[20] with smallest known PAPR values for a given length andsmall alphabet size. The proposed preambles have a PAPRvalue of atmost 1.93 dB (and at most 2.55 dB when extendingto a set of 144 sequences). The one and only one trainingsymbol used, has two halves in the time domain. It has thefollowing pattern given by (1) and shown in fig. 2.

Fig. 2. Proposed preamble structure for OFDM system with insertion ofmodified polyphase training sequence.

Seq = [A,B] (1)

Where A is the seed sequence which is produced by [20] foreven length sequence and B is conjugate anti-symmetric to A(seed sequence) i.e.,

B(n) = −A∗(−n) (2)

In order to exploit the autocorrelation property of seed se-quence at receiver side we need to correlate it in the samedomain, as it is feed to preamble at transmitter side. Now, toproduce the pilots for preamble we take FFT of this sequenceover N points as shown in (3), where N is the number ofsubcarriers in one OFDM symbol.

Seqfft = FFT ([A,B]) (3)

This preamble symbol formed in this manner is appendedwith all data symbols to produce the frame and this frameis transmitted.

C. Analysis of Complexity for Polyphase and PN-sequences

It is worthwhile to mention that polyphase codes havealready been proposed to appear in IEEE 802.16/22 OFDMmode. The complexity of polyphase and PN sequences arecompared by two cases:

1) For acquiring initial timing: In this case, a time-domaincorrelator of window length Nsd is used with a delay of halfsymbol duration. The coefficients of the correlator and thenoise are complex for both PN and polyphase sequences. Infact, the polyphase sequence in frequency domain is also apolyphase sequence in time domain, which can help even inthe implementation. Therefore, we prefer polyphase sequenceinstead of PN sequence.

2) After timing is obtained: In this case, the best way todetect the transmitted sequence is to correlate the receivedsignal with all sequences, which can be performed in time ormore efficiently, in frequency domain. For frequency domain,we take the FFT; divide the sequence at each subcarrier, andIFFT back to time. The autocorrelation of PN sequences canbe good enough to detect the cell ID. For polyphase sequence,it is a multiplication process at each subcarrier, versus asign change for BPSK PN sequences. In case of frequencydomain correlation of data with the PN sequence (assumingtiming is obtained), which adds the results at each subcarrierafter dividing the sequence. The problem arises when datasubcarrier sees a frequency selective channel, where somesubcarriers can be in fade relative to the other subcarriers.As a result, only a portion of PN sequence is contributing tothe sum. Even in the case of a single-tap channel (i.e. a nonfrequency selective channel), if the arrival time is not zero, aphase ramp occurs in the frequency domain after dividing that

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sequence. The sum of the phases at all subcarriers is then zeroor close to zero, since we have null subcarriers; not a peakthat is expected.In summary frequency domain correlation with a PN sequencecannot give reliable sequence detection. Thus keeping in mindthe above mentioned analysis we choose polyphase sequencesas our basic sequence.

III. THE OFDM SYSTEM

After inserting preamble with modified training sequenceand adding it to data symbols, the frame is formed. This frameis being modulated symbol-by-symbol, by an IFFT block.Then CP is added to each symbol. After up-conversion thesamples of the transmitted baseband OFDM signal is givenby (4)

x(k) =1√N

N−1∑

n=0

cn. exp (j2πknN

) (4)

Where −Ng ≤ k < N − 1, cn is the complex valued infor-mation symbol, N is the number of subcarriers and Ng is thenumber of samples in the guard interval. When these samplesare transmitted given by (5) and subjected to wireless fadingenvironment with multipath then channel impulse response hm

of length L affects the signal with τm path delays and w1(k)is the additive white gaussian noise (AWGN). There are totalNg +N samples in a OFDM symbol.

r(k) =L−1∑

m=0

hmx(k − τm) + w1(k) (5)

The sample at the receiver side is given by (6)

y(k) = r(k − nε) exp (jφ) exp (j2πkvN

) + w2(k) (6)

Where φ is an arbitrary phase factor, v is carrier frequencyoffset normalized by subcarrier spacing, nε is the timing offsetand w2(k) is AWGN. After seeing additive and multiplicativechannel effects by the transmitted frame it is being receivedby receiver as y(k) as mentioned by (6).

A. Timing Synchronization

The primary goal of pre-FFT processing is to provide atiming index to the FFT process, such that ISI and ICI areminimized; otherwise the output from the FFT gets degraded.The circular convolution property of the DFT is exploited bymaking the CP a replica of the last samples of the symbol. TheCP is chosen to exceed the largest expected multipath delay.The initial timing acquisition stage is based on CP-based autocorrelation approach mentioned in [22], where [22] is com-putationally efficient than [21]. Assuming that the maximumdelay spread due to multipath channel is less than the CPduration i.e. Ncp/2, now we correlate the received signalover a window size of Nsd, which is the length of seedsequence, with a delayed replica of itself. The delay is oflength half OFDM symbol. This sample-by-sample correlationis performed at least over a length of one OFDM frame.For the received signal y(k) the correlation is given by (7)

which is iteratively calculated from (8) whose computationalcomplexity is very less as discussed in [22].

P (k) =Nsd−1∑

m=0

(y∗(k +m)y(k +m+N

2)) (7)

P (k+1) = P (k)+y∗(k+Nsd)y(k+Nsd+N

2)−y∗(k)y(k+N

2)

(8)Where ’k’ is the total number of samples in one OFDM frame.The iterative correlation results in a pointed peak whereascorrelation output, as compared to classical paper [10], is aplateau as shown in fig. 3. Here, comparison with PN sequencebased preambles is not shown as the algorithm presentedhere is less complex and polyphase sequence based. In theproposed algorithm, peak of correlation output appears atthe perfect time index, which exactly points out the startingpoint of FFT window. However, in case of all other proposedpreamble structure [9] - [16] we need to average out thecorrelated output, which was either in the form of plateauor in the form of series of peaks. In this preamble basedrobust synchronization algorithm we don’t need to do movingaverage filtering, as the correlation peak is sharp and accurateenough to direct us to the exact FFT window starting point.The kth sample at the output of iterative correlator is givenby (8) and the timing metric is defined by (9). Thus byusing the iterative correlation given by (8) and getting thedesired timing index by correlation itself, here we save lots ofmultiplications/additions involved in averaging. The memoryrequired in previous approaches to preserve the data outputof (8) to perform moving average filter is also saved in theproposed algorithm.

T (k) = |P (k)|2 (9)

Fig. 3. Comparison of correlation output of Proposed algorithm and Schmidland Cox

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B. Coarse frequency offset estimation

Once the timing estimate is done, the correlation output (8)is used to estimate the frequency offset. The phase of thecorrelation output is equal to the phase drift between thesamples that are N/2 OFDM samples apart. The estimate ofthe normalized fractional frequency offset is given by (10) asmentioned in [22].

∆f̂frac = ± 12πangle(

Nsd−1∑

n=0

y∗(k)y(k +N

2)) (10)

The fractional frequency offset is removed by multiplying thereceived samples y(k) with the compensational exponent. Theequation for compensated received samples is given by (11)

ymodified.frac.off (k) = y(k) exp (−j2πk∆f̂frac

N) (11)

IV. SIMULATIONS

A. Parameters used for Simulations :

FFT size is Nfft = 512, Cyclic prefix length is Ncp =32, Bandwidth is BW = 5 MHz, Sampling frequency is Fs

= 5MHz, Subcarrier spacing is ∆f = Fs/Nfft = 9.7656kHz,Length of seed sequence is Nsd = 54, Data length is Nd= 428,Ofdm symbol per frame=5, Number of frame=1 and Dopplerfrequency is Fd = 10 Hz.

B. Simulations Results

The simulations carried out in Matlab according to IEEE802.16e frame structure. The fading environment used herewas proposed by Z. Wu [23] to create PedB conditions. Theauthors [10] - [16] proposed a plateau averaging because, themetric suffers from a plateau which leads some uncertaintyin determining the start of the frame. The averaging methodfurther increase computational complexity and is still not goodat low SNR. The proposed algorithm does not use moving

Fig. 4. Histogram Plot for AWGN channel SNR = 10 dB of timing offsetand CP = 20, so correct index for FFT is 21.

Fig. 5. Histogram Plot for AWGN at SNR = 2 dB of timing offset for CP= 20, so correct index for FFT is 21.

average filter, as the correlation peak itself is very sharp.The simulation results are obtained for AWGN and Multipathfading environment as mentioned below:The proposed estimator is compared with only classical paperof Schmidl and Cox because other estimators or preamblestructures are not based on polyphase sequences.

1) AWGN Performance: In AWGN environment at SNR= 10 dB, as shown in fig. 4. The x-axis is index of sam-ples of OFDM frame and y-axis is number of iterations orinstances for all histogram plots of Timing offset estimator.The histogram plot has only one bar, which means that for100 different instances of AWGN channel at SNR = 10 dB thetiming metric estimates only one value, the proposed algorithmdetects correct timing index at all instances and thus, perfectsynchronization is achieved. Whereas, at SNR = 2 dB, as

Fig. 6. Histogram Plot for PEDB Multipath channel with rayleigh fading atSNR = 10 dB of timing offset for CP = 20, so correct index for FFT is 21.

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Fig. 7. Histogram Plot for PEDB Multipath channel with rayleigh fading atSNR = 2 dB of timing offset for CP = 20, so correct index for FFT is 21.

shown in fig. 5, has minute variations due to weak signalstrength.

2) Multipath Fading Performance: The fading environmentused here was proposed by Z. Wu [23]. This model is modifiedand has computational complexity half than that of Jakesmodel for simulation of rayleigh fading environment. Aftersimulating for multipath conditions, specifically PED-B modelat SNR = 10 dB, as shown by fig. 6, due to multipath thetiming index shows little bit variations, which can be correctedby thresholding the timing index. At SNR = 2 dB, in multipathcase, the variation is comparatively more as shown by fig. 7.

V. CONCLUSION

We presented a robust, efficient and computationally lesscomplex OFDM synchronization algorithm which is compat-ible to IEEE 802.16 standard. As shown in simulation resultsproposed algorithm is accurate compared to existing methods.The proposed algorithm does not need moving average filter,which helps in avoiding extra computations and reduces thecomplexity at algorithmic level. In presence of additive andmultiplicative noise, proposed algorithm and proposed trainingsequence structure performs better than the existing algorithmsand structures respectively.

ACKNOWLEDGMENT

The author would like to thank Prof. Devendra Jalihal ofIndian Institute of Technology Madras and Mr. Arun AyyarProject Officer of TeNeT Group, IIT-Madras, Chennai, India,for their help in reviewing the manuscript and giving theirvaluable suggestions which helped in making this manuscriptbetter.

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