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OFDM Burst Frequency Synchronization by Single Carrier ... - ICE

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<strong>OFDM</strong> <strong>Burst</strong> <strong>Frequency</strong> <strong>Synchronization</strong> <strong>by</strong> <strong>Single</strong> <strong>Carrier</strong>Training DataUwe Lambrette, Michael Speth and Heinrich MeyrOctober 10, 1997AbstractIn this paper, we propose a burst frequency synchronization procedure which is based on theusage of single{carrier training data and <strong>OFDM</strong> payload modulation. The payload modulationformat is similar to the one that is used in the DAB standard [1], whereas training data is chosenas simple CAZAC sequences. It is shown that the resulting modulation and transmission schemeis suitable for burst transmission and single{burst demodulation. Performance degradation dueto synchronization errors is shown to be small.1


1 IntroductionIn this paper, we propose a burst format for <strong>OFDM</strong> transmission[2, 3] that allows burst frequencysynchronization of individual data bursts. We propose algorithms for frequency synchronizationthat satisfy the requirements of high phase stability ofan<strong>OFDM</strong>system.The frequency synchronizationtechnique is based on the use of single{carrier training data in contrast to the techniquesin[4,5,6]which use <strong>OFDM</strong> symbols, only.2 Signal and <strong>Burst</strong> ModelFigure 1 displays the respective burst formats.Data bursts consist of multiplexed single carriertraining data and multicarrier <strong>OFDM</strong> payload data (transferring encoded information on thedownlink) grouped in data blocks.The training data consists of a B times repeated CAZAC(Constant{Amplitude{Zero{Autocorrelation[7]) sequence c of length S.The choice of the CAZAC sequence is motivated <strong>by</strong> the fact that it is also suitable for framesynchronization[8], and, secondly, because its at power spectrum equally weights contributionsat all frequencies in the relevant bandwidth. Furthermore, the periodic structure of the trainingsequence is needed for the frequency synchronization algorithms below.The payload consists of <strong>OFDM</strong> symbols of length T OSym , enclosing a guard time T G trainingdata and payload data forms a block. M blocks form a data burst. An <strong>OFDM</strong> symbol is described<strong>by</strong>w m =N1 u=2;1XpTOSyml=;N u=2mTsj2l Ta nNu+l e sub (1)m 2 f; T GT s+1:::0 1::: T subT sg (2)where N u denes the number of subcarriers used. The sampling rate 1=T s =2=T sub N FFT will leadto an aliasing{free reception and undistorted (<strong>by</strong> the transmission lter) subcarriers if N u =N FFT =1; and is the rollo of a discrete{tie root{raised cosine lter = [f ;T :::fT] with cuto frequency1=2T s that is used to limit the out{of{band power of w. Each of the subcarriers is modulatedwith symbols a nNu+l from a QPSK alphabet. The symbols a jNu;Nu=2 :::a jNu+Nu=2;1 are hencetransmitted with the jth <strong>OFDM</strong> symbol. <strong>Single</strong> carrier training data with symbol duration T =2T sis multiplexed with the <strong>OFDM</strong> signal described above prior to transmit ltering.2


We use a fading channel with rays and ray power according to table 1 represented at the samplingrate 1=T s . Any rayofthe time{variant channel impulse response h k =[h 0k :::h 31k ] is subject toJakes fading with bandwith f d =4kHz. Due to the band limitation in the transmit lter, the tapsof the channel impulse response h k are correlated with each other. The channel impulse responseis 32 taps long.Coded data information symbols b k are transmitted <strong>by</strong> the symbols a k <strong>by</strong> means of dierentialmodulation, which extends over the frequency domain a k+1 = b k a k , only a nNu;Nu=2 must beknown to the receiver a priori.Let s be the vector of one burst's samples' according to gure 1, f the frequency oset, k =0the correct frame start position, L B =2BS(M +1)+M T OSymT sthe burst and L = T OSym =T s the<strong>OFDM</strong> symbol length. Samples n k are taken from complex gaussian noise with variance such that(E S =N 0 ) (T sub =T OSym ) is the signal - to noise ratio of the subcarriers. The received signal is given<strong>by</strong>s = [c 0 0 :::c S;1 0 :::c 0 0 :::c S;1 0 w o :::w L;1 c 0 0 :::c S;1 0 :::c 0 0 :::c S;1 0] (3)t k =TXj=;Tr k = exp(j2kfT s )s k;j f j (4)31Xj=03 <strong>Frequency</strong> <strong>Synchronization</strong>t k;j h jk + n k (5)Weuseatwo{stage frequency synchronization algorithm. The rst stage provides a coarse frequencyestimate which is based on computing the average phase change during a single CAZAC block. Theestimate is computed under the assumption of the presence of correct frame synchronization. Asimple way to compute a frequency estimate in this case is to compute[9]d fT s (k) coa = 12 arg MXm=02(B;2)S;1Xl=0r k+kp r k;2S+k pk p = m (2BS + L)+4S + l (6)where only the self{interfering part of the CAZAC blocks is taken into consideration and thismotivates a periodic repetition of the CAZAC blocks. However, it turns out that the variance of3


this estimate even for the AWGN channel, eg. [10]Var(2 d fTscoa ) =14SL 2 W (E S=N 0 ) + 18S 2 L W (E S =N 0 ) 2L W = S(B ; 1)(M +1) (7)is too high for <strong>OFDM</strong> systems. However, the estimator has a relatively large acquisition range.Due to the high variance, a second frequency estimation stage is used, which computes the residualfrequency estimate based on two CAZAC blocks separated <strong>by</strong> an <strong>OFDM</strong> block. This frequencyestimate is then used to correct the residual frequency error within this <strong>OFDM</strong> block. It is possibleto space training segments <strong>by</strong> more than one <strong>OFDM</strong> block, in this case, however, both fading(channel dynamics) and phase jitter of analog components severely degrade the estimate. For thene frequency error estimator, henceXfT d s (k) ne = 1 2BS;12 arg r k+l rk+l;kl=2Sk = 2(B ; 1)S + L: (8)The range of correctable frequency osets is limited <strong>by</strong> the fact that the absolute value of the carrierphase change during k samples should not exceed as otherwise ambiguities of the estimatecannot be resolved. Hence, the frequency oset remaining after coarse frequency correction has tofullljfT s j12(2(B ; 1)S + L : (9)in order to avoid ambiguities. Similar ambiguities occur eg. in [6]. For a static channel, theestimation accuracy also is much better, mainly because the time interval between the samplesused for estimating the phase dierence is much larger. Using the second stage alone, the varianceof the estimate on the AWGN channel is given <strong>by</strong>Var(d2fTsne ) =2(10)(2(B ; 1)S + L) 2 S EsN 0because due to the non{overlapping of the delay product terms of the estimator in fact a phaseestimation is carried out taking into account the noise power of two samples. As indicated, on adynamic channel, a large k may cause variance oors.4


4 Performance EvaluationSimulation results for the novel burst frequency synchronization strategy are given in gure 2.The applied sync. strategy was to rstly estimate the frame start [8] and to compute and correctthe coarse andthentocompute and correct the ne frequency estimate in the following from thecoarsely corrected samples.The variance of the ne estimate approaches the computed valuesfor the AWGN channel. The ne frequency estimate provides the lower bounds for the SNR ofinterest, and the variance of the coarse estimator should be so low that no additional errors of thene estimator occur caused <strong>by</strong> the violation of (9). Violations of (9) can be reduced <strong>by</strong> increasingM,S or B, or, similarly, ltering the coarse frequency estimate over several bursts. The error oorobserved is caused <strong>by</strong> the inclusion of a frame sync estimator and secondly <strong>by</strong> the time{variantchannel (Note that f D T sub =0:05).In gure 3, it is shown that for an example, coded dierentially{demodulated (frequency direction)<strong>OFDM</strong> system the BER degradation caused <strong>by</strong> frame synchronization errors and frequencysynchronization errors is small. For these simulation results, the real[8] (not ideal) frame synchronizationhas been used. It can be seen that for S =16,B =3and M =0:::3, the degradationcaused <strong>by</strong> the synchronization units reduces to approximately one dB. (M = 0 relates to the use ofa single CAZAC block and a single <strong>OFDM</strong> block.) As the algorithms can be used with arbitraryB, S and M, a wide scalability of the frequency estimation accuracy is provided.5 Comparison to other approachesIn [4], a full <strong>OFDM</strong> symbolisusedtoachieve frequency and frame synchronization and the trainingoverhead is larger, the same holds for [1]. In [6], the inherent periodicity of guard interval and<strong>OFDM</strong> symbol is used which can for an extension of the guard interval be used to correct ane frequency oset. A similar training overhead as in here is expected. No coarse frequencyacquisition unit is provided, however, allowing spontaneous burst synchronization (this also holdsfor [5]. Comparing our approach to the ones mentioned, fewer training symbols are needed andboth coarse acquisition and ne frequency correction is provided with very few training symbols.5


6 ConclusionsWe have proposed a burst transmission technique using <strong>OFDM</strong> modulation for the payload transmissionand single carrier training data. The proposed synchronization algorithms come close tothe theoretical optimum and provide a means to devise low complexity per{burst demodulationof digital data in wireless networks. Besides its simplicity, its main advantage is that the samestrategy may be used for single carrier modulation, as well.AcknowledgementsThe anonymous reviewers helped to greatly improve the quality of the presented material.6


References[1] European Broadcasting Union, \Radio Broadcasting Systems Digital Audio Broadcasting(dab) to mobile, portable and xed receivers,"Tech. Rep., European TelecommunicationsStandards Institute, February 1995.[2] R. W. Chang, \Synthesis of band{limited orthogonal signals for multichannel data transmission,"the Bell System Technical Journal, vol. 45, pp. 1775{1796, 1966.[3] J. A. C. Bingham, \Multicarrier Modulation for Data Transmission: An Idea whose Time hascome," IEEE Communications Magazine, vol. 28, pp. 5{14, May 1990.[4] T. M. Schmidl and D. C. Cox, \Low{Overhed, Low{Complexity [<strong>Burst</strong>] <strong>Synchronization</strong> for<strong>OFDM</strong> Transmission," in Proceedings of the International Conference on Communications,1996.[5] F. Classen and H. Meyr, \<strong>Frequency</strong> <strong>Synchronization</strong> Algorithms for <strong>OFDM</strong> Systems suitablefor Communications over <strong>Frequency</strong> Selective Fading Channels," in Proceedings of the IEEEInternational Conference on Vehicular Technology, Stockholm, Sweden, June 1994, pp. 1655{1659.[6] F. Daara and O. Adami, \A New <strong>Frequency</strong> Detector for Orthogonal Multicarrier TransmissionTechniques," in Proceedings of the Vehicular Technology Conference, July 1995.[7] A. Milewski, \Periodic Sequences with Optimal Properties for Channel Estimation and FastStart-Up Equalization," IBM J. RES. DEVELOP., vol. 27, no. 5, pp. 426{431, September1983.[8] U. Lambrette, J. Horstmannsho, and H. Meyr, \Techniques for frame synchronization onunknown frequency selective channels," in Proceedings of the IEEE International Conferenceon Vehicular Technology, May 1997.[9] P. R. Chevillat, D. Maiwald, and G. Ungerboeck, \Rapid Training of a Voiceband Data-Modem Employing an Equalizer with Fractional-T Spaced Coecients," IEEE Transactionson Communications, vol. COM-35, no. 9, pp. 869{876, September 1987.7


[10] H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers, John Wiley &Sons, 1997, to be published.[11] W.C. Jakes, Microwave Mobile Communications, Wiley & Sons, 1974.8


k=0 Frame Start, M <strong>OFDM</strong> Symbols, (M+1) CAZAC BlocksCAZAC <strong>OFDM</strong>-Symbol CAZAC CAZAC0 B-1 Tg TsubS Symbols2S samplesL samples<strong>Burst</strong> Length2BS(M+1)+MLFigure 1: <strong>Burst</strong> format of the proposed scheme0.0 32.4 64.8 97.2 121.4 m [ns]0.0539 0.3232 0.2502 0.1022 0.0285 m129.6 145.8 178.2 283.5 m [ns]0.022 0.017 0.194 0.009 mTable 1: 9 path channel model, tap delay and tap power Doppler f D = 4kHz, Jakes spectrum[11],T s =12:5ns f D T Sub =0:04 CIR (including TX, RX lter) truncated to 32 taps.Figure 2: <strong>Frequency</strong> estimate variance for the novel frequency synchronization strategy.9


Figure 3: Bit Error Rate with novel burst frequency and frame synchronization strategy using frequencydierential DQPSK modulation and an RS(112,80) code, no interleaving.10

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