A simple and efficient timing offset estimation for OFDM systems ...

A Simple and Efficient Timing Offset Estimation for OFDMSystemsH. Minn and V. K. Bhargava, Fellow, IEEEDepartment of Electrical and Computer EngineeringUniversity of VictoriaVictoria, B.C., Canada V8W 3P6.Email: bhargava@ece.uvic.caAbstract - A simple timing offset estimation method for orthogonalfrequency division multiplexing (OFDM) systems asa modification to Schmidl & Cox’s method [14] is presented.By designing the training symbol, the timing metric plateauinherent in [14] is eliminated and hence performance is improved.The performances of the proposed method and [14] areevaluated by computer simulation in terms of estimator variance.The timing offset estimator of [16] is also included in theperformance comparison as another reference. The simulationresults show that the proposed method achieves significantlysmaller estimator variance. Using more samples in calculationof half symbol energy required in timing metric is shown togive more robustness against dispersive channel.I. IntroductionOFDM has been a major interest for wireline andwireless applications (e.g., ADSL, DAB[l], DVB[2],wireless LAN [3][5], and cellular and PCS data [4])due to its high data rate transmission capability withhigh bandwidth efficiency, its robustness to multipathdelay spread and its feasibility in applying adaptivemodulation and/or power distribution across the subcarriersaccording to the channel conditions. However,it is also accompanied with many practical issuesand one major issue is synchronization. OFDMsystems are much more sensitive to synchronizationerrors than single carrier systems [6], [7]. Synchronizationin OFDM usually includes symbol timingsynchronization, carrier frequency synchronizationand sampling clock synchronization. The first two aremore dominant factors and usually performance offrequency synchronization also depends on the accuracyof symbol timing synchronization. Hence, highaccuracy of symbol timing synchronization is muchdesirable and in this paper, only symbol timing synchronizationis considered.Regarding symbol timing synchronization, [8-91 proposesto use the correlation of cyclic prefix with itscopy part. [lo] also uses correlation of cyclic prefixin a two stage timing estimation but it has long acquisitiontime. Since guard interval (cyclic prefix) isusually affected by intersymbol interference (ISI), theresult of the methods using correlation of cyclic prefixdepends on the 6 priori assumption about the channel.Hence, [ll, 121 use a larger guard interval whereIS1 free part of the guard interval is used for timingestimation. However, it fails under some channel conditionsand they propose a second method where bymaking use of the channel estimate, timing metric ismaximized by a search varying the position of FFTwindow. Hence, the acquisition time may not allowThis work was supported by a Strategic Project Grantfrom the Natural Sciences and Engineering Research Council(NSERC) of Canada.burst mode transmission and the behavior of trackingloop in mobile environment remains subject tofurther investigation. In [13], an m-sequence or chirpsynchronization burst is used which is correlated atthe receiver with locally generated one. Due to frequencyoffset, locally generated synchronization burstwould be different from the received one. Hence thetiming estimation would not be reliable in the presenceof large frequency offset. [14] proposes a robustmethod using a training symbol with two identicalhalve which can be applied in either continuous orburst mode transmission. However, the timing metricplateau inherent in it causes uncertainty in choosingthe best timing point, hence causing large timingestimator variance. In [15] differential in frequencydetection together with raising fourth power of thesignal to cancel QPSK modulation format is applied.However, initial timing offset is required to be withinone-eighth of the FFT size. Alternatively in [16],cyclic prefix and pilot symbols used for channel estimationare exploited for timing estimation.In brief, most of the previous timing estimation methodshave one or more of the following drawbacks:(a) not applicable for both burst mode and continuousmode transmission, (b) depending on the a’ prioriassumption about the channel , (c) restricted tosome modulation formats, (d) limited for small frequencyoffset cases, and (e) having tendency of estimatorperformance degradation caused by timingmetric plateau. In this paper we present a timing offsetestimation as a modification to Schmidl & Cox’smethod [14]. By eliminating timing metric plateauinherent in [14], the proposed method also avoids thedrawbacks described above. The paper is organizedas follows. Section I1 briefly describes the systemconsidered and the timing estimation method of [14].Section I11 presents the proposed method. In sectionIV, the performance of the proposed method and themethods of [14] and [16] are compared in terms ofestimator variance obtained by simulation. Conclusionsare given in section V.11. System DescriptionThe samples of transmitted baseband OFDM symbolcan be given byNu-1~(Ic) = - c,ezp(p(j27rkn/~), -N~5 IC 5 N-I,fl n=O(1)where cn is modulated data on the nth subcarrier,N is the number of inverse Fast Fourier Transform(IFFT) points, Nu(< N ) is the number of subcarri-0-7803-5718-3/00/$10.00 02000 IEEE. 51 VTC2000

ers, Ng is the number of guard samples, j = fland the sampling period is Tu/N with l/Tu beingsubcarrier spacing. Consider a discrete-time channelcharacterized byK-1h(k) = hlb(k - 71)l=Owhere b(k) represents dirac-delta function, {hl} complexpath gains, (71) path time delays which are assumedin multiple of OFDM samples, and K the totalnumber of paths. Then the received samples, assumingperfect sampling clock, can be given byK-1r(k) = ezp(j2nkw/~) hls(k - 71 +E) + n(k)l=O(3)where w is the carrier frequency offset normalizedto subcarrier spacing, E is timing offset in units ofOFDM samples and n(k) is the sample of zero meancomplex Gaussian noise process with variance 0:.Suppose the sample indexes of perfectly synchronizedOFDM symbol be {-Ng, ..., -1, 0, 1, ..., N - 1)and maximum channel delay spread be T, . Then ifE E {-Ng +T,~~, -Ng + T + 1,. ~ .. ~ , 0}, the ~ orthogonalityamong the subcarriers will not be destroyedand the timing offset will only introduce a phase rotationin every subcarrier symbol Ym at the FFT outputasY, = e~p(j2~me/N)c,H~+n,, -Ng+rmaZ 5 E < 0(4)where m is subcarrier index, H, is channel frequencyresponse to the mth subchannel, i.e., {Hm} =DFT(h(lc)), and nm is complex Gaussian noise term.For coherent system, this phase rotation is compensatedin channel equalization which sees it as a channelintroduced phase shift. If the timing estimateis outside the above range, the orthogonality amongthe subcarriers will be destroyed by the resulting ISI.Then the FFT output subcarrier symbols are givenbYcapacity efficiency can be obtained. With this aspect,the performance of the symbol timing synchronizationalgorithms will be evaluated by the timingestimator variance.The symbol timing estimator finds the start of theOFDM symbol. The correct symbol timing point willbe taken as the start of the useful part of the OFDMsymbol (i.e., the start of FFT window for demodulation).Let the training symbol (excluding cyclic prefix)contain two identical halves in time domain eachhaving L = N/2 samples. At the receiver there willbe a phase difference between the samples in the firsthalf and their replica in the second half caused bythe carrier frequency offset. Training data is usuallya PN sequence. Then the Schmidl & Cox's timingestimator [14] takes as the start of the symbol themaximum point of the timing metric given bywhere d is a time index corresponding to the firstsample in a window of 2L samples and Pl(d) is correlationmetric given byL-1Pi(d)= xr*(d+m).r(d+m+L) (7)m=Owhere ()* represents conjugation and Rl(d) representsenergy of half OFDM symbol and is includedfor normalization of the correlation metric in accountfor the large fluctuation of the OFDM sample amplitudesand given byL-1Rl(d) = (r(d + m + L)12 (8)m=OThe timing metric reaches a plateau (see Fig. 2)which leads to some uncertainty as to the start ofthe frame. To alleviate this, [14] proposes an averagingmethod where the maximum point is first foundand then two points with 90% of the maximum value,one to the left and the other to the right of the maximumpoint, are found. The timing estimate is takenas the average of the two 90% points.111. Proposed Methodwhere the extra term IE(m) results from IS1 and interchannelinterference (ICI) caused by the loss oforthogonality among the subcarriers (see [13] for details).The useful term also suffers a slight gain lossbut for large N, it is negiligible. The main detrimentaleffect is caused by the extra ISI+ICI term.Thus, the guard interval should be long enough forthe timing estimate to lie within the range describedabove. On the other hand, longer guard intervaltranslates into more system capacity loss due to overhead.Hence high performance timing synchronizationis much desirable for higher system performanceand capacity efficiency. The smaller the variance oftiming estimator is, the shorter the guard interval canbe designed, and hence less overhead and increasedThe samples of the training symbol (excluding cyclicprefix) are designed to be of the forms=[AA -A -A] (9)where A represents samples of length L = N/4 generatedby N/4 point IFFT of N,/4 length modulateddata of a PN sequence. If desired, the abrupt amplitudechange due to sign conversion in the trainingsymbol can easily be avoided by modifying the PN sequencesuch that the sum of the corresponding modulateddata equals zero. The timing metric is givenby0-7803-5718-3/00/$10.00 02000 IEEE. 52VTC2000

correlationwindow ------A correlation window -.................... ..........CP + +CP = Cyclic Prefix(a) at exact symbol timing point(b) before exact symbol timing pointFig. 1. Correlation of the training symbol: Schmidl & Cox’s method (upper), Proposed method (lower)where1 L-1&(d) = r*(d+ 2Lk + m) . r(d+ 2Lk+ m + L)k=O 7n=Oand1 L-1R2(d) = Jr(d + 2Lk +VI + L)I2 (12)k=O m=OIn above equations, P2(d) and R2(d) can be calculatediteratively. The training symbol patterns of[14] and proposed method are shown in Fig.(l). Alsoshown is the elimination of timing metric plateau inherentin [14] by proper design of the training symbolin the proposed method. For training symbol of [14],the correlation metric has its peak for the whole intervalof cyclic prefix (under no noise and distortioncondition) while the proposed training symbol has itspeak of correlation metric at the correct FFT windowstarting point since off that point, correlation ofsome samples results in negative values as shown inFig. (1) hence eliminating the correlation metric peakplateau.The timing metrics of [14] (Eq. (6)), and the proposedmethod (Eq. (10)) are shown in Fig. 2 underno noise and distortion condition with the system parametersgiven in section IV. The correct timing point(index 0 in the figure) is taken as the start of theuseful part of training symbol (after cyclic prefix).As discussed previously, the proposed method doesnot have timing metric plateau and consequently itachieves better accuracy in timing offset estimation.In calculation of half symbol energy, N samples insteadof N/2 samples can be used to get more reliableresult. Then for both methods, Rl(d) and R*(d) canbe replaced by the following:, \ < .ow’ ’-400 -300 -200 -100 0 100 200 300 400Time (sample)Fig. 2. Timing metric under no noise and distortion conditionIV. SIMULATION RESULTS AND DISCUSSIONPerformance of the timing offset estimators have beeninvestigated by computer simulation for five cases: (I)Schmidl & Cox method (Eq. (6) with 90% maximumpoints averaging), (11) Schmidl & Cox method withmodified R(d) (same as (I), except that Rl(d) is replacedby R(d)), (111) the method from [16],(IV) ProposedMethod (Eq. (lo)), and (V) Proposed Methodusing R(d) in stead of R2(d). The system used is1000 subcarriers OFDM system with 1024 point FFT,10% guard interval (102 samples), carrier frequencyoffset of 12.4 subcarrier spacing, QPSK modulationand 10000 simulation runs. Two channel conditions0-7803-5718-3/00/$10.00 02000 IEEE. 53 VTC2000

30Lz=J-*--*--*---E 205z -10-vE .-$ -20 -cB3=0 -30 ~5 -5t-1%- II. Schmidl& Coxwith Eq(13)+ 111. Ref.[16]46. IV. Proposed Method+ V. ProposedMethodwith Eq.(13)' 11EI30 -lotp -20-0- 11. Schmidl &Coxwith Eq.(13)-3- 111. Ref.[16]. +#. IV. Proposed Method+ V. ProposedMethodwith Eq.(13)-60 10 5 10 15 20 25SNR (dB)Fig. 3. Mean of the timing offset estimators in AWGN channel-50 ' I0 5 10 15 20 25SNR (dB)Fig. 5. Mean of the timing offset estimators in IS1 channel0 5 10 15 20 25SNR (dB)Fig. 4. Timing offset estimator variance in AWGN channel0 5 10 15 20 25SNR (dB)Fig. 6. Timing offset estimator variance in IS1 channelare considered: a) An AWGN channel with no intersymbolinterference (ISI) (it will be called AWGNchannel) and b) An AWGN channel with IS1 (it willbe called IS1 channel). The IS1 channel is modelledas sixteen paths with path delays ~i of 0,4,8,. . . ,60samples and path gains given byFor the timing estimator of [16], the additional parametersare: one pilot every 40th subcarrier anddummy SNR value SNR = 5dB.The means and variances of the timing offset estimatesin AWGN channel are shown in Figs. (3) and(4), and in IS1 channel are in Figs. (5) and (6) respec-tively. For AWGN channel, the means of the cases Iand I1 are about the middle of timing metric plateau(within the cyclic prefix) while the means of the cases111, IV, and V are about the correct timing point. ForIS1 channel, the means are observed to be shifted tothe right in time axis (i.e. delayed) by some amountdepending on the shapes of the timing metric and IS1channel profile. Note that if the timing estimate is desiredto lie within guard interval, then the means ofthe cases 111, IV, and V can easily be shifted to theleft (i.e., advanced) by appropriate design amount.As for the variances, the following are observed:In AWGN channel, cases I, I1 and I11 show floorin estimator variance curves while the proposedmethods (cases IV and V) do not. In IS1 channel,all methods have estimator variance floor.Performance of case I1 is better than case I forall conditions considered, at the expense of some0-7803-57 18-3/00/$10.00 02000 IEEE. 54VTC2000

additional complexity. The smaller variance ofcase I1 is due to using more samples to calculatehalf symbol energy used in timing metric.Proposed methods (cases IV and V) have significantlysmaller estimator variance than Schmidl& Cox’s method (case I) for all conditions considered.The better performance of the proposedmethods is generally due to the absence of timingmetric plateau.Comparing proposed methods to case I11(Ref.[l6]), in AWGN channel, we see that casesIV and V have significantly smaller estimatorvariance; while in IS1 channel, case IV hasslightly larger variance for SNR values greaterthan 10 dB but case V has significantly smallervariances.In AWGN channel, the slope of the timing metricoff the correct timing point determines the estimatorvariance (see cases I and I1 vs cases IV,and V in Fig. 4).In IS1 channel, using all the samples over onesymbol period (excluding cyclic prefix) to calculatethe half symbol energy (i.e. using R) hasmore effect on reducing the estimator variancethan the slope of the timing metric (see case IVvs. cases I1 and V in Fig. 6).As an overall evaluation for both channel conditions,case V (proposed method using R) performsthe best.The cases I1 and V have some additional complexitydue to using R as compared to the case I. However,cases IV and V do not need averaging of timing metricas required in cases I and 11. Hence case IV has evensmaller complexity than case I.Similar to the proposed training symbol in this paperwhich is composed of 4 parts, the training symbolcan be designed to be composed of more partsand have steeper roll-off timing metric off the correcttiming point so that better timing estimation can beachieved.V. ConclusionsA simple timing offset estimation method for OFDMsystems is presented as a modification to Schmidl &Cox’s method [14] where a training symbol containingtwo identical halves is used. The proposed methoduses a training symbol containing four equal lengthparts: the first two are identical and the last twoare the negative of the first two. By eliminating thetiming metric plateau inherent in [14], the proposedmethod achieves a performance improvement. Moreover,using all samples over one symbol period (excludingguard interval), instead of over half symbolperiod, in the calculation of half symbol energy requiredin timing metric is shown to give more robustnessto dispersive channel. The simulation resultsshow that proposed method has significantly smallerestimator variance than [14] under both AWGN channeland IS1 channel. The performance of the methodin [16] is also included in the comparison as anotherreference. As an overall performance for both channels,the proposed method using all samples over onesymbol period in calculation of half symbol energygives the best result.References[l] P. Shelswell, “The COFDM modulation system: the heartof digital audio broadcasting,” Elec. Commun. Eng. Journal,June 1995, pp. 127-136.[Z] U. Reimers, “Digital - video broadcasting,” - ZEEE CommunicationsMagazine, Vol. 36, No. 6, Jun 1998, pp. 104-110.M. Aldinger, “Multicarrier COFDM scheme in high bit rateradio local area networks,” Pmc. 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Cox, “Robust frequency and timingsynchronization for OFDM,” IEEE Rans. on Comms.,Vol. 45, No. 12, Dec 1997, pp. 1613-1621.[15] B. McNair, L.J. Cimini Jr. and N. Sollenberger, “A robusttiming and frequency offset estimation scheme for orthogonalfrequency division multiplexing (OFDM) systems,”Proc. Vehicular Tech. Conf., Houston, Texas, USA, May1999, pp. 690-694.[E] D. Landstrom, S.K. Wilson, 5.3. van de Beek, P. Odlingand P.O. Borjesson, “Symbol time offset estimation in coherentOFDM systems,” Proc. Intl Conf. on Communications,Vancouver, BC, Canada, June 1999, pp. 500-505.0-7803-5718-3/00/$10.002000 IEEE. 55 VTC2000