An all-digital frequency synchronization scheme for OFDM systems

An all-digital frequency synchronization scheme for OFDM systems

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Unformatted text preview: An All—Digital Frequency Synchronization Scheme for OFDM Systems Li Zhenhong, Aame Mammelal V I I Electronics, PO. Box 1100, FIN—90571, Oulu, Finland Tel.: +358 8 551 2111, fax: +358 8 551 2320 Email: [email protected], [email protected]fi ABSTRACT The main purpose of this paper is to study the frequency synchronization problem in OFDM systems. A new fre- quency synchronization method is achieved by means of an all—digital synchronization loop including acquisition and tracking modes. The frequency offset is estimated only once per frame. The acquisition algorithm is based on periodi- cally inserted reference symbols, and the tracking algorithm on the cyclic prefix of the OFDM symbols. The algorithm performance is assessed in an AWGN channel with a low SNR value and in the presence of a timing inaccuracy. The simulations show that the algorithm is accurate and the sug- gested frequency synchronization scheme works well. I. INTRODUCTION The research and development work on the orthogonal fre- quency division multiplexing (OFDM) technique for high- speed digital data transmission has received considerable attention and has made a great deal of progress [1]. As is well known, OFDM systems are very sensitive to frequency offsets [2], as an offset of a small fraction of the subcarrier distance may lead to intolerable degradation. Frequency synchronization therefore is one of the most important tasks in an OFDM receiver. A frequency synchronization algorithm conventionally in- cludes acquisition and tracking algorithms, also called coarse and fine frequency synchronization algorithms, re- spectively, in some papers. Several methods focusing on frequency tracking algorithms for OFDM systems have been presented. P. H. Moose [3] introduced such an algorithm using repeated data symbols, while the approaches proposed in [4-5] exploit cyclic prefix to estimate the fine frequency offset. In [4] the algorithm was derived from the maximum likelihood function and in [5] the available information provided by the estimator is the imaginary part, which is an approximation of the phase. The above algorithms are lim— ited to tracking frequency offsets of less than half of the subcarrier distance, however, and few proposals have con- cerned a large frequency offset. One of these is based on iterative maximization of the likelihood function through the stochastic gradient method [6]. In addition, techniques that include data-aided acquisition and decision-directed track- 0-7803-3871-5/97/$10.00 © 1997 IEEE 327 ing, are suggested in [7-8], in which known symbols are utilized to cope with a large frequency offset. A brief gen- eral description of the tracking loop is provided in [8]. This paper presents a new all-digital frequency synchroni- zation scheme in which the synchronization principles de- rived for single carrier systems by F. M. Gardner [9] are applied to OFDM systems after suitable modifications. The frequency estimators in our scheme were suggested by P. Mandarini and A. Falaschi, who analyzed the performance of the fine frequency estimator in [10]. Moreover, the syn- chronization task is divided into an acquisition and a track- ing mode. The acquisition mode, based on reference sym— bols, provides an initial estimate for the tracking mode. The tracking mode then exploits the cyclic prefix to estimate the rotated phase, which contains the frequency offset informa— tion. In particular, an all-digital synchronization loop struc- ture suitable for TDMA/OFDM systems is introduced in detail in this paper. Since frequency offset is estimated once per frame and the frequency is corrected in each received sample, a hold circuit is used as an interpolator in the syn- chronization loop. This paper is organized as follows: A description of the system model and the proposed frequency synchronization scheme is provided in Section H, the frequency estimation algorithm is presented in Section III, and the performance of the synchronization scheme is then evaluated in detail with simulations in section IV. Finally, Section V contains our conclusions. II. SYSTEM MODEL The transmission system considered here is based on the OFDM technique [11] with N" used subcarriers. After the addition of N—Nu null data corresponding to the virtual carri- ers at the edges of the spectrum, the resulting N samples are processed by an Inverse Fast Fourier Transform (IFFT) of size N. A cyclic prefix made up of the last NS samples is added at the beginning of each OFDM symbol. The N+Ng samples generated during the lth OFDM symbol can be rep— resented by 1 N-l xk =Fm§0Xm(l)e j27t(k-Ng )m/N OSk<N+Ng (1) where the data XMU) represent complex M-ary PSK symbols in the lth OFDM symbol. In order to estimate the coarse frequency offset, a known reference symbol is transmitted between every F-l OFDM data symbols. Thus one frame consists altogether of F symbols. In the presence of a noise and frequency offset 5f, the re- ceived signal can be written by yk=xw“”f“”+nk a) where "n, are assumed to be independent zero mean complex Gaussian random variables, T is the time interval between the transmitted signal samples and (p is a random phase with a uniform density in the range [-75, 1c). Fig. 1 High-level block diagram of the frequency synchronization scheme A frequency synchronization loop generally consists of a frequency corrector, a frequency estimator, a loop filter and a number controlled oscillator (NCO). The frequency offset is corrected with information provided by the frequency estimator, filtered by the loop filter and integrated by the NCO as described in {9]. The functional block diagram of the proposed frequency synchronization scheme in Fig. 1 contains suitable modifications based on [9]. The coarse frequency estimator provides a coarse estimate as soon as possible at the beginning of transmission, and the frequency offset can have large values. Since we are not operating in a burst transmission mode, the acquisition mode is activated only once at the beginning of transmission. In contrast to the acquisition mode, the tracking performance should show excellent behaviour and only small frequency fluctuations have to be dealt with. The control signal, which is indicated by the dotted lines in Fig. 1, is a binary signal dependent on the estimated coarse frequency offset. Both the tracking mode and the acquisition mode work in a closed loop, as the tracking algorithm needs the initial coarse frequency estimate due to its limitations. Coarse fre- quency estimation is first carried out in the acquisition mode. In order to bring the frequency offset within the ex- pected range rapidly, the first frame is always used for coarse frequency estimation. The control signal in the first frame is therefore fixed at zero and that in the next frames is /\ dependent on the estimated coarse frequency offset 61?an . Once the estimated coarse frequency offset is less than half 328 of the subcarrier distance, the control signal is fixed at one, the received signal goes into the tracking mode by a denial- tiplexer and fine frequency estimation starts. The estimated A fine frequency offset & crack then goes into the synchroni- zation loop based on the initial coarse frequency estimate by a multiplexer. The frequency estimate is processed only once per frame. The frequency synchronization loop equivalent digital model is illustrated in Fig. 1. The digital loop filter transfer function is given by 1 l m H(z):a-z_ l — z _ where (X is the loop filter gain and could be onacq or am, which is dependent on the control signal. Due to the re- quirements of the acquisition mode, the gain oram should be selected carefully. Thus an initial coarse frequency estimate can be provided only after a few frames, and an am close to 1.0/F could be a good choice. In the tracking mode 0cmk is quite small in order to obtain a fine estimate and small vari— ance. Two zero—order holds are included in the proposed loop structure, in order to upsample back to the sampling rate of the received signal. The first one repeats the received signal F times and the hold time for the second one is N+Ng. One hold circuit placed after the loop filter with a hold time equal to F - (N+Ng) would be an alternative choice. In order to achieve similar performance to that of the loop shown in Fig. l, the loop filter gain could be multiplied by F. The NCO is implemented according to the difference equa— tion 90¢) = [0(k — 1) + e(k)]mod— 27: (4) where e(k) is the estimated and scaled frequency offset A 27m? including the coarse and fine frequency estimates. When the loop is stable, 6(k) is approximately equal to (27réfkT) mod— 2n . To fit the causality requirements of the system, at least one symbol interval delay is unavoidable before the frequency correction. The frequency offset can be corrected by n=nrwm to in which the delay is ignored. Once the estimated coarse frequency offset is larger than half of the subcarrier distance, the acquisition mode will restart and the corresponding steps will be repeated. III. FREQUENCY ESTIMATION ALGORITHM Since the frequency tracking will be usually out of control when the frequency offset exceeds half of the subcarrier distance, a strategy for initial acquisition must be developed to bring the offset within the limitations of the tracking al- gorithm. This section concentrates on the algorithms of the frequency estimators. A maximum timing error less than half of the prefix is assumed. A. Acquisition Algorithm The acquisition algorithm will provide a coarse frequency estimate by analysis of the reference symbols after the FFI‘. It is not so sensitive to the timing error, by virtue of the protection given by the prefix. The reference symbol, which is the same for each frame, consists of virtual carriers and M, pilot tones spaced by D virtual carriers (M, and D are an even and an odd number, respectively). The method of modulation for the pilot tones is the same as for the data symbols. In order to keep the transmitted power the same in the reference and data symbols, the amplitude of the pilot tones is multiplied by a factor 7 = N u / M , . (6) We assume that Y[l], ..., Y[N] indicate the samples of the reference symbol at the receiver after the FFT, the vector V'] of D components is evaluated from Y[1] to Y[N]: . _ . . 2 V[J]= 221;; Mm. +M. 0] (7) with -—(D— 1) / 2 S j S (D— 1) / 2 , where j: represents the index of the first pilot tone in the reference symbol. index The value of VD] and its j= jm =argmax{V[j]} will be searched through the J maximum vector. Once the corresponding j1m is found, the values v_,=v[jmx—1], V0=V[j ] and V,=V[jm+1] are considered. In order to achieve the estimated coarse frequency offset, the following processing is done: p1 = m, (8) 10-1 = WM—Vo, (9) d =(p1-p_,)/2.O, (10) $3,, = Aroma, +sgn{d},fle7l) (11) where Af represents the subcarrier distance. According to the above equations, the acquisition range is clearly depend- ent on the parameter D, which controls the possible maxi- mum index of j. We assume that the actual frequency offset is equal to éf=AfU+§l (12) 329 where J is an integer and < 05. Thus jmax is an estimate of J and sgn{d is an estimate of g. The same reference symbol can be used for the coarse frame synchronization, as explained in [12]. B. Tracking Algorithm The fine frequency estimator, the frequency tracking algo- rithm provides a precise estimate of the frequency offset based on the cyclic prefix of the OFDM symbols. We as- sume that y[0], ..., y[N+Ng—1] represent the samples of the OFDM data symbol at the receiver before the FFT. By vir- tue of the periodic nature of the OFDM signal, the presence of the cyclic prefix results in the equality x, = x,”v with N S k S N+ N8 —1. In the absence of noise, i.e., n, = 0, we obviously obtain “k = Yr ‘Yk—N = xk .x*(k-N),ej27’&trackNT [2 eflflé’uack/Af k s (13) =5), Thus a simple implementation of a low variance estimator A for t? track is given by A warm = Af-(tan‘1(22'§0“uk)) (14) in the presence of noise and a frequency offset lower than half of the subcarrier distance Af . The phase rotation due to the frequency offset is estimated and scaled in (14) to achieve the frequency estimation. The quality of the esti- mate depends on the signal-to-noise ratio per bit (SNR). IV. SIMULATION RESULTS Many simulations have been performed, each with different parameters. This section presents the key results, to support the conclusions set out in Section V. All the simulations are performed in a COSSAP environ- ment, the COSSAP models developed are of the floating point type. The subcarrier modulation method is QPSK. The main parameters in the simulation models are: F = 64, N = 512, N" = 424, NR = 64, M, = 28, D = 15 and j: = 54. The number of classes between the minimum and maximum class values in the histograms is 50, including the negative minimum value. A total of 20,000 events are taken into ac- count. The performance of the coarse frequency estimator is evaluated with a simulation model which contains an OFDM transmitter, an AWGN channel and a coarse fre- quency estimator. The corresponding results are shown with histograms (number of events vs. coarse frequency estima- tion error normalized by the subcarrier distance) in Fig. 2, with SNR = 10.0 dB. Typically, we choose Q to be 0.0-0.5 with step 0.1. The histograms show two peaks for g, of 0.0 and 0.5, lo— cated approximately symmetrically with respect to zero. Though there may be a small bias, most of the values are located in the range [—0.10, 0.10). r_____._____________._____.____ coarse frequency estimation error with J = 5.0 .E-- 0.0 L- 0.1 number of event: : , , . . . . , . . . . , . . l . —o.1o -o.05 0.00 0.05 come frequency mun-um crew now-d by th- mbcartler dim .___________________J Flg. 2 Histograms of the normalized coarse frequency estimation error The numerical results give an inaccuracy of half of the sub- carrier distance with a probability of approximately 1.0, even when the SNR is 5.0 dB and the PET processor win- dow starts somewhere within the prefix. The timing error in the simulations was generated by delaying the received sig- nal by ‘6 samples, where 't is an integer. These results are accurate enough for fine frequency estimation. Furthermore, this guarantee is confirmed with one of the worst cases (é = 0.0 and 0.5 in Fig. 2) by the standard deviation (std) of the normalized coarse frequency estimation error as shown in Fig. 3. coarse frequency estimation error withJ =5.0and§= 0.0 std of lhe normalized coax-so frequency animation error . , . . I . . . 5.0 10.0 15.0 signal—to—neise ratio per bit 0.0 I [‘13] Fig. 3 Std of the normalized coarse frequency estimation error The behaviour of the tracking loop, including a fine fre- quency estimator and the proposed all-digital loop structure with two hold circuits, is measured by the histograms and the std of the tracking loop error. Random OFDM data sym- bols are used to estimate the frequency offset in the simula— tion model with 8f :04. The simulated results are illustrated in Fig. 4 and 5 when the loop is in the steady state. 330 When the prefix is sampled correctly, i.e., 1:: 0 even at low SNR (SNR = 5.0 dB), the normalized frequency tracking loop error is almost always less than 0.01 and its std is less than 0.003. Even when the prefix is sampled with t: 32 and SNR = 5.0 dB, almost all of the values are still in the range [-0.05, 0.05). The std of the normalized tracking loop error is less than 0.01. frequency tracking loop error --"-:‘m-ao.oa-édr-o +—+-:sun-s.odsuiav-o o—e-:SKR- runaway-:2 sun-seams 1-32 8000 — r:-: 6000- numbar of event. 2000- 0 - l | t 0.050 . K . . . 0.025 mmwmmhymnwm .‘...x....l... -0.050 -0.025 0.000 Fig. 4 Histograms of the normalized frequency tracking loop error with the filter gain am = 0.003 T_'—-——_'——"-‘__—_—_‘~‘1 frequency tracking loop error “~‘—: 7 - O x—x—z 7 - 32 . , . 15.0 lld of tho normalized frequency lnoklng loop error . I . 10.0 stands—min "do per hit. [dB] l___________._______ Fig. 5 Std of the normalized frequency tracking loop error with the filter gain am = 0.003 20.0 The behaviour of the tracking loop is also affected to a cer- tain extent by the gain am. The larger am is, the shorter the convergence time and the larger the variance in the tracking loop error. Thus it is important to obtain a good compromise between estimation accuracy and short conver- gence time. V. CONCLUSIONS This paper suggests an all-digital frequency synchronization scheme suitable for OFDM systems and shows that the pro- posed closed synchronization loop structure provides fast acquisition and accurate tracking in an AWGN channel. The frequency synchronization scheme is practicable and is able to deal with a large frequency offset. A similar structure can be applicable to the future W'LAN systems, in which ex- tremer large bit rates will be necessary and OFDM signals should be used. Although the present simulations were limited to an AWGN channel, the scheme can be easily applied to a fading multi- path channel. The corresponding performance of the algo- rithms will be analyzed in the future. ACKNOWLEDGMENT The authors gratefully acknowledge the financial support given by the MEDIAN project and they also wish to thank Prof. P. Mandarini and A. Falaschi for the frequency esti- mation algorithms and to express their gratitude to the DSP group members at VTI‘ Electronics for their comments. REFERENCES [1] W. Y. Zou, “COFDM: An Overview,” IEEE Trans- actions on Broadcasting, Vol.41, No. 1, March 1995, pp. 1-8. [2] T. Pollet, M. V. Blade] and M. Moeneclaey, “BER Sensitivity of OFDM Systems to Carrier Frequency Offset and Wiener Phase Noise,” IEEE Transactions on Communications, Vol. 43, No. 2/3/4, Febru- ary/March/April 1995, pp. 191-193. [3] P. H. Moose, “A Technique for Orthogonal Fre- quency Division Multiplexing Frequency Offset Cor- rection,” IEEE Transactions on Communications, Vol. 42, No. 10, October 1994, pp. 2908-2914. [4] M. Sandell, J. -J. van de Beck and P. O. Borjesson, “Timing and Frequency Synchronization in OFDM Systems using Cyclic Prefix,” International Sympo- sium on Synchronization, Essen, Germany, Decem— ber14—15, 1995, pp. 16-19. [5] F. Daffara, O. Adami, “A New Frequency Detector for Orthogonal Multicarrier Transmission Tech- niques,” IEEE 45th Vehicular Technology Confer- ence, Chicago, USA, July 15—28, 1995, pp. 804—809. [6] F. Daffara, A. Chouly, “Maximum Likelihood Fre— quency Detectors for Orthogonal Multicarrier Sys— tems,” IEEE ICC’93, Geneva, Switzerland, May 1993, pp. 766-771. [7] F. Classen, H. Meyr, “Frequency Synchronization Algorithms for OFDM Systems Suitable for Com- munications over Frequency Selective Fading Chan- nels,” IEEE 44th Vehicular Technology Conference, Stockholm, Sweden, June 10, 1994, pp. 1655-1659. [8] M. Luise, R. Reggiannini, “Carrier Frequency Ac- quisition and Tracking for OFDM Systems,” IEEE Transactions on Communications, Vol. 44, No. 11, November 1996, pp. 1590—1598. [9] F. M. Gardner, “Frequency Granularity in Digital Phaselock Loops,” IEEE Transactions on Communi- cations, Vol. 44, No. 6, June 1996, pp. 749-758. [10] A. Falaschi, P. Mandarini, “Performance Analysis of a Fine Frequency Error Estimator for OFDM Transmission,” ACTS Mobile Communication Summit, Granada, Spain, November 27-29, 1996, pp. 457-463. 331 [11] [12] J. A. C. Bingham, “Multicarrier Modulation for Data Transmission: An Idea Whose Time Has Come,” IEEE Communications Magazine, May 1990, pp. 5- 14. M. Kiviranta, A. Mammela, “Coarse Frame Syn- chronization Structures in OFDM,” ACTS Mobile Communication Summit, Granada, Spain, November 27-29, 1996, pp. 464-470. ...
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