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414 IEEE COMMUNICATIONS LETTERS, VOL. 4, NO. 12, DECEMBER 2000

Carrier Frequency Offset Compensation for Uplink ofOFDM-FDMA Systems

Jihoon Choi, Changoo Lee, Hae Won Jung, and Yong Hoon Lee

AbstractA frequency offset compensation method for OFDM-FDMA, that can correct offsets after the DFT via circular convo-lution, is proposed as an alternative to the direct method that cor-rectsfrequency offsets by multiplying thecomplex exponentsof theoffset estimates before the DFT. In contrast to the direct methodwhose complexity increases proportional to the number of users,the computational load of the proposed scheme decreases as thenumber of users increases. It is shown that the proposed methodis simpler to implement than the direct method when the numberof users is greater than two. Furthermore, the former can outper-form the latter, because a frequency offset compensation for oneuser after the DFT does not affect the data of other users. Com-puter simulation results demonstrate the advantage of the pro-

posed method.

Index TermsCarrier synchronization, frequency offset correc-tion, OFDM, OFDM-FDMA.

I. INTRODUCTION

DUE TO the fact that orthogonal frequency division multi-plexing (OFDM)is based on using a numberof subcarriers,

the frequency division multiple access (FDMA) method thatassigns clusters of subcarriers to different users has been rec-ognized as a basic multiple access scheme for OFDM [ 1][6].OFDM using such a FDMA method, herein referred to asOFDM-FDMA, is conceptually simple, however, its imple-

mentation needs some caution: in particular, OFDM-FDMAnot only requires accurate receiver timing and a carrier fre-quency for each user, but also requires precise synchronizationamong all users in order to avoid any intercarrier interference(ICI). Synchronization between users is difficult in the uplinkcommunication (from mobile stations to a base station). Oneapproach to overcoming this difficulty is to use a downlinkcontrol channel which conveys the estimated synchronizationinformation to each user [2], [3]. An alternative is to achievesynchronization via signal processing at the uplink receiverwithout the help of a control channel. This paper will befocused on the latter: in particular, an efficient carrier fre-quency compensation method at the uplink receiver will bedeveloped.

Carrier frequency synchronization at the uplink receiveris achieved via frequency offset estimation and correction.

Manuscript received March 27, 2000. The associate editor coordinating thereview of this letter and approving it for publication was Dr. N. Van Straleen.

J. Choi and Y. H. Lee are with the Department of Electrical Engineering,Korea Advanced Institute of Science and Technology, Taejon, 305-701, Korea(e-mail: yohlee@ee.kaist.ac.kr).

C. Lee and H. W. Jung are with the Wireless ATM LAN Team, Electronicsand Telecommunications Research Institute, Taejon, 305-350, Korea.

Publisher Item Identifier S 1089-7798(00)11509-1.

Estimating the frequency offsets for OFDM-FDMA is ratherstraightforward: the method in [7], which was developed fora single user OFDM, can be applied, as shown in Section IIbelow. In contrast, the direct correction of a frequency offsetby multiplying the complex exponents of the estimated offsetsbeforethe discreteFouriertransform(DFT)tendsto requireheavycomputation and may cause some performance degradation.Since the frequency offsets associated with different users aredifferent to each other, an offset correction followed by theDFT should be performed separately for each user. Therefore,the direct frequency compensation for OFDM-FDMA with

users requires DFT blocks. Performance degradationin the direct method is caused by the fact that a frequencycompensation for one user before the DFT can increase thefrequency offsets in the data of other users within the DFTblock.

In this letter, an alternative signal processing method for fre-quency offset compensation is developed. This method correctsfrequency offsets after the DFT using circular convolution. Itis shown that the complexity of the proposed method decreasesas the number of users increases and that it is simpler to im-plement than the direct method when . Furthermore, theproposed method can outperform direct compensation, becausea frequency offset compensation for one user after the DFT does

not affect the data of the other users.Throughout this paper, for the sake of simplicity, the number

of subcarriers, denoted by , and the number of users, , areassumed to be a power of two. In addition, it is assumed thateach user is assigned subcarriers.

II. FREQUENCY OFFSET COMPENSATION INOFDM-FDMA SYSTEMS

In this section, for the sake of simplicity the frequency offsetcompensation algorithm will be explained for OFDM-FDMAwith two users, however, its complexity will be analyzed for

users.

A. Estimation

Fig. 1 illustrates OFDM-FDMA with two users. Half of theinputs to the inverse DFT (IDFT) are set to zero, because eachuser occupies half of the subcarriers. To assist frequency offsetestimation, a training symbol at the transmitter is shared by theusers and is repeated. If the received symbols after the -pointDFT ( subcarriers), corresponding to the 1st and 2nd trainingsymbols are denoted by and

, respectively, then the maximum likelihood estimate

10897798/00$10.00 2000 IEEE

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CHOI et al.: CARRIER FREQUENCY OFFSET COMPENSATION FOR UPLINK OF OFDM-FDMA SYSTEMS 415

Fig. 1. Transmitters and channels in uplink of OFDM-FDMA with two users.

of each users frequency offset [7] can be given by

(1)

where and are the frequency offsets normalized by thesubcarrier spacing.

B. Correction

The frequency offsets can be corrected before the DFT, asshown in Fig. 2. In this structure, which will be referred to asthe direct method, two -point DFT blocks are employed and

is pre-multiplied for the frequency offset correc-tion of the received sequence for user , . Afterthe DFT for each user, only the data recovered from the sub-carriers associated with the user are retained and the rest arediscarded. It should be noted that after the pre-multification of

, the frequency offset of the th users data for, becomes which is close to zero when ;

however, may be larger than when . Thisfact tends to cause some performance degradation. The numberof complex multiplications for this compensator is given by

. Ob-viously, the complexity increases as the number of users grows.

Accordingly, in an attempt to reduce the computational load,frequency offset correction after the DFT is considered. Againreferring to Fig. 2, if the output of the th DFT is denoted by

, then

(2)

Fig. 2. Frequency offset compensation before DFT (direct method).

Fig. 3. Frequency offset compensation after DFT (proposed).

where denotes the -point DFT;; represents the -point circular convolution;

and which can be rewritten as

(3)The calculation of using (2) is more complex than the cal-culation in Fig. 2 because a circular convolution generally re-quires a much heavier computation than the DFT. To reducethe computational load, in (2) is re-placed with for user 1,

for user 2. The use ofand instead of is justified by the fact that each

user only occupies one half of the subcarriers (Fig. 1). Futher-more, can be approximated by

(4)

where is the number of nonzero elements in . It is as-sumedthat is anodd number. The use of is justified be-cause thevalues of in(3) are close tozero unless is closeto zero or . Using and , Fig. 2 is modified asin the structure in Fig. 3, which is the proposed method. In thismethod, the frequency offset compensation for one user does

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416 IEEE COMMUNICATIONS LETTERS, VOL. 4, NO. 12, DECEMBER 2000

TABLE INUMBER OF COMPLEX MULTIPLICATIONS REQUIRED FOR FREQUENCY

OFFSET COMPENSATION

Fig. 4. Comparison of BER performances when N = 6 4 and P = 4 ( =0 : 1 0 , = 0 0 : 1 0 , = 0 0 : 0 5 , = 0 : 0 5 ).

not influence the data of the other users. The number of com-plex multiplications required by the compensator can be givenby

where represents the multiplications re-quired by the DFT block (in case that the fast Fourier trans-form is used). It is interesting to note that for a given thecomputational complexity of the proposed method decreases asthe number of users increases. This is because the number ofzeros in increases linearly with .

Table I compares the complexity of the direct method andthe proposed method for certain values of , , and . Fortwo users ( ), the direct method is the simplest, however,it becomes the most complex one when , whereas the

complexity of the proposed method decreases as the number ofusers increases. The proposed method with is thesimplest when .

III. SIMULATION RESULTS

To compare the performances of the direct and the pro-

posed method, computer simulations were performed forOFDM-FDMA. In the simulation, the following system param-eters were assumed: DQPSK signaling with a rate of 25 Mbaud,

, cyclic prefix duration of 12, and 1/2 convolutionalcode with constraint length of 5. The number of users was4. The channel was a frequency selective Rayleigh fadingmodel with an exponentially decaying delay profile. The rootmean square delay spread was assumed to be 50 ns, and themaximum mobile speed was 5 km/h. Fig. 4 shows the bit errorrate (BER) of the compensators when the frequency offsetswere , , , and . Asexpected, the performance of the OFDM-FDMA system wassignificantly improved by employing the compensators. The

direct and proposed compensators acted in a similar mannerwhen dB. However, for dB theproposed method performed better than the direct method.The performances of the proposed method when and

, were almost comparable. Therefore, the use of theproposed method is recommended with .

IV. CONCLUSION

A frequency offset compensation method for OFDM-FDMAwas proposed. This method corrects frequency offsets after theDFT, and is able to outperform the direct method which com-pensates offsets before the DFT. It was shown that the com-

putational complexity of the proposed method decreases as thenumber of users increases, plus the proposed method is simplerto implement than the direct method when the number of usersis greater than two.

REFERENCES

[1] L. Wei and C. Schlegel, Synchronization requirements for multi-userOFDM on satellite mobile and two-path Rayleigh fading channels,

IEEE Trans. Commun., vol. 43, pp. 887895, Feb./Mar./Apr. 1995.[2] M. Wahlqvist, R. Larsson, and C. stberg, Time synchronization in the

uplink of an OFDM system, in Proc. IEEE 46th Veh. Technol. Conf.,Atlanta, GA, 1996, pp. 15691573.

[3] J. J. van de Beek, P. O. Brjesson, M. L. Boucheret, D. Landstrm, J. M.Arenas, P. dling, C. stberg, M. Wahlqvist, and S. K. Wilson, A timeand frequency synchronization scheme for multiuser OFDM, IEEE J.

Select. Areas Commun., vol. 17, pp. 19001914, Nov. 1999.[4] H.Rohlingand R. Grnheid, Performancecomparison of differentmul-

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[5] N. R. Sollenberger and L. J. Cimini Jr., Receiver structures for multipleaccess OFDM, in Proc. IEEE 49th Veh. Technol. Conf., Houston, TX,1999, pp. 468472.

[6] C. Y. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, MultiuserOFDM with adaptive subcarrier, bit, and power allocation, IEEE J. Se-lect. Areas Commun., vol. 17, pp. 17471757, Oct. 1999.

[7] P. H. Moose, A technique for orthogonal frequency division multi-plexingfrequency offset correction,IEEE Trans. Commun., vol.42, pp.29082914, Oct. 1994.