ON THE UPLINK SYNCHRONIZATION OF OFDMA SYSTEMS

Erdem Bala and Leonard J. Cimini, Jr.Department of Electrical and Computer EngineeringUniversity of Delaware, Newark, Delaware 19716Email: erdemgudel.edu, ciminigece.udel.edu

ABSTRACTIn this paper, we study symbol timing synchronization

for the uplink of an OFDMA system in a multipath fadingchannel. The effects oftiming offsets on both synchronized andunsynchronized users are investigated andperformance degra-dation is illustrated Then, a simple timing offset estimator isdeveloped and its performance is evaluated The symbol-errorrate of the compensated system is also presented Simulationresults demonstrate that this estimator performs well even forlarge offsets and in the presence of significant levels of noise.

I. INTRODUCTION

Orthogonal frequency division multiple access

(OFDMA) is a multiple access technique in whichthe subchannels of an OFDM symbol are shared bymultiple users. This technique is used in the IEEE802.16 fixed wireless standard [1] and has beenproposed for broadband wireless networks and wirelessad hoc networks. It is well known that the performanceof OFDM is sensitive to frequency and symboltiming synchronization. Imperfect synchronizationcauses interchannel (ICI) and intersymbol interference(ISI) which can result in a significant performancedegradation. In the downlink of an OFDMA system,the synchronization task is relatively straightforwardbecause each user has to synchronize to only one

transmitter. The uplink synchronization, however, ismore challenging. In this case, OFDM symbols are

received from multiple users, each with differentfrequency and timing offsets.

Synchronization techniques for single-user OFDMlinks, which can also be applied to the downlink of an

OFDMA system (for example, see [2] and the referencestherein), have been investigated widely. Some previouswork has addressed the performance analysis of the

Prepared through collaborative participation in the Communica-tions and Networks Consortium sponsored by the U. S. Army Re-search Laboratory under the Collaborative Technology Alliance Pro-gram, Cooperative Agreement DAAD19-01-2-001 1. The U. S. Gov-ernment is authorized to reproduce and distribute reprints for Gov-ernment purposes notwithstanding any copyright notation thereon.

effects of frequency and timing offsets in the uplinkfor OFDMA, as well as offset estimation techniques. In[3], a frequency and timing offset estimation techniquebased on the redundancy of the cyclic prefix is presented.This technique is based on a maximum likelihood (ML)estimation method previously introduced in [4]. An al-ternative ML approach that uses training sequences isgiven in [5]. In these works, the frequency and timingoffsets of a new user are estimated while it is assumedthat other users have already been synchronized. Thisrestriction is relaxed in [6] and simulation results fortwo unsynchronized users are provided. The offset com-pensation is carried out separately at each transmitterbecause, in the uplink of an OFDMA system, the receivercannot synchronize to all users simultaneously [3], [5],[6]. After the receiver estimates the frequency and timingoffsets, the transmitters are informed of their own offsetsvia a downlink control channel, and each transmittercompensates for its offset. In several other works, thefrequency offset problem for OFDMA is addressed (forexample, see [7], and the references therein).

Timing offset occurs as a result of the misalignment ofthe FFT window at the receiver. If there is a single user inthe system, the receiver can synchronize to that user andthe FFT window can be properly aligned. If, however,there are multiple users, the transmitted OFDM symbolsfrom different users may experience a wide range ofdelays. In this case, the FFT window alignment wouldbe imperfect for some users because the receiver cannotsynchronize to all users at a given time. The cyclic prefix(CP) added to the OFDM symbols provides protectionagainst the timing offset if its duration is long enough.The work mentioned above assumes that the total delayis within the duration of the CP. The CP, however, isusually just long enough to compensate for the channelimpulse response. Extending this duration results in anadditional reduction in the spectral efficiency.

If the CP is not long enough, a symbol timing offsetresults in ICI both from the subchannels of a givenuser as well as from the subchannels of other users inthe uplink. In [8], the analysis of an uplink OFDMA

system when the timing offset is larger than the CP ispresented. This work, however, ignores the delay dueto the channel impulse response, and only considersthe specific user to which the receiver is synchronized.In [9], performance degradation in an uplink OFDMAsystem due to multipath fading and frequency and sym-bol timing offsets is studied. In this paper, the authorsassume that, at the receiver, there is a separate FFTmodule for each transmitter; this limits the practicalityof the system considered. Motivated by these findings,we study the timing offset problem in the uplink of anOFDMA system. In this analysis, timing offset is notlimited to the length of the CP, and the performancedegradation of both synchronized and unsynchronizedusers is investigated

In Section II, we present the system model. In SectionIII, we analyze the performance of an uplink OFDMAsystem with timing offsets. In Section IV, we introducea timing offset estimation technique which uses thephase difference between consecutive received OFDMsubcarriers. This approach is particularly robust to noiseand multiple access interference. A similar idea based ondifferential phase estimation has been proposed in [10]for OFDM systems. The proposed estimation techniqueis then evaluated through simulations. Finally, Section Vconcludes the paper.

II. SYSTEM MODEL

We consider the uplink of an OFDMA system whereU transmitting terminals are trying to communicate witha common receiver. Each user is assigned a block ofconsecutive subcarriers from the N available subcarriers,i.e., user u is assigned the set of subcarriers Yu =

[(u -1)B + 1, ..., uB], where B = N/U is the blocksize. A vector S of N information symbols is generatedby each user. The elements of this vector that correspondto the assigned subcarriers of that user are complexinformation symbols, Sj, chosen from a modulationscheme such as QAM or PSK, and the others are setto zero, e.g., S = [0,0,...,So: S1, ..., SB-1, O, ..., O]. Thisvector is then processed by an IFFT during duration T.After parallel-to-serial conversion and the addition of aCP, the OFDM symbol is converted to an analog time-domain signal before being transmitted through a fadingmultipath channel.

The time-domain baseband signal at user u's transmit-ter can then be written as

oo N-1

xu() = k Sm0(k)j2-FkAf(t-mTs)m=-oo k=0

where m is the OFDM symbol time index, Sm(k) is theinformation symbol corresponding to the mth OFDMsymbol and the kth subcarrier, Af = 1/T is theintercarrier spacing, Ts = T + Tcp is the total OFDMsymbol duration, and Tcp is the duration of the CP.The OFDM signal transmitted by each user is affected

by a fading multipath channel. The time-varying channelbetween the uth user and the receiver is modeled as

p1

(2)

where P is the total number of paths, ozp is the complexgain of the pth path, and Tp is the delay of the pth path. Inthis paper, the channel is assumed to be slowly varying,i.e., the fading coefficients are assumed to be constantduring one OFDM symbol. The gains are modeled ascomplex Gaussian random variables with an exponentialpower delay profile.

The received signal, in the absence of noise, denotedas y(t), is the superposition of the transmitted OFDMsymbols from all users and can be written as

u P

8(t) = p 1 ap,uu (t-Tp, - u)u=lp=l

(3)

where ,u, is the delay experienced by user u. This delaycould be due to propagation delay, for example.

III. SYMBOL TIMING OFFSET ANALYSIS

The symbol timing offset is caused by the misalign-ment of the FFT window at the receiver, which, in turn,results from the delay the transmitted OFDM symbolsexperience. In a single-user OFDM system, the receivercan synchronize to the transmitter, and the alignmentof the FFT window would be perfect. In this case,the orthogonality of the subcarriers is preserved and nointerference occurs. If, however, there are multiple users,the receiver cannot synchronize to them all simultane-ously because alignment of the FFT window with oneparticular user would misalign the other users. The CPprovides a protection mechanism against this as long asthe delay is within the duration of the CP.

The timing offset problem is illustrated in Figure 1 forfour users. In this figure, user 1 does not experience anydelay, user 2 experiences a delay that is within the CP,and users 3 and 4 experience delays that are longer thanthe duration of the CP (Ncp samples). In the receiver,the first Ncp samples are discarded and the FFT windowis from n = 0 to N -1. Users 1 and 2 are notmisaligned with the FFT window, i.e., the contribution in

2

the window is only from their current OFDM symbols.The FFT window, however, spans samples from theprevious OFDM symbols of users 3 and 4. Two basicerror mechanisms occur as a result of this timing offset:

. Self-interference:(I) The FFT window spans samples from the

previous time symbol causing interference onthe subcarriers of the current OFDM symbol.

(II) The truncation of the current OFDM symbolcauses ICI on the subcarriers of this OFDMsymbol.

* Multiple access interference (MAI): Due to theloss of orthogonality, the other users also generateinterference.

To investigate the effect of timing offset on the per-formance of an OFDMA system, we first consider asimplified model where we have only a single user and aflat fading channel. Later, the result will be generalized tomultiple users and frequency-selective fading channels.With this model, the sampled time-domain signal x(n)transmitted by user u during the mth time interval is

N-1 kj2w rn

xm(n) = E Sm(k)e N nk=O

Ncp,.., N-1 (4)

The signal x(n) arrives at the receiver with a delay of

D samples, where D = A T . If we assume that D <

Ncp, then the signal in the frequency domain for the£th subcarrier, Ym(t ), is

0-Nc

+-User 1

IUser 2

User 3

User 4

Discarded

N-1

ni

I

Current Symbol

Previous Symbol

II

Fig. 1. Uplink received OFDM symbols with timing offsets

y(n) in the FFT window are given as

(6)

Xm-l(n+N+Ncp -D):

y(n) =0 < n < D-Ncp-1

D-Ncp< n < N-1

and the resulting signal on the £th subcarrier is

1 D-Ncp-1ym(f) > xmT- (n + N+ Ncp -D)e N

n=O

N-1D)N xmExm(n- D)- (7)

n=D-Ncp

After inserting xm(n) and xm-1(n) into (7), the result-ing Ym(f) can be partitioned into three terms as

ym(f) Sm(T)(N-1-D+NcP+1) -j27eD

+ Srn (I)D

1N-1yM ()N= X(n- D)e NjiUi

n=O

1N-1 N-1j2knD 27n

{ E E Sm(k)e j(N D Nn=O k=0

1 Ni j27N-1

j2(k-e)

N E Sm(k)e N E j N

k:=O n=O

(5)

The sum over n is equal to N5(k -) so that Ym( ) =-j2 7r D

Sm(t)e N So, as long as the delay is less than theCP, the received symbol is just a phase rotated versionof the original symbol; there is no loss of orthogonality.Now, consider the case where the delay D is larger

than Ncp. In this case, as illustrated in Figure 1, the FFTwindow spans samples from the current OFDM symbolas well as from the previous OFDM symbol. The samples

- Ncp j27r-(D-NCp)N )

N-1 - j27rr(k-1)(D-NCp)

+ O27r 1) X

k=O,k:A L 1eJ

( S (k)e jN +Sm (k)e ) (8)

The first term in (8) is the desired subcarrier informationwhich has been attenuated and rotated. The second termis the interference from the information symbol on thesame subcarrier of the previous OFDM symbol; and thelast term represents the ICI from the other subcarriers.The total ICI power for any one user is then

E(ICI_2) (D

2 N-1

N2 Ek=O,kof

-NCR)NJ

COs(2wr(k-£)(D-Ncp))

1 -COS(27r(k-£))

(9)

3

=

where we have assumed that the information symbols ondifferent subchannels are i.i.d. and have unit energy.

With the channel model given in (2), the receivedsignal y(n) would have P copies each scaled with a

different amplitude ao and delay A/, where A =n TNThen, for a specific user u, similar to (6), we can write

p1

yu(n) 0UKn<D+Ap-NcpZ apxm(n-D - )p=1D + Ap-Ncp+ 1 < n < N- 1

(10)where we have assumed that the channel remains con-stant over two OFDM symbols. Then, the informationsymbol on the £th subcarrier is given as

Y(I)= E0p{Sm()NI 1 D+NcpP=o

xe N+2 S (l( )(

1N-1+- ,)

k=O,kof

+ 1)

- Ncp j27re(D -NCp)N )

-j2-x(k-1)(Dp-NCp)

j2[i(k-1) X

1i-e N

( Sm(k)e N +D( j2rr(Ycp Dr)) }

where Dp = D + Ap. The ICI power is then

E[ ICIsif 2]=

2N-1

k=O,kof

aP{(DONcpN ~

1 -cos( 2F(k-f) (DI -Ncp) )

1 COS(2w7(k-£)) '}where ICIsif denotes that the interference is self-interference, i.e., from the user's own subcarriers.When there are multiple users in the system,

u

y (n) = :Eyu (n) (13)u=l

Each user transmits information on a subset, Yu, of theavailable N subcarriers. In this case, the MAI due tothe timing offsets of the other users will also contributeto the total interference. By using (13) in (7)-(12), wecan get a general formula that includes the effects of themultipath channel and MAI from other users, as well as

self-interference. The power of MAI from user u, ICIU,on the £th subcarrier of the user of interest is

E[IC_12]= 2 1 ICe 12N2Z

p0O (1 4)Ni~~~>ii:-1 cos(2r(k

C )(DS2 NcP))keY 1-cos(2wj(T£)) J

Then, the total interference is the sum of the self-interference and MAI from all other remaining users.

Simulation results are presented here to quantify theinterference due to the timing offset. In the simulations,the number of subcarriers N = 256. There are U = 8users and a subband of 32 subcarriers is allocated toeach user. We assume that the total system bandwidthis 2 MHz. The channel is a multipath Rayleigh fadingchannel with an exponential delay profile. The samplingperiod is 0.5 ,usec and the rms delay spread of thechannel is set to 2.5 ,usec. The length of the cyclicprefix is set to 16 samples (8 ,usec), which is enoughto absorb the channel impulse response. The additionaldelay results in self-interference and MAI. In Figure 2,we first compare the theoretical analysis with simulationresults. The fourth user is chosen as the user of interestand its delay is set to 0 or 60 samples, which resultsin MAI only or self-interference and MAI, respectively.The remaining users have 60 sample delays. The figureshows that the analytical and simulation results match.We can see that the ICI due to self-interference is muchlarger than the ICI due to MAI.

Next, we investigate the effect of timing offset on thesystem performance. In this case, OFDM symbols aregenerated by each user and transmitted to the receiver.We study the performance of a synchronized user (user4 in this case) and an unsynchronized user (user 6)who experiences the largest delay. We assume that user4 has a delay of zero, user 6 experiences a delay ofD samples, and the remaining users experience randomdelays between 0 and D. The synchronized user suffersfrom the MAI from other users, and the unsynchronizedusers suffer from self-interference as well as MAI.

Figure 3 shows that the signal-to-interference ratio(SIR) of the synchronized user's edge subcarriers de-creases significantly as the timing offsets of the otherusers increase. The rest of the subcarriers, however, arenot significantly affected and the SIR of these subcarriersdoes not change much with increased timing offsets.These prove that the allocation of subcarriers in blocks isa better choice than interleaved allocation. The behavioris, however, not similar for the unsynchronized user, as

4

illustrated in Figure 4; here, the SIR decreases signifi-cantly with increasing timing offsets due to an increasein self-interference.

0.5Simulation

0.45 --- ---- --- Theoretical

0.4 ..... ...... ...... .... ..... ...... ...... ...... ...... ...... ...

0.35 ...

X 0.3 ..................................... ...........................

0.25 ..- .. .. .. .. .. ...... ..... ....... ..... ...a-

0.2 . . .. ...... ..... ...... ...... ...... ...... ...... ...... ...

a-)

0 1 5

I. ,, # .. ... ..--- --- --- ---'--- --- ---- ;--''- i--

25

20

-D=20D=40D=60D=80-D=100

1 5

1 0 .. ..

5

......

-5160 165 170 175 180 185 190 195

Subcarrier Index

0.05

0 _95 100 105 110 115 120

Subcarrier Index125 130

Fig. 4. Signal-to-interference ratio for the unsynchronized user

Fig. 2. Interference power for user 4 with DD = 60 (solid), with D = 60 for all other users

1 -10

25

20

15

g! 10

nD

D=20

---D=400 ....... =6 ......................

D=80

D=100-5 _95 100 105 110 115 120

Subcarrier Index

IY 10U)

01)

> 10-3

0o-4 _=-D =0-- -D=20...- D=40.... D=60

10-5

125 130

Fig. 3. Signal-to-interference ratio for the synchronized user

Figure 5 shows the average symbol error rate (SER)of the synchronized user and the unsynchronized user

for different timing offsets and using 16 QAM. As thetiming offset increases, the SER performance degradessignificantly. The degradation is more significant forthe unsynchronized user. These results demonstrate thenecessity of synchronization for all of the users at thereceiver.

IV. TIMING OFFSET ESTIMATION

As the results in the previous section show, theperformance degradation of an uplink OFDMA systemcould be significant in the presence of a symbol timingoffset. The synchronization task cannot be achieved at

10SNR (dB)

15 20

Fig. 5. SER performance of the synchronized and unsynchronizedusers (with circles)

the receiver because synchronization of the receiver withone transmitter would result in misalignment of thereceiver with the other transmitters. Therefore, it mustbe the responsibility of the transmitters to correct theirtiming offsets. To achieve this, the receiver estimates thetiming offsets of the individual users, and informs themof their offsets. Then, using these estimates, the users

correct their timing [3], [5], [6].Some estimation techniques based on the ML ap-

proach have been previously proposed in [4]-[6]. Thesetechniques, however, assume that the symbol timingoffset is within the duration of the CP. If the offset islarger than the CP, then interference occurs and theseestimation techniques do not perform well. Therefore,an estimation technique that is robust to interference

5

0 (dotted) and 100

is required. A particularly useful technique based ondifferential estimation for OFDM systems has beendemonstrated in [10]. In this paper, we propose a similartechnique that estimates the timing offset by using thephase differential between the OFDM subchannels in agiven subband.

For a single-user OFDM link where the delay iswithin the CP, the frequency domain symbol for the kthsubchannel in the absence of noise is

Y(k) = S(k)H(k)e N2wND (15)Similarly, the symbol on the adjacent subchannel is

Y(k + 1) = S(k + 1)H(k + 1)e- NNDej2w ND (16)

2

1 : . .......

0 0.5 1 1.5rms dE

2 25 3elay spread (~1sec)

If we differentially detect the two symbols, we get

Y(k+l)Y*(k) = S(k+l)S*(k)e i2WN H(k+l)H*(k)

(17)Assuming the channel coherence bandwidth is muchlarger than Af, then Hk+1 _Hk and, using a trainingsequence such that Sk+1 = Sk, the delay D can beestimated from (17). Improved noise performance can

be obtained by averaging the phase differential statisticover all subchannels in a block, i.e.,

B-2

Q = Y(k + 1)Y*(k) (18)k=O

The delay can then be estimated as

I N~~~D = ( )tn-' (Tm(Q)) (19)

If the delay is not within the CP and there are

multiple users, the frequency domain symbols wouldinclude interference as well as additive white Gaussiannoise. However, both the noise and interference are

uncorrelated for different subcarriers, so averaging thedifferential estimate, as in (18), improves the robustnessto noise and interference. The optimality of this approachin an ML sense, is shown in the Appendix.

Next, we discuss the performance of the differentialtiming offset estimator given in (19). The same parame-

ters as in the previous section are used in the simulations.Figure 6 illustrates the mean estimation error in samplesas a function of the rms delay spread and signal-to-noiseratio (SNR). The timing offset of an unsynchronized user

who experiences the maximum delay among all users

is estimated. The delay for this user is either 20 or

60 samples, and the delays of the remaining users are

random integers between 0 and the maximum delay. Therms delay spread values range from 1 nsec to 4 ,usec,

Fig. 6. Mean estimation error in samples for SNRand SNR= 20 dB (solid)

0 dB (dashed)

100

o-1

100

wU)

01)CU

>10

D=20D=60

10-55 10

SNR (dB)

Fig. 7. Performance comparison theuncompensated (dashed) systems

15 20

compensated (solid) and

which correspond to flat fading and highly frequencyselective channels, respectively. We can see that thebehavior of the estimation algorithm is very dependenton the amount of delay. Consider first the case where thedelay is only a little bit larger than Ncp. Here, the dom-inating factor is the noise. In this case, the performanceof the estimation algorithm improves with increasingSNR. When the noise power is much larger than thesignal power, the estimation error is unacceptable. Atacceptable noise levels, the performance of the algorithmdegrades with increasing rms delay spread because thefading on adjacent subchannels becomes uncorrelated.The degradation, however, is not significant. With an rms

delay spread of 4 ,usec, the estimation error is still only

6

10- D=20- D=60

a)

-S

0

a)

Q)-C

.2W

35 4

w

a few samples.When the delay is relatively large, for example, 60

samples, the behavior of the algorithm is quite differ-ent. The dominating factor is the interference and theestimation error decreases with increasing rms delayspread values. This can be explained by observing thatincreasing the rms delay spread decreases the correlationbetween consecutive subcarriers. Therefore, the interfer-ence terms on these subcarriers are less correlated andthe averaging reduces its effect. Figure 7 shows the SERperformance of the estimation algorithm for an rms delayspread of 4 pusec. The results demonstrate that this timingoffset estimator can provide an adequate and simplecompensation for the timing offsets even when the delayis larger than the CP.

Although the results are not shown here, the robust-ness of the proposed estimator to frequency offsets isalso verified with simulations. In this case, the frequencyoffset for each user is randomly set to be uniformlydistributed between Af and 'Af . The performanceof the proposed estimation algorithm with frequencyoffsets does not degrade.

V. CONCLUSIONS

The performance of an uplink OFDMA system withtiming offsets has been studied. The degradation due tothe resulting interference can be significant, and com-pensation is required. A timing offset estimator based ona simple differential operation in the frequency domainwas proposed. Simulation results demonstrate that thisestimator performs well even for large offsets and in thepresence of significant levels of noise.

APPENDIX

In general, Y(k) = S(k)H(k)e j2wkND + W(k)where W(k) represents additive white Gaussian noise.When the delay is larger than the CP, interferenceoccurs. We assume the interference is Gaussian withzero mean and embed the interference terms into W(k).We can also write Y(k + 1) S(k + 1)H(k +1)e2KNDeJ2N ND+ W(k+1). By assuming S(k)=

S(k + 1), and H(k) H(k + 1), Y(k + 1) =

S(k)H(k)e j2wkNDe J2ND + W(k+1)Over a subband k E {(u- 1)B +1,...,uB -1},

collect Y(k) into the vector Y, S(k)H(k)e N2wkD intothe vector X, and W(k) into the vector Wl, such thatY = X + Wl. Similarly, Z = F(D)X + W2, whereF(D) e NJ2 .ND Given Y and Z as observations, theML estimate of D is D = arg maxDf (ZID, Y) wheref (ZID, Y) is the probability distribution function of

Z given D and Y. Writing Z in terms of Y, we getZ F(D)(Y -W1) + W2 = F(D)Y + W whereW -F(D)W1+W2 is also Gaussian with zero meanand covariance matrix a2I. The multivariate complexGaussian distribution function f (.) can be specified withthe mean vector F(D)Y and covariance matrix a2I. To

Hfind D, G(D) = (Z -F(D)Y) (Z -F(D)Y) mustbe minimized. Taking the derivative of G and settingit equal to zero, we get sin(2N)(ZYH + YZH)j cos(27D)(ZyH _ yZH), which, in turn, gives

D = - ()tan-

B-2

E IM(ZkYk)-1 <k=0

B-2XE Re(ZkYk*))k=o

(Al)

which is equivalent to (19).

REFERENCES

[1] IEEE standard for local and metropolitan area networks, part 16,IEEE Std. 802.16a, 2003.

[2] S. Barbarossa, M. Pompili, and G.B. Giannakis, "Channel-independent synchronization of orthogonal frequency divisionmultiple access systems," IEEE JSAC, pp. 474-486, Feb. 2002.

[3] J.J. van de Beek, P.O. Borjesson, M.L. Boucheret, D. Landstrom,J.M. Arenas, O. Odling, M. Wahlqvist, and S.K. Wilson, "A timeand frequency synchronization scheme for multiuser OFDM,"IEEE JSAC, pp. 1900-1914, Nov. 1999.

[4] J. J. van de Beek, M. Sandell, and P. 0. Borjesson, "MLestimation of timing and frequency offset in OFDM systems,"IEEE Trans. Signal Processing, pp. 1800-1805, July 1997.

[5] M. Morelli, "Timing and frequency synchronization for theuplink of an OFDMA system," IEEE Trans. Commun., pp. 296-306, Feb. 2004.

[6] M. Puny, M. Morelli, and C.-C. J. Kuo, "Maximum likelihoodsynchronization and channel estimation for OFDMA uplinktransmissions," Submitted to IEEE Trans. Commun., Oct. 2004.

[7] Z. Cao, U. Tureli, and Y.-D. Yao, "Deterministic multiusercarrier-frequency offset estimation for interleaved OFDMA up-link," IEEE Trans. Commun., pp. 1585-1594, Sept. 2004.

[8] M. Park, K. Ko, H. Yoo, and D. Hong, "Performamce analysisof OFDMA uplink systems with symbol timing misalignment,"IEEE Comm. Letters, pp. 376-378, Aug. 2003.

[9] A. M. Tonello, N. Laurenti, and S. Pupolin, "Analysis of theuplink of an asynhronous multi-user DMT OFDMA system im-paired by time offsets, frequency offsets, and multi-path fading,"IEEE VTC Fall-2000.

[10] B. McNair, L. J. Cimini, and N. Sollenberger, "A robust timingand frequency offset estimation scheme for orthogonal frequencydivision multiplexing (OFDM) systems," IEEE VTC 1999.

The views and conclusions contained in this document are thoseof the authors and should not be interpreted as representing theofficial policies, either expressed or implied, of the Army ResearchLaboratory or the U. S. Government.

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