2006 6th Intertional Conference on ITS Telecommunications Proceedings

Frequency-Domain Fractionally-Spaced MMSE

Multiuser Receiver for Multicarrier MA

Qinghua SIi, Yong Liang Guan, and Choi Look LawPositioning and Wireless Technology Centre

School of Electrical and Electronic EngineeringNanyang Technological University

50 Nanyang Drive, Researc TechnoPlaza, Level 4, BordeX Block, SingVpore 637553Emails: qhshi@ntu.edu.sg; EYLGuan@ntu.edu.sg; ecllaw@ntu.edu.sg

Abstract-An important problem for multicarrier systems isfrequency offset between a transmitter and receiver, which cansubstantially deteriorate system performance. In this paper, wepropose a frequency-domain fractionally-spaced minimum meansquare error (FDFS-MMSE) multiuser detector for multicarriercode-division multiple-access (MC-CDMA) systems. Numericalresults show that with frequency-domain oversampling by afactor of two, the proposed FDFS-MMSE receiver can combatfrequency offset efficiently, in addition to its near-far resistanceand MAI elimination capability.

I. INTRODUCTION

Multicarrier modulation (MCM) [1] has emerged as apromising approach for high data rate applications, becauseit fkilitates simpler frequency-domain equalization whereassingle-carrier systems need more complex equalization in thetime domain to compensate for severe inter-symbol inter-ference. In addition, being parallel transmission by nature,MCM is suitable for adaptive bit and/or power loadimg acrosssubcarriers to make full use of the channel potential. MCM hastlherefore received considerable attention over the past decade.In particular, the integration of orthogonal frequency divisionmiultiplexing (OFDM, the most popular MCM form) and code-division multiple-access (CDMA) has created the so-calledmulti-cafrier CDMA (MC-CDMA) [2], whose advantage in biterror rate (BER) performance compared to conventional directsequence CDMA (DS-CDMA) has been shown, especially inthe downlink [3].

However, as a combination of OFDM and CDMA, MC-CDMA suffers from disadvantages of both OFDM andCDMA. On the one hand, a carrier frequency offset betweenthe transmitter and receiver, due to oscillator instability andDoppler effect, incurs heavy loss in the performance of MC-CDMA. On the other hand, a base station needs to transmitdifrent powers to users in different locations to achievepower efficiency, thereby causing a notorious near-tar prob-lein for a downlink of CDMA systems. In this pape we'try to handle these two problems at the same time. It iswell known that a time-domain fractionally-spaced receivercan be used to combat timing jitter [4]. This idea hasbeen applied in a time-domain partial sampling multiuserreceiver for asynchronous MC-CDMA [5]. From the dualitybetween time and frequency domains, it is natural to expect

that a frequency-domain fractionally-spaced receiver will berobust to frequency mismatch. Accordingly, we propose afrequency-domain fractionally-spaced minimum mean squareerror (FDFS-MMSE) inultiuser detector to deal with thefrequency offset and near-far problems for the downlink ofMC-CDMA. We notice that in a recent publication [6] thefrequency-domain oversampling technique has been used toeliminate multiple access intefference (MAI) in the uplink ofMC-CDMA. However; our approach is fundamentally differentfrom [6] in the way of processing the oversampled signalsand making decisions. In particular, our approach is basedon multiuser detection whereas the receiver proposed in [61is a single-user detector with group structure. Numericalresults indicate that frequency-domain upsainplig by a factorof 2 is sufficient to achieve our goal. Besides, a desirablefeature of the proposed FDFS-MMSE multiuser receiver is thatmulticarrier demodulation and oversampling can be readilyimplemented via zero-padding FFT. It is interesting to notethat time-domain T/2 fractionally-spaced (i.e., upsampling inthe time domain by a factor of 2) equalization is also mostcoimnonly used.

Notation: Denote matrices by bold uppercase letters andcolumnn vectors by bold lowercase letters; (.)T and (.)t denotetranspose and conjugate transpose, respectively; IN representsan A x N identity matix and diag{ } is a diagonal matrix;E[-] denotes expectation and Var[-] denotes variance; Re{ }and Imn. } denote real and imagmary part, respectively.

II. PERFORMANCE ANALYSIS

Consider the downlink of an MC-CDMA system sufferingfrom both the frequency offset and near-far problems. Weassume that there are N subcariers and K users in this system.The received signal can be expressed by

r(t) X-N Nbk(0) Ec k hihi/= -it

n-expK27[-

(0 < t <Tb1)fD + fj t) (t)

(1)

where h,, denotes the quasi-static channel gain on the nthsubcarier, described by a complex Gaussian random variable

0-7803-9586-7/06/$20.00 C 2006 IEEE. 1342:

with zero-mean and unit variance andRh transmitted signal power of usa k,bk (0) BPSK data bit sent by user k over [0, T],{Ck 1 user k's spreading code,Tb bit duration,fD frequency offset between the transmitter

and receiverft radio frequency,

q'(t) background Gaussian noise wit zero meanand variance N0.

Motivated by the fact that time-domain fractionally spacedequalization [4] is robust to timing jitter, we use FDFS-MMSEmultiuser detector to comibat tie detrimental effects introducedby tie frequency offset and near-far problems. Consequently,at the receiver, multicarrier demodulation is carried out byupsampling, in the frequency domain, the received signal bya factor ofM (M is a positive integer) 1. Thlis means that thereceived signal is projected onto NM subcaiers that occupythe same banidwidth as the N subcarriers of the transmitterThe output of multicarrier demodulation on the lth subcarrier(1 1, 2, NM) can be written as

is

wA- (E[yyt]) 1E[yb(}0)]g (I7HCPICtHtFt ± r) - .Hc1 (6N_

where r A~E[rrnqtl with elements

T71hiNo I I/ - 1 1/I -Tep (371/NI) sinle (M

1,'= 1, 2, N V[M

1)

(7)and c, A ci2, cN] is user i's spreading code. It canbe verified that when fD = 0 and M = £2 and r reduce toIN and j 'IN, respectively. Then, (6) agrees with eq. (8) of[7] as expectd.Without loss of generality, we assume b, (0) ±+1 was sent.

The decision variable for user i is given by

z = Rewy}w Re{wtHCPb} Re wt}7 (8)

and then the corresponding BER, conditioned on b (withb,(0) = +1) and H, can be calculated by

1' = TF i(t)exp i-2 [j ± fc t) dtT I IIr

wh e r e (0) E CnkhnWln + Vtk=i n=1

whoe

JDTb- -)sinc(n

1 T ,(=- (t) exp y j2rrill

oI

Peib, H(2)

fD_Tb-I

(3)

+± fj t) dt.

Stacking {yi}1V into a column vector, we can write (2) inmatrix form as

y = QHCPb + 7 (5)

where

y

H

- [1,Y2, ,---YNM]IA

AL

{ WIn IN}y x N,

C A {Crt} K,v3

PA diag §v,

b7/

A

AL

PK}

[bi(0),b2(0.. bK(0)],[q1,q2, ,^ T N_M].

Here we consider a linear MMSE multiuser receiver based onWiener filta theory. The optimal weighting vector for user i

IIn practical implementations, the demodulation process can be readilyaccom-plished by means of zero-padding FFT.

(9)2Vr Re {w }Jedrf

Pb

where the calculation of the variance of Re{wt} is elab-orated in Appendix. The final BER can be obtained byaveraging (9) over b ad H via Monte Carlo integration.

III. NUmERICAL RESULTS AND DISCUSSIONWe compare the BER performance of the proposed FDFS-

MMSE multiuser detector with the conventional MMSE mul-tiuser detector taken from [7] under diffrent frequency offsetad near-far conditions. In all the numerical examples, a fully-loaded system employing 32 subcarriers (i.e., N KK 32)is assumed and, unless otervise specified, Walsh-Hadamardspreading codes are employed, the first user is the desireduser (i.e. i 1), the signal-to-noise ratio is set to Eb/No=lOdE. The channel gains {bi}7IN are geerated accordingto the channel model [9], [8] with a normalized delay spreadT/Tb = 0.1. When near-far effect is considered, we assumethat all interfering users have the same power Pk while thedesired user's power is P,.

Fig. 1 shows the comparison of BER performance betweenthe conventional MMSE [7] and the proposed FDFS-MMSEinultiuser receivers in the presence of frequency offset butwithout the near-ar problem. Clearly, the performance of theMMSE receiver is very sensitive to frequency offset, but theperformance of the FDFS-MMSE receiver is satisfactory forM > 2. It appears that frequency upsampling by a fatorof M = 2 gives a good tradeoff between performance andcomplexity. In Fig. 2, the near-far effect is incorporated. Wehave similar observations as in Fig. 1.

In Fig. 3, we investigate the robustness of the MMSE andFDFS-MMSE multiuser receivers to the near-far effect. It is

2

1343

Cl-Iln exp I-F n

found that both receivers work well in handling the near-arproblem. However; the FDFS-MMSE receiver with M 2can also combat the detrimental effect of frequency offset.

In Fig. 4 we show the BER comparison between the MMSEand the proposed FDFS-MMSE receivers as a function ofsignal-to-noise ratio. We can see that the performance of theMMSE receiver is determined by MAI (not Gaussian noise)

due to the frequency offset whereas the FDFS-MMSE receiver

(particularly with M = 2) can be regarded as noise-limited dueto its MAI elimination capability.

Finally, we study the influence Of spreading codes on theperformance of the proposed FDFS-MMSE multiuser receiver

in Fig. 5 where the orthogonal Gold sequences are obtained byappending "-1" to the end of correspondmng Gold sequences,which are derived by a preferred pair of rn-sequence withgenerator polynomials 45 and 67 in octal. We can see that

when M 1, the performance difference among differentusers is noticeable, but it becomes negligible when MA 2.This means tiat the FDFS-MMSE multiuser receiver withM 2 can eliminate the MAI sufficiently even in thepresence frequency offset and near-far problems, no matterwhat spreading codes are employed.

IV. CONCLUSION

In this paper, we considered the downlink of MC-CDMAsuffering from both frequency offset and near-far effect. Weproposed to address these problems jointly by means offrequency-domain ovesampling and MMSE principle. Ournumerical results show that with frequency upsampling by a

factor of two, the proposed FDFS-MMSE multiuser receivercan cope with fequeincy offset, near-far problem, and MAIefficiently. An attractive feature of the FDFS-MMSE receiver

is that at the receiver frequency-domam upsampling can easilybe imuplemented by zero-padding FFT algorithms.

APPENDIXBy defining

PT AW - [Refwtl -Imfwtl]1 - [R 1rflT [,q,l: qR*7V Re{nTIAqR [ti 24 * NMI

[ 4,1 4 <

N T },we can wnte

Vt [Re {wt}] wE [<]

Wb0E [nRqh] E [ >]jw

(10)

Fron (4), we have

tRe{'(t)} cos (2urt + 1)

+Im{fq'(t)} sin (2mrt + ij) }dt

jT, {I trn{i'(t)}cos (2F >b fcl

-Ref{((t)} sin (2wtAlT0

After some manipulations, we obtain

[nRRE jE] BE [] o: ) i'(M i)

E[q¾4] [u/tiP]= fE sin M

) sine

Substituting ( 11) into (10) gives Var [Re {wt}]RDEFEREN CES

[1] J. A. C. Bingham. "Mu'lticarrier modulation tor data transm-fission: anidea whose time has come, LEEE Commun. Mag., vol. 28, pp. 5-14,

May 1990.[2] K. Fazel and S. Kaiser, Multi-Carrier and Spread Spectrum Systems,

John Wiley & Sons: Chichester, England. 2003.[3] S. Hara and R. Prasad, "Ovenriew of multicarrier CDMA," IEEE

Commun. Ag., vol. 35, pp. 126 133, Dec. 1997.[4] J. R. Treichler, I. Fijalko and C. R. Johnson, "Fractionally spaced

equalizers, IEEE Signal Process. Mag., vol. 13, pp. 65-81. May 1996.[5] Pingping Zong, Kunjie Wang, and Y. Bar Ness, "Partial sampling

MMSE inteiference suppression in asynchronous multicarrier CDMAsystem, EEE Ji Select Areas. Commun., vol. 19, pp. 1605-1613, Aug.

2001.[6] B. Hombs and J. S. Lehnert, "Multiple-access interference suppression

for MC-CDMA by frequency-domain oversamplinig IEEE rans.

Commun., vol.53, pp. 677-686, April 2005.

[7] J.-F. Helard, J.-Y Baudais, and J. Citerne, "Linear MMSE detectiontechnique for MC-CDMA," LEE Electron. Lett. vol 36, pp. 665-666,March 2000.

[8] W C. Jr (Ed.) Jakes, 'Microwave Mobile Communications' Wiley: NewYork, USA, 1974.

[9] N. C. Beaulieu and M. L. Merani, "Efficient simulation of correlated di-versity channels," Wireless C6mmunications and Networkidg Conrnce,Sept. 2000, Chscago, USA, pp. 207-210.

10-

w

m

10o -

I I4 -3 -2 -1 0 1 2 3

Normalized frequency offset fDTb4 "

Fig. 1. BER as a function of the normalized frequency offset JDT5 whenconventionial MMSE and the proposed FDFS-MMSE multiuser receivers are

employed and there is no near-far problem (PkIP OdE).

3

1344

P /P,=OdB

MMSE

M=1I

C%-'D" "P ~M=2M=3:

FDFS-MMSE

1-1,1

1I I

1 10-

In2

I o-I -,

w

m

1o03 -I I I-5 -4 -3 -2 -1 0 1 2 3 4 5

Normalized frequency offset fDTt

Fig. 2. BER as a function of the normalized frequency offset fDT whenconventional MMSE and the proposed FDFS-MMSE multiuser receivers are

emploed and the near-far effect is considered ( PkP1 1OdB).

I I0 2 4 6 8 10 12 14

E0 No (dB)16 18 20

Fig. 4. BER performance of the MMSE and FDFS-MMSE multiuserreceivers as a function of signal-to-noise ratio in the presence of frequencyoffset and near-far problems.

U***

*M-MMSEa FDFS-MMSE (M=1)-*- FDFS-MMSE (M=2)

1.OxilO'

9.OxlO-2

8.OxlO

7.0x10'8.OxlO_

5.OxlO0-2

4.Oxl102

fDTb =223 P/ P=1OdB-b Walsh-HadamardA Orthogonal Gold

A. Ak

A A A A A A A At ^ E

AAO .AA~ .A i:

M-1A

A

A

3.ox -_jo:k t2A Ai, o

2.Ox10'2 -

1 .Ox, -. . I I

4 8 12 16 20Desired user index i

24 28 32

I I I I I0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Near-far ratio Pk Pl (dB)

Fig. 3. BER comparison of MMSE and FDFS-MMSE multiuser receivers

under different near-far conditions.

Fig. 5. Effect of spreading codes and frequency upsampling factor M on

the BER performance of the FDFS-MMSE multiuser receiver in the presenceof frequency offset and near-far problems.

4

1345

P /P,=lOdB MMSE-

-0 ~~~~~~M=1CU

0 ~~~~M=2-

FDFS-MMSE

f%T =2/3, P,/ P=lIOdB

D

- M-MMSE-o- FDFS-MMSE (M=1)

FDFS-MMSE (M=2)

fjTb 2/3

10-

wLLco

102

2

10

| j r1 * B 8 , W 8 * , i: :: * * * i: | * | s X X s * i s w w | w w i fin, XEX |....

loD*v

.w

0"

Ml

j