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Multiuser TH-precoding for TDDCDMA overmultipath channels

I. Berenguer, A. Hst-Madsen and X. Wang

Abstract: Nonlinear precoding schemes for downlink time-division duplexCDMA systems overmultipath fading channels, are considered. First, the capacity results of a downlink CDMA systemwith either multiuser detection or precoding, were obtained and compared. It is seen that the twoschemes exhibit similar capacity regions for both sum rate and maximum equal rate, which motiv-ates the development of efficient nonlinear transmitter precoding techniques to reduce the receivercomplexity at the mobile units without degrading the system performance. We then develop bothbit-wise and chip-wise TomlinsonHarashima (TH) multiuser precoding methods for downlinkCDMA with multipath, to remove multi-user interference, inter-chip interference and inter-symbolinterference. Efficient algorithms for multiuser power loading and ordering are also developed.Implementation of the proposed TH-precoding schemes in time-varying channels based onchannel prediction is addressed as well. Simulations results are provided to demonstrate the effec-tiveness of the proposed techniques in suppressing interference in downlink CDMA.

1 Introduction

Multiuser detection (MUD) techniques are consideredpowerful for interference suppression in CDMA systems,especially in uplinks, where the base-station receiver hasthe knowledge of all users spreading sequences andchannel states, and can perform sophisticated signal proces-sing [1]. In the downlinks, however, the mobile receivertypically has only the knowledge of its own spreadingsequence and channel state. Although adaptive linearMUD (either training-based or blind) can be employed forsuch scenario, the performance can be limited because ofthe linear constraint on the detector. Moreover, the powerconstraint of the mobile calls for simple receiver processing.On the other hand, the precoding schemes for downlinkCDMA effiectively transfer the signal processing forinterference suppression from the mobile receiver to thebase-station transmitter. This approach is feasible if thebase-station can estimate the downlink channels of allusers [e.g. in systems employing time-division duplexing(TDD) where the uplink and downlink channels are recipro-cal]. In [2], a precoding method was proposed which isessentially an implementation of the RAKE receiver at thetransmitter. Hence this approach does not attempt to miti-gate the multiple-access interference (MAI). Recently,different linear precoding techniques have been proposedto combat MAI and inter-chip interference but without con-sidering inter-symbol interference (ISI) [3, 4]. If the ISI ispresent then the complexity of these techniques becomes

# The Institution of Engineering and Technology 2007

doi:10.1049/iet-com:20060510

Paper first received 31st August 2006 and in revised form 22nd January 2007

I. Berenguer is with the Department of Engineering, University of Cambridge,Cambridge, UK

A. Hst-Madsen is with the Department of Electrical Engineering, University ofHawaii, Honolulu, Hawaii

X. Wang is with the Department of Electrical Engineering, Columbia University,New York, NY, USA

E-mail: [email protected]

IET Commun., 2007, 1, (4), pp. 739750

prohibitive since the dimension of the matrix filter is pro-portional to the data frame length multiplied by thenumber of users (i.e. block processing). More recently,bit-wise linear precoding methods have been proposed toreduce the precoding complexity in the presence ISI [5].

The downlink CDMA is a special case of broadcast chan-nels. There has been significant recent interest in character-ising the capacity of broadcast channels. In particular, it hasbeen shown that when the interference is non-causallyknown to the transmitter and unknown to the receiver, thecapacity is the same as if the interference were notpresent a result known as dirty paper coding. Theseresults were originally proved for Gaussian channels [6],and have been generalised to other types of causal interfer-ence [79]. Several practical suboptimal implementationsof dirty paper coding based on TomlinsonHarashima(TH) precoding [10, 11] have been proposed, for examplefor digital subscriber line systems [12], for multi-antennasystems [13, 14] and CDMA systems [15].

In this paper, we first obtain the capacity regions of adownlink CDMA system employing either MUD or precod-ing. It is seen that these two approaches provide similarcapacity regions, but not equivalent, suggesting that precod-ing can potentially achieve similar performance offered byMUD and reduce the complexity of the mobile user. Thismotivates the development of practical approaches to dirty-paper coding for downlink TDDCDMA systems that willbe presented in the second part of the paper.

In the second part of the paper, we extend the nonlinearprecoding method in [15] to systems with simpler receivers,that is without channel state information (CSI) and with ISI.Note that the work in [15] assumes that each userimplements a RAKE receiver and hence assumes the knowl-edge of CSI at the receiver. In CDMA systems, we havemore degrees of freedom: the combination of (a) the spread-ing at the transmitter, (b) despreading at the receiver, (c)operations at the receiver and (d) precoding operation forcancelling MUI, ICI and ISI can be implemented in manydifferent ways given different results, as shown in thispaper. In particular, in this paper, we propose a new

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chip-wise precoding scheme that combines the spreadingand TH-precoding operations. Our results show that witha similar complexity at the transmitter, our chip-wise sol-ution with only a fixed matched filter (to the original spread-ing sequence) at the receiver can outperform the THprecoder with a RAKE receiver (i.e. with CSI at the recei-ver) proposed in [14, 15]. Furthermore, efficient algorithmsfor multiuser power loading and ordering are developed.Implementation of the proposed TH-precoding schemes intime-varying channels based on channel prediction is alsoaddressed.

2 Downlink capacity regions of MUD andprecoding

In TDD systems, the uplink channel and the downlinkchannel for each individual user is the same. Hence thebase station can use the uplink channel information toperform preprocessing for the downlink and thereby transfersophisticated signal processing from the receiver end to thetransmitter end, that is to replace MUD (receiver proces-sing) by precoding (transmitter processing). In thissection, we present and compare the capacity results of pre-coding and MUD in the downlink of a CDMA system.These two approaches for downlink CDMA are illustratedschematically in Fig. 1. Note that this is a special case ofthe multiple-input multiple-output (MIMO) broadcastchannel for which recent progressive developments [7,1619] have led to what is considered as the final solutionto the capacity region for the general broadcast channel[20]. In what follows, we use results from [7, 20] toobtain and compare the capacity regions of precoding andMUD in the downlink of a CDMA system.

Consider a synchronous CDMA system with K users sig-nalling over a real-valued AWGN channel. Let fk and sk bethe channel gain and the spreading signature of the kth user,respectively. Denote S [s1, . . ., sK]. Then R STS is theK K cross-correlation matrix of the spreading waveformsof all users.

2.1 Multiuser detection

Assume that the users are ordered according to theirpath gains so that f1 f2 fK. The received signalat the kth mobile receiver is given by rk fkPK

1 xs nk , where nk N (0, I). Note that in thiscase symbols from different users x1, . . . , xK are indepen-dently encoded. Denote x [x1, . . . , xK]T. A sufficient

Fig. 1 Schematic illustration of MUD and precoding in downlinkCDMA systems

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statistic for x is the output of a bank of matched-filters [1]

yk W [sT1 rk , s

T2 rk , , sTKrk]T fkRx vk (1)

with E{vkvTk } R. The kth user then makes a decision on its

own data xk based on yk. Denote rk as the kth column of Rand

Qk WR f 2kXk11

PrrT (2)

where Pk WE{x2k}. Denote PT W

PKk1 Pk as the total trans-

mit power. We have the following result regarding an outerbound on the rate region.

Proposition 1: Consider the channel model (1) and supposethat each users data is encoded independently. Then themultiuser rate tuple (R1, . . . , RK) must satisfy

Rk 1

2log 1 Pk f 2k rTkQ1k rk

, k 1, . . . ,K (3)

for some Pk 1, . . . ,K, satisfying Pk 0 andPKk1 Pk PT.

Proof: Define y0k yk=fk . Then we can rewrite the follow-ing equivalent model to (1)

y01 Rx u01 and y0k y0k1 u0k , k 2, . . . , K (4)

where the u01, . . . , u0K are independent, zero-mean Gaussian

vectors, and E{u0ku0Tk } f 2k R. The model (4) is the same as

the aligned degraded broadcast channel model in [20]. Thedifference is that here each xk is encoded independently.This corresponds to the model in [20] with Bi zero exceptfor the ith diagonal element and S a diagonal matrix. Itcan be checked that the proof still applies with these restric-tions, and we therefore obtain a rate given in [20], whichhere becomes

Rk 1

2log

detPk

1 PrrT

Pk1 E{u

0u

T }

det

Pk11 Prr

T

Pk1 E{u

0u

T }

1A

12

logdet (Qk f 2k PkrkrTk

detQk

(5)

Let Fk be a Cholesky factor of Qk, that is FkFTk Qk . Then

det (Qk Pkf 2k rkrTk )

det Fk I ffiffiffiffiffiPk

pfkF

1k rk

ffiffiffiffiffiPk

pfkF

1k rk

T FTk

(1 Pkf 2k rTkQ1k rk) detQk (6)

where in (6) we used the following identity det (AB) det(BA) det (A) det (B), and det (I aaT) aTa 1, wherea is a vect