EURASIP Journal on Wireless Communications and Networking 2005:2, 155–162c© 2005 Hindawi Publishing Corporation

Adaptive Iterative Soft-Input Soft-OutputParallel Decision-Feedback Detectors forAsynchronous Coded DS-CDMA Systems

Wei ZhangSchool of Information Technology and Engineering (SITE), University of Ottawa, 800 King Edward Avenue, Ottawa,ON, Canada K1N 6N5Email: weizhang@site.uottawa.ca

Claude D’AmoursSchool of Information Technology and Engineering (SITE), University of Ottawa, 800 King Edward Avenue, Ottawa,ON, Canada K1N 6N5Email: damours@site.uottawa.ca

Abbas YongacogluSchool of Information Technology and Engineering (SITE), University of Ottawa, 800 King Edward Avenue, Ottawa,Ontario, Canada K1N 6N5Email: yongacog@site.uottawa.ca

Received 29 April 2004; Revised 4 October 2004

The optimum and many suboptimum iterative soft-input soft-output (SISO) multiuser detectors require a priori informationabout the multiuser system, such as the users’ transmitted signature waveforms, relative delays, as well as the channel impulseresponse. In this paper, we employ adaptive algorithms in the SISO multiuser detector in order to avoid the need for this a prioriinformation. First, we derive the optimum SISO parallel decision-feedback detector for asynchronous coded DS-CDMA systems.Then, we propose two adaptive versions of this SISO detector, which are based on the normalized least mean square (NLMS)and recursive least squares (RLS) algorithms. Our SISO adaptive detectors effectively exploit the a priori information of codedsymbols, whose soft inputs are obtained from a bank of single-user decoders. Furthermore, we consider how to select practicalfinite feedforward and feedback filter lengths to obtain a good tradeoff between the performance and computational complexityof the receiver.

Keywords and phrases: soft-input soft-output multiuser detection, adaptive multiuser detection, parallel decision-feedback de-tection, adaptive soft-input soft-output parallel decision-feedback detection, asynchronous coded CDMA systems.

1. INTRODUCTION

Iterative soft-input soft-output (SISO) multiuser receiversfor coded multiuser systems have received widespread atten-tion since they can provide near single-user performance ina system with multiple-access interference (MAI) by itera-tively combining multiuser detection and single-user decod-ing. The optimum SISO multiuser detector employs eitherthe cross-entropy minimization [1] or the maximum a pos-teriori (MAP) algorithm [2]. The computational complex-ity of these techniques is exponentially proportional to the

This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.

number of users which can be prohibitive for large systems.Therefore, much work has been done on reduced-complexitysuboptimum SISO multiuser detectors.

SISO multiuser detection based on the reduced-com-plexity MAP algorithms which are applied to the trellis of themultiple-access channel is proposed in [3, 4]. The simplestSISO multiuser detector is the soft interference canceller pro-posed in [5, 6], which has a linear computational complexityin terms of the number of users. However, it slowly convergesto the performance of the single-user system. Linear itera-tive SISO multiuser detectors, which employ a decorrelator[7] or a minimum mean square error (MMSE) filter [8] onthe output of the soft interference cancellation, significantlyimprove the system performance. Moreover, their compu-tational complexity is only a cubic function of the number

156 EURASIP Journal on Wireless Communications and Networking

Channelencoder 1

......

......

IModulator &

spreader 1

IChannelencoder 2

Modulator &spreader 2

Channelencoder K

Modulator &spreader K

I

Channel

AdaptiveSISO

multiuserdetector

D SISOdecoder1

I

D SISOdecoder2

I

D SISOdecoderK

I

Final decisions

Final decisions

Final decisions

Figure 1: A general coded DS-CDMA system with an iterative receiver (I and D denote interleavers and deinterleavers, respectively).

of users. In [9, 10], nonlinear MMSE-based SISO decision-feedback detectors are investigated.

The above optimum and suboptimum SISO multiuserdetectors require accurate a priori information about themultiuser system, such as all users’ received signature wave-forms which are functions of their transmitted signaturewaveforms, relative delays, and the channel impulse re-sponse. In practical situations, this information may not beeasily obtainable for time-varying fading channels.

Fortunately, if the system parameters are constant orslowly varying, adaptive detectors (non-SISO) can success-fully track these parameters from the received signal [11,12, 13, 14, 15]. In [16], an adaptive SISO parallel decision-feedback detector for synchronous direct-sequence code-division multiple-access (DS-CDMA) systems with shortspreading sequences is presented. By employing an approxi-mate least squares algorithm and soft symbol estimates, thedetector exploits the joint statistics of soft symbol estimatesand transmitted symbols.

In this paper, we use adaptive algorithms in the iterativeSISO parallel decision-feedback detector (PDFD) for asyn-chronous coded DS-CDMA systems in order to avoid theneed for the a priori information about system parameters,such as multiple users’ spreading codes and relative delaysbetween users. First, we derive the optimum SISO paral-lel decision-feedback detector assuming the receiver knowsthe transmitted signature waveforms and relative delays be-tween all the users. Then, we propose two adaptive versionsof this SISO detector, which employ the normalized leastmean square (NLMS) and recursive least squares (RLS) al-gorithms to estimate the filter coefficients of the detector. Allusers are assumed to employ short spreading codes. A train-ing sequence is required for each user. Our adaptive SISO de-tectors effectively exploit the a priori information of codedsymbols, which is obtained from the soft outputs of a bankof single-user decoders, to further improve their convergenceperformance.

Furthermore, for adaptive implementation of the SISOPDFD for asynchronous DS-CDMA systems, we select prac-tical finite feedforward and feedback filter lengths to obtaina good tradeoff between the system performance and com-putational complexity of the receiver. We employ a feedfor-ward filter which covers a two-symbol duration for each userand we consider several options for the feedback filter length.

Monte-Carlo simulation results for these adaptive SISO de-tectors are presented and compared.

The outline of the rest of this paper is as follows. A systemmodel of asynchronous coded DS-CDMA systems is intro-duced in Section 2. The optimum SISO PDFD with a generalprocessing window for asynchronous coded DS-CDMA sys-tems is derived in Section 3. Adaptive SISO PDFDs are pro-posed in Section 4, which are based on the NLMS and RLS al-gorithms. Monte-Carlo simulation results are presented andcompared in Section 5. Finally in Section 6, the conclusionsare given.

2. SYSTEM MODEL AND NOTATION

Throughout the paper, matrices and vectors are denoted asboldface uppercases and lowercases, respectively. Notations(·)∗, (·)H , and (·)T denote the complex conjugate, Hermi-tian transpose, and transpose, respectively.

A general coded DS-CDMA system with an iterative re-ceiver is shown in Figure 1. There are K active users inthe system. The information bits of each user are first en-coded, then interleaved, modulated, and spread before theyare transmitted over the channel. The iterative receiver con-sists of two parts, an adaptive soft-input soft-output mul-tiuser detector and a bank of SISO single-user decoders,which are separated by deinterleavers and interleavers. Thesetwo parts cooperate iteratively by transferring updated ex-trinsic soft information of coded symbols between them.

In our paper, we consider an asynchronous coded DS-CDMA system over the additive white Gaussian noise(AWGN) channel. The equivalent baseband received mul-tiuser signal is

r(t) =K∑k=1

Nb∑i=1

bk(i)sk(t − iT − τk

)+ n(t), (1)

where K is the number of active users, Nb is the number ofsymbols transmitted by each user, bk(i) is the ith coded sym-bol of the kth user, sk(t) is its transmitted signature wave-form, τk and T are the delay of user k and the symbol inter-val, respectively, and n(t) is an additive white Gaussian noiseprocess with double-sided power spectral density N0/2. Eachuser’s information bits are encoded and then BPSK modu-lated, that is, bk(i) ∈ {+1,−1}.

Adaptive Iterative SISO Parallel Decision-Feedback Detectors 157

Sk =

τk/Tc

N

0

(N − τk/Tc) N(Nb + 1)×Nb

0

. . .

Figure 2: System signature matrix Sk of user k, where the nonzeropart of each column is the signature vector sk of user k.

For simple implementation, we consider a chip-synchro-nous and symbol-asynchronous DS-CDMA system. All us-ers’ delays are uniformly distributed in [0,T] and are mul-tiples of Tc, which is the chip interval. In the receiver, firstwe employ a chip-matched filter on the received signal r(t)and then sample its output at frequency 1/Tc. If the systemis chip-asynchronous, we can oversample the output of thechip-matched filter and design a fractionally spaced feedfor-ward filter instead. Without loss of generality and for sim-plicity of notation, we assume the delays of multiple userssatisfy the following inequality:

0 ≤ τ1 ≤ τ2 ≤ · · · ≤ τK ≤ T. (2)

The symbol vector consisting of the transmitted symbolsof all users is denoted as

b =[

bT1 , . . . , bT

k , . . . , bTK

]TKNb×1

, (3)

where

bk =[bk(1), bk(2), . . . , bk

(Nb)]T

. (4)

The received signal vector r at the output of the chip-matched filter during the whole symbol transmission intervalcan be expressed as follows:

r = Sb + n, (5)

where S is the system signature matrix and can be expressedas

S = [S1, . . . , Sk, . . . , SK]N(Nb+1)×KNb

. (6)

The construction of Sk in (6) is shown in Figure 2, where thenonzero part of each column is the signature vector sk of userk and N is the number of chips per coded symbol. The vec-tor n in (5) is an N(Nb + 1) × 1 column vector which repre-sents the output noise component of the chip-matched filter.It has zero mean and covariance matrix σ2

nI, where σ2n is the

variance of the output noise component.

3. OPTIMUM SISO PDFD FOR ASYNCHRONOUSDS-CDMA SYSTEMS

In general, the optimum SISO PDFD filters for asynchronousDS-CDMA systems have infinite lengths [17]. For imple-mentation purposes, we consider finite-length feedforwardand feedback filters. Furthermore, these filters are suitablefor use in adaptive applications. The use of these filters in ouradaptive detectors will be discussed in detail in Section 4.

In the receiver, we assume that the processing windowlength is Np, which is measured in chips and is much lessthan Nb × N . In each processing window, the received sig-nal vector is denoted as rNp×1, which consists of Np rows of rfalling to this processing window. The windowed system sig-nature matrix SNp×KNb and noise vector nNp×1 consist of Np

corresponding rows of S and n, respectively. Therefore, wehave the following equation:

r = Sb + n. (7)

We can write b as the following sum:

b = bU + bD, (8)

where bU consists of the symbols which are not fedback andits other elements are zeros. The nonzero elements of bD con-sist of the fedback symbols. They have no common elements.In the same way by which we construct bU and bD, we extractcolumns of S and construct the corresponding signature ma-trices SU and SD. Therefore, the windowed received signalvector r can also be expressed as

r = SUbU + SDbD + n. (9)

The feedforward filter of user k has Np taps and is de-noted by a column vector m f k. The feedback filter mbk ofuser k has the size KNb×1, whose nonzero elements are cor-responding to fedback symbols. That is, its effective numberof taps is determined by the number of fedback symbols. Theoptimum filters satisfy the following minimum mean squareerror (MMSE) criterion:

minm f k ,mbk

E[bk(i)−mH

f k · r−mHbk · bD

]2. (10)

Nonzero elements of bD are soft symbol estimates of those el-ements of bD, respectively. We will introduce the soft symbolestimate of each coded symbol in the following.

The soft inputs of a SISO multiuser detector, {λin[bk( j)],1 ≤ k ≤ K , 1 ≤ j ≤ Nb}, are extrinsic log-likelihood ratios(LLRs) of {bk( j)} provided by a bank of K single-user de-coders. Based on these inputs, we can obtain the soft symbolestimate of {bk( j)}:

bk( j)=E[bk( j)

∣∣λin[bk( j)

]] = tanh(λin[bk( j)

]2

). (11)

Furthermore, we have the following a priori statistics (12) fornonzero elements of bU and bD. For fedback symbols, theirmean values are their soft symbol estimates, while nonfed-back symbols have zero mean. Note that bk(i) in (10) belongs

158 EURASIP Journal on Wireless Communications and Networking

to nonfedback symbols. Denote u and v as one of the nonzeroelements of bU and bD, respectively. The soft symbol estimateof v is denoted as v. Thus, we have

E[u] = 0,

E[u2] = 1,

E[v] = v,

E[v2] = 1− (v)2.

(12)

We also assume that all users’ transmitted symbols are inde-pendent of one another and of the background noise vectorn as well.

Employing the above statistics about the coded symbols,we can get the optimum feedforward and feedback filters ofuser k which satisfy the MMSE criterion in (10):

m f k =(

RU + RD + σ2nI)−1 · sbk(i), (13)

mbk = −SHD ·m f k, (14)

where

RU = SUSHU ,

RD = SD

⌊I− diag

(bDbH

D

)⌋SHD ,

(15)

and sbk(i) is a one column of SU , whose column index is thesame as the row index of bk(i) in bU . The feedforward filterin (13) is actually a linear MMSE filter which suppresses theinterference from non-fedback symbols, as well as the resid-ual interference after canceling the fedback symbols and thebackground Gaussian noise.

From (15), we can see that the optimum feedforward andfeedback filters require the knowledge of all users’ signaturevectors and delays. In order to avoid the need for this infor-mation, we can adaptively implement the SISO PDFD, whichwill be discussed in the next section.

4. ADAPTIVE SISO PDFD FOR ASYNCHRONOUSDS-CDMA SYSTEMS

In this section, we assume that both short spreading codesand delays of all users are unknown to the receiver. We designand employ adaptive SISO PDFDs to track these parametersfrom the received signal directly.

It is well known that the asynchronous system perfor-mance can be improved by using detection filters with an in-creased number of taps. However, increasing the number oftaps increases the computational complexity of the detector.Moreover, this will have an adverse effect on the convergencespeed. Therefore, we need to select suitable filter lengths toachieve a good tradeoff among the system performance, de-tector complexity, and system overhead.

In the parallel decision-feedback detector, the feedfor-ward and feedback filters cooperate to suppress the multiple-access interference. Specifically, the feedback filter tries tocancel some interfering symbols, while the feedforward filter

τ1

τ2

τK

b1(i− 1)

b2(i− 1)

The processing window for the ith symbol

b1(i) b1(i + 1)

b2(i) b2(i + 1)

bK (i− 1) bK (i) bK (i + 1)

...

Figure 3: An asynchronous system.

suppresses the remaining MAI, as well as the residual inter-ference due to imperfect cancellation by the feedback filterand the background Gaussian noise. Therefore, if the feed-back filter effectively cancels most of the interference causedby the interfering symbols, the remaining interference to besuppressed by the feedforward filter is reduced.

On each iteration except for the first one, the SISO PDFDcan obtain soft symbol estimates of all symbols from soft in-puts. Thus, we have both causal and noncausal soft symboldecisions of interfering symbols for the interested symbol.We may cancel part or all of them by the feedback filter.

In this paper, we employ a feedforward filter which coversa two-symbol duration and consider several options for thefeedback filter length. The length of the observation intervalis 2T , which is the minimum length such that one completesymbol of each user falls in this interval regardless of its rel-ative delay. Figure 3 shows the processing window of the de-tector in the ith signaling interval. The output vector r(i) ofthe chip-matched filter in this processing window is

r(i) = [P− P0 P+]b(i− 1)

b(i)b(i + 1)

+ n(i), (16)

where b(i) = [b1(i) b2(i) · · · bK (i)]T and n(i) is a Gaus-sian random vector with zero mean and covariance matrixσ2nI(2N×2N). We define the punctured signature vectors of userk as

p−k =[(

srk)H

0H]H

(2N×1),

p0k =

[0H

(1×Nrk ) sHk 0H

(1×Nlk)

]H(2N×1)

,

p+k =

[0H

(slk)H]H

(2N×1),

(17)

where 0 is a column vector. slk and srk are denoted in Figure 4and are parts of sk:

sk =[(

slk)H (

srk)H]H. (18)

Adaptive Iterative SISO Parallel Decision-Feedback Detectors 159

slk srk

Nlkchips Nr

kchips

The processing window edge

Figure 4: Punctured signatures of the kth user in the asynchronoussystem.

The matrices P−, P0, and P+ in (16) are constructed as fol-lows:

P− = [p−1 p−2 · · · p−K],

P0 = [p01 p0

2 · · · p0K

],

P+ = [p+1 p+

2 · · · p+K

].

(19)

Thus, when multiple users’ delays are unknown to the re-ceiver, for the symbol of interest bk(i) of user k, it has atmost (3K − 1) interfering symbols. For implementation ofthe adaptive SISO multiuser detector in Figure 1, we considerthree adaptive SISO PDFDs with the same feedforward filterlength, that is, 2N taps. The feedback filter of the first de-tector (labeled as detector1) has (K − 1) taps which tries tocancel the current (K − 1) interfering symbols for the de-sired symbol. Detector2 has a feedback filter with (2K − 1)taps which tries to cancel the current (K − 1) and previousK interfering symbols. The feedback filter of detector3 has(3K − 1) taps and tries to cancel all possible previous, cur-rent, and future interfering symbols.

In the following, we employ the NLMS and RLS algo-rithms in adaptive SISO PDFDs to update the feedforwardfilter m f k and feedback filter mbk. Moreover, the a priori in-formation of coded symbols is employed efficiently to im-prove the performance of the adaptive detector. The adaptiveSISO PDFD requires only a training sequence for each userto estimate all filter coefficients.

The adaptive detector employing the NLMS algorithm toresolve the MMSE criterion in (10) updates the feedforwardand feedback filters of user k as follows for m = 0, 1, 2, . . .:

m f k(m + 1) = m f k(m)− µ f

a +∥∥r(m)

∥∥2

∣∣∣bk(m)∣∣∣e∗k (m)r(m),

mbk(m + 1)=mbk(m)− µb

a +∥∥∥bD(m)

∥∥∥2

∣∣∣bk(m)∣∣∣e∗k (m)bD(m),

(20)

where m is the recursive index and also the time index, µ f

and µb ∈ (0, 2) and are step sizes for the feedforward andfeedback filters, respectively. a is a small positive constant.The error signal for the mth recursion is

ek(m) = bk(m)−mHf k(m) · r(m)−mH

bk(m) · bD(m), (21)

where bk(m) = bk(m) and bD(m) = bD(m) in the training

mode, bk(m) = bk(m) and bD(m) = bD(m) in the decision-

directed mode. Furthermore, in the decision-directed mode,|bk(m)| is used as the reliability of the error signal ek(m) in(20). Both filters are updated per symbol and their initialstates are m f k(0) = 0 and mbk(0) = 0.

When the detector employs the RLS algorithm, we denotewk(m)=[mH

f k(m) mHbk(m)]H and u(m)=[rH(m) bH

D (m)]H .Then the filters are updated for m = 0, 1, 2, . . .:

gk(m + 1) = λ−1Pk(m)u(m + 1)1 + λ−1uH(m + 1)Pk(m)u(m + 1)

,

ξk(m + 1) = bk(m + 1)−wHk (m)u(m + 1),

wk(m + 1)=wk(m)+gk(m+1)∣∣∣bk(m+1)

∣∣∣ξ∗k (m+1),

Pk(m+1)=λ−1Pk(m)−λ−1gk(m+1)uH(m+1)Pk(m).

(22)

The algorithm is initialized with Pk(0) = δ−1I, where δ is asmall positive number and wk(0) = 0.

Both of the adaptive detectors described above try to ex-ploit the joint statistics of the received signal vector r, the

transmitted symbol bk or its soft estimate bk, and the soft

symbol estimates bD which are fedback. In the first iteration,since there is no fedback information of coded symbols, weonly employ a linear MMSE feedforward filter and set thefeedback filter coefficients to zeros for each user.

The output of the adaptive SISO PDFD is

yk(m) = mHf k(m) · r(m) + mH

bk(m) · bD(m). (23)

Applying the Gaussian assumption to the output in (23), wecan calculate the soft outputs of the SISO PDFD. For the mthsymbol of the kth user, the output yk(m) can be expressed as

yk(m) = µkbk(m) + ηk, (24)

where µk is a constant and ηk is a Gaussian random variablewith zero mean and variance σ2

ηk :

µk = E[b∗k (m)yk(m)

],

σ2ηk = E

[yk(m)− µkbk(m)

]2.

(25)

Estimates of (25) can be obtained by the corresponding sam-ple averages in (26), respectively, where we replace bk(m) bybk(m) in these equations:

µk = 1Nb

Nb∑m=1

b∗k (m)yk(m),

σ2ηk =

1Nb

Nb∑m=1

[yk(m)− µkbk(m)

]2.

(26)

The soft output, that is, the extrinsic log-likelihood ratio, ofbk(m) is

λok(m) = logP[yk(m)

∣∣bk(m) = +1]

P[yk(m)

∣∣bk(m) = −1] = 2µk yk(m)

σ2ηk

. (27)

160 EURASIP Journal on Wireless Communications and Networking

5. SIMULATION RESULTS

The DS-CDMA system which we simulate in this section has12 active users. All users employ the same convolutional codewith rate 1/2, constraint length 7, and generators [1011011],[1111001]. Each user has a randomly selected short spread-ing code. The spreading factor is 16 chips per informationbit. The system load is 12/16 (K/spreading factor). Multipleusers’ delays are randomly selected and fixed during simula-tion.

There are 300 training symbols which are randomly se-lected and inserted at the beginning of coded symbol framesof each user. SISO single-user decoders are based on thelog-MAP algorithm in [18]. Noise random variables at theoutput of the chip-matched filter are identical independentGaussian random variables with zero mean and N0/2 vari-ance.

At the first iteration, since there are no soft inputs fromsingle-user decoders, only a feedforward filter is employedfor each user. That is, at this time, a linear minimum meansquare error filter is used instead. It is initially trained by thetraining symbols, and then is used for the following trans-mitted coded symbols. For the later iterations, both the feed-forward and feedback filters are employed. After the train-ing mode, they are updated by fedback symbol decisions.In the first two iterations, the filter coefficients are initial-ized to zeros before the adaptive algorithm is employed. Ineach of the following iterations, the filter coefficients areset to the values obtained at the end of the previous itera-tion.

We consider an asynchronous DS-CDMA system overthe additive white Gaussian noise (AWGN) channel. It isassumed that the receiver has no knowledge of the shortspreading codes used by the users and their delays. Threeadaptive SISO PDFDs proposed in Section 4 are simulated.Figures 5 and 6 show average bit error rates of all users in thefirst, second, and tenth iterations provided by three adaptivedetectors based on the NLMS and RLS algorithms, respec-tively. In (20) of the NLMS algorithm, we use a = 0.00001,and step sizes µ f = µb = 0.2 in the training mode andµ f = µb = 0.05 in the decision-directed mode. Parametersin (22) of the RLS algorithm are λ = 1 and δ = 0.04. Forcomparison, we also show the bit error rate performance ofthe single-user system in these two figures, where the user’sspreading code and delay are known to the receiver. In Fig-ures 5 and 6, we observe that after the first iteration, all threedetectors have similar performances and their curves appearto overlap. A similar behaviour is observed for the second it-eration of detector1 and detector2 in Figure 5 and all threedetectors in Figure 6.

We can see that with our adaptive SISO detectors, thesystem performance is improved with the increased num-ber of iterations. Furthermore, Figure 6 shows that the per-formance provided by the adaptive RLS receiver approachesthe performance of the single-user system after a few itera-tions at high signal-to-noise ratios. Among the three adaptiveSISO PDFDs proposed in Section 4, detector3 provides thebest performance, though it has the highest computational

100

10−1

10−2

10−3

10−4

10−5

2 3 4 5 6 7 8

Eb/N0(dB)

Bit

erro

rra

te

Detector1, 1 iter.Detector1, 2 iter.Detector1, 10 iter.Detector2, 1 iter.Detector2, 2 iter.

Detector2, 10 iter.Detector3, 1 iter.Detector3, 2 iter.Detector3, 10 iter.SU

Figure 5: Bit error rate performance provided by three NLMS adap-tive SISO PDFDs for the asynchronous DS-CDMA system at thefirst, second, and tenth iterations, and that of the single-user system(SU).

100

10−1

10−2

10−3

10−4

10−5

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

Eb/N0(dB)

Bit

erro

rra

te

Detector1, 1 iter.Detector1, 2 iter.Detector1, 10 iter.Detector2, 1 iter.Detector2, 2 iter.

Detector2, 10 iter.

Detector3, 1 iter.Detector3, 2 iter.Detector3, 10 iter.SU

Figure 6: Bit error rate performance provided by three RLS adap-tive SISO PDFDs for the asynchronous DS-CDMA system at thefirst, second, and tenth iterations, and that of the single-user system(SU).

complexity, since its feedback filter has the maximum num-ber of taps compared with the other two detectors.

Adaptive Iterative SISO Parallel Decision-Feedback Detectors 161

2.5

2

1.5

1

0.5

00 50 100 150 200 250 300

Update number in the adaptive algorithms

Squ

ared

erro

r

RLS algorithm

NLMS algorithm

Figure 7: Comparison between the experimental learning curvesof the adaptive SISO PDFD detector3 based on the NLMS and RLSalgorithms after the second iteration during the training mode atSNR = 6 dB.

By comparing average bit error rates of all the usersprovided by the adaptive detector based on the RLS algo-rithm in Figure 6 and those obtained by the NLMS algo-rithm in Figure 5, we can see that the bit error rate per-formance provided by the adaptive SISO PDFD based onthe RLS algorithm is better than the one provided by thedetector based on the NLMS algorithm. For example, ata bit error rate 10−3, detector3 based on the RLS algo-rithm has about 0.7 dB gain with respect to detector3 basedon the NLMS algorithm. This is due to the faster conver-gence property of the RLS algorithm, which is shown byFigure 7. The averaged squared errors e2

k(m) and ξ2k (m) af-

ter the second iteration of the adaptive detector3 duringthe training mode versus the number of updates in theNLMS and RLS algorithms, respectively, are shown andcompared in Figure 7. We set the signal-to-noise (SNR) ra-tio of each user to 6 dB. Each curve of the squared er-ror is averaged over 200 independent trials of the exper-iment. However, the RLS algorithm has a greater com-putational complexity. Denote the length of the adaptivefilter as L. The computational complexity of the RLS andthe NLMS algorithms are ∼ O(L2) and ∼ O(L) per update,respectively.

6. CONCLUSIONS

In this paper, first we presented an optimum SISO paral-lel decision-feedback detector for asynchronous coded DS-CDMA systems, and then proposed an adaptive implemen-tation of it when all users’ signature waveforms and relativedelays were unknown to the receiver. All users were assumedto employ short spreading codes. A chip-synchronous andsymbol-asynchronous DS-CDMA system was considered.

A training sequence was required by each user. We showedthat the resulting system performance provided by adaptiveSISO PDFDs approaches that of the single-user system af-ter a few iterations at high signal-to-noise ratios. Moreover,the adaptive detector employing the RLS algorithm providesa better bit error rate performance than the adaptive detec-tor based on the NLMS algorithm, though at the expense ofhigher computational complexity. For asynchronous codedDS-CDMA systems, we further showed that the adaptive de-tector with more feedback filter taps gives a better bit errorrate performance.

REFERENCES

[1] M. Moher, “An iterative multiuser decoder for near-capacitycommunications,” IEEE Trans. Commun., vol. 46, no. 7, pp.870–880, 1998.

[2] L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decodingof linear codes for minimizing symbol error rate (Corresp.),”IEEE Trans. Inform. Theory, vol. 20, no. 2, pp. 284–287, 1974.

[3] P. D. Alexander, M. C. Reed, J. A. Asenstorfer, and C. B.Schlegel, “Iterative multiuser interference reduction: turboCDMA,” IEEE Trans. Commun., vol. 47, no. 7, pp. 1008–1014,1999.

[4] Z. Qin, K. C. Teh, and E. Gunawan, “Iterative multiuser de-tection for asynchronous CDMA with concatenated convolu-tional coding,” IEEE J. Select. Areas Commun., vol. 19, no. 9,pp. 1784–1792, 2001.

[5] P. Alexander, A. Grant, and M. Reed, “Iterative detection incode-division multiple-access with error control coding,” Eu-ropean Transactions on Telecommunication, vol. 9, no. 5, pp.419–426, 1998.

[6] Z. Shi and C. Schlegel, “Joint iterative decoding of seriallyconcatenated error control coded CDMA,” IEEE J. Select. Ar-eas Commun., vol. 19, no. 8, pp. 1646–1653, 2001.

[7] W. Zhang and C. D’Amours, “Iterative multiuser detectionand decoding for highly correlated narrowband systems andheavily loaded CDMA systems,” Canadian Journal of Electricaland Computer Engineering, vol. 28, no. 2, pp. 75–80, 2003.

[8] X. Wang and H. V. Poor, “Iterative (turbo) soft interferencecancellation and decoding for coded CDMA,” IEEE Trans.Commun., vol. 47, no. 7, pp. 1046–1061, 1999.

[9] H. E. Gamal and E. Geraniotis, “Iterative multiuser detec-tion for coded CDMA signals in AWGN and fading channels,”IEEE J. Select. Areas Commun., vol. 18, no. 1, pp. 30–41, 2000.

[10] B. F. Beidas, H. E. Gamal, and S. Kay, “Iterative interferencecancellation for high spectral efficiency satellite communica-tions,” IEEE Trans. Commun., vol. 50, no. 1, pp. 31–36, 2002.

[11] M. L. Honig and H. V. Poor, “Adaptive interference suppres-sion in wireless communication systems,” in Wireless Commu-nications: Signal Processing Perspectives, Prentice-Hall, UpperSaddle River, NJ, USA, 1998, chapter 2.

[12] H. V. Poor, “Adaptivity in multiple-access communications,”in Proc. 34th Conference on Decision and Control, pp. 835–840,New Orleans, La, USA, December 1995.

[13] P. B. Rapajic and B. S. Vucetic, “Adaptive receiver structuresfor asynchronous CDMA systems,” IEEE J. Select. Areas Com-mun., vol. 12, no. 4, pp. 685–697, 1994.

[14] P. B. Rapajic and D. K. Borah, “Adaptive MMSE maximumlikelihood CDMA multiuser detection,” IEEE J. Select. AreasCommun., vol. 17, no. 12, pp. 2110–2122, 1999.

[15] D. K. Borah and P. B. Rapajic, “Optimal adaptive multiuserdetection in unknown multipath channels,” IEEE J. Select. Ar-eas Commun., vol. 19, no. 6, pp. 1115–1127, 2001.

162 EURASIP Journal on Wireless Communications and Networking

[16] M. L. Honig, G. Woodward, and P. D. Alexander, “Adaptivemultiuser parallel-decision-feedback with iterative decoding,”in Proc. IEEE International Symposium on Information Theory(ISIT ’00), p. 335, Sorrento, Italy, June 2000.

[17] A. Duel-Hallen, “A family of multiuser decision-feedback de-tectors for asynchronous code-division multiple-access chan-nels,” IEEE Trans. Commun., vol. 43, no. 234, pp. 421–434,1995.

[18] A. J. Viterbi, “An intuitive justification and a simplified imple-mentation of the MAP decoder for convolutional codes,” IEEEJ. Select. Areas Commun., vol. 16, no. 2, pp. 260–264, 1998.

Wei Zhang received the B.A.Sc. degree fromXiDian University, China, in 1995, and theM.A.Sc. degree from Beijing University ofPosts and Telecommunications, China, in1998. Now she is pursuing a Ph.D. de-gree at the University of Ottawa, Canada.All of these are in electrical engineering.She worked as a software engineer in CTCCommunication Development Ltd, China,in 1998. In 1999, she joined Agilent Tech-nologies, Beijing, China, as a Research Scientist. Her research inter-est is in signal processing for the physical layer of wireless commu-nications.

Claude D’Amours graduated with the de-grees of B.A.Sc., M.A.Sc., and Ph.D. in elec-trical engineering from the University ofOttawa in 1990, 1992, and 1995, respec-tively. He was employed briefly at the Com-munications Research Centre in Ottawa as aSystems Engineer in 1995. From 1995–1999,he was employed as an Assistant Professorin the Department of Electrical and Com-puter Engineering, the Royal Military Col-lege in Kingston, Ontario, Canada. He is presently employed as anAssistant Professor in the School of Information Technology andEngineering, the University of Ottawa.

Abbas Yongacoglu received the B.S. degreefrom Bogazici University, Turkey, in 1973,the M. Eng. degree from the University ofToronto, Canada, in 1975, and the Ph.D. de-gree from the University of Ottawa, Canada,in 1987, all in electrical engineering. Heworked as a researcher and a System En-gineer at TUBITAK Marmara Research In-stitute, Turkey, Philips Research Labs, Hol-land, and Miller Communications Systems,Ottawa. In 1987, he joined the University of Ottawa as an AssistantProfessor. He became an Associate Professor in 1992 and a Full Pro-fessor in 1996. His area of research is digital communications withemphasis on modulation, coding, equalization, and multiple accessfor wireless and high-speed wireline communications.

Photograph © Turisme de Barcelona / J. Trullàs

Preliminary call for papers

The 2011 European Signal Processing Conference (EUSIPCO 2011) is thenineteenth in a series of conferences promoted by the European Association forSignal Processing (EURASIP, www.eurasip.org). This year edition will take placein Barcelona, capital city of Catalonia (Spain), and will be jointly organized by theCentre Tecnològic de Telecomunicacions de Catalunya (CTTC) and theUniversitat Politècnica de Catalunya (UPC).EUSIPCO 2011 will focus on key aspects of signal processing theory and

li ti li t d b l A t f b i i ill b b d lit

Organizing Committee

Honorary ChairMiguel A. Lagunas (CTTC)

General ChairAna I. Pérez Neira (UPC)

General Vice ChairCarles Antón Haro (CTTC)

Technical Program ChairXavier Mestre (CTTC)

Technical Program Co Chairsapplications as listed below. Acceptance of submissions will be based on quality,relevance and originality. Accepted papers will be published in the EUSIPCOproceedings and presented during the conference. Paper submissions, proposalsfor tutorials and proposals for special sessions are invited in, but not limited to,the following areas of interest.

Areas of Interest

• Audio and electro acoustics.• Design, implementation, and applications of signal processing systems.

l d l d d

Technical Program Co ChairsJavier Hernando (UPC)Montserrat Pardàs (UPC)

Plenary TalksFerran Marqués (UPC)Yonina Eldar (Technion)

Special SessionsIgnacio Santamaría (Unversidadde Cantabria)Mats Bengtsson (KTH)

FinancesMontserrat Nájar (UPC)• Multimedia signal processing and coding.

• Image and multidimensional signal processing.• Signal detection and estimation.• Sensor array and multi channel signal processing.• Sensor fusion in networked systems.• Signal processing for communications.• Medical imaging and image analysis.• Non stationary, non linear and non Gaussian signal processing.

Submissions

Montserrat Nájar (UPC)

TutorialsDaniel P. Palomar(Hong Kong UST)Beatrice Pesquet Popescu (ENST)

PublicityStephan Pfletschinger (CTTC)Mònica Navarro (CTTC)

PublicationsAntonio Pascual (UPC)Carles Fernández (CTTC)

I d i l Li i & E hibiSubmissions

Procedures to submit a paper and proposals for special sessions and tutorials willbe detailed at www.eusipco2011.org. Submitted papers must be camera ready, nomore than 5 pages long, and conforming to the standard specified on theEUSIPCO 2011 web site. First authors who are registered students can participatein the best student paper competition.

Important Deadlines:

P l f i l i 15 D 2010

Industrial Liaison & ExhibitsAngeliki Alexiou(University of Piraeus)Albert Sitjà (CTTC)

International LiaisonJu Liu (Shandong University China)Jinhong Yuan (UNSW Australia)Tamas Sziranyi (SZTAKI Hungary)Rich Stern (CMU USA)Ricardo L. de Queiroz (UNB Brazil)

Webpage: www.eusipco2011.org

Proposals for special sessions 15 Dec 2010Proposals for tutorials 18 Feb 2011Electronic submission of full papers 21 Feb 2011Notification of acceptance 23 May 2011Submission of camera ready papers 6 Jun 2011