robust blind pic

8/12/2019 Robust blind PIC

1/23

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMSInt. J. Commun. Syst. (2008)Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/dac.953

Robust blind PIC with adaptive despreader and improvedinterference estimator

Indu Shakya, Falah H. Ali, and Elias Stipidis

Communications Research Group, Department of Engineering and Design, School of Science and Technology,

University of Sussex, Brighton BN1 9QT, U.K.

SUMMARY

An effective design of multistage parallel interference cancellation (PIC) receiver using blind adaptive(BA) despreader and pre-respreader interference estimator for uplink CDMA is proposed and analysed.A novel algorithm is designed, which exploits constant modulus (CM) property of the users transmittedsignals and inherent channel condition to perform adaptive despreading based on minimum error variancecriteria. This is carried out by BA weighting of each chip signal for accurate tracking of the desired userssignal power and hence for more improved data detection at the output of each stage of PIC. Furthermore,the despreader weights are used within the adaptive pre-respreader interference estimation and cancellationto obtain online scaling factors during every symbol period, without any knowledge of users channels orthe use of training sequences. It is found that this way of estimation is optimal in minimum mean squarederror sense, and hence, significant reduction in interference and noise variance is observed in detectionand estimation of the desired users signals compared with conventional PIC. Bit error probability of theproposed PIC is obtained using Gaussian Approximation method. Extensive simulation results are shown,which demonstrate impressive performance advantage in fading environments, high system loading, andsevere near far conditions. Copyright q 2008 John Wiley & Sons, Ltd.

Received 21 November 2007; Revised 18 April 2008; Accepted 13 June 2008

KEY WORDS: CDMA; parallel interference cancellation; blind channel estimation

1. INTRODUCTION

It is well known that the performance of CDMA systems that use conventional matched filter (MF)

receivers is limited by the effect of multiple access interference (MAI) caused by users sharing the

same bandwidth with non-orthogonal spreading sequences. This problem of conventional receivers

has drawn significant attention of researchers, leading to a substantial number of works on thedesign of multiuser receivers to greatly reduce the effects of MAI. The multiuser receiver proposed

Correspondence to: Falah H. Ali, Communications Research Group, Department of Engineering and Design, Schoolof Science and Technology, University of Sussex, Brighton BN1 9QT, U.K.

E-mail: [email protected]

Copyright q 2008 John Wiley & Sons, Ltd.


2/23

I. SHAKYA, F. H. ALI AND E. STIPIDIS

by Verdu[1] based on the Viterbi Algorithm though optimum in performance is prohibitivelycomplex even when the number of users is moderate. Varieties of less complex multiuser receivers

using decorrelation and interference cancellation (IC)-based techniques have also been proposed.

A good simulation comparison study of their performances and complexity can be found in

[2

].

Due primarily to lower computational complexity, allowance of strong error correcting codes,and no restriction on structure of spreading sequences, the IC receivers are more suitable for

implementation in future wireless cellular systems than the linear decorrelation-based counterpart

[3]. It is important to note that there also exist a family of more advanced hybrid receivers consistingof decorrelators as initial stage followed by full or partial cancellation of the estimated signals

in the next stage as investigated by Duel-Hallen in[4]. Among the type of IC receivers, parallelinterference cancellation (PIC)[5] is long known as an effective receiver technique that greatlyalleviates the MAI problem using multistage architecture and with reasonable latency. This has

attracted large number of works on improving the performance of PIC in the past[612].The works in[5 7] have considered the design of PIC primarily in AWGN channel; when

applied in fading channel environments, its performance is significantly degraded due to additional

impairment of the fading process on top of MAI[

8]. PIC that uses the MF output at each stage

to form a soft (linear) estimate of MAI is used for fading channel conditions and referred to

here as conventional PIC[2, 6]. Recently weighted linear PIC for operation in Rayleigh fadingchannels is investigated in[9] to improve the signal-to-interference ratio (SIR) at each stageof the PIC. Optimum weight for IC for each user is derived using the knowledge of cross-

correlations of users sequences for maximizing the average SIR. This has been shown to provide

considerable performance improvement compared to the conventional PIC operating in the same

system environments. However, the scheme considers only the statistics of users channels and

therefore it may not perform well in the system with severe near far user conditions (although the

receive diversity is used to partly solve this problem). It is very important to note that what is

essential for improved performance of PIC receivers is not some partial weights but the accurate

amplitude estimate of the users detected signals. It is also well known that inaccurate channel

estimation leads to severe error propagation, contributing to susceptibility of the system to higheruser loading and near far conditions[2, 3]. Therefore, to provide an effective solution to thisimportant problem, coupled with the desire to improve bandwidth efficiency by avoiding use of any

training sequences, motivates us to consider blind techniques that do not require channel parameter

estimation.

Another stream of researchers have focused their efforts on adaptive filtering type of receivers

such as non-blind e.g.[13, 14]as well as blind adaptive (BA) receivers such as[1519]. Similar toconventional MF receivers, these techniques do not require much information about other users

signals for performing the detection process. The interference is suppressed using either reference

signals, i.e. training data based on minimum mean squares error (MMSE)[13] criterion or afixed target output value, e.g. minimum output energy (MOE)[15] or constant modulus (CM)[19] criteria. The implementation involves use of tapped delay lines and with adaptive weight foreach tap, which are updated to meet the predefined criteria. The BA multiuser detection technique[15] proposed by Honig et al. employs the MOE criterion to suppress MAI without any trainingsequence and knowledge of interfering users signals. It is shown to perform very well under static

channels and also with severe near far conditions. However it is also known to be sensitive to the

mismatch in the desired users received signature sequence estimates and may not be easily applied

in Rayleigh fading environment, where power of users vary significantly even over a very short

time period. In summary, it is noted that the adaptive receivers provide improved performance

Copyright q 2008 John Wiley & Sons, Ltd. Int. J. Commun. Syst. (2008)

DOI: 10.1002/dac


3/23


4/23


results are shown to confirm our analysis and to demonstrate that significant performance gain

compared to conventional PIC can be achieved under various system loads and channel conditions.

The rest of the paper is organized as follows. In Section 2, a generalized system model is

presented. In Section 3, we formulate the principles of the proposed blind PIC receiver technique

and its detection and cancellation algorithm including its complexity. In Section 4, we present theBER performance analysis at different stages of the system. The simulation performance results

and comparisons under different system conditions are presented in Section 5. Finally, the paper

is concluded in Section 6.

2. SYSTEM MODEL

We consider a synchronous DS-CDMA system of K users under Rayleigh flat fading channels

with AWGN. The received composite signal r(t) can be written as

r(t)=K

k=1k(t)sk(t)+v(t) (1)where sk(t)=

Pkbk(t)ck(t) is the transmitted signal of the kth user, Pk is the signal power

assumed to be unity unless stated otherwise,k(t)= gk(t)ejk(t) is the fading channel presented bycircularly symmetric complex Gaussian random variable CN(0,1) consisting of amplitudegk(t)

and phasek(t)components.bk(t)=

m= bk(m)p(tmTb)is the data signal, where bk(m)isa binary sequence taking values[1,+1] with equal probabilities, p(t)is rectangular pulse withperiod Tb. The spreading sequence is denoted as ck(t)=

n= ck(n)p(tnTc) with antipodal

chips ck(n) of rectangular pulse shaping function p(t) of period Tc and normalized power over

a symbol period equal to unityTb

0 ck(t)2 dt=1. The spreading factor is N= Tb/Tc and v(t) is

the AWGN with two-sided power spectral density N0/2. Throughout the paper we assume that

coherent phase reference of all users signals is available and without loss of generality the kth

user is the desired user. To gain better exposition of our blind PIC approach and to note maindifferences later, we briefly describe the operation of conventional PIC and weighted PIC first.

2.1. Conventional and weighted PIC techniques

Although we are referring to PIC used in[2, 6]as described earlier to obtain a conventional PIC, allits main functional blocks are the same with other PICs including the proposed receiver. Therefore,

the signal model described here applies equally well to the proposed PIC.

At every symbol period m, the received signal is first chip-matched filtered, and sampled to

form received signal vectorr(m). In a conventional PIC, first the initial estimation of thekth users

data signal at stage 0 (l =0) is carried out by obtaining a decision variable signal z 0k(m) from theoutput of bank of MFs matched to users spreading sequences as follows:

z0k(m)= mTb(m1)Tb

{r(m)}Tck k

=

Pk(m)k(m)bk(m)+K

i=1,i=k

P ikii(m)bi (m)+vk(m)

=Dk(m)+Ik(m)+vk(m) (2)


DOI: 10.1002/dac


5/23

ROBUST BLIND PIC WITH ADAPTIVE DESPREADER

where{r(m)}T denotes transpose of r(m), ck is a vector consisting of the kth users spreadingsequence, ki is the magnitude of cross-correlation between the kth and i th users spreading

sequences, Dk(m)and Ik(m)are denoted as the desired and interfering users received data signals,

respectively, vk(m) is the correlated AWGN term. The estimation of the desired kth users data

bk(m) in the lth stage 1lL , where L is the total number of PIC stages, is carried out bysubtracting from r(m)the sum of MAI contribution of other users. The MAI estimates are formed

by summing the remaining users decision variables from previous stagez l1i (m); i =kmultipliedby their spreading sequences c i . This process is shown as follows:

zlk(m)= mTb(m1)Tb

r(m)

Ki=1,i=k

zl1i (m)ci

Tck k (3)

where is the weighting factor used for the MAI cancellation. The conventional PIC as given in

[2]and[6]is obtained from (3) by setting =1. The conventional MF receiver can be derived as aspecial case of the PIC described here by setting

=0. The partial PIC

[6

]and also the weighted

PICs as described in[9] can be obtained from (3) by setting a positive and non-zero value of.The estimate of the kth user data is then obtained as follows:

blk(m)=sgn[Re{zlk(m)k(m)}] k (4)

where sgn{.}, Re{.}, and denote sign, real, and complex conjugation operation, respectively. Theprocesses in (3) and (4) are carried out at each stage of the PIC(l =1,2, . . . ,L)for all users datasignals to be estimated/detected.

3. PROPOSED BLIND PIC

3.1. Main principles

The proposed PIC addresses the problems of conventional PIC in two ways. First, we identify that

the performance of correlation and integration process used for despreading in conventional PIC

can be improved by using feedback from the output signal. To achieve this, an improved adaptive

despreading is employed to blindly suppress the interference using minimum error variance criteria

of CMA. Specifically, the input signal for each users despreader is multiplied with weights updated

using the CM criterion to form the decision variables. Secondly, to minimize the interference

propagated to the next stage, the despreader weights are fed forward to the next stage to obtain

scaling factor for improved interference estimation. This is obtained by multiplying the soft output

signal of the adaptive despreader with the scaling factor prior to the respreader of the next stage

and cancellation is carried out.The system architecture ofl th, l1 stage of the proposed PIC is shown in Figure 1. At every

symbol period, the received signal, r(t) is sampled at the chip rate to form the vector r(m) of

length Nchips. The estimates of data signal for each user is obtained from the output of improved

adaptive despreader. The CM cost function embedded within the despreader is used to adjust the

desired users signal amplitude using weight for each chip signal, thus providing N degree of

freedom for amplitude adjustment. A block diagram of the adaptive despreader for the kth user at


DOI: 10.1002/dac


6/23


Figure 1. Proposed blind PIC at l th stage.

the l th stage of the proposed PIC is shown in Figure 2. Note that superscripts are used to denote

the elements of signal vectors for convenience. The despreading process generates output signal

by suppressing part of MAI and also used for obtaining an adaptive scaling factorl+1k (m)for thenext stage of the PIC. The initial stage l =0 of the PIC is obtained from a bank of K adaptivedespreaders with their common input being the received signal vector r(m). In the successive

stagesl1 as in Figure 1, the input signal vector for each user, ylkis obtained by canceling from

r(m) the sum of MAI contributions of interfering users signals xlk(m). The despreading of ylk

gives decision variable signal, zlkand a hard decision is made to obtain the data estimate. Next,

the output signal for each user zlk,kare weighted utilizing the scaling factorl+1k (m) obtainedfrom the despreader of the lth stage, spread with ck and subtracted from the received signal to

form the input to the next stage yl

+1

k . The above processes are repeated for multiple stages witheach additional stage contributing to further improved performance. A more detailed description

of the detection and estimation processes of the proposed receiver is given next.

In any CDMA receiver, the decision error for the desired user signal occurs when the effects of

the total MAI contributions flip the polarity of the users decision variable signal, i.e. sign {zk(m)}=bk(m) or causes the combined MAI and users signal magnitude to be very near to zero so that

receiver noise becomes the dominant source of the decision error. The conditions for probability


DOI: 10.1002/dac


7/23


Figure 2. Improved adaptive despreading and weights generation for the kth user.

of error Pr{bk(m)=bk(m)} can be written as

Pr{bk(m)=bk(m)}

Dk(m){Ik(m)+vk(m)}0 ifbk(m)=1

(5)

It is known that the alphabet of the BPSK modulated signal Dk(m) can take only two values.

The linear receivers do not exploit this information within their signal processing algorithms[23].The finite alphabet property of users signals is exploited in the proposed receiver using a CM

criterion. It should be noted here that the receiver can operate for higher alphabet schemes such as

MPSK or MQAM with appropriate set-up of dispersion constant within the CM cost function[19].Assuming that the use of the CM cost function at each stage always forces the output signal z k(m)

towards the correct polarity of the transmitted signalbk(m), we can set conditions for minimizingthe decision error for the proposed blind receiver as follows:

Pr{bk(m)=bk(m)}0 if(1) |zk(m) |21(2) |Ik(m)+vk(m) |20

(6)

The first condition in (6) can be met asymptotically for static and noiseless channel conditions

by a receiver employing any form of CM criterion for the given input signal[16, 1820]. Inwireless environments, the users signal powers vary from near zero to several (or tens) dB.

In such conditions, the use of CM criterion does not guarantee stable recovery of the desired

users data signal, particularly when the strong interfering users are present in the system, i.e.

|Ik(m) |2

> |Dk(m) |2

. Our objective is to recover the desired users data signals in a realistic wirelessenvironment with fading and near far conditions. Therefore it is intuitive to incorporate an IC

stage to enhance the detection of CM despreaders output. Since all the users signals are detected

simultaneously in a PIC, accurate estimation of both the desired users and MAI users signal

power variations need to be taken into account for the detection of desired users data signals. The

proposed receiver attempts to satisfy both conditions of (6) for the minimum decision error by its

unique design exploiting the adaptive weights of the despreader.


DOI: 10.1002/dac


8/23


The cancellation signals are generated based on the conditions of decision error due to each

users independent and varying amount of MAI contribution as shown in (5). The weight calculation

process of the CM criterion within the proposed PIC can be shown below:

wlk(m +1)=

alk(m)wk(1) if|zlk(m) |1

(7)

where a lk(m)>1 is a positive scaling factor that the despreader uses to adjust the elements of the

weight vectorwk(m)during each symbol period, wk(1)is the initial weight vector of the kth user,

which is set as a vector of unit norm consisting of chips of the kth users spreading sequence ck,

i.e.wk(1)=ck;k. The estimatelk(m)of the scaling factor a lk(m)is used in the proposed receiverfor IC. Whenlk(m)zlk(m)Dk(m), the cancellation process completely removes the effect ofthe kth users MAI contribution so that other users signals will be detected and estimated more

accurately. The practical CM algorithm however does not perform perfectly and there are bound

to be some inevitable misconvergence problems. Also in the presence of strong interfering signals,the use of CM cost function may not be able to lock to the desired weak user. However, the useful

properties of the CM algorithm is exploited and its performance is enhanced using PIC stages in

the proposed receiver. The description of the algorithm for each stage of this blind multistage PIC

receiver is described next.

3.2. BA-PIC algorithm

At the first symbol period (m =1), the despreader weights for all users at all stages are initializedwith vectors of the users spreading sequences wlk(1)=ck,k,l. The input to the initial stage(l =0)of the proposed PIC is the received signal vector, i.e. y0k(m)=r(m)and the decision variablez0k(m)is obtained by performing adaptive despreading. For the purpose of clarity, we describe the

processes of proposed PIC algorithm for thel th stage (l1)only. A similar procedure is followedfor other stages (except for the initial stage as described earlier). At the lth stage, the decision

variable for the kth user, zlk(m) is obtained by multiplying elements of input signal vector ylk(m)

with the elements of weight vector wlk(m) and the product is summed over the symbol period as

follows:

zlk(m)={ylk(m)}Twlk(m) (8)The CM criterion JCM applied to z

lk(m) can be written as minimization of the following cost

function:

JCM =E{{zlk(m)}2}2 (9)

where E(.) is the expectation operator, is the dispersion constant, which is equal to unity forBPSK signals. The instantaneous error signal e lk(m) is calculated as

elk(m)=zlk(m){{zlk(m)}2} (10)The estimated gradient vector from the error signal is then calculated as

lk(m)=ylk(m)elk(m) (11)


DOI: 10.1002/dac


9/23


Using the gradient, the weight vector for the next symbol wlk(m +1) is updated as follows:

wlk(m +1)=wlk(m)klk(m) (12)

wherekis a small step size that is used to adapt the elements of the weight vector to minimize thecost function in (9). Finally, the output signal zlk(m) is delivered to the decision-making process

to perform decision on the kth user datablk(m) at the l th stage as follows:

blk(m)=dec{zlk(m)} (13)where dec{.} is simply a sign function for BPSK data.

The cancellation process requires an amplitude estimate of the detected users signal along

with the users spreading sequence. We first obtain an estimated scaling factor l+1k (m) using thespreading sequence of the user and weights of the despreader as follows:

l+1k (m)

=

ck(m)

w

l

k(m)

(14)

whereck(m) and wlk(m) are the mean amplitude of chips of the users spreading sequence andelements of the weight vector updated by using the CM criterion, respectively, and are given by

ck(m)= 1

N

Nn=1

|ck((m 1)N+n)| (15)

wk(m)= 1

N

Nn=1

|wk((m 1)N+n)| (16)

The despread soft output signal zlk(m) is then multiplied with l+1k (m) and spread using ck togenerate the cancellation term of the kth user for the detection of other users i =1, . . . ,K; i =ksignals in the next stage. The MAI estimate for the kth user xlk(m) is obtained by summing thecancellation signals of all other users i, i=k spread with their corresponding sequences ci asfollows:

xl+1k (m)=K

i=1,i=kl+1i (m)z

li (m)ci (17)

The improved signal estimate for the kth user for the next l +1 stage is obtained after performingthe IC as follows:

yl+1k (m)=r(m)xl+1k (m) (18)

The resulting signal vectors of users{yl

+1

1 ,yl

+1

2 , . . . ,yl

+1

K }Yl+

1

serve as inputs to the next PICstage for further improvement of each users data signal detection and estimation. This is done

by following the processes derived in (8)(18) with the new signal sets for the desired number of

stages.

It is well known that the CMA is a low-complexity algorithm with computational complexity

of the order of O(N) floating point operations (FLOPs) per symbol. In Table I, we also show

the complexity of the proposed PIC employing the CM algorithm, which is within the range of


DOI: 10.1002/dac


10/23


11/23


model[25]of fading channels consisting of the sum of uniform scatterers represented by individualsinusoids defined by the carrier frequency fc and Doppler rate fd. The channel autocorrelation

R() over a time period is obtained as follows:

R()=J0(2fd) (21)where J0(.)is a zero-order Bessel function of the first kind. We now proceed with BER analysis of

PIC receivers at stage 0 and 1. For the clarity in the analyses to follow, we use subscripts ba-pic

and conv-pic to denote the signals of proposed and conventional PIC, respectively.

4.1. Stage 0

Observing the expression of (20), we note that the SINR value is maximized when the variance

of the decision variable z l(m)is minimized. The use of CM criterion tries to achieve this goal by

adapting the weights recursively using the weights of previous symbols as such to maintain the

absolute magnitude of the output signal zl equal to the dispersion constant . This minimizes theinstantaneous error signal el(m) as shown in (10) and thus attempts to satisfy the first condition

of (6). The task of our analysis is to show that the variance of the adaptive despreader (error) isless than that of the output of correlator used in conventional PIC, which can be shown as

var{z0ba-pic}var{z0conv-pic}


12/23


by the Doppler shift R(t), the degree of freedom for weight adaptation N, and the choice of

step size [18]. Therefore var{z0ba-pic} will be minimized, when Nis sufficiently large and R(t)does not change significantly for the given period. Assuming R(t)1 during the period of Msymbols, due to recursive nature of the CM cost function, var

{z0

ba-pic} for a given period M can

also be represented as the averaged value of a geometric series consisting of sum of decaying

numbers e 0(m) (the rate of decay can be assumed constant for simplicity).

var{z0ba-pic}= 1

M

var{z0conv-pic(1)}+ K

Mm=2

{e0(m)}2N


13/23


It will not be difficult to see that when (28) is satisfied this also leads to perfect cancellation of

interfering users signals, i.e. j = i;j .To assess the accuracy of the amplitude estimation of proposed PIC from kas shown in (14),

let us first assume that the CM criterion for the kth user signal has converged by generating perfect

weights wk(m)for the given input signal zk(m)=wk(m)Tyk(m) as follows:ek(m)=zk(m)(zk(m)2)2 0 (29)

It is known that when CM algorithm is used for blind channel estimation in an interference free

channel, the estimategk(m)is simply obtained as the inverse of the weights[21]. Since the userssignals are sampled at chip rate in CDMA systems, the estimate can be obtained as

gk(m)=

wk(m)

ck

wk(m)(30)

The weight vector wk(m)consists ofNadaptive elements that serve the purpose of both suppressing

the MAI and also providing unbiased estimates of users data signals. Since a system with time-

varying fading and near far environment is considered, in this work a scaling factor lk(m) usingthe weightswk(m)as shown in (14) is used along with despreader output at previous stage z

l1k (m)

for obtaining the joint data and amplitude estimate of the kth user[2].Now the task of analysis is to show that the variance of the proposed PIC at Stage 1, var {z1ba-pic}

is smaller compared to that of the conventional PIC. In conventional PIC the data signal estimate

for the kth user Dk(m) is simply taken as the absolute magnitude of MF output z0k(m), while

ignoring Ik(m)+vk(m) as in (3). Therefore the variance of decision variable for the desired uservar{z1conv-pic} can be shown as

var{z1conv-pic} =K

i=1,i=k{2ki i j2k j }var{z0conv-pic}

i j=

1 ifi = j1 ifi = j

; j =1, . . . ,K; j =k (31)

In the case of BA-PIC, the variance of decision variable of desired user z1ba-pic is dependent upon

the individual users amplitude estimation error k(m),kand also the variance of decision variablefor the desired in the previous stage var{z0ba-pic} as follows:

var{z1ba-pic} = 2k+K

i=1,i=k2i {2ki i j2k j }var{z0ba-pic}

i j=1 ifi = j1 ifi = j ; j =1, . . . ,K; j =k (32)From (31) and (32), we observe the following: The reduction in variance of decision statistic of

conventional PIC var{z1conv-pic} is dependent on the variance in the previous stage var{z0conv-pic}and how reliably the current stage generates the MAI estimates for cancellation quantified by

the residual signal 2 =2ki 2k j . As noted in (2) and (3), the variance of2 could be high due


DOI: 10.1002/dac


14/23


to inaccurate estimation of the channel power variation var{gi} of interfering users signals. Theconventional PIC detection becomes vulnerable to MAI particularly when the desired users signal

is weak and there are strong interferers. Unlike the conventional and other PIC found in the

literature

[6 8

], where the cancellation weights are selected based on random guess or signal

statistics, in the proposed PIC the cancellation weights are generated using the algorithm that isadaptive in the MMSE sense to instantaneous changes in the power variations of both the desired

and interfering users signals. Based on this heuristic and analysis of the previous stage, the SINR

of the proposed PIC is always higher than the conventional PIC and can be shown to be

SINR1

ba-pic =E{(z1ba-pic)2}var{z1ba-pic}

2

var{z1ba-pic}(33)

The SINR1

ba-pic value can be used in (19) to obtain the BER for the desired user signal at the output

of stage 1. The extension of the analysis to more stages is straightforward. It can be expected that

each additional stage will further reduce the variance of decision variables of each user and thus

lead to further performance improvement.

5. NUMERICAL RESULTS

A baseband model of synchronous uplink DS-CDMA system with K users and coherent BPSK

demodulation is assumed. Short binary Gold sequences [26] of lengthN=31 are used for spreadingusers data. The channel is Rayleigh flat fading with normalized Doppler rate fdTb of 0.003. A

fixed step size ofk=0.0001 for all users is assumed in the CM algorithm. The selection of stepsize in CDMA receivers is generally based on the spreading factor used, the dynamic range of the

received signal, and effects the convergence of the algorithm[18].The BER performance results for K=10 users of the proposed technique with l =0 (BA-PICStage 0) and l =1 (BA-PIC Stage 1) are compared with conventional PIC (conventional PIC Stage 0

and conventional PIC Stage 1) as shown in Figure 3. It is evident from the results that by employing

the CM criterion for adaptive despreading at the initial stage of the proposed PIC, much improved

BER performance than the conventional PIC can be achieved. This result confirms our analysis

in (22)(26), as the improvement in BER is directly related to the SINR improvement using the

adaptive despreading within the PIC. We also show the average BER performance of 10 users at

the output of the first stage (BA-PIC Stage 1) of the proposed PIC, obtained from the analysis using

Gaussian Approximation in (19). The BER conditioned on variances of users random decision

variable signals at despreader outputs were obtained using the Monte-Carlo integration method.

As predicted, the analytical result shows a close match with the simulation result. With an extra

PIC stage, the BA-PIC showed a superior BER performance compared to the conventional PIC

reaching very near to the single-user BPSK signal bound. This is due to the improved accuracy ofamplitude estimates for the IC of the users signals of the BA-PIC.

In Figures 4(a) and (b), for the purpose of visualization, we show the signals at the output of

the initial and first stages of PIC receivers for 20 users and average Eb/N0 =30dB. The MSEperformance metric derived in (28) is used to quantify the accuracy of the estimation processes.

The BA-PIC shows much improved MSE performance compared to conventional PIC for both

stages. The MSE performance of PIC receivers at the output of different stages are compared in


DOI: 10.1002/dac


15/23


Figure 3. BER performance results of proposed blind PIC in flat Rayleigh fadingchannels with K=10 and N=31 (Gold sequence).

Figure 4. Amplitude estimation performance of the proposed blind PIC inflat Rayleigh fading channels with K=20, N=31 (Gold sequence), average

Eb/N0 =30dB: (a) at Stage 0 and (b) at Stage 1.


DOI: 10.1002/dac


16/23


Table II. For example, the BA-PIC achieves an MSE of 0.0024 at Stage 1, whereas the conventional

PIC requires more than three stages to achieve the same MSE performance.

In Figure 5, we show the BER at different stages of the proposed BA-PIC and conventional PIC

receivers in fading channels under a system load of 20 users. The performance of both receivers are

shown to degrade compared to the 10-user system. Therefore, additional PIC stages are employedto cope with the situation. The BA-PIC shows significant improvement in BER with increase

in additional PIC stages. As noted from the figure, the BER of the BA-PIC receiver at Stage 1

has identical performance to that of conventional PIC at Stage 3. The performance of BA-PIC

at Stage 2 is shown to approach very near that of a single user, thus giving impressive capacity

advantage with our approach. The BER performance obtained confirms the superiority of the

BA-PIC approach and corresponds very well to the improvement in MSE of amplitude estimation

plotted in Figures 4(a) and (b).

In Figure 6, we show the performance of the proposed PIC at different stages for MAI cancel-

lation while all the users signals have equal average Eb/N0 =30dB. For the reference, the BERperformances of the single-user BPSK and conventional MF receiver (Stage 0) under the same

Table II. MSE performance comparison of PIC receivers in flat Rayleigh fadingchannels with Eb/N0 =30dB, K=20, N=31 (Gold sequence).

Scheme Stage 0 Stage 1 Stage 2 Stage 3

BA-PIC 0.01272 0.0024 0.0013 0.0011Conventional PIC 0.038 0.0146 0.0061 0.0029

Figure 5. Performance of the proposed blind PIC in flat Rayleigh fadingchannels with K=20, N=31 (Gold sequence).


DOI: 10.1002/dac


17/23


Figure 6. Performance of the proposed blind PIC in flat Rayleigh fading channels,average Eb/N0 =30dB, N=31 (Gold sequence).

fading conditions are also shown. We observe that the initial stage of proposed BA-PIC removes

considerable amount of MAI under all user loading conditions. Interestingly, most of the perfor-

mance gain of the PIC comes from the first stage of IC and the results show near single-user

performance for a large number of users. For example, even at Stage 1 the BA-PIC shows signif-

icantly improved performance compared with conventional PIC with Stage 2. This confirms that

the blind PIC approach indeed performs very accurately and removes significant amount of MAIfrom the system. The error performance is further improved by adding more stages as expected.

In Figure 7, the BER performance of BA-PIC in Rayleigh fading channels for 10 equal power

users with Eb/N0 =30dB is compared with conventional PIC and partial PIC[6] for differentweighting factors (from 0 to 2.6), hence referred to as weighted PIC in the figure. It can be

clearly seen from the figure that the proposed BA-PIC achieves the best performance, which is

independent of . It is found that the optimum weight for the partial or weighted PIC is when

opt =1.4, under which BER performances of the BA-PIC and the weighted PIC are very similar.Figure 8 shows the performance of BA-PIC and conventional PIC with 20 users in fading

channels and under different near far ratio =max{Pi }/Pk[0,20]dB,i, i =k conditions. Thereceived signal power of the desired user k is assumed to be unity with Eb/N0 =20dB. Thereceived power of all the interferers i are assumed to be uniformly distributed between 0 dB and

dB. Here, the step size k=0.0001/10(/10)

is assumed in the CM algorithm in all stages. Itcan be clearly seen from the figure that the BA-PIC shows more robust performance compared

to conventional PIC under the whole range of near far ratio conditions. It is noted that Stage 1

of the proposed PIC can offer near single-user performance under the near far ratio as high as

15 dB. With conventional PIC, even with Stage 2, the performance rapidly degrades as the near

far ratio increases, performing far worse than the proposed BA-PIC at Stage 1. This significant

result of proposed PIC can be attributed to the adaptive design approach used. At each stage of


DOI: 10.1002/dac


18/23


Figure 7. Performance the proposed blind PIC in flat Rayleigh fading channels for K=10,Eb/N0 =30dB and Gold sequences of N=31.

Figure 8. Performance of the proposed blind PIC in near far conditions in flat Rayleigh fading channels,K=20 with Eb/N0 of the weakest user=20dB, N=31 (Gold sequence).

BA-PIC, the MAI cancellation process takes into account the power variations of the desired and

interfering users signals on individual basis and amplitude estimates are obtained more accurately

to minimize the effects of MAI for the final decision.


DOI: 10.1002/dac


19/23


We also present the user capacity performance of BA-PIC in AWGN-only channel environments

but with severe near far problems. Such an environment may be practical when the users are

slowly moving and are under direct line of sight from the base station. The received signal power

of the desired user is assumed to be unity. The signal powers of all the other users are assumed

to be uniformly distributed between[0,20]dB. In Figure 9, we show the BER performance ofBA-PIC under the above-described scenario of users signal power. We observe the effect of near

far conditions caused by the presence of interfering high-power users to the desired weak user with

its effective Eb/N0 =7dB. The number of users in the system is varied from 5 to 25. The BA-PICshows improved performance at Stages 0 and 1; it shows rapid performance gain as we expected.

The additional stages improve the performance even further; but as can be seen, the gain is not as

high as in Stage 1. The conventional PIC shows good performance under low system load of up

to 12 users. As the load increases, the performance degrades dramatically and approaches that of

conventional MF receivers.

Figure 10 shows the performance of the proposed BA-PIC and conventional PIC with 20 users

in the AWGN channel environment and under different near far ratio =max{Pi }/Pk[0,20]dB,

i, i

=k conditions. The received signal power of the desired kth user is assumed to be unity

and the signal powers of interferers are assumed uniformly distributed between 0 dB and dB.

Here, the step size k=0.0001/10(/10) is assumed in all stages similar to the case of fadingchannels. The signal-to-noise ratio of the desired (weakest) user is Eb/N0 =7dB. It can be clearlyseen from the figure that the BA-PIC offers more robust performance compared to the conventional

PIC under all ranges of near far ratio conditions. It is noted that the proposed PIC at Stage 1

can offer near single-user performance under all the near far ratio conditions. This becomes more

apparent for severe near far conditions, e.g. >15dB, indicating that the BA-PIC performs better

Figure 9. Performance of the proposed blind PIC in a near far ratio of 20 dB in AWGN channels, withEb/N0 of the weakest user =7dB, N=31 (Gold sequence).


DOI: 10.1002/dac


20/23


Figure 10. Performance of the proposed blind PIC in near far conditions in AWGN channels, K=20 withEb/N0 of the weakest user =7dB, N=31 (Gold sequence).

Figure 11. Performance of the proposed blind PIC in frequency-selective multipath channelswith AWGN, Eb/N0

=15dB and Gold sequences of N

=31.

in static AWGN channels compared to that in time-varying fading channels as shown in Figure 8.

This is because the AWGN-only environment provides enough time for convergence of weights of

the CM algorithm to optimal valueswoptk . As expected, we can infer from the results that amplitude

estimates generated are very accurate and thus the IC process of the BA-PIC shows resilience

under all near far ratio conditions considered. With conventional PIC, even at the output of Stage 2,


DOI: 10.1002/dac


21/23


the performance rapidly degrades as the near far ratio increases and performs far worse than the

proposed BA-PIC with Stage 1.

The performance of the BA-PIC as well as conventional PIC operating in a two-path frequency

selective channel with AWGN and Eb/N0

=15dB is shown in Figure 11. The average power of

the first and second paths are assumed to be 0.8 and 0.2, respectively. Both receivers (BA-PICand conventional PIC) perform IC on each path using RAKE structure, followed by maximum

ratio combining to obtain the decision variables at each stage. As can be seen from the figure, the

BA-PIC still shows improved BER at different stages.

From the analysis and range of simulation performance results, we can conclude that the blind

adaptive approach of the proposed PIC receiver is a very effective way of improving the performance

of uplink CDMA. Besides the improved performance, it also greatly relaxes the requirements on

accurate power control.

6. CONCLUSIONS

We proposed a novel blind adaptive multistage PIC receiver for DS-CDMA exploiting the CM

property of users signals. An effective algorithm using adaptive despreading based on minimum

error variance criterion for data detection and improved interference estimation in the MMSE sense

before respreader for IC is proposed to mitigate the error propagation effect and fading channel

estimation problem of conventional PIC. Besides being blind and low-complexity PIC, it showed

significant performance improvement in both fading and AWGN environments. For example, with

the same single stage of cancellation it showed approximately twofold increase in user capacity for

desired BER under the same SNR, and better error performance than conventional PIC with three

stages under high system load of K/N0.65. With two stages of cancellation, the proposed PICshowed near single-user performance for the weakest (unity power) user while power of interferers

was as high as 15 dB. It is established that the first stage of cancellation provides the highest gain,

for example, at SNR of desired user 7 dB and power of interferers as high as 20 dB, impressive BER

of 0.002 compared with 0.08 at the initial stage is observed. The BA-PIC is also investigated in

frequency-selective channels and shown to achieve improved performance gains over conventional

PIC. For future work it is proposed to investigate the performance of the BA-PIC combined with

multicarrier CDMA.

REFERENCES

1. Verdu S. Minimum probability of error for asynchronous Gaussian multiple-access channels. IEEE Transactions

on Information Theory 1986; 32(1):8596.2. Buehrer R, Correal-Mendoza N, Woerner B. Simulation comparison of multiuser receivers for cellular CDMA.

IEEE Transactions on Vehicular Technology 2000; 49(4):10651085.3. Andrews JG. Interference cancellation for cellular systems: a contemporary overview. IEEE Wireless

Communications Magazine 2005; 12(2):1929.

4. Duel-Hallen A. A family of multiuser decision-feedback detectors for asynchronous code-division multiple-accesschannels. IEEE Transactions on Communications 1995; 43(2/3/4):421434.

5. Varanasi M, Aazhang B. Multistage detection in asynchronous code-division multiple-access communications.

IEEE Transactions on Communications 1990; 38(4):509519.6. Divsalar D, Simon M. Improved parallel interference cancellation for CDMA. IEEE Transactions on

Communications1998; 46(2):258268.7. Xue G, Weng J. Adaptive multistage parallel interference cancellation for CDMA. IEEE Journal on Selected

Areas in Communications 1999; 17(10):18151827.


DOI: 10.1002/dac


22/23


8. Ghotbi M, Soleymani M. Performance of parallel interference cancellation in large CDMA over a fading channel.

Proceedings of IEEE GLOBECOM Conference, Dallas, TX, U.S.A., vol. 5. December 2004; 28332837.

9. Tikiya V, Manohar S, Chockalingam A. SIR-optimized weighted linear parallel interference canceller on fading

channels. IEEE Transactions on Wireless Communications 2006; 5(8):19982003.

10. Hui A, Letaief K. Successive interference cancellation for multiuser asynchronous DS/

CDMA detectors inmultipath fading links. IEEE Transactions on Communications 1998; 46(3):384391.

11. Achim Nahler A, Irmer R, Fettweis G. Reduced and differential parallel interference cancellation for CDMA

systems. IEEE Journal on Selected Areas in Communications 2002; 20(2):237247.

12. Annalingam D, Ali F, Stipidis E. Blind multi-user parallel interference canceller for DS-CDMA. Proceedings of

Communication Systems and Networks, Benidorm, Spain, September 2005; 106110.

13. Madhow U, Honig ML. MMSE interference suppression for direct sequence spread spectrum CDMA. IEEE

Transactions on Communications 1995; 42(12):31783188.

14. Lim TJ, Roy S. Adaptive filters in multiuser (MU) CDMA detection. Wireless Networks1998; 4(4):307318.

15. Honig ML, Madhow U, Verdu S. Blind adaptive multiuser detection. IEEE Transactions on Information Theory

1995; 41(4):944960.

16. Lambotharan S, Chambers J, Constantinides A. Adaptive blind retrieval techniques for multiuser DS-CDMA

signals. IEE Electronics Letters 1999; 35(9):693695.

17. Gelli G, Paura L, Verdoliva L. Adaptive interference suppression in CDMA systems by LCL-PTV filtering.

Proceedings of EUSIPCO 2000 Conference, vol. IV, Tampere, Finland, September 2000; 23252328.

18. Yuvapoositanon P, Chambers J. Adaptive step-size constant modulus algorithm for DS-CDMA receivers innonstationary environments. Signal Processing 2002; 82(2):311315.

19. Zeng H, Tong L, Johnson R. An analysis of constant modulus receivers. IEEE Transactions on Signal Processing

1999; 47(11):29902999.

20. Lee W, Vojcic BR. Constant modulus algorithm for blind multiuser detection. Proceedings of IEEE Symposium

on Spread Spectrum Systems, vol. 3, Mainz, Germany, September 1996; 12621266.

21. Xu C, Le-Ngoc T. CMA-based channel estimation for space-time block coding transmission systems. Wireless

Personal Communications 2004; 28(4):241258.

22. Ochi H, Onaga K, Kinjo S. A generalized block constant modulus algorithm and its VLSI architecture. Proceedings

of Midwest Symposium on Circuits and Systems, vol. 2. Sacramento, CA, U.S.A., August 1997; 853856.

23. Poor V. Iterative multiuser detection. IEEE Signal Processing Magazine 2004; 21(1):8188.

24. Pursley M. Performance evaluation for phase-coded spread-spectrum multiple-access communicationPart I:

system analysis. IEEE Transactions on Communications 1977; 25(8):795799.

25. Goldsmith A. Wireless Communications. Cambridge University Press: Cambridge, 2005.

26. Hanzo L, Yang L-L. Single and Multi-carrier DS-CDMA: Multi-user Detection, Space-time Spreading,Synchronisation, Networking and Standards. IEEE-Wiley: 2003.

AUTHORS BIOGRAPHIES

Indu Shakya was born in Nepal. In 1997, he completed specialist Engineers andMasters degree in Radio Electronics Systems engineering from Moscow State Academyof Instrument Engineering and Computer Sciences, Moscow, Russia. From 1999 to2001, he was involved in various projects on computer networks, systems adminis-tration and software training. In June 2001, he completed postgraduate certificate in

Digital Electronics from universities of Brighton and Sussex. He worked as a softwareengineer with research and development department of Electronics Temperature Instru-ments Ltd., U.K., until November 2002. From October 2003, he has been workingfor the DPhil degree in Wireless Communications at the Communications ResearchGroup, University of Sussex. His research interests are in multiuser detection andinterference cancellation for CDMA, blind adaptive estimation, collaborative communi-cations and space diversity, detection and estimation techniques for multicarrier CDMA,OFDMA.


DOI: 10.1002/dac


23/23


Falah H. Ali received his BSc in Electrical and Electronics Engineering and MSc inElectronic Systems from Cardiff University, U.K., in 1984 and 1986, respectively. In1992 he received his PhD from the University of Warwick in the area of MultiuserCommunications. From 1992 to 1994 he took postdoctoral research post at LancasterUniversity. In 1994 joined the University of Sussex as a Lecturer in Electronics Engi-neering, and in 2000 promoted to Senior Lecturer. Currently, he is a Reader in DigitalCommunications and Director of the Communications Research Group. His researchexpertize is in the area of wireless and mobile communications. He is a Fellow of IET,Senior Member of IEEE and Chartered Engineer.

Elias Stipidis is a Senior Lecturer at the Department of Engineering and Design,University of Sussex. He holds a first class honours BEng in Electronics and DPhil inElectronics and Communications from the same university. He has numerous publicationsand a number of Government and Industrial funded programmes in the subject area.He is a Charter Engineer, member of BCS, IEEE and IEICE, a Fellow in the IET, andholds a Business Fellowship with the London Technology Network.


DOI: 10.1002/dac

robust blind pic

Documents