8/6/2019 10.1.1.64.96

1/5

Abstract The robustness against errors in the estimation of

channel parameters such as time delay and phase is studied

for different multiuser detectors in a direct-sequence code-

division multiple access system. Simulations indicate that

most of the studied detectors perform well in a system with

no errors in the parameter estimation. Synchronization

errors cause a significant degradation of the performance of

all studied detectors. In a realistic situation were the phase is

also imperfectly estimated, the performance of the multiuser

detectors approach that of the conventional detector. Fur-

thermore the detectors loose their near-far resistance under

such non-ideal conditions.

I. INTRODUCTION

In the future it is expected that many different services such as

speech, fax, video, data and electronic billing will be part of a

wireless personal communication system. Some of these services

require very high data rates, maybe as high as 2 Mbit/s. For such

a wireless multimedia system to be successful, as investment for

the operators and beneficial for the customers, it must have a high

spectral efficiency so that a high market penetration is possible. It

should be well designed so that the infrastructure and handhelds

can be low-cost equipment. In the race for a system that fulfils all

these properties, much research has focused on the access meth-ods such as time-division multiple access (TDMA) and code-divi-

sion multiple access (CDMA). In this paper we assume a direct-

sequence CDMA (DS-CDMA) system, and turn our attention to

possible receiver structures.

A DS-CDMA system has the advantage of a frequency reuse fac-

tor of one, meaning that the whole available frequency band is

used in all cells. However, this is a major drawback when detect-

ing one user, due to the interference caused by the non-orthogo-

nality between the spreading waveforms of different users. This

interference, which comes both from users within the cell and

from adjacent cells, results in degraded performance and the sys-

tem may in many cases be severely interference limited. Also, if

not an accurate and fast power control is applied such that theusers powers differ by only a few dB at the base station, a strong

user may partially or even completely mask out a weak user (the

near-far problem). One possible solution that may increase the

capacity of the system and/or alleviate the near-far problem is to

apply a multiuser detector that jointly detects all users (at least

the ones within a cell) to combat the interference. The optimum

multiuser detector has been found [1], but is much to complex for

practical use. Research has therefore focused on finding good

suboptimum detectors which have been subject to much study in

recent years [2], but usually with the assumption of perfect esti-

mates of channel parameters such as time delays, amplitudes and

phases. Recently, however, it has been indicated that a multiuser

detector (the decorrelator) is very sensitive to errors in the time

delay estimation [3], while other studies have claimed that some

other algorithms are robust against such errors [4][5]. The scope

of this paper is to present a more comprehensive investigation of

the robustness of multiuser detectors. We investigate the perfor-

mance of multiuser detectors when errors in timing and phase

estimates are present. The near-far resistance of multiuser detec

tors under these more realistic conditions is also investigated.

II. SYSTEM MODEL

We begin by describing the model of the system that is studied

All users transmit simultaneously on the same channel and at the

same frequency band. The composite low pass equivalent signa

from the Kusers, entering the base station, is then

, (1

where are the time delays modeled as uniformly distributed

on , and is the complex additive white Gaussian

noise (AWGN) with independent real and imaginary parts, both

with the spectral density . User ks signal is given as

, (2

where the energy is given by , the symbol period by T, the

received signal phase by and the waveform by

. (3

Here is the BPSK modulated data (i.e. ) transmitted

at time i and is the spreading waveform consisting of

chips, , of rectangular pulse shape and duration

. That is

. (4

The receiver performs joint detection of the users by means of a

multiuser detector (MUD).

r t( ) sk t k( )k 1=

K

n t( )+=

k0 T,[ ] n t( )

N0 2

sk t k( )2EkT

---------dk t k( )ejk=

Ekk dk t( )

dk t( ) bk i( )ck t iT( )i

=

bk i( ) 1{ }ck t( ) N

cki( ) 1{ } p t( )

Tc

ck t( ) cki( )p t iT c( )i 0=

N 1

=

Robustness of DS-CDMA Multiuser Detectors

Pl Orten and Tony Ottosson

Dept. of Information Theory, Chalmers University of Technology, S-412 96 Gteborg, Sweden

email: Pal.Orten@it.chalmers.se, Tony.Ottosson@it.chalmers.se

8/6/2019 10.1.1.64.96

2/5

III. MULTIUSER DETECTORS

A. Conventional detector (matched filter detector)

The conventional detector is an optimum multiuser detector when

we have orthogonal waveforms. It is therefore not optimal for

asynchronous systems and/or dispersive channels where the

waveforms can not be made orthogonal. The output of the

matched filter for user kand time i is

(5)

where and are estimated time delay and phase of user k.

The estimates of the transmitted bits are then given as

. (6)

B. Decorrelator Detector

The decorrelator detector performs a linear transformation on the

outputs from the conventional correlation detectors. This trans-

formation removes the interference between the users and the

performance is therefore independent of the different users

received powers. The disadvantage is that, like the zero forcingequalizer, it causes noise enhancement. Using a block based

model of the system [6], with a block-length of Mbits per user,

the decorrelator estimates of the transmitted bits can be expressed

as

, (7)

where is an estimate of the correlation matrix , and the out-

put from the bank of matched filters (correlation receivers) is

, (8)

where

(9)

(10)

(11)

and the noise vector is additive Gaussian and colored. The

amplitude matrix is a diagonal matrix containing the ampli-

tudes of all users and all times during the block length

(see [6] for more details). Furthermore the entries in the correla-

tion matrix are given by

. (12

C. Minimum Mean-Square-Error Detector

The transformation done by the decorrelator completely decorre-

lates the users. The Minimum Mean-Square-Error (MMSE

detector, on the other hand, performs the linear transformation on

the matched filter outputs that minimizes the mean square error

(MSE). The detected bit sequence can be expressed as [7]

. (13

As the signal-to-noise ratio goes to infinity the decorrelator and

the MMSE detectors become equal. For low signal-to-noise

ratios the MMSE detector outperforms the decorrelator due to the

noise enhancement property of the decorrelator.

A different approach to multiuser detection is that of first detect

ing one or several users using the conventional detector, estimate

their transmitted low-pass equivalent signals and then subtrac

these signals from the received signal. The whole procedure

might then be repeated. This method is named interference cancellation. Two main types exist; successive- and parallel interfer

ence cancellation.

D. Successive Interference Cancellation

In successive interference cancellation one user at a time is

detected and cancelled [8]. The obvious solution is to detect and

cancel the users in the order of decreasing powers. Hence, a rank

ing based on powers is needed. This ranking results in a renum

bering of users such that , where the are

the reordered users. Now the received low-pass equivalent signa

before applying the conventional receiver to user is

. (14

In the estimation of either a nonlinear device based on

decisions for user l or a linear device based on the matched filter

outputs can be used. We will in the following use the nonlinear

approach: decisions are taken by the conventional receiver and

these are then respread and subtracted from the composite signal

It is possible to generalize this cancellation procedure to more

than one stage ,[9], using

(15

as the estimate of the received signal at stage n before using the

conventional receiver ((5) and (6) substituting with

to detect user . At each stage the users may be reordered.

yk i( )

yk i( ) Re r t( )e jk{ }ck t iT k( ) tdiT k+

i 1+( )T k+

=

k k

bk i( ) yk i( )( )sgn=

bde c R1 y( )sgn=

R R

y RWb n+=

y yT 1( ) y 2( ) yT M( ), ,,[ ]T=

y i( ) y1 i( ) y2 i( ) yK i( ), ,,[ ]T=

b bT 1( ) bT 2( ) bT M( ), ,,[ ]T=

b i( ) b1 i( ) b2 i( ) bK i( ), ,,[ ]T=

R

R 0( ) R 1( ) 0 0R 1( ) R 0( ) R 1( ) 0 0

......

......

... ...

0 0 R 1( ) R 0( ) R 1( )0 0 0 R 1( ) R 0( )

=

n

W

2Ek T

R i( )

Rkl i( ) k l( ) ck t k( )cl t iT l+( ) td

cos=

bmmse R1

2---N 0W

2+

1

y sgn=

E1' E2' EK'> > > k'{ }

k'

rk' t( ) r t( ) sll 1'=

k' 1

t l( )=

sl t l( )

n 1>( )

rk'n( ) t( ) r t( ) sl n( )

l 1'=

k' 1

t l( ) sl n 1( )l k' 1+=

K'

t l( )=

r t( ) rk'n( ) t( )k'

8/6/2019 10.1.1.64.96

3/5

E. Parallel Interference Cancellation

The parallel interference cancellation scheme differs from the

successive cancellation in that it detects all users at the same time

(in parallel) and then cancels the interfering signals. Hence, the

received signal at stage n before detection of user k(no reorder-

ing needed) is

. (16)

As the zeroth stage we use the conventional detector given by (5)

and (6).

IV. NUMERICAL RESULTS

A. Introduction

The DS-CDMA system described in Section II has been simu-

lated to obtain numerical results under different non-perfect con-

ditions, for each of the detectors presented. Using these results it

is then possible to compare the detectors and their robustness.

The detectors investigated here have different complexity, but are

in this paper only compared with regard to their robustness. Forall of the results presented we have K= 10 users, a spreading fac-

tor of N = 32 and random spreading sequences. The different

users have uniformly distributed random phases, and time delays

uniformly distributed over the symbol interval.

Fig. 1 shows the performance of the detectors described in Sec-

tion II with perfect chip synchronization, no phase estimation

errors and perfect power control. These results serve as a refer-

ence for what can be achieved for this system under ideal condi-

tions. We see that there is little difference between the

decorrelator and the MMSE detector. The MMSE detector is

slightly better due to the noise enhancement caused by the decor-

relator. The performance of these two detectors improves andbecomes equal as the signal to noise ratio increases. For the lower

and medium signal to noise ratios, successive interference can-

cellation (2 stages) yields the better performance among the

detectors presented. However, like the parallel interference can-

celler, the successive canceller reaches a floor on the bit error

rate.

B. Synchronization errors

It is interesting to see how much degradation we will have when

the synchronization is not perfect. In this work we want to inves-

tigate the effect of non-ideal timing estimation for different

detectors. We therefore apply a given constant synchronization

error to all users. In a practical system all users will of course notexperience this synchronization error, and this scenario can there-

fore be considered as worst case. Fig. 2 shows the performance of

the detectors as a function of the synchronization error, for

= 8 dB. As can be seen the multiuser detectors are more

sensitive to synchronization errors than the conventional detector.

Even for a synchronization error of only 10% of the chip interval

(0.1 Tc), the degradation is significant. From the results in Fig. 2

it can be seen that the multiuser detectors are equally sensitive to

synchronization errors, and they all approach the conventiona

receiver as the synchronization error increases.Phase error

In a realistic situation the phase estimates will not be perfect. For

an AWGN channel the phase estimates will be rather accurate

but in mobile radio systems one can not expect negligible phase

estimation errors. Similar to what we did for timing errors, we

assume a given constant phase error. The results presented shows

the performance that can be expected if all users experience this

amount of phase estimation error. The bit error rate for the detec

tors as function of the phase error at = 8 dB is given in

Fig. 3. We see that all detectors have about the same degradation

rkn( ) t( ) rn 1( ) t( ) sl n 1( )

l 1=l k

K

t l( )=

Eb/N0

Figure 1. Bit error rate for the different detectors as

function of with perfect synchronization, perfect

phase estimates and equally strong users.

Figure 2. Bit error rate as function of the synchronization

error for different multiuser detectors at = 8 dB,

perfect phase estimates and equally strong users.

0 2 4 6 8 10 12

105

104

103

102

101

BitErrorRate

Eb

/N0

[dB]

Conventional

Parallel 1 stage

Parallel 2 stages

Successive 1 stage

Successive 2 stages

Decorrelator

MMSE

Eb/N0

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.410

4

103

102

101

BitErrorRate

Synchronization error [t/Tc]

Conventional

Parallel 1 stage

Parallel 2 stages

Successive 1 stage

Successive 2 stages

Decorrelator

MMSE

Eb/N0

Eb/N0

8/6/2019 10.1.1.64.96

4/5

as the phase error increases. The effect of phase estimation errors

seem however, to be less severe than that of synchronization

errors.

To have an idea about the combined effect of synchronization-

and phase estimation errors, the bit error rate as function of

is plotted in Fig. 4 for a synchronization error of 0.2 Tc,

and a phase error of 10o. Note that the scaling on the axis is dif-

ferent from that of Fig. 1. The bit error rates for the best detectors

at = 10 dB, have increased by approximately a factor of

10 compared to that shown in Fig. 1.

C. Near-far effect and synchronization error

Fast and accurate power control is hard to obtain in a practical

system, and it is therefore likely that the users will have different

powers. The decorrelator, which removes the interference, is ide-

ally not sensitive to different signal powers. Successive interfer

ence cancellers utilize the fact that different users have differen

strength by detecting the stronger user first. It is interesting to see

how near-far resistant different detectors are when the synchroni

zation- and phase estimation is non-perfect. Fig. 5 presents

results for the detectors as function of the near-far ratio for per-

fect synchronization and perfect phase estimation. By near-far

ratio we mean the difference between the energy Ek, of each of

the interfering users, and the energy E1 of the wanted user. Al

the multiuser detectors are rather insensitive to the variations in

the interfering signal strengths, and are thus near-far resistant

The decorrelator removes all interference and is therefore not a

all influenced by other users being stronger. In Fig. 6 the bit error

rates for different near-far ratios are plotted when the synchroni-

zation error is equal to 0.2Tc, and the phase error is equal to 10o

We now see that none of the detectors are near-far resistant. Com

pared to the case with perfect parameter estimation, they have al

come much closer to the conventional detector, and their sensitiv

ity for changes in the near-far ratio is the same as for the conven

tional detector forEk- E1 > 2 dB. None of the detectors seem to

be more (or less) near-far resistant than the other detectors. In

practical systems with non-ideal estimators it is therefore vital to

have good power control regardless of which detector is usedNote that in the near-far plots the MMSE detector has been taken

out since it can hardly be distinguished from the decorrelator.

V. CONCLUSIONSWe have studied the performance of a DS-CDMA system using

either a conventional matched filter detector or a multiuser detec-

tor in the presence of errors in the channel parameters. The stud-

ied multiuser detectors are the decorrelator, the MMSE detector

and the successive and parallel interference cancellation detec

Figure 3. Bit error rate as function of the phase error for

different multiuser detectors at = 8 dB, perfect

synchronization and equally strong users.

Figure 4. Bit error rate for the multiuser detectors with

synchronization error of 20% of the chip interval, and

phase error of 10 degrees.

Eb/N0

Eb/N0

0 5 10 15 20 25 3010

4

103

102

101

BitErrorRate

Phase error [degrees]

Conv.

PIC 1

PIC 2

SIC 1

SIC 2Decorr.

MMSE

Eb/N0

0 2 4 6 8 10 1210

4

103

102

101

BitErrorRate

Eb

/N0

[dB]

Conventional

Parallel 1 stage

Parallel 2 stages

Successive 1 stage

Successive 2 stages

Decorrelator

MMSE

Figure 5. Bit error rate for the multiuser detectors as

function of the near-far ratio, no synchronization error and

no phase error, = 8 dB. E1 denotes the energy of

the wanted user,Ekdenotes the energy of the other users.

6 4 2 0 2 4 6 8 1010

4

103

102

101

100

EkE

1[dB]

Conv.

PIC 1

PIC 2

SIC 1

SIC 2

Decorr.

Eb/N0

8/6/2019 10.1.1.64.96

5/5

tors. According to the results presented in this paper there is no

significant difference in the robustness of the different detectors.

The performance degrades rapidly as the synchronization error

increases, and all detectors experience almost the same degrada-

tion. Phase errors also affect the different detectors equally. For

moderate phase errors however, the impact on performance is

rather small. Furthermore the near-far resistance of the detectors

are severely affected by synchronization and phase errors. The

conclusion is therefore that the studied detectors are not robust

against parameter estimation errors in a realistic situation. In

spite of this discouraging result, the multiuser detectors still out-

perform the conventional matched filter detector, but the question

is whether this rather small benefit in performance is worth the

increase in complexity a complexity that may be better spent

on the decoding of a powerful channel code.

VI. FUTURE WORK

For future work it will be interesting to investigate the robustness

of multiuser detectors on fading mobile channels, and a different

loading of the system. It is reasonable to believe that pulse shap-

ing will have impact on the robustness against synchronization

errors and so investigations should be done with pulse shaping

other than rectangular. Pulse shaping also affects the correlation

properties of the signature waveforms.

ACKNOWLEDGMENT

This work has been performed in the framework of the project

ACTS AC090 FRAMES, which is partly funded by the European

Community.

REFERENCES

[1] S. Verd, Minimum probability of error for asynchronous

Gaussian multiple access channels, IEEE Transactions on

Information Theory, vol. IT-32, no. 1, pp. 85-96, January

1986.

[2] S. Moshavi, Multi-user detection for DS-CDMA communi

cations, IEEE Communications Magazine, vol. 34, no. 10

pp. 125-136, October 1996.

[3] S. Parkvall, E. Strm, and B. Ottersten, The impact of tim

ing errors on the performance of linear DS-CDMA receiv-

ers, IEEE Journal on Selected Areas in Communications

vol. 14, no. 8, pp. 1660-1668, October 1996.

[4] R. M. Buehrer, A. Kaul, S. Striglis, and B. D. Woerner

Analysis of DS-CDMA parallel interference cancellation

with phase and timing errors, IEEE Journal on Selecte

Areas in Communications, vol. 14, no. 8, pp. 1522-1535

October 1996.

[5] F.-C. Cheng and J. M. Holtzman, Effect of tracing error on

DS/CDMA successive interference cancellation, in Proc

Communication Theory Mini-Conference (GLOBECOM94), San Francisco, USA, 1994, pp. 166-170.

[6] R. Lupas and S. Verd, Near far resistance of multiuser

detectors in asynchronous channels,IEEE Transactions on

Communications, vol. 38, no. 4, pp. 496-508, April 1990.

[7] Z. Xie, R. T. Short, and C.K. Rushforth, A family of subop

timum detectors for coherent multi-user communications,

IEEE Journal on Selected Areas in Communications, vol. 8

no. 4, pp. 683-690, May 1990.

[8] P. Patel and J. Holtzman, Analysis of a Simple Successive

Interference Cancellation Scheme in a DS/CDMA system,

IEEE Journal on Selected Areas in Communications, vol12, no 5, pp. 796-807, June 1994.

[9] A. Johansson and A. Svensson, Multistage interference

cancellation in multi-rate DS/CDMA systems, in Proc

PIMRC95, Toronto, Canada, 1995, pp. 965-969.

[10] M. K. Varanasi and B. Aazhang, Multistage detection in

asynchronous code-division multiple access communica-

tions,IEEE Transactions on Communications, vol. 38, no

4, pp. 509-519, April 1990.

Figure 6. Bit error ratio for the multiuser detectors as

function of the near-far ratio, synchronization error equal

to 0.2Tc and phase error equal to 10 degrees, = 8

dB.

6 4 2 0 2 4 6 8 1010

3

102

101

100

BitErrorRate

EkE

1[dB]

Conv.

PIC 1

PIC 2

SIC 1

SIC 2

Decorr.

Eb/N0