Performance comparison of multi-user detectors for the downlink of a broadband MC-CDMA system

Abstract

In this paper multi-user detection techniques, such as Parallel and Serial Interference Cancellations (PIC & SIC), General Minimum Mean Square Error (GMMSE) and polynomial MMSE, for the downlink of a broadband Multi-Carrier Code Division Multiple Access (MCCDMA) system are investigated. The Bit Error Rate (BER) and Frame Error Rate (FER) results are evaluated, and compared with single-user detection (MMSEC, EGC) approaches, as well. The performance evaluation takes into account the system load, channel coding and modulation schemes.

Full text

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Performance comparison of multi-user detectors for the
downlink of a broadband MC-CDMA system

F. Portier***, R. Legouable*, L. Maret **, F. Bauer ****, N.Neda *****,
J-F. Hélard***, E. Hemming****, M. des Noes**, M. hélard*
*France Télécom R&D: 4 rue du clos courtel, 35510 Cesson-Sévigné, France
rodolphe.legouable/maryline.hélard@francetelecom.com
**CEA-LETI: 17 rue des Martyrs 38054 Grenoble cedex 09
mathieu.desnoes/luc.maret@ cea.fr
***IETR/INSA: 20 Ave. des Buttes de Coësmes, 35043 Rennes Cedex, France
fabrice.portier/ jean-francois.helard@insa-rennes.fr
**** Nokia Research Center, Meesmannstr. 103, 44807 Bochum, Germany
franziskus.bauer/erwin.hemming@nokia.com
***** Centre for Comm. Syst. Research, University of Surrey,Guildford, Surrey GU2 7XH
n.neda@surrey.ac.uk

ABSTRACT
In this paper multi-user detection techniques, such as
Parallel and Serial Interference Cancellations (PIC & SIC),
General Minimum Mean Square Error (GMMSE) and
polynomial MMSE, for the downlink of a broadband
Multi-Carrier Code Division Multiple Access (MC-
CDMA) system are investigated. The Bit Error Rate (BER)
and Frame Error Rate (FER) results are evaluated, and
compared with single-user detection (MMSEC, EGC)
approaches, as well. The performance evaluation takes into
account the system load, channel coding and modulation
schemes.

I. INTRODUCTION

Since 1993, a modulation technique called MC-CDMA has
been proposed for multimedia services in high data rate
wireless networks [1]. This promising multiple access
scheme with high bandwidth efficiency combines the
CDMA as a multiple access technique and the OFDM as a
Multi-Carrier transmission system. Unfortunately, it
suffers from multiple access interference (MAI) which
limits its performance.
In this paper, the performance of various multi-user
detectors that mitigates MAI for the downlink of a MC-
CDMA transmission are evaluated.
In section II, the system parameters defined in the IST
MATRICE project [2] are described.
In section III, the multi-user detectors (MUD) that have
been evaluated are described, and in section IV the
simulation results are given. Eventually, section V
summarises the results and draws conclusions.

II. SYSTEM DESCRIPTION

The general scheme of the MultiCarrier (MC) system used
in this work is depicted in Figure 1. The convolutional or
turbo encoded, punctured and interleaved data signal is
modulated with either QPSK or 16 QAM and fed into a
discrete Hadamard Transform for spreading. The resulting
chips are then frequency interleaved and distributed over
the whole bandwidth. This signal is then processed into a
N points IFFT, provided with a guard interval and
transmitted into the channel. At the receiver the guard
interval is removed and the signal is transformed into the
frequency domain by an FFT. In the investigations
presented herein perfect channel knowledge is assumed.
The frequency domain signal and the channel coefficients
are handed over to the multi-user detector modules that are
compared in this contribution. The output of the MUD
module is despread and soft demapped. The soft bits are
deinterleaved, depunctured and then processed by a
channel decoding unit,
convolutional/Viterbi or a turbo decoder.

which is either a
Binary
sourcesource
Channel
codingcoding
Punct. Punct.
Π Π Π ΠΠ Π Π Π
Freq.
MUXMUX
OFDM
modul.modul.
BER
FERFER
Channel
decodingdecoding
De-
Punct.Punct.
Soft de-
mappingmapping
OFDM
demod. demod.
Freq.
DMUXDMUX
SISO
channelchannel
AWGNAWGN
Π Π Π Π-1
Π Π Π Π-1
MappingMappingSpreadingSpreading
Despread.Despread.
MUD MUD
BinaryChannel Freq.OFDM
BERChannelDe-Soft de-OFDMFreq.
SISO

Figure 1: System Overview.
Representing the transmission process in the frequency
domain, the MC system states in a very simple form:
−
1K

nxHy
+= ∑
=
0k
k
(1)
where xk is the Nx1 vector of the signal transmitted by user
k, y is the Nx1 vectors representing the received signal, n
is the additive white Gaussian noise vector with
E{nnH} = σn
diagonal matrix collecting the channel frequency response
at subcarriers frequencies :
2.IN where IN is the identity matrix, and H is a
{}








==
−
N
k
j
kN
eHHHHHdiag
π
2
110
with
L
H

A general expression for a downlink MC-CDMA system is
the following:

Page 2

()dCIxx
u
N⊗==∑
k
−
=
1
0
K
k
(2)
where C =(c1, …, cK) is SFxK the matrice containing all the
used spreading codes and d is the (KNux1) vector
collecting the transmitted symbols (SF is the spreading
factor, K the number of active codes, Nc is the number of
modulated carriers and Nu = Nc / SF). They are grouped by
Nu blocks of K symbols :
d = (d1, d2, ..., dNu)T

dm= (d1m, d2m, ..., dKm)T is the (Kx1) vector collecting the K
symbols to be transmitted in mth sub-band. Expression (2)
is depicted schematically in Figure 2.

HH
++
nn
yy
++
c1
c1
d11...d1Nu
d11...d1Nu
c2
c2
cK
cK
d21...d2Nu
d21...d2Nu
dK1...dKNu
dK1...dKNu

Figure 2: Frequency transformed, schematic view of
MC-CDMA.
In the sequel, the equalizer works on each subband
separately. Thus the received signal in the mth subband is :
n CdHy
+=
mmm
where Hm =diag (HmNu, …, HmNu + SF-1). For shake of
simplicity, the index m will be dropped.
The received signal y includes the code multiplexed
symbols of all users. As the channel disrupts the
orthogonality of the codes multiple access interference
(MAI) occurs, leading to bad decisions at the receiver side.

III. MUD DESCRIPTION

The multi-user detectors can be split in two families: linear
equalizers and interference cancellation schemes.
In this paper the MMSE Combining (MMSEC), Global
MMSE (GMMSE) equalizers
implementation of GMMSE are evaluated. Then, non-
linear Interference Cancellation algorithms are introduced,
using Successive or Parallel SUD schemes combined with
the despreading process.

A. MMSEC

The best performance among Single-User (SU) detectors
are obtained with MMSEC, which is a trade-off between
(3)
and a polynomial
MAI reduction (restoring the orthogonality among users),
and noise enhancement. It minimizes the mean square
2
ˆ
kk
xx −
the channel and SNR over each sub-carrier.
At the receiver side, the equalizer is characterized by a
diagonal matrix G followed by a despreading operation :
ckk
d
=
Equalizer coefficients, applied independently on each
carrier, are equal to:
value of the error
and needs information about
Gy
H
ˆ


ρ
γc
l
l
+
S
l
H
H
|
g
/ 1|
2
*
=
(4)

∑
=
n
−
+
=
1
0
2
2
/ 1||
||
F
S
cn
n
F
H
H
γ
ρ
(5)
where
is the normalization factor in order to cope with high order
modulations, as 16 QAM for example.

B. GMMSE

Performing the Mean Square Error criterion on the
received signal, we obtain a generalized detection joining
equalization and despreading [6]. Contrary to MMSEC
which works at chip level (per sub-carrier), GMMSE
inverts the channel at symbol level, taking into account
both the spreading codes and the propagation channel. As
well, it makes a trade-off between MAI reduction and
noise enhancement.
2
ˆ
kk
dd −
, the optimal weighting vector,
according to Wiener filtering, is:


ΓG
=

where Γ Γ Γ Γyy is the autocorrelation matrix of the received
vector y and Γ Γ Γ Γydk is the cross-correlation between the
desired symbol dk and the received vector y. The sub-
carrier noises have the same variance and are independent.
In the downlink, since the user signals have the same
power (E{dk
E{ddH} = Es.IK. Then, the equalization coefficient matrix,
assuming a normalized code matrix C, is:

c γ is the signal to noise ratio per sub-carrier, and ρ
To minimize
k
yd
1
yyΓ
−
(6)
2} = Es) and are independent, we can write

1
2
N
−






+=
IH HCCHcG
S
HHHH
k
E
σ
(7)

In case of full load (K = SF), C.CT = IK, Eq.(7) leads to the
same equalizer as MMSEC. On the other hand, when the
capacity is not full (K < SF), the equalization coefficient
matrix G is no more diagonal. In that case, the Global
MMSE (GMMSE) algorithm outperforms MMSEC, since
it minimizes the decision error taking into account the
despreading process instead of minimizing the error
independently on each sub-carrier. However, whatever the

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number of active users K, this solution implies to solve a
SF x SF linear system.
An alternative formulation, which is strictly equivalent,
consists in applying the matched filter to received vector y
before MMSE filtering. With this solution, used for
implementation, we get a new expression :

( ) ()
HH
S
N
H
E
HCI HC HCeG
H
k
1
2
−






+=
σ
ρ
(8)

where ek is the column vector with zeros everywhere
excepted in the kth position.
This equalization is normalized in order to cope with high
order modulations. The normalization coefficient is:




=





However, by contrast with equation (7), applying equation
(8) only implies to solve a K x K linear system.

C. polynomial GMMSE

The optimal GMMSE receiver offers very good
performance, but its complexity is high due to the matrix
inversion operation. Moreover, if a long scrambling code is
used in addition to the Walsh-Hadamard channelization
codes, the equalizer has to be computed for every new
MC-CDMA symbol. This prevents to use this latter
receiver at the mobile terminal. One solution is to replace
matrix inversion by a polynomial expansion of this matrix.
For practical reasons, this sum shall be truncated, leading
to lower performance than the infinite polynomial MMSE
receiver:
(
∑
=
i
The principle of this receiver is to compute the coefficients
(ak(i))i=0, …, I-1 of the polynomial which minimize the mean
2
ˆ
kk
dd −
:

1
2
n
()
HH
s
diag
E
σ
ρ
−







+
C HC HCI HC (9)
)()
−
−
−=+
1
0
1
) 1(
I
i
HHiHHH HCCHC HCI

square error
yH HCCHck
iHH
I
i
k
HH
k
i ( )(ad
ˆ
)
1
0∑
=
−
=

The solution of this minimization problem was first found
by Moshavi and al [7]. Unfortunately, the polynomial
coefficients depends on a complex way of the spreading
codes and channel coefficients which makes its
implementation very complex. In this study we
implemented a solution developed in [8] for DS-CDMA
systems. It consists in applying results from the random
matrix theory in order to eliminate the dependence of the
polynomial coefficients on the actual code values. Only the
property that the codes are orthogonal is taken into
account.


D. PIC / SIC
In order to handle a large number of users, receivers can
also implement sub-optimal non-linear interference
cancellation (IC). The principle of IC is to detect the
information of the interfering users and to reconstruct the
interfering contribution in order to subtract it from the
received signal. IC can be performed in parallel for all
interfering users with Parallel Interference Cancellation
(PIC) detectors, or successively
Interference Cancellation (SIC) detectors where only the
strongest interferer remaining after the previous IC stage is
cancelled [5]. In our simulations, the SUD technique used
at each stage is MMSE, and the number of stages is fixed.

with Successive
Successive Interference Cancellation
The SIC detector first detects the most powerful interfering
user and then cancels its contribution from the received
signal. The second strongest interferer is then cancelled
and so on. The processing may be repeated for a few or for
all users. A complete detector would consider all users, but
commonly only the interferers stronger than the useful one
are suppressed. SIC detector is generally used when the
power of some users are higher than the power of the
useful user. Since processing one supplementary stage
leads to an additive time delay, a trade-off between the
number of stages and the total acceptable delay has to be
found. The process is carried out iteratively until the
remained interferers are considered insignificant. The
resulting signal is finally despread. The data detection may
be either hard or soft.
Parallel Interference Cancellation
The Parallel Interference Cancellation (PIC) structure is
based on an estimation of the total interference due to the
simultaneous other users in order to remove it from the
received signal. The contribution of all interfering users is
cancelled in parallel reducing the time delay of a SIC
detector. The expression of this iterative system for the ith
stage and the kth user is given by the following:

ˆ
H
i
k
dHyGc
k









−=
∑
=
j
−
≠
−
1
0
k
) 1(
j
)(
)(
ˆ
K
j
j
i
idc
(i)
(10)


with the expression of the initial stage given by:
i
k
d

yGc
(0)
k
H
=
)( ˆ


The received signal is first equalised by a SU technique,
then it is despread by each code. An Inverse Fast
Hadamard Transform (IFHT) can be implemented since
the system is synchronous. As for SIC detector, data
detection may be either hard or soft. After detection, the
data is spread again, tapped by the channel coefficients H
and then subtracted from the received signal. Finally, the
resulting signal with lower MAI term is then equalised,

Page 4

despread and detected. We can note that the second
equalizer structure (G(i)) may be different from the first one
(G(i-1) ).


III. SIMULATIONS RESULTS

In order to compare all the proposed detection techniques,
simulation results have been carried out in terms of Bit
error Rate (BER) and Frame Error Rate (FER) according to
the system load. The BRAN E propagation channel model,
representative of urban environment and defined into the
ETSI-BRAN project for HIPERLAN2 [3], has been
considered. The simulations have been launched with the
following simulation parameters:
•
Sampling frequency = 57.6MHz;
•
Velocity of 60km/h;
•
FFT size N = 1024;
•
Guard interval of 216 samples, allowing the
absorption of all echoes;
•
Number of available modulated carriers Nc = 736,
leading to a signal bandwidth of 41.46MHz;
•
Walsh Hadamard spreading codes of length of 32
chips are used, leading to Nu = 23 spread data
symbols per OFDM symbol;
•
The frame structure is composed of 30 OFDM
symbols
•
Random time and regular frequency interleaving
are implemented

Simulation results have been obtained either with the
UMTS convolutional or turbo channel coding schemes
(CC and TC) [4].
In order to show the behaviour of all techniques according
to the system load, some performance results have been
extracted from the BER and FER curves to obtain the
necessary energy per bit to noise ratio, Eb/N0, to reach a
fixed BER or FER according to the number of active users.
Figure 3 and Figure 4 present the required Eb/N0 values to
reach a BER equals to 10-4 when using respectively CC
and TC schemes. We note that the performance decreases
as the system load increases and the MAI is not totally
mitigated by the simulated MUD. In Figure 3, for capacity
superior to one half, we also remark that MMSEC
outperforms the one-stage PIC and global SIC detectors,
showing that IC detectors lead to bad decisions into the
iterative process, generating errors. In addition, as some
errors have been made into the IC process, it generates bad
metric computations at the input of the decoder, leading to
error propagations at the decoder level. This result
confirms the one obtained in [5]. Even if these results have
been obtained with implementation of hard decisions into
the IC process, no significant gain would have been
recorded with soft decisions. However, even if the
GMMSE detector gives the best performance, especially at
half load, the IC detectors, the MMSEC and GMMSE
receivers are very closed in terms of performance (within
0.5 dB), while EGC and asymptotic polynomials receiver
performance are worse. As previously mentioned in
mathematical formulations, MMSEC and GMMSE
techniques have similar performance results at full load.
In Figure 4, as opposed to the QPSK modulation, the
receivers can be clearly ranked. The linear detectors
(GMMSE and MMSEC) offers the best performance
results. PIC and SIC detectors with turbo-coded scheme do
not provide good performance at low signal to noise ratios
(which is the case with usual turbo codes) due to bad
decisions of the estimation of the interferers into the IC
process. GMMSE is the scheme, which offers the best
results mainly with non full load systems. Compared to the
MMSEC scheme, the gain is of 2dB for 3/4 rate turbo
coded 16QAM and half loaded system. This gain is
significant but leads to an increase of the system
complexity. In Figure 4, performance results of EGC and
asymptotic polynomials receiver have not been plotted
because of high error floor. In fact, EGC and asymptotic
polynomials receivers are too much sensitive to MAI with
a 16 QAM constellation. Using a large constellation will
increase the global level of MAI, and at the same time, the
detector is more sensitive to noise level since the distance
between 2 points of the constellation is smaller than with a
QPSK modulation. Eventually, EGC and asymptotic
polynomials receivers are not suited for the downlink of a
high bit rate MC-CDMA system.
Figure 5 and Figure 6 present the required Eb/N0 values to
reach a FER equals to 10-2 when using respectively CC and
TC schemes until half load. The general behaviour of these
FER curves is identical to the BER one, leading to the
same conclusions.



CC 1/2 - QPSK - BER = 10-4
4,00E+00
5,00E+00
6,00E+00
7,00E+00
8,00E+00
9,00E+00
1,00E+01
1,10E+01
08 1624 32
Nb of codes (K)
Eb/No (dB)
EGC
PIC (1 stage)
SIC
MMSEC
GMMSE
Poly MMSE

Figure 3 : Influence of system load on BER for CC and
QPSK.

Page 5

TC 3/4 - 16-QAM - BER = 10-4
9,00E+00
1,00E+01
1,10E+01
1,20E+01
1,30E+01
1,40E+01
1,50E+01
1,60E+01
1,70E+01
08 1624 32
Nb of codes (K)
PIC (1 stage)
SIC
MMSEC
GMMSE

Figure 4 : Influence of system load on BER for TC and
16-QAM.
CC 1/2 - QPSK- FER = 10-2
4,00E+00
5,00E+00
6,00E+00
7,00E+00
8,00E+00
9,00E+00
1,00E+01
1,10E+01
08 16
Nb of codes (K)
Eb/No (dB)
EGC
PIC (1 stage)
SIC
MMSEC
GMMSE
Poly MMSE

Figure 5 : Influence of system load on FER for CC and
16-QAM.
TC 3/4 - 16 QAM- FER = 10-2
8,00E+00
9,00E+00
1,00E+01
1,10E+01
1,20E+01
1,30E+01
1,40E+01
1,50E+01
1,60E+01
08 16
Nb of codes (K)
Eb/No (dB)
PIC (1 stage)
SIC
MMSEC
GMMSE

Figure 6 : Influence of system load on FER for TC and
16-QAM.

VI. CONCLUSION

The bit error rate and frame error rate performance of
multi-user detection techniques for the downlink of a MC-
CDMA system were presented. It was seen that the
GMMSE outperforms all other multi-user detection
techniques, especially for high bit rate scenarios, whereas
the EGC and polynomial MMSE schemes results in very
poor performances. However,
computationally excessive. It was also observed that the
MMSEC could provide a better trade-off between
performance and complexity, especially under high load
conditions.

ACKNOWLEDGEMENTS

The work presented in this paper was carried out in the
project Matrice (MC-CDMA Transmission Techniques for
Integrated Broadband Cellular Systems) that is supported
from the European Commission in the framework of FP5
with the contract number IST-2001-32620. The authors
would like to acknowledge for this support and the
possibility to carry out the research work.

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the GMMSE is
wireless radio networks.
Type 2, Technical
of wireless information