Int. J. Communications, Network and System Sciences, 2010, 3, 767-772
doi:10.4236/ijcns.2010.39102 Published Online September 2010 (http://www.SciRP.org/journal/ijcns)
An Efficient Noisy-ICA Based Approach to
Multiuser Detection in IDMA Systems
Abdelkrim Hamza1,2 , Salim Chitroub1, Gérard Salut2
1LCPTS Laboratoire de Communication et du Traitement du Signal, FEI-USTHB, Alger, Algeria
2Laboratoire d’Analyse et d’Architecture des Systèmes-CNRS;LAAS, F-31077 Toulouse, France
Received July 3, 2010; revised August 7, 2010; accepted September 5, 2010
Abstract
Interleaved Division Multiple Access (IDMA) is a new access scheme that has been proposed in the literature
to increase the capacity of wireless channels. The performance of such systems depends on the accuracy of
the channel state information at the receiver. In this paper, a Noisy-Independent Component Analysis
(N-ICA) based IDMA receiver for multiple access communication channels is proposed. The N-ICA com-
ponent is applied as a post processor. Unlike other IDMA receivers, the proposed scheme detects and separates
the transmitted symbols without channel state information tracking. The performance of the proposed tech-
nique is presented in terms of raw bit error rate (BER) without channel coding for different signal to noise
ratios (SNR). Simulation results demonstrate that N-ICA post processor provides an improvement in perfor-
mance in BER in loaded systems. When the system is not loaded, the proposed post processor has the same
performance as conventional IDMA receiver with less iterations leading to a complexity reduction.
Keywords: IDMA, ICA, Multi-User Detection
1. Introduction
One of the challenges of next generation wireless sys-
tems is the spectral efficiency. The goal is to provide
sufficient quality and capacity to the diverse and rich
multimedia content that need to be transmitted. Recently
proposed Interleave-Division Multiple-Access (IDMA)
communication system is one of the most promising
technologies for high data rate wireless networks [1].
IDMA can be regarded as a special case of Code Divi-
sion Multiple Access (CDMA). In CDMA systems, users
are separated using signatures or spreading codes; while
in IDMA systems, distinct interleavers are employed to
separate users [2].
At the receiver of IDMA system, the signal of the user
of interest needs to be extracted out of the Multiple
Access Interference (MAI) and the Inter Symbol Interfe-
rence (ISI). Moreover, since conventional IDMA detec-
tor is sensitive to channel estimation errors [3], a good
channel tracking algorithm is mandatory. This might
drastically increase the overall complexity at the receiver.
To overcome those drawbacks, in this paper, we propose
a new blind receiver for IDMA systems. In our approach, a
noisy Independent Component Analysis (N-ICA) scheme
is introduced as a post processor. Independent Component
Analysis (ICA) has attracted special attentions in the wire-
less communication fields for interference suppression of
CDMA systems [4,5].
In this paper, we propose to detect and separate the
transmitted symbols without channel tracking and by in-
cluding the noise in the global model; leading to the N-ICA
model. We will show that our model is very suitable for
symbol detection and separation in the IDMA context. In
terms of complexity, as a post processor, the proposed
solution starts the processing just after conventional IDMA
processing. In this case, a hardware reuse is possible if an
FPGA implementation is carried on for example (currently
being finalized). Therefore, the proposed N-ICA block
does not represent a complexity increase in the overall
system.
The remainder of this paper is organized as follows. The
next section is devoted to the IDMA system model. In Sec-
tion 3, we detail the proposed N-ICA model for IDMA. In
Section 4, an estimation algorithm is presented for N-ICA
in an IDMA context. Using some evaluation criteria,
computer simulation results are presented in Section 5 to

768 A. HAMZA ET AL.
provide a comparative study. Conclusions are drawing in
Section 6.
2. IDMA System Model
As shown in Figure 1 (the upper plot is the transmitter
and the lower one is the receiver), we consider an IDMA
system with K users. A single path channel hk and BPSK
modulation are considered here. The nth bit in the se-
quence dk of kth user is spread, generating a sequence
vector denoted ck=[ck(1), ck(2), ..., ck(J)]T where J is the
frame length, C is the spreading factor and the super-
script T is the transpose operator. Then ck is permuted by
an interleaver πk and at the output of the interleaver, the
vector xk=[ xk(1), xk(2), ..., xk(J)]T is obtained. The ele-
ments in ck and xk are considered as chips. The chip rate
is C times higher than the bit rate. Users are distin-
guished mainly by their respective interleavers πk. Each
user can have its own signature sequence or all users can
share the same spreading code [3]. The received signal
can be modeled as:
 
1()
K
kk
k
rjhx jnj


 j=1…J (1)
As illustrated in figure 1, this sub optimal receiver
consists of an elementary signal estimator (ESE) and K
single user a posteriori probability (APP) decoders (DEC)
[1]. The multiple access and coding constraints are con-
sidered separately in the ESE and DEC. The outputs of
the ESE and DEC are extrinsic log likelihood ratios
(LLRs) about {xk(j)} defined in [2]. These LLRs are fur-
ther distinguished by subscripts, eESE(xk(j)) and
Figure 1. IDMA-N-ICA system model.
eDEC(xk(j)), depending on whether they are generated by
the ESE or DEC. A global turbo-type iterative process is
then applied to process the LLRs generated by the ESE
and DEC, as detailed below [1,3].




 
Pr |1,
() log,
Pr |1,
kk
k
kk
rx jh
ex jkj
rx jh


 (2)
2.1. The Basic ESE
The Equation (1) can be rewritten as:




()
kk k
rjhx jj  
(3)


()
kkk
j
rjhx j   (4)
where k

is the distortion including interference plus
noise in r(j) with respect to user-k [3]. The mean and the
variance functions are noted by E(.) and Var(.) respec-
tively.


k
j

can be approximated by a random Gaussian va-
riable.
with mean and variance :






() (())
kkk
EjErjhExj   (5)


()
k
Varj Var  (2
()) ||(())
kk
rjhVarxj (6)
where
  


1(())
K
kk
k
Er jEhxjEnj


 (7)



 

22
1
K
kk
k
Var rjhVarxj



 (8)
Therefore, the log likelihood ratio [1] is given by:










2.() /(())
ESE kkkk
exjhrjE jVarj   (9)
2.2. The DEC Function
The Dec in our structure performs despreading operation
and the extrinsic LLRs eDEC(ck(j)) are used to update
E(xk(j)) and V ar(xk(j)) as [3]:




()tanhtanh()/2
kDECk
Ex jex j (10)






2
1( )
kk
VarEx jEx j (11)
This iterative process is repeated a preset number of
times.
2.3. The ESE Function for Multi-Path Channels
When we consider a multipath fading channel with L
paths; the received signal is represented by:

1
,
10
KL
kl
kl
rjhxjlnjj



 
 (12)
where hk,l are the coefficients related to user k.
Following a similar principle as that for single path we
obtain Algorithm 1 below for detection in a multipath
channel:
Algorithm 1: Detection in a Multi-Path Channel
1) Estimation of interference Mean

A. HAMZA ET AL. 769
 
1
,
10
()( )
KL
kl
kl
ErjhEx jl



 (13)


  
,,
(
klkl k
EjErjlhExj   (14)
2) Estimation of interference variance
  
2
12
,
10
() KL
kl
kl
Var rjhVarxjl




 (15)
     
2
,,klkl k
VarjVar rjlhVarxj   (16)
3) LLR generation
  

 
,
,
,
()2.kl
ESEklk l
kl
rj lEj
exjh Var j



 (17)
 


1
0()
L
E
SEkESE kl
l
exj exj


 (18)
3. ICA and N-ICA Principle
The application of ICA consists of estimating the un-
known input signals from the output signals without
prior knowledge of the channel state information [6].
Let’s suppose that the sources are statistically in-
dependent. This is a fundamental assumption for using
ICA that is generally verified in communication systems [6].
The extraction of the sources can be done by ICA by
exploiting the essential features of the sources and system
[7]. In the simplest form of ICA, we observe n scalar
variables r1, r2, … rn which are linear combinations of l
unknown independent sources or components ICs de-
noted by b1, b2, ..., bl.
If we express the observed random variables with the
vector, r = (r1, r2, ..., rn)T and the ICs variables bj with the
vector b = (b1, b2, ..., bl)T then the relationship is given by
[8]:
mmm
rGbn (19)
where m r is the mth observed data vector, G is an
unknown full rank mixing matrix, m bis an unknown non
Gaussian source vector and m n is an additive Gaussian
noise process.
The goal is to estimate the noise free ICsm busing only
the observations m r and the assumption of the inde-
pendence of the sources. This means that a set of vectors
w1, w2, should be estimated such that W = [w1,w2, ...] is
the separating matrix; therefore, the output source esti-
mations 1, 2, ., .
TT
mm
rrww... i.e.:
T
mm
yWr (20)
are independent and each of them can be used to
represent one of the sources.
3.1. Mathematical Representation of IDMA by
N-ICA Model
In this subsection, we develop the theoretical frame-
work and show the similarity between Noisy ICA
model and IDMA system model. We focus our atten-
tion on synchronous IDMA systems for simplicity and
brevity. However, the method can be extended to an
asynchronous system by extending the observation
interval.
After chip rate sampling i.e. C equal spaced samples
per symbol are taken, the sampled data is processed
within a window of specific size. For synchronous model,
data propagated through a single path channel fall into
the same window of size Tb for desired and interfering
symbols.
The samples are then collected into a C×1 vectors
rm.
,
1
K
mkkmkm
k
rhdsn



 (20)
here k
s
is the C×1 vector representation of kth user’s
interleaved signature sequence andm ndenotes the noise
vector.
The last equation can be rewritten in a matrix form:
bm = [d1,m, d2,m, ..., dK,m]
s1 = [s1,1, s2,1, ..., sC,1]T C×1 vector

11,1
1
,
0
,,
0
m
mK
KKm K
hbn
rss
hb n





















11
,,
mKKmm
rshshbn

 (22)
Equation (22) can be represented in a more compact
form:
mmm
rGbn

 (23)
where the C×K matrix G is assumed full rank. We can
see the similarity between the IDMA model of Equa-
tion (23) and the N-ICA model of Equation (19). The
goal of the Noisy-ICA based IDMA detection is to
recover the symbol vector bm for each user k without
knowing the parametric form of G which depends on
the channel coefficients.
4. N-ICA Estimation Algorithm
The proposed system is a hybrid structure composed of
two parts where a classical IDMA receiver is combined
with a N-ICA block as shown in figure 1. Block IDMA,
described in the previous section, works for a number
of iterations (it) after which the block N-ICA takes
over. The proposed N-ICA will act as a post processor
attached to an IDMA receiver in the presence of noise.
The aim of our N-ICA block is to avoid continuous
tracking of channel state information [9]. In this section,
we will derive estimation algorithms for the proposed
N-ICA post processor in IDMA context.
4.1. Principal Component Analysis Processing
The Principal Component Analysis (PCA) based part of
the model consists of whitening the input signals. This

770 A. HAMZA ET AL.
step of processing is achieved by using the PCA in [10]
to extract the Principal Components (PCs). This can be
done for the noiseless case as follows:
1/2 T
YUGB

 (24)
where the matrix U corresponds to the Eigen vector of
the data covariance matrix C and the diagonal matrix

that contains the related Eigen values

:
1/2
= diag [1/2 1/21/2
12
,,,
n
 
 
] (25)
This PCA processing can be extended to noisy data
using bias removal technique [8]. In the regular ICA
process, the covariance matrix of the noise free data nf
m
r
can be given by:


()
nfnfTT
mm
CErr GG (26)
On the other hand, the covariance matrix of the observed
noisy data can be written as:


TT
mm
Err GG +2n
I
CC   (27)
where 2

is the noise power andn C is the diagonal
noise covariance matrix. In the noise bias removal tech-
nique, the Eigen values and vectors of matrix n C

 is
used for whitening instead of matrix  which is called
quasi-whitening [10].
In fact, quasi whitening can be performed on the noisy
data as follows:
21/2
()
Tm
zIUr 

 (28)
The covariance matrix of quasi white data is then given by:


221
()
T
Ezz II 

  (29)
From (29), we notice that the covariance matrix is
different from the identity matrix. Therefore, we have to
take into account the non-whiteness of the data.
This is achieved by using the fast ICA algorithm that
is presented in the next subsection.
4.2. Fast ICA Algorithm
Since only the second order statistics are used to com-
pute the matrix, the PCA used in the first part of the
model does not provide the best results. Higher order
statistics of the received signals contain additional in-
formation about the non Gaussian properties of the noise.
The purpose of this work is to establish a new scheme
in which the system can take into account such random
deformations in the detection step. To improve the per-
formance, the presence of the noise should be reduced to
the minimum using the extracted PCs without additional
prior knowledge of their statistical properties. This is the
purpose of the ICA based part of the model. Therefore,
the ICA model should include a noise term as well in its
linear transform matrix.
The ICA approach that we present here is our contri-
bution to take into account the noise in the ICA model.
This means that the bias due to noise should be removed,
or at least reduced.
Noisy-FastICA has been applied to the blind source
separation and interference suppression in multiple
access communications before in [11] and FastICA in [9],
[10]. The Noisy-FastICA algorithm performs as follows
(Algorithm 2):
Algorithm 2: Noisy-FastICA
Let k be the desired user,m r, m = 1, .., M the received
block data and b

denotes the estimate of the symbol b.
1) First perform PCA for dimension reduction
2) Quasi- whitened the noisy data using (28)
3) Start ICA
Let t=1 and update




13
(( 1))
T
mm
wtEzwtz





2
3((1) )(1)
Tm
Ewtz wt


where 221 ()
I
I 

 
Normalize w(t) :
 
T
(t)()
wt
wt wt w
If |

(1)
T
wt wt

| < (1 – 10-4), let t= t+1 and go to step
3.
4. Output the estimated desired user’s bit: ,km
b

= sgn
(Zm)
5. Simulation Results
In this section, we present the simulation results of the
proposed Noisy-Independent Component Analysis
(N-ICA) based Interleaved Division Multiple Access
(IDMA) presented in this paper. In all simulation results,
the following notations have been adopted:
It is the iterations number used in IDMA block. Τ
represents the percentage of load rate defined by the ratio
between the number of users and the spreading factor
(K/C). IDMA is the conventional IDMA receiver described
in Section 2.
IDMA-ICA is the hybrid structure described in [12].
IDMA-N-ICA is the proposed hybrid structure described
in Section 3 using the noisy fast ICA algorithm.
To evaluate the detection and separation ability of the
proposed N-ICA model, performances are presented in
terms of raw Bit Error Rate (BER) before decoding for
different Signal to Noise Ratios (SNR). We consider a
time varying channel, BPSK modulation and Gold
spreading codes of length C. Among the parameters that
influence the performances are the effect of load rate and
the number of iterations for IDMA block. The obtained
results are presented in Figures 2-6.
In Figures 2 and 3 we show a comparison between
our proposed post processor N-ICA and the IDMA re-
ceiver for single path and multipath channel respectively.
In Figure 4, performances of our proposed receiver
are presented for different values of τ (rate of load) and a
spreading factor of 63.

A. HAMZA ET AL. 771
Figure 2. Performance comparison between IDMA-N-ICA
and IDMA systems in single path.
Figure 3. Performance comparison between IDMA-N-ICA
and IDMA systems in single path.
Figure 4. IDMA-N-ICA performance comparison for dif-
ferent rate load and C = 63.
Figure 5. Performance comparison between IDMA-N-ICA
and IDMA receiver when c = 31 and τ = 50%.
Figure 6. Performance comparison between IDMA-N-ICA
and IDMA receiver when c = 31 and τ = 100%.
We notice that our proposed scheme handles very well
the MAI interferences since convergence is warranted
even at very loaded systems (τ100%).
Figure 5 shows the added value of our proposed
post-processor N-ICA when compared to the conven-
tional IDMA receiver for loading rate 50% and for a
spreading factor of 31. We notice that both convergence
speed and better BER performances are achieved. There-
fore, the proposed N-ICA approach can be employed in
high loading rate in order to improve the performance of
the system in terms of quality of service. Moreover, in
case of low loading rate (50%), the proposed post processor
allows a reduction in the number of iterations needed by
the IDMA block leading to complexity reduction of the
overall receiver.
In the last simulation scenario, we evaluate the added
value of the noisy ICA post processor over the ICA post
processor. Figure 6 provides a comparison between

772 A. HAMZA ET AL.
IDMA, IDMA-ICA and IDMA-N-ICA receivers when
the spreading factor is 31 and the load rate is 100%.
When SNR is low, N-ICA outperforms the ICA post
processor. However, when SNR is high, both receivers
present the same performance. These observations are
expected since N-ICA takes into account the presence of
noise.
It is worth noting also that both IDMA-ICA and ID-
MA-N-ICA receivers outperforms the conventional
IDMA receiver.
6. Conclusions
In this paper, N-ICA post processor is proposed in ID-
MA context. N-ICA algorithm constitutes an efficient
tool for symbol recovery and it offers an efficient alter-
native to the IDMA systems with block channel estima-
tion.
The major contribution of this work is the application
of blind detection technique in the IDMA context. The
proposed algorithm has better performance compared to
the IDMA receiver in loaded systems because it allows
dimension reduction (PCA) which helps to reduce the
amount of noise in the system.
For unloaded systems, the proposed post processor
allows a complexity reduction by reducing the number of
iterations needed by the IDMA block. In future work, to
better analyze the complexity of the proposed scheme,
FPGA implementation of IDMA and proposed post pro-
cessor will be realized.
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