23
Telecommunications
This chapter deals with applications of independent component analysis (ICA) and
blind source separation (BSS) methods to telecommunications. In the following,
we concentrate on code division multiple access (CDMA) techniques, because this
specific branch of telecommunications provides several possibilities for applying
ICA and BSS in a meaningful way. After an introduction to multiuser detection and
CDMA communications, we present mathematically the CDMA signal model and
show that it can be cast in the form of a noisy matrix ICA model. Then we discuss
in more detail three particular applications of ICA or BSS techniques to CDMA
data. These are a simplified complexity minimization approach for estimating fading
channels, blind separation of convolutive mixtures using an extension of the natural
gradient algorithm, and improvement of the performance of conventional CDMA
receivers using complex-valued ICA. The ultimate goal in these applications is to
detect the desired user’s symbols, but for achieving this intermediate quantities such
as fading channel or delays must usually be estimated first. At the end of the chapter,
we give references to other communications applications of ICA and related blind
techniques used in communications.
23.1 MULTIUSER DETECTION AND CDMA COMMUNICATIONS
In wireless communication systems, like mobile phones, an essential issue is division
of the common transmission medium among several users. This calls for a multiple
access communication scheme. A primary goal in designing multiple access systems
is to enable each user of the system to communicate despite the fact that the other
417
Independent Component Analysis. Aapo Hyv
¨
arinen, Juha Karhunen, Erkki Oja
Copyright

2001 John Wiley & Sons, Inc.
ISBNs: 0-471-40540-X (Hardback); 0-471-22131-7 (Electronic)

In its simplest form, the code is a pseudorandom sequence of
1
s, also called a
chip sequence or spreading code. In this case we speak about direct sequence (DS)
modulation [378], and call the multiple access method DS-CDMA. In DS-CDMA,
each user’s narrow-band data symbols (information bits) are spread in frequency
before actual transmission via a common medium. The spreading is carried out by
multiplying each user’s data symbols (information bits) by his unique wide-band
chip sequence (spreading code). The chip sequence varies much faster than the
MULTIUSER DETECTION AND CDMA COMMUNICATIONS
419
time
-1
-1
-1
+1
+1
+1
T
T
c
binary data
spreading code
modulated data
time
time
Fig. 23.2
Construction of a CDMA signal [382]. Top: Binary user’s symbols to be trans-
mitted. Middle: User’s specific spreading code (chip sequence). Bottom: Modulated CDMA
signal, obtained by multiplying user’s symbols by the spreading code.

s(t)=0
when
t =2 0T)
. The length of the chip
sequence is
C
chips, and the time duration of each chip is
T
c
=
T=C
. The number of
bits in the observation interval is denoted by
N
. In Fig. 23.2, the observation interval
contains
N =4
symbols, and the length of the chip sequence is
C =5
.
420
TELECOMMUNICATIONS
Using these notations, the CDMA signal
r(t)
at time
t
arising in this simple
example can be written
r(t)=
N

while the codes of the other users are unknown. There is less processing power than
in the base station. Also the mathematical model of the signals differs slightly, since
users share the same channel in the downlink communications. Especially the first
two features of downlink processing call for new, efficient and simple solutions.
ICA and BSS techniques provide a promising new approach to the downlink signal
processing using short spreading codes and DS-CDMA systems.
Figure 23.3 shows a typical CDMA transmission situation in an urban environ-
ment. Signal 1 arrives directly from the base station to the mobile phone in the car.
It has the smallest time delay and is the strongest signal, because it is not attenuated
by the reflection coefficients of the obstacles in the path. Due to multipath propa-
gation, the user in the car in Fig. 23.3 receives also weaker signals 2 and 3, which
have longer time delays. The existence of multipath propagation allows the signal
to interfere with itself. This phenomenon is known as intersymbol interference (ISI).
Using spreading codes and suitable processing methods, multipath interference can
be mitigated [444].
MULTIUSER DETECTION AND CDMA COMMUNICATIONS
421
Time delay
Magnitude
Fig. 23.3
An example of multipath propagation in urban environment.
There are several other problems that complicate CDMA reception. One of the
most serious ones is multiple access interference (MAI), which arises from the fact
that the same frequency band is occupied simultaneously. MAI can be alleviated by
increasing the length of the spreading code, but at a fixed chip rate, this decreases
the data rate. In addition, the near–far problem arises when signals from near and
far are received at the same time. If the received powers from different users become
too different, a stronger user will seriously interfere with the weaker ones, even if
there is a small correlation between the users’ spreading codes. In the FDMA and
TDMA systems, the near–far problem does not arise because different users have

k
()
is
k
:th user’s binary chip sequence
(spreading code). For each user
k
, the spreading code is defined quite similarly as in
Example 23.1. The combined signal of
K
simultaneous users then becomes
r(t)=
N
X
m=1
K
X
k=1
b
km
s
k
(t  mT )+n(t)
(23.2)
where
n(t)
denotes additive noise corrupting the observed signal.
The signal model (23.2) is not yet quite realistic, because it does not take into
account the effect of multipath propagation and fading channels. Including these
factors in (23.2) yields our desired downlink CDMA signal model for the observed

l
to the path. The term
d
l
denotes the delay of the
l
th path, which is assumed to be constant during the
observation interval of
N
symbol bits. Each of the
K
simultaneous users has
L
independent transmission paths. The term
a
lm
is the fading factor of the
l
th path
corresponding to the
m
th symbol.
In general, the fading coefficients
a
lm
are complex-valued. However, we can
apply standard real-valued ICA methods to the data (23.3) by using only the real part
of it. This is the case in the first two approaches to be discussed in the next two
sections, while the last method in Section 23.5 directly uses complex data.
The continuous time data (23.3) is first sampled using the chip rate, so that

b
km
g
kl
]+n
m
(23.5)
where
n
m
denotes the noise vector consisting of subsequent
C
last samples of noise
n(t)
. The vector
g
kl
denotes the “early” part of the code vector, and
g
kl
the “late”
part, respectively. These vectors are given by
g
kl
=s
k
C  d
l
+1]:::s
k

2f0:::(C  1)=2g
,
and
0
T
d
l
is a row vector having
d
l
zeros as its elements. The early and late parts of the
code vector arise because of the time delay
d
l
, which means that the chip sequence
generally does not coincide with the time interval of a single user’s symbol, but
extends over two subsequent bits
b
km1
and
b
km
. This effect of the time delay can
be easily observed by shifting the spreading code to the right in Fig. 23.2.
The vector model (23.5) can be expressed in compact form as a matrix model.
Define the data matrix
R =r
1
 r
2

KL
]
(23.10)
and the
2KL  N
matrix
F
=
f
1
:::f
N
]
contains the symbols and fading terms
f
m
= a
1m1
b
1m1
a
1m
b
1m

(23.11)
::: a
Lm1
b
Km1

. Denote the
independent sources
a
1m1
b
1m1
::: a
Lm
b
Km
by
y
i
(m)i =1:::2KL
. Here
every
2L
sources correspond to each user, where the coefficient 2 follows from the
presence of the early and late parts.
To see the correspondence of (23.9) to ICA, let us write the noisy linear ICA
model
x
=
As + n
in the matrix form as
X = AS + N
(23.12)
The data matrix
X
has as its columns the data vectors

only the desired user’s code is known. To remedy this problem while preserving
acceptable performance, subspace approaches have been proposed for example in
[44]. But they are sensitive to noise, and fail when the signal subspace dimension
exceeds the processing gain. This easily occurs even with moderate system load
due to the multipath propagation. Some other semiblind methods proposed for the
CDMA problem such as the minimum mean-square estimator (MMSE) are discussed
later in this chapter and in [287, 382, 444].
It should be noted that the CDMA estimation problem is not completely blind,
because there is some prior information available. In particular, the transmitted
symbols are binary (more generally from a finite alphabet), and the spreading code
(chip sequence) is known. On the other hand, multipath propagation, possibly fading
channels, and time delays make separation of the desired user’s symbols a very
challenging estimation problem which is more complicated than the standard ICA
problem.
23.3 ESTIMATING FADING CHANNELS
23.3.1 Minimization of complexity
Pajunen [342] has recently introduced a complexity minimization approach as a true
generalization of standard ICA. In his method, temporal information contained in
the source signals is also taken into account in addition to the spatial independence
utilized by standard ICA. The goal is to optimally exploit all the available information
in blind source separation. In the special case where the sources are temporally white
(uncorrelated), complexity minimization reduces to standard ICA [342]. Complexity
minimization has been discussed in more detail in Section 18.3.
Regrettably, the original method for minimizing the Kolmogoroff complexitymea-
sure is computationally highly demanding except for small scale problems. But if the
source signals are assumed to be gaussian and nonwhite with significant time correla-
tions, the minimization task becomes much simpler [344]. Complexity minimization
then reduces to principal component analysis of temporal correlation matrices. This
method is actually just another example of blind source separation approaches based
on second-order temporal statistics; for example [424, 43], which were discussed

y
:
J (y)=
X
i
H (y
i
)+log j det G j
(23.13)
where
H (y
i
)
is the entropy of
y
i
(see Chapter 5). But entropy has the interpretation
that it represents the optimum averaged code length of a random variable. Hence
mutual information can be expressed by using algorithmic complexity as [344]
J (y)=
X
i
K (y
i
)+log j det G j
(23.14)
where
K ()
is the per-symbol Kolmogoroff complexity, given by the number of bits
needed to describe

ing to the first user. Then
y
i
(m)
will actually represent the channel coefficients of all
the first user’s paths. Since we assume that the channel is Rayleigh fading, then these
signals are gaussian and time correlated. In this case, blind separation of the sources
can be achieved by using only second-order statistics. In fact, we can express the
Kolmogoroff complexity by coding these signals using principal component analysis
[344].