Digital Signal Processing Reference
In-Depth Information
s
(
n
)
x
(
n
)
y
(
n
)
v
1
(
n
)
v
2
(
n
)
x
1
(
n
)
x
2
(
n
)
y
1
(
n
)
y
2
(
n
)
s
1
(
n
)
s
2
(
n
)
.
.
.
.
H
(
n
)
W
(
n
)
v
M
(
n
)
x
M
(
n
)
s
k
(
n
)
y
k
(
n
)
G
(
n
)
FIGURE 5.8
General MIMO equalization scheme.
where
W
denote, respectively, the MIMO equalizer and channel
impulse responses, and
(
n
)
and
H
(
n
)
G
(
n
)
=
W
(
n
)
∗
H
(
n
)
(5.93)
equalizer matrix and
ν
(
is the combined channel
+
n
)
=
W
(
n
)
∗
ν
(
n
)
is the
filtered noise.
It is also possible to process the signals in separate, by means of MISO
filters. Each filter, in this case, aims to recover a single signal, so that the
MIMO system is in fact reduced to a collection of MISO ones. Despite the
interest of such an approach, which is usually refereed to as deflation [70,89]
in the related literature, this chapter focuses in the MIMO filter solution.
When we use unsupervised MIMO equalization to recover the signals
transmitted by several users, an additional difficulty may arise from the fact
that all of them belong to the same finite alphabet and present the same
statistical distribution. Due to the characteristics of wireless propagation, it
follows that in the receiver that is closer users experience a higher signal
power when compared to the more distant ones. This phenomenon is known
as near-far effect [65,187,236]. This may lead to recovering errors, as a blind
algorithm may “view” the higher power signal as the desired one, while the
rest tends to be considered as interference. This would lead to the recovery of
multiple copies of this only signal [228]. In order to deal with this limitation,
it is necessary to employ additional strategies over the criterion for unsuper-
vised MIMO equalization. In the sequel, we discuss two main families that
have been adopted in most of the works of the literature.
5.4.1 Multiuser Detection Methods Based on Decorrelation Criteria
The objective of multiuser detection (MUD) methods based on decorrelation
criteria is to force the estimates of different users to be mutually decorrelated
as possible at the output of the MIMO equalizer. This aims to ensure that the
equalizer will provide a correct estimate of all source signals. The key point
