Digital Signal Processing Reference
In-Depth Information
algorithms. Important results regarding the convergence analysis of the
FS-CMA can be found in [155]. The relationship between equalizers obtained
with the CM and Wiener criteria is investigated in [132,312].
5.3.2 Blind Equalization Based on Subspace Decomposition
Schemes based solely on second-order moments of the received signal have
an advantage over cumulant-based methods with respect to computational
complexity. The existing methods to solve the problem of SIMO blind
equalization/identification based exclusively on second-order statistics can
be grouped in two main classes: those based on subspace decomposition and
those based on linear prediction. In the following, we will present the main
characteristics associated with both approaches.
In simple terms, subspace methods rely on the decomposition of the auto-
correlation matrix of the received signal [287, 289]. For instance, in [211],
the main idea is to explore the orthogonality between signal and noise sub-
spaces. The problem consists of estimating a vector
LP
1
composed of all
coefficients from all
P
subchannels, organized in the following manner:
×
h
S
=
h
0
h
1
h
P
−
1
T
···
(5.62)
Estimation is based on a set of
K
observations of the received signals, and is
founded on the following theorem [139,288].
THEOREM 5.4
H
The convolution matrix
associated with the channel has full column rank
if and only if the following conditions hold:
•
The polynomials composed by the coefficients of each subchannel
have no common zeros.
•
At least one of the polynomials has maximum degree
L
1
.
−
•
The length
K
of the vector containing samples from each subchannel
should be
K
>
L
−
1.
)
present in (5.33) are obtained from mutually independent wide-sense sta-
tionary processes. The transmitted signal is zero mean, and its correlation
matrix is defined as
We assume that the input symbol vector
s
(
n
)
and the noise vector
ν
˜
(
n
E
s
s
H
R
s
=
(
n
)
(
n
)
(5.63)
