Digital Signal Processing Reference
In-Depth Information
to an open-eye condition. After the conclusion of the supervised training
period, the DD algorithm could be employed to refine the obtained equal-
izer parameters, further reducing the ISI level and tracking eventual channel
variations.
4.3.2 The Sato Algorithm
In 1975, Yoichi Sato proposed a blind algorithm for the recovery of M-PAM
multilevel signals [260] that was based on recovering the most signifi-
cant bit of the modulation and to treat the remaining information as a
kind of noise. In accordance with this idea, the following nonlinearity was
proposed:
ψ
Sato
y
)
=
γ sign
y
)
(
n
(
n
(4.22)
where
E
s
2
)
(
n
γ
=
(4.23)
E
[
|
s
(
n
)
|
]
is a “gain control” scaling factor. The update rule then becomes
μ
γ sign
y
)
−
)
x
w
(
n
+
1
)
=
w
(
n
)
+
(
n
y
(
n
(
n
)
(4.24)
which represents an LMS-like algorithm for the minimization of the follow-
ing cost function:
E
2
y
)
γ sign
y
)
−
J
Sato
(
w
)
=
(
(
n
(
n
)
(4.25)
Sato's proposal is historically very important as a first robust technique
that allows operation in a completely blind fashion.
4.3.3 The Godard Algorithm
In 1980, Dominique Godard proposed a blind equalization criterion whose
main feature was its immunity to phase recovery errors [124]. The goal was
to develop a method capable of reducing the distortions introduced by the
channel to a level that could be handled by conventional methods like the
DD algorithm.
The idea behind Godard's proposal was to establish a measure of dis-
persion around a predetermined value without having to resort to phase
information, which can be accomplished considering the following cost
