Digital Signal Processing Reference
In-Depth Information
is to provide an overview of some representative structures and algorithms,
with a clearly specific regard on our problems of interest. Hence, the chapter
is organized as follows:
•
In
Section 7.1
,
we discuss the DFE. The DFE is a very efficient device
for performing deconvolution whenever one deals with digital sig-
nals. In a certain sense, we may consider DFE as a historical link
between linear and nonlinear approaches in equalization, which
justifies our choice for it as the starting point of the chapter. An
alternative solution proposed for blind equalization, the so-called
predictive DFE, is also presented.
•
In
Section 7.2
, we turn our attention to a class of nonlinear devices
based on polynomial expansions: the
Volterra filters
. These filters
are based on polynomial expansions and have, as generic approx-
imators, a wider scope of application than that associated with the
DFE. On the other hand, they also preserve points of contact with
the linear filtering theory as far as the parameter optimization is
concerned.
•
In
Section 7.3
,
we analyze the problem of
digital equalization as a
classification task
. As mentioned above, this point of view leads
us to search for synergy with machine learning-based solutions.
In addition, this formulation also allows the formal derivation
of the Bayesian equalizer, which is our fundamental reference of
optimality.
•
In
Section 7.4
, we present the two main neural approaches to be con-
sidered in our applications: the
multilayer perceptron
(MLP) and the
radial-basis function
(RBF) network. In addition to that, we state the
similarities between the MLP and the Bayesian filter.
Historical Notes
The proposal of the DFE is attributed to Austin in [21]. From this time, a
really significant number of articles, patents, and book chapters have dealt
with the subject. As an example for reference, we can mention the inter-
esting surveys in [30, 246]. Later, a number of works has been devoted to
the use of blind criteria for DFE updating, among which we can mention,
e.g., [61].
The use of polynomial filters was also an important initial step toward a
more widespread adoption of nonlinear models in signal processing applica-
tions. Some pioneer efforts in the context of equalization and echo cancella-
tion, for instance, can be traced to the 1970s and 1980s [5,39,43,107,284]. The
proposal of iterative learning algorithms in the context of polynomial filters
