Introduction - Unsupervised Signal Processing - page 9

multiuser systems, the importance of which is notorious in modern wireless
communications.
Chapter 6 deals with blind source separation (BSS), the other central sub-
ject for the objectives of this topic. We start this chapter by stating the main
models to be used and the standard case to be considered first, that of a
linear, instantaneous, and noiseless mixture. Then, we introduce a tool of
major interest in BSS: the independent component analysis (ICA). The first
part of Chapter 6 is devoted to the main concepts, criteria, and algorithms
to perform ICA. Afterward, we deal with alternative techniques that exploit
prior information as, in particular, the nonnegative and the sparse compo-
nent decompositions. Then, we leave the aforementioned standard case to
consider two relevant problems in BSS: those of convolutive and nonlinear
mixtures. Both of them can be viewed as open problems with significant
research results in the recent literature. So we focus our brief presentation on
some representative methods with emphasis on the so-called post-nonlinear
model.
Chapters 4 through 6 establish the fundamental core of the topic, as we
try to bring together blind equalization and source separation under the
same conceptual and formal framework. The two final chapters consider
more emergent techniques that can be applied in the solution of those two
problems.
The synergy between the disciplines of machine learning and signal pro-
cessing has significantly increased during the last decades, which is attested
by the several regular and specific conferences and journal issues devoted
to the subject. From the standpoint of this topic, it is quite relevant that
a nonnegligible part of this literature is related to unsupervised problems.
Chapter 7 presents some instigating connections between nonlinear filter-
ing, machine learning techniques, and unsupervised processing. We start
by considering a classical nonlinear solution for adaptive equalization—
the DFE structure—since this remarkably efficient approach can be equally
used in supervised and blind contexts. Then we turn our attention to more
sophisticated structures that present properties related to the idea of uni-
versal approximation, like Volterra filters and artificial neural networks.
For that, we previously revisit equalization within the framework of a
classification problem and introduce an important benchmark in digital
transmission: the Bayesian equalizer, which performs a classification task
by recovering the transmitted symbols in accordance with the criterion of
minimum probability of error. Finally, we discuss two classical artificial neu-
ral networks: multilayer perceptron (MLP) and radial basis function (RBF)
network. The training process of these networks is illustrated with the aid
of classical results, like the backpropagation algorithm and the k -means
algorithm.
The methods and techniques discussed all through this topic are issued,
after all, from a problem of optimization. The solutions are obtained, as