Digital Signal Processing Reference
In-Depth Information
theoretical conditions for blind equalizations, over which effective
methods and algorithms may be implemented.
•
Once the theoretical foundation is established, we turn our attention
to adaptive techniques in
Section 4.3
.
We discuss the so-called
Buss-
gang algorithms
, which play a central role in this chapter, devoted to
SISO channels. Among the great number of proposals found in the
literature, we focus on a representative group: the
decision-directed
(DD),
Sato
,and
Godard algorithms
.
•
fers from the previous ones in its underlying mathematical basis,
since it is derived from the corresponding SW theorem. The section
includes both constrained and unconstrained versions of the SWA.
•
also derived from SW framework, with the aim of accelerating the
convergence of the techniques presented previously.
•
In
Section 4.6
,
we turn our attention to the study of
equilibrium solu-
tions
of blind equalization criteria. Due to their practical relevance,
we give specific attention to the DD and the constant modulus (CM)
criteria.
•
Finally, in
Section 4.7
, we discuss the
relationships between the CM and
the SW criteria
and consider the relationships between these criteria
and supervised approaches.
Historical Notes
The application of adaptive solutions in digital communications and, specif-
ically, in channel equalization, dates back to the 1960s, with the work of
Lucky [190,191], who is referred to as the inventor of the adaptive equalizer.
Lucky was the first to propose the so-called zero-forcing (ZF) method to
be applied in FIR equalization. The ZF criterion is an ingenious approach that
is rather intuitive for communications engineers, since it aims to minimize
(force to zero) the intersymbol interference (ISI) caused by the dispersive
effect of the channel. The ZF algorithm proposed by Lucky is an adap-
tive procedure to adjust the coefficients of the FIR equalizer, so that the IIS
be set to zero. In a noiseless situation, the optimal ZF equalizer tends to be
the inverse of the channel.
In a second proposal, Lucky extended his approach to the tracking mode
of operation and introduced the so-called decision-directed equalizer. As
discussed later in this chapter, the DD method is an unsupervised but not
robust strategy, since its effectiveness depends on the initial condition of the
equalizer coefficients.
The first application of a robust unsupervised strategy is credited to
Sato in 1975 [260]. Sato proposed an adaptive equalizer to work with pulse
