Convergence analysis of finite length blind adaptive equalizers
Ye Li; Zhi Ding
Signal Processing, IEEE Transactions on
Volume 43, Issue 9, Sep 1995 Page(s):2120 - 2129
Digital Object Identifier 10.1109/78.414774
Summary:The paper presents some new analytical results on the convergence
of two finite length blind adaptive channel equalizers, namely, the
Godard equalizer and the Shalvi-Weinstein equalizer. First, a one-to-one
correspondence in local minima is shown to exist between the Godard and
Shalvi-Weinstein equalizers, hence establishing the equivalent
relationship between the two algorithms. Convergence behaviors of finite
length Godard and Shalvi-Weinstein equalizers are analyzed, and the
potential stable equilibrium points are identified. The existence of
undesirable stable equilibria for the finite length Shalvi-Weinstein
equalizer is demonstrated through a simple example. It is proven that
the points of convergence for both finite length equalizers depend on an
initial kurtosis condition. It is also proven that when the length of
equalizer is long enough and the initial equalizer setting satisfies the
kurtosis condition, the equalizer will converge to a stable equilibrium
near a desired global minimum. When the kurtosis condition is not
satisfied, generally the equalizer will take longer to converge to a
desired equilibrium given sufficiently many parameters and adequate
initialization. The convergence analysis of the equalizers in PAM
communication systems can be easily extended to the equalizers in QAM
communication systems
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