TABLE OF CONTENTS The design of update algorithms to speed up the convergence of adaptive filters has been a topic of intense study for more than a decade. Rapid convergence is important for adaptive equalizers designed for use with channels, such as troposcatter and HF radio, whose characteristics are subject to time variations [Proakis, 12.87]. In voiceband telephone applications, reduction of the initial setup time of the equalizer is important in polling multipoint networks [Forney, 12.26] where the central site receiver must adapt to receive typically short bursts of data from a number of transmitters over different channels.
In this section we present an overview of three classes of techniques devised to speed up equalizer convergence.
Recall from Section 12.3.1 that for the deterministic gradient algorithm, no single value of the step size ? leads to fast convergence of all the coefficient deviation components when the eigenvalues of the equalizer input covariance matrix A have a large spread. Using the independence assumption, the same is true regarding the convergence of the mean of the coefficient deviations for the LMS gradient algorithm (see (12.51) in Section 12.3.2). The excess MSE is a sum of the meansquared value of each coefficient deviation weighted by the corresponding eigenvalues of A. Slow decay of some of these mean-squared deviations, therefore, slows down the convergence of the excess MSE. Substituting the best initial ? from (12.55) in (12.54), we obtain the recursion
Observe that the initial decay...
