Theory on the Speed of Convergence in Adaptive Equalizers for Digital Communication

TLDR

Previous work has shown that extreme values of the unequalized signal’s power spectrum limit the speed of convergence. The study analyzes how the number of taps, step-size, and signal spectrum affect the convergence speed of adaptive transversal equalizers minimizing mean‑square distortion. The authors examine expected mean‑square distortion convergence using approximations that replace higher‑order statistics with second‑order parameters. Simulation confirms the theory accurately predicts convergence, revealing that tap count dominates mean‑square distortion and providing a simple criterion to achieve fastest convergence.

Abstract

This paper presents an analysis of the convergence properties of adaptive transversal equalizers minimizing mean-square distortion. The intention is to reveal the influence on the speed of convergence exerted by the number of taps, the step-size parameter in the adjustment loops, and the spectrum of the unequalized signal. Attention is focused on the convergence of the expected mean-square distortion. Several approximations are made in the analysis, among them the approximation of higher-order statistics by second-order statistical parameters. Comparison with results obtained by computer simulation, however, shows that the theory developed renders a quite accurate picture of the convergence process. Previous work in this field demonstrated the limits set to the speed of convergence by the extreme values of the power spectrum of the unequalized signal. It is shown here that, with regard to the mean-square distortion, the influence of the number of taps will usually dominate by far. The theory provides a simple criterion for convergence and answers the question of how to attain the fastest convergence.