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

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.