Static and Dynamic Convergence Behavior of Adaptive Blind Equalizers

Abstract

This paper presents a theoretical analysis of the static and dynamic convergence behavior for a general class of adaptive blind equalizers. We first study the properties of prediction error functions of blind equalization algorithms, and then we use these properties to analyze the static and dynamic convergence behavior based on the independent assumption. We prove in this paper that with a small step-size, the ensemble average of equalizer coefficients will converge to the minimum of the cost function near the channel inverse. However, the convergence is not consistent. The correlation matrix of equalizer coefficients at equilibrium is determined by a Lyapunov equation. According to our analysis results, for a given channel and step-size, there is an optimal length for an equalizer to minimize the intersymbol interference. This result implies that a longer-length blind equalizer does not necessarily outperform a shorter one, as contrary to what conventionally conjectured. The theoretical analysis results are confirmed by computer simulations.