Static and dynamic convergence behavior of adaptive blind equalizers

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 independence 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 or equalizer coefficients at equilibrium are determined by a Lyapunov equation. According to our analysis results, for a given channel and stepsize, 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, which is contrary to what is conventionally conjectured. The theoretical analysis results are confirmed by computer simulations.