Performance Analysis of Adaptive Volterra Filters in the Finite-Alphabet Input Case

Abstract

This paper deals with the analysis of adaptive Volterra filters, driven by the LMS algorithm, in the finite-alphabet inputs case. A tailored approach for the input context is presented and used to analyze the behavior of this nonlinear adaptive filter. Complete and rigorous mean square analysis is provided without any constraining independence assumption. Exact transient and steady-state performances expressed in terms of critical step size, rate of transient decrease, optimal step size, excess mean square error in stationary mode, and tracking nonstationarities are deduced.