Statistical-mechanical analysis of adaptive Volterra filter for nonwhite input signals

Abstract

The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal processing system with the Volterra filter for nonwhite input signals by a statistical-mechanical method. Assuming the self-averaging property with an infinitely long tapped-delay line, we derive simultaneous differential equations that describe the behaviors of macroscopic variables in a deterministic and closed form. We analytically solve the derived equations to reveal the effect of the nonwhiteness of the input signal on the adaptation process. The results for the second-order Volterra filter show that the nonwhiteness decreases the mean-square error (MSE) in the early stages of the adaptation process and increases the MSE in the later stages.