Statistical-mechanical analysis of adaptive filter with clipping saturation-type nonlinearity

TL;DR

This paper applies a statistical-mechanical approach to analyze the behavior of adaptive filters with clipping saturation nonlinearities, revealing critical points affecting stability and explaining observed simulation phenomena.

Contribution

It introduces a novel statistical-mechanical analysis of adaptive filters with saturation nonlinearities, identifying critical points for stability and deriving their exact values.

Findings

Saturation value has a critical point for stability transition

The theory explains strange behaviors near the critical point

Exact critical point value is derived

Abstract

In most practical adaptive signal processing systems, e.g., active noise control, active vibration control, and acoustic echo cancellation, substantial nonlinearities that cannot be neglected exist. In this paper, we analyze the behaviors of an adaptive system in which the output of the adaptive filter has the clipping saturation-type nonlinearity by a statistical-mechanical method. We discuss the dynamical and steady-state behaviors of the adaptive system by asymptotic analysis, steady-state analysis, and numerical calculation. As a result, it has become clear that the saturation value has the critical point at which the system's mean-square stability and instability switch. The obtained theory well explains the strange behaviors around the critical point observed in the computer simulation. Finally, the exact value of the critical point is also derived.