Coefficient-dependent step-size for adaptive second-order Volterra filters

In this contribution we propose a coefficient-dependent and time-variant step-size for the least mean square (LMS) algorithm applied to adaptive second-order Volterra filters. The optimum step-size is derived by introducing a novel optimality criterion which is given by the minimum mean squared error between the coefficient error of an adaptive Volterra filter coefficient and the respective LMS update term of that coefficient. As the optimum step-size includes statistical terms that are in general not accessible, we also present models for estimating these quantities for the application in nonlinear acoustic echo cancellation.