Advances in identification and compensation of nonlinear systems by adaptive volterra models

In this contribution, we present some recent advances in the modeling of unknown nonlinearities by adaptive Volterra filters. In particular, a system identification scenario in the form of the nonlinear acoustic echo cancelation problem is considered, which is most challenging due to large kernel sizes and excitation by colored (noise) and/or nonstationary signals (speech). After reviewing the general filter structure and discussing a possibly more efficient DFT-domain realization by resorting to a multichannel representation, mainly two aspects are covered: On the one hand, convergence aspects are addressed (i) by framewise iterated updating that is shown to result in a faster adaptation for DFT-domain implementations and (ii) by combining Volterra kernels with different adaptation parameters, thus yielding an elegant method of robust step-size control. On the other hand, a modification of these combination schemes lends itself to an especially promising approach that enables an evolutionary self-configuration of the adaptive nonlinear structure while providing estimates for the optimum memory size parameters. From these developments, conclusions are drawn and some guidelines for future work are given.