Proportionate NLMS Algorithm for Second-order Volterra Filters and it’s Application to Nonlinear Echo Cancellation

The performance of linear acoustic echo cancelers degrades if non- negligible nonlinear distortion is introduced into the echo path as, e.g., caused by low-cost loudspeaker systems driven at high vol- ume. Adaptive second-order Volterra filters are known to effec- tively model nonlinear acoustic echo paths. In this contribution we propose an extension of the proportionate NLMS (PNLMS) to second-order Volterra filters. For the case that the amplitude of the input has an even probability density function a simplification of that algorithm is introduced, including an adaptation control which is crucial especially for nonstationary input. Simulation results show that the proposed algorithm leads to an increased conver- gence speed compared to an NLMS-based adaptive Volterra filter. An important feature of the presented approach is the inherent in- variance of the performance of the adaptation with respect to a scaling of the input/output signals.