Proportionate Nlms Algorithm for Second-order Volterra Filters and Its Application to Nonlinear Echo Cancellation

The performance of linear acoustic echo cancelers degrades if nonnegligible nonlinear distortion is introduced into the echo path as, e.g., caused by low-cost loudspeaker systems driven at high volume. Adaptive second-order Volterra filters are known to effectively 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 convergence speed compared to an NLMS-based adaptive Volterra filter. An important feature of the presented approach is the inherent invariance of the performance of the adaptation with respect to a scaling of the input/output signals.