Adaptive Combination of Second Order Volterra Filters with Nlms and Sign-nlms Algorithms for Nonlinear Acoustic Echo Cancellation

In this paper, starting from a robust statistics (RS) adaptive approach presented in a previous work entitled the combined NLMS-Sign (CNLMS-S) adaptive filter, an automatic combination technique with similar performances is proposed. Thus, in order to obtain better performances in acoustic echo cancellation (AEC) setups than with the normalized least-mean square (NLMS) algorithm, in the CNLMS-S case the decision between the two algorithms (NLMS and Sign) is based on a set error threshold. The error threshold can be empirically determined or known a priori if the signal-to-noise ratio (SNR) value from the loudspeaker-enclosure-microphone (LEM) setup is available or if the local noise levels can be determined from the silences. Here, to overcome this shortcoming, an adaptive combination of the two algorithms involved in RS is highlighted, providing similar results regarding convergence and final misadjustment. Also, the need of the error threshold set by the user is removed, the combination being controlled only by a step-size parameter, independent on the LEM, constrained only by the stability range. The proposed method is compared to the CNLMS-S in nonlinear LEM setups using measured linear and quadratic Volterra kernels, tracking the behavior of the echo-return loss enhancement (ERLE) characteristic. As input sequences, audio signals with different PDFs are used and WGN is added as local noise. Simulation results justify the efficiency of the proposed method, both in convergence and steady-state error against the CNLMS-S and, implicitly the NLMS and the Sign-NLMS algorithms.