Volterra Filtering Scheme using Generalized Variable Step-size NLMS Algorithm for Nonlinear Acoustic Echo Cancellation

This correspondence presents a nonlinear acoustic echo cancellation algorithm, which includes two distinct modules in cascade. The first module is a polynomial Volterra filter, which is an equivalent paradigm for a loudspeaker with nonlinear distortion. The second module in the presented cascaded structure is a linear tapped-delay- line (finite impulse response) filter, which is analogous to the impulse response of the acoustic path. In the proposed adaptive structure, the adaptive nonlinear filter in the first module tackles the nonlinear constituents of the Volterra model, which uses the conventional fixed step-size normalized least mean square (FSS-NLMS) algorithm. However, the adaptive linear filter in the second module deals with the linear constituents of the Volterra model as well as the linear impulse response of the acoustic path, in which the generalized variable step-size (GVSS) NLMS algorithm is incorporated to suppress the adverse effects of nonstationarity / distortion. Computer simulation results demonstrate that the presented GVSS-NLMS algorithm based approach outperforms the FSS-NLMS algorithm based Volterra filtering, as far as convergence and tracking characteristics are concerned. In simulations of the real-time environment and appropriate parameter setting for the third-order polynomial model, it provides approximately 5 dB performance advantage over the conventional nonlinear filtering approach in the tracking mode, in terms of the reduction in mean square error. Moreover, the presented adaptive technique exhibits lower computational complexity than the conventional NLMS based polynomial Volterra filtering used for the acoustic echo cancellation.