Error-dependent step-size control of adaptive normalized least-mean-square filters used for nonlinear acoustic echo cancellation

This paper proposes novel acoustic echo cancellation (AEC) approaches based on linear and Volterra structures. The AECs use modified normalized least-mean-square (NLMS) updates to improve the convergence and to maintain the same steady-state misadjustment. In the first case, starting from a new cost function, the resulting variable step size depends on the instant error value and on an estimated error threshold. Secondly, the need of beforehand steady-state error threshold estimation is removed by an automatic step-size control involving the absolute error envelope evolution. The methods are tested for an acoustic enclosure setup modeled using measured linear and quadratic kernels, and their behavior is compared to that of the traditional NLMS and another technique found in the open literature. Also, they are tested for a change in the echo path and for assorted nonlinearity and local signal powers. The comparison is made in terms of the echo-return loss enhancement for WGN and speech as excitation. The simulations show that the proposed adaptations offer increased convergence rates for the same steady-state error.