Robust Adaption Algorithm Based On M-estimate For Echo Cancellation

Adaptive echo cancellation has become popular in the field of modern communications. Owing to easy to implement, the normalized least mean square (NLMS) algorithm is widely used in the field of echo cancellation. Aim at the speech signal, which is a kind of non-stationary signal, the affine projection algorithm (APA) and normalized subband adaptive filter (NSAF) algorithms have better convergence property than other algorithms. These algorithms are the two extended form of the NLMS algorithm. However, the convergence property will degrade of these algorithms under impulse interference. In this paper, the APA and NSAF algorithms are modified for echo cancellation under the impulse noise environment. Moreover, to further improve the convergence rate, the convex combination strategy is utilized in the proposed algorithm.First, to overcome the impulse noise in echo cancellation problem, a novel proportional affine projection M-estimate algorithm is derived by using the M-estimate. This algorithm has a rapid convergence rate under different input signals, and has the robustness against impulse interference. Besides, it has low computational complexity. Simulation studies are carried out to verify the feasibility and superiority of the proposed algorithm.Second, to further improve the proposed proportional affine projection M-estimate algorithm, in this paper, a convex combination strategy is used to overcome the confliction between convergence and misadjustment. Three convex combination schemes are proposed to further obtain fast convergence rate. Simulation studies are illustrated to demonstrate the effectiveness of the proposed algorithm.Finally, to enhance the robustness of the proposed algorithm in impulse noise, the derived MSAF combines the benefits of the M-estimate and NSAF algorithm. And, a novel PMSAF algorithm is developed by using the concept of proportional algorithm to deal with echo cancellation problem. Simulation results show that the new algorithm has good convergence property in a variety of input signals, and has capability against impulse noise interference.