Exact performances analysis of a selective coefficient adaptive algorithm in acoustic echo cancellation

In the hands-free communications, the identification of long impulse response in acoustic echo cancellation requires very important load calculations. One way to reduce the complexity of the classical normalized least mean square (NLMS) adaptive algorithm, is to use the Mmax NLMS algorithm (Aboulnasr and Mayyas 1999). It is shown that this algorithm is a very promising one, that maintains closest performance to the full update NMLS filter in spite of the updating of a small number of coefficients. However, due to its complexity, the mean square analysis uses an unrealistic hypothesis. It was then not possible to consider the practical context such as high input correlation or high step size. In this paper, we present an exact performances analysis, inspired from Besbes et al. (1999), when the input signal remains in a finite alphabet set. With this realistic hypothesis, dedicated to the digital context, we can describe accurately the Mmax NLMS´ behavior without any unrealistic assumption. In particular, we evaluate the exact value of critical and optimal step size and we provide the exact mean square error (MSE) for all step sizes and input correlations. The influence of high order statistics can be enhanced