On the behavior of a combination of adaptive filters operating with the NLMS algorithm in a nonstationary environment

Abstract

This paper presents a stochastic model describing the behavior of either affine or convex combination scheme involving two adaptive filters operating in parallel with the normalized least-mean-square (NLMS) algorithm under a nonstationary environment. Specifically, considering both uncorrelated and correlated Gaussian input data, model expressions are obtained for predicting the evolution of the mean weight vector, learning curve, and weight-error correlation matrices, as well as the steady-state values of both the mixing parameter and the excess mean-square error (EMSE). Based on these model expressions, some characteristics of combination schemes operating in a nonstationary environment are then discussed. Simulation results are shown, confirming the accuracy of the proposed model for different operating conditions.