Analysis of normalized least mean modulus algorithm for adaptive filters in impulsive noise environments

This paper develops theoretical convergence analysis of adaptive filters using normalized least mean modulus (NLMM) algorithm that is highly robust in the presence of two types of impulse noise: one in additive observation noise and another at filter input, for which we propose “stochastic” models. We develop analysis of the NLMM algorithm which is only applicable to adaptive filters with a small number of tap weights. Approximate analysis is also developed for a large number of tap weights. In the analysis, we derive a set of difference equations for iteratively calculating filter convergence in terms of mean square tap weight misalignment (MSTWM). Experiment is carried out to demonstrate robustness of the NLMM algorithm against both types of impulse noise. Good agreement between simulated and theoretically calculated filter convergence in the transient phase and in the steady state proves the validity of the analysis.