Analysis of recursive least moduli algorithm for adaptive filters in impulsive noise environments

This paper first reviews an adaptation algorithm named Recursive Least Moduli (RLM) algorithm for complex-domain adaptive filters. The RLM algorithm achieves significant improvement in the filter convergence speed when the filter input is strongly correlated. Stochastic models are presented for two types of impulse noise found in adaptive filtering systems: one in observation noise and another at filter input. Then, analysis of the RLM algorithm in the presence of both types of impulse noise is fully developed for calculating the transient and steady-state behavior of filter convergence. Through experiments with simulations and theoretical calculations of filter convergence for the RLM algorithm, we demonstrate its effectiveness in making adaptive filters fast convergent and robust against not only the impulsive observation noise but also the impulse noise at filter input. We observe good agreement between simulated and theoretical convergence behavior that validates the analysis.