Transient and steady-state analysis of Adaptive Step-Size Least Mean Modulus algorithm

This paper proposes Adaptive Step-Size Least Mean Modulus (ASS-LMM) algorithm for fast convergent and robust adaptive filtering in the presence of impulse noise. The ASS-LMM algorithm for use in adaptive filters defined in the complex-number domain is basically the LMM algorithm combined with a new adaptive step-size control algorithm to improve the convergence speed of the LMM algorithm while preserving its robustness against additive impulsive observation noise. Through analysis and experiment, we demonstrate effectiveness of the proposed ASS-LMM algorithm in making adaptive filters fast convergent and highly robust in the presence of impulse noise. Good agreement between simulated and theoretical convergence behavior in the transient phase and in the steady state proves the validity of the analysis.