On convergence and steady state behavior in the median LMS adaptive filter

The authors examine the performance of the MLMS (median least mean square) adaptive filter subjected to zero-mean independent, identically distributed inputs corrupted by sparse impulsive interference. They demonstrate exponential convergence in the mean to the minimum mean squared error solution. They find approximations for the convergence rates corresponding to different impulsive conditions and compare these to LMS. It is shown that, in contrast to LMS, MLMS enjoys smooth exponential convergence largely unaffected by the impulses. They also compare the impact of a single impulse on MLMS and LMS when the algorithms are operating in steady state. A reduced performance cost for MLMS, measured by the mean deviation of the filter coefficients from the optimal values, is demonstrated