Performance characteristics of the median LMS adaptive filter

The performance of gradient search adaptive filters, such as the least mean squares (LMS) algorithm, may degrade badly when the filter is subjected to input signals which are corrupted by impulsive interference. The median LMS (MLMS) adaptive filter is designed to alleviate this problem by protecting the filter coefficients from the impact of the impulses. MLMS is a modification of LMS, obtained by applying a median operation to the raw gradient estimates of the mean squared error performance surface. An analysis of the MLMS algorithm is provided for the class of independent and identically distributed inputs. For these inputs we establish exponential convergence of the MLMS algorithm. The rate of convergence is shown to depend on order statistics of the input, but unlike that for LMS shows little dependence on characteristics of the impulsive interference. The steady state performance of the LMS and MLMS is also examined. The average deviation of the parameter estimates from their optimal values caused by the arrival of an impulse is assessed. This analysis indicates a significantly improved performance for MLMS compared to LMS. Analytic predictions for both convergence and steady state behavior are supported by simulations.