Two-dimensional median least mean squares adaptive algorithm

Abstract

A two-dimensional adaptive algorithm which resists impulsive interference is presented. The proposed two-dimensional median least mean squares (TDMLMS) algorithm is a gradient-based steepest descent algorithm and employs the sample median of the instantaneous gradients within a suitable window as a measure of the true gradient. The nonlinear action of the median filtering operation smooths the gradients and significantly enhances the adaptive process. Transferring from two- to one-dimensional operation shows that the TDMLMS is convergent, in the mean, to the optimum Wiener solution with some widely used assumptions. The TDMLMS is somewhat slower than the conventional two-dimensional LMS (TDLMS) when no impulsive interference is present. The vastly improved performance of the proposed TDMLMS over the TDLMS in an impulsive noise environment is demonstrated.