A variable diagonal-matrix-step-size APA robust to impulsive noises

Abstract

This study introduces a variable diagonal-matrix-step-size affine projection algorithm (APA), which shows robustness against to impulsive noises. Unlike the normal scalar step-size method, the independent step size for each input vector is used as the entry of the diagonal matrix, and the optimal step size at each time step is ascertained by conducting mean-square-deviation (MSD) analysis. In addition, a recursive equation of weight update has been derived without approximating posteriori error as priori error. Using the Lagrange multiplier method, we formulate a scalar step size affine projection algorithm that shows resilience to impulsive noises. This algorithm emerges as a solution to a constrained optimization problem. To further enhance convergence performance, a diagonal-matrix-step size is introduced and its MSD is analyzed. The step size at each time step is optimized by interpreting the MSD mathematically, resulting in the variable diagonal-matrix-step size APA (VDMSS-APA). Various simulations exhibit low steady-state error and fast convergence rate of the proposed algorithm.