Robust Shrinkage Affine-Projection Sign Adaptive-Filtering Algorithms for Impulsive Noise Environments

Abstract

Two robust affine projection sign (RAPS) algorithms, both of which minimize the mixed norm of $l_1$ and $l_2$ of the error signal, are proposed. The direction vector of the RAPS algorithms is obtained from the gradient of an $l_1$ norm-based objective function, while two related $l_2$ norm-based minimization problems are solved to obtain the line search of the two RAPS algorithms. The $l_1$ norm-based direction vector reduces the impact of impulsive noise, whereas the $l_2$ norm-based line search produces an unbiased solution in the proposed algorithms. In addition, one of the two RAPS algorithms shares the data selective adaptation used in the set-membership (SM) affine projection (SMAP) algorithm. The proposed algorithms are shown to offer a significant improvement in the convergence speed as well as a significant reduction in the steady-state misalignment relative to the pseudo affine projection sign (PAPS) algorithm. In addition, the proposed algorithms offer robust performance with respect to impulsive noise and improved tracking of the unknown system in comparison to that provided by the PAPS and Affine projection sign (APS) algorithms. These features of the proposed algorithms are demonstrated using simulation results in system-identification and echo-cancellation applications.