Variable step-size saturation affine projection algorithm against impulsive noise

Abstract

This study proposes a variable step-size saturation affine projection algorithm (VSS-sat-APA) robust to impulsive noise. The proposed algorithm is analytically derived from the optimal solution, which minimizes a newly defined ℓ2 cost function of a posteriori output error with weight-estimate variation limited by the step-size threshold. In contrast, the conventional robust VSS APA (RVSS-APA) is geometrically derived from a suboptimal solution, which minimizes an ℓ2 cost function of a posteriori output error with weight-estimate variation limited by the step-size threshold. The proposed algorithm operates as the original APA with the unit step-size when the magnitude of the normalized a priori output error is saturated with the step-size threshold and as a modified APA with the step-size when it is not saturated. This study derives a VSS scheme by analyzing the propagation of the mean square deviation of the weight-error vector when the saturation occurs and when it does not. The simulation results show that the proposed algorithm performs better with a fast convergence rate and small steady-state error compared to the conventional algorithms in both non-impulsive and impulsive noisy environments.