An Affine Projection Sign Algorithm Robust Against Impulsive Interferences

Abstract

A new affine projection sign algorithm (APSA) is proposed, which is robust against non-Gaussian impulsive interferences and has fast convergence. The conventional affine projection algorithm (APA) converges fast at a high cost in terms of computational complexity and it also suffers performance degradation in the presence of impulsive interferences. The family of sign algorithms (SAs) stands out due to its low complexity and robustness against impulsive noise. The proposed APSA combines the benefits of the APA and SA by updating its weight vector according to the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm optimization criterion while using multiple projections. The features of the APA and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm minimization guarantee the APSA an excellent candidate for combatting impulsive interference and speeding up the convergence rate for colored inputs at a low computational complexity. Simulations in a system identification context show that the proposed APSA outperforms the normalized least-mean-square (NLMS) algorithm, APA, and normalized sign algorithm (NSA) in terms of convergence rate and steady-state error. The robustness of the APSA against impulsive interference is also demonstrated.