Variable step-size weighted zero-attracting sign algorithm

Abstract

The classical sign algorithm (SA) has been widely used in adaptive filters due to its low computational complexity and robustness against impulsive noise. In some applications the system to be estimated may be sparse. To improve the convergence rate of the SA for sparse system estimation, this paper incorporates a weighted l1-norm into the cost function built for the SA to develop a weighted zero-attracting SA (WZA-SA). Since the WZA-SA uses a constant step-size, it requires to take a tradeoff between fast convergence rate and small steady-state misalignment. To address this problem, we present a variable step-size (VSS) for the WZA-SA based on the mean-squared deviation (MSD) model-driven method. Simulation results are provided to verify its good performance for white or not highly correlated input signals.