Variable Step-Size Affine Projection Sign Algorithm

This brief proposes a novel variable step-size affine projection sign algorithm (APSA), which is characterized by its robustness against impulsive noises. To obtain a step size reasonably, the proposed algorithm investigates the mean-square deviation (MSD) of APSA. Because it is impossible to accurately compute the MSD of APSA, the proposed algorithm derives the upper bound of the MSD using the upper bound of the L
₁
-norm of the measurement noise. The optimal step size is calculated at each iteration by minimizing the upper bound of the MSD, which improves the filter performance, with respect to the convergence rate and the steady-state estimation error. The simulation results demonstrate that the proposed algorithm improves the filter performance in a system-identification scenario in the presence of impulsive noises.