ℒp-Norm-like Affine Projection Sign Algorithm for Sparse System to Ensure Robustness against Impulsive Noise

An improved affine projection sign algorithm (APSA) was developed herein using a ℒp-norm-like constraint to increase the convergence rate in sparse systems. The proposed APSA is robust against impulsive noise because APSA-type algorithms are generally based on the ℒ1-norm minimization of error signals. Moreover, the proposed algorithm can enhance the filter performance in terms of the convergence rate due to the implementation of the ℒp-norm-like constraint in sparse systems. Since a novel cost function of the proposed APSA was designed for maintaining the similar form of the original APSA, these have symmetric properties. According to the simulation results, the proposed APSA effectively enhances the filter performance in terms of the convergence rate of sparse system identification in the presence of impulsive noises compared to that achieved using the existing APSA-type algorithms.