Normalized Combinations of Proportionate Affine Projection Sign Subband Adaptive Filter

Abstract

The proportionate affine projection sign subband adaptive filter (PAP-SSAF) has a better performance than the affine projection sign subband adaptive filter (AP-SSAF) when we eliminate the echoes. Still, the robustness of the PAP-SSAF algorithm is insufficient under unknown environmental conditions. Besides, the best balance remains to be found between low steady-state misalignment and fast convergence rate. In order to solve this problem, we propose a normalized combination of PAP-SSAF (NCPAP-SSAF) based on the normalized adaption schema. In this paper, a power normalization adaptive rule for mixing parameters is proposed to further improve the performance of the NCPAP-SSAF algorithm. By using Nesterov’s accelerated gradient (NAG) method, the mixing parameter of the control combination can be obtained with less time consumed when we take the l1-norm of the subband error as the cost function. We also test the algorithmic complexity and memory requirements to illustrate the rationality of our method. In brief, our study contributes a novel adaptive filter algorithm, accelerating the convergence speed, reducing the steady-state error, and improving the robustness. Thus, the proposed method can be utilized to improve the performance of echo cancellation. We will optimize the combination structure and simplify unnecessary calculations to reduce the algorithm’s computational complexity in future research.