Robust Set-Membership Normalized Subband Adaptive Filtering Algorithms and Their Application to Acoustic Echo Cancellation

Abstract

This paper presents a family of robust set-membership normalized subband adaptive filtering (RSM-NSAF) algorithms for acoustic echo cancellation (AEC). By using a new robust set-membership error bound, the RSM-NSAF algorithm obtains improved robustness against impulsive noises and decreased steady-state misalignment relative to the conventional set-membership NSAF (SM-NSAF) algorithm. To exploit the sparsity of the impulse response, the L0 norm constraint robust set-membership NSAF (L0-RSM-NSAF), robust set-membership improved proportionate NSAF (RSM-IPNSAF), and L0 norm constraint robust set-membership improved proportionate NSAF (L0-RSM-IPNSAF) algorithms are derived by minimizing a differentiable cost function that utilizes the Riemannian distance between the updated and previous weight vectors as well as the L0 norm of the weighted updated weight vector. Simulations in AEC application confirm the improvements of the proposed algorithms in performance.