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

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 L
₀
norm constraint robust set-membership NSAF (L
₀
-RSM-NSAF), robust set-membership improved proportionate NSAF (RSM-IPNSAF), and L
₀
norm constraint robust set-membership improved proportionate NSAF (L
₀
-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 L
₀
norm of the weighted updated weight vector. Simulations in AEC application confirm the improvements of the proposed algorithms in performance.