Sign subband adaptive filter with ϕ1-norm minimisation-based variable step-size

A new variable step-size sign subband adaptive filter (VSS-SSAF), not requiring any a priori information, is proposed by minimising the ℓ₁-norm of the subband a posteriori error under a box-constraint on the step-size. In addition, an efficient numerical procedure for updating its VSS is introduced to solve the non-differentiable convex problem. The proposed algorithm provides comparable or better convergence performance, when compared with the recent VSS-SSAF (minimising the mean-squares deviation with a priori knowledge of noise variance) or other conventional algorithms aimed at robustness against impulsive interferences.