The proportionate normalized least mean square algorithm (PNLMS) greatly improves the convergence of the sparse impulse response. It exploits the shape of the impulse response to decide the proportionate step gain for each coefficient. This is not always suitable. Actually, the proportionate step gain should be determined according to the difference between the current estimate of the coefficient and its optimal value. Based on this idea, an approach is proposed to determine the proportionate step gain. The proposed approach can improve the convergence of proportionate adaptive algorithms after a fast initial period. It even behaves well for the non-sparse impulse response. Simulations verify the effectiveness of the proposed approach.

Recently, proportionate adaptive algorithms have been proposed to speed up convergence in the identification of sparse impulse response. Although they can improve convergence for sparse impulse responses, the steady-state misalignment is limited by the constant step-size parameter. In this article, based on the principle of least perturbation, we first present a derivation of normalized version of proportionate algorithms. Then by taking the disturbance signal into account, we propose a variable step-size proportionate NLMS algorithm to combine the benefits of both variable step-size algorithms and proportionate algorithms. The proposed approach can achieve fast convergence with a large step size when the identification error is large, and then considerably decrease the steady-state misalignment with a small step size after the adaptive filter reaches a certain degree of convergence. Simulation results verify the effectiveness of the proposed approach.