Proportionate Normalized Least Mean Square Algorithms Based on Coefficient Difference

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.