An improved PNLMS algorithm

TLDR

The PNLMS algorithm was developed for network echo cancellation. The authors propose a new, more reliable rule to replace the original PNLMS rule. The original PNLMS converges quickly for sparse echoes but much slower for dispersive impulse responses, indicating its rule is suboptimal. Simulations demonstrate that the improved PNLMS consistently outperforms both NLMS and the original PNLMS regardless of impulse response characteristics.

Abstract

Recently, the proportionate normalized least mean square (PNLMS) algorithm was developed for use in network echo cancelers. In comparison to the normalized least mean square (NLMS) algorithm, PNLMS has very fast initial convergence and tracking when the echo path is sparse. Unfortunately, when the impulse response is dispersive, the PNLMS converges much slower than NLMS. This implies that the rule proposed in PNLMS is far from optimal. In many simulations, it seems that we fully benefit from PNLMS only when the impulse response is close to a delta function. In this paper, we propose a new rule that is more reliable than the one used in PNLMS. Many simulations show that the new algorithm (improved PNLMS) performs better than NLMS and PNLMS, whatever the nature of the impulse response is.