Relative proportionate NLMS: Improving convergence for acoustic channel identification

It is known that the proportionate normalized least mean square (PNLMS) algorithm outperforms traditional normalized least mean square(NLMS) algorithm, in terms of fast initial convergence rate. However, the PNLMS has been widely observed to not be optimal. This study presents a new perspective into the "proportionate" gain (step-size) allocation scheme. A relative proportionate scheme is established and shows better performance than the original absolute proportionate scheme. Although the correspondingly derived relative proportional LMS (R-PNLMS) algorithm is similar to PNLMS, it differs greatly in terms of conception and convergence behavior. Simulation results for the problem of acoustic channels identification, show improved performance over existing methods.