A reconsideration of improved PNLMS algorithm from metric combining viewpoint

In this paper, we show the importance of considering metric in adaptive filtering through a reconsideration of the improved proportionate normalized least mean square (IPNLMS) algorithm for sparse systems from a viewpoint of metric combining. IPNLMS convexly combines a positive-definite diagonal matrix (whose diagonal elements are proportional to the absolute values of the adaptive filter to reflect the system sparsity) with the identity matrix. We present the metric-combining NLMS (MC-NLMS) algorithm and derive, as its special example, the natural PNLMS (NPNLMS) algorithm. NPNLMS can be regarded as a modified version of IPNLMS and we show that NPNLMS is more natural (and performs better) than IPNLMS.