Towards analytical convergence analysis of proportionate-type nlms algorithms

To date no theoretical results have been developed to predict the performance of the proportionate normalized least mean square (PNLMS) algorithm or any of its cousin algorithms such as the µ-law PNLMS (MPNLMS), and the ε-law PNLMS (EPNLMS). In this paper we develop an analytic approach to predicting the performance of the simplified PNLMS algorithm which is closely related to the PNLMS algorithm. In particular we demonstrate the ability to predict the Mean Square Output Error of the simplified PNLMS algorithm using our theory.