Analytical analysis of transient and steady-state properties of the proportionate NLMS algorithm

Using reasonable approximations we do analytical analysis of properties of the proportionate normalized least mean square algorithm (PNLMS) in the case of white and stationary input signal. This work extends ideas applied to the simplified-PNLMS algorithm to the PNLMS algorithm. In particular, the analysis incorporates the max function employed by the PNLMS algorithm which is not present in the simplified-PNLMS algorithm. The properties of the PNLMS are predicted for both the transient and steady state. An expression for the mean weight deviation in steady state is also presented. Theoretical expectations are compared with results obtained by numerical simulations.