Filter proportionate normalized least mean square algorithm for a sparse system

Abstract

In this paper, the proportionate normalized least mean square (PNLMS) and its modifications, such as improved PNLMS (IPNLMS) and mu-law PNLMS (MPNLMS) algorithms, developed for a sparse system, are analyzed for a compressed input signal. This analysis is based on a comparative study of the steady-state error and convergence time for the original signal and the compressed signal. Further, in this paper, a filter PNLMS (FPNLMS) algorithm that is a modification of the IPNLMS algorithm is proposed. The FPNLMS algorithm uses a step size varying in time to adapt to the sparse system. Simulations are carried out to compare the proposed FPNLMS algorithm for different signal-to-noise ratio for a compressed input signal with existing algorithms, ie, PNLMS, MPNLMS, and IPNLMS algorithms. The FPNLMS algorithm achieves a better steady-state and convergence time compared with other existing algorithms in both low and high SNRs. The FPNLMS algorithm is further simulated for a real transfer function to show its robustness compared with existing algorithms.