On the steady-state MSE performance of the set-membership NLMS algorithm

The aim of this paper is to investigate the steady-state mean square error (MSE) performance of the set-membership (SM) normalized least-mean-square (NLMS) algorithm. Until recently there was no analysis tool available for the SM-NLMS algorithm, mainly due to its inherent nonlinear selective update which requires more involved mathematical treatment. The few recent available works invoke some unrealistic assumptions in order to simplify the problem. This paper investigates the validity of these assumptions and their influence in the accuracy of the resulting relations. Some simulation results are included in order to verify how reliable and accurate are the discussed analysis methods of the SM-NLMS algorithm.