Tracking performance analysis of the set-membership NLMS Adaptive Filtering Algorithm

In this paper, we analyze the tracking performance of the set-membership normalized least mean squares (SM-NLMS) adaptive filtering algorithm using the energy conservation argument. The analysis leads to a nonlinear equation whose solution gives the steady-state mean squared error (MSE) of the SM-NLMS algorithm in a nonstationary environment. We prove that there is always a unique positive solution for this equation. The results predicted by the analysis show good agreement with the simulation experiments.