Steady-state analysis of the set-membership affine projection algorithm

Among the adaptive filtering algorithms the set-membership affine projection (SM-AP) algorithm has the attractive feature of not trading off misadjustment with convergence speed. This paper presents an analysis of the steady-state mean-square error (MSE) of the SM-AP algorithm. Our analysis relies on the energy conservation method and does not assume a specific probability distribution for the input vector. Moreover, since the SM-AP algorithm with a fixed-modulus error-based constraint vector generalizes some important algorithms, such as the SM normalized least-mean-square (SM-NLMS) algorithm, the results can be directly applied to these algorithms. Simulation results confirm the accuracy of our analysis.