Steady-state performance of hyperslab projection algorithm

This paper presents an analysis of the steady-state mean-square error of an adaptive filtering algorithm using the metric projection onto a closed hyperslab, which we refer to as the hyperslab projection algorithm (HSPA). HSPA is not only a generalization of both the normalized least mean square (NLMS) algorithm and the set-membership NLMS (SM-NLMS) algorithm but also a special case of the adaptive parallel subgradient projection (PSP) method. It is known that HSPA possesses both fast convergence and robustness against noise. The approach of this paper is to employ the energy conservation relation, which enables us to avoid the transient analysis of HSPA. Under different assumptions, we obtain two results, which are generalizations of well-known results of the steady-state performance of NLMS. Extensive simulations show the good match between the theories and experiments.