Steady-State Performance of Non-Negative Least-Mean-Square Algorithm and Its Variants

The Non-Negative Least-Mean-Square (NNLMS) algorithm and its variants have been proposed for online estimation under non-negativity constraints. The transient behavior of the NNLMS, Normalized NNLMS, Exponential NNLMS and Sign-Sign NNLMS algorithms have been studied in the literature. In this letter, we derive closed-form expressions for the steady-state excess mean-square error (EMSE) for the four algorithms. Simulation results illustrate the accuracy of the theoretical results. This work complements the understanding of the behavior of these algorithms.