Reweighted nonnegative least-mean-square algorithm

Statistical inference subject to nonnegativity constraints is a frequently occurring problem in signal processing. The nonnegative least-mean-square (NNLMS) algorithm was derived to address such problems in an online way. This algorithm builds on a fixed-point iteration strategy driven by the Karush-Kuhn-Tucker conditions. It was shown to provide low variance estimates, but it however suffers from unbalanced convergence rates of these estimates. In this paper, we address this problem by introducing a variant of the NNLMS algorithm. We provide a theoretical analysis of its behavior in terms of transient learning curve, steady-state and tracking performance. Simulations are conducted to validate the theoretical results. We also introduce a potential application of this algorithm to sparse system identification.