Exact NLMS Algorithm with <formula formulatype="inline"> <tex Notation="TeX">${\ell _p}$</tex></formula>-Norm Constraint

Abstract

This letter presents the exact normalized least-mean-square (NLMS) algorithm for the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm-regularized square error, a popular choice for the identification of sparse systems corrupted by additive noise. The resulting exact lp-NLMS algorithm manifests differences to the original one, such as an independent update for each weight, a new sparsity-promoting compensated update, and the guarantee of stable convergence for any configuration (regardless the choice of lp norm and sparsity-tradeoff constant). Simulation results show that the exact lp-NLMS is stable and it outperforms the original one, thus validating the optimality of the proposed methodology.