Exact NLMS Algorithm with ${\ell _p}$ -Norm Constraint

This letter presents the exact normalized least-mean-square (NLMS) algorithm for the l_p-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.