Sparse SM-NLMS algorithm based on correntropy criterion

A sparse set-membership normalised least mean square (SM-NLMS) algorithm with a correntropy penalty is proposed and its performance is investigated for estimating a sparse echo channel. The proposed sparse SM-NLMS algorithm is derived by minimising an unconstraint cost function that utilises the correntropy on the weight vector as well as the sum of a symmetric and positive definite matrix constrained Euclidean norm of the differences between the instantaneous error and the upper bound of the SM filtering. Simulation results over a sparse echo channel show that the proposed algorithm is superior to the existing algorithms with respect to the steady-state misalignment.