A Norm Penalized Noise-free Maximum Correntropy Criterion Algorithm

l
₁
-norm penalty and noise-free approach are considered in this paper to contribute to a maximum correntropy criterion (MCC) based algorithm. The introduced l
₁
-norm constrained noise-free MCC (L
₁
-NFMCC) algorithm inherits the good behavior of MCC in non-Gaussian environments. The cost function of the L
₁
-NFMCC algorithm is created by introducing l
₁
-norm penalty into the traditional cost function of MCC. In this regard, the L
₁
-NFMCC algorithm can fully use the sparse characteristics which exist in many real systems. In addition, the noise-free method is used in the L
₁
-NFMCC algorithm to provide a variable convergence step (VCS). The VCS is obtained by minimizing the noise-free (NF) a posteriori error signal with respect to the convergence step. As a consequence, the proposed L
₁
-NFMCC algorithm holds an excellent mean square deviation (MSD) behavior. Meanwhile, it shows particularly good property in sparse system. Numerical simulations are utilized to investigate the superiority of the L
₁
-NFMCC algorithm in non-Gaussian noises.