Sparse normalized maximum correntropy criterion algorithm with li-norm penalties for channel estimation

Sparse normalized maximum correntropy criterion (NMCC) algorithms are proposed on the basis of ℓ₁-norm penalties to exploit the sparseness characteristics in the non-Gaussian environment. The proposed sparse NMCC algorithms are realized by integrating a ℓ₁-norm or a reweighted ℓ₁-norm into the cost function of the NMCC algorithm to create zero attracting NMCC (ZA-NMCC) and reweighted ZA-NMCC (RZA-NMCC) algorithms. The proposed algorithms are mathematically derived in detail by using Lagrange multiplier method. From the derivation of the proposed sparse NMCC algorithms, we found that desired zero attractors are established to give expected zero attraction in their iterations. The proposed sparse NMCC algorithms are evaluated through sparse channel models to discuss their performance. The results obtained from the computer simulations give a conformation that the proposed sparse NMCC algorithms can provide a superior performance for estimating the designated sparse channels by using the criterion of the convergence speed rate and mean square errors.