Performance and Analysis of Recursive Constrained Least Lncosh Algorithm Under Impulsive Noises

We propose a recursive constrained least lncosh (RCLL) adaptive algorithm to combat the impulsive noises. In general, the lncosh function is used to develop a new algorithm within the context of constrained adaptive filtering via solving a linear constrained optimization problem, where the lncosh function is a natural logarithm of hyperbolic cosine function, which can be regarded as a combination of mean-square-error (MSE) and mean-absolute-error (MAE) criteria. Compared with other typical recursive methods, the proposed RCLL algorithm can obtain superior steady state behavior and better robustness for combating impulsive noises. Besides, the mean-square convergence condition and theoretical transient mean-square-deviation of the RCLL algorithm is presented. Simulation results verified the theoretical analysis in non-Gaussian noises and shown the superior performance of the proposed RCLL algorithm.