Transient Convergence Analysis of Least Lncosh Algorithm

Lncosh function has been used for constructing a cost function for devising an adaptive filter algorithm to provide a desired performance under non-Gaussian noise, naming as least Lncosh algorithm (LLA). However, its transient behavior analysis has not been analyzed and investigated. As an important characteristic for the LLA, the transient behavior affects its performance in real-world applications. Herein, we present the theoretical model for evaluating the mean weight behavior and the transient excess mean square error (EMSE) behavior of the LLA. In addition, the proposed models can also be used to predict the transient behavior of the adaptive filtering algorithms with error nonlinearities {under non-Gaussian noises}. The experiment results have verified the validity of the presented models.