Convergence and tracking analysis of the ε-NSRLMF algorithm

In this work, the convergence and tracking behavior of the ε-normalized sign regressor least mean fourth (NSRLMF) algorithm are analyzed in the presence of white and correlated Gaussian data. Furthermore, the stability bound on the step-size of the ε-NSRLMF algorithm to ensure convergence in the mean, which also leads us to the mean convergence of the ε-normalized sign regressor least mean mixed-norm (NSRLMMN) algorithm is derived. Finally, simulation results are conducted to confirm the validity and performance of the proposed adaptive algorithm for both white and correlated Gaussian regressors.