An Analytical Model for Predicting the Convergence Behavior of the Least Mean Mixed-Norm (LMMN) Algorithm

The Least Mean Mixed-Norm (LMMN) algorithm is a stochastic gradient-based algorithm whose objective is to minimum a combination of the cost functions of the Least Mean Square (LMS) and Least Mean Fourth (LMF) algorithms. This algorithm has inherited many properties and advantages of the LMS and LMF algorithms and mitigated their weaknesses in some ways. The main issue of the LMMN algorithm is the lack of an analytical model for predicting its behavior, the fact that has restricted its practical application. To address this issue, an analytical model is presented in the current paper that is able to predict the mean-square-error and the mean-weights-error behavior with a high accuracy. The accuracy of the derived model is verified using various simulation tests.