Tensor Least Mean Fourth Algorithm

Abstract

The tensor Least Mean Square (LMS) algorithm is a recent contribution in the field of adaptive algorithms whose aim is to provide better estimation in the presence of a large number of unknown parameters. This algorithm is designed by employing separability of linear operators on the standard LMS and by minimizing the standard stochastic gradient-based optimization of the Mean-Square-Error (MSE) cost function. Since the MSE criterion is known to have a superior performance in Gaussian environments only, the performance of the Tensor LMS is expected to degrade in non-Gaussian environments; while, the classical Least Mean Fourth (LMF) algorithm is known to have superior performance in non-Gaussian environments. In this work, a Tensor LMF algorithm which is designed by minimizing the Mean-Fourth-Error (MFE) criterion using the tensor factorization. We also provide the convergence in the mean sense of the proposed developed tensor LMF algorithm and found its stability bounds that ensure the convergence of the proposed algorithm. We provide various simulation experiments in different non-Gaussian environments to show the superiority of the proposed Tensor LMF algorithm over the Tensor LMS algorithm. For this purpose, examples of rank one two-way are presented. Simulation results are provided to validate our theoretical claims.