Comments on "Design of fractional-order variants of complex LMS and NLMS algorithms for adaptive channel equalization"

TL;DR

This paper critically examines recent fractional-order variants of complex LMS and NLMS algorithms, highlighting their convergence issues and lack of advantages over traditional methods through analytical and simulation evidence.

Contribution

It provides a critical analysis of fractional-order CLMS and NLMS algorithms, revealing their convergence problems and limited benefits compared to classical algorithms.

Findings

Fractional-order variants do not always converge.

No clear advantage over traditional CLMS and NLMS when they do converge.

Analytical reasoning supports simulation results.

Abstract

The purpose of this note is to discuss some aspects of recently proposed fractional-order variants of complex least mean square (CLMS) and normalized least mean square (NLMS) algorithms in ``Design of Fractional-order Variants of Complex LMS and Normalized LMS Algorithms for Adaptive Channel Equalization'' [Nonlinear Dyn. 88(2), 839-858 (2017)]. It is observed that these algorithms do not always converge whereas they have apparently no advantage over the CLMS and NLMS algorithms whenever they converge. Our claims are based on analytical reasoning and are supported by numerical simulations.