Design and Analysis of the Fractional-Order Complex Least Mean Square (FoCLMS) Algorithm

In this work, a new class of stochastic gradient algorithm is developed based on fractional calculus. Unlike the existing algorithms, the concept of complex fractional gradient is introduced by employing Caputo’s fractional derivative which results in a fractional steepest descent algorithm and a fr...

Full description

Saved in:
Bibliographic Details
Published inCircuits, systems, and signal processing Vol. 40; no. 10; pp. 5152 - 5181
Main Authors Ahmad, Jawwad, Zubair, Muhammad, Rizvi, Syed Sajjad Hussain, Shaikh, Muhammad Shafique
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2021
Springer Nature B.V
Subjects
Online AccessGet full text

Cover

Loading…
More Information
Summary:In this work, a new class of stochastic gradient algorithm is developed based on fractional calculus. Unlike the existing algorithms, the concept of complex fractional gradient is introduced by employing Caputo’s fractional derivative which results in a fractional steepest descent algorithm and a fractional-order complex LMS (FoCLMS) algorithm. We demonstrate that with the Caputo’s fractional gradient definition, the Weiner solution remains invariant. Convergence analysis of the proposed FoCLMS algorithm is presented for both transient and steady state scenarios. Consequently, expressions for the learning curves and steady state EMSE are derived. Our theoretical developments are validated by simulation experiments. Extensive simulations are presented to investigate all possible scenarios: channel with negative weights and real input data, channel with positive weights and complex input data, and channel with complex weights and complex input data.
ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-021-01715-8