TY - JOUR
T1 - Self correction fractional least mean square algorithm for application in digital beamforming
AU - Shah, Syed Asghar Ali
AU - Jan, Tariqullah
AU - Shah, Syed Muslim
AU - Raja, Muhammad Asif Zahoor
AU - Zafar, Mohammad Haseeb
AU - Haq, Sana Ul
A2 - Chaudhary, Sushank
N1 - Publisher Copyright:
Copyright: © 2024 Shah et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
PY - 2024/6/21
Y1 - 2024/6/21
N2 - Fractional order algorithms demonstrate superior efficacy in signal processing while retaining the same level of implementation simplicity as traditional algorithms. The self-adjusting dual-stage fractional order least mean square algorithm, denoted as LFLMS, is developed to expedite convergence, improve precision, and incurring only a slight increase in computational complexity. The initial segment employs the least mean square (LMS), succeeded by the fractional LMS (FLMS) approach in the subsequent stage. The latter multiplies the LMS output, with a replica of the steering vector (Ŕ) of the intended signal. Mathematical convergence analysis and the mathematical derivation of the proposed approach are provided. Its weight adjustment integrates the conventional integer ordered gradient with a fractional-ordered. Its effectiveness is gauged through the minimization of mean square error (MSE), and thorough comparisons with alternative methods are conducted across various parameters in simulations. Simulation results underscore the superior performance of LFLMS. Notably, the convergence rate of LFLMS surpasses that of LMS by 59%, accompanied by a 49% improvement in MSE relative to LMS. So it is concluded that the LFLMS approach is a suitable choice for next generation wireless networks, including Internet of Things, 6G, radars and satellite communication.
AB - Fractional order algorithms demonstrate superior efficacy in signal processing while retaining the same level of implementation simplicity as traditional algorithms. The self-adjusting dual-stage fractional order least mean square algorithm, denoted as LFLMS, is developed to expedite convergence, improve precision, and incurring only a slight increase in computational complexity. The initial segment employs the least mean square (LMS), succeeded by the fractional LMS (FLMS) approach in the subsequent stage. The latter multiplies the LMS output, with a replica of the steering vector (Ŕ) of the intended signal. Mathematical convergence analysis and the mathematical derivation of the proposed approach are provided. Its weight adjustment integrates the conventional integer ordered gradient with a fractional-ordered. Its effectiveness is gauged through the minimization of mean square error (MSE), and thorough comparisons with alternative methods are conducted across various parameters in simulations. Simulation results underscore the superior performance of LFLMS. Notably, the convergence rate of LFLMS surpasses that of LMS by 59%, accompanied by a 49% improvement in MSE relative to LMS. So it is concluded that the LFLMS approach is a suitable choice for next generation wireless networks, including Internet of Things, 6G, radars and satellite communication.
KW - Algorithms
KW - Computer Simulation
KW - Least-Squares Analysis
KW - Models, Theoretical
KW - Signal Processing, Computer-Assisted
UR - http://www.scopus.com/inward/record.url?scp=85196884996&partnerID=8YFLogxK
M3 - Article
C2 - 38905213
SN - 1932-6203
VL - 19
SP - e0304018
JO - PLoS ONE
JF - PLoS ONE
IS - 6 June
M1 - e0304018
ER -