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A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

Chinese Physics B 2014年第3期23卷 159-164页

作者： Bilal Shoaib Ijaz Mansoor Qureshi Ihsanulhaq Shafqatullah Department of Electronic Engineering Faculty of Engineering and Technology International Islamic University Department of Electrical Engineering AIR University School of Engineering and Applied Sciences ISRA University

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.

关键词： fractional least mean square kernel methods Reimann-Lioville derivative Mackey glass timeseries

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fractional Processing Based Adaptive Beamforming Algorithm

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Computers, Materials & Continua 2023年第7期76卷 1065-1084页

作者： Syed Asghar Ali Shah Tariqullah Jan Syed Muslim Shah Ruhul Amin Khalil Ahmad Sawalmeh Muhammad Anan Department of Electrical Engineering University of Engineering and TechnologyPeshawar25120Pakistan Department of Electrical Engineering Capital University of Science and TechnologyIslamabad44000Pakistan Department of Computer Science Northern Border UniversityArar91431Saudi Arabia Department of Software Engineering Alfaisal UniversityRiyadh11533Saudi Arabia

fractional order algorithms have shown promising results in various signal processing applications due to their ability to improve performance without significantly increasing *** goal of this work is to inves-tigate the use of fractional order algorithm in the field of adaptive beam-forming,with a focus on improving performance while keeping complexity *** effectiveness of the algorithm will be studied and evaluated in this *** this paper,a fractional order least mean square(FLMS)algorithm is proposed for adaptive beamforming in wireless applications for effective utilization of *** algorithm aims to improve upon existing beam-forming algorithms,which are inefficient in performance,by offering faster convergence,better accuracy,and comparable computational *** FLMS algorithm uses fractional order gradient in addition to the standard ordered gradient in weight *** derivation of the algorithm is provided and supported by mathematical convergence *** is evaluated through simulations using mean square error(MSE)minimization as a metric and compared with the standard LMS algorithm for various *** results,obtained through Matlab simulations,show that the FLMS algorithm outperforms the standard LMS in terms of convergence speed,beampattern accuracy and scatter *** outperforms LMS in terms of convergence speed by 34%.From this,it can be concluded that FLMS is a better candidate for adaptive beamforming and other signal processing applications.

关键词： Adaptive beamforming adaptive array fractional processing least mean square fractional least mean square

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