Fractional Processing Based Adaptive Beamforming Algorithm

Fractional order algorithms have shown promising results in various signal processing applications due to their ability to improve performance without significantly increasing complexity. The goal of this work is to investigate the use of fractional order algorithm in the field of adaptive beamforming, with a focus on improving performance while keeping complexity lower. The effectiveness of the algorithm will be studied and evaluated in this context. In this paper, a fractional order least mean square (FLMS) algorithm is proposed for adaptive beamforming in wireless applications for effective utilization of resources. This algorithm aims to improve upon existing beamforming algorithms, which are inefficient in performance, by offering faster convergence, better accuracy, and comparable computational complexity. The FLMS algorithm uses fractional order gradient in addition to the standard ordered gradient in weight adaptation. The derivation of the algorithm is provided and supported by mathematical convergence analysis. Performance is evaluated through simulations using mean square error (MSE) minimization as a metric and compared with the standard LMS algorithm for various parameters. The results, obtained through Matlab simulations, show that the FLMS algorithm outperforms the standard LMS in terms of convergence speed, beampattern accuracy and scatter plots. FLMS 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.