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Self correction fractional least mean square algorithm for application in digital beamforming.

Syed Asghar Ali Shah1, Tariqullah Jan1, Syed Muslim Shah2

  • 1Department of Electrical Engineering, University of Engineering and Technology Peshawar, Peshawar, Pakistan.

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A new self-adjusting dual-stage fractional order least mean square (LFLMS) algorithm improves signal processing convergence and precision. LFLMS enhances performance over traditional least mean square (LMS) methods for future wireless networks.

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Area of Science:

  • Digital Signal Processing
  • Adaptive Filtering
  • Fractional Calculus Applications

Background:

  • Traditional least mean square (LMS) algorithms offer simplicity but can be limited in convergence speed and precision.
  • Fractional order algorithms present an opportunity to enhance signal processing performance while maintaining implementation feasibility.
  • There is a need for advanced adaptive filtering techniques to meet the demands of next-generation wireless communication systems.

Purpose of the Study:

  • To introduce and analyze a novel self-adjusting dual-stage fractional order least mean square (LFLMS) algorithm.
  • To improve convergence rate and precision in adaptive filtering applications.
  • To evaluate the performance of LFLMS against existing methods in signal processing.

Main Methods:

  • Development of the LFLMS algorithm, combining an initial least mean square (LMS) stage with a subsequent fractional LMS (FLMS) stage.
  • The FLMS stage incorporates a fractional-ordered weight adjustment and multiplication with a replica of the steering vector.
  • Mathematical convergence analysis and derivation, followed by performance evaluation through simulations measuring mean square error (MSE).

Main Results:

  • The LFLMS algorithm demonstrates significantly superior performance compared to conventional methods.
  • LFLMS achieves a 59% faster convergence rate than the standard LMS algorithm.
  • A 49% improvement in mean square error (MSE) was observed with LFLMS relative to LMS.

Conclusions:

  • The proposed LFLMS algorithm offers enhanced convergence and precision with only a marginal increase in computational complexity.
  • LFLMS is a promising adaptive filtering solution for advanced wireless communication technologies.
  • The algorithm is well-suited for applications such as the Internet of Things (IoT), 6G networks, radar systems, and satellite communications.