Variable step-size LMS algorithm with hybrid weight coefficients based on the Rayleigh distribution curve

Due to the limitations of existing variable step-size LMS adaptive filtering algorithms in addressing convergence speed, tracking performance, and steady-state errors, a variable step-size LMS algorithm with hybrid weight coefficients based on the Rayleigh distribution curve was proposed. The impact of the new variable step function parameters <italic>α</italic>, <italic>β</italic>, <italic>γ</italic> and the hybrid filter weight coefficient <italic>W</italic>(<italic>n</italic>) on the proposed algorithm performance and interference suppression analysis were discussed in detail. Simulation and experimental results demonstrate that the proposed algorithm reduces computational complexity while improving convergence speed by at least 12%. Moreover, it exhibits superior convergence speed, tracking performance, and steady-state errors across various signal-to-noise ratios. The proposed algorithm is suitable for electromagnetic interference cancellation in complex environments.