Research on Fuzzy Variable Step Size LMS Adaptive Filtering Algorithm Based on Convex Combination

This study investigates the convergence speed and mean square error capability of the Least Mean Square (LMS) adaptive filtering algorithm, presenting a novel approach termed the Fuzzy Variable Learning Rate LMS algorithm based on convex combination. Firstly, in order to enhancing convergence speed, an enhanced LMS algorithm employing variable learning rate based on sine functions, denoted as the Improved Variable Step Size LMS Algorithm based on Sine Function (γ-SLMS), is introduced. Building upon this, to mitigate the steady-state error, the Fuzzy Variable Learning Rate LMS Algorithm based on Mamdani Model (FMS-LMS) is proposed. Finally, utilizing a convex combination framework, the Fuzzy Variable Learning Rate LMS Adaptive Filtering Algorithm Based on Convex Combination (cFMS-LMS) is formulated. Simulation results indicate that the cFMS-LMS algorithm surpasses traditional LMS algorithms in both convergence speed and mean square error. Furthermore, it shows lower computational complexity compared to LMS algorithms utilizing Sugeno fuzzy inference.