Self-Developed Variable Step-Size LMS Filtering Algorithm Implementation

I have developed a MATLAB implementation of a variable step-size LMS (Least Mean Squares) filtering algorithm and would like to share it with the community to facilitate better understanding and application of this adaptive filtering technique. This program performs signal filtering by dynamically adjusting the step-size parameter in response to changing signal characteristics, thereby enhancing filtering performance through improved convergence speed and steady-state error control. The implementation utilizes a variable step-size mechanism that typically employs a nonlinear function (such as sigmoid or exponential functions) to modify the step-size based on instantaneous error measurements, allowing the filter to maintain optimal adaptation behavior across different signal conditions. Key functions include real-time coefficient updates using the LMS recursion formula with adaptive step-size, signal preprocessing routines, and performance evaluation metrics calculation. This program serves as both an educational tool for studying LMS algorithm variations and a practical solution for real-world signal processing applications where non-stationary signals require adaptive filtering approaches. The code structure includes modular components for easy modification and extension to different step-size adaptation strategies. Please feel free to contact me with any questions, suggestions, or improvement ideas regarding the algorithm implementation or its applications. Thank you for your support and interest in this work!