Nonlinear Adaptive Filter: VLMS and VRLS Algorithms with MATLAB Implementation

This article provides a comprehensive overview of a MATLAB implementation for nonlinear adaptive filters. The program features two distinct algorithms: Variable Step-Size Least Mean Square (VLMS) and Variable Step-Size Recursive Least Squares (VRLS). The VLMS algorithm implements an adaptive filtering approach particularly effective for noise removal in signal processing applications, where the step-size parameter dynamically adjusts to optimize convergence speed and steady-state error. The VRLS algorithm is designed for system identification and prediction tasks, utilizing a forgetting factor that varies according to input signal characteristics to enhance tracking capabilities in non-stationary environments. The implementation includes comprehensive input/output file handling, enabling users to easily test the algorithms with custom datasets and modify parameters through configuration files. The code structure separates algorithm cores from utility functions, with clear interfaces for adjusting parameters like step-size adaptation rates and regularization factors. Subsequent sections will demonstrate program usage patterns and guide parameter optimization strategies to adapt filter performance for specific application requirements, including real-time processing considerations and computational efficiency improvements.