MATLAB Simulation Program for Normalized LMS Filtering Algorithm

This document presents a MATLAB simulation program for the normalized LMS (Least Mean Squares) filtering algorithm. The normalized LMS algorithm is a widely used adaptive filtering technique applied in signal processing and communication systems. Through MATLAB simulation, we can effectively analyze the algorithm's performance characteristics and behavioral patterns.

The implementation includes key components such as step size normalization calculation, weight update iterations, and error signal generation. The core algorithm features a variable step size mechanism that normalizes the adaptation rate based on the input signal power, providing improved stability compared to standard LMS implementations.

We will detail the simulation program's implementation steps including parameter configuration (filter length, step size parameter, regularization constant), signal generation methods, and performance evaluation metrics. The code structure demonstrates real-time weight adaptation using vectorized operations for computational efficiency.

Additionally, we discuss the algorithm's advantages (faster convergence, better stability) and limitations (computational complexity), along with potential enhancement directions such as variable regularization techniques and complex signal handling. Through this documentation, readers will gain comprehensive understanding of normalized LMS algorithm implementation and practical application scenarios.

The MATLAB code includes fundamental functions for filter initialization (init_nlms), adaptive filtering (adapt_nlms), and performance visualization, providing a complete framework for algorithm experimentation and analysis.