MATLAB Program for Plotting LMS Algorithm Convergence Rate Curve

This article presents a comprehensive MATLAB implementation for analyzing the convergence behavior of the Least Mean Squares (LMS) algorithm. The LMS algorithm is an adaptive filtering technique that continuously adjusts its coefficients based on input signals to optimize output performance. The program begins by generating synthetic random signals using MATLAB's randn() function to simulate realistic input conditions. Key implementation aspects include: - Initialization of filter coefficients with proper step size parameter (mu) selection - Real-time coefficient updates using the LMS weight adjustment formula: w(n+1) = w(n) + μ*e(n)*x(n) - Error calculation between desired and filtered signals at each iteration The core algorithm implementation involves: 1. Signal generation and normalization 2. Iterative filter coefficient adaptation 3. Convergence metric computation (typically Mean Square Error) 4. Data logging for performance analysis The program features specialized plotting functions to visualize the convergence curve, demonstrating how the algorithm's error decreases over iterations. Optimization techniques include: - Signal preprocessing for numerical stability - Adaptive step size adjustments - Vectorized operations for computational efficiency Advanced visualization capabilities provide: - Real-time convergence monitoring - Multiple trial averaging for statistical significance - Customizable plot parameters (axis labels, grid settings, legend placement) The complete MATLAB code package enables thorough analysis of LMS algorithm performance characteristics, including convergence speed, stability, and steady-state error behavior. The implementation serves as both an educational tool and practical framework for adaptive signal processing applications.