Blind Equalization Simulation Using LMS Algorithm

This article presents a blind equalization simulation program utilizing the LMS algorithm, applicable in signal processing and communication fields. Blind equalization is a technique that extracts desired signals by estimating transmission channel characteristics and signal statistics without training sequences. The LMS algorithm, a widely adopted adaptive filter for blind equalization, autonomously adjusts its filter coefficients to minimize the error between the output signal and the desired response. Key implementation aspects include: initializing filter weights to zero, calculating the error term as the difference between the filter output and a nonlinearly transformed version of the output (using signum or decision-directed methods for blind adaptation), and updating weights through the recursion w(n+1) = w(n) + μ·e(n)·x(n) where μ denotes the step size controlling convergence. We provide a comprehensible MATLAB-based simulation demonstrating these operations, including channel impulse response modeling, signal constellation plotting, and mean-square error trajectory visualization to evaluate equalization performance.