Performance Comparison of LMS and NLMS Algorithms

LMS_Identify.m implements a performance comparison between the LMS (Least Mean Squares) and NLMS (Normalized Least Mean Squares) algorithms. The LMS algorithm is an adaptive filtering technique based on gradient descent, which iteratively adjusts filter weights to approximate the desired response using a fixed step-size parameter. The NLMS algorithm enhances LMS by adaptively normalizing the step-size parameter using the input signal power, resulting in improved convergence speed and stability. In the implementation within LMS_Identify.m, both algorithms are coded with weight update equations: LMS uses w(n+1) = w(n) + μ*e(n)*x(n), while NLMS employs w(n+1) = w(n) + [μ/(δ+||x(n)||²)]*e(n)*x(n), where δ is a regularization constant preventing division by zero. The performance comparison evaluates both algorithms through Mean Squared Error (MSE) curves and convergence speed analysis. Results demonstrate that while LMS achieves smaller steady-state MSE, it exhibits slower convergence. Conversely, NLMS provides faster convergence but may yield higher MSE in certain scenarios due to its variable step-size mechanism. Therefore, practical applications require careful algorithm selection based on specific system requirements regarding convergence speed and steady-state accuracy.