Algorithms for Adaptive Signal Processing: LMS, NLMS, and RLS

Adaptive signal processing involves various algorithms, including the Least Mean Squares (LMS) algorithm, Normalized Least Mean Squares (NLMS) algorithm, and Recursive Least Squares (RLS) algorithm. The LMS implementation typically uses gradient descent with a fixed step-size parameter to minimize the mean square error, while NLMS enhances stability by normalizing the step size based on the input signal power. The RLS algorithm employs a recursive approach to compute optimal weights by minimizing the weighted least squares error, offering faster convergence at the cost of higher computational complexity. Beyond these core algorithms, numerous other adaptive algorithm examples can be referenced. By applying these algorithms with appropriate parameter tuning and system identification techniques, adaptive signal processing capabilities can be achieved to better meet practical requirements in applications such as noise cancellation, system identification, and channel equalization.