Performance Comparison of LMS and RLS Adaptive Algorithms

In this paper, we examine the adaptive performance comparison between Least Mean Squares (LMS) and Recursive Least Squares (RLS) algorithms. The adaptive performance refers to these algorithms' capability to handle different types of data streams effectively. We will investigate both algorithms' performance across various data types including but not limited to image, audio, and text data processing. The LMS algorithm implements a gradient descent approach with a simple weight update mechanism (w(n+1) = w(n) + μe(n)x(n)), making it computationally efficient but potentially slower in convergence. In contrast, RLS utilizes a recursive matrix inversion technique with exponential weighting, offering faster convergence at the cost of higher computational complexity O(n²). Through comprehensive performance analysis and comparison metrics such as convergence speed, steady-state error, and computational requirements, we will derive deeper insights to better understand and apply these adaptive filtering algorithms in practical implementations.