MATLAB Implementation of Adaptive Equalizer Using RLS Algorithm

This paper presents a MATLAB implementation of an adaptive equalizer using the Recursive Least Squares (RLS) algorithm, providing readers with a clear understanding of the algorithm's implementation steps and underlying principles. We begin by detailing the background and fundamental principles of the RLS algorithm, including the computational methods for weight vectors and error signals. The algorithm employs a recursive approach to update filter coefficients, minimizing the sum of squared errors through efficient matrix operations using the inversion lemma. Next, we demonstrate the application of this algorithm in adaptive equalizers, highlighting its practical effectiveness and real-world scenarios through performance metrics like convergence speed and mean-square error analysis. The implementation includes key MATLAB functions such as filter initialization, error calculation, and weight update procedures using matrix manipulations. Finally, we provide a step-by-step demonstration of writing the RLS-based adaptive equalizer program in MATLAB, complete with fully commented code that includes initialization parameters, iterative updating processes, and result visualization sections for reference and learning purposes.