MATLAB Implementation of LMS Algorithm

The Least Mean Squares (LMS) algorithm is a classic adaptive filtering algorithm widely used in signal processing, system identification, and communication systems. Its core principle involves iteratively adjusting filter coefficients to minimize the mean square error between the output signal and the desired signal.

Implementing the LMS algorithm in MATLAB typically involves the following steps: First, define the input signal and desired signal, then initialize the filter weights to zero or small random values. During each iteration, compute the filter's output signal and compare it with the desired signal to obtain the error. Update the filter weights using this error and the current input signal, typically controlled by a step-size parameter that regulates convergence speed.

The algorithm's performance can be evaluated through error convergence curves, where appropriate step-size selection is crucial—too large causes oscillation while too small results in slow convergence. Practical applications must also consider the statistical properties of input signals and noise effects.

This implementation requires no additional paid toolboxes and can be accomplished with pure MATLAB code, making it suitable for teaching demonstrations and simple engineering applications. Developers can further extend it to normalized LMS or variable step-size LMS for improved robustness. For real-time signal processing requirements, integration with MATLAB's hardware support packages enables deployment.