MATLAB Simulation of LMS Adaptive Algorithm for Minimum Variance Distortionless Response Beamformer

This document discusses the MATLAB simulation of the Least Mean Squares (LMS) adaptive algorithm applied to a Minimum Variance Distortionless Response (MVDR) beamformer, specifically examining its amplitude response across different steering angles. The LMS adaptive algorithm is a widely used signal processing technique that automatically adjusts filter parameters to minimize the mean square error between desired and actual outputs. In MATLAB implementation, we typically initialize parameters such as step size (mu), filter weights, and input signal characteristics before implementing the core LMS update equation: w(n+1) = w(n) + μ*e(n)*x(n), where w represents weight vectors, e denotes error signals, and x is the input vector. The simulation involves generating steering vectors for various angles, applying the MVDR constraint to maintain distortionless response in the desired direction, and visualizing amplitude response patterns through polar plots or array response functions. By analyzing these simulation results, we can evaluate the algorithm's performance in different scenarios, including its null-steering capability against interference and mainlobe preservation toward target directions. This experimental approach provides valuable insights into the practical implementation of LMS adaptive filtering and its effectiveness in beamforming applications.