Minimum Variance Distortionless Response (MVDR) Beamforming Algorithm Source Code

This document provides the complete source code implementation of the Minimum Variance Distortionless Response (MVDR) beamforming algorithm along with simulation results for a 16-element sensor array. The MVDR algorithm is an advanced signal processing technique that optimizes signal reception through intelligent weight vector calculation and phase alignment. The core implementation involves computing the optimal weight vector w = R⁻¹a(θ)/(aᴴ(θ)R⁻¹a(θ)), where R represents the covariance matrix of received signals and a(θ) is the steering vector for the desired direction. This formulation ensures distortionless response in the target direction while minimizing output power from interference sources. The simulation results demonstrate the algorithm's effectiveness using a 16-element uniform linear array configuration. The beam pattern visualization clearly shows significant signal enhancement in the target direction (achieving unity gain) and substantial interference suppression in other directions (typically achieving nulls deeper than -20 dB). The implementation includes key functions for covariance matrix estimation, eigenvalue decomposition for numerical stability, and adaptive weight updates for dynamic environments. The provided source code features modular design with separate functions for array geometry setup, signal generation, covariance matrix computation, and beam pattern visualization. The implementation handles practical considerations such as diagonal loading for robust performance against estimation errors and includes comprehensive documentation for parameter tuning and performance optimization.