Gerschgorin Disk Estimator (GDE) for Source Number Detection in Uniform Linear Arrays (ULA) with SNR Performance Analysis

This program utilizes the Gerschgorin Disk Estimator (GDE) method to analyze how source number detection performance in Uniform Linear Arrays (ULA) varies with Signal-to-Noise Ratio (SNR). We employ Monte-Carlo simulations to generate statistically reliable results through multiple random trials. The core algorithm involves computing the sample covariance matrix from received array signals, performing eigenvalue decomposition, and applying GDE's disk radius criterion to estimate source count. Key implementation aspects include: - SNR variation through controlled noise power addition to signal models - Array manifold matrix generation for ULA geometry - Eigenvalue sorting and GDE threshold calculation based on Gerschgorin disk radii - Statistical performance metrics calculation (detection probability, error rates) across Monte-Carlo iterations The program systematically adjusts SNR values to observe detection performance trends, providing insights into SNR's impact on source enumeration accuracy. This analysis offers practical guidance for real-world applications where optimal source number detection is critical for subsequent signal processing stages like DOA estimation.