Accuracy of Signal Source Number Estimation Using Information Theoretic Criteria and Gerschgorin Disk Theorem

In this paper, we conduct a comprehensive analysis of the accuracy rates for signal source number estimation using Information Theoretic Criteria (ITC) and Gerschgorin Disk Theorem under varying Signal-to-Noise Ratio (SNR) conditions. Our implementation typically involves covariance matrix computation from received sensor array data, followed by eigenvalue decomposition where ITC methods (like Akaike Information Criterion and Minimum Description Length) apply penalty functions to determine the optimal source number, while Gerschgorin Disk Theorem utilizes the radius properties of eigenvalue distribution clusters. Our findings demonstrate that higher SNR levels consistently yield improved estimation accuracy for both criteria. The performance improvement can be quantified through Monte Carlo simulations where we repeatedly generate signal scenarios with known source numbers and compare estimation results. For lower SNR conditions, we analyze potential estimation errors where both methods may suffer from over-estimation or under-estimation issues due to noise dominance in eigenvalue spectra. To address these challenges, we propose several enhancement methods including covariance matrix smoothing techniques, forward-backward averaging for improved eigenvalue separation, and adaptive threshold adjustments based on noise floor estimation. These improvements can be implemented through algorithmic modifications that incorporate robust statistical tests and noise variance estimation routines. Overall, our research provides valuable insights for signal source number estimation in array signal processing applications and suggests promising directions for future algorithm development, particularly focusing on hybrid approaches that combine the strengths of both criteria for enhanced robustness across diverse operational scenarios.