Source Number Estimation using Information Theory Methods - MATLAB Source Code

This document provides a comprehensive discussion of spatial spectrum estimation principles and algorithms, with particular emphasis on information theory-based methods for estimating the number of signal sources. The implementation includes detailed MATLAB source code demonstrating these techniques. Spatial spectrum estimation represents a fundamental challenge in signal processing with widespread applications in wireless communications, radar systems, and sonar technology. The primary objective of this technique involves estimating directions of arrival for multiple signal sources using measurements collected from sensor arrays. A critical aspect of spatial spectrum estimation involves accurately determining the number of signal sources present. Traditional statistical approaches often demand substantial computational resources and require strong assumptions about underlying data distributions. Information theory methods offer a more flexible, data-driven alternative that adapts better to real-world scenarios. The provided MATLAB implementation demonstrates an information-theoretic approach using the Minimum Description Length (MDL) criterion, which optimally balances model complexity against data fitting accuracy. The code structure includes: 1. Data preprocessing functions for sensor array signal handling 2. Covariance matrix computation modules for spatial correlation analysis 3. Eigenvalue decomposition routines for signal subspace identification 4. MDL criterion implementation with model order selection algorithms 5. Visualization tools for result interpretation and validation Key algorithmic components include: - Automated threshold detection for source number determination - Efficient matrix operations leveraging MATLAB's built-in linear algebra capabilities - Configurable parameters for different array geometries and signal conditions - Comprehensive error handling and validation checks The implementation features extensive code comments and modular design, allowing straightforward adaptation to various sensor configurations and application requirements. Each function includes detailed documentation covering input parameters, output specifications, and algorithmic methodology. This resource offers both theoretical foundation and practical implementation guidance, enabling researchers and engineers to apply advanced spatial spectrum estimation techniques to diverse signal processing challenges. The codebase emphasizes computational efficiency while maintaining mathematical rigor, suitable for both educational purposes and production deployments.