MATLAB Code Implementation for DOA Estimation with Four Key Algorithms

This documentation presents DOA (Direction of Arrival) estimation along with four prominent algorithms: MUSIC, RootMUSIC, ESPRIT, and MVDR. Each algorithm is implemented in MATLAB with corresponding code structure and key functions. The MUSIC algorithm employs eigenvalue decomposition of the covariance matrix, where the signal subspace and noise subspace are separated. In MATLAB implementation, we typically use the `eig()` or `svd()` functions for decomposition, followed by peak detection through spectrum search to estimate source directions. The algorithm's resolution is particularly effective when sources are well-separated. RootMUSIC algorithm enhances the standard MUSIC approach by incorporating root-finding techniques. After performing eigenvalue decomposition, polynomial rooting is applied using MATLAB's `roots()` function. This method demonstrates superior performance in high Signal-to-Noise Ratio (SNR) scenarios and provides more accurate root locations compared to spectral searching. ESPRIT algorithm utilizes the rotational invariance property of signal subspaces without requiring exhaustive spectral searches. The implementation involves partitioning the sensor array into subarrays and computing the covariance matrices. Key MATLAB operations include matrix partitioning and eigenvalue decomposition to extract phase information directly from the signal subspace. MVDR (Minimum Variance Distortionless Response) algorithm, also known as Capon's method, employs minimum variance unbiased estimation principles. The MATLAB implementation focuses on calculating the inverse covariance matrix using `inv()` or pinv() functions, with constraint optimization to suppress noise while maintaining distortionless response in the look direction. This approach significantly improves DOA estimation accuracy in noisy environments. All algorithms include code segments for array configuration, covariance matrix computation, and direction estimation functions. The implementations demonstrate practical considerations for real-world applications, including array calibration and performance validation through simulation scenarios. In summary, DOA estimation and these four algorithms play crucial roles in signal processing applications, with MATLAB providing an excellent platform for algorithm development, testing, and performance comparison through systematic code implementation.