DOA Estimation Algorithms for Linear Arrays: CBF, Capon, MUSIC, ESPRIT, and ML Implementation

In this article, we explore MATLAB implementations for Direction of Arrival (DOA) estimation using linear arrays. We present four fundamental algorithms: Conventional Beamforming (CBF), Capon's minimum variance method, MUSIC (Multiple Signal Classification), and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques). Each algorithm is accompanied by detailed MATLAB code that demonstrates practical implementation aspects, including array signal processing techniques, covariance matrix computation, eigenvalue decomposition, and spectral estimation. The CBF method implements classical delay-and-sum beamforming, while Capon's algorithm provides adaptive beamforming with optimal SNR characteristics. MUSIC leverages eigenvalue decomposition to achieve super-resolution capabilities, and ESPRIT utilizes rotational invariance properties for computational efficiency. The code includes functions for array manifold calculation, signal subspace extraction, and peak detection algorithms for accurate angle estimation. These implementations enable researchers to experimentally validate DOA estimation principles, compare algorithm performance under various SNR conditions, and gain deeper insights into practical array signal processing applications.