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

DOA estimation with linear arrays is a classical problem in array signal processing, primarily used to determine the direction of arrival of multiple signal sources in space. The following is a comparative analysis of fundamental principles of several commonly used algorithms: Conventional Beamforming (CBF) The most basic spatial spectrum estimation method that mechanically scans all directions to find power peaks. Its advantage lies in computational simplicity, but resolution is limited by the Rayleigh limit, making it unable to distinguish between closely spaced signal sources. In MATLAB implementation, this typically involves calculating array steering vectors for different angles and performing power summation. Capon Beamforming An improved adaptive beamforming method that optimizes the beam pattern by minimizing noise and interference power. Compared to CBF, it offers higher resolution but is more sensitive to signal-to-noise ratio and requires heavier computation. Code implementation often involves inverse covariance matrix calculations and adaptive weight vector optimization. MUSIC Algorithm A high-resolution algorithm based on signal subspace decomposition that constructs spatial spectrum using the orthogonality between noise subspace and array manifold. Theoretically capable of achieving super-resolution estimation, it requires accurate covariance matrix estimation and source number detection. MATLAB implementation typically involves eigenvalue decomposition of the covariance matrix and peak search in the MUSIC spectrum. ESPRIT Algorithm Utilizes the translational invariance structure of arrays to achieve parameter estimation through rotational subspace matching. It requires less computation than MUSIC and avoids spectrum peak search, but has specific requirements for array geometry. Implementation commonly involves signal subspace rotation and parameter extraction through eigenvalue decomposition. Maximum Likelihood (ML) Algorithm An optimal statistical estimation method that solves parameters by maximizing the likelihood function. Maintains good performance under low SNR conditions and with small snapshot numbers, but has the highest computational complexity. Implementation often requires iterative optimization algorithms and multidimensional parameter search. These algorithms typically involve the following key steps in MATLAB implementation: array manifold matrix construction, received data covariance matrix estimation, eigenvalue decomposition (for subspace-based methods), and spatial spectrum function calculation. Practical applications require selecting appropriate algorithms based on array configuration, signal environment, and real-time requirements.