MATLAB Implementation of DOA Estimation Algorithms

Direction of Arrival (DOA) estimation is a fundamental problem in array signal processing, primarily used to determine the arrival direction of signal sources. Below are implementation approaches for several classical DOA estimation algorithms: MUSIC Algorithm The Multiple Signal Classification (MUSIC) algorithm leverages the orthogonality between signal and noise subspaces. Implementation involves computing the covariance matrix of received data, performing eigenvalue decomposition to separate signal and noise subspaces, then constructing a spatial spectrum function. The peak search in this spectrum identifies signal source directions. In MATLAB implementation, key functions include cov() for covariance matrix calculation and eig() for eigenvalue decomposition. MUSIC performs excellently under high SNR conditions with uncorrelated signals but requires significant computational resources. RootMUSIC Algorithm As an enhanced version of MUSIC, RootMUSIC transforms spectrum peak search into polynomial root-finding. The algorithm directly solves roots of the Root-MUSIC polynomial, eliminating exhaustive search in conventional MUSIC. MATLAB implementation can utilize root() function for polynomial solutions and poly() for polynomial construction. This method offers higher computational efficiency and is particularly suitable for Uniform Linear Arrays (ULA). ESPRIT Algorithm Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) utilizes array translational invariance to estimate DOA directly through rotational properties of signal subspaces. The implementation avoids spectrum search entirely, resulting in lower computational complexity. In code implementation, array geometry must satisfy strict requirements (e.g., twin parallel subarrays). Key operations involve matrix partitioning and eigenvalue decomposition of rotational operators. MVDR Algorithm Minimum Variance Distortionless Response (MVDR) is a beamforming-based DOA estimation approach. It designs optimal weight vectors to maintain unity gain in target directions while minimizing output power (interference suppression). MATLAB implementation typically uses adaptive beamforming techniques with constraints. MVDR demonstrates stable performance with limited snapshots but generally has lower resolution compared to subspace-based algorithms. Implementation Considerations: - Array manifold matrix construction must match actual array geometry - Covariance matrix estimation typically employs sample averaging; regularization is needed with insufficient snapshots - RootMUSIC and ESPRIT are sensitive to array errors, requiring careful array response calibration - Code implementation should include proper matrix conditioning checks and snapshot validation routines