Signal and Information Processing - MATLAB Algorithms for Array Signal Processing DOA Estimation

DOA (Direction of Arrival) estimation in array signal processing is a critical technology in wireless communications, radar systems, and acoustic applications. This article presents MATLAB implementation approaches for two classical algorithms - Root-MUSIC and MVDR, helping readers understand their core principles and application scenarios with enhanced code-related descriptions.

Root-MUSIC Algorithm Root-MUSIC is an improvement over the conventional MUSIC algorithm, replacing spectral peak search with polynomial rooting to significantly reduce computational complexity. The core implementation steps include: Covariance Matrix Calculation: Construct spatial covariance matrix using array received data through MATLAB's cov() function or manual matrix multiplication. Subspace Decomposition: Perform eigenvalue decomposition using eig() or svd() functions to separate signal and noise subspaces. Polynomial Construction and Rooting: Transform noise subspace projection into polynomial equations, then extract roots near the unit circle using roots() function, where the angles correspond to DOA estimates.

The algorithm's advantage lies in eliminating global spectrum scanning, making it particularly suitable for real-time applications requiring high computational efficiency.

MVDR Algorithm (Minimum Variance Distortionless Response) MVDR is a beamforming-based DOA estimation method that minimizes output power (i.e., suppresses interference) while constraining gain to unity in specific directions. Key implementation aspects include: Weight Vector Calculation: Compute optimal weights using covariance matrix inversion (inv() or pinv() for numerical stability) and steering vectors. Spatial Spectrum Generation: Scan different directions by applying weight vectors to calculate output power patterns. Peak Detection: Identify peak positions in the spatial spectrum corresponding to signal directions using findpeaks() or custom peak detection algorithms.

MVDR performs excellently in low SNR environments but requires substantial computation, with particular attention needed for numerical stability in matrix inversion operations.

Implementation Recommendations Root-MUSIC is suitable for scenarios requiring multiple snapshots and high precision estimates. MVDR is more appropriate for weak signal detection in strong interference environments. Practical implementation should consider preprocessing requirements like array calibration and source number estimation, while techniques like spatial smoothing can enhance algorithm robustness against coherent sources.