Real-Valued MUSIC Algorithm for DOA Spectrum Estimation

The real-valued MUSIC algorithm is an efficient enhancement for Direction of Arrival (DOA) estimation that transforms the traditional complex-valued covariance matrix into the real domain through mathematical operations. This transformation preserves all directional signal information while significantly reducing computational complexity - the eigenvalue decomposition computation is reduced to approximately one-quarter of the original complex-valued processing.

The algorithm's core advantage lies in its ability to effectively resolve coherent signal sources. Traditional MUSIC experiences severe performance degradation when signals are highly correlated, whereas the real-valued transformation maintains orthogonality between noise and signal subspaces through specific matrix reconstruction strategies, enabling stable detection of coherent sources. In practical implementations, special attention must be paid to the unique handling of array manifolds during transformation and proper determination of signal subspace dimensionality after real-domain eigenvalue decomposition.

Compared to complex-domain algorithms, the real-valued version maintains similar estimation accuracy while being more suitable for real-time engineering systems, particularly advantageous in scenarios with limited computational resources such as large-scale arrays or mobile platforms.

From a coding perspective, implementation typically involves: converting the complex covariance matrix to real form using unitary transformation matrices, performing real-valued eigenvalue decomposition using optimized linear algebra libraries, and applying subspace separation techniques with threshold-based signal dimension detection. Key functions would include matrix transformation routines, efficient eigenvalue solvers, and noise subspace identification algorithms.