Real-valued root-MUSIC for DOA estimation with reduced-dimension EVD/SVD computation

A novel real-valued formulation of the popular root multiple signal classification (root-MUSIC) direction of arrival (DOA) estimation technique with substantially reduced computational complexity is developed. The proposed real-valued root-MUSIC (RV-root-MUSIC) algorithm reduces the computational burden mainly in three aspects. First, it exploits the eigenvalue decomposition or the singular value decomposition (EVD/SVD) of a real-valued covariance matrix to extract a real-valued noise subspace, which reduces the complexity by a factor about four as compared to root-MUSIC. Next, based on the bisymmetric or the anti-bisymmetric structure of the real-valued covariance matrix, the real-valued EVD/SVD in RV-root-MUSIC is optimized to be equivalently performed on two sub-matrices with reduced dimensions of about half sizes, which further reduces the complexity by another factor about four as compared to most state-of-the-art real-valued estimators including unitary root-MUSIC (U-root-MUSIC). Finally, the eigenvectors and the singular vectors of those sub-matrices are found of centrosymmetrical or anti-centrosymmetrical structures while the roots of RV-root-MUSIC are proven to appear in conjugate pairs with the form a+jb,a−jb, which also allows fast coefficient computation and real-valued rooting using Bairstow's method. Numerical simulations illustrate that with significantly reduced complexity, the proposed technique is able to provide good root mean square errors (RMSEs) close to the Cramér-Rao Lower Bound (CRLB).