Real-Valued MUSIC for Efficient Direction of Arrival Estimation With Arbitrary Arrays: Mirror Suppression and Resolution Improvement

Existing real-valued subspace-based direction of arrival (DOA) estimation methods mainly face two problems: the limitations of uniform linear array (ULA) in practical applications and the presence of virtual mirrored angles. This paper exploits the properties of the virtual signal model of forward/backward average of the array covariance matrix (FBACM), in particular of the eigenvalue-eigenvector decomposition (EVD) of the real part (R-FBACM) and imaginary part (I-FBACM) of the FBACM. Our theoretical analysis proves that the subspace leakage is the cause of virtual mirrored angles. We further prove that FBACM has the same real eigenvalues as the sum of R-FBACM and I-FBACM. Based on this result, we propose a new compound real-valued MUSIC (CRV-MUSIC) algorithm to reconstruct the MUSIC pseudo-spectrum without virtual mirrored angles, which is applicable into arbitrary array configurations. Numerical analysis demonstrate that the proposed CRV-MUSIC algorithm has lower computational complexity, better resolution, and similar estimation accuracy than classical MUSIC and other existing methods.