Real-valued MUSIC for efficient direction estimation with arbitrary array geometries

Most of the existing methods for direction-of-arrival (DOA) estimation are based on numerical characteristics behind the entire array output covariance matrix (AOCM). Since the AOCM is generally a complex matrix, those approaches require tremendous complex computations accordingly. This paper addresses the problem of DOA estimation with real-valued computations by considering the real part of AOCM (R-AOCM) and the imaginary part of AOCM (I-AOCM) separately. It is shown that the null space of R-AOCM and that of I-AOCM are the same subspace, which coincides with the intersection of the original noise subspace and its conjugate subspace. Using such a mathematical fact, a novel real-valued MUSIC (RV-MUSIC) estimator with a real-valued subspace decomposition on only R-ACOM (or I-AOCM) instead of the entire ACOM is derived. Compared with most state-of-the-art unitary algorithms suitable for only centro-symmetric arrays (CSAs), the proposed technique can be used with arbitrary array geometries. Unlike conventional MUSIC with exhaustive spectral search, RV-MUSIC involves a limited search over only half of the total angular field-of-view with a real-valued noise subspace, and hence reduces the complexity by 75%. Theoretical performance analysis on the mean square error (MSE) and numerical simulations demonstrate that RV-MUSIC shows a very close accuracy to the standard MUSIC.