Real-valued root-MUSIC algorithm with forward/backward averaging

The root-multiple signal classification (Root-MUSIC) algorithm is one of the most important techniques for direction of arrival (DOA) estimation. This paper proposes a novel real-valued Root-MUSIC DOA estimation algorithm. Compared with the conventional complex algorithms, the proposed algorithm reduces the computational complexity in the eigen-analysis stage of Root-MUSIC due to exploiting the eigenvalue decomposition (EVD) of a real-valued covariance matrix. By using Forward/Backward (FB) averaging, the FB covariance matrix of the received signal data is used instead of the conventional (forward-only) covariance matrix in the proposed algorithm. Then the FB covariance matrix is converted into a real-valued one further via utilizing the properties of the centro-Hermitian matrix. Hence, the complex EVD of conventional covariance matrix is transformed into the real-valued EVD of the symmetric real-valued covariance matrix, and it will reduce the computation cost by a factor of four. Since the proposed algorithm is an improved Root-MUSIC-based algorithm, it can greatly accelerate DOA estimation without tedious spectral peaks searching process compared with the representative MUSIC algorithm. Meanwhile, because the EVD of the covariance matrix is transformed into the real domain, the computational complexity of the algorithm can be greatly reduced without losing the performance of the algorithm compared with the Root-MUSIC algorithm. In addition, the theoretical computational amount of the proposed algorithm and Root-MUSIC algorithms is discussed. The Cramer-Rao bound (CRB) of DOA estimation is derived as well. The simulation results confirm that the proposed algorithm achieves superior precision and accuracy in DOA estimation, and has lower computational amount compared with Root-MUSIC algorithm.