Unitary Root MUSIC and Unitary MUSIC with Real-Valued Rank Revealing Triangular Factorization

This paper presents two methods to estimate the two dimensional (2-D) direction of arrival (DOA) for coherent and non-coherent sources. The proposed methods have many advantages over existing schemes. First, they construct the data from a single snapshot in a Toeplitz form, whose rank is directly related to the DOA of signals, whether the signals are coherent or not; hence, the algorithm does not require any forward/backward spatial smoothing. Second, the two proposed methods can rapidly estimate the 2-D DOAs of incident signals without requiring singular value decomposition (SVD) or eigenvalue decomposition (EVD), even in the case of coherent signals and a single snapshot. The two methods are: (1) orthogonal projection real-valued rank revealing QR factorization (OPRRRQR), and (2) orthogonal projection real-valued rank revealing LU factorization (OP-RRRLU). The proposed methods reduce computational complexity and the cost at least by a factor of four by applying a unitary transformation, to the complex Toeplitz form to real data without forming the covariance matrix. The proposed algorithms employ the unitary root MUSIC and unitary MUSIC using cross array configuration to estimate the 2-D DOA azimuth and elevation angles without using the extensive 2-D MUSIC search. Hence, they can reduce the computational load and cost significantly and can be applied in real-time radar/sonar and commercial wireless systems. The simulation results show that the proposed algorithms can efficiently estimate the 2-D DOAs from different sources.