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In this paper, we propose a vectorized noncircular MUSIC (VNCM) algorithm based on the concept of the coarray, which can construct the difference and sum (diff–sum) coarray, for direction finding of the noncircular (NC) quasi-stationary sources. Utilizing both the NC property and the concept of the Khatri–Rao product, the proposed method can be applied to not only the ULA but also sparse arrays. In addition, we utilize the quasi-stationary characteristic instead of the spatial smoothing method to solve the coherent issue generated by the Khatri–Rao product operation so that the available degree of freedom (DOF) of the constructed virtual array will not be reduced by half. Compared with the traditional NC virtual array obtained in the NC MUSIC method, the diff–sum coarray achieves a higher number of DOFs as it comprises both the difference set and the sum set. Due to the complementarity between the difference set and the sum set for the coprime array, we choose the coprime array with multiperiod subarrays (CAMpS) as the array model and summarize the properties of the corresponding diff–sum coarray. Furthermore, we develop a diff–sum coprime array with multiperiod subarrays (DsCAMpS) whose diff–sum coarray has a higher DOF. Simulation results validate the effectiveness of the proposed method and the high DOF of the diff–sum coarray.

A unitary transformation-based algorithm is proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation of coherent signals. The problem is solved by reorganizing the covariance matrix into a block Hankel one for decorrelation first and then reconstructing a new matrix to facilitate the unitary transformation. By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly. In addition, a fast and computationally attractive realization of the 2-D unitary transformation is given by making a Kronecker product of the 1-D matrices. Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry. The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT)-Like method and the forward-backward averaging, which can decorrelate the impinging signals more thoroughly. Simulation results and computational order analysis are presented to verify the validity and effectiveness of the proposed algorithm.

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