Multiple Matrix Reconstruction for Two-Dimensional Direction Estimation of Mixed Signals Without Eigen Decomposition

In this paper, a novel method based on multiple matrix reconstruction without eigen decomposition is proposed for solving the problem of two-dimensional (2-D) direction-of-arrival (DOA) estimation of mixed signals impinging on a planar array composing of two parallel uniform linear arrays (ULAs). Utilizing the correlation information between the array elements of two ULAs, four novel virtual covariance matrices are achieved for avoiding the interference from additive Gaussian white noise (AWGN). To eliminate the coherence between incident signals and improve the estimation accuracy, these four matrices and their backward versions are reassembled to obtain a new joint matrix. The new joint matrix is constructed again, so that we can calculate the suitable propagator for estimating the one-dimensional (1-D) angle only by a series of linear operations. Apart from this, parting the same joint matrix, we also can directly obtain a new propagator and extend it into a virtual orthogonal space, and further estimate the 1-D angle by the subspace-based method in this paper. After we obtain the 1-D estimation outcome, a novel union matrix is constructed for the estimation of 2-D angle with correct pair-matching. We derive the Cramer-Rao bound (CRB) under the signal model assumptions and array conditions in this paper. The performance is demonstrated, and the simulation results indicate that the proposed method can distinguish 2-D mixed signals with efficiency computational complexity and high estimation accuracy.