Tensor Reconstruction-Based Sparse Array Interpolation for 2-D DOA Estimation of Coherent Signals

This paper proposes a tensor-based two-dimensional (2-D) direction-of-arrival (DOA) estimation method for coherent sources using a 2-D coprime array. The proposed method preserves the structural characteristics of multi-dimensional signals with multiple snapshots by constructing a covariance tensor of the received signal. To address the issue of rank-deficiency of the covariance tensor due to the coherency of the impinging signals, a structural tensor reconstruction method is employed to decorrelate the covariance tensor. Additionally, the use of a coprime array results in a non-contiguous difference coarray, leading to missing measurements in the reconstructed covariance tensor. To fully leverage the aperture provided by the coprime array, the missing correlations are interpolated by solving a convex optimization problem. The canonical polyadic decomposition method is applied to the interpolated covariance tensor to detect the coherent sources. The conditions for source resolvability are also analyzed.