Coarray Tensor Direction-of-Arrival Estimation

Augmented coarrays can be derived from spatially undersampled signals of sparse arrays for underdetermined direction-of-arrival (DOA) estimation. With the extended dimension of sparse arrays, the sampled signals can be modeled as sub-Nyquist tensors, thereby enabling coarray tensor processing to enhance the estimation performance. The existing methods, however, are not applicable to generalized multi-dimensional sparse arrays, such as sparse planar array and sparse cubic array, and have not fully exploited the achievable source identifiability. In this paper, we propose a coarray tensor DOA estimation algorithm for multi-dimensional structured sparse arrays and investigate an optimal coarray tensor structure for source identifiability enhancement. Specifically, the cross-correlation tensor between sub-Nyquist tensor signals is calculated to derive a coarray tensor. Based on the uniqueness condition for coarray tensor decomposition, the achievable source identifiability is analysed. Furthermore, to enhance the source identifiability, a dimension increment approach is proposed to embed shifting information in the coarray tensor. The shifting-embedded coarray tensor is subsequently reshaped to optimize the source identifiability. The resulting maximum number of degrees-of-freedom is theoretically proved to exceed the number of physical sensors. Hence, the optimally reshaped coarray tensor can be decomposed for underdetermined DOA estimation with closed-form solutions. Simulation results demonstrate the effectiveness of the proposed algorithm in both underdetermined and overdetermined cases.