SubTTD: DOA Estimation via Sub-Nyquist Tensor Train Decomposition

Conventional tensor direction-of-arrival (DOA) estimation methods for sparse arrays apply canonical polyadic decomposition (CPD) to the high-order coarray covariance tensor for retrieving angle information. However, due to the low convergence rate of CPD-based algorithms for high-order tensors, these methods suffer from a high computation cost. To address this issue, a sub-Nyquist tensor train decomposition (SubTTD)-based DOA estimation method is proposed for a three-dimensional (3-D) sparse array, where an augmented virtual array is derived from the sub-Nyquist tensor statistics. To reduce computational complexity of processing the 6-D coarray covariance tensor, the proposed SubTTD model efficiently decomposes it into a train of head matrix, 3-D core tensors, and tail matrix. Based on that, a core tensor decomposition and a change-of-basis transformation for the head matrix are designed to retrieve canonical polyadic factors of the coarray covariance tensor for DOA estimation. The computational efficiency of the proposed method is theoretically analyzed, and its effectiveness is verified via simulations.