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.

中文翻译：

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SubTTD：通过亚奈奎斯特张量训练分解的 DOA 估计

用于稀疏阵列的传统张量到达方向 (DOA) 估计方法将规范多元分解 (CPD) 应用于高阶协阵列协方差张量以检索角度信息。然而，由于基于 CPD 的高阶张量算法收敛速度低，这些方法的计算成本很高。为了解决这个问题，针对三维（3-D）稀疏阵列提出了一种基于亚奈奎斯特张量序列分解（SubTTD）的DOA估计方法，其中从亚奈奎斯特张量统计中导出了一个增强的虚拟阵列。为了降低处理 6-D 协阵列协方差张量的计算复杂度，所提出的 SubTTD 模型有效地将其分解为一系列头矩阵、3-D 核心张量和尾矩阵。基于此，设计了核心张量分解和头部矩阵的基变变换，以检索用于 DOA 估计的 coarray 协方差张量的规范多元因子。对所提方法的计算效率进行了理论分析，并通过仿真验证了其有效性。