Two-Dimensional DOA Estimation for Three-Parallel Nested Subarrays via Sparse Representation.

Nested arrays are considered attractive due to their hole-free performance, and have the ability to resolve sources with physical sensors. Inspired by nested arrays, two kinds of three-parallel nested subarrays (TPNAs), which are composed of three parallel sparse linear subarrays with different inter-element spacings, are proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation in this paper. We construct two cross-correlation matrices and combine them as one augmented matrix in the first step. Then, by vectorizing the augmented matrix, a hole-free difference coarray with larger degrees of freedom (DOFs) is achieved. Meanwhile, sparse representation and the total least squares technique are presented to transform the problem of 2-D DOA searching into 1-D searching. Accordingly, we can obtain the paired 2-D angles automatically and improve the 2-D DOA estimation performance. In addition, we derive closed form expressions of sensor positions, as well as number of sensors for different subarrays of two kinds of TPNA to maximize the DOFs. In the end, the simulation results verify the superiority of the proposed TPNAs and 2-D DOA estimation method.

嵌套阵列因其无孔洞性能而被认为具有吸引力，并且能够用物理传感器分辨信源。受嵌套阵列的启发，本文提出了两种三平行嵌套子阵列（TPNA），它们由三个具有不同阵元间距的平行稀疏线性子阵列组成，用于二维到达方向（DOA）估计。我们首先构建两个互相关矩阵，并将它们组合为一个增广矩阵。然后，通过对增广矩阵进行向量化，得到一个具有更大自由度（DOF）的无孔洞差分共阵列。同时，提出了稀疏表示和总体最小二乘法，将二维DOA搜索问题转化为一维搜索。因此，我们可以自动获得成对的二维角度，并提高二维DOA估计性能。此外，我们推导了两种TPNA的不同子阵列的传感器位置以及传感器数量的闭式表达式，以最大化自由度。最后，仿真结果验证了所提出的TPNA和二维DOA估计方法的优越性。