This paper presents an efficient gridless sparse reconstruction algorithm for the coprime planar array in two-dimensional (2-D) direction-of-arrival (DOA) estimation problem. According to the equivalent second-order statistic signals derived from the covariance matrix of the coprime planar array, we construct a virtual 2-D difference co-array extended from the coprime line arrays along two directions. The virtual array has a double-sized array aperture leading to an increased number of degree-of-freedoms (DOFs). To address the discontinuity of the virtual planar array, and to reduce the computation complexity for the increased array size, decoupled atomic norm minimization approach is investigated to interpolate the missing sensors without discarding any virtual sensors. The problem of decoupled atomic norm minimization can be solved by semidefinite programming with significantly lower computational cost. Besides, the ratio of the number of missing sensors to full sensors in the interpolated virtual uniform array is smaller than that of the physical coprime array, which further improves the recovery accuracy of decoupled atomic norm minimization algorithm. The numerical examples are provided to demonstrate the practical ability of the proposed method in terms of DOF, computational complexity, and DOA estimation error.

中文翻译：

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基于解耦原子范数最小化的互质阵列高效无网格二维波达方向估计

本文针对二维 (2-D) 到达方向 (DOA) 估计问题中的互素平面阵列提出了一种有效的无网格稀疏重建算法。根据互素平面阵列协方差矩阵导出的等效二阶统计信号，我们构造了一个虚拟二维差分协阵列，从互素平面阵列沿两个方向扩展。虚拟阵列具有双倍尺寸的阵列孔径，从而增加了自由度 (DOF) 的数量。为了解决虚拟平面阵列的不连续性，并降低阵列尺寸增加的计算复杂度，研究了解耦原子范数最小化方法，以在不丢弃任何虚拟传感器的情况下插入丢失的传感器。解耦原子范数最小化问题可以通过半定规划来解决，并且计算成本显着降低。此外，插值虚拟均匀阵列中缺失传感器数量与完整传感器数量之比小于物理互质阵列，进一步提高了解耦原子范数最小化算法的恢复精度。数值例子证明了所提出的方法在自由度、计算复杂度和自由度估计误差方面的实际能力。进一步提高了解耦原子范数最小化算法的恢复精度。数值例子证明了所提出方法在自由度、计算复杂度和自由度估计误差方面的实际能力。进一步提高了解耦原子范数最小化算法的恢复精度。数值例子证明了所提出的方法在自由度、计算复杂度和自由度估计误差方面的实际能力。