Abstract Two-dimensional (2D) direction-of-arrival (DOA) estimation with arbitrary planar sparse array has attracted more interest in massive multiple-input multiple-output application. The research on this issue recently has been advanced with the development of atomic norm technique, which provides super resolution methods for DOA estimation, when the number of snapshots is limited. In this paper, we study the problem of 2D DOA estimation from the sparse array with the sensors randomly selected from uniform rectangular array. In order to identify all azimuth and elevation angles of the incident sources jointly, the 2D atomic norm approach is proposed, which can be solved by semidefinite programming. However, the computational cost of 2D atomic norm is high. To address this issue, our work further reduces the computational complexity of the problem significantly by utilizing the atomic norm approximation method based on the concept of multiple measurement vectors. The numerical examples are provided to demonstrate the practical ability of the proposed method to reduce computational complexity and retain the estimation performance as compared to the competitors.

中文翻译：

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任意平面稀疏阵列的无网格超分辨率到达方向估计

摘要 具有任意平面稀疏阵列的二维 (2D) 到达方向 (DOA) 估计在大规模多输入多输出应用中引起了越来越多的兴趣。最近随着原子范数技术的发展，在快照数量有限的情况下，该技术为 DOA 估计提供了超分辨率方法，对此问题的研究取得了进展。在本文中，我们研究了从均匀矩形阵列中随机选择传感器的稀疏阵列的二维 DOA 估计问题。为了联合识别入射源的所有方位角和仰角，提出了二维原子范数方法，可以通过半定规划求解。然而，二维原子范数的计算成本很高。为了解决这个问题，我们的工作通过利用基于多测量向量概念的原子范数逼近方法，进一步显着降低了问题的计算复杂度。提供了数值例子来证明所提出的方法与竞争对手相比降低计算复杂度并保持估计性能的实际能力。