We address the two-dimensional direction-of-arrival (2-D DOA) estimation problem for L-shaped ULA by developing an algorithm represented by the convex optimal method. In this paper, the generalized conjugate symmetry property of L-shaped ULA is fully developed to increase not only virtual array aperture but virtual snapshots, which not only increases the maximum resolvable sources but yields better 2-D DOA estimation performance. Specifically, we first formulate the cost function as a quadratically constrained complex quadratic programming (QCCQP) problem via the subspace theory. The QCCQP problem can then be relaxed to a series of semidefinite programming (SDP) problems, which can be solved via the CVX solvers in polynomial time complexity per iteration. To avoid complex 2-D global iterations during the implementation of SDP problems, the PM-ESPRIT-like method is first applied to estimate azimuths, based on which, the proposed method can then be transformed to 1-D local iterations with no additional angles pairings needed. Furthermore, the superb performance of the proposed method still holds whether the spatial angles are very close or separate apart. Performances evaluations are confirmed based on multiple simulations examples and some criteria.

中文翻译：

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基于凸优化的二维 DOA 估计，具有增强的虚拟孔径和 L 形阵列的虚拟快照扩展

我们通过开发由凸优化方法表示的算法来解决 L 形 ULA 的二维到达方向 (2-D DOA) 估计问题。在本文中，L 形 ULA 的广义共轭对称性得到了充分的发展，不仅增加了虚拟阵列孔径，还增加了虚拟快照，不仅增加了最大可分辨源，而且产生了更好的二维 DOA 估计性能。具体来说，我们首先通过子空间理论将成本函数表述为二次约束复二次规划 (QCCQP) 问题。然后可以将 QCCQP 问题简化为一系列半定规划 (SDP) 问题，这些问题可以通过 CVX 求解器以每次迭代的多项式时间复杂度求解。为了在 SDP 问题的实现过程中避免复杂的 2-D 全局迭代，类 PM-ESPRIT 方法首先应用于估计方位角，在此基础上，所提出的方法可以转换为一维局部迭代，而无需额外的角度配对。此外，无论空间角度非常接近还是分开，所提出方法的卓越性能仍然适用。基于多个模拟示例和一些标准来确认性能评估。