Estimating the direction of arrival (DOA) of sources is an important problem in aerospace and vehicular communication, localization, and radar. In this article, we consider a challenging multisource DOA estimation task, where the receiving antenna array is composed of noncoherent subarrays, i.e., subarrays that observe different unknown phase shifts at every snapshot (e.g., due to waiving the demanding synchronization of local oscillators across the entire array). We formulate this problem as the reconstruction of joint sparse and low-rank matrices and solve the problem’s convex relaxation. To scale the optimization complexity with the number of snapshots better than general-purpose solvers, we design an optimization scheme, based on integrating the alternating direction method of multipliers and the accelerated proximal gradient techniques, which exploits the structure of the problem. While the DOAs can be estimated from the solution of the aforementioned convex problem, we further show how an improvement is obtained if, instead, one estimates from this solution only the subarrays’ phase shifts. This is done using another, computationally light, convex relaxation that is practically tight. Using the estimated phase shifts, “phase-corrected” observations are created and a final plain (“coherent”) DOA estimation method can be applied. Numerical experiments show the performance advantages of the proposed strategies over existing methods.

中文翻译：

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非相干子阵的到达方向估计和相位校正：凸优化方法


估计源的到达方向 (DOA) 是航空航天和车辆通信、定位和雷达中的一个重要问题。在本文中，我们考虑一个具有挑战性的多源 DOA 估计任务，其中接收天线阵列由非相干子阵列组成，即在每个快照处观察到不同未知相移的子阵列（例如，由于放弃了跨越整个系统的本地振荡器的严格同步）整个数组）。我们将该问题表述为联合稀疏低秩矩阵的重构，并解决该问题的凸松弛问题。为了比通用求解器更好地通过快照数量来衡量优化复杂性，我们设计了一种优化方案，该方案基于集成乘法器交替方向方法和加速近端梯度技术，该方案利用了问题的结构。虽然可以根据上述凸问题的解来估计 DOA，但我们进一步展示了如果从该解中仅估计子阵列的相移，则如何获得改进。这是使用另一种计算上较轻、实际上很紧的凸松弛来完成的。使用估计的相移，创建“相位校正”观测结果，并可以应用最终的简单（“相干”）DOA 估计方法。数值实验表明所提出的策略相对于现有方法具有性能优势。