A full multi–dimensional characterization of the angle of arrival (AoA) has immediate applications to the efficient operation of modern wireless communication systems. In this work, we develop a compressed sensing based method to extract multi-dimensional AoA information exploiting the sparse nature of the signal received by a sensor array. The proposed solution, based on the atomic $\ell _{0}$ norm, enables accurate gridless resolution of the AoA in systems with arbitrary 3D antenna arrays. Our approach allows characterizing the maximum number of distinct sources (or scatters) that can be identified for a given number of antennas and array geometry. Both noiseless and noisy measurement scenarios are addressed, deriving and evaluating the resolvability of the AoA propagation parameters through a multi–level Toeplitz matrix $ \mathop {\mathrm {rank}}\nolimits $ –minimization problem. To facilitate the implementation of the proposed solution, we also present a least squares approach regularized by a convex relaxation of the $ \mathop {\mathrm {rank}}\nolimits $ -minimization problem and characterize its conditions for resolvability.

中文翻译：

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任意 3D 天线阵列的无网格多维到达角估计

到达角 (AoA) 的完整多维表征可立即应用于现代无线通信系统的高效运行。在这项工作中，我们开发了一种基于压缩感知的方法，利用传感器阵列接收到的信号的稀疏特性来提取多维 AoA 信息。建议的解决方案，基于原子 $\ell _{0}$ 标准，在具有任意 3D 天线阵列的系统中实现 AoA 的准确无网格分辨率。我们的方法允许表征可以为给定数量的天线和阵列几何识别的最大数量的不同源（或散射）。解决了无噪声和有噪声测量场景，通过多级 Toeplitz 矩阵推导和评估 AoA 传播参数的可分辨性 $ \mathop {\mathrm {rank}}\nolimits $ ——最小化问题。为了促进所提出的解决方案的实施，我们还提出了一种通过凸松弛正则化的最小二乘方法 $ \mathop {\mathrm {rank}}\nolimits $ - 最小化问题并描述其可解性条件。