In this work we consider a mmWave pulse radar and study the problem of super-resolving the echoes produced by multiple prospective targets. We derive a novel signal model wherein an observed echo is represented in term of a conveniently-structured steering vector and its associated multi-dimensional frequency vector related to the target location; we consider a five-dimensional measurement space, including the delay and Doppler dimensions and the Cartesian axes of a 3-dimensional array. Upon exploiting the atomic norm to harness sparsity in the continuous parameter domain, the unknown frequency vectors and the corresponding atoms are recovered by resorting to the Vandermonde decomposition of a canonical multi-level Toepliz matrix. Conditions for unique resolvability in the noiseless case are provided and discussed; also, a low-complexity formulation of the recovery problem is proposed, wherein the available data samples are conveniently parsed into multiple smaller groups described by the same set of atoms. Finally, numerical results are provided to validate the theoretical analysis and to verify the effect of the additive noise in practical operating scenarios.

中文翻译：

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汽车脉冲雷达的超分辨率

在这项工作中，我们考虑毫米波脉冲雷达并研究超分辨多个预期目标产生的回波的问题。我们推导出一种新的信号模型，其中观察到的回波用结构方便的导向向量及其与目标位置相关的相关多维频率向量表示；我们考虑一个五维测量空间，包括延迟和多普勒维度以及 3 维阵列的笛卡尔轴。在利用原子范数来控制连续参数域中的稀疏性后，通过对规范的多级 Toepliz 矩阵进行 Vandermonde 分解来恢复未知频率向量和相应的原子。提供并讨论了无噪声情况下唯一可分辨性的条件；还，提出了恢复问题的低复杂度公式，其中可用数据样本方便地解析为由同一组原子描述的多个较小的组。最后，提供数值结果以验证理论分析并验证加性噪声在实际操作场景中的影响。