AI 中文总结
该研究提出宽带大阵列处理的角度成像方法，引入覆盖准则推导非均匀稀疏阵列设计，可在全视场下用远少于角度像素的物理天线实现稳定恢复，经仿真验证其设计能支持十倍以上角度像素的恢复。
AI 中文摘要
本文表明，宽带大阵列处理能够用少得多的天线单元恢复大量角度像素。宽带信号的关键优势在于不同频率会诱导出不同的虚拟阵列，这些虚拟阵列的并集形成了有效虚拟单元数量大幅增加的虚拟阵列。因此，稀疏物理阵列能支持比物理天线多得多的空间采样。受此能力驱动，我们研究在全视场[-90°, 90°)范围内的角度响应恢复，该范围按改进的角度分辨率离散化，我们将这种感知机制称为角度成像。然而，由此产生的虚拟阵列本质上是不规则、聚类的，无法自动保证稳定恢复。为应对这一挑战，我们引入了一种覆盖准则，用于估计可稳定恢复的角度像素数量，无需对候选图像维度进行计算密集型的基于奇异值的条件测试。对于满足该准则的系统，我们从理论上建立了确定性条件数边界，以表征稳定的角度成像。基于该准则，我们推导了非均匀稀疏阵列设计，该设计在维持全视场恢复能力的同时最小化物理天线数量。仿真结果表明，所提出的准则为稳定系统设计提供了实用指导，且由此得到的稀疏阵列能够恢复比物理天线多得多的角度像素，代表性设计支持的角度像素数量是物理天线的十倍以上。
英文摘要
This paper shows that wideband large-array processing can recover a large number of angle pixels with far fewer antenna elements. The key advantage of wideband signaling is that different frequencies induce different virtual arrays, whose union forms a virtual array with a substantially increased number of effective virtual elements. Thus, a sparse physical array can support far more spatial samples than physical antennas. Motivated by this capability, we study the recovery of angular responses across the full field of view $[-90^\circ, 90^\circ)$, discretized according to the improved angular resolution, and refer to this sensing regime as angle imaging. However, the resulting virtual array is inherently irregular, clustered, and does not automatically guarantee stable recovery. To address this challenge, we introduce a coverage criterion that estimates the number of stably recoverable angle pixels, without computationally intensive singular-value-based conditioning tests over candidate image dimensions. For systems satisfying this criterion, we theoretically establish deterministic condition-number bounds that characterize stable angle imaging. Building on this criterion, we derive non-uniform sparse array designs that minimize the number of physical antennas while maintaining recovery over the full field of view. Simulation results show that the proposed criterion provides practical guidance for stable system design, and that the resulting sparse arrays can recover substantially more angle pixels than the number of physical antennas, with representative designs supporting over ten times as many angle pixels as physical antennas.
CommentsSubmitted to IEEE Transactions on Signal Processing. 13 pages, 9 figures
