In this paper, we develop a general framework of multi-frequency sparse array to estimate the direction-of-arrival (DOA) of a significantly higher number of targets than the number of physical sensors. The multi-frequency sparse arrays are designed to offer zero lag redundancy in the rendered difference coarray so that the available degrees of freedom are fully utilized to enable high-resolution DOA estimation. A modified sensor interpolation technique is developed to accurately estimate the signal correlation matrix so that the effect of holes in the difference coarray is mitigated. The proposed technique accounts for both self-lags between signals corresponding to the same frequencies and the cross-lags between signals corresponding to different frequencies. As such, it enhances the DOA estimation performance compared to existing methods that either perform array interpolation utilizing only the self-lags or carry out group sparse reconstruction without exploiting array interpolation. Simulation results verify the offerings of the multi-frequency sparse arrays.

中文翻译：

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利用多频稀疏阵列的增强型 DOA 估计


在本文中，我们开发了一个多频稀疏阵列的通用框架，用于估计数量明显多于物理传感器数量的目标的到达方向（DOA）。多频稀疏阵列旨在在渲染的差分协同阵列中提供零滞后冗余，以便充分利用可用的自由度来实现高分辨率 DOA 估计。开发了一种改进的传感器插值技术来准确估计信号相关矩阵，从而减轻差异协同阵列中的孔洞的影响。所提出的技术考虑了对应于相同频率的信号之间的自滞后以及对应于不同频率的信号之间的交叉滞后。因此，与仅利用自滞后执行阵列插值或在不利用阵列插值的情况下执行组稀疏重建的现有方法相比，它增强了 DOA 估计性能。仿真结果验证了多频稀疏阵列的性能。