This paper presents a method to estimate the direction of arrival (DOA) of multiple sources received by a uniform linear array (ULA) with a reduced number of radio-frequency (RF) chains. The receiving array relies on antenna switching so that at every time instant only the signals received by a randomly selected subset of antennas are downconverted to baseband and sampled. Low-rank matrix completion (MC) techniques are then used to reconstruct the missing entries of the signal data matrix to keep the angular resolution of the original large-scale array. The proposed MC algorithm exploits not only the low-rank structure of the signal subspace, but also the shift-invariance property of ULAs, which results in a better estimation of the signal subspace. Further, the effect of MC on DOA estimation is discussed under the perturbation theory framework. The simulation results suggest that the proposed method provides accurate DOA estimates even in the small-sample regime with a significant reduction in the number of RF chains required for a given spatial resolution.

本文提出了一种方法，该方法可以通过减少了射频（RF）链数量的均匀线性阵列（ULA）来估计多个源的到达方向（DOA）。接收阵列依赖于天线切换，因此在每个时间点，只有随机选择的天线子集接收到的信号才会下变频到基带并进行采样。然后，使用低秩矩阵完成（MC）技术来重建信号数据矩阵的缺失条目，以保持原始大规模数组的角分辨率。所提出的MC算法不仅利用信号子空间的低秩结构，而且利用ULA的移位不变性，从而更好地估计了信号子空间。此外，在摄动理论框架下讨论了MC对DOA估计的影响。