In this paper, we investigate the uplink signal detection approaches in the cell-free massive MIMO systems with unmanned aerial vehicles (UAVs) serving as aerial access points (APs). The ground users are equipped with multiple antennas and the ground-to-air propagation channels are subject to correlated Rician fading. To overcome huge signaling overhead in the fully-centralized detection, we propose a two-layer distributed uplink detection scheme, where the uplink signals are first detected in the AP-UAVs by using the minimum mean-squared error (MMSE) detector depending on local channel state information (CSI), and then collected and weighted combined at the CPU-UAV to obtain the refined detection. By using the operator-valued free probability theory, the asymptotic expressions of the combining weights are obtained, which only depend on the statistical CSI and show excellent accuracy. Based on the proposed distributed scheme, we further investigate the impacts of different distributed deployments on the achieved spectral efficiency (SE). Numerical results show that in urban and dense urban environments, it is more beneficial to deploy more AP-UAVs to achieve higher SE. On the other hand, in suburban environment, an optimal ratio between the number of deployed UAVs and the number of antennas per UAV exists to maximize the SE.

翻译：本文研究了以无人机作为空中接入点的无小区大规模MIMO系统中的上行信号检测方法。地面用户配备多根天线，地空传播信道受相关莱斯衰落影响。为克服全集中检测中巨大的信令开销，我们提出了一种两层分布式上行检测方案：首先，AP-UAV基于局部信道状态信息，采用最小均方误差检测器对上行信号进行初步检测；随后，CPU-UAV对这些检测结果进行收集与加权合并，以获得精化检测。通过运用算子值自由概率理论，推导出仅依赖于统计信道状态信息的合并权值渐近表达式，该表达式具有极高的准确性。基于所提分布式方案，我们进一步研究了不同分布式部署对频谱效率的影响。数值结果表明，在城市和密集城市环境中，部署更多AP-UAV有利于获得更高的频谱效率；而在郊区环境中，存在使频谱效率最大化的部署无人机数量与单架无人机天线数之间的最优比例。