Mounting compact and lightweight base stations on unmanned aerial vehicles (UAVs) is a cost-effective and flexible solution to provide seamless coverage on the existing terrestrial networks. While the coverage probability in UAV-assisted cellular networks has been widely investigated, it provides only the first-order statistic of signal-to-interference-plus-noise ratio (SINR). In this paper, to analyze high-order statistics of SINR and characterize the disparity among individual links, we provide a meta distribution (MD)-based analytical framework for UAV-assisted cellular networks, in which the probabilistic line-of-sight channel and realistic antenna pattern are taken into account for air-to-ground transmissions. To accurately characterize the interference from UAVs, we relax the widely applied uniform off-boresight angle (OBA) assumption and derive the exact distribution of OBA. Using stochastic geometry, for both steerable and vertical antenna scenarios, we obtain mathematical expressions for the moments of condition success probability, the SINR MD, and the mean local delay. Moreover, we study the asymptotic behavior of the moments as network density approaches infinity. Numerical results validate the tightness of the theoretical results and show that the uniform OBA assumption underestimates the network performance, especially in the regime of moderate altitude of UAV. We also show that when UAVs are equipped with steerable antennas, the network coverage and user fairness can be optimized simultaneously by carefully adjusting the UAV parameters.

翻译：在现有地面网络上部署轻量化紧凑型基站于无人飞行器（UAVs）上，是一种经济高效且灵活的解决方案，可实现无缝覆盖。虽然UAV辅助蜂窝网络中的覆盖概率已被广泛研究，但其仅提供信干噪比（SINR）的一阶统计特性。本文为分析SINR的高阶统计特性并刻画各链路间的差异性，提出了一种基于元分布（MD）的UAV辅助蜂窝网络分析框架，其中考虑了空地传输中的概率性视距信道和实际天线方向图。为准确表征无人机干扰，我们放宽了广泛应用的均匀离轴角（OBA）假设，并推导出OBA的精确分布。利用随机几何理论，针对可转向天线和垂直天线两种场景，我们获得了条件成功概率的矩、SINR元分布以及平均本地时延的数学表达式。此外，我们研究了网络密度趋于无穷时矩的渐近行为。数值结果验证了理论结果的紧致性，并表明均匀OBA假设会低估网络性能，尤其是在无人机中等高度区域。我们还证明，当无人机配备可转向天线时，通过精细调整无人机参数，可同时优化网络覆盖与用户公平性。