This paper studies the statistical characterization of ground-to-air (G2A) and reconfigurable intelligent surface (RIS)-assisted air-to-ground (A2G) communications with unmanned aerial vehicles (UAVs) in terrestrial and non-terrestrial networks under the impact of channel aging. We first model the G2A and A2G signal-to-noise ratios (SNRs) as non-central complex Gaussian quadratic random variables (RVs) and derive their exact probability density functions, offering a unique characterization for the A2G SNR as the product of two scaled non-central chi-square RVs. Moreover, we also find that, for a large number of RIS elements, the RIS-assisted A2G channel can be characterized as a single Rician fading channel. Our results reveal the presence of channel hardening in A2G communication under low UAV speeds, where we derive the maximum target spectral efficiency (SE) for a system to maintain a consistent required outage level. Meanwhile, high UAV speeds, exceeding 50 m/s, lead to a significant performance degradation, which cannot be mitigated by increasing the number of RIS elements.

翻译：本文研究了在地面与非地面网络中，受信道老化影响的无人机（UAV）地面-空中（G2A）及可重构智能表面（RIS）辅助空中-地面（A2G）通信的统计特性。我们首先将G2A和A2G信噪比（SNR）建模为非中心复高斯二次型随机变量（RV），并推导了其精确概率密度函数，其中A2G信噪比可独特地表征为两个缩放非中心卡方随机变量的乘积。此外，我们发现当RIS单元数量较大时，RIS辅助A2G信道可等效为单个莱斯衰落信道。研究结果表明，在低无人机速度下A2G通信存在信道硬化现象，此时我们推导了系统在维持恒定目标中断概率下的最大目标频谱效率（SE）。然而，当无人机速度超过50米/秒时，性能显著恶化，且无法通过增加RIS单元数量来缓解。