This paper studies the statistical characterization of ground-to-air (G2A) and reconfigurable intelligent surface (RIS)-assisted air-to-ground (A2G) communications in RIS-assisted UAV networks under the impact of channel aging. A comprehensive channel model is presented, which incorporates the time-varying fading, three-dimensional (3D) mobility, Doppler shifts, and the effects of channel aging on array antenna structures. We provide analytical expressions for the G2A signal-to-noise ratio (SNR) probability density function (PDF) and cumulative distribution function (CDF), demonstrating that the G2A SNR follows a mixture of noncentral $\chi^2$ distributions. The A2G communication is characterized under RIS arbitrary phase-shift configurations, showing that the A2G SNR can be represented as the product of two correlated noncentral $\chi^2$ random variables (RVs). Additionally, we present the PDF and the CDF of the product of two independently distributed noncentral $\chi^2$ RVs, which accurately characterize the A2G SNR's distribution. Our paper confirms the effectiveness of RISs in mitigating channel aging effects within the coherence time. Finally, we propose an adaptive spectral efficiency method that ensures consistent system performance and satisfactory outage levels when the UAV and the ground user equipments are in motion.

翻译：本文研究了在信道老化影响下，可重构智能表面（RIS）辅助的无人机网络中地面到空中（G2A）通信以及RIS辅助的空中到地面（A2G）通信的统计特性。我们提出了一个综合的信道模型，该模型包含了时变衰落、三维（3D）移动性、多普勒频移以及信道老化对阵列天线结构的影响。我们推导了G2A信噪比（SNR）的概率密度函数（PDF）和累积分布函数（CDF）的解析表达式，证明了G2A SNR服从非中心$\chi^2$分布的混合分布。A2G通信的特性在RIS任意相移配置下进行了表征，表明A2G SNR可以表示为两个相关的非中心$\chi^2$随机变量（RV）的乘积。此外，我们给出了两个独立分布的非中心$\chi^2$ RV乘积的PDF和CDF，这精确地表征了A2G SNR的分布。本文证实了在相干时间内，RIS在缓解信道老化效应方面的有效性。最后，我们提出了一种自适应频谱效率方法，该方法在无人机和地面用户设备移动时，能够确保一致的系统性能和令人满意的中断水平。