In this paper, we characterize the performance of a three-dimensional (3D) two-hop cellular network in which terrestrial base stations (BSs) coexist with unmanned aerial vehicles (UAVs) to serve a set of ground user equipment (UE). In particular, a UE connects either directly to its serving terrestrial BS by an access link or connects first to its serving UAV which is then wirelessly backhauled to a terrestrial BS (joint access and backhaul). We consider realistic antenna radiation patterns for both BSs and UAVs using practical models developed by the third generation partnership project (3GPP). We assume a probabilistic channel model for the air-to-ground transmission, which incorporates both line-of-sight (LoS) and non-line-of-sight (NLoS) links. Assuming the max-power association policy, we study the performance of the network in both amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. Using tools from stochastic geometry, we analyze the joint distribution of distance and zenith angle of the closest (and serving) UAV to the origin in a 3D setting. Further, we identify and extensively study key mathematical constructs as the building blocks of characterizing the received signal-to-interference-plus-noise ratio (SINR) distribution. Using these results, we obtain exact mathematical expressions for the coverage probability in both AF and DF relaying protocols. Furthermore, considering the fact that backhaul links could be quite weak because of the downtilted antennas at the BSs, we propose and analyze the addition of a directional uptilted antenna at the BS that is solely used for backhaul purposes. The superiority of having directional antennas with wirelessly backhauled UAVs is further demonstrated via simulation.

中文翻译：

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具有无线回程无人机的 3D 两跳蜂窝网络：建模和基础知识

在本文中，我们描述了三维（3D）两跳蜂窝网络的性能，其中地面基站（BS）与无人机（UAV）共存以服务于一组地面用户设备（UE）。具体而言，UE 通过接入链路直接连接到其服务地面 BS，或者首先连接到其服务 UAV，然后无线回程到地面 BS（联合接入和回程）。我们使用第三代合作伙伴项目 (3GPP) 开发的实用模型考虑 BS 和 UAV 的实际天线辐射模式。我们假设空对地传输的概率信道模型包含视距 (LoS) 和非视距 (NLoS) 链路。假设最大功率关联策略，我们研究了网络在放大转发 (AF) 和解码转发 (DF) 中继协议中的性能。使用来自随机几何的工具，我们在 3D 设置中分析了最近（和服务）无人机到原点的距离和天顶角的联合分布。此外，我们确定并广泛研究了关键数学结构作为表征接收到的信号干扰加噪声比 (SINR) 分布的构建块。使用这些结果，我们获得了 AF 和 DF 中继协议中覆盖概率的精确数学表达式。此外，考虑到回程链路可能由于 BS 处的下倾天线而非常弱的事实，我们建议并分析在 BS 处添加一个仅用于回程目的的定向上倾天线。