In this paper, we establish a foundation for the multi-layer aerial networks (MANs), which are modeled as $K$ layer aerial networks (ANs), where each layer has unmanned aerial vehicles (UAVs) with different densities, floating altitudes, and transmission power. To make the framework applicable for various scenarios in MAN, we consider the transmitter- and the receiver-oriented node association rules as well as the air-to-ground and air-to-air channel models, which form line of sight links with a location-dependent probability. We then newly analyze the association probability, the main link distance distribution, successful transmission probability (STP), and area spectral efficiency (ASE) of MAN. The upper bounds of the optimal densities that maximize STP and ASE are also provided. Finally, in the numerical results, we show the optimal UAV densities of each AN that maximize the ASE and the STP decrease with the altitude of the network. We also show that when the total UAV density is fixed for two layer AN, the use of single layer in higher(lower) altitude only for all UAVs can achieve better performance for low(high) total density case. Otherwise, distributing UAVs in two layers, i.e., MAN, achieves better performance.

中文翻译：

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多层无人机网络：建模与性能分析

在本文中，我们为多层空中网络 (MAN) 建立了基础，这些网络被建模为 $K$ 层空中网络 (AN)，其中每一层都有具有不同密度、浮动高度、和传输功率。为了使该框架适用于城域网中的各种场景，我们考虑了面向发射机和接收机的节点关联规则以及空对地和空对空信道模型，它们与位置相关的概率。然后我们重新分析了城域网的关联概率、主链路距离分布、成功传输概率（STP）和区域频谱效率（ASE）。还提供了最大化 STP 和 ASE 的最佳密度的上限。最后，在数值结果中，我们展示了每个 AN 的最佳 UAV 密度，使 ASE 和 STP 随着网络高度的降低而最大化。我们还表明，当两层 AN 的总无人机密度固定时，仅对所有无人机在较高（较低）高度使用单层可以在低（高）总密度情况下实现更好的性能。否则，将无人机分布在两层，即 MAN，可以获得更好的性能。