# Joint Trajectory and Communication Design for Buffer-Aided Multi-UAV Relaying Networks
## 1 Introduction  
With the rapid development of unmanned aerial vehicle (UAV) technology and wireless communication technology, UAVs are beginning to be widely used in military and civil applications. Meanwhile, due to its promising performance, much research has been done on UAV assisted wireless communications [1; 2; 3; 4; 5; 6]. In terms of UAV assisted wireless communications, UAVs can be used as mobile base stations (BSs) and /or relays. For example, employing UAVs as BSs can quickly restore wireless communication services when the ground infrastructure is damaged [1]. Another example is adopting UAVs as mobile relays to help provide reliable communication when the end-to-end distance is very long or direct communication is obstructed [2]. In this paper, we consider the UAVs as the mobile relays to assist terrestrial communications. Compared with traditional static relays, employing the dynamic UAVs as relays has several key advantages. First, the high flexibility of the UAV relay allows it to have the opportunity to improve the performance of the considered network by adaptively adjusting its location [2]. Second, on-demand deployment makes UAVs be widely used in emergency and extreme environments, such as border monitoring, forest fire prevention, emergency rescue, etc. [3]. Furthermore, the UAV relay has wide coverage because of its mobility. Studies have shown that the buffer aided relaying technique can effectively solve the adverse effects brought by time varying channels. It enables relays to have the ability of data storage, breaks through the traditional transmission mode, and flexibly uses the best channel [7,8]. Therefore, in this paper, it is considered that all UAV relays are equipped with a buffer and employed in delay tolerant applications [4]. Benefiting from both relay node mobility and buffer aided relaying, UAV relays equipped with a buffer can store and forward the information under more favorable conditions when certain quality-of-service (QoS) requirements are satisfied. Note that many studies have been done on UAVs, but little work considers buffer aided UAV relaying networks. In [2,6], the authors maximized the throughput of single-UAV and multi-UAV relaying systems, respectively, via jointly optimizing UAV trajectory and transmit power design. In [5], the authors deduced a closed form propulsion power consumption model for rotary wing UAVs and minimized the total energy consumption of the network by joint UAV trajectory and communication time allocation optimization. In [9], a basic principle combining the path loss exponent and small scale fading was proposed, which analyzed the optimization problem of large scale wireless networks by combining air-to-ground systems and widely used ground-to-ground channel models. In [10], the authors investigated the use of a UAV as a hybrid access point to provide wireless power transfer and assist obstructed ground communications in wireless powered communication networks. In [11, 12, 13], a new cooperative jamming method was studied to guarantee the communication security between UAVs and ground nodes, which leveraged the jamming from other nearby UAVs to prevent the eavesdropping and combined UAV trajectory and communication design to maximize the average secrecy rate. The works in [14, 15, 16] focused on buffer aided UAV relaying networks. The authors in [14,15] considered the secrecy rate maximization problem with a two phase buffer aided single UAV relaying network. Based on the buffer constraint, the work in [16] considered a hybrid communication link consisting of free space optical and radio frequency links and maximized the average security rate with the consideration of information causality. The channel models between UAVs and ground nodes can be divided into three types: the light-of-sight (LoS) channel [2], the probabilistic LoS channel [17], and the Rician fading channel [18,19]. Due to the fact that the LoS channel model ignores the shadow fading and small scale fading, the channel is perhaps inappropriate in urban/suburban areas.