## 1 Introduction  
Recently, unmanned aerial vehicles (UAVs) have attracted wide attention in many research fields for their ability to provide wireless service [1]. Using UAVs as base stations is considered a promising way to improve wireless network coverage and rate performance. Moreover, UAV-BSs can assist in terrestrial communication in a variety of scenarios, such as surveillance, monitoring, aerial imaging, and cargo delivery. UAVs can be deployed to assist the existing communication infrastructure when ground stations are unable to provide communication services, due to various incidents [2]. For example, the base station cannot work normally, due to a fault or the network congestion caused by high user density. UAVs cannot only be used as wireless relay to improve a wireless connection and cover the ground device, but also as an aerial base station to provide reliable downlink and uplink communication for ground users [3]. At present, the research of mobile UAV as an aerial base station is increasing day by day. In Reference [4], the coexistence of UAVs and D2D networks transmitting data in downlink is studied. The work of Reference [5] shows that for cases of Rician fading, there exists optimum height that maximizes the coverage area. In References [6; 7], the coverage probability performance of multiple UAVs is studied, and the flexibility of the scalable dynamic network is considered. In Reference [8], a new method is proposed to deploy UAVs to collect uplink data from mobile ground IoT devices. The work in [9] considers the deployment of two UAVs with and without interference. The work in Reference [10] studied how to reduce the transmission energy of UAVs, while meeting the requirement of users. In Reference [11], the trajectory and heading of multiple UAVs are deduced when the ground user is stationary. The work in Reference [12] improves the network throughput significantly by jointly optimizing relay trajectory and power distribution. The work in Reference [13] studies the 3D deployment of multiple UAVs in consideration of fairness. The work in Reference [14] established the channel model of LoS probability, and the relation between maximum coverage radius and height is given. The work in Reference [15] studied the deployment of the UAV in a novel way. The work in Reference [16] studied the emergency deployment of UAV base station to minimize transmission delays. The work in Reference [17] studied the deployment of UAVs in both horizontal and vertical dimensions. The work in Reference [18] studies the 3D deployment of the UAV in the case that users have different QoS. The work in Reference [19] maximized the weighted sum-rate for the downlink transmission in Multi-cell Multi-association OFDMA heterogeneous networks. The work of Reference [20] studies UAV's energy-saving deployment can optimize the trajectory of UAV. The work of Reference [21] proposed a new cyclical multiple access scheme. UAVs are able to change its location based on user requirements, which is quite different from ground base stations. Although UAV-BS waves many advantages, many challenges remain in UAV-aided communication. Fairness is an important indicator metrics in communication or disaster-affected network, and they should be considered for the trajectory of the UAV-BS [13]. According to the characteristics of the air-to-ground channel model, users far away from UAV-BS have higher path losses than users close to the UAV-BS [14]. Therefore, the QoS requirements of users at the edge of the coverage area cannot be reached; that is, the UAV-BS cannot provide wireless service for users at the edge of the coverage area. The deployment of multiple UAVs with the consideration of fairness is studied in Reference [13]. However, multiple UAVs are needed, and the hardware costs are high. The total logarithm rate of users is considered in Reference [13], and the fairness of the user transmission rate is measured by optimizing the average logarithm rate of users connected to each UAV.