In this paper, the effective use of multiple quadrotor drones as an aerial
antenna array that provides wireless service to ground users is investigated.
In particular, under the goal of minimizing the airborne service time needed
for communicating with ground users, a novel framework for deploying and
operating a drone-based antenna array system whose elements are single-antenna
drones is proposed. In the considered model, the service time is minimized by
minimizing the wireless transmission time as well as the control time that is
needed for movement and stabilization of the drones. To minimize the
transmission time, first, the antenna array gain is maximized by optimizing the
drone spacing within the array. In this case, using perturbation techniques,
the drone spacing optimization problem is addressed by solving successive,
perturbed convex optimization problems. Then, the optimal locations of the
drones around the array's center are derived such that the transmission time
for the user is minimized. Given the determined optimal locations of drones,
the drones must spend a control time to adjust their positions dynamically so
as to serve multiple users. To minimize this control time of the quadrotor
drones, the speed of rotors is optimally adjusted based on both the
destinations of the drones and external forces (e.g., wind and gravity). In
particular, using bang-bang control theory, the optimal rotors' speeds as well
as the minimum control time are derived in closed-form. Simulation results show
that the proposed approach can significantly reduce the service time to ground
users compared to a fixed-array case in which the same number of drones form a
fixed uniform antenna array. The results also show that, in comparison with the
fixed-array case, the network's spectral efficiency can be improved by 32%
while leveraging the drone antenna array system.

本文探讨了将多个四旋翼飞行器作为天线阵列，为地面用户提供无线服务的有效性。提出了一种使用单天线无人机元素部署和操作基于无人机的天线阵列系统的新框架，以最小化与地面用户通信所需的空中服务时间。通过最小化无线传输时间和无人机的运动和稳定所需的控制时间来最小化服务时间。首先通过优化阵列内的无人机间距来最大化天线阵列增益。然后根据无人机的最佳位置，使用户的传输时间最小化。最后，通过加入 bang-bang 控制理论来优化转子速度，以最小化四旋翼无人机的控制时间。仿真结果表明，相对于固定天线阵列情况，该方法可以显著降低地面用户的服务时间，并且可以提高 32％的网络频谱效率。

无线无人机天线阵列的通信与控制

Communications and Control for Wireless Drone-Based Antenna Array

In this paper, the effective use of flight-time constrained unmanned aerial
vehicles (UAVs) as flying base stations that can provide wireless service to
ground users is investigated. In particular, a novel framework for optimizing
the performance of such UAV-based wireless systems in terms of the average
number of bits (data service) transmitted to users as well as UAVs' hover
duration (i.e. flight time) is proposed. In the considered model, UAVs hover
over a given geographical area to serve ground users that are distributed
within the area based on an arbitrary spatial distribution function. In this
case, two practical scenarios are considered. In the first scenario, based on
the maximum possible hover times of UAVs, the average data service delivered to
the users under a fair resource allocation scheme is maximized by finding the
optimal cell partitions associated to the UAVs. Using the mathematical
framework of optimal transport theory, a gradient-based algorithm is proposed
for optimally partitioning the geographical area based on the users'
distribution, hover times, and locations of the UAVs. In the second scenario,
given the load requirements of ground users, the minimum average hover time
that the UAVs need for completely servicing their ground users is derived. To
this end, first, an optimal bandwidth allocation scheme for serving the users
is proposed. Then, given this optimal bandwidth allocation, the optimal cell
partitions associated with the UAVs are derived by exploiting the optimal
transport theory. Results show that our proposed cell partitioning approach
leads to a significantly higher fairness among the users compared to the
classical weighted Voronoi diagram. In addition, our results reveal an inherent
tradeoff between the hover time of UAVs and bandwidth efficiency while serving
the ground users.

本文研究了以飞行时间有限的无人机为基础站点，向地面用户提供无线服务的有效方法。提出了一种针对该类基于无人机的无线系统优化性能的新框架，并考虑了两种实际场景：一是基于最大可能悬停时间的情况下，找到与无人机相关的最优单元格划分，以使得平均传输给用户的数据服务最大。二是在给定地面用户的负载要求下，推导出为其完全服务所需的最小平均悬停时间，并因此提出了优化带宽分配方案的方法。结果表明，我们的提出的单元划分方法在用户公平性方面要比传统的加权 Voronoi 图方法高得多。此外，研究还揭示了在为地面用户提供服务时，无人机悬停时间与带宽效率之间的固有权衡。