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Volume 7 Issue 2
Mar.  2020

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Hailong Huang, Chao Huang and Dazhong Ma, "A Method for Deploying the Minimal Number of UAV Base Stations in Cellular Networks," IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 559-567, Mar. 2020. doi: 10.1109/JAS.2019.1911813
 Citation: Hailong Huang, Chao Huang and Dazhong Ma, "A Method for Deploying the Minimal Number of UAV Base Stations in Cellular Networks," IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 559-567, Mar. 2020.

# A Method for Deploying the Minimal Number of UAV Base Stations in Cellular Networks

##### doi: 10.1109/JAS.2019.1911813
Funds:  This work was supported by the National Natural Science Foundation of China (61903076, 61773109) and Liaoning Revitalization Talents Program (XLYC1807009)
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• In this paper, we consider the scenario of using unmanned aerial vehicles base stations (UAV-BSs) to serve cellular users. In particular, we focus on finding the minimum number of UAV-BSs as well as their deployment. We propose an optimization model which minimizes the number of UAV-BSs and optimize their positions such that the user equipment (UE) covered ratio is no less than the expectation of network suppliers, the UEs receive acceptable downlink rates, and the UAV-BSs can work in a sustainable manner. We show the NP-hardness of this problem and then propose a method to address it. The method first estimates the range of the number of UAV-BSs and then converts the original problem to one which maximizes the UE served ratio, given the number of UAV-BSs within that range. We present a maximizing algorithm to solve it with the proof of convergence. Extensive simulations based on a realistic dataset have been conducted to demonstrate the effectiveness of the proposed method.

• 1 A supplier defined constant.
2 The definition of vertex is provided in Fig. 1.
3 It is worth noticing that the range of n shown in (5) is to cover M street points instead of $\alpha$ percent of UEs in the area. Further, it is based on the Assumption 1, which does not always hold in practical street graphs. Thus, it is only a rough range. However, we claim that this rough estimation is still reasonable in our problem setting. Firstly, the lower and upper bounds are theoretical results and n is unlikely to take either of them. Secondly, in practice the network supplier may expect $\alpha$ to be close to 100%, e.g., 98%, which does not influence the bounds significantly.
4 When looking for the position for the first UAV-BS, constraints (2) and (3) are not applied.
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## Highlights

• We mathematically formulate an optimization problem which minimizes the number of UAV-BSs subject to the three types of constraints: coverage, downlink rate, and the charging requirement.
• We propose a solution to the formulated problem which involves the estimation of the bounds of the number of UAVBSs and a coverage maximizing algorithm to place UAV-BSs.
• The convergence of such a coverage maximizing algorithm is proved.

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