# UAV-BS Site Planning Based on Circular Coverage Strategy
## 4 Methodology
### Circle Coverage Power Optimization Strategy  
To effectively solve the problem P1, this study employs a site planning strategy based on the Cooperative Coverage and Power Optimization (CCPO) approach, taking into account the number of deployed UAV-BSs and the system transmission power. A power function is utilized to fit the relationship between the coverage radius and the number of small circles. To minimize the system's communication power consumption, an optimal UAV-BS site planning strategy is determined through [PERSON]'s iteration method, establishing the optimal number of UAV-BSs and coverage radius. Equation (16) shows that the system transmit power is affected by the SNR threshold, the communication distance between UAV-BSs and users, and the number of UAV-BSs. Due to unknown user location information, UAV-BS site planning is a challenge in the case of power constraints. The ground radiation coverage area of a UAV-BS equipped with an omnidirectional antenna can be modeled as a conical area, and its ground projection is positive circle. In the above modeling process, the covering problem can be regarded as a kind of geometric problem, similar to the disk placement problem in the position problem [27]. Disk placement problems are divided into two categories: one is the Circle Packing Problem (CPP), such as shown in Figure 2a, where a container is packed with a number of circles, each with a maximum radius--these smaller circles do not need to be exactly the same. The other is CCP, which is the question of how much the area of a container can be completely covered by a given circle. The shape of the container can be a simple circle, square, rectangle, or a combination of lines and arcs [28]. Figure 2b shows the optimal placement of 5 equal circles within a larger circle. Assume the radius of the large circle is 1. The radius of the small circles in the CCP and the number of circles required to completely cover the large circle satisfy Table 2[28]. It can be seen from the table that the radius \(r_{0}(n)\) of each circle decreases as the number of circles \(n\) increases. There is a specific placement strategy for the small circles for each value of \(n\). It is challenging in mathematics to find a generally optimal placement strategy for any \(n\), which means that a specific coverage strategy needs to be provided for each value of \(n\)In the full coverage scenario, the coverage area of each UAV-BS is considered a small circle, and the target area is the large circle that needs to be covered without distinction. Since multiple UAVs of the same type are used, the coverage range of each UAV is indistinguishable. Therefore, the UAV-BS site planning problem in this scenario can be solved using the CCP geometric model. Based on the CCP, this chapter describes the UAV-BS site planning problem as the mathematical problem shown in P2. **P2:**  
\[\min_{n}P_{s}(n)=nP_{g}\bigg{(}\sqrt{(Rr_{0}(n))^{2}+H^{2}}\bigg{)}+(n-1)P_{u}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Small Circles (\(n\))** & \begin{tabular}{c} **Radius of Small Circle** \\ **(\(r_{0}(n)\))** \\ \end{tabular} & \
\begin{tabular}{c} **Number of Small Circles** \\ **(\(n\))** \\ \end{tabular} &
\begin{tabular}{c} **Radius of Small Circle** \\ **(\(r_{0}(n)\))** \\ \end{tabular} \\ \hline \(n=1,2\) & \(1\) & \(n=14\) & \(0.3318\) \\ \(n=3\) & \(\sqrt{3}/2\) & \(n=15\) & \(0.3182\) \\ \(n=4\) & \(\sqrt{2}/2\) & \(n=16\) & \(0.3083\) \\ \(n=5\) & \(0.61\) & \(n=17\) & \(0.2986\) \\ \(n=6\) & \(0.556\) & \(n=18\) & \(0.2902\) \\ \(n=7\) & \(0.5\) & \(n=19\) & \(0.2774\) \\ \(n=8\) & \(0.437\) & \(n=20\) & \(0.2709\) \\ \(n=9\) & \(0.422\) & \(n=21\) & \(0.2629\) \\ \(n=10\) & \(0.398\) & \(n=22\) & \(0.2533\) \\ \(n=11\) & \(0.38\) & \(n=23\) & \(0.2500\) \\ \(n=12\) & \(0.361\) & \(n=24\) & \(0.2453\) \\ \(n=13\) & \(0.3467\) & \(n=25\) & \(0.2392\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Existing solutions for CCP problem. Figure 2: (**a**) is the CPP diagram when \(n=19\). (**b**) is the CCP diagram when \(n=5\).