# UAV-BS Site Planning Based on Circular Coverage Strategy
## 4 Methodology
### UAV-BS Full Coverage Network Energy Consumption Model  
In the UAV-BS network, there are two types of downlink channels: the communication link between the central UAV-BS and other UAV-BSs, and the communication link between the UAV-BS and ground users. It is assumed that the communication links between the central UAV-BS and other UAV-BSs, as well as between the UAV-BS and users, all utilize Orthogonal Frequency-Division Multiple Access (OFDMA) technology for channel multiplexing to avoid severe co-channel interference. Considering the need for site planning for \(n\) UAV-BSs, the total communication energy consumption of the system is the sum of the total transmission power of the UAV-BSs to the ground and the communication power between UAV-BSs, that is, the following:  
\[P_{\rm{s}}(n,d)=\sum_{i=1}^{n}P_{g,i}(d)+\sum_{i=1}^{n-1}P_{u,i}, \tag{13}\]  
where \(P_{g,i}(d)\) represents the transmission power required by the \(i\)-th UAV-BS when \(n\) UAV-BSs provide full coverage to ground users. \(P_{u,i}\) is the channel allocation power between the central UAV-BS and the \(i\)-th UAV-BS. It is assumed that all UAV-BSs are identical rotary-wing UAVs, equipped with the same type of base station, and have the same coverage capability. The signal propagation distance is \(d\), and the transmission power required is \(P_{g}(d)\). If the Signal-to-Noise Ratio (SNR) at any location within the target area is greater than the SNR threshold \(\gamma_{th}\), it is considered that the UAV deployment can meet the user requirements and achieve full coverage. The SNR for ground users is as follows:  
\[\gamma=P_{g}(d)-P_{\rm{noise}}-PL(d,f), \tag{14}\]  
where \(P_{\rm{noise}}\) is the noise power. The minimum transmission power required for each UAV to serve ground users under full coverage is \(P_{g}(d)\).  
\[P_{g}(d_{n})=10^{\frac{\gamma+P_{\rm{noise}}+PL(d_{n})}{10}},0<P_{g}(d_{n})<P _{\rm{max}}, \tag{15}\]  
where \(d_{n}\) is the maximum distance over which each UAV can connect when \(n\) UAVs are deployed. By combining Equations (12), (13), and (15), the transmission power of the UAV communication system required to ensure full coverage is the following:  
\[P_{\rm{s}}=nP_{g}(d_{n})+(n-1)P_{u}. \tag{16}\]  
The objective is to ensure full coverage of the network while minimizing the power consumption of the UAV communication system. This problem can be described mathematically as follows:  
**P1:**  
\[\min_{n}P_{\rm{s}}=nP_{g}\bigg{(}\sqrt{r(n)^{2}+H^{2}}\bigg{)}+(n-1)P_{u}\]subject to:_  
C1: \(0<P_{g}<P_{\text{max}}\);  
C2: \(S_{c}(n)-S\geq 0\);  
C3: \(n\leq N\);  
C4: \(n\in\mathbb{N}^{+}\);  
where \(r(n)\) represents the maximum coverage radius of each base station when \(n\) UAV-BSs are deployed. \(P_{\text{max}}\) denotes the maximum transmission power that a UAV-BS can use when communicating with ground users. \(S_{c}(n)\) is the area that can be covered by the planned deployment of \(n\) UAV-BSs, and \(S\) represents the total area of the target region. Constraints \(C3\) and \(C4\) ensure that under the condition where the transmission power of each UAV-BS is limited, deploying fewer than \(N\) UAV-BSs can still achieve full coverage of the target area.