## 2 System Model
### Modeling the Line of Sight Probability  
In this part, the channel model used in the multi-UAV formation network is introduced. The channel model consists of the channel model of the U2U and U2B data transfer. The U2U and U2B links are different due to the different line-of-sight (LoS) characteristics and the elevation angle in the actual environment. For the U2U channel model, the free space channel model of the U2U link was used in the multi-UAV formation network. The values \(P_{ntr}\) and \(P_{mre}\) denote the transmitter and receiver power of the \(n\)th U2U link reusing the \(m\)th uplink. The relationship between them can be expressed as  
\[P_{mre}(t)=P_{ntr}h(d_{ntr,nre}(t))^{-\omega}, \tag{3}\]  
where \(h\) is the constant channel gains factor related to the amplifier and antenna, \(d_{ntr,nre}\) is the distance between the transmitter and receiver UAVs of the \(n\)th U2U link and \(\omega\) is the channel path loss constant. The receiver interference of the \(n\)th U2U link consists of the data that comes from the \(n\)th U2B link and other U2U links that reuse the same \(m\)th uplink. _The valueP\({}_{m}^{U2B}\)_ is labeled as the transmitter power of the \(m\)th U2B link, and, then, the receiver interference of the \(n\)th U2U link \(I_{nre}\) is expressed as follows. \[I_{nre}(t)=P_{m}^{U2B}h(d_{ntr,nre}(t))^{-\omega}+\sum_{n^{\prime}=1,n^{\prime} \
eq n}^{N}\rho_{n^{\prime},m}P_{n^{\prime}}^{U2U}h(d_{ntr,nre}(t))^{-\omega}+ \sigma^{2}, \tag{4}\]  
where \(P_{n^{\prime}}^{U2U}\) is labeled as the transmitter power of the \(n^{\prime}\)th U2U link, \(\rho_{n^{\prime},m}\) indicates whether the \(n^{\prime}\)th U2U link reuses the \(m\)th uplink and \(\sigma^{2}\) is the variance of the additive white Gaussian noise (AWGN) with a mean equal to zero. The data transfer rate of the U2U link can be calculated as follows. \[R_{n}^{U2U}(t)=log_{2}(1+\frac{P_{nre}(t)}{I_{nre}(t)}). \tag{5}\]  
For the U2B channel model, the model of air-to-ground (ATG) propagation adopts the U2B data transmission proposed in the existing literature [30; 31]. To predict the ATG path loss, [32] designed a statistical propagation model. In time slot \(t\), the path loss of LoS and non-line-of-sight (NLoS) of the \(k\)th U2U link is indicated as  
\[ \begin{split} PL_{LoS,k}(t)=L_{FS,k}(t)+20 log(d_{k,BS(t)})+\eta LoS,\\ PL_{NLoS,k}(t)=L_{FS,k}(t)+20 log(d_{k,BS(t)})+\eta NLoS,\end{split}  \tag{6}\]  
where \(d_{k,BS}\) is the distance between the BS and transmitter UAV of the \(k^{th}\) U2U link, the values \(\eta LoS\) and \(\eta NLoS\) are attenuation factors that are caused by the LoS and NLoS transmission, respectively. The value \(L_{FS,k}(t)\) is the free space path loss that is expressed as follows. \[L_{FS,k}(t)=20 log(f)+20 log(\frac{4\pi}{c}), \tag{7}\]  
where \(f\) is the carrier frequency. Recommended by the International Telecommunication Union (ITU), as mentioned in the reference [33], the probability of the LoS link data transfer is expressed as  
\[P_{LoS,k}(t)=\frac{1}{1+\alpha exp(-\beta(\theta_{k}(t)-\alpha))}, \tag{8}\]  
where \(\alpha\) and \(\beta\) are constants that are related to the environment and \(\theta_{k}(t)\) is the elevation angle of the \(k\)th UAV. The sight probability model is adapted to the low-altitude aerial platforms of the UAV network. This probability is closely related to three statistical parameters in the environment: the average number of buildings per unit area; the proportion of construction land area in the total land area; the building height distribution based on the Rayleigh probability density function. The average path loss in decibels (dB) is expressed as follows. \[ \begin{split} PL_{avg,k}(t)=P_{LoS,k}(t)*PL_{LoS,k}(t)+P_{NLoS,k} (t)*PL_{NLoS,k}(t)\\ =P_{LoS,k}(t)*PL_{LoS,k}(t)+P_{NLoS,k}(t)*(1-PL_{LoS,k}(t)).\end{split}  \tag{9}\]  
The average power received by the BS from the \(m\)th U2B link is denoted as  
\[P_{m,BS}(t)=\frac{P_{m}^{U2B}}{10^{PL_{avg,k}(t)/10}}, \tag{10}\]where \(P_{m}^{UL2B}\) is the transmitter power of the \(m\)th U2B link.