## 2 System Model
The power transmitted to the LoS and NLoS links can be obtained with the following formula:  
\[P_{T}(\theta)=P_{T}+A_{\theta}, \tag{5}\]  
where \(P_{T}\) is the original transmitting power of the base station, whose value is set as 46 dBm. When signals are transmitted in the LoS link and NLoS link, corresponding power losses are generated. Considering the different link attributes, the power losses of the two links are also calculated differently. In 3 GPP, the path loss formula of the LoS link is:  
\[PL_{LoS}=28+22\log_{10}(d)+20\log_{10}(f), \tag{6}\]  
where \(d\) is the distance between the signal transmitting point at the base station and the UAV, and \(f\) is the carrier frequency. The power loss of the NLoS link also changes with the increase in the path, and the path loss expression is different before and after 22.5 m. The expression of the function between the distance and power of the NLoS link is as follows:  
\[PL_{NLoS}(x)=\left\{ \begin{array}{l}\max(PL_{LoS},PL_{0}(x)),H_{UAV}<22.5\, \mathrm{m}\\ PL_{1}(x),H_{UAV}>22.5\,\mathrm{m}.\end{array} \right. \tag{7}\]  
In the above formula, the expressions of \(PL_{0}(x)\) and \(PL_{1}(x)\) are as follows:  
\[PL_{0}(x)=13.54+39.08\log_{10}(x)+20\log_{10}(f)-0.6(H_{UAV}-1.5), \tag{8}\]  
\[PL_{1}(x)=-17.5+\big{(}46-7\log_{10}(H_{UAV})\big{)}\log_{10}(x)+20\log_{10} \bigg{(}\frac{40\pi f}{3}\bigg{)}. \tag{9}\]  
Given the above path loss power expression for the NLoS link, we divide the NLoS link into two paths: the path from the BS to element K and the path from element K to the UAV. Assuming that the distance between the base station and a component of the IRS is \(d_{1}(k)\), then the power loss from the base station to element K is:  
\[PL_{BS-k}=PL_{NLoS}(d_{1}(k)). \tag{10}\]  
Assuming that the distance from element K to the UAV is \(d_{2}(k)\), then the power loss from element K to the UAV is:  
\[PL_{k-UAV}=PL_{NLoS}(d_{1}(k)+d_{2}(k))-PL_{NLoS}(d_{1}(k)) \tag{11}\]  
After the transmission power and path loss are obtained, the receiving power \(P_{R}(LoS)\) and \(P_{R}(k)\) of the LoS link and NLoS link is:  
\[P_{R}(LoS)=P_{T}(\theta_{0})-PL_{LoS}, \tag{12}\]  
\[P_{R}(k)=P_{T}(\theta_{k})-PL_{BS-k}-PL_{IRS}-PL_{k-UAV}. \tag{13}\]  
In the above formula, \(\theta_{0}\) and \(\theta_{k}\) are the angle between the UAV and the base station and the angle between the IRS element K and the base station, respectively. The received power of the two links can be obtained, and \(h_{0}\) and \(h_{k}\) are:  
\[h(0)=\sqrt{P_{R}(LoS)}e^{-j\varphi_{0}}, \tag{14}\]  
\[h(k)=\sqrt{P_{k}(k)}e^{-j\varphi_{k}}. \tag{15}\]  
In order to obtain the optimal signal, we set the phases \(\varphi_{0}\) and \(\varphi_{k}\) to 0, and then obtain the signal expression of the UAV receiver:  
\[y_{UAV}=h_{0}+\sum_{i=1}^{K}h(k). \tag{16}\]  
Therefore, combined with additive white Gaussian noise, the SNR at the UAV is expressed as:  
\[r=\frac{|y_{UAV}|^{2}E_{s}}{N_{0}}, \tag{17}\]  
where \(N_{0}\) is the power of the additive white Gaussian noise, and \(E_{s}\) is the average transmitted energy of each symbol. According to communication coding theory, the SER can represent the quality of a signal, and it can be expressed as:  
\[PL_{1}(x)=-17.5+\big{(}46-7\log_{10}(H_{UAV})\big{)}\log_{10}(x)+20\log_{10} \bigg{(}\frac{40\pi f}{3}\bigg{)}. \tag{9}\]0  
The error function (ERF) is expressed as:  
\[PL_{1}(x)=-17.5+\big{(}46-7\log_{10}(H_{UAV})\big{)}\log_{10}(x)+20\log_{10} \bigg{(}\frac{40\pi f}{3}\bigg{)}. \tag{9}\]1  
The right-tail function of the standard normal distribution--the \(Q\) function, which is also known as the complementary accumulative distribution of the standard normal distribution. It is commonly used to represent the bit error rate of transmitted signals.