## 2 System Model  
In this section, we will introduce the model of a UAV-assisted cellular network communication system based on an IRS and the model of the UAV's optimal deployment position. The right half of Figure 1 shows the model of the BS-IRS-UAV system. The whole system is divided into two links for signal transmission: the LoS link, in which the signal is transmitted from the base station to the UAV side, and the NLoS link, in which the IRS is used to promote the signal transmission of the link. The downdip antenna of the base station sends most of the signals to the angle at which the IRS is located. After receiving the signals from the downdip antenna, the IRS composed of K = M x N reflecting elements dynamically programs and reconfigures the signals, which are reflected to the position of the UAV [25]. The UAV receives the signals directly from the line-of-sight path and the non-line-of-sight path reflected by the IRS elements. By using the IRS to align the phase of individually reflected signals with that of the line-of-sight path, these signals are constructively combined on the UAV to improve the received signal power. Assume that the signal sent by the base station is expressed as:  
\[y_{t}=\sum_{1}^{M}\sum_{1}^{N}A_{m,n}e^{i\theta_{m,n}}, \tag{1}\]  
where \(A_{(}m,n)\) is the amplitude of the \(m\)th row and \(n\)th column signal sent from the base station to the IRS, and \(e^{i\theta_{m,n}}\) is the phase of the \(m\)th row and \(n\)th column signal sent from  
Figure 1: UAV-based cellular data network using an IRS system. the base station to the IRS. Due to the base station itself and the influence of the channel environment, the amplitudes and phases of the signal received by each element on the reflecting surface are different, so the overall signal expression is actually composed of multiple signals with different amplitudes and phases. In order to facilitate the reception of signals, the IRS adjusts the amplitude and phase of the received signals. The signal's expression after being reflected by the IRS is:  
\[y_{r}=\sum_{1}^{M}\sum_{1}^{N}A_{m,n}E_{m,n}e^{i\theta_{m,n}}e^{i\varphi_{m,n}}, \tag{2}\]  
where \(E_{m,n}\) is the amplitude adjustment factor of the IRS element at the \(m\)th row and \(n\)th column, and \(e^{i\varphi_{m,n}}\) is the phase adjustment factor of the IRS element at the \(m\)th row and \(n\)th column. The choice of IRS is based on the actual needs of the application and the received signal for adaptive adjustment and change. The IRS will flexibly adjust the received signal according to the actual needs. According to the above analysis, the expression of the signal received by the UAV should be [26]:  
\[y=h_{0}X+\sum_{i=1}^{K}h_{k}X+n_{0}. \tag{3}\]  
where \(h_{0}X\) is the signal received at the LoS link, and \(h_{k}X\) is the signal reflected by the \(K\)th IRS element. The \(k\) elements of the IRS are superimposed to form the received signal of the NLoS link, and \(n_{0}\) is the additive white Gaussian noise at the UAV receiver, with a mean value of 0 and a variance of \(\sigma^{2}\). Next, we deduce the channel coefficients \(h_{0}\) and \(h_{k}\) of the two links through the relationship between the transmitted power and lost power. Since cellular network data base stations are already equipped with down-sloping antennas to serve terrestrial users, the power over the NLoS link is much higher than that over the LoS link. By querying a 3 GPP website [27], the following expression of the signal power of the base station downdip angle can be obtained:  
\[A(\theta)=-\min\left[12\left(\frac{\theta-\theta_{\text{etilt}}}{\theta_{3 dB }}\right)^{2},SLA\right], \tag{4}\]  
where \(\theta\) is the angle between the line between the BS and IRS or the line between the BS, UAV, and the horizontal line (which is negative if it is higher than the horizontal line); \(\theta_{\text{etilt}}\) is the dip angle of the base station antenna, which can be found by querying 3 GPP and is set to \(15^{\circ}\). \(\theta_{3 dB}\) is equal to 10 and \(SLA=20\) dB.