# Time-Varying Communication Channel High Altitude Platform Station Link Budget and Channel Modeling
## 2 System Model  
The HAPS-based air-ground integrated aeronautical telecommunication network architecture is shown in Figure 1. The HAPS network includes a set of HAPS communication nodes that can perform routing, forwarding, and traffic management, and microwave communication can be implemented between each HAPS node. The link problem between HAPS is a technical problem, and the geometric relationship of the communication system is shown in Figure 1.  
Use a stable communication platform as a microwave relay station in the near-Earth space. a communication system with ground control equipment, entry equipment, and a variety of wireless users. The high-altitude platform can be integrated with the satellite ground or separately from the ground. Consider the communication platform as a synchronous communication satellite, that is, the communication platform is synchronized with the Earth's rotation. Can stay in the air for a long time. High-altitude platform communication utilizes good radio wave transmission characteristics, realizing communication connections between ground users, between platforms or between platforms and satellites through platforms. It has the advantages of flexible layout, wide application, low cost, safety and reliability. The schematic diagram of the HAPS space communication network is shown in Figure 2.  
Figure 1: System frame diagram of the High Altitude Platform Station (HAPS).  
Figure 2: _Cont._  
It can be seen from Figure 2 that HAPS is a highly dynamic space platform. The communication between them is related to the atmospheric environment, multipath fading, space flicker and other factors.  
According to the geometric relationship of Figure 2, it can be calculated using the following equation:  
\[\frac{\sin(90-\varepsilon_{\text{min}}\ -\delta)}{R_{E}+h_{H}}=\frac{\sin(90+ \varepsilon_{\text{min}})}{R_{E}+h_{S}} \tag{1}\]  
where \(R_{E}\) is the radius of earth. \(h_{H}\) is the altitude of HAPS, \(h_{S}\) is the altitude from HAPS to earth ground. \(\varepsilon_{\text{min}}\) is the pitch angle of the HAPS, \(\delta\) is the central angle of the HAPS, which can be seen in Figure 2b. According to the geometric relationship, the central angle \(\delta\) can be obtained through the following Equation (2).  
\[\delta=90-\varepsilon_{\text{min}}\ -\arcsin\biggl{(}\frac{R_{E}+h_{H}}{R_{E}+h _{S}}\cos(\varepsilon_{\text{min}})\biggr{)} \tag{2}\]  
In Equation (2), the relevant coefficients have been explained in Equation (1).  
The central angle \(\beta\) of the HAPS can be calculated by the following equation:  
\[\beta=2\arcsin\biggl{(}\frac{|SH|}{2(R_{E}+h_{H})}\biggr{)} \tag{3}\]  
where \(SH\) is the distance between HAPS and point \(H\). \(R_{E}\) is the radius of earth. \(h_{H}\) is the altitude of HAPS. The pitch angle \(\varepsilon_{SH}\) of the HAPS can be described by the Equation (4).  
\[\varepsilon_{SH}\ =\arctan\biggl{(}\frac{1}{\sin\beta}\biggl{(}\cos\beta- \frac{R_{E}+h_{H}}{R_{E}+h_{S}}\biggr{)}\biggr{)} \tag{4}\]  
As can be seen from Equation (4), the pitch angle \(\varepsilon_{SH}\) is related to the central angle \(\beta\), radius of earth \(R_{E}\), HAPS altitude \(h_{H}\) and \(h_{S}\) (the distance from HAPS to earth ground), it has a nonlinear function relationship. \(x(t)\) is the distance at time \(t\).  
\[x(t)=x(t+(i-1)\Delta) \tag{5}\]  
Figure 2: Space network diagram and link geometry of HAPS. (**a**) Network diagram; (**b**) Geometry diagram.  
where \(i\) is the \(i\)-th slot time, \(\Delta\) denotes the time step.