# Learning-Based Traffic Scheduling in Non-Stationary Multipath 5G Non-Terrestrial Networks
## 2 Materials and Methods  
### Channel Model  
Figure 1 shows the reference scenario considered in this paper. We studied LOS estimation and link selection in the presence of dual connectivity in NTNs with simultaneous use of two radios, as envisioned by the 3 GPP [2]. In this architecture, the LEO satellites are equipped with the gNB Distributed Unit (DU) [22], while the Centralized Unit (CU) is located on the ground. We considered a scenario in which the satellites and a UAV equipped with two pieces of UEs were moving relative to each other. We made use of the StarLink satellite system with a mass constellation of 3000 LEO satellites. The UE could connect to two satellites simultaneously. To allow our framework to overcome energy constraints, our AC agent ran on the Ground Control Station (GCS) of the UAV which had enough computational resources. After computations, the GCS sent the traffic scheduling policy to the energy-constrained UE (UAV), which only performed traffic scheduling over the satellite links. (see Figure 1). According to [23], a satellite in the constellation moves in a circular orbit with inclination \(t\) at an altitude \(h\) and an orbit radius \(r_{S}=r_{E}+h\), and the satellites move independently of each other. The same authors in [23] defined  
\[\gamma(\theta)=cos^{-1}((r_{E}/r_{S})\cdot cos(\theta)-\theta) \tag{1}\]  
as the central angle between the Earth station (the UE in this case) and the locus of the trajectory points of the satellite corresponding to an elevation angle \(\theta\), with \(\theta_{min}\leq\theta\leq\theta_{max}\). For any single point of the satellite's locus, the maximum elevation angle \(\theta_{max}\) determines the visibility time of the satellite and the distribution of the elevation angles in the visibility  
Figure 1: Reference scenario: a UE (UAV) accessing two satellites in an NTN in a dense urban environment. region [23]. The visibility region is defined as the smallest angle \(\gamma(\theta_{max})\) for which the satellite is visible from the UE along its whole trajectory. Therefore, given the UE latitude \(\phi_{0}\), the probability for a satellite in its trajectory to be visible from the UE can be determined from the Probability Density Function (PDF) of \(\theta_{max}\), denoted by  
\[ \begin{split} f_{\Theta_{max}}(\theta_{max})&=\frac{G( \theta_{max})}{K}.\\ &\cdot\Bigg{(}\frac{cos(\phi_{0}+\gamma(\theta_{max}))}{\pi\sqrt {sin^{2}(\iota)-sin^{2}(\phi_{0}+\gamma(\theta_{max}))}}\,+\,\frac{cos(\phi_{ 0}-\gamma(\theta_{max}))}{\pi\sqrt{sin^{2}(\iota)-sin^{2}(\phi_{0}-\gamma( \theta_{max}))}}\Bigg{)}\end{split}  \tag{2}\]  
where \(\theta_{min}\leq\theta_{max}\leq\frac{\pi}{2}\) and  
\[G(\theta_{max})=\frac{1+(r_{E}/r_{S})^{2}-2(r_{E}/r_{S})cos(\gamma(\theta_{max }))}{1-(r_{E}/r_{S})cos(\gamma(\theta_{max}))}\]  
\[K=\frac{1}{\pi}sin^{-1}\bigg{(}\frac{sin(\phi_{0}+\gamma(\theta_{min}))}{sin( \iota)}\bigg{)}sin^{-1}\bigg{(}\frac{sin(\phi_{0}-\gamma(\theta_{min}))}{sin( \iota)}\bigg{)} \tag{3}\]  
The PDF in Equation (2) may assume different shapes according to \(\iota\), \(\phi_{0}\) and \(\gamma(\theta_{max})\), as detailed in [23]. For space limitations, we will only account for the PDF of elevation angles considering the points of the satellite's trajectory in the visibility region. The authors in [23] derived the PDF \(f_{\Theta}(\theta)\) as the marginalization of the joint probability \(f_{\Theta,\Theta_{max}}(\theta,\theta_{max})\), defined as in the following equation:  
\[f_{\Theta}(\theta)=\int_{\theta}^{\theta_{max}}f_{\Theta,\Theta_{max}}(\theta, \theta_{max})d\theta_{max} \tag{4}\]  
where \(\theta_{min}\leq\theta\leq\theta_{max}\) and  
\[ \begin{split} f_{\Theta,\Theta_{max}}(\theta,\theta_{max})=\frac {G(\theta)sin(\gamma(\theta))}{\sqrt{cos^{2}(\gamma(\theta_{max}))-cos^{2}( \gamma(\theta))}}\cdot\\ \cdot\frac{f_{\Theta_{max}}(\theta_{max})}{\int_{\theta_{min}}^{ \theta_{max}}f_{\Theta_{max}}(x)\cdot cos^{-1}\bigg{(}\frac{cos(\gamma(\theta_{ min}))}{cos(\gamma(x))}\bigg{)}dx}.\end{split}