## 3 System Model and Problem Formulation
### Network Model
To distinguish access nodes from service nodes, an access point set \(\mathcal{J}\subset\mathcal{N}\) is defined, comprising all base stations \(j\). The set of links \(\mathcal{L}\) includes all wireless and wired links. To support user video services, nodes must cooperate and share resources to ensure smooth video data stream transmission, which may traverse multiple paths. This paper's scheme aims to determine the set of paths for all video streams by solving the proposed algorithm. Initially, a candidate path set for users is constructed. Let \(\mathcal{P}_{m}\) denote user \(m\)'s candidate paths, and \(\mathcal{P}_{mn}\subset\mathcal{P}_{m}\) represent candidate paths from node \(n\) to user \(m\). The complete set of candidate paths for all users forms the path set \(\mathcal{P}\). Constructing the candidate path set relies primarily on the adjacency matrix for candidate service and relay nodes. The relay nodes' adjacency matrix is established during network setup. Selecting candidate service nodes involves matching user demands with the cached content at service nodes. Specifically, a hit event \(h_{mn}=1\) indicates that user \(m\) has been successfully matched with service node \(n\), therefore designating node \(n\) as a candidate service node for user \(m\). Path \(p_{mn}^{k}\in\mathcal{P}_{m}\) represents the \(k\)-th path from service node \(n\) to user \(m\). If this path is selected, the data rate of this path is \(r_{mn}^{k}\in\Re^{+}\). Therefore, the achievable rate of user \(m\) is the aggregate rate of all selected paths, i.e., \(\sum_{p_{mn}^{k}\in\mathcal{P}_{m}}r_{mn}^{k}\). According to the _Article 5.523A_ of the ITU Radio Regulations [29], Non-Geostationary Orbit (NGSO) satellites can share the 18.8-19.3 GHz and 28.6-29.1 GHz frequency bands with geostationary orbit (GEO) satellites, provided they do not cause unacceptable interference to GEO satellites. To ensure compliance, the ITU has established an EPFD limit [29]. EPFD is the aggregate power flux density received by a ground station or a GEO orbit receiving station from all transmitting stations within the NGSO satellite system, accounting for the off-axis discrimination of a reference receiving antenna. The ITU specifies the EPFD value, which is controlled by LEO satellites to limit interference to GEO satellites; it is  
Figure 1: Heterogeneous Satellite Network Scene Model. not determined through GEO-LEO satellite interaction. The EPFD expression is given as follows [30; 31]:  
\[EPFD=10\log\left(\sum_{i=1}^{N}p_{i}\frac{G_{t}(\theta_{i})}{4\pi d_{i}^{2}} \cdot\frac{G_{r}(\varphi_{i})}{G_{r\max}}\right) \tag{1}\]  
where \(p_{i}\) represents the transmit power of the LEO satellite, \(G_{t}(\theta_{i})\) is the antenna gain of the LEO satellite at off-axis angle \(\theta_{i}\), \(G_{r}(\varphi_{i})\) is the antenna gain of the GEO satellite ground station at off-axis angle \(\varphi_{i}\), \(d_{i}\) is the distance between the LEO satellite and the GEO satellite ground station, and \(G_{r\max}\) is the maximum gain of the receiving antenna. Figure 2 illustrates the off-axis angles \(\theta\) and \(\varphi\), and the interference distance \(d\). As shown in Equation (1), the interference EPFD received by the GEO satellite is inversely proportional to the interference distance and off-axis angles and directly proportional to the transmit power. Since the distance and off-axis angles can be calculated based on the physical positions of the nodes, the EPFD value can be adjusted by controlling the transmit power. Table 2 lists the EPFD thresholds set by the ITU, where the carrier bandwidth for interference scenarios is 40 kHz. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & **Frequency (GHz)** &
\begin{tabular}{c} **EPFD Threshold** \\ **(dB(W/m2))** \\ \end{tabular} \\ \hline Uplink & 28.6–29.1 & \(-162\) \\ Downlink & 18.8–19.3 & \(-164\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: GEO–LEO satellite interference thresholds [29]. Figure 2: Schematic diagram of antenna off-axis angle and interference distance.