# Beam-Hopping-Based Resource Allocation in Integrated Satellite-Terrestrial Networks
## 6 Simulation Results  
Consider the downlink transmission scenario in an ISTN, which consists of one LEO satellite system and multiple terrestrial systems. The LEO satellite system consists of an LEO satellite and \(N_{sat}=16\) satellite terminals. Within the footprint of the satellite, the locations of the satellite terminals are generated by a Poisson point process [30]. The inter-system protection distance \(d_{pro}^{st}\), is set to 52 Km, which is equal to the coverage radius of the satellite beam [10; 24]. According to the analysis in [23; 24], the inter-beam distance threshold \(d_{th}^{sat}\) used in the greedy algorithms is set to twice the diameter of the satellite beam, so the CCI among the satellite beams is negligible. There are \(N_{ter}=16\) terrestrial systems within the footprint of the satellite. The locations of the terrestrial BSs are modeled by an MHP [30]. The path loss model and the shadowing standard deviation in the urban microcell (UMi) line-of-sight (LOS) scenario are considered in the terrestrial systems. Assuming \(d_{j}^{ter}\) denotes the distance between the terrestrial BS and the terrestrial terminal in the \(j\)-th terrestrial system, the path loss in dB can be expressed as [32]  
\[L_{j}^{ter}(\text{dB})=32.4+21\log_{10}(d_{j}^{ter})+20\log_{10}(f). \tag{32}\]  
The UMi cell radius is typically set to 500 m [32]. The capacity requirements and the average traffic demands of the satellite terminals and the terrestrial systems are independent random variables that follow the uniform distribution. These random variables are independently generated, which makes the distribution of the capacity requirements and the traffic demands uneven. The simulation parameters are summarized in Table 1.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline \multicolumn{3}{c}{ISTN common parameters} \\ Carrier frequency & \(f\) & 19.5 GHz \\ Transmission bandwidth & \(W\) & 500 MHz \\ Number of time slots in a BH time window & \(N_{slot}\) & 50 \\ Time slot period & \(T_{slot}\) & 1 ms \\ Inter-system protection distance & \(d_{pro}^{st}\) & 52 Km \\ Weighting factor & \(\gamma\) & 0.1 \\ \hline \multicolumn{3}{c}{Satellite system parameters} \\ Satellite orbit height & \(h_{s}\) & 1000 Km \\ Number of satellite terminals & \(N_{sat}\) & 16 \\ Number of spot beams & \(N_{b}\) & 4 \\ Transmit power per beam & \(P_{b}^{sat}\) & 4 dBw \\ Boltzmann constant & \(K\) & \(1.38\times 10^{-23}\) \\  & & \(\text{W}/(\text{Hz}\cdot\text{K})\) \\ Receiver noise temperature & \(T_{n}\) & 293 K \\ Peak transmitting antenna gain & \(G_{T,0}^{sat}\) & 31 dBi \\
3 dB beam width of the transmitting antenna & \(g_{MB}\) & 2.98\({}^{*}\) \\ Peak receiving antenna gain & \(G_{R,0}^{sat}\) & 36 dBi \\ inter-beam distance threshold & \(d_{th}^{sat}\) & 200 Km \\ \hline \multicolumn{3}{c}{Terrestrial system parameters} \\ Number of terrestrial terminals & \(N_{ter}\) & 16 \\ Transmit power per BS & \(p_{j}^{ter}\) & 0 dBw \\ Noise power & \(N_{0}^{totr}\) & \(-113\) dBw \\ Transmitting antenna gain & \(G_{T}^{trr}\) & 10 dBi \\ Receiving antenna gain & \(G_{R}^{latr}\) & 3 dBi \\ Scenario of path loss model & & UMi LOS \\ Shadowing standard deviation & & 4 dB \\ UMi cell radius & \(d_{j}^{tor}\) & 500 m \\ Minimum separation distance & \(\delta\) & 52 Km \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.