# Hierarchical Resource Management for Mega-LEO Satellite Constellation
## 7 Performance Assessments
### Simulation Results  
To validate the performance improvement in the presented hierarchical resource management architecture for the MLSCS, we conducted several simulations using STK10 and Matlab 2018b in this section and the simulation parameters in Table 3.  
Figure 10 presents the simulation results of the bandwidth utilization rate for both the two-stage game management and the single SBS management. The figure shows that the bandwidth utilization rate of the two-stage game management is approximately 37\(\sim\)50% higher than that of the single SBS management. This significant improvement in bandwidth utilization results in substantial savings of spectrum resources in systems with limited spectrum availability.  
The throughput per beam against the number of UTs in a cell is simulated and presented in Figure 11. As shown in the figure, with the increase in the number of users per beam, the throughput per beam gradually increases. However, due to the limited beam capacity, the increase in user numbers leads to collision issues, resulting in a non-linear increase that gradually plateaus. When user scheduling is implemented, compared to without user scheduling, the throughput improves by approximately 25%. Additionally, the throughput of high-order MODCOD sets is larger than that of low-order ones.  
Figure 12 gives the throughput per SBS against the number of UTs in the coverage area of this SBS with user scheduling. The figure presents the simulation results of throughput under different modulation and coding schemes, comparing scenarios with and without beam scheduling (Algorithm 1) in a single SBS. As the number of users increases, the throughput gradually increases, but the growth is not linear and eventually reaches a bottleneck. In the case with beam scheduling, the throughput can be improved by over 30% at maximum, and the advantage becomes more pronounced as the number of users increases.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Constellation type & Polar walker \\ Number of satellites & 288 \\ Number of beams per satellite & 8 \\ Altitude of LEO satellites & 1025 km \\ Speed of satellites & 7.447 km/s \\ LEO satellite 3 dB beamwidth & 3\({}^{\circ}\) \\ LEO satellite coverage radius & 1189 km \\ LEO beam coverage radius & 53.8 km \\ Number of user terminals & 10,000 \\ User distribution & Random \\ Mean value of Poisson arrival for service & 0.3 \\ Interval of beam-hopping & 200 ms \\ Cycle of beam-hopping & 10 s \\ Maximum total power of LEO satellites & 1000 W \\ Maximum power on each subchannel of LEO satellites & 40 W \\ LEO satellite antenna \(\eta\) & 20 dB \\ Terminal antenna \(\eta\) & 20 dB \\ Noise power spectral density & \(-\)173 dBm/Hz \\ Average radius of hot-spot regions & 10 km \\ Carrier frequency of Ka band & 30 GHz \\ Bandwidth & 5/25 MHz \\ Coding & \(\frac{1}{2}\)Turbo \\ Modulation & BPSK/QPSK \\ Packet size & 1024 bits \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation parameters.  
Figure 11: Throughput per beam (Mbps) with different number of UTs and different MODCOD sets.  
Figure 12: Throughput per SBS (Mbps) vs. UTs per SBS with different beam scheduling schemes and MODCOD sets.  
Figure 10: Bandwidth utilization rate of only SBS management and two-stage game management.  
Figure 13 presents the system throughput with 288 SBSs against the number of UTs all over the world with user and beam scheduling. As can be seen from the figure, spectrum sensing and scheduling bring a certain gain to the system throughput. With the increase in the number of global users, the system throughput also increases, following a similar trend to that observed in Figures 12 and 13. However, when spectrum sensing and scheduling capabilities are in place, the system throughput can be improved by up to 38% or more. Furthermore, the gain from spectrum resource scheduling becomes more significant as the number of users increases.