# A Beam Hopping Scheme Based on Adaptive Beam Radius for LEO Satellites
## 4 Presentation and Analysis of Simulation Results
### Comparison of Proposed and Traditional Algorithms with an Increasing Population  
In this simulation, we change each cell's population from 0.6 times the population to 1.4 times the population to examine the gap between two kinds of algorithms.  
Figure 14 depicts the variation in system performance based on the proposed algorithm and the traditional algorithm as the number of users increases from 0.6 times to 1.4 times the original number. It can be observed that as the number of users increases, the system throughput also increases. This is because when calculating throughput, the actual throughput is considered, i.e., the minimum value between user demand and provided throughput. Therefore, when user demand increases, the system throughput either in-creases or remains unchanged. The increase in throughput indicates that the system capacity fully meets the total business requests of the benchmark user population; conversely, if the system throughput does not increase further, it suggests that the total business re-quests of the user population cannot be met. The simulation results in the figure also indicate that the increase in system throughput is not linear but slows down over time, influenced by the upper limit of system throughput.  
Considering the variation in system delay, it can be observed that as the number of users increases, the total system delay also increases. This is because LEO broadband  
Figure 13: Comparison of the proposed and traditional algorithms with an increasing number of beams.  
satellites are typical resource-constrained communication nodes with limited payload capacity. Therefore, they cannot serve all users simultaneously. When the number of users in-creases, the number of users served by LEO broadband satellites also increases, but at the same time, the number of unserved users also increases, leading to an overall increase in system delay.  
Considering the performance variation of the algorithm with changes in the number of users, it can be seen that as the number of users increases, the gap between the system performance based on the proposed algorithm and that based on the traditional algorithm gradually widens. Specifically, as the number of users increases, the gap in system delay between the traditional algorithm and the proposed algorithm gradually increases. This is because with more users, the number of non-hotspot area users also increases, and the proposed algorithm is better able to ensure their QoS, thereby reducing the total system delay. On the other hand, considering the throughput of the proposed algorithm and the traditional algorithm, it is observed that as the number of users increases, under equal user conditions, the system throughput obtained by the proposed algorithm gradually decreases compared to that obtained by the traditional algorithm. This is because, on one hand, the proposed algorithm introduces wide beams, leading to stronger potential  
Figure 14: Comparison of the proposed and traditional algorithms with an increasing number of beams.  
interference and reduced system throughput. On the other hand, as the number of users in-creases, the service demand of former non-hotspot areas exceeds the service capacity of large beams, making them hotspot areas. Limited by the weaker service capability of large beams, the system throughput cannot achieve the same level of system performance as the traditional algorithm.