## 6 Conclusions  
In this paper, we proposed a beam-hopping resource scheduling algorithm to efficiently allocate time slots, bandwidth, and power resources in the LEO communication scenario that shares spectrum with GEO communication systems. While achieving interference avoidance, the throughput and access success rate of the system are improved, and the communication delay is reduced. First, the illumination pattern is determined through a weighted greedy strategy, which ensures the fairness of cell services to a certain extent. Then, the active cells in the current time slot are clustered by interference clustering to reduce the search space. Finally, the joint allocation of bandwidth and power is carried out in each cluster through a genetic algorithm with optimal control.  
Simulation results show that compared with the polling or random beam hopping strategy, our algorithm can flexibly achieve on-demand services for differentiated user needs, and has more advantages in scenarios with uneven user demand distribution. Meanwhile, compared with the traditional genetic algorithm (GAWIC-BH), our improved algorithm can obtain a solution with better performance at 1/4 the number of iterations, and with the increase of traffic intensity, this advantage is gradually significant. Specifically, in the scenario of uneven traffic distribution, when the traffic intensity is large, the system capacity obtained by our proposed mechanism is 70.3%, 150%, and 8.2% higher than that of polling-BH, random BH and GAWIC-BH, respectively. Our mechanism achieves the maximum access success rate of 92.7% and minimum average delay of 132 ms among all schemes while ensuring service fairness between cells.  
With the development of satellite Internet, the efficient and flexible scheduling of low-orbit satellite resources is the focus of future research. This paper mainly focuses on downlink beam scheduling, and we can comprehensively take the uplink scenario into consideration in future research. Furthermore, considering the dynamic mobility of LEO satellites and the multiple coverage of mega-constellations, multi-satellite joint resource scheduling will be studied to achieve more flexible resource allocation and interference avoidance of GEO systems.  
Conceptualization, S.G. and X.J.; methodology, S.G., K.H., L.L. and F.T.; investigation, S.G. and K.H.; writing--original draft preparation, S.G.; writing--review and editing, W.G. and F.T.; supervision, W.G.; project administration, S.G. and W.G.; funding acquisition, F.T. and W.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Youth Innovation Promotion Association of Chinese Academy of Sciences (grant number 2021291) and Shanghai Industrial Collaborative Innovation Project (grant number 2021-CYXT2-KJ03).  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Beam** & **Traffic** & **Throughput** & **Access** & **Average** & **Delay** \\
**Acheme** & **Distribution** & **(Gbps)** & **Success Rate** & **Delay (ms)** & **Variance** \\ \hline \multirow{2}{*}{Polling-BH} & even & 2.789 & 87.6\% & 132.96 & 9543 \\  & uneven & **1.739** & **54.5\%** & **157.10** & **15,643** \\ \hline \multirow{2}{*}{Random-BH} & even & 1.407 & 44.22\% & 341.91 & 2930 \\  & uneven & **1.185** & **37.1\%** & **259.35** & **6815** \\ \hline \multirow{2}{*}{GAWIC-BH} & even & 2.851 & 89.6\% & 167.20 & 324 \\  & uneven & **2.738** & **85.7\%** & **219.82** & **1527** \\ \hline \multirow{2}{*}{Our Algorithm} & even & 3.039 & 95.5\% & 99.03 & 145 \\  & uneven & **2.962** & **92.7\%** & **131.96** & **4326** \\ \hline \hline \end{tabular}  
* Large traffic demand is defined as: Poisson arrival intensity is 700 packages under even distribution, 3100 in hotspots and 310 in non-hotspots under uneven distribution.  
\end{table}
Table 5: Comparison of the results of each algorithm in the two scenarios when traffic is large 1.