## 4 Conclusions  
This paper focuses on interference avoidance with the existence of NGSO communication satellites equipped with multi-beam antennas. Channel allocation is chosen as our penetration point to reduce the interference of NGSO satellites system to other communication systems. A new channel allocation method to mitigate the interference based on the beam search algorithm has been developed. In our analysis, we take the scenario of sharing spectrum resources with a GSO satellite as an example. The relationship between the level of interference and the distance of beam centers has been explored. It is worth noticing that, for beams with a tilting angle, which is a common feature for satellites with multi-beam antennas, the tilting angle could bring about a significant change for the relationship between the distance of beam centers and off-axis angles. Therefore, a revised distance is introduced in order to reflect the interference more accurately using beam distance. We constrain that the distance between different co-channel beams with the condition that they should not be too close to each other to avoid severe interference. Furthermore, the rotation of the complete coverage area is taken into consideration as well to testify its effectiveness on mitigation of interference. The enumeration method is used to obtain the solution to the proposed optimization problem when the number of beams is small, and the beam search algorithm is selected when the scale of the problem is large so it would result in a shorter computational time.  
Several numerical simulations have demonstrated that the proposed channel allocation method could very effectively augment the SINR and total capacity of the interfered satellite system. The potential interference can be significantly mitigated. The simulation tells that the rotation of configuration of coverage areas has a slight impact on the increment of the total capacity of the communication system. It should be noted that, although in this article we select a GSO system to be the interfered system, the proposed channel allocation method is well suited for the scenario of an NGSO system suffering interference from other systems.  
[PERSON] completed preliminary research and provided the numerical part; [PERSON] and [PERSON] conceived and wrote the paper; and [PERSON] and [PERSON] supervised the overall work and reviewed the paper. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (No. 12022214).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Orbital Parameters** & **GSO** & **NGSO** \\ \hline Orbital altitude, \(h\) & 35,786.14 km & 1450 km \\ Eccentricity, \(e\) & 0 & 0 \\ RAAN, \(\Omega\) & 0 & 301\({}^{\circ}\) \\ Orbital inclination, \(i\) & 0 & 87.5\({}^{\circ}\) \\ Argument of perigee, \(\omega\) & 0 & 0 \\ True anomaly, \(\theta\) & 300\({}^{\circ}\) & 350\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Orbital parameters of GSO and NGSO satellites.