## 3 Simulation and Results
As shown in Figure 10, the total capacity of the NGSO satellite, due to its close relationship with the SINR of each link, appears significantly improved as well. Although the rotation angle of the equilateral hexagon configuration of the coverage area brings about a slight improvement in total capacity, it changes a lot during the simulation period. As time passes, the rotation angle progressively drops to \(0\) from \(30^{\circ}\) in the beginning. After jumping a few times, the rotation angle gradually decreases from nearly \(60^{\circ}\)to \(30^{\circ}\). For the scenario where GSO and NGSO satellites are equipped with \(19\) beams and \(37\) beams, it is difficult for the enumeration method to solve for the solution, so we only use the beam search algorithm. It takes about ten minutes and half an hour to find the solutions for the \(19\)-beam and \(37\)-beam scenarios, respectively. For the \(19\)-beam scenario, it is clear from Figure 11 that, after channel allocation, the minimum SINR raises from about \(-10\) dB to \(31\) dB. Moreover, compared with the seven-beam scenario, before channel allocation, five GSO ground stations bear much more severe interference than other stations. It is because when the NGSO satellite moves from south to north, the subsatellite point will directly cross the five GSO beams in the \(19\)-beam scenario. As shown in Figure 12, due to the tremendous increment in SINR after channel allocation, total capacity presents less sharp variation compared with the seven-beam scenario. As for the change of rotation angle, it has much jumping in its value during the simulation period, and it is hard to find the rule of change behind it. The variation of SNR and SINR are presented in Figure 13 and the change of total capacity and rotation angle are presented in Figure 14 for the \(37\)-beam scenario. It is evident that, after channel allocation, the SINR has an apparent elevation, and the total capacity rises to a level where the interference is negligible, demonstrating the effectiveness of the presented channel allocation method. The rotation angle stays close to \(60^{\circ}\)at the beginning and the end of the simulation, but its value is widely distributed within a reasonable range. Figure 10: Change of total capacity with and without channel allocation and variation of rotation angle for the seven-beam scenario. (**a**) Change of total capacity with and without channel allocation for the seven-beam scenario; (**b**) Variation of rotation angle for the seven-beam scenario. Figure 11: SNR and SINR of different GSO ground stations in different beams for the 19-beam scenario without and with channel allocation. (**a**) SNR and SINR of different GSO ground stations in different beams for the 19-beam scenario without channel allocation; (**b**) SNR and SINR of different GSO ground stations in different beams for the 19-beam scenario with channel allocation. Figure 12: Change of total capacity with and without channel allocation and variation of rotation angle for the 19-beam scenario. (**a**) Change of total capacity with and without channel allocation for the 19-beam scenario; (**b**) Variation of rotation angle for the 19-beam scenario. Figure 13: SNR and SINR of different GSO ground stations in different beams for the 37-beam scenario without and with channel allocation. (**a**) SNR and SINR of different GSO ground stations in different beams for the 37-beam scenario without channel allocation; (**b**) SNR and SINR of different GSO ground stations in different beams for the 37-beam scenario with channel allocation.