## 5 Simulation Results and Performance Analysis  
In this paper, the proposed multi-beam satellite cooperative transmission scheme based on cross-layer and cross-dimension resources optimization and irregular gradient adaptive packet segmentation is evaluated by simulation based on MATLAB R2019a. In order to verify the proposed algorithm in this paper, the multi-beam satellite communication system is built, where the satellite constellation mainly adopts the features of OneWeb, whose parameters are shown in Table 1.  
As shown in Figure 7, the user generates multiple packets. Firstly, each packet is mapped to the radio bearer according to QoS. Secondly, the packets are segmented according to allocated radio resources, and each segmented packet \(a_{qi}^{c}\) is tagged with \(c\). Thirdly, each segmented packet is mapped to the different beams for transmission and processed in satellite. The receiver receives the packets of each beam separately. The PSS and SSS received are autocorrelated with the local SSS and PSS in order to complete the frame and time slot synchronization within each beam. Then the receiver caches the received packets. After multiple TTIs, when all segmented packets of one packet had been received, the segmented packets are sorted and reassembled according to their own label \(c\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Value** & \\ \hline \multirow{6}{*}{**LEO Constellation**} & **Altitude** & 1200 km \\  & **Number of orbital planes** & 18 \\  & **Number of satellite** & 40 per orbital plane \\  & **Frequency band** & Ka/Ku \\  & **User beam** & 4 elliptical beams \\  & **Feed beam** & 1 \\  & **EIRP** & 29.9 dBW \\  & **Service area** & 75,000 km\({}^{2}\) per satellite \\  & **Beam footprint size** & \(5000\) km\({}^{2}\) per beam \\  & **Beam pattern** & \(\theta=\pm 55^{\circ}\) \\ \hline \multirow{6}{*}{**Packet**} & **Transmission delay** & \multicolumn{2}{c}{450 ms} \\  & **Voice** & Delay: 100 ms, Priority: 2 \\ \cline{1-1}  & **Video** & Delay: 150 ms, Priority: 3 \\ \cline{1-1}  & **Game** & Delay: 50 ms, Priority: 1 \\ \cline{1-1}  & **Http** & Delay: 300 ms, Priority: 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The simulation parameters. Under multi-beam satellites coverage, we mainly consider the normalized system throughput and user satisfaction index with four communication scenarios as shown in Figure 8, that is, single-satellite single-beam multi-user, single-satellite multi-beam multi-user, multi-satellite single-beam multi-user, and multi-satellite multi-beam multi-user. In the simulation, the parameters of the firefly algorithm are shown in Figure 8. Comparing scenario (a) with (b), it can be clearly seen that the normalized system throughput is significantly improved due to the increase of beam. Comparing scenario (b) with (c), there is interference between users when the beams of different satellites share bandwidth. The SINR is reduced. The normalized system throughput is reduced. Comparing scenario (b) with (d), when multiple satellites serve multiple users, while the quality of resources that users can allocate become worse, the normalized system throughput is even much higher than that of other scenarios because of the large bandwidth, coordination transmission between multi-beam and flexible allocation according to user demands. As shown in Figure 9, Figure 9a abstractly represents the part of radio resources of multi-beam satellites, where the yellow parts are available resources that can be allocated to users. Figure 9b abstractly shows the part of radio resources that are allocated to different packets in scenario (d). Different colors indicate radio resources that are allocated to different packets. Figure 10 shows the index of the optimal resources that are selected in an iteration by using the cross-layer and cross-dimension radio resources optimization model based on the weighted discrete firefly algorithm. Figure 8: Normalized throughput for different scenarios. (a) Single-satellite single-beam multi-user.