# High Reliable Uplink Transmission Methods in GEO-LEO Heterogeneous Satellite Network
## 5 Simulation Results
### Outage Probability Without Channel Ordering  
In this subsection, we focus on the outage probability performance without Assumption 1. We first consider the FHS channel condition. The values of achievable rate for \(U_{1}\) and \(U_{2}\) are set as \(R_{1}=0.4\) bps and \(R_{2}=0.3\) bps. The power factor for \(U_{2}\) is assumed as \(\alpha=0.2\). Figure 3 illustrates the results of outage probability with variable \(\beta\). It is clearly shown that the curves of analytical expressions perfectly match with those of numerical simulations, which validates the correctness of Theorems 1 and 2. From Figure 3, we can deeply find out that the NOMA method outperforms the cooperative OMA in the low-SNR region; even \(U_{2}\) could not be guaranteed in the OMA scheme. It can be explained by the fact that interference from \(x_{2}\) exists when decoding the signal of \(U_{1}\) in uplink NOMA. In this case, the outage probability of \(U_{1}\) could not be improved; even SNR grows to high values. Since\(x_{1}\) should also be demodulated when decoding the signal of \(U_{2}\), the outage probability error floor could not be avoided for the curve of \(U_{2}\). In addition, by substituting (10) and (14) into (24), respectively, the diversity order can be found as zero. Thus, the outage probability could not be improved even in the high-SNR region. However, we can choose to apply cooperative OMA when SNR is relatively high.  
Figure 4 shows the result in an AS transmission environment. It is noteworthy that the outage probability can be greatly improved since the channel condition is better compared with FHS. Again, we can derive the conclusion that the NOMA scheme performs better in the low-SNR region and is more friendly for beam-edge users. This is because the uplink signals of the beam-edge user experience more transmission path loss when the beam-edge user connects the GEO satellite in a cooperative OMA scheme. When we allocate more power resources to \(U_{2}\), cooperative OMA is more promising compared with NOMA, which can be clearly determined in Figure 5.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**System Parameter** & **Value** \\ \hline Orbit height of GEO satellite \(d_{g}\) & 36,000 km \\ \hline Orbit height of LEO satellite \(d_{l}\) & 700 km \\ \hline Carrier frequency & 28 GHz \\ \hline Angle of 3 dB beam width at the LEO satellite \(\theta_{3 dB}\) & 2.5\({}^{\circ}\) \\ \hline Beam gain of the GEO receive antenna \(G_{s}\) & 54 dB \\ \hline Normal-direction beam gain of LEO receive antenna \(G_{l}\) & 50 dB \\ \hline Transmit beam gain of user terminals \(G_{i}\) & 45 dB \\ \hline \hline \end{tabular}
\end{table}
Table 1: System parameters.  
Figure 3: Outage probability without channel ordering in FHS when \(\alpha=0.2\).  
From Figure 5, it can be clearly noticed that the outage probability performance of \(U_{1}\) in both methods degrades since more transmission power has been allocated to the beam-edge user. Fortunately, the performance of \(U_{2}\) can be improved by taking more power resources, which may help the cooperative OMA to be practicable in the low-SNR region.