## 4 Numerical and Simulation Results  
This section provides the numerical results along with the relevant discussion. To verify the accuracy of the expressions, we compare the analytical results with Monte Carlo simulation results and the parameters for numerical results can be seen in Table 2.  
Figure 2 shows the outage probability as a function of increasing values of SNR. In general, one can note that the outage probability decreases with an increase in the values of SNR. This is true for both the NOMA and OMA schemes. As expected, for the same values of SNR, the outage probability of DF relays is less than that of AF relays. This is independent of multiple access techniques. However, NOMA outperforms OMA for both DF and AF relaying. Additionally, the simulation results closely follow the analytical curves which indicate the accuracy of the derived expressions. \begin{table}
\begin{tabular}{l l} \hline \hline
**Definition** & **Values** \\ \hline Monte Carlo simulations repeated & \(10^{6}\) iterations \\ Power allocation coefficients & \(\Xi_{1}=0.8\) and \(\Xi_{2}=0.2\) \\ Target rate & \(R_{1}=0.5\) and \(R_{2}=1\)(BPCU) in which BPCU is short for bit per channel use. \\ The average shadowing (AS) & \((m_{SR}=5,b_{SR}=0.251,\Omega_{SR}=0.279)\) \\ The heavy shadowing (HS) & \((m_{SR}=1,b_{SR}=0.063,\Omega_{SR}=0.0007)\) \\ The energy conversion efficiency & \(\eta=0.9\) \\ The power splitting factor & \(\chi=0.1\) \\ The factor and mean of \(D_{i}\) & \(\Omega_{1}=\Omega_{2}=1\) and \(m_{1}=m_{2}=1\) \\ The antennas of satellite and \(D_{i}\) & \(M=1\) and \(N_{i}=1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Table of parameters for numerical results. Figure 3 indicates the impact of power allocation coefficients \(\Xi_{1}\) on the outage performance. The lowest outage probability can be observed in the range of \(\Xi_{1}\) from 0.5 to 1 for case of users \(D_{1}\) and \(D_{2}\) in AF mode. It is worth noting that the performance gap among two users in NOMA scheme is resulted from different power allocation coefficients while outage probability remains unchanged in OMA scheme. Figure 4 shows the outage probability of \(D_{1}\) as the function of transmitting SNR. It can be seen that the outage probability decreases with an increase in transmitting SNR. The comparison is provided between the outage probabilities of AS and HS communication conditions. Please note that the outage probability of HS is significantly higher than the outage probability of AS. This is because the outage probability is hampered by the communication conditions between satellite and relay. It can also be noted that the difference between the outage probabilities of AF and DF relays is reduced for larger values of Nakagami-\(m\) factors. Figure 3: The outage probability versus the power allocation coefficients \(\Xi_{1}\). Figure 2: The outage probability versus transmit SNR. Similar trends can be observed in Figure 5 where the outage probability of \(D_{2}\) is plotted against the transmitted SNR. However, we note that the Nakagami-\(m\) factor has a completely different impact on the outage probabilities in this scenario. As opposed to Figure 4, the outage probability curves of AF and DF in Figure 5 are closer to each other at lower values of the Nakagami-\(m\) factor. This shows that the larger values of \(m\) have more impact on the outage performance of AF and DF relays. Figure 6 shows the outage probability against the power-splitting factor of \(\chi\). Please note that larger values of \(\chi\) indicate that the more power is reserved for information processing while the rest is reserved for energy harvesting. One can observe that with an increase in the values of \(\chi\), the outage probability first decreases and then increases illustrating a convex trend. This is mainly due to the functionality of the terrestrial relay. Initially, more power is reserved at relay for energy harvesting, and, around \(\chi=0.3\), the outage probability reaches the lowest value.