# Outage Probability Analysis in Relaying Cooperative Systems with NOMA Considering Power Splitting
## 4 Numerical Results  
In this section, we prove the correctness of the system by providing simulation results. In addition, comparisons with Monte Carlo performance results are also given. It is noted that we generate \(10^{6}\) realizations of Rayleigh distribution. In addition, we assume \(S\), \(R\) and \(D\) are collinear with \(R\) located between \(S\) and \(D\). For simplicity of presentation, we summarize the used parameters in Table 1.  
In Figure 3, we compare \(OP\) with two defined thresholds in two cases, i.e., Case 1: \(\gamma_{0}=1\) and Case 2: \(\gamma_{0}=3\) (\(\mathrm{bps}/\mathrm{Hz}\)). It is clear that the lower the threshold is, the better \(OP\) becomes. In contrast, the \(OP\) falls when \(\beta\) climbs. In principle, when \(\beta\) rises, both \(S\) and \(R\) harvest more energy, so there is more energy for IT in the next hop. In this situation, the outage performance of \(x_{1}\) is superior to that of \(x_{2}\) due to the deployment of \(R\). In Figure 4, the throughput in the delay-limited transmission mode is presented as a function of \(\beta\) in the two cases regarding distances, including Case 1: \(d_{SR}=0.2\) and Case 2: \(d_{SR}=0.3\). We can see that \(x_{1}\) enjoys better throughput due to its lowest \(OP\), the short distance between \(S\) and R, and the higher amount of harvested energy. It also presents the throughput ceilings at high SNR regime because the \(OP\) increasingly approaches zero, and the throughput is determined by the pre-defined data rate. However, regarding \(x_{2}\), the throughput is worse because of the lack of energy for information decoding, so outage events can occur which compromise the throughput performance. As a result, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbols** & **Parameter Names** & **Values** \\ \hline \(R_{0}\) & Source rate & \(1\) (\(\mathrm{bps}/\mathrm{Hz}\)) \\ \(\rho\) & PS ratio & 0.2 \\ \(m\) & Path-loss & 2.7 \\ \(\eta\) & Energy harvesting efficiency & 0.8 \\ \(d_{SD}\) & Distance of \(S\)-D link & 1 \\ \(d_{SR}\) & Distance of \(S\)-R link & 0.3 \\ \(d_{RD}\) & Distance \(R\)-D link & \(d_{SD}-d_{SR}\) \\ \(\Omega_{f_{1}}\) & Mean of the exponential RVs \(|f_{1}|^{2}\) & 1 \\ \(\Omega_{f_{2}}\) & Mean of the exponential RVs \(|f_{2}|^{2}\) & 1 \\ \(\Omega_{f_{3}}\) & Mean of the exponential RVs \(|f_{3}|^{2}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 3: Outage probability (\(OP\)) versus the transmit SNR, \(\beta\). the suitable placement of \(R\) in the design of practical CR-NOMA transmission systems is proved to be important. As illustrated in Figure 5, the throughput performance of both CR-NOMA and traditional CR-OMA is depicted versus the PS ratio. It is noted that we set the transmit power, \(P_{S}\) to two fixed values of 0 (dB) and 5 (dB). It is clear that the throughput performance of CR-NOMA is significantly higher compared to CR-OMA, in which the performance gap becomes clear during the end of the period. This is because due to the deployment of SIC at \(D\) in the second time slot, the transmission of data symbol \(x_{2}\) becomes possible. In addition, thanks to the use of R, the distance between \(R\) and \(D\) can be effectively reduced to minimize the fading gain of \(x_{1}\). In Figure 6, the ABEP is presented as a function of the transmit SNR, \(\beta\). It is obvious that due to the high quality of the \(R\)-\(D\) link, the ABEP for the data symbol \(x_{1}\) also improves. Nevertheless, the gap between the corresponding curves becomes noticeable as \(\rho\) climbs, especially with the data symbol \(x_{2}\). Additionally, the ABEP of \(x_{2}\) is limited to the transmit power of the \(R\)-\(D\) link. Figure 4: Throughput versus the transmit SNR, \(\beta\). Figure 5: Throughput versus power splitting (PS) ratio, \(\rho\). As depicted in Figure 7, we present the transmission rate as a function of the transmit SNR, \(\beta\) when \(a_{1}=0.9,a_{2}=0.1\), and \(\Omega_{f_{1}}=\Omega_{f_{2}}=10\)(dB), and \(\Omega_{f_{3}}=1\)(dB).