# RIS-Assisted Fixed NOMA: Outage Probability Analysis and Transmit Power Optimization
## 6 Simulations and Discussion  
In this section, outage, and sum capacity performances of RIS-SR-FNOMA and RIS-AP-FNOMA are simulated and analyzed using MATLAB R2023a. Table 1 lists the parameters assessed for the simulation. The results of the MC simulation are obtained by averaging the outage probability across \(10^{5}\) iterations. The outage performance results are shown in Figure 3 for the FU and NU in RIS-SR-FNOMA and conventional FNOMA. It is assumed that \(\alpha_{NU}=0.1\) and \(\alpha_{FU}=0.9\). The total RIS elements of \(N=64\) with 32 elements each for NU and FU are considered. In comparison with RIS-SR-FNOMA, FNOMA without RIS has poor outage performance. In the RIS-SR-FNOMA system, the SNR requirements to procure the target probability of outage are \(-22\) dB and \(-13\) dB for FU and NU, respectively. Since more power is allocated to FU, the outage performance of FU is better than NU for both systems. It is shown that the MC simulation curves closely or exactly match with the analytical results. The outage performance results of the FU and NU of RIS-SR-FNOMA are indicated in Figures 4 and 5, respectively, at various numbers of reflective elements with \(\alpha_{NU}=0.2\) and \(\alpha_{FU}=0.8\). With \(N=32\), \(N=64\), \(N=128\) and \(N=256\), the FU of RIS-SR-FNOMA achieves the expected outage probability at an approximate SNR of \(-8\) dB, \(-21\) dB, \(-28\) dB and \(-35\) dB, respectively. The amount of reflecting elements in RIS is found to improve outage performance. As the CLT approximation of \(B\) holds true for higher \(N\), at \(N=128\) and \(N=256\), a close match between MC simulation and analytical curves is observed compared to \(N=32\) and \(N=64\). On comparing the outage performance of the NU and FU in Figures 4 and 5, it is evident that the FU outage performance is superior to the NU outage performance. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Typical Value** \\ \hline Number of RIS components (\(N\)) & 32, 64, 128, 256 \\ Number of users & 2 \\ Mean channel gain of NU & 5 \\ Mean channel gain of FU & 1 \\ Desired rate of NU (\(\tilde{R}_{NU}\)) & \(1\) b/s/Hz \\ Desired rate of FU (\(\tilde{R}_{FU}\)) & \(1\) b/s/Hz \\ Target outage probability & \(10^{-4}\) \\ Block length & \(10^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 3: Analysis of outage probability between RIS-SR-FNOMA and FNOMA. The sum capacity of RIS-SR-FNOMA is shown in Figure 6 for different \(N\). The sum capacity for all \(N\) increases as the transmit SNR increases. At SNR of \(-10\) dB, the sum capacities are approximately 6.1 b/s/Hz, 8.1 b/s/Hz, 10.2 b/s/Hz and 12.2 b/s/Hz when \(N=32\), \(N=64\), \(N=128\) and \(N=256\) respectively. When the optimal powers are allocated, there is an improvement in the sum capacity over the sub-optimal power assignment for lower SNR. At higher SNR, the optimal and sub-optimal methods have essentially identical sum capacities. Figure 4: Comparison of RIS-SR-FNOMA FU outage probability by varying \(N\). Figure 5: Comparison of RIS-SR-FNOMA NU outage probability by varying \(N\). The simulation parameters for the RIS-AP-FNOMA system are assumed to be the same as those given in Table 1. The outage performance results of RIS-AP-FNOMA and conventional FNOMA are shown in Figure 7. The desired rates and power for FU and NU, as well as \(N\), are set as being similar to Figure 3. In comparison with RIS-AP-FNOMA, FNOMA without RIS has poor outage performance. In the RIS-AP-FNOMA system, the SNR requirements to achieve expected outage probability are \(-25\) dB and \(-15\) dB for FU and NU, respectively. Since more power is assigned to the FU, the outage performance of the FU is better than the NU for both systems. It is shown that the MC simulation curves closely or exactly match the analytical results. When comparing Figures 3 and 7, RIS-AP-FNOMA has a modest improvement over RIS-SR-FNOMA in terms of outage performance.