# RIS-Assisted Fixed NOMA: Outage Probability Analysis and Transmit Power Optimization
## 6 Simulations and Discussion
The outage performance results of the FU and NU of RIS-AP-FNOMA are shown in Figures 8 and 9, 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-AP-FNOMA achieves the expected outage probability at approximately \(-15\) dB, \(-24\) dB, \(-31\) dB and \(-37\) dB, respectively. It is observed that increasing \(N\) in RIS enhances the  
Figure 6: Sum capacity (b/s/Hz) of RIS-SR-FNOMA for optimal and sub-optimal power assignments and varying \(N\). Figure 7: Analysis of outage probability between RIS-AP-FNOMA and FNOMA. outage performance. As the CLT approximation of \(C\) holds true for higher values of \(N\), at \(N=64\), \(N=128\) and \(N=256\), a close match between the MC simulation and analytical curves is observed compared to \(N=32\). On comparing the outage performance of the NU and FU in Figures 8 and 9, it is evident that the FU outage performance is superior to the NU outage performance. When comparing Figures 4 and 5 with Figures 8 and 9, RIS-AP-FNOMA has a modest improvement over RIS-SR-FNOMA in terms of outage performance. The sum capacity (\(\mathrm{b/s/Hz}\)) of the RIS-AP-FNOMA is shown in Figure 10 for different \(N\) in RIS. The sum capacity for all \(N\) increases as the transmit SNR increases. At SNR of \(-10\) dB, the sum capacities are 6.5 b/s/Hz, 8.5 b/s/Hz, 10.5 b/s/Hz and 12.5 b/s/Hz when \(N=32\), \(N=64\), \(N=128\) and \(N=256\), respectively. When optimal powers are assigned, 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 8: Comparison of RIS-AP-FNOMA FU outage probability by varying \(N\). Figure 3:0 Comparison of RIS-AP-FNOMA NU outage probability by varying \(N\). For optimal and sub-optimal power assignments, the sum capacities (b/s/Hz) of ENOMA, RIS-AP-ENOMA, and RIS-SR-ENOMA systems are analyzed in Figure 3:1 The sum capacities of the RIS-AP-ENOMA and RIS-SR-ENOMA systems are calculated for the number of passive elements \(N=32\). The ENOMA system has reasonable sum capacities for positive values of SNR, whereas the RIS-SR-ENOMA and RIS-AP-ENOMA systems have good sum capacities, even for negative SNR values. The array and diversity gains via RIS-assisted communication result in an increase in capacity. With higher SNR values of RIS-AP-ENOMA and RIS-SR-ENOMA systems, the sum capacity difference between optimal and sub-optimal power assignments decreases. The RIS-AP-ENOMA system has a slightly higher sum capacity compared with the RIS-SR-ENOMA system. When optimal power allocation is employed at RIS-AP-ENOMA and FNOMA systems, the approximate sum capacities of 13.2 b/s/Hz and 5 b/s/Hz are achieved, respectively, for an SNR of 10 dB. The RIS-AP-ENOMA system has a 62% higher sum capacity than the FNOMA system. Figure 3:2 Sum capacity (b/s/Hz) comparison of FNOMA, RIS-SR-ENOMA and RIS-AP-ENOMA for optimal and sub-optimal power assignments. Figure 3:3 Sum capacity (b/s/Hz) of RIS-AP-ENOMA for optimal and sub-optimal power assignments and varying \(N\).