## 4 Simulation Results and Discussion
As per (23), a larger value of \(\delta_{H}^{2}\) decreases the term \(\left(-\frac{D_{WUI}}{(\alpha_{1}-\alpha_{2}D_{WUI})\mathrm{e}_{6}\delta_{H}^{ 2}}\right)\). The smaller value of negative exponential increases the \(exp\left(-\frac{D_{WUI}}{(\alpha_{1}-\alpha_{2}D_{WUI})\mathrm{e}_{6}\delta_{H}^ {2}}\right)\). This decreases the probability of outage for _WUI_. As \(N\) increases, there is a decrease in outage probability and simulation and analytical results are almost identical. It is observed that probability of outage performance of _SU_ is better than _WUI_ for various \(N\). In Figure 6, the outage performance of proposed system is analyzed for symmetric and asymmetric allocation of RIS elements to _SU_ and _WUI_. In symmetric scenario, equal number of RIS elements is allocated for _SU_ and _WUI_, whereas in asymmetric scenario, 75% of the elements are allocated to _WUI_ and remaining 25% of elements are allocated to _SU_. At SNR of 5 dB and for \(N=512\), the probability of outage of _SU_ is \(1.55\times 10^{-5}\) and \(2.03\times 10^{-5}\) for symmetric and asymmetric scenarios respectively. Similarly, the probability of outage of _WUI_ is \(0.0017\) and \(0.0014\) for symmetric and asymmetric scenarios respectively. Due to the allocation of 75% of the elements to _WUI_, the probability of an outage decreases in asymmetric scenario, whereas 25% of elements are allocated to _SU_, resulting in an increased probability of an outage of the asymmetric scenario. Figure 4: Probability of outage analysis of blind RIS-SR-ONOMA _SU_ with distinct \(N\). Figure 5: Probability of outage analysis of blind RIS-SR-ONOMA _WU_ with distinct \(N\). Figure 6: Probability of outage analysis of blind RIS-SR-ONOMA for symmetric and asymmetric scenarios. The sum capacity analysis of blind RIS-SR-ONOMA for distinct values of \(N\) is carried out in Figure 7. The sum capacities (b/s/Hz) observed are 12.3883, 13.3942, 14.3978, 15.3936 and 16.3913 for \(N=32\), 64, 128, 256, and 512 respectively. In order to validate the performance of optimal power allocation, we used the following suboptimal power allocation for _SU_ and _WU_:  
The suboptimal power is the average of \(\alpha_{2}^{min}\) and \(\alpha_{2}^{max}\). The suboptimal value of \(\alpha_{2}\) is  
\[\alpha_{2}^{subopt}=\frac{\alpha_{2}^{min}+\alpha_{2}^{max}}{2} \tag{48}\]  
The suboptimal value of \(\alpha_{1}\) in RIS-SR-ONOMA is given as  
\[\alpha_{1}^{subopt}=1-\alpha_{2}^{subopt} \tag{49}\]  
For all \(N\), optimal power allocation is giving slightly higher capacity than the suboptimal power allocation at low SNR regions. The sum capacity of the system increases with a higher \(N\) value. Figures 8-11 examine the performance of blind RIS-AP-ONOMA system. For Figures 8-11, the explanations are the same as those for Figures 3-5 and 7. Figure 8: Comparison of probabilities of outage of _WU_ and _SU_ for FNOMA, ONOMA and blind RIS-AP-ONOMA. Figure 3:0 Probability of outage analysis of blind RIS-AP-ONOMA _SU_ with distinct \(N\). Figure 3:1 Sum capacity analysis of optimal vs. suboptimal blind RIS-AP-ONOMA for distinct \(N\). Figure 3:2 Probability of outage analysis of blind RIS-AP-ONOMA _WUI_ with distinct \(N\). The throughput expression for RIS-SR-ONOMA is given by [32]  
Figure 3:3  
Figure 13 compares the throughput performance of blind RIS-SR-ONOMA, FNOMA and ONOMA systems. To achieve target throughput of 3/b/s/Hz, FNOMA and ONOMA systems require SNR of \(\approx\)30 dB and \(\approx\)26 dB, respectively. Since ONOMA system considers channel gains for deciding the decoding order of the users, the SNR required to achieve the target throughput for ONOMA is lower than FNOMA system. Inclusion of RIS decreases SNR requirements. To achieve the same target throughput \(N\) = 32, 64, 128, 256 and 512 requires SNRs of \(\approx\)11 dB, \(\approx\)8 dB, \(\approx\)5 dB, \(\approx\)2 dB and \(\approx\)0 dB respectively. As \(N\) increases improvement in performance is observed.