## 5 Results and Discussion
A drastic reduction in outage probability is observed for user 2 when blind-RIS elements are introduced. The outage analysis is repeated in Figure 4 by keeping everything the same as in Figure 3 except the power factors. Users 1 and 2 have been given power fractions of 0.7 and 0.3, respectively. User 1's outage probability in the blind-RIS-SR-NOMA and traditional NOMA is 0.0798 and 0.1049, respectively, for 10 dB SNR. User 2's outage probability in the blind-RIS-SR-NOMA and traditional NOMA is 0.0901 and 0.3767, respectively, for 10 dB SNR. It has been noted that the possibility of an outage for both systems has increased as a result of the reduction in power allocated to user 1. The probability of an outage for both systems is decreased by the increased power factor allocation for user 2. Figure 4: Outage probability comparison between blind-RIS-SR-NOMA and NOMA for \(\mu_{1}=0.7\) and \(\mu_{2}=0.3\). Figure 3: Outage probability comparison between blind-RIS-SR-NOMA and NOMA for \(\mu_{1}=0.9\) and \(\mu_{2}=0.1\). For various choices of \(N\), the outage probability of user 1 in the blind-RIS-SR-NOMA uplink is shown in Figure 5. User 1 of blind-RIS-SR-NOMA has a lower outage probability than user 2 due to the higher channel gain and greater power allocation. The probability of an outage decreases as the number of reflecting elements grows. The outage probabilities of the proposed blind-RIS system are 0.0219, 0.0221, 0.0224, 0.0231, and 0.0244, with the number of elements 512, 256, 128, 64, and 32 at 4 dB SNR. At low SNR, it is observed that there is a gap between the theoretical and simulation curves, due to the assumptions made in (4) and (5) for mathematical tractability. However, the theoretical and simulation curves are nearly identical for higher values of \(N\). For various choices of \(N\), the outage probability of user 2 of the blind-RIS-SR-NOMA uplink is shown in Figure 6. The probability of an outage falls as the number of reflecting elements grows. The outage probability of a blind-RIS system is 0.0297, 0.0375, 0.053, 0.0833, and 0.1409 with \(N=512,\ 256,\ 128,\ 64,\ \text{and}\ 32\), at 4 dB SNR. For higher values of \(N\), the analytical and simulation curves are found to be very similar. According to the configuration of the simulation, user 1 has a stronger channel than user 2. The capacity of user 2 is reduced as a result of improper random power allocation. The sum capacity is finally reduced as a result. In the proposed work, the power factors are optimally chosen with the objective of maximizing the sum capacity while also satisfying the minimum rate requirements of each individual user. For various values of \(N\), the sum capacity (b/s/Hz) of the blind-RIS-SR-NOMA uplink is shown in Figure 7. It has been observed that increasing \(N\) increases the sum capacity regardless of optimal or sub-optimal power allocations. To validate the performance of optimal power allocation, the following sub-optimal power allocation is used for comparison:  
\[\mu_{1}^{sub-opt}=\frac{\mu_{1 min}+\mu_{1 max}}{2} \tag{40}\]  
\[\mu_{2}^{sub-opt}=1-\mu_{1}^{sub-opt} \tag{41}\]  
Figure 5: Outage probability comparison of blind-RIS-SR-NOMA user 1 for various choices of \(N\). The sum capacity is maximized when optimal powers are allocated as per (36) and (37), compared to sub-optimal power allocations as per (40) and (41). The sum capacity of  
Figure 6: Outage probability comparison of blind-RIS-SR-NOMA user 2 for various choices of \(N\). Figure 4:0 Sum capacity (b/s/Hz) comparison of blind-RIS-SR-NOMA for optimal and sub-optimal power allocations and various choices of \(N\). the optimal and sub-optimal power allocations for \(N=32\) and \(20\) dB SNR are \(13.21\) b/s/Hz and \(12.71\) b/s/Hz, respectively. Other values of \(N\) show nearly identical gains. In Figure 8, the outage performance of the proposed blind-RIS-AP-NOMA and traditional NOMA is shown.