## 2 Related Work
NOMA and CR are integrated in [21] to improve spectrum efficiency. For a two-user case, the closed-form outage probability expressions are constructed. It is also proven that fairness between two users is realized through proper power factor allocation. NOMA does not surpass orthogonal multiple access (OMA) in terms of spectral efficiency gain when the channel gains of various users are not significantly different [22]. In these circumstances, classic OMA is preferable. In NOMA, fairness among users can be attained through effective power allocation. However, increasing the rate of weaker users may result in a decrease in the rate of stronger users. The addition of RIS to NOMA can improve its performance by enabling stronger combined channels. The effects of coherent and random phase shifting on the performance of RIS-aided NOMA are investigated in [23]. Analytical and simulation results reveal the trade-off between complexity and reliability. To improve reception reliability, a low-complexity phase selection approach is also presented. In [24], multiple RIS are used in NOMA to increase the quality of each user's received signal. Based on the availability of a line-of-sight (LoS) between the BS and the user, the outage probability expressions are derived. For high signal-to-noise-ratio (SNR) regimes, the upper and lower bounds of outage probability expressions are derived. It is proven that the diversity order is not degraded when using a discrete phase shifter. It is also proven that RIS with a three-bit discrete phase shifter achieves near-optimal outage performance. The simulation results further demonstrate that RIS outperforms full duplex DF relays. In [25], the outage probability of RIS-assisted NOMA downlink transmission is examined for two users. RIS is used here between the source and the users. It has been shown that the introduction of RIS increases the performance of the far user. Analysis is also done on the impact that the number of RIS elements, power factor allocation, desired rates, and SNR have on the probability of an outage. Fairness among users is ensured by the implementation of RIS. In [22], the joint optimization of transmit beamforming at the BS and phase shifts at the RIS are solved by block coordinated descent and semi-definite relaxation techniques to improve the user fairness in a downlink scenario of RIS-assisted NOMA system. Depending on the channel strength, the users are ordered. It is shown that the suggested RIS-assisted NOMA outperforms the traditional NOMA and traditional OMA with and without RIS in terms of the downlink sum capacity. It employs a low-resolution phase shifter with a performance that is nearly identical to that of an ideal RIS with an infinite resolution phase shifter. Here, the outage probability of ordered users is not investigated. It is noted that even for more passive controllable reflecting elements, the improvements in sum capacity are not appreciably greater. The authors intended to increase user fairness in this case. As a result, even with higher SNR, the sum capacity remains nearly constant. In this study, an LoS is assumed to exist between the BS and the RIS, and the BS-RIS channel is modeled using the Rician distribution. Rayleigh distribution is used to model the RIS-users channel since it is expected that there is a non-line-of-sight (NLoS) between the RIS and the users. The LoS assumption between BS and RIS is not realistic in many cases. The system has not been analyzed for RIS as an AP setup. In [26], the performance of the cell edge user device is improved by employing IRS-assisted NOMA in both the uplink and the downlink. In this paper, a blind-RIS system is proposed for the uplink scenario of both users in a NOMA system. For each case, closed-form outage probability and Ergodic rate expressions are derived. The number of RIS elements appears to have an effect on the diversity order. Furthermore, the RIS-assisted system outperforms the full duplex DF relay system.