# RIS-Assisted Fixed NOMA: Outage Probability Analysis and Transmit Power Optimization
## 2 Related Work
All of the preceding works are based on static channel conditions. [PERSON], [PERSON] et al. developed a joint optimization framework for resource allocation and deciding phase shift angles to maximize the sum capacity of SISO RIS-NOMA downlink [32]. The analysis was carried out under fading channels. To optimize beamforming vectors and phase shift matrices, [PERSON], [PERSON] et al. employed several convex algorithms [33]. The goal of this approach is to minimize the total transmit power for multiple input-single output (MISO) RIS-NOMA. [PERSON], [PERSON] et al. combined active beamforming at BS and passive beamforming at RIS to maximize the sum capacity [34]. [PERSON], [PERSON] et al. developed the theoretical framework to analyze the outage performance of RIS-aided communication over generalized fading channels and in the existence of phase noise. It was demonstrated that when the fading channels are independent, RIS-aided communication achieves full diversity, even with the existence of phase noise [35]. [PERSON], [PERSON] and [PERSON], [PERSON] proposed a cooperative cognitive radio NOMA, in which primary and secondary users share a secondary DF relay via NOMA [36]. The closed-form outage probability expressions were developed assuming imperfect CSI and successive interference cancellation (SIC). The influence of channel estimate inaccuracy, power allocated to individual users, and threshold for detection on outage probability was also investigated in this study. MC simulations were used to substantiate the accuracy of analytical outage expressions. [PERSON], [PERSON] et al. investigated the implications of hardware impairments on the reliability of RIS-assisted NOMA [37]. The closed-form analytical outage probability and throughput expressions were developed. The number of reflective components and power assignment factors were found to be important in enhancing the performance of RIS-assisted NOMA over OMA. [PERSON] and [PERSON] employed RIS-assisted NOMA for PLS [38]. The analytical expressions for secrecy outage probability were derived. When compared to traditional NOMA systems, it was observed that using RIS can improve secrecy performance. [PERSON], [PERSON] et al. suggested the blind RIS-assisted FNOMA framework with SR and AP configurations for uplink transmission [39]. An optimization problem for power allocations was constructed to maximize the sum capacity of NU and FU. The analytical outage expressions were validated using extensive computer simulations. Blind RIS-SR-NOMA outperformed traditional NOMA by \(\approx\)38% for 32 reflective elements and a 20 dB SNR. [PERSON], [PERSON] et al. examined the active RIS with virtual NOMA for uplink system [40]. Instead of using user-side controlling powers, the concept of power disparity was applied to achieve virtual NOMA. The end-to-end system model, analytical outage probability, and error probability expressions were developed and affirmed using computer simulations. [PERSON], [PERSON] and [PERSON], [PERSON] studied the downlink blind RIS-assisted framework for ordered NOMA, where channel gains determine user decoding order [41]. The closed-form outage probability and optimal powers to be assigned expressions were developed for stronger and weaker users. As there are more reflecting elements, the sum capacity increased accordingly. The suggested approach outperformed traditional FNOMA and ordered NOMA systems in terms of outage, bit error rate, and sum capacity. The suggested approach outperformed the ordered NOMA system by \(\approx\)33% for 20 dB SNR and 32 reflective elements. In this paper, the performance of RIS-assisted FNOMA is evaluated in light of these considerable benefits of RIS and NOMA. The major contributions of this paper are threefold:  
* Analytical outage probability expressions are developed for NU and FU in a RIS-SR-FNOMA and RIS-AP-FNOMA. * Analytical expressions are developed for optimal power assignment to NU and FU in both RIS-SR-FNOMA and RIS-AP-FNOMA systems.