## 1 Introduction  
During the practical implementation of several of the core fifth-generation (5G) technologies, there are significant hurdles [1]. The network service providers in China, for example, recently announced the shutdown of a few 5G base stations (BS) mounted with massive multiple input multiple output (MIMO) [2]. The increased number of radio frequency (RF) chains necessitates higher hardware costs and higher energy consumption. To meet the growing traffic demands, cell size must be shrunken. This necessitates an increasing number of BSs or access points (AP). This raises the expense of maintenance while also causing practical concerns, such as interference and backhaul management.  
Exploiting higher frequency bands causes considerable propagation losses, necessitating more complicated signal processing.  
Following the completion of the standardization and commercialization of 5G networks, wireless researchers have begun looking for new technologies to support sixth-generation (6G) networks. Since they reconfigure the environment with nearly passive, low-cost elements, reconfigurable intelligent surfaces (RIS) or intelligent reflecting surfaces (IRS) have been identified as viable components for next-generation networks. The RIS system uses abundant low-cost, passive reflecting elements mounted on a planar surface to regulate the amplitude and phase of incident signals [34]. Active RF chains are not required for RIS, and nearly passive reflecting elements are required. When compared to massive MIMO, the hardware cost and energy consumption are significantly lower. They do not cause noise amplification or self-interference in the way that full duplex transmission does. As a result, it is more appealing than half-duplex relays. RIS can be readily installed on walls, billboards, automobiles, lampposts, and so on. With the help of RIS, cell coverage and network throughput can be greatly boosted.  
The number of wirelessly connected devices, as well as the range of wireless services available, such as the internet of everything (IoE), virtual reality (VR), augmented reality (AR), and so on, is rapidly increasing. As a result, next-generation multiple access strategies should be capable of serving a high number of users with additional resources, while maintaining a low level of complexity [5; 6]. While permitting a certain degree of multiple access interference at the receivers, non-orthogonal multiple access (NOMA) boosts spectral efficiency and facilitates massive connectivity [7]. In NOMA, the signals pertaining to several users are superimposed in the power domain to more effectively utilize the spectrum. NOMA is classified into two types: fixed and ordered NOMA. In ordered NOMA, the decoding order is determined based on the channel gain of the users, as opposed to fixed NOMA, where the decoding order is predetermined. Because of its appealing qualities, RIS can be combined with other cutting-edge technologies such as NOMA, physical layer security, simultaneous wireless information and power transfer (SWIPT), cognitive radios, autonomous cars, and unmanned aerial vehicles (UAV)-assisted communication, etc. [8; 9; 10]. The integration of power-domain NOMA with RIS can increase its spectral efficiency and massive connectivity. The symbols used in this work are listed in Nomenclature.  
The order in which the remaining manuscript is arranged is as follows: Section 2 lists the works connected to RIS and NOMA. The closed-form outage probability expressions for blind-RIS-smart reflector (SR)-NOMA uplink and blind-RIS-AP-NOMA uplink are derived in Section 3. The optimum powers to allocate for maximizing uplink sum capacity are detailed in Section 4. In Section 5, Monte-Carlo simulations are performed to verify the obtained analytical expressions. Section 6 wraps up the work by considering future works.