## 1 Introduction  
Non-orthogonal multiple access (NOMA) is a suitable technique to achieve the goals of the massive machine-type communication (mMTC) in the 5G wireless networks [1]. NOMA serves multiple users in the same frequency band and time slot by assigning different transmit powers [2]. At the base station (BS) of the downlink NOMA system, a composite signal is generated by superimposing the constellations of all users belonging to any particular cluster [3]. At the receiver's end, the desired signal for each user is detected from the composite signal using the successive interference cancellation (SIC) technique [3]. By using NOMA, we can serve the massive connecting devices simultaneously, which is not possible if the network resources are shared in orthogonal ways [1]. However, in NOMA, the transmit power levels for all users in a cluster are required to be sufficiently high to mitigate the AWGN noise and the interference due to signals of other users present in the same composite signal [3]. Furthermore, the stand-alone NOMA downlink system does not have any control over the channel gain between BS and the users [4]. If the channel quality is poor between the source and destination (due to long distances or obstacles), then there is no alternate path for communication to occur [4]. One way to resolve the problem of poor channel quality is addressed in [5], where the author has considered the NOMA downlink system for the relay-to-relay cooperative communication as a solution. Another way to handle these challenges in the downlink NOMA system is by using the RIS [6]. The RIS is an array of a large number of passive reflecting meta-surfaces (called meta-atoms). The electromagnetic properties of these meta-atoms can be reconfigured to control the amplitude and phase shift of the reflected signal from each meta-atom to focus the beam at the desired location [7]. Hence, RIS can control the radio environment intelligently [8]. The main advantages of using RIS are as follows: (i) Each meta atom contributes to a separate path from RIS to the user [9]. (ii) By adjusting the phase shift provided by the meta-atom to the reflected signal, constructive interference condition is achieved among the signals received from the different meta-atoms towards the desired user in a point-to-point communication model. This improves the SNR for the received signal. Consequently, the data rate of the user also increases. (iii) Another advantage of RIS is that if the direct path from BS to the user is blocked, then the system has a better coverage area by more indirect wireless paths from BS-RIS-User [7]. From the current literature on NOMA, it has been observed that sum data rate (SR) maximization is a common problem to encounter [10; 11]. But, the problem with the SR in the NOMA downlink system is that when power allocation is conducted to maximize the SR, the more and more the data-rate is increased for the highest channel gain (CG) user and the data rates of lower CG users do not increase significantly. During the literature survey, we found that in the stand-alone NOMA downlink system, although optimization work has been conducted to maximize SR, the lower CG users could not achieve the upper bound of their individual data rate (IDR). The drawback of a stand-alone NOMA downlink cluster is that lower CG users could not achieve the upper bound of their IDRs. This drawback can be overcome in the RIS-assisted TDMA-NOMA point-to-point communication model by allocating a sufficient number of meta-atoms such that the SINR of each user becomes saturated to reach the upper bound of IDR. There are two popular resource allocation strategies: one is concentrating on SR maximization [11] and the other is focusing on fairness Index equalization [12; 13; 14] for the IDRs of all users present in the NOMA downlink cluster.