## 7 Simulation Results and Discussion  
Table 3 describes the simulation parameters. The AWGN noise power is calculated according to the \(\sigma^{2}=-130+10\log_{10}(B)+F_{n}\), where \(F_{n}\) is in dB, \(\sigma^{2}\) is in dBm, \(B\) is in Hz [17]. Monte-Carlo simulations are performed for 100,000 samples and the average value of normalized IDR in bits per sec per Hertz is calculated for different cluster sizes. For RIS-NOMA simulations, the total transmit power (\(P_{T}\)) is taken as 23 dBm [24]. For simulation of stand-alone NOMA without RIS system, the total transmit power is taken as 46 dBm [11]. Tables 1 and 4 present the theoretical upper bounds of IDRs and the Monte-Carlo simulation results to verify the theoretical benchmark, respectively, for proposed GP-based power allocation in the RIS-NOMA downlink cluster with different cluster sizes. The results shown here validate the proposed hypothesis that each lower CG user (user 2 to user 'n') present in a NOMA downlink cluster cannot achieve the IDR higher than its upper bound benchmark, irrespective of higher channel gain or higher cluster power provided to it. The empty places in these tables are intentionally left blank to show that the cluster is already full and no more users can be accommodated in the cluster than the cluster size. Similarly, Table 5 shows the theoretical upper bound of IDRs for the magic matrix-based power allocation [22] in RIS-NOMA downlink cluster and Table 6 verifies the theoretical benchmark set in Table 5 by showing Monte-Carlo simulation-based results in deep agreement with the benchmark of Table 5. The results obtained in Tables 4 and 6 again validate the proposed hypothesis about the upper bound of IDR for each lower CG user belonging to a NOMA downlink cluster. Tables 7 and 8 highlight the simulation results for stand-alone NOMA downlink cluster without RIS for different cluster sizes, when Magic matrix-based power allocation [22] and optimal power allocation [11] have been performed, respectively. Now, if we compare the results obtained in Tables 4 and 8, then it clearly shows that IDRs for all the users are better in RIS-NOMA as compared to stand-alone NOMA without RIS. The same conclusion can also be drawn by comparing the results of Tables 6 and 7. This comparison shows that RIS-NOMA is better than NOMA without RIS for all cases of power allocation. A reduction of 23 Dbm in total power is achieved in the RIS-NOMA system while improving the data-rates as compared to their non-RIS counter part. Figure 5: Data-rate plot analysis for lower channel gain user devices in downlink NOMA system. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cluster Size** & **User 1** & **User 2** & **User 3** & **User 4** & **User 5** & **User 6** \\ \hline n = 3 & Variable & 1.2224 & 1.0995 & - & - & - \\ \hline n = 4 & Variable & 1.2224 & 1.1926 & 1.0875 & - & - \\ \hline n = 5 & Variable & 1.2224 & 1.0995 & 1.0931 & 1.0224 & - \\ \hline n = 6 & Variable & 1.5850 & 1.1155 & 1.0544 & 1.0265 & 1.0131 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Normalized IDRs’ Monte-Carlo simulation analysis in bits per sec per Hertz for Magic matrix-based power allocation [22] in downlink RIS NOMA clusters.