## 7 Simulation Results and Discussion
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Description of the Parameter** & **Symbol** & **Value** \\ \hline Total number of devices present in the system & \(M\) & 12 \\ \hline Number of devices included in a cluster (cluster size) & \(n\) & \(3/4/6\) \\ \hline Total number of meta-atoms in the RIS & \(N\) & 10 to 300 \\ \hline Minimum distance between RIS and devices & \(d_{min}\) & 50 m \\ \hline Fixed distance between RIS and Access point & \(d_{fix}\) & 50 m \\ \hline Distance between \(i\)th device \(D_{il}\) to RIS & \(D_{il}\) & 50 m to 300 m \\ \hline Carrier frequency & \(f_{c}\) & 3 GHz \\ \hline Bandwidth for each device & \(B\) & 180 kHz \\ \hline Transmit power from AP & \(P_{T}\) & 23 dBm \\ \hline AWGN power spectral density in dBm & \(w\) & \(-130\) dBm \\ \hline Minimum data-rate requirement for each device & \(R_{min}\) & 100 kbps \\ \hline Noise Figure in dB & \(F_{n}\) & 10 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation Parameters. \begin{table}
\begin{tabular}{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 & 14.2965 & 1.5849 & 1.2224 & & - \\ \hline n = 4 & 12.5822 & 1.5848 & 1.2223 & 1.0995 & & - \\ \hline n = 5 & 10.7713 & 1.5844 & 1.2222 & 1.0995 & 1.0473 & - \\ \hline n = 6 & 9.9945 & 1.5838 & 1.2219 & 1.0993 & 1.0472 & 1.0230 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Normalized IDR Monte-Carlo simulation analysis in bits per sec per Hertz for GP-based optimal power allocation in downlink TDMA-RIS-NOMA clusters. \begin{table}
\begin{tabular}{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 5: Normalized IDRs’ theoretical upper bound in bits per sec per Hertz for different cluster sizes in Downlink RIS-NOMA, when magic matrix-based power allocation [22] is adopted. Results of Table 4 also show the optimality of the proposed GP-based power allocation technique for all users of the RIS-NOMA cluster because IDRs in Table 4 are highest among Tables 5-8. As shown in Figure 5, the saturation point is reached for all the lower CG users in the downlink NOMA clusters as the effective CG is increased. The highest CG user for RIS-NOMA cluster is not saturated with respect to effective CG. This fact is shown in the Figure 6 where the number of meta-atoms is increased to enhance the effective CG. The curves for different cluster sizes are plotted in this graph. The graph shows that the IDR of the highest CG user increases as the effective CG increases. The simulation results confirmed the analysis conducted in Section 4. The data rate increases as the number of meta-atoms increases before the saturation point. After this point, \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** & 5.2786 & 1.1676 & 1.0169 & - & - & - \\ \hline
**n = 4** & 4.3149 & 1.1361 & 1.1206 & 0.9919 & - & - \\ \hline
**n = 5** & 3.5750 & 1.0935 & 1.0118 & 1.0180 & 0.9224 & - \\ \hline
**n = 6** & 2.4561 & 1.2822 & 0.9790 & 0.9571 & 0.9449 & 0.9073 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Normalized IDR analysis in bits per sec per Hertz of Magic matrix-based power allocation [22] in downlink NOMA clusters without IRS.