## 4 Simulation Results
### Sum-Rate Analysis  
Figure 4 shows the sum-rate performance according to the number of RIS elements. It is shown that the RSMA transmit scheme outperformed the spatial division multiple access (SDMA) transmit scheme. With the proposed grouping scheme, the performance of the RSMA scheme had a gain of 7.7% and 9.8%, respectively, over the SDMA performance, when \(N_{I}\) was 48. Additionally, the proposed grouping achieved higher performance than the general grouping. This means that the proposed grouping had the proper grouping strategy. For \(N_{G}=4\), better performance was also seen; in other words, fewer groups resulted in higher sum-rate performance. However, fewer groups required more impedance value computation. Therefore, the reduction of the number of groups increased the complexity of the system. By using the RSMA scheme, the amount of RIS computation can be reduced and the sum-rate performance can also be increased. Moreover, the sum-rate of the proposed grouping scheme with \(N_{G}=8\) achieved the sum-rate of the general grouping with \(N_{G}=4\) in both the RSMA scheme and the SDMA scheme. It was seen that it had a low computational complexity and improved the performance effectively.  
Figures 5 and 6 show that the proposed RIS-assisted RSMA scheme had a higher sum-rate performance than the conventional RIS-assisted SDMA, because the proposed grouping was more adaptive and the RSMA scheme was more flexible in managing the interference. In the simulations, Algorithms 1 and 2 were applied as the proposed grouping scheme and the optimization of RS power-splitting ratio. Furthermore, the number of groups in the simulation was a number that could be divided by the number of elements. Since the number of users was set to 3, the number of groups should be greater than 3 to apply Algorithm 1. Therefore, in this paper, the number of groups was set to 4 and 8. Figure 5 shows the sum-rate performance according to the transmit power of the BS. The RSMA scheme achieved almost the same performance with about 10 dBm lower power than the SDMA scheme. Furthermore, the proposed RIS had more improved performance than the conventional RIS. Therefore, it is demonstrated that proposed RIS-assisted RSMA scheme that had a similar performance with a low transmit power was more energy efficient than the conventional RIS-assisted SDMA scheme. In Figure 6, it is shown that the sum-rate performance improved when the position of the RIS was close to the UEs. However the  
Figure 4: Sum-rate versus the number of RIS elements.  
RSMA scheme ensured a higher sum-rate than the SDMA scheme, even if the RIS was far away from the UEs.  
Figure 7 shows the sum-rate performance according to the number of users. To apply Algorithm 1, the number of users should be less than or equal to the number of groups. The RSMA scheme had higher performance than the SDMA scheme, and the performance of the proposed RIS was also higher than the conventional RIS. When the RSMA scheme was used, the system supported eight users with an appropriate sum-rate. In contrast, the system using the SDMA scheme could support up to four users. This shows that the RSMA scheme had higher scalability than the SDMA scheme.  
Figure 5: Sum-rate versus transmit power with \(N_{G}=4\) and \(N_{I}=16\).  
Figure 6: Sum-rate versus X position of the RIS with \(N_{G}=4\) and \(N_{I}=16\).