## 5 Results and Validations
The rate attained by the \(l\)-th user in a continuous phase shifter RIS is given by  
\[R_{l}=\frac{1}{L}\log_{2}(1+\epsilon) \tag{22}\]  
For the discrete reflection RIS, the rate attained by the \(l\)-th user can be obtained by replacing \(\epsilon\) in (22) by \(e^{\prime}\). The sum rate of the proposed system for multiple users can be obtained through \(\sum_{l=1}^{L}R_{l}\). Figures 12-14 present the sum rate performance under various conditions. The figures are plotted for \(N_{t}=16\), two users with a single antenna (\(N_{r}=1\)) and 256 RIS elements. Figure 12 depicts the sum rate performance of two users in indoor and outdoor scenarios at varying mmWave frequencies. The figure shows that the increase in SNR enhances the sum rate performance. The figure clearly shows that the 28 GHz mmWave range outperforms the 73 GHz range. This is due to the higher dispersion and absorption  
Figure 9: ABER performance of \(N=256\) RIS-M-MIMO for UMi—street canyon environment at 28 GHz and varying \(N_{T}\). properties of the mmWave band, which dominate at the higher mmWave frequencies. The figure indicates that the indoor scenario has better sum rate performance than the outdoor. An important observation is that even under an indoor environment, the higher mmWave frequency (73 GHz) transmission severely degrades compared to the outdoor scenario. This demonstrates how higher mmWave frequencies are sensitive to external objects. Figure 11: ABER comparison between continuous and discrete phase \(N=64\) RIS for \(1\times 4\) M-MIMO under UMi—street canyon environment at 28 GHz. Figure 10: ABER comparison between continuous and discrete phase \(N=64\) RIS for \(1\times 4\) M-MIMO under InH- indoor office environment at 28 GHz. Figures 13 and 14 demonstrate the sum rate performance of two users in the InH--office and UMi--street canyon, respectively, at 28 GHz with continuous and discrete phase RIS. In this analysis, three distinct curves are presented, each representing different types of RIS: the continuous phase RIS, indicated by red squares; the 1-bit discrete phase RIS, represented by green circles; and the 2-bit discrete phase RIS, marked with blue triangles. The findings reveal a clear trend: the overall sum rate improves significantly as the SNR increases and \(b\) grows. Notably, the continuous phase RIS consistently outperforms  
Figure 12: Comparison of sum rate (\(\text{bps}/\text{Hz}\)) for two users in InH—office and Umi—street canyon scenarios at varying mmWave frequencies. Figure 5:0 Comparison of the sum rate (\(\text{bps}/\text{Hz}\)) for two users in the InH—office at 28 GHz with continuous and discrete phase RIS. the other configurations across the entire SNR range, achieving the highest sum rate. However, producing continuous or infinite resolution is impractical and increases hardware complexity. The discrete phase shift RIS, which operates with finite resolutions and thus reduces hardware complexity, does experience some performance degradation compared to the continuous phase shift RIS. As illustrated in Figures 13 and 14, the 1-bit discrete phase shift RIS can only achieve 2 levels, which leads to significant performance degradation. In contrast, the 2-bit discrete phase shift RIS, which provides four levels of resolution, shows improved performance. This demonstrates that increasing quantization bits results in a better sum rate. This observation highlights an essential trade-off in communication systems: while enhancing quantization resolution improves SE, it also introduces greater hardware complexity. Ultimately, finer phase resolution in RIS allows for better network performance, reflecting a crucial balance between efficiency and practicality in the design of advanced communication systems. Table 7 compares the sum rate (\(\text{bps}/\text{Hz}\)) under continuous and discrete phase RIS at 28 GHz mmWave frequency. It shows that the increase in quantization levels reaches the near-optimal solution.