## 3 Proposed Optimization Algorithm
### BS Transmit Power Allocation
#### 3.1.2 Two-Layer Approach for Solving Problem (P1)
For our simulations, we utilize the urban macro (UMa) path loss model as specified in the 3 GPP technical standard. We set \(N=4\) RISs/users, \(M=20\) BSs as shown in Figure 3, where BSs are distributed in a square area around users with a side length of 2 km and each RIS is deployed 200 m away from its assisted user. We assume that all BSs and users are equipped with an omnidirectional antenna. Unless otherwise specified, the setting of simulation parameters is outlined in \[F=(v_{1}-v_{2})P_{m,n}-v_{3}. \tag{33}\]1 For comparison, we consider several benchmark schemes as follows: (1) CF network without RISs, (2) one nearest selection with RISs, and (3) one nearest selection without RISs. \[F=(v_{1}-v_{2})P_{m,n}-v_{3}. \tag{33}\]2 System setup. ### Comparison with Benchmarks

Figure 4 shows the weighted sum-SINR of the RIS-CF system versus the transmit power budget per BS. It is evident that the weighted sum-SINR of all evaluated schemes improves significantly as the transmit power budget increases. Moreover, it is observed that the weighted sum-SINR performance of the CF network surpasses that with the nearest selection schemes by a considerable margin, regardless of whether RISs are employed or not. This is because the CF network has many distributed BSs compared to that with the nearest selection scheme, which provides a higher degree of macro-diversity for communication. It is evident that the performance of both the RIS-CF network and that with the nearest selection with RISs surpasses that of the case without RISs. This improvement is attributed to the fact that signals are transmitted via more propagation paths, i.e., the additional reflected links, indicating that RISs can more efficiently utilize spatial resources. Notably, our proposed RIS-CF network exhibits the best weighted sum-SINR performance among all the evaluated schemes. ### Impact of RIS-Reflecting Elements

To better understand the influence of RISs on the performance of the CF system, we conducted experiments with various numbers of reflecting elements per RIS. Figure 5 clearly demonstrates the weighted sum-SINR with and without BS power allocation. In the absence of power allocation, the transmit power per BS was fixed at 40 dBm. This comparison offers a valuable insight into how our proposed algorithm compares to the benchmark scheme as the number of reflecting elements \(L\) varies. It can be observed that, as the number of reflecting elements \(L\) increases, the weighted sum-SINR also rises. As

\[F=(v_{1}-v_{2})P_{m,n}-v_{3}. \tag{33}\]3 Weighted sum-SINR versus BS transmit power budget. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of BSs, \(M\) & 20 \\ Number of RISs/users, \(N\) & 4 \\ Number of RIS-reflecting elements, \(L\) & 1000 \\ Noise power spectrum density, \(\sigma^{2}\) & \(-164\) dBm/Hz \\ Distance between users and RISs, & 200 m \\ Total transmit power budget of each BS & 40 dBm \\ System bandwidth & 20 MHz \\ Path loss & \(128.1+37.6\log_{10}d_{\left[\text{km}\right]}\) dB \\ Shadow fading & 8 dB \\ Number of Monte Carlo simulations & 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: System parameters. expected, all methods that incorporate RISs outperform their counterparts without RISs (\(L=0\)) in terms of performance. Additionally, the weighted sum-SINR of the RIS-CF network significantly surpasses that with the one nearest selection scheme due to the optimized BS selections. It is worth noting that the weighted sum-SINR performance of the evaluated schemes with power allocation is superior to those without power allocation. However, we can see that, compared with the schemes without BS power allocation, BS power allocation brings more gains to the one nearest selection benchmark than the schemes with optimized BS selections, which shows that SINR balancing is more flexible with BS power allocation. ## 5 Conclusions

In this study, we conducted an analysis of an RIS-CF system that involves multiple BSs collaborating with multiple RISs to serve distinct users.