## 2 System Model  
### Reconfigurable Intelligent Surface System Model  
As a passive element that does not provide any amplification, RISs are practically placed close to either the BS or the user position. In this paper, without a loss of generality, RISs are arbitrarily distributed at the cell edge to assist the cell edge user as shown in Figure 1. We designed a RIS system that could provide maximum suppression of the co-channel interference; six RISs are considered to be arbitrarily distributed at the cell edge, which is closer to the cell-edge users [7]. R is the radius of the whole system while r is the distance between the reference BS (BS\({}_{0}\)) and the reference RIS (RIS\({}_{0}\)), which is fixed and equivalent to (2/3)R. The mobile device or reference user, \(U\) is assumed to be randomly distributed inside the RIS\({}_{0}\) coverage area with a distance d and can only receive the interference reflected signal from the RIS\({}_{0}\) without having any LOS signal from the BS of the home cell. For the co-channel interference (CCI), as an intelligent surface, we assume that RISs do not forward the signal to users as all undesired signals are reflected away [6]. Therefore, we only consider the interfering signal from the k\({}_{\text{th}}\) co-channel (CC) BS to the RIS\({}_{0}\) reference user \(U\) with a distance of l\({}_{\text{k}}\). Without a loss of generality, we also assume that RISs have ideal channel estimation and utilize a continuous phase shift. For the RIS\({}_{0}\) configuration with N number of reflective elements per RIS, the reflected signal received by \(U\) in the presence of CCI from M neighboring cells can be expressed as [5; 6]:  
\[ \begin{array}{c}y_{RIS}=\sqrt{P}x_{0}\Big{(}\sum\limits_{i=1}^{N}h_{s,i}\,h_{r,i }\,\sqrt{r^{-\beta_{s,i}}\,d^{-\beta_{r,i}}}\,\,e^{-j(\sigma_{i}-\theta_{s,i}- \theta_{r,i})}\Big{)}+\\ \sum\limits_{k=1}^{M}\sqrt{P}x_{k}h_{c,k}\sqrt{l^{-\beta_{c,k}}\delta_{k}}+w_{ 0},\end{array}  \tag{1}\]  
where the first term is the useful signal, the second term is the CC interference signals and \(w_{0}\) represents the additive white Gaussian noise (AWGN) that satisfies \(E\left[\left|w_{0}\right|^{2}\right]=\sigma^{2}\). \(x_{0}\) and \(x_{k}\) are the transmitted signals from useful and interfering signal from the \(k_{th}\) BS, respectively, while \(P\) is the transmitted signal power from any BS. \(\left|h_{s,i}\right|^{2}\) and \(\left|h_{r,i}\right|^{2}\) are the random channel gains from BS to RIS\({}_{0}\) and RIS\({}_{0}\) to \(U\), respectively, while \(\left|h_{c,k}\right|^{2}\) is the random channel gain from CC BS to \(U\). \(\theta_{s,i}\) and \(\theta_{r,i}\) are the phase components of BS-RIS\({}_{0}\) and RIS\({}_{0}\)-U while \(\varnothing_{i}\) is the reconfigurable phase induced by the ith reflector of the RIS. \(\beta_{s,i}\), \(\beta_{r,i}\) and \(\beta_{c,k}\) are the path loss exponents of BS-RIS\({}_{0}\), RIS\({}_{0}\)-\(U\) and CC-\(U\), respectively, and \(\delta_{k}\) (\(k=0,\,1,\,\ldots,\,M\)) is the binary RV that represents each channel of the interfering BS's traffic activity, where \(\delta_{k}=1\) if channel k is active and \(\delta_{k}=0\), otherwise. Without a loss in generality, RIS is assumed to have the knowledge of the channel phase terms such that the RIS-induced phases can be adjusted to maximize the received SNR through appropriate phase cancellations and proper alignment of reflected signals from the intelligent surface, where \(\varnothing_{i}=\theta_{s,i}+\theta_{r,i}\) for useful signals. Presuming that the values of all path-loss exponents in the equation are the same, where \(\beta=\beta_{s,i}=\beta_{r,i}=\beta_{c,k}\), the  
Figure 1: RIS-aided system model. instantaneous signal-to-interference noise ratio of RIS (\(SINR_{RIS}\)) at \(U\) using (1) is calculated as:  
\[SINR_{RIS}=\frac{\sum_{i=1}^{N}\left|h_{s,i}h_{r,i}\right|^{2}\left(rd\right)^{- \beta}}{\sum_{k=1}^{M}\left|h_{c,k}\right|\left|l_{k}{}^{-\beta}\delta_{k}+ \frac{1}{\rho}\right.}, \tag{2}\]  
where \(\rho=\frac{P}{\sigma^{2}}\) is the SNR.