## 2 System Model
### Distributed Antenna System (DAS) System Model  
DAS is an architecture wherein many antenna elements are geographically distributed and connect to a central BS in order to shorten the distance to the end users [14]. DAS provide coverage to the nearby users, and they are connected to the central BS via high-speed low-latency links, fiber or microwave [16; 17], or connected to the CPU at the central BS through fronthaul links [18]. Intuitively, uniformly distributed antenna clusters in each cell provide a significantly higher chance for a cell-edge user to be close to some BS antenna in the neighboring cell [19]. Here, we also assumed that all users have an identical number of antennas serving them [20]. Consider the same system model as the RIS model, but instead of user \(U\) receiving signals from the nearest DAS, user \(U\) is receiving signals from all DASs collocated with the BS [1] as in Figure 2. Hence, the signal received by the reference user \(U\) in the presence of C collocated DAS and CCI from \(M\) neighboring cells can be expressed as:  
\[y_{DAS}=\sqrt{P}x_{0}\left(\sum_{i=1}^{C}h_{i}\sqrt{r_{i}^{-\beta}}\ \right)+\sum_{k=1}^{M}\sqrt{P}x_{k}\left(\sum_{i=1}^{C}h_{i,k}\sqrt{l_{k,i} ^{-\beta}}\right)\delta_{k}+w_{0}, \tag{17}\]  
where the first term is the useful signal while the second term is the interfering signal, 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 BS, respectively, while \(P\) is the transmitted power from BS. \(\left|h_{i}\right|^{2}\) and \(\left|h_{i,k}\right|^{2}\) are the channel gains from home cell DASs to \(U\) and first-tier CC DASs to \(U\), respectively. \(\beta>2\) is the path loss exponent and \(\delta_{k}\) is the traffic-activity factor. The instantaneous SINR at \(U\) for DAS system is defined as:  
\[SINR_{DAS}=\frac{\sum_{i=1}^{C}\left|h_{i}\right|^{2}r_{i}^{-\beta}}{\sum_{k=1 }^{M}\sum_{i=1}^{C}\left|h_{i,k}\right|^{2}}l_{k,i}^{-\beta}\delta_{k}+\frac{1 }{\rho}. \tag{18}\]From the [PERSON] capacity formula, the ergodic capacity achieved by user \(U\) can be estimated as:  
\[C_{DAS}=E\left[log2\left(1+\frac{\sum_{i=1}^{C}|h_{i}|^{2}\ r_{i}^{-\beta}}{\sum_ {k=1}^{M}\sum_{i=1}^{C}|h_{i,k}|^{2}l_{k,i}\lx@math@degree^{-\beta}\delta_{k}+ \frac{1}{\rho}}\right)\right]. \tag{19}\]  
A non-direct method based on (4) is used to simplify the expression of the ergodic capacity into MGF terms. Including the PDF of reference of \(U\) schemes at radius \(d\) and angle \(\theta\) relative to DAS given by (9) and \(p_{d}(d)=\frac{2d}{\left(\frac{\theta}{3}\right)^{2}}\) for \(0\ \leq\ d\ \leq\ \frac{\theta}{3}\), the ergodic capacity can be simplified as:  
\[C_{DAS}=log_{2}e^{\int_{0}^{\infty}\int_{0}^{\frac{\theta}{3}}\int_{0}^{2\pi} \frac{1}{z}\left(1-\prod_{i=1}^{C}M_{2}(z)\right)\times\prod_{k=1}^{M}\prod_{i =1}^{C}M_{3}(z)\ e^{\frac{-\theta}{\rho}}\ \frac{2d}{\left(\frac{\theta}{3}\right)^{2}} \delta_{k}\ \frac{1}{2\pi}d\theta ddz, \tag{20}\]  
where  
\[M_{2}(z)=\left[1+\frac{z}{m}\left(\left(x_{i}-dcos(\theta)\right)^{2}+\left(y _{i}-dsin(\theta)\right)^{2}\right)^{\frac{-\beta}{2}}\right]^{-m}, \tag{21}\]  
and  
\[M_{3}(z)=\left[1+\frac{z}{m}\left(\left(x_{i,k}-dcos(\theta)\right)^{2}+\left( y_{i,k}-dsin(\theta)\right)^{2}\right)^{\frac{-\beta}{2}}\right]^{-m}. \tag{22}\]  
where \(x\) and \(y\) are the coordinate of DAS in a Cartesian plane. Regarding the effect of partially loaded traffic or traffic activity on the interfering cells, \(\delta_{k}\)= 1 if channel \(k\) is active, \(\delta_{k}\)= 0 otherwise. We include MGF of the Bernoulli distribution,  
Figure 2: DAS-aided system model.