## 2 System Model
As a result, RU \(l\) transmits the following signal to UE \(i\) at RB \(r\) if scheduled:  
\[\mathbf{X}_{i,l,r}=\sqrt{\frac{p_{i,l,r}}{12}}\delta_{i,r}\mathbf{D}_{i,l} \mathbf{A}\mathbf{w}_{i,l,r}^{T}\xi_{i}, \tag{2}\]  
where \(p_{i,l,r}\) is the power allocated to UE \(i\) by RU \(l\) at RB \(r\); \(\mathbf{w}_{i,l,r}\) is the vertical vector of the precoder weights with a mean power equal to one; \(\delta_{i,r}\) represents the result of radio resource scheduling (\(\delta_{i,r}=1\) if RB \(r\) is allocated to UE \(i\); otherwise, it is equal to zero); \(\mathbf{D}_{i,l}\) is a matrix that is the result of serving cluster formulation, defined as \(\mathbf{D}_{i,l}=\mathbf{I}_{M_{l}}\) if the \(i\)-th UE is being served by the \(l\)-th RU and otherwise, \(\mathbf{D}_{i,l}=\mathbf{0}_{M_{i}}\); \(\mathbf{A}_{l}\) is a diagonal matrix of size \(M_{l}\), with each element \(\alpha_{m,l}\) being the nonlinear attenuation of the desired signal for the \(m\)-th antenna of RU \(l\) (see Section 3); and \(\xi_{i}\) is the vector of 12 downlink QAM symbols of UE \(i\), i.e., one symbol per subcarrier. We can treat each element of \(\xi_{i}\) as an uncorrelated random variable of zero mean and a variance equal to one. Considering that there are \(N_{\text{UE}}\) users in total in the considered UCCF M-MIMO network, the total downlink signal received by UE \(i\) at RB \(r\) is given by:\[ \begin{split}\mathbf{y}_{i,r}&=\sum_{l=1}^{N_{\text{BU}}} \sum_{k=1}^{N_{\text{UE}}}\mathbf{h}_{i,l,r}^{H}\cdot\mathbf{X}_{k,l,r}+n_{i,r} +n_{\text{dis},i}\\ &=\underbrace{\left(\sum_{l=1}^{N_{\text{BU}}}\sqrt{\frac{p_{i, l,r}}{12}}\delta_{i,r}\mathbf{h}_{i,l,r}^{H}\mathbf{D}_{i,l}\mathbf{A}_{i} \mathbf{w}_{i,l,r}^{T}\right)}_{\text{Desired Signal}}\xi_{i}+\\ &+\underbrace{\sum_{\begin{subarray}{c}k=1\\ k\
eq i\end{subarray}}^{N_{\text{UE}}}\left(\sum_{l=1}^{N_{\text{BU}}}\sqrt{ \frac{p_{k,l,r}}{12}}\delta_{k,r}\mathbf{h}_{i,l,r}^{H}\mathbf{D}_{k,l} \mathbf{A}_{i}\mathbf{w}_{k,l,r}^{T}\right)}_{\text{Inter-user interference}}\xi_{k}+ \underbrace{n_{i,r}}_{\text{Noise}}+\underbrace{n_{\text{dis},i,r}}_{\text{ Distortion}},\end{split}  \tag{3}\]  
where \(n_{i,r}\) denotes the thermal noise, and \(n_{\text{dis},i,r}\) denotes the nonlinear distortion term that is the result of RU's PA characteristics, which is described in Section 3. It can be seen that both the desired signal and inter-user interference terms contain summation over all RUs. In this work, we consider that RUs are perfectly synchronized and connected with a backhaul of negligible latency. This is the best-case scenario in the context of a UCCF M-MIMO network, as it allows for the highest gains in the desired signal. Based on Equation (3), we can formulate the Signal-to-Interference-plus-Noise Ratio (SINR) for UE \(i\) at RB \(r\):  
\[ \begin{split}\text{SINR}_{i,r}&=\frac{\left|\sum_{l =1}^{N_{\text{BU}}}\sqrt{p_{i,l,r}}\delta_{i,r}\mathbf{h}_{i,l,r}^{H}\mathbf{D} _{i,l}\mathbf{A}_{i}\mathbf{w}_{i,l,r}^{T}\right|^{2}}{\sum_{k=1}^{N_{\text{ UE}}}\left|\sum_{l=1}^{N_{\text{BU}}}\sqrt{p_{k,l,r}}\delta_{k,r}\mathbf{h}_{i,l,r}^{H} \mathbf{D}_{k,l}\mathbf{A}_{i}\mathbf{w}_{k,l,r}^{T}\right|^{2}-\left|\sum_{l =1}^{N_{\text{BU}}}\sqrt{p_{i,l,r}}\delta_{i,r}\mathbf{h}_{i,l,r}^{H}\mathbf{ D}_{i,l}\mathbf{A}_{i}\mathbf{w}_{i,l,r}^{T}\right|^{2}+\sigma_{i,r}^{2}+ \sigma_{\text{dis},i,r}^{2}},\end{split}  \tag{4}\]  
where \(\sigma_{r}^{2}\), and \(\sigma_{\text{D},i,r}^{2}\) are the power of the thermal noise and nonlinear distortion per RB, respectively. As the radio channels between the users and precoder weights are known in the CU-DU at the stage of resource scheduling, the SINR can be relatively well approximated. Unfortunately, this is not the case when considering nonlinear distortion. However, the UE is capable of reporting interference levels that can be used to estimate the distortion terms, e.g., interference can be calculated based on Channel Quality Indicator (CQI) reports. Such an estimation is necessary to select the proper MCS by the CU-DU.