## 2 System Model
We assume that a single MCS is allocated for each scheduled user. For this purpose, an effective signal quality metric must be obtained for all RBs allocated to this user, i.e., the so-called effective SINR. It has been shown in the literature that for the considered multicarrier OFDM system that is prone to frequency-selective fading of radio channels, the proper effective SINR metric is Exponential Effective SINR Mapping (EESM) [17]. The EESM for UE \(i\) depends on the selected MCS and can be calculated as follows:  
\[ \begin{split}\text{EESM}_{i,mcs}&=-\beta_{mcs}\ln \left(\frac{1}{N_{\text{rb}}}\sum_{r\in\mathcal{R}_{i}}\exp\left(-\frac{\text{ SINR}_{i,r}}{\beta_{mcs}}\right)\right),\end{split}  \tag{5}\]  
where \(\mathcal{R}_{i}\) is a set of indices of the RBs allocated to UE \(i\), and \(\beta_{mcs}\) serves as an approximate value to adjust for the selected modulation alphabet and coding rate. It will be adjusted by the CU-DU based on the selected MCS (see Section 4.4). As in practice, both the virtualized CU-DU and each of the physical RUs have limited computational resources, it is of high importance to ensure reasonable scaling of the UCCF M-MIMO network. Following the definition in [3], the UCCF M-MIMO network is scalable when each of the following tasks has finite computational complexity and resource requirements concerning each RU as \(N_{\text{UE}}\rightarrow\infty\) in the whole network:  
1. Signal processing for channel estimation. 2. Signal processing for data reception and transmission. 3. Fronthaul signaling for data and Channel State Information (CSI) sharing. 4. Power allocation optimization. One of the possible solutions to meet scalability tasks 1-3 is to limit the number of users that a single RU can serve. Naturally, the single RU can only serve users that are within range of its reference signals. This limits the number of users for the channel estimation. Moreover, M-MIMO networks usually utilize a limited number of pilot sequences that put a boundary on the channel estimation computational resources, allowing them to meet scalability task 1. In the considered network, the result of serving cluster formulation is not directly related to signal processing for data reception and transmission. It can be that the RU serves many UEs but only a fraction of them currently have radio resources allocated. To set the maximum complexity of data reception and transmission in the considered UCCF M-MIMO network, we assume that there is a maximum number of Multi-User MIMO (MU-MIMO) layers that a single RU can create, i.e., a single RB can be allocated to a maximum of \(N_{\text{L}}\) users within a single RU. This allows us to meet the requirements of scalability task 2. With the fixed maximum number of MU-MIMO layers, the size of the precoding matrices will be limited, resulting in finite computational complexity of reception and transmission. As each of the RUs can support only a finite number of pilot sequences for channel estimation and MU-MIMO layers, the fronthaul signaling overhead (task 3) also has finite computational complexity. Finally, the computational complexity of power allocation optimization depends highly on the utilized algorithm. However, one can imagine low-complexity algorithms that can be applied independently for users served by each RU, e.g., an equal-power division that would offer finite computational complexity requirements, meeting scalability task 4.