## 2 System Model  
In this paper, we consider a downlink in a UCCF M-MIMO network deployed according to the open RAN architecture with a centralized virtual CU-DU managing \(N_{\text{RU}}\) RUs. The RU of index \(l\) is equipped with an M-MIMO antenna array of \(M_{l}\) elements and has a total maximum radiation power of \(P_{l}\). We assume a full-digital antenna array, i.e., each of the \(M_{l}\) antennas is associated with a dedicated transceiver chain. At the end of the \(m\)-th transceiver chain, just before the antenna, there is a PA with a maximum output power (sometimes called saturation power) of \(P_{\max,l}=\frac{P_{l}}{M_{l}}\). In the literature, there exists the concept of hybrid beamforming, where a single transceiver chain is connected to several antennas to reduce implementation costs and computational complexity [16]. However, the full digital approach allows us to set precoder weights far more accurately, i.e., individually for each antenna. This enables us to achieve an upper bound of user throughput. While at the current stage of implementation of 5G systems hybrid beamforming is most likely to be practically used, future 6G systems can be expected to utilize more advanced solutions, e.g., due to more optimized hardware design. The operation point of all PAs can be set to the \(l\)-th RU in terms of a so-called Input Back-Off (IBO) \(\gamma_{l}\), which is the ratio between the input saturation power of the PA and the average power of the input signal. Lowering the operation point of the PA can avoid signal clipping and reduce the resultant nonlinear distortion, which is discussed in Section 3. In the case of a _perfect_ PA, as considered typically in the literature, it is assumed that the average signal power at the PA output is equal to the saturation power. However, in this case, no nonlinear distortion will be modeled. The considered UCCF M-MIMO network is OFDMA-based and utilizes bandwidth \(B\) allocated at carrier frequency \(f\). The bandwidth is split into \(N_{\text{rb}}\) resource blocks (RBs). Each of them exploits 12 OFDM subcarriers in the frequency domain and lasts one time slot of \(T_{\text{slot}}\). We assume that within a single RB of index \(r\), the radio channel is flat. Thus, the vector of the complex radio channel coefficients between the \(i\)-th single-antenna User Equipment (UE) and the M-MIMO RU \(l\) for RB \(r\) is given by:  
\[\mathbf{h}_{i,l,r}=\big{[}h_{i,l,r,1}\quad h_{i,l,r,2}\quad\cdots\quad h_{i,l,r,M_{l}}\big{]}^{T}. \tag{1}\]  
We assume that each radio channel coefficient already takes into account the antenna gain. The radio channel coefficients are estimated by the RUs and then transferred to the CU-DU for the purpose of centralized formulation of serving clusters, radio resource scheduling, calculation of precoder weights, power allocation, and MCS selection. To reduce the computational complexity of the considered UCCF M-MIMO system, we assume that the calculations of the precoder weights and power allocation are performed independently for each RU, as this allows for avoiding inversions of large matrices while utilizing a Zero-Forcing (ZF) precoder. As we are considering a multicarrier system, we also assume that both the precoder weights and power allocation are calculated independently for each RB \(r\).