# Interference Aware Resource Control for 6G-Enabled Expanded IoT Networks
## 2 System Model
### Data Transmission  
For the data transmission in the downlink, AP \(l\) transmits the data to user node \(k\), which is precoded using the precoder \(w_{kl}\) given below:  
\[w_{kl}=\frac{\hat{w}_{kl}}{\sqrt{E\{||\overline{w}_{kl}||^{2}\}}} \tag{8}\]  
The precoder is selected such that \(E\big{\{}||w_{kl}||^{2}\big{\}}=1\). The role of precoder is to cancel the interference caused by the neighbouring user nodes. The transmission to the intended user may be interference to the other users. The interference can be mitigated using optimal precoding schemes [51]. In the centralized operation, all the signal processing including precoding is performed at the CPU, where interference can be cancelled by varying the transmit powers and phases of the transmitting APs. In distributed operation, where the signal processing takes place at the AP, suitable precoding schemes are used [52]. Let \(x_{i}\) be the transmitted data signal intended for user node \(k\). The signal received by user node \(k\) from the transmission of AP \(l\) is  
\[y_{k}^{DL}=\sum\limits_{l=1}^{L}h_{kl}^{H}\sum\limits_{i=1}^{K}\eta_{il}w_{il} x_{i}+n_{k} \tag{9}\]  
where \(\eta_{il}\) is the power AP \(l\) assigned to user node \(i\) with \(\eta_{DL}\) being the maximum transmission power of each AP in the downlink. Depending on the network operation, different transmit precoding methods or schemes can be used [39]. Two main schemes used in the distributed operation are maximal ratio (MR) precoding and local partial minimum mean square error (LPMMSE) precoding.  
MR precoding--The scalable precoding scheme to cancel out the interference caused by the AP is MR precoding, which is described by the equation below:  
\[w_{il}^{MR}=\sqrt{\eta_{i}}\frac{\hat{h}_{il}}{\sqrt{E\left\{||\hat{h}_{il}|| ^{2}\right\}}} \tag{10}\]  
LPMMSE precoding--This precoding scheme is the optimal and scalable extension of local minimum mean square error (LMMSE) precoding where only the nodes serviced by AP are considered [53].  
\[w_{il}^{LPMMSE}=\eta_{i}\left(\sum\limits_{i\in U_{l}}\eta_{il}(\hat{h}_{il} \hat{h}_{il}^{H}+C_{il})+\sigma^{2}I_{N}\right)^{-1}\hat{h}_{il} \tag{11}\]  
where \(C_{il}=E\Big{\{}\widetilde{h}_{il}\;\widetilde{h}_{il}^{H}\Big{\}}\) is the error correlation matrix with \(\widetilde{h}_{il}\;=h_{il}-\hat{h}_{il}\) and \(U_{l}\) specifies the set of user nodes served by AP \(l\).  
In the centralized operation of cell-free systems, the scalable precoding scheme used is partial regularized zero forcing (PRZF) precoding.  
\[w_{il}^{PRZF}=\left[\hat{H}_{A_{k}}\left(\hat{H}_{A_{k}}^{H}\ \ \hat{H}_{A_{k}}+ \sigma^{2}P_{A_{k}}^{-1}\right)^{-1}\right]_{;1} \tag{12}\]  
where \(\hat{H}_{A_{k}}=\sum_{i}\hat{h}_{il}\) for \(i\in A_{k}\) and \(P_{A_{k}}=diag(\eta_{il})\)  
Another scalable precoding for centralized cell-free operation is partial minimum mean square error (PMMSE) precoding.  
\[w_{il}^{PMMSE}=\eta_{il}\left(\sum_{i\in A_{k}}\eta_{il}\hat{h}_{il}^{H}+\sum_{i \in A_{k}}\eta_{il}C_{il}+\sigma^{2}I_{N}\right)^{-1}\hat{h}_{il} \tag{13}\]  
The achievable sum spectral efficiency is given by  
\[SE_{k}=\left(1-\frac{\tau_{p}}{\tau_{c}}\right)log_{2}(1+\ SINR_{k}) \tag{14}\]  
\[\ SINR_{k}=\frac{\left|E\left\{\sum_{l=1}^{L}\eta_{il}h_{il}^{H}w_{kl}\right\} \right|^{2}}{\sum_{i=1}^{K}\left|E\left\{\sum_{l=1}^{L}\eta_{il}h_{kl}^{H}w_{il }\right\}\right|^{2}-\left|E\left\{\sum_{l=1}^{L}\eta_{kl}h_{kl}^{H}w_{kl} \right\}\right|^{2}} \tag{15}\]