# Interference Aware Resource Control for 6G-Enabled Expanded IoT Networks
## 2 System Model  
In this section, an IoT-enabled communication scenario involving large number of user nodes is considered where their communication is assisted by large number of access points (APs). Suppose \(K\) be the number of user nodes and \(L\) be the number of APs in a given IoT network. The user nodes are assumed to be equipped with a single antenna while the APs have multiple \(N\) antennas. The communication framework is shown in Figure 1. It assumes a user-centric cell-free approach in which a set of APs serves a particular user node. Let \(A_{k}\) define a subset of APs that serve a particular user node \(k\) such that \(A_{k}\subset\{1,2,\ldots L\}\) and for every \(k\) and \(l\)  
\[q_{kl}=\left\{\begin{matrix}1&l\in A_{k}\\ 0&l\
otin A_{k}\end{matrix}\right\} \tag{1}\]  
The communication model that supports the transmission between each AP and each node adopts the block fading channel where the channel coefficients \(h_{kl}\) between user \(k\) and AP \(l\) remain constant for each coherence block consisting of \(\tau_{c}\) transmission symbols. The channel characteristics are estimated using uplink pilot training in the pilot transmission  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Description** \\ \hline \(L\) & Number of APs \\ \hline \(N\) & Number of antennas at each AP \\ \hline \(K\) & Number of user nodes \\ \hline \(\alpha\) & Path loss exponent \\ \hline \(\eta_{k}\) & Transmit power of user \(k\) \\ \hline \(\tau_{p}\) & Pilot length \\ \hline \(\psi\) & A set of \(t_{p}\) pilot sequences \\ \hline \(x_{i}\) & Transmitted signal \\ \hline \(A_{k}\) & Set of APs serving node k \\ \hline \(n_{tl}\) & Receiver noise \\ \hline \(N_{n}\) & Receiver noise during pilot transmission phase \\ \hline \(h_{kl}\) & Channel coefficients between node \(k\) and AP \(l\) \\ \hline \(\widehat{h}_{kl}\) & Estimated channel coefficients \\ \hline \(\zeta_{kl}\) & Large scale fading coefficients \\ \hline \(r_{kl}\) & Distance between AP \(l\) and node \(k\) \\ \hline \(w_{kl}\) & Precoding vector \\ \hline \(y_{k}^{DL}\) & Received downlink signal \\ \hline \(U_{l}\) & Set of nodes served by AP \(l\) \\ \hline \(R_{kl}\) & Spatial correlation matrix \\ \hline \(\varphi_{t_{k}l}\) & Correlation matrix of the received signal \\ \hline \(C_{il}\) & Error correlation matrix \\ \hline \(L_{\tau,k}\) & Set of interfering APs of node \(k\) \\ \hline \(U_{\tau,k}\) & Interfering nodes to node \(k\) \\ \hline \(I_{\tau,k,l}\) & Interference metric \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of notations.  
phase. The fading associated with the channels in each block is spatially correlated Rayleigh fading denoted as  
\[h_{kl}\sim\mathcal{N}(0,R_{kl}) \tag{2}\]  
\(h_{kl}\) are the independent and identically distributed channel elements drawn from Gaussian distribution with mean 0 and variance \(R_{kl}\). Here, \(R_{kl}\) is the spatial correlation matrix, which is related with the large scale fading given by  
\[\zeta_{kl}=tr\bigg{(}\frac{R_{kl}}{N}\bigg{)} \tag{3}\]  
The large scale fading includes path loss with exponent \(\alpha\) and shadowing \(F_{kl}\) denoted as [50]  
\[\zeta_{kl}[dB]=-30.5-36.7 log_{10}(\frac{r_{kl}}{1m})+F_{kl} \tag{4}\]  
with \(r_{kl}\) being the distance between AP \(l\) and user node \(k\). The network operation is assumed in which the \(\tau_{c}\) symbols of coherence block comprise of \(\tau_{p}\) symbols for pilot training and \(\tau_{c}-\tau_{p}\) for data transmission.