## 2 System Model  
In this paper, we investigate an industrial wireless network in which some devices, referred to as eMBB devices (such as monitoring cameras), transmit video information to a centralized controller, while devices referred to as mMTC devices (such as sensors and actuators), transmit short blocklength packets to their adjacent devices to promote inter-device cooperation and industrial automation. The system model is illustrated in Figure 1, where \(N\) eMBB devices and \(M\) mMTC devices are randomly distributed, represented by sets \(\mathcal{N}=\left\{CU_{1,...,C}U_{i,...,C}CU_{N}\right\}\) and \(\mathcal{M}=\left\{MU_{1,...,M}U_{j,...,M}U_{M}\right\}\), respectively. The mMTC devices transmit information from the transmitters to receivers by the D2D communication mode, and the mMTC pairs reuse the eMBB devices' uplink resources in order to improve the spectrum efficiency. The mMTC pairs and eMBB devices are represented by \(MU_{j}\) and \(CU_{i}\), respectively. Each mMTC pair is composed of one mMTC transmitter and one mMTC receiver represented by \(MU_{j}^{t}\) and \(MU_{j}^{t}\), respectively. All available spectrum resources are divided into sub-carriers with the same bandwidth. Each eMBB device occupies mutually orthogonal sub-carriers. Therefore, there is no co-channel interference between the eMBB devices. We assume that the eMBB device \(CU_{i}\) occupies the subcarrier \(i\). Considering the impact of devices on each other, each mMTC pair is allowed to access no more than one subcarrier, and each subcarrier can be accessed by multiple mMTC devices. All of the channels in the system are assumed to be quasi-static Rayleigh fading channels. The channel gain remains constant for each symbol transmission period but varies independently between different symbol periods. The parameters in the article are shown in Table 1.  
We define a binary subcarrier allocation matrix \(A\in\{0,1\}^{M\times N}\), where \(\alpha_{ij}=1\) indicates that \(M\)U\({}_{j}\) occupies subcarrier \(i\), otherwise \(\alpha_{ij}=0\), \(i\in\mathcal{N}\), \(j\in\mathcal{M}\). Thus, the received signal of the base station on subcarrier \(i\) is  
\[y_{i}=\sqrt{P_{i}^{c}}g_{i,B}x_{i}+\sum_{j\in\mathcal{M}}\alpha_{ij}\sqrt{P_{j} ^{d}}h_{j,B}x_{j}+n_{0}, \tag{1}\]  
where \(x_{i}\) and \(x_{j}\) are the transmitted signals of the eMBB devices \(CU_{i}\) and the mMTC transmitter \(M\)U\({}_{j}^{t}\), respectively. \(n_{0}\) represents normalized additive white Gaussian noise, \(n_{0}\sim\mathcal{CN}\left(0,\sigma_{0}^{2}\right)\). When the centralized controller receives the uplink signals of the eMBB device \(CU_{i}\), the SINR at centralized controller can be calculated as  
\[\gamma_{cu}^{i}=\frac{\left|g_{i,B}\right|^{2}P_{i}^{c}}{I+\sigma_{0}^{2}B}, \tag{2}\]  
where \(B\) is the subcarrier bandwidth and \(I\) represents the interference caused by the mMTC pairs which access the subcarrier \(i\):  
\[I=\sum_{j=1}^{M}\alpha_{ij}P_{j}^{d}\left|h_{j,B}\right|^{2}. \tag{3}\]  
Since the eMBB devices transmit long packet data, the achievable transmission rate of the eMBB device \(CU_{i}\) can be obtained by [PERSON]'s theorem:  
\[R_{cu}^{i}=B\log\left(1+\gamma_{cu}^{i}\right). \tag{4}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Description** \\ \hline \(g_{j}\) & Gain between \(M\)U\({}_{j}^{t}\) and \(M\)U\({}_{j}^{t}\) \\ \(g_{i,B}\) & Gain between \(CU_{i}\) and the centralized controller \\ \(h_{i,j}\) & Interference gain between \(CU_{i}\) and \(M\)U\({}_{j}^{t}\) \\ \(h_{j,B}\) & Interference gain between \(M\)U\({}_{j}^{t}\) and the centralized controller \\ \(f_{i^{\prime},j}\) & Interference gain between \(M\)U\({}_{j}^{t}\) and \(M\)U\({}_{j}^{t}\) \\ \(P_{i}^{c}\) & The transmit power of \(CU_{i}\) \\ \(P_{j}^{d}\) & The transmit power of \(M\)U\({}_{j}^{t}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters. Figure 1: System model.