## 2 System Model and Problem Formulation
### Optimization Model  
The objective of this article is to optimize the aggregate data rate of VUEs by integrating subcarrier allocation and power control techniques for both CUEs and VUEs, while simultaneously guaranteeing the minimum data rate requirements of all CUEs. This study examines a multiaccess resource matching strategy as a means to enhance the system throughput of VUEs. The optimization problem is formulated as a mixed-integer nonlinear programming (MINP) problem, which is generally difficult to solve. Therefore, the problem is divided into two subproblems: the resource-allocation problem and the power control problem. The resource-allocation problem determines the binary variables\(C_{i}^{p}\) and \(C_{j}^{p}\) using a heuristic algorithm that assigns subcarriers to CUEs and VUEs in a multiaccess manner. The power control problem determines the continuous variables using a successive convex approximation (SCA) method that transforms the non-convex problem into a convex problem.  
The optimization problem formulation is presented as follows.  
\[\begin{split} Problem\ 1:\max_{\{C_{i}^{p},C_{j}^{p},W_{i}^{p}\}}& \sum_{i=1}^{X}\sum_{\varpi=1}^{V}\left(\log(1+\psi_{i}^{p})\right),\\ \text{s.t}\\ c1:\ C_{i}^{p},C_{j}^{p}\in\{0,1\},\forall v\in V,\forall j\in Y, \forall i\in X,\\ c2:\sum_{j}^{Y}C_{j}^{p}\leq 1,\forall v\in V,\\ c3:W_{i}^{p}\leq W_{i}^{max},\forall i\in X,\\ c4:W_{j}^{p}\leq W_{i}^{max},\forall j\in Y,\\ c5:\sum_{\varpi=1}^{V}\Psi_{j}^{\varpi}\geq\Psi_{j}^{size}, \forall j\in Y\end{split} \tag{4}\]  
Equation (4) is the objective function and the constraints for maximizing the sum of the data rates of the VUEs. Here are the parameters in Equation (4): \(C_{i}^{p}\) and \(C_{j}^{p}\) are the binary variables that indicate the mapping relationship between subcarrier \(v\) and VUEi or CUEj. If VUEi or CUEj is allowed to use the subcarrier \(v\), then \(C_{i}^{v}\) or \(C_{j}^{v}\) is 1; otherwise it is 0. \(W_{i}^{v}\) and \(W_{j}^{v}\) are the transmit power of VUEi or CUEj on the subcarrier \(v\). \(\psi_{i}^{p}\) and \(\psi_{j}^{p}\) are the SINR of VUEi or CUEj on the subcarrier \(v\), which depends on the channel power gains and the interference from other users. \(\Psi_{j}^{v}\) is the data rate of CUEj on the subcarrier \(v\), which is a function of \(\psi_{j}^{v}\). \(\Psi_{j}^{size}\) is the minimum data rate requirement size of CUEj, which is a constant value. The objective function is to maximize the sum of the logarithms of \((1+\psi_{i}^{v})\) for all VUEs and subcarriers, which is equivalent to maximizing the sum of the data rates of the VUEs. For the constraints, \(c1\) represents that the binary variables \(C_{i}^{p}\) and \(C_{j}^{p}\) must be either 0 or 1. \(c2\) is that each subcarrier can only be used by one CUE, to avoid interference among CUEs. \(c3\) and \(c4\) are the transmit power of VUEs and CUEs and must not exceed their maximum values, which are \(W_{i}^{max}\) and \(W_{j}^{max}\), respectively. \(c5\) is the sum of the data rates of CUEj on all subcarriers which must be greater than or equal to \(\Psi_{j}^{size}\), to ensure the quality of service of CUEs.