## 3 Multiaccess Resource Allocation Algorithms and Power Control
### Power-Optimization Algorithms  
The utilization of a multiaccess channel matching system in this study enables the possibility of several users sharing a common subcarrier. Consequently, the issue of interference among users inside the same channel becomes significantly complicated. Therefore, in order to alleviate the accumulated interference between users using the same channel, and further improve the throughput of VUEs while ensuring the data rate requirements of CUEs, it is necessary to perform power control. The issue of allocating spectrum resources has been addressed in the preceding section, where the binary variables {\(C_{i}^{v}\), \(C_{j}^{v}\)} were determined. The signal-to-interference-plus-noise ratio (SINR) of VUEi on the \(v\)-th subcarrier is now being redefined. \[\psi_{i}^{v}=\frac{W_{i}^{v}a_{i}^{v}}{\theta^{2}+\sum_{i^{\prime}\in B_{v},i^ {\prime}\
eq i}W_{i}^{v}a_{i^{\prime}}^{v}+\sum_{j\in E_{v}}W_{j}^{v}a_{j}^{v}}, \tag{6}\]  
The corresponding power control problem is then formulated as  
\[\textit{Problem 3}:\max_{\{W_{i}^{v}\}}\sum_{i=1}^{X}\sum_{v=1}^{V}(\log(1+ \psi_{i}^{v})),\]  
s.t  
\[ \begin{split} c3:W_{i}^{v}&\leq W_{i}^{max},\forall i \in X,\\ c4:W_{j}^{v}&\leq W_{j}^{max},\forall j\in Y,\\ c5:\sum_{v=1}^{V}C_{j}^{v}\Psi_{j}^{v}&\geq\Psi_{j }^{size},\forall j\in Y,\end{split}  \tag{7}\]We examine the inherent non-convexity of the optimization problem, which presents significant challenges in its resolution, particularly within the context of multiaccess resource allocation. Since _Problem 3_ has a non-convex objective function and the constraint \(c5\), _Problem 3_ is a non-convex optimization problem, and it is usually difficult to solve in the scenario of multiaccess resource allocation. In order to tackle this issue, we utilize the SCA technique. The fundamental concept underlying SCA involves the conversion of a non-convex problem (_Problem 4_) into a convex problem (_Problem 5_). The problem is solved iteratively using a convex optimization toolbox called CVX [49] until convergence is attained. By applying the characteristics of logarithmic functions, we can convert the given expression into the conventional D.C form, where \(q(W)\) and \(s(W)\) represent concave functions, as will be demonstrated in _Problem 4_. The process of transformation encompasses the alteration of both the objective function and the constraint \(c5\). First, the objective function transformation  
\[q_{i}(W)-s_{i}(W), \tag{8}\]  
where \(q_{i}(W)\) and \(s_{i}(W)\) are, respectively,  
\[q_{i}(W)=\sum_{\
u=1}^{V}\log(W_{i}^{\
u}a_{i}^{\
u}+\theta^{2}+\sum_{i^{ \prime}\in B_{\
u^{\prime}},i^{\prime}\
eq i}W_{i}^{\
u}a_{i^{\prime},i}^{ \
u}+\sum_{j\in E_{\
u}}W_{j}^{\
u}a_{jj}^{\
u}), \tag{9}\]  
\[s_{i}(W)=\sum_{\
u=1}^{V}\log(\sum_{i^{\prime}\in B_{\
u^{\prime}},i^{\prime} \
eq i}W_{i}^{\
u}a_{i^{\prime},i}^{\
u}+\sum_{j\in E_{\
u}}W_{j}^{\
u}a_{jj}^ {\
u}+\theta^{2}), \tag{10}\]  
Second, we construct and update the constrain c5 with this conversion  
\[q_{j}(W)-s_{j}(W), \tag{11}\]  
where \(q_{j}(W)\) and \(s_{j}(W)\) are, respectively,  
\[q_{j}(W)=\sum_{\
u=1}^{V}\log(W_{j}^{\
u}a_{j}^{\
u}+\theta^{2}+\sum_{i}^{X}C_ {i}^{\
u}W_{i}^{\
u}a_{i,D}^{\
u}), \tag{12}\]  
\[s_{j}(W)=\sum_{\
u=1}^{V}\log(\theta^{2}+\sum_{i}^{X}C_{i}^{\
u}W_{i}^{\
u}a_ {i,D}^{\
u}), \tag{13}\]  
Problem reformulation: By inserting Equations (8) and (11) into Equation (7) as a result of the aforementioned transformation, Problem 3 can be restated. \[\text{\emph{Problem 4}}:\underset{\{W_{i}^{\
u}\}}{\max} \sum_{i=1}^{X}q_{i}(W)-s_{i}(W), \tag{14}\] \[\text{s.t}\] \[\text{c3}:W_{i}^{\
u}\leq W_{i}^{max},\forall i\in X,\] \[\text{c4}:W_{j}^{\
u}\leq W_{j}^{max},\forall j\in Y,\] \[q_{i}(W)=\sum_{\
u=1}^{V}\log(W_{i}^{\
u}a_{i}^{\
u}+\theta^{2}+\sum_{i^{ \prime}\in B_{\
u^{\prime}},i^{\prime}\
eq i}W_{i}^{\
u}a_{i^{\prime},i}^{ \
u}+\sum_{j\in E_{\
u}}W_{j}^{\
u}a_{jj}^{\
u}), \tag{9}\]0  
Problem 4 can be characterized as a conventional D.C. expression, representing the difference between two concave functions.