## 4 Simulation Results, Theoretical Calculation, and Analysis
### Multi-Path Design (\(M\geq 1\)) and Simulation Results  
In the case of multi-path transmission under the AUA scheme, we set a parameter \(M\) in the system to limit the maximum number of simultaneous transmissions for the cooperation node. Parameter \(k\) represents the transmission times (\(t=k\)). Multiple cooperation nodes or UE transmitting at the same time was counted as one time. Supposing that there were \(N_{\text{C}}\) cooperation nodes in the cell, the angle (\(\theta_{k}\)) between the UE and the farthest cooperation node that successfully decoded the UE data in the direction of the BS at the \(k\)th time unit could be expressed as  
\[\theta_{k}= \begin{cases}\arccos\frac{r^{2}+d_{\text{UB},i}^{2}-kd_{\text{th}}^{2 }}{2n_{\text{UB},i}}&,|d_{\text{UB},i}-r|<\sqrt{k}d_{\text{th}}<|d_{\text{UB},i }+r|,k>0\\ 0&,\text{elsewhere}\end{cases}  \tag{11}\]  
where \(r\) is the distance between the cooperation node and BS, \(d_{\text{UB},i}\) is the distance between the \(i\)th UE and BS, and \(\sqrt{k}d_{\text{th}}\) is the maximum radius that can be covered when the \(i\)th UE transmits \(k\) times. This means that \(\eta_{k}\) of the cooperation nodes successfully decoded the UE's information after the \(k\)th transmission of the UE, and then these cooperation nodes could assist in the next time unit (\(t=k+1\)). Meanwhile, \(\eta_{k}\) can be expressed as\[\eta_{k}= \begin{cases}\frac{\theta_{k}}{\gamma}&k=1,2,3,\cdots\\ 0&k=-1,0\end{cases}  \tag{12}\]  
In order to realize the effect of the multi-path scheme, we introduced three regulators to accomplish this task, which are \(p\), \(q\), and \(\mu\). These three regulators can calculate the number of assisted transmission cooperation nodes for each transmission time, whether the cooperation node assists, and whether the UE stops transmitting at this time:  
\[\gamma=\sum_{i=1}^{k}\left(\sum_{j=1}^{i}p_{j}\mu_{j}\Delta M_{j}\gamma_{\text{ CB}}+q_{i}\gamma_{\text{UB}}\right) \tag{13}\]  
\[\Delta M_{j}=\left\lfloor\eta_{j-1}N_{\text{C}}\right\rfloor-\left\lfloor\eta _{j-2}N_{\text{C}}\right\rfloor \tag{14}\]  
where \(\gamma\) is the information that the base station has already decoded, \(\Delta M_{j}\) is the amount of new successfully decoded cooperation nodes at the \(j\)th time unit, \(\mu_{j}\) is used to dynamically select the number of cooperation nodes for each new assistance cooperation node, and \(p_{j}\) and \(q_{j}\) represent whether the cooperation node assists the UE in sending information at the \(i\)th time unit and whether the UE needs to reserve energy and not send information in this time unit, respectively. Through the aforementioned \(\alpha\) and \(\beta\), the UE with a cell can be divided into three groups: UE-only transmission, UE aggregation, and cooperation node-only transmission, which is the main idea of adaptive UE aggregation. If user equipment is located in a UE-only transmission area, then just set \(p_{i}=0,q_{i}=1\), and \(\mu_{i}=0\). When the position of the user equipment is close to the cooperation node, the more cooperation nodes assist, the lower the delay will become. However, the maximum number of simultaneous assisted cooperation nodes can be set in the system, which is denoted by \(M\). In this case, \(M\) cooperation nodes decode the information successfully when the \(i\)th UE transmits \(\sigma-1\) times (\(t=\sigma-1\)), which means that \(M\) cooperation nodes can assist the UE to transmit data at \(t=\sigma\). The corresponding regulators can be defined as \(p_{1}=p_{2}=\cdots=p_{\sigma}=1,p_{\sigma+1}=p_{\sigma+2}=\cdots=0,q_{i}=1\), and \(\mu_{j}\) is defined as in Equation (15). Moreover, if the location of the UE is far away from the BS, then there is no need for the UE to transmit information when enough cooperation nodes can assist it. This can save energy for the specified UE. In this case, the corresponding regulators can be defined as \(p_{1}=p_{2}=\cdots=p_{\sigma}=1,p_{\sigma+1}=p_{\sigma+2}=\cdots=0,q_{1}=q_{2}= \cdots=q_{\sigma-1}=1,q_{\sigma}=q_{\sigma+1}=\cdots=0\).