## 4 Simulation Results, Theoretical Calculation, and Analysis
### Theoretical Calculation and Simulation of \(\alpha\) and \(\beta\)  
In order to optimize the EDP of the whole system, the calculation of energy consumption and latency plays an important role in the whole simulation, and this is expressed in the following equations:  
\[E_{i}=\min\left\{\underbrace{T_{\text{UC},i1}+2T_{\text{CB},i1},\cdots,T_{ \text{UC},iN_{\text{U}}}+2T_{\text{CB},iN_{\text{U}}},T_{\text{UB},i}}_{N_{ \text{U}}+1}\right\}\cdot P_{i}t_{0} \tag{4}\]  
\[T_{i}=\min\left\{\underbrace{T_{\text{UC},i1}+T_{\text{CB},i1},\cdots,T_{ \text{UC},iN_{\text{U}}}+T_{\text{CB},iN_{\text{U}}},T_{\text{UB},i}}_{N_{ \text{U}}+1}\right\}\cdot t_{0} \tag{5}\]  
Figure 9: The performance critical values vs. distance under different schemes. **(a)** Latency performance. (**b**) Energy performance. (**c**) EDP. \[\text{EDP}_{i}=E_{i}\cdot T_{i} \tag{6}\]  
where \(E_{i}\) represents the overall energy consumption when the BS successfully decodes the data of the \(i\)th UE, \(T_{i}\) represents the overall latency when the BS successfully decodes the data of the \(i\)th UE, \(T_{\text{UC},ij}\) is the transmission number of the \(i\)th UE data successfully decoded at the \(j\)th cooperation node, \(T_{\text{UB},i}\) is the transmission number of the \(i\)th UE transmitting to the BS without cooperation node assistance, \(T_{\text{CB},ij}\) is the transmission number of the \(j\)th cooperation node assisting the \(i\)th UE to the BS, \(\text{EDP}_{i}\) represents the energy-delay product of the \(i\)th UE, \(P_{i}\) is the unit of transmission power, and \(t_{0}\) is the unit of time. In addition, we have  
\[\left\{ \begin{array}{l}T_{1}=\left\lceil 10^{\frac{7\text{th}-7\text{UC}}{10}} \right\rceil\\ \\ T_{2}=\left\lceil 10^{\frac{7\text{th}-7\text{UB}}{10}}\right\rceil\\ \\ T_{3}=\left\lceil\frac{10^{\frac{7\text{th}}{10}}-10^{\frac{7\text{th}}{10}} \cdot T_{1}}{10^{\frac{7\text{th}}{10}}+10^{\frac{7\text{th}}{10}}}\right\rceil \\ \\ \text{EDP}_{1}=T_{2}^{2}\cdot P_{\text{t}}t_{0}\\ \\ \text{EDP}_{2}=(T_{1}+2T_{3})(T_{1}+T_{3})\cdot P_{\text{t}}t_{0}\end{array} \right. \tag{7}\]  
where \(T_{1}\) represents the transmission number of the UE to the cooperation node if the cooperation node assists, \(T_{2}\) represents the transmission number of the UE to the BS if the cooperation node does not assist, \(T_{3}\) represents the transmission number of the UE and cooperation node to the BS after the cooperation node successfully decodes the data and prepares to assist the UE, \(\text{EDP}_{1}\) is the EDP of Case 2 with the combination scheme, and \(\text{EDP}_{2}\) is the EDP of the multi-path transmission scheme. In order to find out the best \(\alpha\) here, the value of \(\text{EDP}_{2}\) must be less than \(\text{EDP}_{1}\); that is, \(T_{2}^{2}>(T_{2}+2T_{3})(T_{2}+T_{3})\). When the simulation settings were as displayed in Table 2, we could calculate the distance between the UE and BS to be \(d\approx 275.3\) m. The value of \(\alpha\) was \(\alpha\approx 5.1833\) dB under the current simulation settings:  
\[T_{4}=\left\lceil 10^{\frac{7\text{th}-7\text{CB}}{10}}-10^{\frac{7\text{UB}-7 \text{CB}}{10}}\cdot T_{1}\right\rceil \tag{9}\]  
\[\left\{ \begin{array}{l}\text{EDP}_{3}=(T_{1}+T_{4})^{2}\cdot P_{\text{t}}t_ {0}\\ \\ \text{EDP}_{4}=(T_{1}+2T_{3})(T_{1}+T_{3})\cdot P_{\text{t}}t_{0}\end{array} \right. \tag{10}\]  
where \(T_{4}\) represents the transmission number of the cooperation node to the BS after the cooperation node received data and assisted the UE, \(\text{EDP}_{3}\) is the EDP of Case 2 with the combination scheme, and \(\text{EDP}_{4}\) is the EDP of the multi-path transmission scheme. In order to find out the best \(\beta\) value here, the value of \(\text{EDP}_{4}\) must less than \(\text{EDP}_{3}\); that is, \((T_{1}+T_{4})^{2}>(T_{1}+2T_{3})(T_{1}+T_{3})\). When the simulation settings were as displayed in Table 2, we could calculate the distance between the UE and BS to be \(d\approx 716\) m. The value of \(\beta\) was \(\beta\approx 3.1189\) dB under the current simulation setting.