## 4 Simulation Results, Theoretical Calculation, and Analysis
### Multi-Path Design (\(M\geq 1\)) and Simulation Results
After that, the overall energy consumption and overall latency can be expressed as in Equations (16) and (17):  
\[\mu_{j}= \begin{cases}0&,\Delta M_{j}=0\\ \min\left\{\frac{\max\left\{M-\left\lfloor\eta_{j-2}N_{\text{C}}\right\rfloor \right\rfloor}}{\Delta M_{j}},1\right\}&,\text{elsewhere}\end{cases}  \tag{15}\]  
\[T_{k}=k\cdot t_{0} \tag{16}\]  
\[E_{k}=\sum_{i=1}^{k}\left(\sum_{j=1}^{i}p_{j}\Delta M_{j}+q_{i}\right)\cdot P_ {\text{t}} \tag{17}\]  
\[\text{EDP}_{k}=k\cdot\sum_{i=1}^{k}\left(\sum_{j=1}^{i}p_{j}\Delta M_{j}+q_{i} \right)\cdot P_{\text{t}}t_{0} \tag{18}\]  
According to Section 4.3, the values of \(\alpha\) and \(\beta\) were set to be 3 dB in this subsection. The simulation results are In summary, the analysis results have been conveniently compiled in Table 5. Notably, when considering Case 2 without the combination as the benchmark, simulating the latency and energy performance for Case 1 became unnecessary. Moreover, as the maximum number of assisted nodes increased, the system network demonstrated improved latency performance, consequently leading to enhanced URLLC capabilities. This enhancement in URLLC performance holds significant promise for meeting the demanding requirements of critical applications. In addition, in this article, we did not consider the impact of interference on the UE, and the time of each transmission was assumed to be fixed. The final result may have been inaccurate, but the basic trend was correct. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Schemes** & **Description** & **Latency Gain 1** & **Energy Gain 1** & **Latency Gain 2** & **Energy Gain 2** \\ \hline Case 1 & One direct link between UE & 0\% & 0\% & - & - \\  & and BS. & & & & \\  & Indirect link between UE & & & & \\  & and BS via a cooperation & & & & \\ Case 2 wo combination & node. No data combination & 28.56\% & 30.23\% & 0\% & 0\% \\  & at BS across UE and the & & & & \\  & cooperation node. & & & & \\  & Sequential direct path and & & & & \\  & indirect path for data & & & & \\ Case 2 with combination & transition between UE and & & & & \\  & BS. Data combination at BS & 32.96\% & 33.49\% & 6.20\% & 4.00\% \\  & across UE and the & & & & \\  & cooperation node. & & & & \\  & Simultaneous direct and & & & & \\ Case 3 non-AUA (\(M=1\)) & & indirect transmission to BS & 47.99\% & 19.77\% & 27.19\% & \(-12.06\%\) \\  & from UE and one & & & & \\  & cooperation node. & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of latency performance gain and energy consumption gain under different schemes. Figure 10: The latency performance gain of different schemes (R/2, AUA with \(\alpha=\beta=3\) dB). The overall latency and overall energy consumption would change with the differences in \(M\). Figure 11a,b show the overall latency and overall energy consumption of different distances under \(M=1,2,3,4\). The closer the UE was to the cooperation node, the lower the overall latency. The curve for the latency is easier to understand, but the curve for energy consumption is more complicated. It can be clearly seen that there is a phenomenon of jitter in the figure. Because users who are closer to each other may have the same overall number of transmissions (the same overall latency), the successful decoding time of the \(j\)th cooperation node may be different, resulting in users who are closer to the base station possibly consuming more energy. In addition, if the last transmission does not require \(M\) cooperation nodes to assist in the transmission for successful decoding, then there will be energy loss. Both of these two aspects can lead to fluctuations in the curves. Figure 11: The performance critical values vs. distance under multi-path AUA with different cooperation numbers (\(\alpha=\beta=3\) dB). (**a**) Latency performance. (**b**) Energy performance. (**c**) EDP.