## 4 Numerical Results
### Numerical Results
#### 4.2.3 EE Performance with Different \(y_{s}\)  
\(y_{s}\) represents the distance between the vehicle and the IRS in the direction of the road. Since the vehicle is moving, \(y_{s}\) is dynamically changing. Figure 6 illustrates the EE versus \(\mathbf{N}\) with different \(y_{s}\) when \(R_{min}=40\) Mbps and \(\sigma^{2}=-98\) dBm.  
As can be seen from Figure 6, EE increases first and then decreases when \(y_{s}=10,\ 20,\ 30,\ 40,\ 50\) m, which is a unimodal function. When the \(y_{s}\) is smaller, the larger \(EE(N)\) is obtained using the same number of mirrors. According to Formula (6), the increase of \(y_{s}\) means that \(\text{R}_{\text{ij}}\text{D}\) and \(\text{R}_{\text{ij}}\text{S}\) are increase, resulting that the channel gain corresponding to each mirror decreases. The reduction of channel gain makes the received power and the SNR smaller. In this way, \(R(N)\) and EE will also be reduced.  
Like the analysis in Section 4.2.3, with the smaller \(y_{s}\), the \(EE(N)\) can reach the maximum value using fewer mirrors and \(EE_{max}(N)\) is also larger at the same time. Taking \(y_{s}=10\) m as an example, the EE can reach the maximum value using 168 mirrors. The \(N_{opt}\) is reduced 74.6% and \(EE_{max}(N)\) is increased by 4.15 times compared to \(y_{s}=50\) m.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\sigma^{2}\) **(dBm)** & \(N_{opt}\) & \(EE_{max}(N)\) **(Mbits/J)** & \
\begin{tabular}{c} **Iterations of** \\ **Bubble Sort** \\ **Method** \\ \end{tabular} &
\begin{tabular}{c} **Iterations of** \\ **Algorithm** \\ \end{tabular} \\ \hline \(-90\) & 235 & 1.2116 & 6189921 & 12 \\ \(-94\) & 197 & 1.4504 & 6295926 & 11 \\ \(-98\) & 168 & 1.7049 & 6363528 & 12 \\ \(-102\) & 145 & 1.9732 & 6406410 & 12 \\ \(-106\) & 128 & 2.2531 & 6435078 & 12 \\ \hline \hline \end{tabular}
\end{table}
Table 4: \(N_{opt}\) and iterations with different \(\sigma^{2}\).  
The smaller \(y_{s}\) causes the smaller the iterative starting point of \(\mathbf{N}\), so that the iterative range of \(\mathbf{N}\) used to solve \(N_{opt}\) becomes larger. If the iterative range of \(\mathbf{N}\) is larger, it is easy to cause the amount of computation becomes larger. Table 5 gives \(N_{opt}\) and iterations with different \(y_{s}\).  
As can be seen from Table 5, with the increasing of \(y_{s}\), the iterative number of the Bubble Sort method decreases. This is because the increase of \(y_{s}\) causes the starting iterative point of \(\mathbf{N}\) to become large, thus the range of iteration reduces. Compared with the bobbling method, the bsci algorithm has fewer iterations and computations.  
When the vehicle is moving, the distance between the vehicle and the IRS is constantly changing. When the distance is closer, \(N_{opt}\) is smaller and \(EE(N)\) is higher. To improve the performance of the \(N_{opt}\) and \(EE(N)\), the distance between vehicle and IRS should be optimized. The multiple IRSs can be installed using the existing traffic infrastructures, and the distance between adjacent IRS is not too large, so that the distance is controlled within an appropriate range, which can solve this problem.