## 4 Numerical Results
### Numerical Results
#### 4.2.2 EE Performance with Different \(\sigma^{2}\)  
For VVLC, the noise will affect the EE performance, especially the background light noise. To facilitate comparison, we set \(R_{min}=40\) Mbps. Figure 5 illustrates the EE versus \(N\) with different noise power \(\sigma^{2}\).  
As can be seen from Figure 5, \(EE(N)\) increases first and then decreases with different noise power \(\sigma^{2}\), which is a unimodal function. When the number of mirrors in IRS is constant, the EE becomes larger with the smaller noise power. When the number of mirrors is fixed, the denominator in Formula (27) is the same and the lower noise power causes SNR to increase, resulting in the continuous increase of \(R(N)\), thus \(EE(N)\) also increases.  
With the noise power becoming lower, the \(N_{opt}\) is smaller and \(EE_{max}(N)\) is larger. According to Formula (41), the \(EE(N)\) is the largest corresponding to \(N_{opt}\). It can be seen from Formula (27) that when the increasing speed of the numerator is greater than that of the denominator, the \(EE(N)\) keeps increasing, otherwise, the \(EE(N)\) keeps decreasing. When the noise power is smaller, the SNR and the \(R(N)\) is larger. Taking the growth ratio  
Figure 5: EE versus N with different noise power \(\sigma^{2}\).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(R_{min}\) (Mbps) & \(N_{opt}\) & \(EE_{max}\)(N) (Mbits/J) & **Iterations of Bubble** & **Iterations of BSCI** \\  & & & **Sort Method** & **Algorithm** \\ \hline
40 & 168 & 1.7049 & 636328 & 12 \\
50 & 168 & 1.7049 & 6313681 & 12 \\
60 & 168 & 1.7049 & 622811 & 12 \\
70 & 168 & 1.7049 & 6414265 & 12 \\
80 & 168 & 1.7049 & 6004845 & 12 \\
90 & 191 & 1.7004 & 5812345 & 1 \\
100 & 270 & 1.6417 & 5546115 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: \(N_{opt}\) and iterations with different \(R_{min}\).  
of the adjacent \(R(N)\) as an example, the denominator in the ratio \(R(N+1)/R(N)\) will also become larger, and the ratio will be less than that at high noise power at this time. Therefore, the numerator grows faster than that of the denominator, easily obtaining the maximum \(EE(N)\). Taking \(\sigma^{2}=-106\) dBm as an example, the EE has the maximum value only using 128 mirrors. The remaining mirrors in the IRS can be used to support the VLC of multiple vehicles, which improves the utilization of mirrors in the IRS.  
However, the lower noise power makes the starting iterative point of \(\mathbf{N}\) smaller when calculating the maximum EE. This is because when the noise power is lower, \(R(N)\) is easier to reach \(R_{min}\) with the increasing of \(\mathbf{N}\). The smaller iterative starting point of \(\mathbf{N}\) means that the iterative range of \(\mathbf{N}\) increases, which may add some computational complexity for finding \(N_{opt}\). Table 4 gives \(N_{opt}\) and iterations with different \(\sigma^{2}\).  
According to Table 4, as the noise power decreases, the number of iterations requirement using the Bubble Sort method increases. Even if the iterative range of \(\mathbf{N}\) changes, the computational complexity using BSCI algorithm changes little, \(N_{opt}\) can still be found quickly without bringing unexpected complexity to the system. Therefore, the BSCI algorithm has better performance.  
As can been from Table 4, it is easier to reach the \(EE_{max}(N)\) with lower noise power, and fewer mirrors are required. This is because the growth rate of the numerator in Formula (27) becomes faster when the SNR is smaller. Therefore, reducing noise power is an effective way to obtain higher EE using fewer mirrors. In VVLC, the background light is the main source of the noise. Although the background light noise cannot be eliminated, the optical filters can be considered to reduce the interference of background light and noise power which can improve EE and resource efficiency.