## 6 Numerical Results  
In this section, the numerical outcomes for the BER of an eSSK VLC system are presented. The LED transmitters are installed on the ceiling of a typical room with the dimensions 10 m \(\times\) 6 m \(\times\) 3 m in the following coordinates: LED1(2,3), LED2(4,3), LED3(6,3), and LED4(8,3). The length and width of the room were chosen to be greater than the standard model, i.e., 5 m \(\times\) 5 m \(\times\) 5 m, in order to cover more space and have an extensive view of the results. However, using the above mentioned expressions, the system's performance can be accurately estimated for any choice of room dimensions. The receiver is placed at the plane of 1.5 m above the floor. The technical characteristics of the LED transmitters and the receiver, which constitute typical values for realistic VLC systems, are presented in Table 1.  
In Figure 4, the BER performance of the specific VLC system, without the use of the VO\({}_{2}\) optical filter, is presented. The maximum and minimum values of the BER are 0.38 and 8.1 \(\times\) 10\({}^{-9}\), respectively. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Transmitted Optical Power—P\({}_{\text{t}}\) & 20 W \\ \hline Semi-angle at half power—\(\Phi_{\text{s}}\) & 35\({}^{\circ}\) \\ \hline Receivers FOV & 70\({}^{\circ}\) \\ \hline Physical Area of the receiver—A & 1 cm\({}^{2}\) \\ \hline Refractive index of the lens—n\({}_{\text{ri}}\) & 1.5 \\ \hline Absolute temperature of the room—T\({}_{\text{k}}\) & 297 K \\ \hline Photodetector’s capacitance—n & 1.12 μm\({}^{-2}\) \\ \hline Noise bandwidth factor I\({}_{2}\) & 0.562 \\ \hline Noise bandwidth factor I\({}_{3}\) & 0.0868 \\ \hline Noise Bandwidth—B & 175 MHz \\ \hline Open loop voltage Gain—G & 10 \\ \hline Channel noise factor—\(\Gamma\) & 1.5 \\ \hline Transconductance—\(\theta_{\text{m}}\) & 30 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Values of noise and system parameters. It is clear that the performance of the VLC system degrades at the edges of the room, where the received power is lower and as a result, the SNR of the system decreases significantly compared with the values which are obtained in the center. Additionally, it can also be observed that the BER increases in the areas between the LED lamps, where the values of channel gain are almost the same for two LED transmitters and thus, the receiver cannot easily recognize the source of the signal. In Figure 5, the BER results are presented in the case where the VO\({}_{2}\) optical filter is used at the receiver of the VLC system. It can be easily seen that the use of the filter can greatly increase the performance of the VLC system as the BER values lie between a minimum value of \(1.5\times 10^{-15}\) and a maximum of 0.33. Therefore, the BER performance improvement which has been achieved is significant as it is almost six orders of magnitude better, in the best case. Figure 6 shows the BER performance of the VLC system when no filter is applied. Figure 7 shows the effect of using the VO\({}_{2}\) filter. More specifically, in the colored area on the left of the panels, in both  
Figure 4: Bit error rate (BER) of the visible light communication (VLC) system under consideration, without the VO\({}_{2}\) optical filter. Figure 5: Bit error rate (BER) of the visible light communication (VLC) system under consideration, using the VO\({}_{2}\) optical filter at the receiver. figures, the BER performance of the system is lower than \(1\times 10^{-6}\), which is an average value of BER for the specific VLC system. It can be seen that the application of the optical filter significantly increases the area with a lower BER, making the VLC system much more reliable. Summarizing the above results, it is demonstrated that the BER performance of the specific VLC system using VO\({}_{2}\) as an optical filter in front of the receiver has been remarkably improved.