## 2 Proposed System
### Simulation Configuration VLC Channel and Signal-To-Noise Ratio (SNR) Analysis  
To locate the current position of the PD, the intensity of the light source from each LED was modulated, then multiplexing protocol was used to correctly transmit this data from all LED lights to the PD. Finally, demodulating process was executed at the optical receiver [8]. In this paper, an On-Off keying (OOK) modulation using Manchester encoding and Time-division multiplexing (TDM) protocol were used as shown in Figure 3. By using OOK modulation, the logic '1' corresponds to the light 'ON\" state, and the logic '0' corresponds to the light 'OFF' state. To send an equal number of positive and negative pulses, Manchester encoding was proposed. After encoding the data, each LED signal was sent to the PD at each time slot by TDM protocol, which divided the overall time into many slots [8]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Object** & **Parameter** & **Value** \\ \hline \multirow{3}{*}{**Simulation space**} & Room dimension (Length \(\times\) Width \(\times\) Height) & \(5\) m \(\times\) 5 m \(\times\) 2.5 m \\  & Reflective rate & 0.8 \\ \hline \multirow{6}{*}{**Optical transmitter**} & LED power & 25 W \\  & Number of LED bulbs & 4 \\  & LED bandwidth & 3 MHz \\  & Data rate & 2 Mbps \\ \cline{2-3}  & & LED 1 (\(-\)1.25, \(-\)1.25, 2.5) \\  & LED position (x, y, z) (m) & LED 2 (1.25, \(-\)1.25, 2.5) \\  & LED 3 (1.25, 1.25, 2.5) \\  & LED 4 (\(-\)1.25, 1.25, 2.5) \\ \hline \multirow{6}{*}{**Optical receiver**} & Half power semi-angle & 70\({}^{\circ}\) \\ \cline{2-3}  & PD active area & 1 cm\({}^{2}\) \\  & Field-of-view & 70\({}^{\circ}\) \\ \cline{1-1}  & Sensitivity & \(-\)30 dBm \\ \cline{1-1}  & Gain of optical filter & 1 \\ \cline{1-1}  & Refractive index of optical & 1.5 \\ \cline{1-1}  & concentrator & 0.54 A/W \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Visible Light Communication (VLC) parameters. Figure 2: Fingerprints on the floor. Depending on the structure of the VLC channel, the RSS and SNR values can be changed. In this work, we analyzed both the line-of-sight (LOS) channel and the diffuse channel. In addition, the influence of multiple noises of the system, including shot noise and thermal noise, was considered in detail. For the direct channel, the DC channel gain is given by the following equation [25]:  
\[H_{LOS}=\left\{ \begin{array}{ll}\left(\frac{n+1}{2\pi}\right)\left(\frac{A}{ I^{2}}\right)\cos^{n}(\phi)T_{s}(\Psi_{d})g(\Psi_{d})\cos(\Psi),&0\leq\Psi_{d} \leq FOV\\ 0,&\Psi_{d}>FOV\end{array} \right., \tag{1}\]  
where \(n\) is the Lambertian order; \(A\) is the active detector area of the PD; \(I\) is the distance between the LED and the PD; \(\phi\) is the irradiance angle; \(\Psi_{d}\) is the incidence angle of the directed channel; \(T_{s}(\Psi_{d})\) is the gain of the optical filter; \(g(\Psi_{d})\) is the gain of the optical concentrator; and FOV is the field of view of the PD. For simplicity, we focus on the effect of the first reflection signal, because other reflected waves have a negligible effect [21]. Thus, the DC channel gain of the first reflection is computed as follows [25]:  
\[H_{NLOS}=\left\{ \begin{array}{ll}\left(\frac{n+1}{2\pi}\right)\left(\frac{A} {I_{1}^{2}}\right)\rho\cos^{n}(\phi)dA_{ref}\cos(\lambda)\cos(\gamma)\cos( \Psi_{r})T_{s}(\Psi_{r})g(\Psi_{r}),&0\leq\Psi_{r}\leq FOV\\ 0,&\Psi_{r}>FOV\end{array} \right., \tag{2}\]  
where \(I_{1}\) is the distance between an LED and a reflective point; \(I_{2}\) is the distance from a reflective point to the PD; \(\rho\) is the reflectance factor; \(d_{Aruf}\) is the reflective element on the wall; \(\lambda\) is the angle of irradiance from an LED group to the reflective point; \(\gamma\) is the angle between a reflective point and the PD; and \(\Psi_{r}\) is the incidence angle from the wall.