## 3 Visible Light Communication Systems  
VLC is a novel technology traditionally based on LED optical wireless communication (OWC) systems [27; 28; 29; 30; 31], but significant research progress on laser-diode (LD) based VLC technology has been achieved in recent years [32; 33; 34; 35; 36]. Traditional LED OWC systems transmit data at high speeds, whereas photo-detectors are used at the receiver side to detect the optical signal, and translatesit into an equivalent electrical current [7; 10]. Traditionally, VLC technologies are characterized as intensity-modulation and direct-detection (IM-DD) systems. Recent developments have enabled LED devices, with high efficiency and brightness to be used as the main transmission source in conventional VLC systems with speeds stretching into hundreds of Mbps [7]. The dual functionality provided by VLC, lighting, and data communication has created a wide range of interesting applications, including home networks [27], high-speed data communication through office lighting infrastructures [28], vehicle-to-vehicle (V2V) communications [29; 37; 38], high speed communications in environments such as hospitals and airplanes [30], to name a few. For further details regarding the VLC channel model used in this work [39], Figure 1 is used. A transceiver \(i\) placed on the roof of the underground tunnel with coordinates \((x_{i},y_{i},h_{i})\), and a transceiver \(p\) placed in the helmet of the miner with coordinates \((x_{p},y_{p},h_{p})\). The angle of incidence of the light is given as \(\Psi\) and \(\phi\) is the irradiation angle. The optical power received by each transceiver \(p\) from the LED \(i\) is described as:  
\[Pr_{(i,p)}=Pt_{i}Hlos_{(i,p)}, \tag{1}\]  
where \(Pt_{i}\) is the power transmitted by LED \(i\) and \(Hlos_{(i,p)}\) is the channel impulse response between the LED \(i\) and the photodetector \(p\). The channel impulse response \(Hlos_{(i,p)}\) can be expressed as [40]:  
\[Hlos_{(i,p)}=\left\{ \begin{array}{ll}\frac{A_{t}(m_{1}+1)}{2\pi d_{(i,p)}} \cos^{m_{1}}(\phi)T_{s}(\Psi)g(\Psi)\cos(\Psi),&0\leq\Psi\leq\Psi_{c}.\\ 0,&otherwise\end{array} \right. \tag{2}\]  
where \(A_{t}\) is the physical area of the photodetector within the receiver, \(d_{(i,p)}\) is the distance between the LED \(i\) and the photodetector \(p\), \(T_{s}(\Psi)\) is the gain of the optical filter, \(\Psi_{c}\) denotes the width of the field of vision of the photodetector, and \(m_{1}\) is the Lambertian emission order and is given by the semi-angle half power LED as follows:  
\[m_{1}=\frac{-\ln{(2)}}{\ln{\left(\cos{\phi_{\frac{1}{2}}}\right)}}. \tag{3}\]  
Whereas the gain of the optical concentrator \(g(\Psi)\) is given by:  
\[g(\Psi)=\left\{ \begin{array}{ll}\frac{n^{2}}{\sin^{2}\Psi_{c}},&0\leq\Psi \leq\Psi_{c},\\ 0,&\Psi>\Psi_{c}\end{array} \right. \tag{4}\]  
where \(n\) represents the refractive index. Based on the three-dimensional coordinate system described in Figure 1, it is possible to find an expression for the irradiation angle as:  
Figure 1: Visible light communication (VLC) channel model used in proposed system. \[\cos(\phi)=\frac{h_{i}-h_{p}}{\left[\left(h_{i}-h_{p}\right)^{2}+\left(x_{i}-x_{p} \right)^{2}+\left(y_{i}-y_{p}\right)^{2}\right]^{\frac{1}{2}}}, \tag{5}\]  
where \(h_{i}\) is the height of LED \(i\) and \(h_{p}\) is the height of the photodetector \(p\). The model also assumes a control system located in each of the safety helmets, which uses an accelerometer to always keep the photo-detector parallel to the roof of the mine, whereby \(\cos(\phi)=\cos(\Psi)\).