## 2 Underground Mining VLC System Model  
In this article, we consider a Single-Input Single-Output (SISO) UM-VLC down-link system, as shown in Figure 1. This scenario includes the following characteristics, which are common in UM environments: (a) a randomly positioned and oriented LED between the ceiling and wall of the mining tunnel, which serves as an optical transmitter, (b) a PD located and randomly oriented at a height determined by the common position of devices on the tunnel, which serves as an optical receiver. (c) Irregular walls, which generate random reflections of the optical signal that directly affect the non-LoS component of the UM-VLC channel (d) Random shadowing produced by heavy machinery, which can partially or totally block the LoS or non-LoS channel components, (e) scattering produced by dust particles, which are generated by the work environment of a mining tunnel [12]. Under this context, this article focuses its study on the interaction of dust particles and the atmosphere with the light beam in the UM-VLC system, its basic absorption and scattering parameters, and the analysis of the dust particles distribution that best adapts to the UMenvironment, in order to obtain a better UM-VLC channel model component produced by dust particles (scattering) in the scenario.  
In this work, the LED transmission is based on the PHY-I mode together with the On-Off Keying (OOK) modulation, which are described in the IEEE 802.1.5.7 standard. On the other hand, the PD reception employs asynchronous symbol-by-symbol detection [25; 26]. Under this context, the received signal, \(r\), is expressed as [25; 26]  
\[r=h_{m}\otimes s+n_{m}, \tag{1}\]  
where \(s\) denotes the transmitted symbol, \(h_{m}\) represents the instantaneous UM-VLC channel-gain coefficient, \(n_{m}\) stands for the noise affecting the UM-VLC system, and \(\otimes\) is the convolution operator. Where \(n_{m}=n_{s}+n_{t}\), \(n_{s}\sim\mathcal{N}(0,\sigma_{s}^{2})\), and \(n_{t}\sim\mathcal{N}(0,\sigma_{t}^{2})\), being \(\sigma_{s}^{2}\) and \(\sigma_{t}^{2}\) the variances of the shot noise, \(n_{s}\), and thermal noise, \(n_{t}\), respectively [25].  
Based on the phenomena and features previously mentioned, the characterization of \(h_{m}\) can be written as [12]  
\[h_{m}=h_{LoS}+h_{NLoS}^{(1)}+h_{sca}, \tag{2}\]  
where \(h_{LoS}\), \(h_{NLoS}^{(1)}\), and \(h_{sca}\) represent the channel gains of the LoS link, the NLoS link, which represents the light reflections on the tunnel walls, and a component produced by the scattering, respectively. We must consider that the shadowing phenomenon harmfully affects the \(h_{LoS}\) and \(h_{NLoS}^{(1)}\) components, which is included in them as a coefficient that takes values between 0 and 1 to indicate a partial or total blocking of the link. The analytical and mathematical derivation together with the justification of the variables included in the components of the UM-VLC channel model are presented in detail for in-depth verification in [12].  
In the next section we will analyze in depth the scattering phenomenon that occurs in the UM scenario and we will present the proposed 3D dust particle distribution model, which is based on a hemispheric area around the user's helmet.