# A Novel and Adaptive Angle Diversity-Based Receiver for 6G Underground Mining VLC Systems
## 2 VLC System Model Applied to Underground Mining Environments
### Channel DC Gain  
Based on the work completed in [21], the UM-VLC channel is modeled by integrating three optical components: the LoS component, the non-LoS component, and the scattering component. The LoS component is obtained directly from the LED lighting that falls on the PD. Thus, the LoS link depends on the LED and PD parameters as seen above. In addition, due to the UM infrastructure, in which large machinery and vehicles move through the tunnels, the effect of shadowing within the expression of the UM-VLC channel is considered. This UM scenario with its components is outlined in Figure 1. By integrating these factors, the Direct Current (DC) gain of the LoS optical wireless channel is formulated as follows:  
\[H_{LoS,j,j} =\frac{(m+1)A_{p}}{2\pi d_{ij}^{m+3}}\Big{\{}\Big{[}x_{j}^{R}-x_{i }^{T},y_{j}^{R}-y_{i}^{T},-\Delta h_{ij}\Big{]}\cdot\big{[}\sin(\beta_{i})\cos (\alpha_{i}),\sin(\beta_{i})\sin(\alpha_{i}),-\cos(\beta_{i})\big{]}\Big{\}}^{m}\] \[\times\Big{\{}\Big{[}x_{i}^{T}-x_{j}^{R},y_{i}^{T}-y_{j}^{R}, \Delta h_{ij}\Big{]}\cdot\big{[}\sin(\beta_{j})\cos(\alpha_{j}),\sin(\beta_{j })\sin(\alpha_{j}),\cos(\beta_{j})\big{]}\Big{\}}G(\theta_{ij}^{tilt})rect \big{(}\frac{\theta_{ij}^{tilt}}{\Theta}\big{)}P_{ij}. \tag{5}\]  
where \(rect\big{(}\frac{\theta_{ij}^{tilt}}{\Theta}\big{)}=1\) for \(0\leq\theta_{ij}^{tilt}\leq\Theta\) and 0 otherwise, \(G(\theta_{ij})\)=\(T_{s}(\theta_{ij})\)\(g(\theta_{ij})\) represents the combined gain of the optical filter and optical concentrator, respectively, and \(P_{ij}\) is a weighting function introduced to consider the random shadowing, which describes the probability that the LoS optical link is not blocked. On the other hand, as a result of obstacles, and the non-flat and irregular walls of the tunnels, a diffuse component of the transmitted light is reflected by these elements. This effect generates the non-LoS component of the VLC channel, which is termed as \(H_{NLoS}\). A common model for diffuse reflection is the Lambertian reflectance where light is reflected with equal radiance in all directions. However, this non-LoS component differs from the non-LoS component of non-mining indoor scenarios. The main differences are in the normal vectors of the non-planar walls, which are not orthogonal to the reflective area of the wall, which is called \(w\). Therefore, these normal vectors (\(\mathbf{n}_{w}^{tilt}\)) can be described in terms of the tilt angle with respect to the z-axis denoted as \(\beta_{w}\), which belongs to the range of \([0^{\circ},180^{\circ})\) and the rotation angle with respect to the x-axis denoted as \(\alpha_{w}\) and takes values in range of \([0^{\circ},180^{\circ})\). The incidence angle with respect to the normal vector to the reflective element \(w\) and the radiance angle of the light component reaching the reflective element \(w\) are symbolized with \(\theta_{iw}^{tilt}\) and \(\phi_{wj}^{tilt}\), respectively. The angles of incidence and radiance are denoted by \(\phi_{wj}^{tilt}\) and \(\phi_{wj}\), respectively, which are measured with respect to the light component that is reflected in the reflective element \(w\) and reaches PD \(j\). The effect of the non-flat walls is noticeable in terms of the following cosines: \(\cos(\phi_{iw}^{tilt})\), \(\cos(\theta_{iw}^{tilt})\), \(\cos(\phi_{wj}^{tilt})\) and \(\cos(\theta_{wj}^{tilt})\) in the following form:  
\[\cos(\phi_{iw}^{tilt})=\frac{V_{i-w}\cdot\mathbf{n}_{i}^{tilt}}{\|V_{i-w}\|\|\mathbf{n }_{i}^{tilt}\|}, \tag{6}\]  
here, \(V_{i-w}\) is the vector from LED \(i\) to \(w\), \(\|V_{i-w}\|=d_{iw}\), where \(d_{iw}\) is the Euclidean distances between LED \(i\) and the reflective element \(w\), and \(V_{i-w}=\big{[}x_{w}^{\text{s}}-x_{i}^{T},y_{w}^{\text{s}}-y_{i}^{T},-\Delta h _{iw}\big{]}\)assuming that the position of \(w\) is \((x_{w^{\prime}}^{S}y_{w^{\prime}}^{S}z_{w}^{S})\), and \(\Delta h_{iw}\) is the difference height between LED \(i\) and \(w\).