## 2 Materials and Methods
### Reference UM-VLC Channel Model
#### 2.3.5 Reference Source of Reflections  
In order to evaluate the reference channel, a simulation scenario is defined in [7], considering two irregular walls as the source of reflections that run the length of the tunnel. Each wall has a surface area of \(L_{x}\times L_{z}\) (m\({}^{2}\)) and is divided by a square grid into squares of equal area \(\Delta A\) (m\({}^{2}\)), implying that each wall has a total of \(L_{x}\times L_{z}/\Delta A\) squares. \(\Delta A\) is a parameter that controls the resolution (hence, the accuracy) of the reflection calculation. We consider one reflector per square element of the gridded wall, with the \(w\)th having a reflective surface area of \(A_{\text{refl},w}\) (to not be confused with resolution area \(\Delta A\)), position \(\mathbf{R}_{w}\), rotation angle \(\alpha_{w}\), and tilt angle \(\beta_{w}\). With this, the total number of reflectors considered, \(W\), is  
\[W=2\frac{L_{x}L_{z}}{\Delta A}\,. \tag{45}\]  
A common simplification is to consider the reflective area of all reflectors to be equal to a unique surface area \(A_{\text{refl}}\)[7], i.e.,  
\[A_{\text{refl},w}=A_{\text{refl}},\quad\forall w=1,\dots,W\,. \tag{46}\]  
In order to characterize the position \(\mathbf{R}_{w}\), we can first define the set of values \(x_{w}\), \(y_{w}\), and \(z_{w}\) it can take. Note that \(x_{w}\) can take \(\ell_{x}=L_{x}/\Delta A\) values, \(y_{w}\) can take two values (one for each wall), and \(z_{w}\) can take \(\ell_{z}=L_{z}/\Delta A\) values, where we select \(\Delta A\) such that \(\ell_{x}\) and \(\ell_{z}\) are natural numbers. The set of possible values of \(x_{w}\), \(\mathcal{X}_{W}\), is then given by  
\[\mathcal{X}_{W}=\left\{x=\Delta A\times n\mid n=0,1,\dots,\ell_{x}\right\}, \tag{47}\]  
the set of possible values of \(y_{w}\), \(\mathcal{Y}_{W}\), is simply  
\[\mathcal{Y}_{W}=\left\{0,L_{y}\right\} \tag{48}\]  
since each wall is located at each extreme of the \(y\)-axis in the simulation scenario. The set of possible values of \(z_{w}\), \(\mathcal{Z}_{W}\), is given by  
\[\mathcal{Z}_{W}=\left\{z=\Delta A\times n\mid n=0,1,\dots,\ell_{z}\right\}. \tag{49}\]With these definitions, the set of \(W\) possible reflector positions is given by  
\[\{\mathbf{R}_{1},\mathbf{R}_{2},\ldots,\mathbf{R}_{W}\}=\mathcal{X}_{W}\times \mathcal{Y}_{W}\times\mathcal{Z}_{W}\,. \tag{50}\]  
To simulate diffuse reflection on irregular walls, a non-deterministic approach is employed, such that the tilt and rotation angles for the \(w\)th reflector, \(\alpha_{w}\) and \(\beta_{w}\), respectively, are modeled as random variables independently drawn from a uniform distribution. In general, we have for the tilt angles \(\beta_{w}\) that  
\[\beta_{w}\sim\mathcal{U}[0,\pi],\quad\forall w=1,\ldots,W\,, \tag{51}\]  
whereas the rotation angles \(\alpha_{w}\) depend on the wall on which the \(w\)th reflector is located, namely,  
\[\alpha_{w}\sim\mathcal{U}[0,\pi],\quad\forall w\in\{w\mid y_{w}=0\}\,, \tag{52}\]  
and  
\[\alpha_{w}\sim\mathcal{U}[\pi,2\pi],\quad\forall w\in\{w\mid y_{w}=L_{y}\}\,. \tag{53}\]  
Additionally, a common simplification is that all reflectors have the same reflectance \(\rho\), i.e.,  
\[\rho_{w}=\rho,\quad\forall w=1,\ldots,W\,. \tag{54}\]