## 2 Materials and Methods
### Reference UM-VLC Channel Model
#### 2.3.3 Reference NLOS Link  
The single-hop NLOS component \(H_{\text{NLOS},(1)}\) can be further expressed as [7]  
\[H_{\text{NLOS},(1)}=\frac{(m+1)A_{R}}{2\pi}\sum_{w=1}^{W}\mathcal{C}_{w} \mathcal{G}_{w}\frac{A_{\text{ref},w}\rho_{w}}{d_{1,w}^{2}d_{2,w}^{2}}\Omega_{ \text{NLOS}}^{(w)}\Psi_{\text{NLOS}}^{(w)}\,, \tag{35}\]  
where \(W\) is the number of diffuse reflectors, modeled as generalized Lambertian virtual light sources (VLS) with Lambertian mode numbers equal to unity [7], such that for the \(w\)th reflector, \(A_{\text{ref},w}\) is its surface area, \(\rho_{w}\in[0,1]\) is its reflectance, \(d_{1,w}\) is the distance from the LED to the reflector, and \(d_{2,w}\) is the distance from the reflector to the PD. \(\mathcal{G}_{w}\) and \(\mathcal{C}_{w}\) are the optical filter and concentrator gain at the receiver, respectively, accounting for the incident angle from the \(w\)th reflector to the PD. \(\Omega_{\text{NLOS}}^{(w)}\in[0,1]\) is a trigonometric expression that depends on the relative position, rotation, and tilt of the LED, the \(w\)th reflector, and the PD. \(\Psi_{\text{NLOS}}^{(w)}\in[0,1]\) is a scaling factor that accounts for the degree of shadowing in the \(w\)th NLOS link.  
Consider that the \(w\)th reflector is modeled as a VLS with position \(\mathbf{R}_{w}=[x_{w},y_{w},z_{w}]^{\text{T}}\). With this, the distance between TX and the \(w\)th reflector, \(d_{1,w}\), is given by  
\[d_{1,w}=||\mathbf{R}_{w}-\mathbf{T}||\,, \tag{36}\]whereas the distance between RX and the \(w\)th reflector, \(d_{2,w}\), is given by  
\[d_{2,w}=||\mathbf{R}_{w}-\mathbf{R}||\,. \tag{37}\]  
Additionally, the \(w\)th reflector is tilted by the tilt angle \(\beta_{w}\in[0,\pi]\) and rotated by the rotation angle \(\alpha_{w}\in[0,\pi]\), defined in the same way as the tilt and rotation angles of the RX. The normal vector to the surface of the \(w\)-reflector is denoted by \(\mathbf{n}_{w}=[n_{w}^{x},n_{w}^{y},n_{w}^{z}]^{\mathrm{T}}\) and can be calculated with [7]  
\[\mathbf{n}_{w}=\begin{bmatrix}\sin(\beta_{w})\cos(\alpha_{w})\\ \sin(\beta_{w})\cos(\alpha_{w})\\ \cos(\beta_{w})\end{bmatrix}. \tag{38}\]  
Figure 2 illustrates the tilt and rotation angle definitions. We denote by \(\theta_{w}\) the incident angle at which the light coming from the \(w\)th reflector reaches the PD, and we calculate it by [7]  
\[\theta_{w}=\arccos\left(\frac{1}{d_{2,w}}(\mathbf{R}_{w}-\mathbf{R})^{\mathrm{ T}}\mathbf{n}_{\mathrm{rx}}\right). \tag{39}\]  
Note that the dependence of \(\mathcal{C}_{w}\) and \(\mathcal{G}_{w}\) on the incident angle \(\theta_{w}\) is implicit. Namely, \(\mathcal{C}_{w}\) can be expressed as  
\[\mathcal{C}_{w}=\begin{cases}\frac{\eta}{\sin^{2}(\Theta_{\mathrm{FoV}})}&0 \leq\theta_{w}\leq\Theta_{\mathrm{FoV}}\\ 0&\theta_{w}>\Theta_{\mathrm{FoV}}.\end{cases} \tag{40}\]  
Finally, the trigonometric parameter \(\Omega_{\mathrm{NLOS}}^{(w)}\) can be expressed as  
\[\begin{split}\Omega_{\mathrm{NLOS}}^{(w)}=& \left(\frac{1}{d_{2,w}}(\mathbf{R}-\mathbf{R}_{w})^{\mathrm{T}}\mathbf{n}_{w }\right)\times\left(\frac{1}{d_{2,w}}(\mathbf{R}_{w}-\mathbf{R})^{\mathrm{T}} \mathbf{n}_{\mathrm{rx}}\right)\\ &\times\left(\frac{1}{d_{1,w}}(\mathbf{T}-\mathbf{R}_{w})^{\mathrm{ T}}\mathbf{n}_{w}\right)\times\left(\frac{1}{d_{1,w}}(\mathbf{R}_{w}-\mathbf{T})^{ \mathrm{T}}\mathbf{n}_{\mathrm{rx}}\right)^{m}.\end{split} \tag{41}\]