## 2 Materials and Methods
### Proposed UIM-VLC Channel Model  
The proposed channel model, not unlike the reference channel model, is a UM-VLC channel model that considers the relative rotation and tilt of the LED and the PD, irregular walls, shadowing, and scattering. The difference is that \(H_{\text{ref}}\) describes the channel transmission for an SISO link considering a monochromatic LED as the TX, whereas our proposed channel model takes into account a multichannel LED and the spectral distribution of different channel parameters. Additionally, our model takes into account attenuation from light scattering and absorption caused by dust particles, which are absent from the reference model.  
The DC gain of the proposed channel model for optical inputs and optical outputs takes the form  
\[H_{\text{opt}}=H_{\text{LOS}}^{\text{opt}}+H_{\text{NLOS},(1)}^{\text{opt}}\,, \tag{65}\]  
where the \(H_{\text{scatter}}\) component is not taken into account due to the small impact it has on the CIR. Instead, in our proposed model, the scattering and absorption effects due to dust particles are integrated directly into the LOS and NLOS components. In general, the DC gain of the optical channel can be expressed as [25]  
\[H_{\text{opt}}=\frac{P_{R}}{P_{T}}\,, \tag{66}\]  
where \(P_{R}\) is the optical power received from the PD and \(P_{T}\) is the optical power emitted by the LED. For an LED with spectral power distribution (SPD), \(\Phi(\lambda)\), \(P_{T}\) can be expressed as [25]  
\[P_{T}=\int_{380\,\text{nm}}^{825\,\text{nm}}\Phi(\lambda)\,d\lambda\,. \tag{67}\]Equivalently, \(P_{R}\) can be expressed as  
\[P_{R}=\int_{380\,\mathrm{nm}}^{825\,\mathrm{nm}}\mathcal{A}(\lambda)\Phi(\lambda) \,d\lambda\,, \tag{68}\]  
where \(\mathcal{A}(\lambda)\) represents a spectral weighting function that accounts for the power attenuation due to environmental and geometric factors. This function can be further divided into the established LOS and single-hop NLOS components, with  
\[\mathcal{A}(\lambda)=\mathcal{A}_{0}(\lambda)+\sum_{w=1}^{W}\mathcal{A}_{w}( \lambda)\,, \tag{69}\]  
where \(\mathcal{A}_{0}(\lambda)\) represents the LOS link weighting function and \(\mathcal{A}_{w}(\lambda)\) the NLOS link weighting function for the \(w\)th reflector. Combining Equations (66), (68), and (69) with Equation (65), one finds that  
\[H_{\mathrm{LOS}}^{\mathrm{opt}}=\frac{1}{P_{T}}\int\mathcal{A}_{0}(\lambda) \Phi(\lambda)\,d\lambda\,, \tag{70}\]  
and  
\[H_{\mathrm{NLOS},(1)}^{\mathrm{opt}}=\frac{1}{P_{T}}\sum_{w=1}^{W}\int \mathcal{A}_{w}(\lambda)\Phi(\lambda)\,d\lambda\,, \tag{71}\]  
where the integral limits are omitted for the sake of simplicity.  
Considering Equation (68) as the definition of the optical power received, the electrical photocurrent \(I_{ph}\) produced at the PD with spectral responsivity \(R(\lambda)\) can be expressed as  
\[I_{ph}=\int_{380\,\mathrm{nm}}^{825\,\mathrm{nm}}R(\lambda)\mathcal{A}(\lambda )\Phi(\lambda)\,d\lambda\,. \tag{72}\]  
The DC gain of the proposed channel model for optical inputs and electrical outputs takes the form  
\[H_{\mathrm{el}}=\frac{I_{ph}}{P_{T}}=H_{\mathrm{LOS}}^{\mathrm{el}}+H_{ \mathrm{NLOS},(1)}^{\mathrm{el}}\,. \tag{73}\]  
Combining Equations (69), (72), and (73), one finds that  
\[H_{\mathrm{LOS}}^{\mathrm{el}}=\frac{1}{P_{T}}\int R(\lambda)\mathcal{A}_{0}( \lambda)\Phi(\lambda)\,d\lambda\,, \tag{74}\]  
and  
\[H_{\mathrm{NLOS},(1)}^{\mathrm{el}}=\frac{1}{P_{T}}\sum_{w=1}^{W}\int R( \lambda)\mathcal{A}_{w}(\lambda)\Phi(\lambda)\,d\lambda\,. \tag{75}\]