# Channel Characteristics and Link Adaption for Visible Light Communication in an Industrial Scenario
## 3 Analysis of Channel Characteristics
### Optical Path Loss  
A VLC-based IIoT channel is characterized by OPL, which can describe the decaying in the received power of the optical signal during its propagation through space. It can be expressed as:  
\[OPL=-10\log_{10}\ (\int_{0}^{\infty}\sum_{i=1}^{N}h_{i}(t)dt), \tag{3}\]  
where the \(h_{j}(t)\) denote the individual optical CIR between the \(i^{th}\) LED and the PD, and \(N\) is the number of rays received by PD. In the realistic environment, the optical path loss is highly related to the environment [6], which requires a model to reflect the actual propagation characteristics. We can model a path loss based on these data samples with the widely used floating-intercept (FI) and close-in (CI) model. The FI and CI model can be expressed as:  
\[PL_{FI}=\alpha_{PL}+10\beta_{PL}\log_{10}(d)+X_{\sigma}^{FI}, \tag{4}\]  
\[\mathrm{PL}^{\mathrm{CI}}(f,d)=20\mathrm{log}_{10}(\frac{4\pi d_{0}f}{c})+10n _{CI}\mathrm{log}_{10}(\frac{d}{d_{0}})+X_{\sigma}^{\mathrm{CI}}\quad\text{for $d \geq d_{0}$, $d_{0}=1\,m$}, \tag{5}\]  
where \(\alpha_{PL}\) is the floating intercept, \(\beta_{PL}\) and \(n_{CI}\) is the path loss coefficient, and \(X_{\sigma}^{FI}\) is a zero-mean Gaussian variable with a standard derivation \(\sigma\) representing the shadowing. For VLC channels, the CI model cannot be applied to model the OPL in VLC bands, because this model requires a specific frequency (i.e., \(f\) in the CI model), while the LEDs work with mixed wavelengths. Furthermore, concerning the works about the indoor VLC channel modeling [17], the floating-intercept (FI) model shows a good performance to characterize the distance dependence of OPL. Therefore, we choose the FI model to fit the OPL for VLC channels in IIoT scenarios. The OPL under the single TX (\(S_{8}\)) case is investigated, and Road 1 and Road 2 are selected to analyze it. Figure 3a shows the OPL fitting results with the FI model for VLC channels. The OPL at \(D_{10}\) is 1.5 dB smaller than that at \(E_{10}\), and we can obtain the same results at other points in this scenario. This is within expectation because of the density of object deployment. As the previous analysis, the objects surrounding Road 1 are denser than that in Road 2, contributing to the stronger specular and diffuse reflection, i.e., more MPCs can be received by the RX. Hence, the total received power is larger and OPL is smaller in \(D_{10}\). Furthermore, the PLE of the FI model in Road 2 (\(\beta_{PL}\) = 3.25) is larger than that of Road 1 (\(\beta_{PL}\) = 2.65). This indicates that the light signals will suffer a faster decay in Road 2 than that in Road 1 with the increasing propagation distance. The differences can also be explained by the environmental configuration around the road. As observed in Figure 1b, in  
Figure 2: (**a**) NLOS components of CIR for PD \(D_{10}\); (**b**) NLOS components of CIR for PD \(E_{10}\). Road 1 with dense machine deployment, the NLOS components are mainly contributed by reflections from the floor and nearby dense machines. However, when machine deployment becomes sparse, the number of reflected rays from nearby devices becomes less, resulting in a weaker received optical power. Hence, the faster decay in the OPL occurs. In addition, compared to the VLC indoor conference model parameter in [15], which is 2.03, the results in this paper have a larger PLE. This can be explained by the unique character of the IIoT scenario. The size of the scenario is larger than that in [15]. The reflected light rays should take longer paths to the RX. Moreover, the light rays split into many random rays and they are reflected in all directions when interacting with the machine with a high specular reflectivity [15]. Finally, only small rays can reach the RX, i.e., a larger PLE can be observed. In addition, the OPL in [28] is also examined by considering LOS and NLOS links. The computed values of the PLE (n) are 1.2 for LOS and 1.4 for the NLOS sub-gallery link, respectively. It can be observed that the PLE in our paper (3.25 and 2.65) is larger than that in [28].