# Multi-Wavelength Path Loss Model for Indoor VLC with Mobile Human Blockage
## 2 Multi-Wavelength Path Loss Model with Human Blockage
### Multi-Wavelength Path Loss with Human Blockage in Single-LED Scenario  
In this subsection, we analyze and model the path loss in the single-LED scenario with the presence of human blockage. When there is a person exists in the environment, the visible light signal in some specific directions will be cut off by the human body resulting in a shadowing area on the receiving plane. The shadowing area is the communication blind area which destroys the full coverage of VLC, as illustrated in Figure 2. In mobile VLC systems, the human body will move along a trajectory, and the position of the human body will vary with time. The shadowing area caused by human blockage will change accordingly. For a receiving position, there will be two states, i.e., in the shadowing area with the blockage state and in the unshadowed area with the free space propagation state. The percentage of time that it is in the shadowing area is the BP. Therefore, to characterize the two-state properties in the single-LED scenario, the conventional distance-dependent path loss model should be modified into the statistical model with two cases. That is, under the BP, the receiving positions can hardly receive any optical signal from the transmitter. While under the other probability, i.e., 1-BP, the path loss is consistent with that under the free space propagation.  
To describe the two-state properties, the multi-wavelength path loss model with human blockage in the single-LED scenario is proposed in the form of a piecewise function  
\[PL_{single}(d,\lambda)=\left\{\begin{matrix}PL^{{}^{\prime}}_{single}(d, \lambda),&1-p_{single}\\ \textit{Blockage},&p_{single}\end{matrix}\right. \tag{10}\]  
Here, \(PL^{{}^{\prime}}_{single}(d,\lambda)\) indicates the path loss model of the free space propagation to describe the path loss in the unshaded area. In \(PL^{{}^{\prime}}_{single}(d,\lambda)\), the Alpha-Beta-Gamma (ABG) model is utilized to simultaneously reflect the wavelength dependence and the distance dependence of path loss. The ABG model can be expressed as  
\[PL^{{}^{\prime}}_{single}(d,\lambda)=10\mathrm{\alpha log}_{10}(\frac{d}{d_{0} })+\beta+10\gamma\mathrm{log}_{10}(\frac{\lambda}{1\,\mathrm{nm}})+X_{\sigma}, \tag{11}\]  
where \(d_{0}\) is the received-power reference point (It is set to 1 m in this paper), \(\mathrm{\alpha}\) and \(\gamma\) are the distance and wavelength dependence on path loss, respectively. \(\beta\) is the optimized offset in path loss. \(X_{\sigma}\) is a zero-mean Gaussian variable with a standard deviation \(\sigma\) representing  
Figure 2: Human blockage in the single-LED scenario.  
the shadowing. In this ABG model, we can see that path loss varies with the wavelength and the spatial distance.  
\(p_{single}\) indicates the BP caused by the human blockage in the single-LED scenario. It is a statistical characteristic of the blockage performance in the time domain which indicates the percentage of the time that a receiving position is in the shadowing area. It is worth noting that there are many factors that will influence the distribution of the shadowing area. Firstly, the shape of the human body affects the location distribution of the shadowing area. The increase in human figures will lead to an extension of the shadowing area. Secondly, the human moving trajectory determines the time distribution of a specific shadowing area. To accurately reflect the blockage performance of a mobile VLC system, both the human body shadowing calculation and the human moving trajectory generation should be consistent with that in the realistic application scenario.