## 2 Materials and Methods  
### Indoor VLC System Model  
The direct visible-light channel is affected by people walking or other obstacles, which can produce shadow effects at the receiver. Due to this shadow, the communication quality of all receiving terminals located in the affected area significantly decreases, and the communication link may even be interrupted. In order to quantify the shadow effect of obstacles, this paper established a channel model for the shadow occlusion of human obstacles with multiple light sources in an indoor VLC system and then analyzed the influence of this model on system performance as a function of the mean square errors of illuminance and signal-to-noise ratio, as well as the interrupt probability.  
An indoor VLC system consists of  
Figure 2 shows the two-dimensional plane projection of shadows formed by human obstacles when \(L_{1}\) and \(L_{2}\) light sources were distributed indoors. In the figure, \(S_{0}\) represents the fully shaded region, while \(S_{1}\) and \(S_{2}\) represent the half-shaded region. When the terminal fell into different shadow areas, the change in illumination intensity and communication performance was different. If the terminal was located in the \(S_{0}\) region, the illumination intensity dropped sharply, and the received power even failed to meet the communication requirements, resulting in link outrage. When the receiver fell into \(S_{1}\) and \(S_{2}\), because the receiver in this region could only perceive the optical power of the non-corresponding light source, the communication quality of the receiver in this region was significantly different from that in any non-shaded region. Therefore, it is necessary to analyze the influence of the shadow effect on multiple indoor light sources with the VLC system according to different shadow areas.  
Combined with the characteristics of the indoor visible light link, the received optical power \(P_{Rx}\)[21] considering the direct path and primary reflection path could be expressed as  
\[P_{Rx}=(H_{LOS}+H_{NLOS})P_{Tx} \tag{1}\]  
where \(P_{Tx}\) is the transmitted optical power and \(H_{LOS}\) and \(H_{NLOS}\) are the channel gain of the direct path and the primary reflection path, respectively.  
According to the Lambert radiation characteristics of multiple LED light sources, the total illumination of the receiving plane [22] was:  
\[E=\sum\left(E_{hor}+\int\limits_{walls}dE_{hor(NLOS)}\right) \tag{2}\]  
Figure 1: Indoor VLC system model.  
Figure 2: Two-dimensional plane projection of two LEDs and one human obstacle.  
where \(E_{hor}\) is the horizontal illuminance of the receiving plane of the line-of-sight link, and \(dE_{hor(NLOS)}\) is the primary reflected illuminance of the non-line-of-sight link.  
The mean square error of the system illuminance [22] was:  
\[D_{E}=\sqrt{\frac{\sum\limits_{i=1}^{n}\left(E_{i}-\overline{E}\right)^{2}}{n}} \tag{3}\]  
where \(n\) is the number of photodetectors on the receiving plane and \(E_{i}\) and \(\overline{E}\) are the horizontal and average illuminance of each receiving point on the receiving plane, respectively.  
The signal-to-noise ratio mean square error was:  
\[D_{SNR}=\sqrt{\frac{\sum\limits_{i=1}^{n}\left(SNR_{i}-\overline{SNR}\right)^{ 2}}{n}} \tag{4}\]  
where \(SNR_{i}\) and \(\overline{SNR}\) are, respectively, the signal-to-noise ratio and average signal-to-noise ratio of each receiving point on the receiving plane.  
To ensure the quality of service in the terminal \(\gamma_{0}\) is the minimum signal-to-noise ratio to meet communication requirements, and the link interruption probability \(P_{0}\)[23] can be defined as the probability that the terminal cannot correctly judge the received data, i.e.,  
\[P_{0}=P_{r}\{SNR\leq\gamma_{0}\} \tag{5}\]