Shadow Effect of Human Obstacles on Indoor Visible Light Communication System with Multiple Light Sources

Abstract

When the direct visible-light channel is affected by people walking or other obstacles, the shadow effect formed in the receiver space affects communication performance and can even lead to communication interruption. In this paper, two numerical methods for calculating the shadow area of the human body were proposed for an indoor multi-light communication system. The influence of shadows on system performance was analyzed using the mean square errors of illuminance and signal-to-noise ratio, as well as the interrupt probability, as parameters. The results showed that shadows had a great influence on the performance of the visible-light communication system. When the number of light sources was fixed, the shadow effect could be effectively reduced by optimizing the layout of the light sources. These research results can provide a theoretical basis for improving the stability of visible-light communication systems.

1. Introduction

In recent years, visible-light communications (VLC) have developed rapidly, and their application has gradually expanded to outdoor, underwater, underground, and other environments [1]. Due to its high transmission rate, strong system reliability, and low communication delay, visible-light communication technology has become a key candidate technology for 6G mobile communications [2], showing great advantages.

High-quality wireless access is one of the main research objectives of VLC systems; in order to achieve this goal, researchers usually focus on the visible-light communication system channel. Cui et al. established a direct vision channel model for visible-light communications based on path loss and received optical power [3]. Ding et al. proposed a visible-light channel model based on the Lambert–Phong reflection mode [4]. Liu et al. established an indoor VLC channel model considering the reflectance of different surfaces [5]. Ramirez-Aguilera et al. established a universal indoor VLC channel model based on MMCA [6]. Zhao Taifei et al. established a Gaussian-like luminescence model for a small-divergence angle transmitter [7]. Eldeeb et al. used ray tracing technology to measure and simulate the channel model of a 2 × 2 MIMO in a conference room with furniture in order to verify the correctness of the channel model generated using the OpticStudio ray tracing method [8].

With the advent of the era of big data and the rapid development of wireless communication technology, it is conservatively estimated that at least 70% of user terminal data visits are carried out in an indoor scene. Accordingly, the indoor VLC system is one of the most important application scenarios. In an actual indoor VLC system, on the basis of the characteristics of visible light, the existence or movement of obstacles can block the visible-light link and form a certain shadow area. Due to the influence of this shadow, the communication quality of all receiving terminals in the affected area deteriorates sharply and can even lead to communication interruption. In order to specifically explore the influence of shadows resulting from obstacles, Xiang et al. proposed a shadow ray tracking (SRT) algorithm [9]. Dong et al. established a channel model for random shadow occlusion based on Poisson stochastic [10]. Singh et al. adopted a method based on random geometry to model and analyze the shadow effect of human obstacles [11]. Tang et al. established a channel model for shadow occlusion under a single light source [12]. Abdalla et al. established a VLC AP switching model for indoor mobile users based on interrupt probability [13]. Donmez and Miramirkhani adopted a nonsequential ray tracing method to obtain the channel impulse response and channel characteristics along the random trajectory of moving human obstacles [14]. Chvojka et al. presented and analyzed the results of a study investigating the influence on the VLC system of human shadows under three different indoor conditions [15]. Similarly, to reduce the influence of shadows due to obstacles, Beysens et al. proposed a NutVLC system [16]. Hass et al. proposed a load-balancing scheme combining Li-Fi and Wi-Fi networks [17]. Farahneh et al. proposed an optical diffraction phenomenon to overcome the effect of shadows on an underwater VLC system [18]. Burton et al. proposed the use of a multidirectional receiver to reduce the shadow effect of obstacles [19]. Komine et al. proposed an increase in the number of light sources to reduce the shadow effect of indoor obstacles [20]. The above studies on the effect of shadows on indoor VLC systems mostly focused on environmental descriptions or analyses of experimental data; however, there remains a lack of systematic theoretical research on the effect of shadows on the channel model of an indoor VLC system. In addition, the above studies only considered the influence of the full shadow generated by obstacles. In reality, obstacles also produce a half shadow in the case of multiple light sources. Since the receiving terminal in the shadow area can only receive the optical power of some indoor light sources, the existence of a half shadow can affect the uniformity of indoor illumination and the distribution of the signal-to-noise ratio, making it difficult for users in different locations to obtain similar lighting effects and communication quality.

Addressing the shadow effect of indoor human obstacles, this paper establishes two different types of shadow occlusion models for the indoor VLC channel and then analyzes their influence on the indoor VLC system as a function of the mean square errors of illuminance and signal-to-noise ratio as well as the interrupt probability. The purpose of this paper was to systematically analyze the shadow effect of obstacles on the performance of indoor VLC systems so as to deeply characterize their mechanism.

2. Materials and Methods

2.1. 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 LED lights located on the ceiling of a room and multiple receiving terminals on the receiving plane, as shown in Figure 1. If there are several users randomly distributed in the room, due to the relationship between the human body and the relative position of the light source, the light source radiation can be hindered, thus forming a certain shadow area on the receiving plane. Specifically, the area of the receiving plane that is not directly irradiated by all light sources is the full shadow (black shadow in Figure 1), whereas the area that is only partially irradiated by the light sources is the half shadow (gray shadow in Figure 1).

Figure 2 shows the two-dimensional plane projection of shadows formed by human obstacles when L₁ and L₂ light sources were distributed indoors. In the figure, S₀ represents the fully shaded region, while S₁ and S₂ 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 S₀ 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 S₁ and S₂, 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

$$P_{Rx}=(H_{LOS}+H_{NLOS})P_{Tx}$$

(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:

$$E={\displaystyle \sum (E_{hor}+{\displaystyle \underset{walls}{\int }d{E}_{hor(NLOS)}})}$$

(2)

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:

$$D_E=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{(E_i-\overline{E})}^2}}{n}}$$

(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:

$$D_{SNR}=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{(SN{R}_i-\overline{SNR})}^2}}{n}}$$

(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 P₀ [23] can be defined as the probability that the terminal cannot correctly judge the received data, i.e.,

$$P_0=P_r\left\{SNR\le {\gamma }_0\right\}$$

(5)

2.2. Calculation of the Shadow Area of Human Obstacles under Multiple Light Sources

2.2.1. Full Shadow Calculation of Human Obstacles

If the size of the receiving plane is $N(m)\times N(m)$ and it is divided into $M\times M$ rectangular grids, then the area of each rectangular grid is $S_{rect}$. The circular arc of the top surface of the cylinder was equally divided into units of 1 degree, and multiple shadow line segments FG were generated on the receiving plane by the vertical line segment (QF in Figure 3a) where the light source L and each discrete circular arc point located are calculated. The total number of Rectangular Grids $R_{total}$ passed by the Shadow Segment FG was counted and $R_{total}$ represent the number of total receivers located in the shadow area. Therefore, the shadow area $S_{shadow}$ of the human obstacle could be expressed as:

$$S_{shadow}=R_{total}\times S_{rect}$$

(6)

The specific solution process for the shadow area of human obstacles can be described as follows. It can be assumed that Point Q is the k-th discrete point of the circular arc on the top surface of a cylinder. From the geometric relation in Figure 3a, it can be seen that the angle between the positive semiaxis of the x-axis and NQ is:

$$\theta =\frac{1}{{360}^{\circ }}\times k$$

(7)

Then, the coordinates $(x_Q,y_{{}_Q},z_Q)$ of Point Q can be obtained by the following formula:

$$\{\begin{array}{l}{x}_Q=X_n+r\cos \theta \\ y_{{}_Q}=Y_n+r\sin \theta \\ z_Q=Z_n\end{array}$$

(8)

The Euclidean distance between Point L and Point Q in position space was:

$$d_{QL}=\Vert l_Q-l_L\Vert$$

(9)

where $l_Q$ represents the position of Point Q and $l_L$ represents the LED position of the light source.

From $d_{QL}$, we know that the unit vector of LQ was:

$${\mathit{e}}_{LQ}=\frac{(\mathit{Q}-\mathit{L})}{d_{QL}}$$

(10)

The length $d_{LG}$ of the Line Segment LG could be obtained from the relation of similar triangles $\Delta QGF$ and $\Delta LGO$.

$$d_{LG}=\frac{d_{QL}{d}_{LO}}{d_{LO}-d_{QF}}$$

(11)

where $d_{LO}$ and $d_{QF}$ are the lengths of Vector $\overrightarrow{LO}$ and Vector $\overrightarrow{QF}$, respectively.

Vector G can be expressed as:

$$\mathit{G}=\mathit{L}+d_{LG}\times {\mathit{e}}_{LQ}$$

(12)

Then, the shadow length generated by the Line Segment QF on the XOY plane under Light Source L was:

$$d_{FG}=\Vert l_F-l_G\Vert$$

(13)

where $l_F$ represents the position of F and $l_G$ represents the position of G.

After the length of the shadow line segment, FG was calculated according to the above derivation process, the shadow line segment FG was discretized according to the size of the rectangular grid, and the position of each discrete shadow point in the shadow area and its corresponding rectangular grid was marked. After marking according to the above steps, the shadow matrix A of the receiving plane under the occlusion of a single light source and a single obstacle could be obtained. Then, the total number of Shadow Grids $R_{total}$ marked in the shadow matrix A (i.e., the rectangular grid marked as 1 in the shadow matrix) could be counted and substituted into Formula (6) to obtain the shadow area generated by the single body obstacle of a single light source.

According to the geometric optics theory, if S_n is the shadow area generated by the n-th light source on a single obstacle, then the total shadow area generated by a single human obstacle under multiple light sources is the intersection of the shadow area S_n generated by all light sources on the obstacle, i.e.,

$$S_{f-s}=S_1\cap S_2\cap \cdots \cap S_n$$

(14)

The above solution method of the shadow area could be converted into its matrix form. If the shadow matrix generated by the n-th light source for a single obstacle was A_n, then the shadow matrix ${\mathit{E}}_{m-s}$ generated by multiple light sources under the occlusion of a human obstacle could be expressed as:

$${\mathit{E}}_{m-s}(x,y,n)={({\mathit{A}}_1\cdot {\mathit{A}}_2\dots {\mathit{A}}_n)}_{xy}$$

(15)

where (x, y) is the receiver position and $\cdot$ represents the dot product, that is, the multiplication of the corresponding elements of the matrix. Moreover, A_n(n ∈ [1,N]) is the shadow matrix generated by the n-th light source against human obstacles in the receiving plane, and A_n could be expressed as:

$${\mathit{A}}_n=\{\begin{array}{l}0,(x,y)\notin S_n\\ 1,(x,y)\in S_n\end{array}$$

(16)

We calculated the number of Shadow Grids $R_{m-s}$ in the shadow matrix ${\mathit{E}}_{m-s}$ and substituted the number of Shadow Grids $R_{m-s}$ into Formula (6) to obtain the full shadow area $S_{f-s}$ of an obstacle under multiple light sources, as shown below.

$$S_{f-s}=R_{m-s}\times S_{rect}$$

(17)

Additionally, according to the geometric optics theory, if the full shadow area $D_m$ is generated by multiple light sources on the m-th human obstacle, then the full shadow area $S_{f-m}$ of multiple obstacles under multiple light sources can be the union of the full shadow area $D_m$ of all obstacles, i.e.,

$$S_{f-m}=D_1\cup D_2\cup \cdots \cup D_m$$

(18)

The above solution method of the shadow area was converted into the matrix form. If the M shadow matrices ${\mathit{C}}_{\mathrm{m}}(m\in [1,M])$ were generated by multiple light sources for M obstacles, then the shadow matrices ${\mathit{E}}_{m-m}$ generated by multiple obstacles under multiple light sources could be expressed as the corresponding addition of M shadow matrices, i.e.:

$${\mathit{E}}_{m-m}(x,y,m)={\displaystyle \sum _{m=1}^{\mathrm{M}}{\mathit{C}}_m(x,y)}$$

(19)

The number of Shadow Grids $R_{m-m}$ in the shadow matrix ${\mathit{E}}_{m-m}$ (rectangular grids whose values were not 0 in the shadow matrix) was counted, and the number of Shadow Grids $R_{m-m}$ was substituted into Formula (6) to obtain the full shadow area $S_{f-m}$ of multiple obstacles under multiple light sources.

2.2.2. Half-Shadow Calculation of Human Obstacles

According to the geometric optics theory and mathematical knowledge, in the case of two or more light sources, the obstacle can produce a half shadow, the intersection of all half shadow areas can constitute the full shadow area of the obstacle, and whether the full shadow area exists is related to the relative position of the light source and human body obstacle. When the obstacle was located within the area enclosed by multiple light sources, as shown in Figure 4a,b, the intersection of all half-shaded areas was zero, and the full-shaded area could not be generated. When the obstacle was located outside the area enclosed by multiple light sources, as shown in Figure 4c,d, the intersection of all half-shaded areas was not zero, and there was a full-shaded area of the human obstacle.

In the case of multiple light sources, each light source produces a half shadow on the obstacle, and according to the two light sources in Figure 2, the number of half shadows of one obstacle was 2, the number of half shadows of one obstacle of the three light sources in Figure 4 was 3, and the number of half shadows of one obstacle of the four light sources was 4. It can be deduced that under multiple light sources, the number of half shadows produced by each human obstacle is proportional to the number of visible light sources. In addition, since the intersection of multiple sets, as a subset of any set, and the full-shaded area was the intersection of the half-shaded area, it could be seen that with the increase in the number of light sources, the half-shaded area increased, and the full- shaded area decreased when the obstacle position was fixed.

The solution of the half-shadow area $S_{h-s}$ of an obstacle under multiple light sources could be combined with the solution of the shadow matrix A of a single obstacle with a single light source. We calculated N shadow matrices A_n generated by N light sources for a single obstacle. Then, N shadow matrices A_n were added to obtain the total shadow matrix ${\mathit{T}}_{m-s}$ generated by an obstacle under N light sources. The total shadow matrix ${\mathit{T}}_{m-s}$ could be expressed as the following formula.

$${\mathit{T}}_{m-s}(x,y,n)={\displaystyle \sum _{n=1}^{\mathrm{N}}{\mathit{A}}_n(x,y)}$$

(20)

where A_n is the shadow matrix generated by the n-th light source to an obstacle in the receiving plane.

The number of rectangular grids $W_{m-s}$ whose value was not 0 and not N in the total shadow matrix ${\mathit{T}}_{m-s}$ was counted. If the value was not 0, the rectangular grid was blocked by a shadow; if the value was not N, the rectangular grid with a full shadow region could not be considered. The half-shadow area $S_{h-s}$ generated by an obstacle under multiple light sources is shown in the following equation:

$$S_{h-s}=W_{m-s}\times S_{rect}$$

(21)

The calculation of the half-shadow area of multiple obstacles under multiple light sources could be solved according to the calculation method of the half-shadow area of one obstacle under multiple light sources. First, according to the solution method of the total shadow matrix of one obstacle under multiple light sources, the M shadow matrices ${\mathit{T}}_{m-s}$ generated by multiple light sources for M obstacles could be obtained. After the addition of M shadow matrices ${\mathit{T}}_{m-s}$, the number of rectangular grids $W_{m-m}$ whose value was not 0 and not N in the total shadow matrix was counted. Finally, the number of shadow grids $W_{m-m}$ was substituted into Formula (6) to calculate the half-shadow area $S_{h-m}$ of multiple obstacles under multiple light sources.

The quantitative analysis of the full shadow effect and half-shadow effect in this paper was to process the impulse response of the signal received by the original photodetector using the visual function $\mathsf{\Gamma }(x)$; that is, the impulse response of the signal in the shaded region could be represented by the function $\mathsf{\Gamma }(x)=0$, and the impulse response of the signal in the non-shaded region could be represented by the function $\mathsf{\Gamma }(x)=1$.

Then, the channel gain $H_{sh}$ of the indoor VLC system channel model with shadow occlusion can be expressed as

$$H_{sh}=H\cdot \mathsf{\Gamma }(x)=\{\begin{array}{l}0,(x,y)\in S_{sh}\\ H, others\end{array}$$

(22)

where $H$ is the channel gain of the channel model of the indoor VLC system without the shadow occlusion described above.

3. Results and Discussion

In this paper, the influence of the shadow effect on the system performance was simulated and analyzed under different numbers of light sources. The room size was assumed, an indoor space coordinate system was established, and the origin of the coordinates was located at the lower left corner of the room. According to the number of light sources, different positions of light sources were set. The layout of the light sources is shown in

Table 1. Visible LED lamp layout table.

Number of Light Sources	Light Source Name	Light Source Position	Light Source Name	Light Source Position
1	LED1	(2.5 m, 2.5 m, 3 m)
2	LED1	(1 m, 2.5 m, 3 m)	LED2	(4 m, 2.5 m, 3 m)
3	LED1	(1 m, 2.5 m, 3 m)	LED2	(4 m, 1 m, 3 m)
	LED3	(4 m, 4 m, 3 m)
4	LED1	(1.25 m, 1.25 m, 3 m)	LED2	(1.25 m, 3.75 m, 3 m)
	LED3	(3.75 m,1.25 m, 3 m)	LED4	(3.75 m, 3.75 m, 3 m)

. It was assumed that the receiving terminals were evenly distributed on a plane 1 m above the ground. Other relevant parameters are shown in

Table 2. System simulation parameters.

Simulation Parameter	Values
Area of the PD, $A_{PD}$	0.01 ${\mathrm{m}}^2$
Optical filter gain, $T(\theta )$	1
FOV, ${\psi }_{FOV}$	70°
LED semi-angle, ${\phi }_{1/2}$	70°
Reflectance coefficient, $\rho$	0.8
Detector responsivity, $R_{PD}$	0.54 A/W
System bandwidth, $B_{vlc}$	20 MHZ
Central luminous intensity, $I(0)$	2700 cd
Transmitted power, $P_t$	8 W
Radius of the cylinder, h	0.3 m
Height of the cylinder, r	1.8 m

.

3.1. Influence of the Obstacle Full Shadow and Half Shadow on Indoor VLC Systems

Since a half shadow could only be generated under multiple light sources, we first analyzed the influence of a full shadow and a half shadow generated by a single human body obstacle on the indoor SNR distribution under different light sources, as shown in Figure 5.

As shown in Figure 5, as the same number of obstacles as the number of light sources increased, the area that did not receive the signal-to-noise ratio in the figure decreased; that is, the full shadow area decreased. In addition, when the human barrier moved within the area enclosed by the light source, no receiving signal-to-noise ratio area could be generated, which indicated that the influence of the total shadow generated by the human barrier on the system signal-to-noise ratio gradually decreased as the light source increased. In addition, there were some areas near the unreceived signal-to-noise ratio area, namely, the half-shadow area. This area increased with an increase in the number of light sources, which also verified the above theoretical derivation; that is, the number of half shadows generated by human obstacles was proportional to the number of visible light sources. Although the receiving signal-to-noise ratio of the receiver in the semi-shadowing region did not change as significantly as that of the receiver in the full shadow region, due to the lack of power of at least one light source, the receiving signal-to-noise ratio of the receiver in the non-shadowing region still decreased significantly. This shows that the shadow effect of obstacles on the system performance cannot be ignored under multiple light sources.

In practical applications, there is often more than one obstacle for indoor personnel. Therefore, in this paper, the relationship between the mean square error of illumination and the SNR of the receiving plane of an indoor VLC system and the number of obstacles under the occlusion of different amounts of light sources and shadows was discussed, as shown in Figure 6.

As shown in Figure 6, under the same number of light sources, the presence of any shadow occlusion made the mean square error of illumination and SNR of the receiving plane increase with an increase in the number of obstacles. By contrast, for the same number of obstacles, the presence of any shadow occlusion could make the mean square error of illumination and SNR of the receiving plane decrease with the increase in the number of light sources. The influence of a half shadow on the mean square error of illumination and signal-to-noise ratio of the receiving plane was significantly higher than that of a full shadow, which could affect the distribution of indoor illumination and the uniformity of the signal-to-noise ratio distribution, making it difficult for users in different indoor locations to obtain similar lighting and communication qualities. In addition, in Figure 6a,b, the mean square error of illumination and signal-to-noise ratio was smaller than when the number of obstacles was large. This was caused by the fact that the position of obstacles set in this paper was randomly generated in the room. Therefore, the shadow area generated when the number of obstacles was large was smaller than when the number of obstacles was small.

To more clearly display the influence of the shadow effect of obstacles on the communication system performance, Figure 7 simulates and analyses the relationship between the link outrage probability and transmitted power and the number of obstacles (N = 0, 1, 8, 16) under different light sources and shade occlusion.

As shown in Figure 7, with the same number of obstacles, the probability of system interruptions under any shadow occlusion can decrease with increasing transmitting power. When the transmission power was the same, the system outrage probability increased with the increase in the number of obstacles, and under the same number of obstacles, the outrage probability generated by half-shadow occlusions was always larger than that of full-shadow occlusions. When the transmission power was 6 W, as shown in Figure 7a, the outrage probability without obstructions was 0, and the outrage probability generated by full shadows and half shadows with 16 obstructions was 0.0952 and 0.2124, respectively. In Figure 7c, the outrage probability was 0 when there were no obstructions, and the outrage probability generated by full shadows and half shadows under 16 obstructions was 0.0332 and 0.1028, respectively. The results show that although increasing the light source could reduce the shadow effect caused by human obstacles, the outrage probability caused by half-shadow occlusion should not be ignored.

3.2. Adaptive Simulation Analysis of Indoor VLC Channel Model with Shadow Occlusion under Multiple Light Sources

To explore the applicability of the indoor VLC channel model with shadow occlusion under multiple light sources, the following is based on the applicability simulation analysis method of the indoor VLC channel model with the shadow occlusion of a single light source in the literature [12]. By changing the size of room size L, the applicability of a single light source shadow occlusion channel model and multiple light source shadow occlusion channel models in different communication room topologies could be analyzed. The outrage probability was still taken as the performance index to measure the communication quality of the system, and the simulation parameters in Table 2 remained unchanged. In the simulation of a single light source, it could be assumed that under different room topologies, the visible light source was located in the center of the ceiling of the room; that is, when the room size was $5 \mathrm{m}\times 5 \mathrm{m}\times 3 \mathrm{m}$, the specific coordinates of the visible light source were [2.5, 2.5, 3]. When the room size was $6 \mathrm{m}\times 6 \mathrm{m}\times 3 \mathrm{m}$, the coordinates of the visible light source were [3, 3, 3]; when the room size is $7 \mathrm{m}\times 7 \mathrm{m}\times 3 \mathrm{m}$, the coordinates of the visible light source were [3.5, 3.5, 3]. In the simulation of multiple light sources, four light sources could be taken as an example. It was assumed that under different room topologies, four LED light sources were located around the room, and their coordinates remained unchanged. That is, when the room dimensions were, respectively, $5 \mathrm{m}\times 5 \mathrm{m}\times 3 \mathrm{m}$, $6 \mathrm{m}\times 6 \mathrm{m}\times 3 \mathrm{m}$ and $7 \mathrm{m}\times 7 \mathrm{m}\times 3 \mathrm{m}$, the coordinates of the four LED light sources could be located in [1.25, 1.25, 3], [1.25, 3.75, 3], [3.75, 1.25, 3], [3.75, 3.75, 3]. In addition, in the simulation of a single light source and multiple light sources, it could be assumed that there were four obstacles randomly distributed in the room. By changing the room size L and the transmitting power, the relationship between the outrage probability of indoor single light source and multiple light sources VLC system and the changing room size and transmitting power was simulated and analyzed, as shown in Figure 8.

As can be seen from Figure 8, with the same transmitting power, the system outrage probability of both single and multiple light sources gradually increased with the increase in room size L. This was because, with the increase in room size L, the communication distance between the photodetector and the visible light source also increased. As the distance increased, the signal-to-noise ratio reaching the photodetector also decreased, and the system outrage probability eventually increased. In the case of the same room size L, the system outrage probability of both single and multi-light sources gradually decreased with the increase in the transmitting power. This was because when the room size L remained unchanged, the signal-to-noise ratio to the photodetector increased with the increase in the transmitting power, and the system outrage probability eventually decreased. At the same time, it could also be seen from Figure 9b that the outrage probability of the half-shadow occlusion was always larger than that of full shadow, and the outrage probability curve of the half-shadow occlusion did not decline smoothly with the increase in the constant amplitude of the transmission power. The reason for this phenomenon was that the position of obstacles set in this paper was generated randomly. Since the position of obstacles generated each time was uncertain, the obstacle generated shadow areas of different sizes in different positions and eventually led to the above phenomenon in the outrage probability of the system.

The above simulation results show that the model can be applied to different room sizes, but in the actual environment, different room sizes should be selected according to different performance requirements to obtain the optimal value of an indoor VLC room.

3.3. Influence of Shadow Effects on Indoor VLC Systems under Optimized Layouts of Light Sources

To solve the above problems, a control variable method was used to optimize the layout of four LED light sources, and then the influence of the total shadow generated by human obstacles on the indoor visible light communication system before and after the optimized layouts of the light sources were compared and analyzed.

Figure 9 shows the variation in the mean square error of illuminance with the distance L between four LEDs and the wall. As seen from the figure, when L = 0, that is, when the four LEDs were located at the four corners of the ceiling, the illumination in the four corners of the room was much larger than that in the center of the room, and the mean square error of illumination was also larger. As the distance L between the LED and the wall gradually increased, the mean square error of illumination on the receiving plane decreased first and then increased. When L = 0.9 m, the mean square error of illumination on the receiving plane reached a minimum value of 90.29 lx, and the distribution of illumination on the receiving plane was the most uniform.

Figure 10 shows the illumination distribution of the receiving plane before and after the optimized layout of the light source, respectively. Before optimization, the illuminance distribution of the system ranged from 328 lx to 1065 lx, and the mean square error was 139.51 lx. After optimization, the illumination of the receiving plane of the system was between 441 lx and 921 lx, and the mean square error was 90.29 lx, both of which met the requirements of international lighting standards. However, after optimization, the illumination distribution of the receiving plane was more uniform.

Figure 11 shows the illumination mean square error and SNR mean square error data of the receiving plane of the system under different numbers of human obstacles before and after the optimal layout of the light source, respectively. As seen from the two figures, both the mean square error of the illumination and SNR on the receiving plane increased with an increase in the number of obstacles before and after the optimized layout of the light source, and the mean square error of the illumination and SNR after the optimized layout were generally smaller than those without the optimized layout of the light source. In Figure 11a, when the number of obstacles was 16, the mean square error of the illumination after optimization was reduced by 58.3 lx compared with that before optimization. In Figure 11b, when the number of obstacles was 16, the mean square error of the optimized SNR was reduced by 0.49 dB compared with that before optimization. This shows that optimizing the layout of the light source could reduce the influence of the shadow effect caused by human body obstacles on the system’s performance. In addition, there was also the phenomenon of an inverse increase in shadow areas caused by the randomness of the obstacle position.

4. Conclusions

In this paper, two different types of shadow area calculation methods for human obstacles were proposed in the case of multiple light sources. By analyzing the distribution variation in the illuminance mean square error, signal-to-noise ratio mean square error, and outrage probability with the number of obstacles, the influence of the human shadow effect on the indoor visible light communication system was illustrated. The results showed that: increasing the light source could significantly reduce the two shadow effects of obstacles and improve the performance of the communication system. However, the outrage probability caused by the half-shadow effect was relatively large. For example, when the number of obstacles was 16, the outrage probability caused by the half-shadow effect reached 0.1028, which indicated that the influence of the half-shadow effect on the system performance could not be ignored even in the case of multiple light sources. In addition, by optimizing the layout of the light source, the influence of the total shadow effect of the optimized human obstacles on the mean square error of illuminance and signal-to-noise ratio of the system was reduced by 58.3 lx and 0.49 dB, respectively, compared with before optimization, which indicated that optimizing the layout of the light source could further improve the communication performance of the system.