Performance Study of Random Layout Light Source for Visible Light Communication System

Abstract

In indoor visible light communication, a rational layout of light sources is required to ensure that multiple users at different locations in the room can obtain better communication quality and achieve uniform coverage of optical power on the receiving surface. The article investigates the performance of an indoor visible light communication system when the random layout of the Matern hardcore point process is used and compares it with the communication performance under the Poisson point process and the binomial point process. A particle swarm optimization algorithm is introduced based on the Matern hardcore point process, where the points generated under the Matern hardcore point process are used as the initial positions of the particles, and optimization adjustments are made according to the objective function to find the optimal layout. The results show that compared with the Poisson point process and the binomial point process, the use of the Matern hardcore point process to randomly lay out the LEDs makes the light intensity in the system more uniform and the numerical fluctuation of the received power is smaller. The uniformity of the indoor illumination after the combination of the Matern hardcore point process and the particle swarm optimization algorithm reaches 0.84, the deviation of the peak power is reduced by 20%, and the average signal-to-noise ratio value is 0.86, which is an increase in the average signal-to-noise ratio compared to the average signal-to-noise ratio before optimization.

1. Introduction

Optical communication technology has gradually replaced traditional wireless communication methods due to the advantages of high signal-to-noise ratio, fast modulation rate, good confidentiality, etc. Visible light communication has also become one of the hot spots of research. Visible Light Communication (VLC) uses a Light Emitting Diode (LED) to realize the dual functions of lighting and communication [1,2]. Compared with traditional radio frequency communication, VLC technology has both lighting and communication functions and has the advantages of a high transmission rate, no spectrum limitation, safety, green, etc. These advantages make it play an important role in the fields of high-speed positioning, sensing, and the Internet of Things [3,4].

The coverage of a single LED is limited and cannot satisfy the lighting and communication of all users in the room. In a visible light communication system to make the light source distribution uniform, the layout of the light source becomes very important. A reasonable layout can improve the signal-to-noise ratio of the transmitted signal and reduce inter-code interference, which is very helpful in improving the rate of data communication [5,6].

In 2017, CHENC and GARG P et al. [7,8] gave quadrilateral LED layout and hexagonal LED layout methods to improve the indoor visible light coverage, respectively, but this only considered the number of LED positions in a specific environment and did not give the specific position and layout number of these LEDs, which makes this method not universal. Zhao and Peng [9] in the traditional layout based on the proposed 4 + 1 layout and optimized the original layout and 4 + 1 layout method in addition to taking into account the uniformity of light, communication effects, and other aspects of the factors. For the above traditional geometric layout of LEDs, in practice, LED sources used to illuminate larger areas may not follow a fixed geometry. Varma [10] et al. introduced randomness. Traditional LED layout methods usually use regular geometry and allocate equal power to each LED source. The article proposes a power allocation for a randomized LED array scheme, in which the positions of LEDs are modeled by a binomial point process, and this method has higher flexibility and efficiency. In 2020, Zhai et al. [11] proposed to optimize the layout of light sources using multiple swarm genetic algorithms with 20 LEDs as an example and solved the problem of non-uniformity in light and power distribution by optimizing the parameters of the position, power, and angle of the light sources. In 2022, He et al. [12] proposed a new polygonal layout based on rectangular planar three-dimensional space, simulated the illumination and signal-to-noise ratio of the polygonal layout and circular layout in a 5 m × 4 m × 3 m room, and further optimized the position and power of the polygonal layout by particle swarm algorithm, respectively, and the uniformity of illumination and the signal-to-noise quality factor of the optimized polygonal layout were improved. In 2023, Chen, Y. et al. [13] proposed a fast whale optimization algorithm based on a fusion improvement strategy for solving the problem of uneven distribution of optical signals in indoor visible light communication systems. The algorithm improves the convergence speed by inverse learning and nonlinear convergence factor and adopts a perturbation search mechanism to achieve global optimization, and the results show that the system illumination uniformity is improved by 7.39% to 109.03% after optimizing 16 LED layout models.

The Matern hardcore point process is a point process with the repulsion property, i.e., the distance between two points inside this process cannot be less than the hard-core radius and is a point process with the repulsion property, where there is a minimum distance constraint between any two points. In general, it is more regular (less aggregated) compared to Poisson point processes. One way to maintain a minimum distance between two points is to use a point process without such constraints as a base point process and then remove points that violate the conditions based on the constraints. It is generally used for base station location planning, blockage modeling, and interference calculation in wireless networks.

Matern hardcore point process compared to other stochastic processes, with the constraints of the parameter hard-core radius, which can make the distance between the light sources not too sparse or too dense, to ensure a reasonable distance between the light sources, will make the light sources have a more uniform distribution.

For the above light source layout of indoor visible light communication systems, researchers have proposed a variety of layout methods and optimization algorithms, but each method has its advantages and disadvantages, and there are some limitations in practical applications. Specifically: Fixed geometric layout methods such as quadrilateral and hexagonal are simpler, easier to implement, and more efficient, but their limitation is the lack of flexibility. These layout methods usually assume a fixed distribution of light sources in uniform geometric positions, which cannot be adapted to the needs of complex practical scenarios such as different room sizes and shapes. In addition, fixed geometric layouts perform poorly in terms of light uniformity and signal-to-noise ratio in edge regions, making it difficult to meet the light and communication requirements of large or irregular rooms. Genetic algorithms and multiple swarm genetic algorithms are widely used to optimize the position and parameters of the light source layout, which can effectively improve the communication performance and illumination uniformity of the system. However, the convergence speed of these algorithms is relatively slow, especially when facing large-scale layout optimization problems that require a large amount of computational resources, which limits the efficiency of their practical applications. Although the particle swarm optimization algorithm has better global search capability, it still needs to be improved in terms of convergence speed and computational complexity.

As can be seen from the above advances, most of the literature uses traditional geometrical methods to arrange the LEDs or optimize the position of the LEDs as well as the parameters of the light source using genetic algorithms, particle swarm algorithms, etc. to improve the performance of indoor visible light communication systems. In practice, LED light sources used for lighting larger areas may not follow a fixed geometry, and using some algorithms requires a lot of iterations and calculations to obtain optimal results. In order to address the above problems, the article adopts the Matern hardcore point process to randomize the position of the light sources and compares the results of this stochastic process with those of the Poisson point process and the binomial point process. In addition, the method of combining the Matern hardcore point process with the particle swarm algorithm is used to optimize the position of the light source so that the optimization starts from a more reasonable initial layout and reduces the number of iterations of the early search simulation. The results show that this process can significantly improve the communication performance and illumination uniformity of the system and reduce the number of iterations of the algorithm.

2. System Model

2.1. Visible Light Communication System Model

As shown in Figure 1 is a traditional indoor visible light communication system model [14]. With a room size of 5 m × 5 m × 3 m, the following coordinate system was established: the center of the floor as the origin of the coordinate system O, respectively, connecting the origin with the midpoint of the width and length of the room, and its connecting line as the x-axis and y-axis, and the xoy plane is coincident with the ground. The light source LEDs are distributed on the ceiling, and the receiver is located on the receiving plane at a height of 0.85 m.

2.2. Illumination Model

Assuming that the radiation intensity of a single LED light source meets the Lambertian radiation intensity model, the luminous intensity of a single LED light source is

$$I\left(\phi \right)=I\left(0\right){\cos }^m\phi$$

(1)

where $\phi$ is the emission angle of the LED? I(0) is the center light intensity of the LED light source, and m is the Lambertian radiation coefficient, which is determined by the luminous half-power angle of the LED $\cos {\mathrm{\Phi }}_{1/2}$.

$$m=-\ln 2/\ln (\cos {\mathrm{\Phi }}_{1/2})$$

(2)

The article considers only the effect of the primary reflected light in the direct and non-direct links, and the received illuminance at (x,y) at any point on the receiving plane is

$$E_{LOS}=I(0){\cos }^m \phi \cos \psi /D^2$$

(3)

$$E_{NLOS}={\displaystyle \frac{1}{\pi D_1^2{D}_2^2}}I(0)\rho dA{\cos }^m \phi \cos \alpha \cos \beta \cos \psi$$

(4)

where D is the distance between the LED and the receiving surface, ρ is the reflectivity of the wall, $D_1$ is the distance from the LED to the reflective point on the wall, $D_2$ is the distance from the reflective point on the wall to a point on the receiving surface, dA is the area of the reflective point on the wall, and α and β are the horizontal angles of the reflective point in relation to the line connecting the LED and the receiving point, respectively. According to the relevant regulations of the International Organization for Standardization on indoor lighting standards, the illuminance of the office should be in the range of 300 to 1500 lx [15]. In order to calculate the power distribution in the receiving plane, the Direct Current (DC) gain H(0) is introduced, and in a single optical link, the DC gain can be expressed as

$$H(0)=\left\{\begin{array}{l}{\displaystyle \frac{(m+1)A}{2\pi D^2}}{\cos }^m \phi T_s(\psi )g(\psi )\cos (\psi ), 0\le \psi \le {\psi }_c\\ \hspace{1em}\hspace{1em}\hspace{1em} 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}, \psi >{\psi }_c\end{array}\right.$$

(5)

where A is the effective receiving area of the receiver, $T_s(\psi )$ is the filter transmission coefficient of the receiver, $g(\psi )$ is the gain of the optical concentrator, ${\psi }_c$ is the field of view of the receiver, and the relationship $g(\psi )$ between and ${\psi }_c$ can be expressed as

$$g(\psi )=\left\{\begin{array}{l}{\displaystyle \frac{n^2}{{\sin }^2{\psi }_c}},\hspace{1em}\hspace{1em}0\le \psi \le {\psi }_c\\ \hspace{1em} 0,\hspace{1em}\hspace{1em}\hspace{1em}\psi >{\psi }_c\end{array}\right.$$

(6)

The received power can be expressed as [16]

$$p_r=H(0)P_t$$

(7)

$P_t$ is the emitted power of a single LED. The power distribution in the receiving plane is the sum of the optical power radiated by each LED in that plane.

The signal-to-noise ratio (SNR) of the system can be expressed as [17]

$$SNR={\displaystyle \frac{{\left(R{P}_r\right)}^2}{{\sigma }_1^2+{\sigma }_2^2}}$$

(8)

where R is the PD conversion efficiency, ${\sigma }_1^2$ is the system bulk noise, and ${\sigma }_2^2$ is the amplifier noise.

2.3. Illumination Uniformity

To better analyze the data, the values of illumination uniformity and peak power deviation are used as measurement parameters. Indoor visible light communication systems for data transmission need to meet the basic requirements of illumination and can be used to test the uniformity of the illumination rate (UIR) of indoor light. UIR is expressed as the ratio of the minimum value of the indoor light distribution to the average value [18]

$$UIR=E_{\min }/E_{mean}$$

(9)

where $E_{\min }$ denotes the minimum value of light level distribution and $E_{mean}$ denotes the mean value of light level distribution. The larger the UIR is, the more uniform the indoor light level distribution is, the smaller the degree of influence on the human eye, and the better the effect of realizing indoor communication. Indoor lighting standards specify that the UIR should not be less than 0.7 and ideally 1. The closer the ratio is to 1, the more uniform the lighting distribution is indicated.

For the received power, since the minimum standard for indoor communication is −2 dBm, Peak Power Deviation (PPD) is used to measure the receiving power fluctuation of the indoor VLC layout. The larger the value, the more violent the fluctuation and the worse the communication quality. The formula is as follows:

$$PPD=(P_{\max }-P_{\min })/P_{\max }$$

(10)

where is the maximum value of the received power and $P_{\min }$ is the minimum value of the received power.

3. Stochastic Process and the Principle of the Algorithm

3.1. Binomial Point Process

The Binomial Point Process (BPP) is a mathematical model for generating a fixed number of random points in a finite region [19]. Assuming a random distribution of n points in a region, for the binomial point process, the set of points can be represented as

$$\mathrm{\Phi }=\left\{X_1,X_2,...,X_n\right\}$$

(11)

where $X_i$ denotes the location of the ith point and is a random variable distributed in the region A. The probability density function of the position of each point is

$$f_{Xi(x)}={\displaystyle \frac{1}{\left|A\right|}},\hspace{1em} \forall x\in A$$

(12)

3.2. Poisson Point Process

The Poisson Point Process (PPP) is a stochastic point process used to describe the random distribution of events (or points) that occur in a given region or time interval, which are considered to occur independently [20]. For a given region or time interval A, if the number of event occurrences N(A) follows a Poisson distribution, we have

$$P(N(A)=k)={\displaystyle \frac{{(\lambda \left|A\right|)}^k{e}^{-\lambda \left|A\right|}}{k!}}$$

(13)

where $\left|A\right|$ is the area of the region A or the length of the time interval, $\lambda$ is the intensity parameter of the event. For a given area or time interval [0, T], a Poisson point process can be generated by the following steps:

(1)

Draw a random variable N~Poisson($\lambda$ T) from the Poisson distribution denoting the number of events in the interval [0, T].

(2)

Generate N points uniformly at random within the interval [0, T].

3.3. Matern Hardcore Point Process

The Matern hardcore point process is a stochastic point process that introduces repulsive distances in a spatial point process. It is developed based on the Poisson point process, which avoids over-densification of points by introducing a minimum distance constraint between points. The process has a wide range of applications in which a certain distance between points needs to be maintained, such as the placement of base stations in wireless communications and the distribution of trees in ecosystems [21].

First, a chi-square Poisson point process ${\mathrm{\Phi }}_b$ with intensity ${\lambda }_b$ is generated as the parent point process, and an independent random variable m(x), called the marked value, is added to each point x. The marked values are uniformly distributed in the interval [0, 1]. The tagged values of all the points are checked, and a point is retained only if it satisfies the requirement that its tagged value is less than the tagged values of all the points within a circle of radius r centered on it; otherwise, the point is deleted. The point process, which consists of the remaining points after such deletion is called the Matern hardcore point process. It is expressed in mathematical notation as

$$\Phi \triangleq \left\{x\in {\mathrm{\Phi }}_b:m(x)<m(y) for all \mathrm{y}\in {\mathrm{\Phi }}_b\cap b(x,r)/\left\{x\right\}\right\}$$

(14)

In this case, the remaining point formation then has a Matern hardcore point process with density ${\lambda }_m$, where

$${\lambda }_m={\displaystyle \frac{1-\exp (-{\lambda }_b\pi r^2)}{\pi r^2}}$$

(15)

As shown in Figure 2, the light source position distribution map is generated using the random process of material hard core points on a 5 m × 5 m square area, indicating that when the hard core radius is 1 m, 16 points are used as the positions of the light source LED.

3.4. Particle Swarm Algorithm

Particle Swarm Optimization (PSO) is a heuristic algorithm that originated from the study of the behavior of bird flock predation. This algorithm starts from a random solution, through iterative optimization search, and information sharing with individual and group optimal values to update themselves. When the algorithm meets the stopping conditions, the global optimal particle is the optimal solution. The particle swarm algorithm is computationally fast, has a strong global search capability, and has been widely used for multi-objective optimization [22].

In this paper, the particle swarm optimization algorithm is improved. Considering the combination of the Matern hardcore point process with the particle swarm algorithm, the points generated by the Matern hardcore point process can be directly used as the initial particle positions of the particle swarm optimization algorithm, which generates an initial layout, so that the algorithm starts with a reasonably distributed layout of the light sources, which helps to accelerate the optimization process and may increase the chances of finding a more optimal solution. In the particle swarm algorithm, the coordinates of these points will be considered as the initial positions of the particles and further adjusted according to the optimization objective to find the best layout. A block diagram of the flow of this algorithm is shown in Figure 3 [23].

Computational Complexity and Time Efficiency Analysis

In particle swarm optimization algorithms (PSO), time efficiency usually refers to the running time required by the algorithm to achieve the desired optimization effect (i.e., to find a solution that satisfies the requirements). Time efficiency reflects the computational speed of the algorithm and is an important indicator for evaluating the performance of the algorithm in practical applications. The computational complexity is mainly determined by the following factors:

(1)

Number of particles N: the number of particles affects the degree of coverage of the search space; a larger number of particles improves the global search capability of the algorithm but also significantly increases the computational burden.

(2)

Maximum number of iterations T: the number of iterations determines the convergence accuracy of the algorithm. Although more iterations can increase the degree of optimization of the solution, the computational time also increases linearly.

(3)

Complexity of the fitness function O(f): the computational complexity of the fitness function (objective function) affects the amount of computation per particle in a single iteration. In practice, the higher the complexity of the fitness function, the heavier the computational burden.

Therefore, the computational complexity of PSO is:

$$O\left(PSO\right)=O\left(N\times T\times f\right)$$

(16)

This means that the increase in the number of particles and the number of iterations increases the total computational complexity exponentially, which may lead to excessive computation time in large-scale light source layout optimization problems.

In this paper, we propose to generate a reasonable initial layout based on the particle swarm algorithm by using the Matern hardcore point process to generate initial values, which effectively reduces the number of invalid searches. The generation complexity of the Matern hardcore point process is O(NlogN), and in combination with the PSO optimization process, the total computational complexity of this scheme can be expressed as:

$$O\left(Matern,PSO\right)=O\left(N\log N\right)+O\left(N\times T^{\prime }\times f\right)$$

(17)

where T′ denotes the smaller number of iterations required under using the points generated by the Matern hard-core point process as the initial layout (T′ < T).

Time efficiency is particularly important in light source layout optimization problems, where a large number of iterations can significantly increase the computational cost. The design of this scheme mentioned in this paper reduces the computational burden to a greater extent, making this scheme more potential for application by improving the computational efficiency while ensuring the optimization accuracy.

4. Simulation Verification and Discussion

In this section, the simulation results of the performance of the indoor visible light communication system under the Poisson point process, binomial point process, and Matern hardcore point process are given and compared with the performance under rectangular and circular fixed shapes, in addition to which the Matern hardcore point process is combined with the particle swarm algorithm to validate the feasibility of adopting this scheme. The main parameters used are shown in

Table 1. Parameters of the indoor VLC system model.

Parameter	Value
Emitted optical power/mW	20
Wall reflection coefficient	0.8
Emission power half angle/°	70
Emitted light center intensity/cd	0.73
Receiver FOV/°	80
PD area/cm2	1.0
Photoelectric conversion efficiency/(A/W)	0.53
Reflection index	1.5
Receiver height/m	0.85

.

4.1. Simulation Analysis of Rectangular and Circular Layout

This section simulates and analyzes the performance of the indoor visible light communication system under rectangular and circular layouts; the detailed parameters are shown in Table 1. As shown in Figure 4a,b, the light source distribution diagram under the rectangular layout and the circular layout are respectively, which consists of 16 lamps.

According to the above parameter conditions, the simulation analysis is carried out under the condition of using 16 LEDs for a flat room of 5 m × 5 m × 3 m. As shown in Figure 5a,b are the simulation results of the light intensity under the rectangular and circular layout, respectively, the rectangular layout of the center of the region with the highest light intensity of 4079.02 lx, gradually decreasing to the surrounding area, and the edge of the region with the lowest light intensity of 1206.38 lx; the average value is 2836.37 lx, far more than the lighting standards, which may be harmful to the human eye. The uniform illuminance ratio is 0.42. The light intensity of the circular layout ranges from 3062.36 to 998.64 lx, with an average value of 2486.64 lx.

As shown in Figure 6a,b are the simulation result graphs of received power under rectangular and circular layouts, respectively. The maximum value of received power in the rectangular layout is 18.52 dBm, and there is a minimum value at the corner of the 5.47 dBm, the average value is 12.88 dBm, the peak power deviation is 0.71, the received power fluctuates greatly, and the communication is not stable. The power in the central region of the circular layout is higher at 16.02 dBm and gradually decreases in all directions and gradually decreases to 5.20 dBm at the edges, with an average received power of 12.79 dBm and a PPD of 0.67. The value of PPD is lower than that under the rectangular layout, which indicates a more stable communication performance than that of the rectangular layout.

As shown in Figure 7a,b are the simulation result graphs of signal-to-noise ratio under rectangle and circle layout, respectively. Figure 8a shows the distribution of signal-to-noise ratio under a rectangle layout, which is 36.65~47.32 dB, and the average value is 43.77 dB, which meets the minimum requirement of communication. The ratio of the minimum value to the maximum value is 0.78, indicating that the communication is best under the LED light source; the further away from the LED light source, the lower the signal-to-noise ratio, and the lowest at the corner. Figure 8b shows the distribution of the signal-to-noise ratio under the circular layout, with the highest signal-to-noise ratio of 45.73 dB in the central area, lower in the edge area, with the minimum value of 36.45 dB, and the average signal-to-noise ratio value of 44.78 dB, and the ratio of the minimum value to the maximum value of 0.79, which indicates that the signal-to-noise ratio is more evenly distributed.

This is due to the fact that in a circular layout, the center of the room is used as a reference point to form a concentric structure, and the light sources are at a more consistent distance from the center in a circular layout, avoiding the excessive signal density in the center area of a rectangular layout. This layout ensures a more balanced distance between light sources. However, for the rectangular layout, the light sources are concentrated at specific geometrical boundaries, which results in overlapping of light near the center, leading to high signal intensity in the central region and weakening of the signal in the edge regions, with a more significant unevenness of signal intensity. In addition, the balanced distribution of light sources makes the signal strength received at each receiving point relatively consistent, thus avoiding dramatic fluctuations in the signal at different receiving locations. This consistency reduces the signal attenuation rate while attenuating the effect of noise, resulting in a higher overall signal-to-noise ratio and a more uniform distribution.

4.2. Simulation Analysis of Random Layout

This section simulates and analyzes the performance of the indoor visible light communication system under three random process layouts, and the detailed parameters are shown in Table 1.

As shown in Figure 8a–c, the simulation results of light intensity under the layout of the binomial point process, Poisson point process, and Matern hardcore point process are presented. It can be seen from the figures that the binomial point process layout achieves the highest light intensity in the central area, reaching 2002 lx. As it spreads outwards, the light intensity gradually decreases, and when it reaches the edge area, the light intensity drops to a minimum of 490 lx, with an average illuminance of 1390 lx, which meets the indoor international lighting standard illuminance. The maximum illumination intensity area of the Poisson point process layout appears near the center to the left, reaching 3700 lx. The illumination intensity of other areas varies greatly, and some areas have significantly lower illumination intensity than the central area. The UIR is 0.27, and the indoor lighting fluctuates greatly. The center of the room is too bright, and prolonged lighting can cause harm to the human eye. For the hardcore point process layout of material, introducing the minimum distance constraint ensures that the light sources are not too close to each other, avoiding the local high-intensity areas caused by excessive concentration of light sources. The light intensity shows a smooth downward trend from the center to the surrounding areas, indicating that the distance between light sources is reasonably controlled and the distribution of light sources is relatively uniform. The UIR is 0.47, indicating an improvement in lighting uniformity compared to the layouts in the other two processes.

As shown in Figure 9a–c are the simulation results of received power under the binomial point process, Poisson point process, and Matern hardcore point process layout, respectively. Matern hardcore point process layout: compared with the other two layout methods, the received power is more uniformly distributed, the power transitions are smooth, and there are no obvious high and low ups and downs. The peak power deviation is 0.59, which is a small value, proving that the fluctuation is not drastic and the communication quality is better. In contrast, in the binomial point process layout and the Poisson point process layout, the values of the received power range from 3 dBm to 20 dBm, and the peak power deviations are 0.79 and 0.82, respectively, indicating that the received power fluctuations are more pronounced in these two stochastic processes, which can lead to an uneven distribution of the received power, which is significantly higher in the center region than in other regions.

As shown in Figure 10a–c are the simulation results of SNR under the layout of the binomial point process, Poisson point process, and Matern hardcore point process, respectively. The SNR value in the layout of a binomial point process is 34.35~47.67 dB, and the average value is 43.61 dB, which meets the minimum requirement of the communication, and it is the best in the communication under the LED light source, and the further away from the LED light source, the lower the SNR is, and the lowest in the corner. The communication is best under the LED light source; the farther away from the LED light source, the lower the signal-to-noise ratio, and the lowest at the corner. The ratio of the minimum value to the maximum value is 0.72. The Poisson point process layout has a signal-to-noise ratio of 32.25–47.49 dB, with an average value of 43.28 dB, and the ratio of the minimum value to the maximum value is 0.68, which indicates that the signal-to-noise ratio is more fluctuating than that of the binomial point process layout. For the Matern hardcore point process layout, on the other hand, the signal-to-noise ratio ranges from 37.27 to 44.87 dB, with an average of 42.89 dB and a minimum-to-maximum ratio of 0.84; the ratio is closer to 1. The distribution of the signal-to-noise ratio is more uniform than the two stochastic processes above. This is due to the fact that the layout of the Matern hardcore point process takes into account the minimum distance between the light sources, thus avoiding the situation where the light sources are too concentrated or too dispersed.

4.3. Data Analysis

To facilitate the comparison, the four layouts are simulated under the condition of using 16 LEDs in a room with the size of 5 m × 5 m × 3 m, and the specific detailed data are shown in

Table 2. Layout comparison.

		Rectangular Layout	Circular Layout	Binomial Point Process Layout	Poisson Point Process Layout	Matern Hardcore Point Process Layout
Light intensity (lx)	maximum	4079.02	3062.36	2002.89	3768.55	2446.01
	minimum	1206.38	998.64	490.31	691.11	836.07
	average	2836.37	2486.64	1390.65	2515.25	1791.55
Received power (dBm)	maximum	18.52	16.02	17.21	21.69	14.05
	minimum	5.47	5.2	3.57	3.81	5.82
	average	12.88	12.79	10.92	12.95	11.2
Signal-to-noise ratio (dB)	maximum	47.32	45.73	47.67	47.49	44.87
	minimum	36.65	36.45	34.35	32.25	37.27
	average	43.77	43.78	43.61	43.28	42.89
Lighting uniformity rate		0.42	0.4	0.35	0.27	0.46
Peak power deviation		0.7	0.67	0.79	0.82	0.59
ratio of minimum to maximum signal-to-noise ratio		0.78	0.79	0.72	0.68	0.84

.

As can be seen from Table 2, compared to the other four layout methods, the illumination uniformity rate of the Matern hardcore point process layout method is the largest of 0.46, indicating that the light distribution of this layout method is more uniform, and the intensity variation is the smallest in the whole coverage area. From the peak power deviation, the value of the Matern hardcore point process layout method is the smallest, indicating that the power fluctuation is small, the communication fluctuation is not obvious in all parts of the room, and the communication effect is good. The ratio of the minimum to the maximum value of the signal-to-noise ratio is the largest, indicating a more uniform distribution of the signal-to-noise ratio. Overall, the performance of the indoor visible light communication system using the Matern hardcore point random process layout method is better than the other four methods.

4.4. Optimization Process Simulation

In the above process, the performance of the communication system under the Matern hardcore point process layout is not yet optimal, and in this section, we will consider optimizing the LED coordinates in the light source layout based on combining the Matern hardcore point process with the PSO algorithm to obtain an optimal layout. The fitness profile of 16 LEDs in a square plane with dimensions of 5 m × 5 m × 3 m obtained after optimization by this process is shown in Figure 11.

The number of iterations refers to the number of cycles executed by the optimization algorithm, and the fitness value reflects how close a solution is to the objective solution. As shown in Figure 11, the red curve represents the relationship between the number of iterations and the fitness value under the traditional particle swarm optimization algorithm. It shows that at the 300th iteration, the fitness function value UIR reaches 0.8. The blue curve represents the relationship between the number of iterations and the fitness under the combination of the Matern hardcore point process and the particle swarm algorithm. This curve shows that the number of iterations levels off around the 150th time and the fitness function UIR reaches 0.82, which is the optimal solution. This indicates that the traditional particle swarm optimization algorithm starts from a completely random initial layout, which cannot control the uniformity of light source distribution, while the particle swarm optimization algorithm based on the Matern hardcore point process mentioned in this paper takes the layout of the Matern hardcore point process that satisfies the minimum distance constraints as the initial position, which reduces the phenomenon of aggregation or dispersion of the light sources and can converge to the layout that meets the requirement of uniformity more quickly. This avoids the time waste caused by the random search in the initial stage of the traditional particle swarm algorithm. This provides a better initial distribution for subsequent optimization. The simulation results of light intensity, received power, and signal-to-noise ratio in optimized coordinates are plotted in Figure 12.

As shown in Figure 12, the light intensity is 1196.89~698.04 lx, the average value is 849.39 lx, which meets the international lighting standard, and the illumination uniformity UIR is 0.83, which indicates that the illumination uniformity in the room is at a high level, the received power is 12.48~6.36 dBm, the average received power is 9.25 dBm, and the peak power deviation is 0.47, which is 20.3% lower than that before optimization, indicating a reduced level of fluctuation and better communication. The SNR is 38.96~44.80 dB, the value of average SNR is 42.13 dB, and the ratio of minimum to maximum value is 0.86, which is an increase in the ratio, indicating a more uniform distribution of the SNR.

5. Conclusions

The article proposes the use of the Matern hardcore point process to randomize the specific location of light sources in indoor environments. It compares the performance of the communication system under the Matern hardcore point process with the rectangular and circular layout methods, the Poisson point process, and the binomial point process. In addition, an optimization scheme combining the Matern hardcore point process with the PSO algorithm is proposed to solve the problem of failing to satisfy the indoor illumination standard under the Matern hardcore point process. The results show that: (1) the Matern hardcore point process layout has better illumination and illumination uniformity relative to several other stochastic processes, and the fluctuations of the received power, signal-to-noise ratio, and PPD are minimized, which can better ensure the stability of the signal transmission of the optical communication. (2) The scheme after the fusion of the algorithms meets the indoor light intensity standard, which guarantees the optimal layout of the light sources. (3) This optimization scheme reduces the number of iterations of the PSO algorithm and improves the UIR. (4) The peak power deviation is reduced by 20% compared to that before the optimization, the signal-to-noise ratio is increased in the whole room, and the quality of communication is improved.

Visible light communication systems usually need to support multi-user access. In the future, consideration can be given to adding the evaluation index of multi-user interference in the optimization and optimizing the light source layout to reduce inter-user interference so as to improve the communication capacity and stability of the system. In addition, deep learning or other intelligent optimization algorithms can be introduced to enable the system to automatically complete the dynamic optimization of the light source layout according to the room structure, user location distribution, and other factors in order to achieve more efficient lighting and communication effects.