Research on Resource Allocation Strategy of Indoor Visible Light Communication and Radio Frequency Systems Integrating Orthogonal Frequency-Division Multiple Access Technology

: Aiming at the problem of resource allocation strategies limiting the system transmission rate in indoor visible light communication and radio frequency (VLC/RF) systems, a new resource allocation method is proposed, and orthogonal frequency-division multiple access (OFDMA) technology is introduced. The capacity of the communication system is effectively increased. In the VLC/RF system model based on OFDMA, the Lyapunov optimization method is used to transform the time averaging problem into a series of single-slot online problems to reduce its computational complexity, the optimization problem is decomposed into three independent subproblems, and the Lagrange relaxation method and convex optimization theory are used to solve the subproblems to maximize the average transmission rate of the system, and the Lyapunov drift is used to ensure the stability of the system. Simulation veriﬁes that the Lyapunov optimization algorithm does not require iteration, which improves the optimization speed to a high extent. The simulation results show that the proposed resource allocation strategy effectively balances the system queue length and transmission rate, improves the average transmission rate of the system to the greatest extent under the premise of ensuring the stability of the system, and compares with other algorithms from the aspects of system stability and transmission rate, which proves the effectiveness of the Lyapunov optimization algorithm.


Introduction
Future 6G networks will support data rates of up to 1T bps while also facing the challenge of coping with a large number of mobile devices [1]. However, limited radio spectrum resources make it difficult to meet the needs of explosive massive data transmission, and visible light communication (VLC) combines the advantages of lighting and communication with hundreds of high-frequency bandwidth spectrum that does not require certification [2], alleviating the pressure of insufficient radio frequency (RF) spectrum. In addition, VLC has several advantages, such as high data rate, low power consumption, high security, and small latency [3]. Therefore, VLC is considered to be a promising complementary technology in emerging wireless communications. Data transmission in VLC systems is achieved through intensity modulation on the transmitter side and direct detection on the receiver side, and as with other high-frequency communication technologies, signal propagation at this frequency is highly susceptible to obstacles. Therefore, data transmission between transmitter and receiver in VLC requires a line-of-sight (LOS) path. When A model of the indoor VLC/RF heterogeneous system is shown in Figure 1. It contains 1 RF AP, l VLC AP, and u users. The VLC AP is mounted on the ceiling, assuming that the RF AP can cover the entire room area. All APs are connected to a central controller that is responsible for collecting user feedback, scheduling, association, and resource allocation. Users are evenly distributed on the receiving plane and are equipped with VLC receivers and RF receivers. The set of APs is L = L VLC + L RF = {0,1,2,···,l}, where L VLC = {1,2,···,l} and L RF = {0} representing the sets of VLC APs and RF APs, respectively. The user set is U = {1,2,···,u}. In this paper, the communication system is divided into T time slots, and the duration of each time slot is ts. Assume that all user locations remain unchanged for a short period. For network selection, the variable a (u,l) (t) is introduced, where a (u,l) (t) = 1 indicates that user u uses AP l for access in the time slot t; otherwise, a (u,l) (t) = 0. Since a single user can only be served by one AP in a time slot, the following constraints are obtained ∑ l∈L a (u,l) (t) = 1, a (u,l) (t) ∈ {0, 1}, ∀l (1) significantly improve the average transmission rate of the system and ensure the stabil of the system.

System Model
The visible light communication system model is a system that uses visible light co munication technology to realize transmission. In this model, the downlink uses VLC a RF technology, and VLC is a complementary technology to RF to transmit information the form of visible light to the receiver through LED lights. The uplink uses RF technolo to transmit the user's feedback signal back to the transmitter using radio waves. T model takes advantage of the high frequency and large bandwidth of visible light, maki data transmission more efficient and reliable. At the same time, by using RF technology an uplink, users can also easily interact and obtain feedback from the system.

Downlink Communication
A model of the indoor VLC/RF heterogeneous system is shown in Figure 1. It conta 1 RF AP, l VLC AP, and u users. The VLC AP is mounted on the ceiling, assuming that RF AP can cover the entire room area. All APs are connected to a central controller tha responsible for collecting user feedback, scheduling, association, and resource allocati Users are evenly distributed on the receiving plane and are equipped with VLC receiv and RF receivers. The set of APs is L = LVLC + LRF = {0,1,2,···,l}, where LVLC = {1,2,···,l} and = {0} representing the sets of VLC APs and RF APs, respectively. The user set is U {1,2,···,u}. In this paper, the communication system is divided into T time slots, and duration of each time slot is ts. Assume that all user locations remain unchanged fo short period. For network selection, the variable a (u,l) (t) is introduced, where a (u,l) (t) = 1 dicates that user u uses APl for access in the time slot t; otherwise, a (u,l) (t) = 0. Since a sin user can only be served by one AP in a time slot, the following constraints are obtained

VLC Channel Model
For indoor VLC systems, directional direct view communication links are genera used [12]; that is, the transmitter and receiver of the VLC system are within their respect field of view (FOV) ranges, as shown in Figure 2. For the VLC system studied in this a cle, the LOS channel gain between VLC APl and user u is

VLC Channel Model
For indoor VLC systems, directional direct view communication links are generally used [12]; that is, the transmitter and receiver of the VLC system are within their respective field of view (FOV) ranges, as shown in Figure 2. For the VLC system studied in this article, the LOS channel gain between VLC AP l and user u is where m= −ln2/ln(cos(FOV)) is the Lambertian order, FOV is the half angle of the light source transmitting power, Ap is the effective area of the receiver photodiode, d represents the distance between AP l and user u, and θ and ϕ represent the irradiation angle and incidence angle, respectively. T l represents the gain of the optical filter, and G l represents the gain of the concentrator.
the distance between APl and user u, and θ and φ represent the irradiation angle and cidence angle, respectively. Tl represents the gain of the optical filter, and Gl represe the gain of the concentrator. In VLC systems, the signal transmission method of intensity modulation and dir detection is adopted. Since the LED operates in its linear region, the output optical pow of the modulated signal is proportional to the input voltage, ensuring that the signal tra mitted to the receiving end is only positive and solid. In addition, the average emitt electrical power Pe is satisfied with the average emitted optical power Po: where β is the DC bias factor of VLC AP. Assuming that there are k subcarriers in the V system, t  indicates that APl assigns subcarrier k to the u for communication in time slot t; otherwise, The signal-to-noise ratio on the kth subcarrier between user u and VLC APl is where ε represents the photoelectric conversion coefficient received by the user, From Shannon's formula, the effective information transfer rate between VLC AP and user u on the subcarrier k of the time slot t is where BVLC is the bandwidth of the subcarrier. Because each subcarrier can only be signed to one user in a single time slot, there are the following constraints for each su carrier k: The transmission rate of VLC APl and user u in the t timeslot is In the timeslot t, the transmit power of VLC APl is In VLC systems, the signal transmission method of intensity modulation and direct detection is adopted. Since the LED operates in its linear region, the output optical power of the modulated signal is proportional to the input voltage, ensuring that the signal transmitted to the receiving end is only positive and solid. In addition, the average emitted electrical power P e is satisfied with the average emitted optical power P o : where β is the DC bias factor of VLC AP. Assuming that there are k subcarriers in the VLC system, b (u,l) k (t) represents the distribution coefficient of user u with the K subcarriers of VLC AP l in time slot t, and b (u,l) k (t) = 1 indicates that AP l assigns subcarrier k to the user for communication in time slot t; otherwise, b (u,l) k (t) = 0. The signal-to-noise ratio on the kth subcarrier between user u and VLC AP l is where ε represents the photoelectric conversion coefficient received by the user, σ 2 VLC represents the noise power in the VLC channel, and p (u,l) k,o represents the transmit power of VLC AP l to user u on the subcarrier k.
From Shannon's formula, the effective information transfer rate between VLC AP l and user u on the subcarrier k of the time slot t is where B VLC is the bandwidth of the subcarrier. Because each subcarrier can only be assigned to one user in a single time slot, there are the following constraints for each subcarrier k: The transmission rate of VLC AP l and user u in the t timeslot is In the timeslot t, the transmit power of VLC AP l is P l To save power, the upper limit of time average power consumption of VLC AP l can be set to where P ave,VLC represents the maximum average power consumption on VLC AP l .

RF Channel Model
RF communication path loss is represented by PL [13] and typically takes the form below where d (u,l) is the distance between the RF AP and the user; f c is the carrier frequency in GHz; A, B, and C are constants that depend on the propagation model; and X represents the loss of shadow effects in different environments. RF communicates using OFDM, in which the RF AP uses I resource blocks (RBs). The t time slot, x (u,0) i (t), represents the allocation relationship between user u and the ith RB.
Since there is only one RF AP in a VLC/RF heterogeneous network, channel interference in the RF system can be ignored. Assuming that the RF AP transmits power to user u on RBi of p (u,0) i (t), the signal-to-noise ratio between user u and the RF AP is where g (u,0) i (t) = 10 −PL[dB]/10 represents the RF channel power gain, and σ 2 RF represents the noise power of the RF channel. According to Shannon's formula, the information transmission rate between the RF AP subchannel i and user u in the time slot t is where B RF is the bandwidth of RB. Since each RB can only serve one user in a time slot, it must be satisfied for each RBi Therefore, in the time slot t, the information transfer rate between the RF AP and user u is The transmit power of the RF AP is derived from the following equation: Considering the power condition, the transmitting power should satisfy where P ave,RF is the maximum average power consumption on the RF AP.

Uplink Communication
When the downlink successfully receives the signal, it will reply to the sender through the RF transmitter, indicating that the response has been successfully received. Since RF communication is carried out indoors, the Rayleigh fading channel [14] was chosen as the upstream RF communication link channel model. The channel coefficient h of the Rayleigh fading channel obeys a complex Gaussian distribution with a mean of 0 and a variance of σ 2 , i.e., h~CN(0, σ 2 ), where σ 2 = d −α , d represents the RF communication distance, α represents the path fading factor in RF communication, and in the indoor environment, the value is usually taken to be 2~4.
The signal transmitted by the RF transmitter is √ P RF χ RF (t), where P RF is the power of the response signal, χ RF (t) is the normalized signal, and χ RF (t) ∈ [−1, 1], E |χ RF (t)| 2 = 1. The signal at the RF receiver can be expressed as y RF (t) = P RF hχ RF (t) + n RF (t) (17) where n RF (t) is additive white Gaussian noise and obeys a complex Gaussian distribution with a mean of 0 and a variance of σ 2 RF .

OFDMA System Model
In this paper, a VLC system model based on OFDMA technology is adopted, which aims to combine optimization objectives with system stability. According to different M-QAM modulation methods, M-ary QAM is adaptively applied to different OFDM subcarriers [15]. A different spectral efficiency (SE) can be achieved on each subcarrier, and S k is used to represent SE on each subcarrier. The value of S k depends on the order of M-QAM. The modulation order of M-QAM is adaptively selected by the signal-to-interference plus noise ratio (SINR) between the user and the VLC AP. The relationship between S k and SINR is determined by the modulation and coding scheme (MCS). The specific value is shown in Table 1. SINR can be expressed as where N 0 represents the noise power spectral density in the VLC channel, B represents the bandwidth of the VLC baseband modulated signal, H represents the channel gain between the VLC AP providing the service and the user u, and H (u,l) represents the channel gain between the non-service VLC AP and the user u, which is regarded as interference noise. The model uses t = 0,1,2, ···,T as variables by allocating subchannels by time slots, studies the changes in the system in the process of time advancement, and reassigns subchannels. This method fundamentally improves the frequency of system resource allocation so that the system can quickly make optimal allocations in the process of time change. In addition, we use the Lyapunov optimization method for this optimization process to ensure that the system remains stable during changes within t = 0,1,2,···,T. Figure 3 shows the OFDMA system resource allocation model. The dark part represents the scale of resource allocation; for each RB, the smallest block of resources whose indivisibility is called the resource unit (RU), the RU allocates resources in each time slot, and each RU allocation process is independent. This allocation process differs from one-dimensional resource allocation in that in each time slot, the resource allocation problem in OFDMA is degraded from two-dimensional to one-dimensional by setting the integer restriction to b u k (t) ∈ {0, 1}, and the integer allocation is reduced to a 0-1 integer allocation problem.
channels. This method fundamentally improves the frequency o tion so that the system can quickly make optimal allocations in th In addition, we use the Lyapunov optimization method for this ensure that the system remains stable during changes within t = 0 the OFDMA system resource allocation model. The dark part re source allocation; for each RB, the smallest block of resources who the resource unit (RU), the RU allocates resources in each time slo process is independent. This allocation process differs from onelocation in that in each time slot, the resource allocation problem from two-dimensional to one-dimensional by setting the integer and the integer allocation is reduced to a 0-1 integer allocation p In VLC systems, it is generally believed that its channel is fading characteristic during communication. Therefore, the cha constant in each time slot. Suppose that the VLC AP providing scriber device subcarrier k can achieve the rate represented by th The transmission rate between the user on subchannel k an the service is The transfer rate provided by the VLC AP to user u is Since a subcarrier can only serve one user per time slot, it must meet the following constraints: OFDMA system resource allocation model.
In VLC systems, it is generally believed that its channel is time-flat, and there is no fading characteristic during communication. Therefore, the channel state information is constant in each time slot. Suppose that the VLC AP providing the service and the subscriber device subcarrier k can achieve the rate represented by the following equation: The transmission rate between the user on subchannel k and the VLC AP providing the service is The transfer rate provided by the VLC AP to user u is Since a subcarrier can only serve one user per time slot, its distribution coefficient must meet the following constraints:

Queue Model
When the system starts transmitting data, let Q u (t) represent the length of the queue that the system maintains for user u at the beginning of the time slot t, and D u (t) represent the amount of data that user u arrives at the time slot t, which is independently and identically distributed across different time slots [17]. Assuming that the average arrival data rate of user u in the time slot t is γ u (t), the following conditions are met for D u (t): where γ u is a bounded variable that guarantees the stability of the system. According to the above analysis, Q u (t) can be expressed as where R u (t) represents the amount of data leaving, [x,0] + = max[x,0]. For each user u, the randomness of D u (t) and the time-varying nature of R u (t) is given to make the queuing process random. If you only consider maximizing the system transfer rate and ignore the impact of the queue, data will accumulate in the queue during transmission, resulting in the system not operating normally. Therefore, a model of queue stability needs to be established. Generally defined as If all queues in the system are stable, then the VLC communication system will also be stable. This means that the average leave rate in the queue is greater than or equal to the average input rate, and once this condition is met, all data in the queue is sent to its corresponding user.

Optimization of the Problem Description
The goal of this article is to achieve the maximum transfer rate while the system remains stable. Within the time slot t, the transmission rate of the entire system can be expressed as To achieve the optimization goal of maximizing the average rate of the system, the above function is designed as a time-averaging expression. Therefore, the stochastic optimization problem is formulated as max lim  (34) indicates that the transmit power of all APs is not negative and meets the actual conditions. There are long-term constraints in the above problem, and to effectively handle longterm time-averaged power constraints, virtual queues in Lyapunov optimization can be used to convert (31) into queue stability constraints [18]. Virtual queues are defined as Z(t) {Z 1 (t),···, Z l (t),···,Z L (t)},Z l (t) and evolved as follows: It should be noted that there is no actual queue data in queue Z l (t), which is only proposed to satisfy the constraint (31). If the virtual queue Z l (t) is average-rate stable, constraint (31) automatically holds [19].
Suppose the order vector of queue length in the system is The Lyapunov function is defined as a measure of the total queue length for each time slot t, denoted by the following equation: In each time slot, the conditional Lyapunov drift is defined as It can be observed that at each time slot, the Lyapunov function can control the final value of the Lyapunov drift by adjusting the final queue length. The purpose of this paper is to maximize the average system transfer rate, and the drift-penalty function term is defined as follows: where V is a non-negative constant parameter used to balance drift with reward. When the V value increases, the system assigns a higher priority to maximize the transmission rate, that is, sacrifice the queue length; when the V value decreases, the system prioritizes the queue length to maintain the stability of the system. For each period, for a given V ≥ 0, the upper bound of the drift-penalty function for any possible Θ(t) is where C is a constant satisfying the following conditions: According to the Lyapunov optimization method [20], the network utility is optimized by minimizing the drift-penalty function term to minimize the queue length. Therefore, Problem (35) can be transformed into minimizing the upper bound of the Lyapunov driftpenalty function on each time slot, which is expressed as The reformulated optimization problem (41) is a constrained mixed-integer programming problem where a (u,l) (t) takes integer values, and p (u,0) i (t) and p (u,l) k (t) take continuous values. Therefore, the optimization problem (41) is decomposed into three relatively independent subproblems, and the corresponding optimization algorithm is proposed.

AP Allocation
The AP allocation variables a (u,l) (t) in the system can be obtained by solving the following subproblems: It can be seen from (42) that the network selection between different users is independent. Therefore, Problem (42) can be decomposed into U subproblems, and each subproblem is where e (u,l) (t) = (Q u (t) + V)v (u,l) . Since (43) is a linear optimization problem, its solution is as follows: Under the above network selection strategy, e (u,l) (t) can be regarded as the congestion cost of the AP serving the user within the time slot t. Then, Equation (44) ensures that the user can connect to the AP with the smallest congestion cost.

VLC AP Joint Subcarrier and Power Allocation
According to the access point allocation variable a(t) obtained from subproblem (42), the joint subcarrier and power allocation subproblem in the VLC system can be solved continuously: Since the selection of subcarriers is independent among different VLC APs, Problem (45) can be decomposed into |L VLC | subproblems, and each subproblem is expressed as where U l denotes the set of users connected to VLC AP. The VLC joint subcarrier and power allocation problem is a hybrid combinatorial optimization problem. To solve this problem, the Lagrange relaxation method can be used to transform the original integer programming mixed problem into a convex optimization problem. Relaxing b 1], the optimization problem is reformulated as (t) and p (u,l) k (t), think of it as a linear function of log 2 Therefore, the given optimization problem is a K × |U l | linear combination of con- (t) be the objective function and find the partial derivative of p (u,l) k (t) for L(P): According to the Karush-Kuhn-Tucker (KKT) conditions, the system can achieve optimal power allocation when the following conditions are satisfied: where µ u k is the multiplier for constructing the Lagrange function. To ensure that (51) holds, then µ u k = 0 or p (u,l) k (t) = 0. The partial derivative of Formula (49) is 0, and the relationship between p (u,l) * k (t) and b (u,l) k (t) can be obtained.
The result of power allocation will be used to obtain the subcarrier allocation. Substituting Equation (53) into Equation L(P), we obtain where Obviously, Problem (54) is a linear assignment problem, which can be decomposed into k subproblems. Each subproblem is represented by the following equation: For subcarrier k, the optimal allocation is to obtain the user with the maximum L u k (P), and the solution can be obtained.

RF AP Joint Resource Block and Power Allocation
In RF communication systems, the RF AP joint resource block and power allocation subproblem can be expressed as It can be seen from the above problems that the joint RB and power allocation problems are independent of each other on different time slots t. Therefore, the objective function of Problem (58) is a function of discrete variables x According to the KKT conditions, the system achieves the optimal power allocation when the following conditions are satisfied.
where µ u i is the multiplier for constructing the Lagrange function. To ensure that Equation (63) holds, then µ u i = 0 or p (u,l) i (t) = 0. When the partial derivative of Equation (61) is 0, the relationship between p (u,l) * i (t) and x (u,l) i (t) can be obtained.
The result of power allocation will be used for the allocation of RF resource blocks. Substituting Equation (63) into L(P), we can obtain where Obviously, Problem (66) is also a linear assignment problem. Therefore, it can be decomposed into i subproblems, and each subproblem is expressed as The objective of this problem is to maximize the L i (P) of all subcarriers. Therefore, for all subcarriers i, the optimal allocation is to select the user with the largest L i (P).

Analysis of Algorithm Simulation Results
In this section, we analyze the simulation results of the Lyapunov optimization algorithm and verify the performance of the proposed indoor VLC/RF system resource allocation scheme with OFDMA technology. Assuming that the room size is 8 m × 8 m × 3 m, as shown in Figure 1, 4 VLC APs are installed on the ceiling, which are located at (3,2,3), (5,2,3), (3,5,3) and (5,5,3), respectively, and each AP has 25 subcarriers. The RF AP is located at (0,0,0), and it has four RBs. Other key simulation parameters of the system are shown in Table 2. To simplify the simulation, we consider the normalized spectrum bandwidth of VLC AP and RF AP, traffic arrival for each user device follows the Poisson distribution, the average traffic arrival rate is expressed in γ, the traffic arrival rate and RF channel conditions remain constant within a time slot and change on the time slot boundary, γ specific values will be given in the simulation. Since the spectral bandwidth is normalized and the unit of transmitted data volume is set to package, assuming that the average communication rate of the VLC AP subcarrier in the system is five packages and the average communication rate of an RF AP single RB is three packages, the average traffic arrival rate is limited to less than five packages. Figure 4a shows the relationship between the penalty parameter V and the average queue length Q under different average traffic arrival rates γ. It can be observed that the Q value in the system increases with the increase in V, and as the average traffic arrival rate γ increases, the average queue length Q also increases. Figure 4b shows the change in penalty parameter V and average transmission rate R under different average traffic arrival rates γ. It can be seen that the average transfer rate R increases with the increase in the V value because when the V value increases, the optimization degree of the algorithm on the average transmission rate increases. In addition, as the average traffic arrival rate γ value increases, the growth rate of the average transmission rate slows down because when the γ value is small, the amount of data transmitted by the system can meet the amount of data arrived. When the γ value is large, the system rejects additional packets to ensure data queue stability. From Little's theorem [21], since the average transmission delay is proportional to the average queue length, the average queue length can be used to describe the average delay, and in the Lyapunov optimization process, selecting the appropriate control parameter V can balance the relationship between the average transmission rate and the average transmission delay.  In addition, the instantaneous change in the system is simulated. Assuming that the user's position is changing in each time slot, the instantaneous change in the user on 30 time slots is given. Figure 5a-c depict the instantaneous transfer rate and queue length change for four users in the system when the penalty parameter V is valued at 50, 150, and 300. It can be observed that for each user, as the length of the user's queue increases, so does the data transfer rate for that user. This is because the Lyapunov optimization algorithm makes the system provide a higher transfer rate to reduce the buffer queue, thus ensuring the stability of the entire system. Another conclusion is that the queue length in the system is longer when V = 300 is longer than when V = 50 and 150. In addition, the instantaneous change in the system is simulated. Assuming that the user's position is changing in each time slot, the instantaneous change in the user on 30 time slots is given. Figure 5a-c depict the instantaneous transfer rate and queue length change for four users in the system when the penalty parameter V is valued at 50, 150, and 300. It can be observed that for each user, as the length of the user's queue increases, so does the data transfer rate for that user. This is because the Lyapunov optimization algorithm makes the system provide a higher transfer rate to reduce the buffer queue, thus ensuring the stability of the entire system. Another conclusion is that the queue length in the system is longer when V = 300 is longer than when V = 50 and 150.  In addition, the instantaneous change in the system is simulated. Assuming that the user's position is changing in each time slot, the instantaneous change in the user on 30 time slots is given. Figure 5a-c depict the instantaneous transfer rate and queue length change for four users in the system when the penalty parameter V is valued at 50, 150, and 300. It can be observed that for each user, as the length of the user's queue increases, so does the data transfer rate for that user. This is because the Lyapunov optimization algorithm makes the system provide a higher transfer rate to reduce the buffer queue, thus ensuring the stability of the entire system. Another conclusion is that the queue length in the system is longer when V = 300 is longer than when V = 50 and 150.  Figure 6 shows the change in average queue length Q and average transfer rate R with the number of users in the system using different algorithms. The Lyapunov optimization algorithm was compared with the minimized distance resource allocation (MD-RA) algorithm and the best channel state information resource allocation (BCSI-RA) algorithm [22]. Obviously, from Figure 6a, it can be seen that with the increase in the number of users, the average queue length of the system gradually increases compared to the MD-RA algorithm and BCSI-RA algorithm, the queue length under the Lyapunov optimization algorithm is smaller, and the growth rate is the slower, indicating that the system has better stability when using the Lyapunov algorithm. It can be seen from Figure 6b that as the number of users in the system increases, the average transmission rate also increases, and the average transmission rate under the Lyapunov optimization algorithm is significantly higher than that of the MD-RA algorithm and BCSI-RA algorithm, and the average transmission rate increases significantly when the number of users is greater than six.  Figure 7 shows the average queue length vs. average transfer rate as a function of the number of users, taking into account the interrupt probability, and compares the performance of the system using the three algorithms. Suppose p represents the probability of LOS availability in VLC systems and generates a random number between 0 and 1; if this number is greater than p, then the LOS of VLC AP is available. Otherwise, LOS is not available. This study shows that the Lyapunov optimization algorithm can achieve higher transmission rates while ensuring that the average queue length of the system is low; that is, the algorithm can provide better system performance.  Figure 6 shows the change in average queue length Q and average transfer rate R with the number of users in the system using different algorithms. The Lyapunov optimization algorithm was compared with the minimized distance resource allocation (MD-RA) algorithm and the best channel state information resource allocation (BCSI-RA) algorithm [22]. Obviously, from Figure 6a, it can be seen that with the increase in the number of users, the average queue length of the system gradually increases compared to the MD-RA algorithm and BCSI-RA algorithm, the queue length under the Lyapunov optimization algorithm is smaller, and the growth rate is the slower, indicating that the system has better stability when using the Lyapunov algorithm. It can be seen from Figure 6b that as the number of users in the system increases, the average transmission rate also increases, and the average transmission rate under the Lyapunov optimization algorithm is significantly higher than that of the MD-RA algorithm and BCSI-RA algorithm, and the average transmission rate increases significantly when the number of users is greater than six.  Figure 6 shows the change in average queue length Q and average transfer rate R with the number of users in the system using different algorithms. The Lyapunov optimization algorithm was compared with the minimized distance resource allocation (MD-RA) algorithm and the best channel state information resource allocation (BCSI-RA) algorithm [22]. Obviously, from Figure 6a, it can be seen that with the increase in the number of users, the average queue length of the system gradually increases compared to the MD-RA algorithm and BCSI-RA algorithm, the queue length under the Lyapunov optimization algorithm is smaller, and the growth rate is the slower, indicating that the system has better stability when using the Lyapunov algorithm. It can be seen from Figure 6b that as the number of users in the system increases, the average transmission rate also increases, and the average transmission rate under the Lyapunov optimization algorithm is significantly higher than that of the MD-RA algorithm and BCSI-RA algorithm, and the average transmission rate increases significantly when the number of users is greater than six.  Figure 7 shows the average queue length vs. average transfer rate as a function of the number of users, taking into account the interrupt probability, and compares the performance of the system using the three algorithms. Suppose p represents the probability of LOS availability in VLC systems and generates a random number between 0 and 1; if this number is greater than p, then the LOS of VLC AP is available. Otherwise, LOS is not available. This study shows that the Lyapunov optimization algorithm can achieve higher transmission rates while ensuring that the average queue length of the system is low; that is, the algorithm can provide better system performance.  Figure 7 shows the average queue length vs. average transfer rate as a function of the number of users, taking into account the interrupt probability, and compares the performance of the system using the three algorithms. Suppose p represents the probability of LOS availability in VLC systems and generates a random number between 0 and 1; if this number is greater than p, then the LOS of VLC AP is available. Otherwise, LOS is not available. This study shows that the Lyapunov optimization algorithm can achieve higher transmission rates while ensuring that the average queue length of the system is low; that is, the algorithm can provide better system performance. As shown in Figure 8, as the penalty parameter V value increases, the average queue length Q and the average transmission rate R in the uplink communication link under different numbers of users also increase. This is because increasing the penalty parameter will cause the system to allocate more resources to the user, thereby optimizing the performance of the system. At the same time, as can be seen from Figure 8a, as the number of users increases, the queue backlog in the system accelerates because the increase in the number of users leads to a decrease in the uplink communication rate, which affects the performance of the entire system. To balance the relationship between queue length and transmission rate, the appropriate penalty parameter V can be selected to make the system communication more stable. Figure 8b also shows that the average transfer rate increases gradually as the number of users increases. Changes in both Q and R values indicate a decrease in the communication rate of the upstream RF link. This is because, with limited spectrum resources and base station processing power, users must share resources, resulting in network congestion and transmission delays, which in turn reduce the communication rate of the entire system.  Figure 9 shows the average queue length Q and average transmission rate R in the OFDMA-VLC/RF system and VLC/RF system as a function of the number of users. As shown in Figure 9a, the queue extrusion speed in the VLC/RF system using OFDMA As shown in Figure 8, as the penalty parameter V value increases, the average queue length Q and the average transmission rate R in the uplink communication link under different numbers of users also increase. This is because increasing the penalty parameter will cause the system to allocate more resources to the user, thereby optimizing the performance of the system. At the same time, as can be seen from Figure 8a, as the number of users increases, the queue backlog in the system accelerates because the increase in the number of users leads to a decrease in the uplink communication rate, which affects the performance of the entire system. To balance the relationship between queue length and transmission rate, the appropriate penalty parameter V can be selected to make the system communication more stable. Figure 8b also shows that the average transfer rate increases gradually as the number of users increases. Changes in both Q and R values indicate a decrease in the communication rate of the upstream RF link. This is because, with limited spectrum resources and base station processing power, users must share resources, resulting in network congestion and transmission delays, which in turn reduce the communication rate of the entire system. As shown in Figure 8, as the penalty parameter V value increases, the average queue length Q and the average transmission rate R in the uplink communication link under different numbers of users also increase. This is because increasing the penalty parameter will cause the system to allocate more resources to the user, thereby optimizing the performance of the system. At the same time, as can be seen from Figure 8a, as the number of users increases, the queue backlog in the system accelerates because the increase in the number of users leads to a decrease in the uplink communication rate, which affects the performance of the entire system. To balance the relationship between queue length and transmission rate, the appropriate penalty parameter V can be selected to make the system communication more stable. Figure 8b also shows that the average transfer rate increases gradually as the number of users increases. Changes in both Q and R values indicate a decrease in the communication rate of the upstream RF link. This is because, with limited spectrum resources and base station processing power, users must share resources, resulting in network congestion and transmission delays, which in turn reduce the communication rate of the entire system.  Figure 9 shows the average queue length Q and average transmission rate R in the OFDMA-VLC/RF system and VLC/RF system as a function of the number of users. As shown in Figure 9a, the queue extrusion speed in the VLC/RF system using OFDMA  Figure 9 shows the average queue length Q and average transmission rate R in the OFDMA-VLC/RF system and VLC/RF system as a function of the number of users. As shown in Figure 9a, the queue extrusion speed in the VLC/RF system using OFDMA technology is significantly slower than that in the VLC/RF system without OFDMA technology, and the Q value change in the OFDMA-VLC/RF system is relatively stable, indicating that the system has strong stability. It can be observed from Figure 9b that as the number of users increases, the average transmission rate of the system gradually increases, and when the number of users increases to 15, the average transmission rate of the OFDMA-VLC/RF system increases by 17 packages compared with the VLC/RF system, because the use of OFDMA technology increases the capacity of the entire communication system, thereby increasing the system transmission rate. technology is significantly slower than that in the VLC/RF system without OFDMA technology, and the Q value change in the OFDMA-VLC/RF system is relatively stable, indicating that the system has strong stability. It can be observed from Figure 9b that as the number of users increases, the average transmission rate of the system gradually increases, and when the number of users increases to 15, the average transmission rate of the OFDMA-VLC/RF system increases by 17 packages compared with the VLC/RF system, because the use of OFDMA technology increases the capacity of the entire communication system, thereby increasing the system transmission rate.

Conclusions
In this paper, the resource allocation problem in indoor OFDMA-VLC/RF systems is studied, and an allocation strategy based on the Lyapunov optimization algorithm is proposed. The purpose of this study is to solve the resource allocation problem by maximizing the average transmission rate of the system under the constraints of system stability and the average power budget: (1) To find the optimal resource allocation strategy, we formulate a random optimization problem, which considers the stability constraints and average power budget of the system and takes the average transmission rate of the system as the optimization goal.
(2) Using the Lyapunov optimization algorithm, the stochastic optimization problem is decomposed into three independent subproblems, and their optimal solutions are given respectively. Through simulation, the effectiveness of the proposed resource allocation strategy is verified. The results show that this strategy significantly improves the average transmission rate of the system while maintaining the stability of the system. This means that our approach can improve system performance by making more efficient use of limited resources in indoor OFDMA-VLC/RF systems.
This study has important practical significance for improving the performance of indoor wireless communication systems and provides a valuable reference for further research. In the future, the results can meet the communication needs between IoT devices and provide efficient communication services. In the smart home system, this technology can realize the interconnection between devices. In addition, the technology can also support real-time interaction and immersive experience of virtual reality (VR) and augmented reality (AR) technologies, providing high-speed and low-latency communication services. In the field of health care, the resource allocation strategy based on this technology can provide high-speed and reliable communication services, support data transmission between medical devices and telemedicine services, and improve the efficiency and quality of health care. In short, the resource allocation strategy of indoor VLC/RF systems based on OFDMA technology and the Lyapunov optimization algorithm has the characteristics Figure 9. The performance of the OFDMA-VLC/RF system is compared with the VLC/RF system: (a) comparison of the average queue length Q of the system; (b) comparison of the average transmission rate R of the system.

Conclusions
In this paper, the resource allocation problem in indoor OFDMA-VLC/RF systems is studied, and an allocation strategy based on the Lyapunov optimization algorithm is proposed. The purpose of this study is to solve the resource allocation problem by maximizing the average transmission rate of the system under the constraints of system stability and the average power budget: (1) To find the optimal resource allocation strategy, we formulate a random optimization problem, which considers the stability constraints and average power budget of the system and takes the average transmission rate of the system as the optimization goal.
(2) Using the Lyapunov optimization algorithm, the stochastic optimization problem is decomposed into three independent subproblems, and their optimal solutions are given respectively. Through simulation, the effectiveness of the proposed resource allocation strategy is verified. The results show that this strategy significantly improves the average transmission rate of the system while maintaining the stability of the system. This means that our approach can improve system performance by making more efficient use of limited resources in indoor OFDMA-VLC/RF systems.
This study has important practical significance for improving the performance of indoor wireless communication systems and provides a valuable reference for further research. In the future, the results can meet the communication needs between IoT devices and provide efficient communication services. In the smart home system, this technology can realize the interconnection between devices. In addition, the technology can also support real-time interaction and immersive experience of virtual reality (VR) and augmented reality (AR) technologies, providing high-speed and low-latency communication services. In the field of health care, the resource allocation strategy based on this technology can provide high-speed and reliable communication services, support data transmission between medical devices and telemedicine services, and improve the efficiency and quality of health care. In short, the resource allocation strategy of indoor VLC/RF systems based on OFDMA technology and the Lyapunov optimization algorithm has the characteristics of high speed, high efficiency, and reliability in communication applications in various fields, which will promote the development of future communication technology.