1. Introduction

In recent years, the over-crowdedness of the radio frequency (RF) spectrum and the diversification of data services have promoted utilizing higher frequency bands such as visible light range [1]. Further, with the rapid development of the Internet of Things (IoT), an unprecedented number of devices will be connected [2]. Due to steadily rising energy scarcity and environmental concerns, energy efficiency (EE) has drawn great attention. Hence, based on widely deployed light-emitting diodes (LEDs), visible light communication (VLC) with a license-free spectral domain has emerged as an attractive candidate. This is especially for an indoor environment where over 90% of data transmission occurs [3]. In addition, VLC is also harmless to human health and can be used in electromagnetic-sensitive scenarios like airports and hospitals [4]. Facilitated by potential high rate and energy efficiency (EE), VLC has been regarded as a promising technology for indoor IoT communication to support sustainable development in the future [5]. Albeit with the aforementioned advantages, VLC exhibits several drawbacks: 1) VLC is failed to provide uplink transmission; 2) optical signal transmission mainly depends on the line of sight (LOS) propagation; 3) In VLC-IoT systems, signal interference is extremely serious while the IoT devices are in the overlapped area of multiple LED arrays. Among all the design challenges, the problem of severe interference from overlapping areas of light is prominent, which leads to dramatic degradation of system performance. To elaborate, due to the limited illumination coverage of a single LED array, multiple LED arrays are usually deployed in VLC-IoT systems to provide communication and lighting functions, resulting in large areas of lighting overlap. When each device selects a specific access point (AP) to access, it may suffer strong interference in the overlapping area that leads to a sharp decrease in the rate. In order to reduce the above interference, researchers have designed several optimal resource allocation strategies to maximize the system performance such as sum rate [1,5] and other network utility function [6].

Besides providing high-speed data services, another outstanding advantage of VLC is energy saving, which can well adapt to the development trend of energy-efficient system design. VLC can change the light intensity by adjusting the current input to the LED, taking the LED arrays as APs. On the receiver side, the received light intensity is converted into electrical signals on the IoT device equipped with a photo detector (PD). In general, data are processed using intensity modulation (IM) at transmitters, and direct detection (DD) at receivers [7]. So the modulated signal must be a non-negative real value. For this reason, the alternating-current (AC) part of the current is used to carry the signal, while adding the direct-current (DC) part ensures that the signal is non-negative [8]. However, in the view of energy saving, the DC power is always wasted. The authors in [9] presented the scheme of simultaneous lightwave information and power transfer (SLIPT) to reduce energy consumption by converting the received DC portion into reusing energy. Considering IoT devices are usually powered by batteries and can operate at extremely low power, it was shown that SLIPT is sufficient to charge up to a satisfactory power of some IoT devices [10].

Moreover, the high-rate communication between APs and a large number of IoT devices within the system leads to a large amount of energy consumption. In this paper, the EE optimization of indoor VLC-IoT systems is regarded as the core issue. There is a paucity of studies on the EE of VLC-IoT systems, although recently some impressive literature was disseminated [11–15]. The authors of [11] designed the network utility function by assigning weights to the throughput and total received energy where a DC bias and power allocation scheme was proposed based on SLIPT. The problem of wireless information and energy transmission in a hybrid VLC/RF system with assisted relay was analyzed in [12,13], where the IoT devices can communicate via the VLC link or the two-hop link powered through SLIPT. The first hop of transmission is LED to the relay, and the power of the DC bias is stored for powering the second hop. In [14], the EE optimization of cooperative visible light communication systems was investigated while considering the inter-cell interference and the LOS blockage. The optimization of subchannel assignment and power allocation is studied under transmit power budgets and minimum rate constraints. The authors of [15] maximized the EE for VLC-IoT communication by an adaptive channel and quality-of-service (QoS)-based user pairing approach. Nevertheless, to the best of our knowledge, the EE optimization of subchannel assignment and power allocation with SLIPT has not been explored in the literature. Though it is more complicated to analyze EE when considering the constraints on power and energy, it is quite critical for the indoor VLC-IoT system.

Motivated by the above observations, this paper proposes a novel resource allocation scheme for indoor VLC-IoT systems, while using SLIPT technology to self-power IoT devices to reduce total energy consumption and support communication. Specifically, a mixed integer nonlinear fractional programming (MINLFP) problem aiming at EE maximization is established under the QoS requirements, the maximum transmission power budget, and linear constraints of LED arrays while satisfying safe illumination and maximum stored energy constraint. Since the MINLFP problem is challenging to solve, we divide it into two stages: subchannel assignment and power allocation. In the first stage, a virtual cell formation and subchannel assignment strategy (VCF-SA) is proposed. The virtual cell (VC) is formed based on the combined transmission (CT) and the location of IoT devices, while the energy state of the IoT device determines whether the device is in the working state. Furthermore, subchannels are assigned to the devices in the working state until QoS requirements are satisfied. In the second stage, since the original problem is still a complex non-convex fractional programming problem, a quadratic transformation-based power allocation algorithm (QTBPA) is designed where the stable solution is obtained using a two-loop iterative approach. Finally, the simulation results show that the proposed VCF-SA-QTBPA scheme can significantly enhance the EE of the VLC-IoT system compared with the benchmarks. In addition, the influence of system parameters on the EE performance is also investigated.

2. System model

2.1 VLC-IoT system

The indoor VLC-IoT system under consideration is depicted in Fig. 1 consisting of multiple VLC-APs, one RF-AP, one central control unit (CCU), and multiple IoT devices. LED arrays are set as VLC-APs which are evenly deployed on the ceiling to provide downlink communication for IoT devices, and it is assumed that the RF-AP can cover the whole room and provide uplink communication. Both VLC-APs and RF-AP are connected via low-latency optical fibers to the CCU whose function is to assign subchannels and allocate power. Both VLC-APs and RF-AP are connected via low-latency optical fibers to the CCU whose function is to assign subchannels and allocate power. Moreover, the orthogonal frequency division multiple access (OFDMA) technology is employed as the multiple access scheme in the system [16]. And IoT devices are equipped with PDs to receive visible light signals. Let ${\rm {V\ =\ \{\ 1,2,\ }}\cdots {\rm {\ ,\ v,\ }}\cdots {\rm {\ ,}}\left | {\rm {V}} \right |{\rm {\}\ }}$, ${\rm {J\ =\ \{\ 1,2,\ }}\cdots {\rm {\ ,\ j,\ }}\cdots {\rm {\ ,}}\left | {\rm {J}} \right |{\rm {\}\ }}$, and ${\rm {K\ =\ \{\ 1,2,\ }}\cdots {\rm {\ ,\ k,\ }}\cdots {\rm {\ ,}}\left | {\rm {K}} \right |{\rm {\}\ }}$ denote the sets of VLC-APs, IoT devices, and available subchannels, respectively. $\left | \bullet \right |$ represents the cardinality of a set. For ease of reference, a list of variables and symbols that appear in this paper are summarized in Table 1.

 

Fig. 1. System model.

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Table 1. Key notations

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We assume that each IoT device has SLIPT-based communication and energy harvesting capabilities as shown in Fig. 2. The dashed block represents the signal receiving unit and the solid block represents the energy receiving unit, while the circuit for energy harvesting and data communication had been studied in [10]. Hence, the IoT device can store the harvested energy in a battery to power the device-self for data collection, processing, and transmission. In addition, the remaining energy in the battery at each moment can be obtained by subtracting the energy consumption of the device from the amount of energy stored up to that moment. With the presence of a LOS link, the process of energy harvesting from the DC part can be regarded as continuous and uniform, so we can set small and equal intervals to observe the energy states of IoT devices. As shown in Fig. 3, the interval between two consecutive energy arriving is termed an epoch, and it is assumed the system parameters are constant within one epoch.

 

Fig. 2. IoT device with SLIPT

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Fig. 3. Energy harvesting process

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2.2 Signal and VLC channel model

Let $y_v^t$ denote the optical transmitted signal of VLC-AP $v$ at time $t$, it can be written as [11]:

According to [8], only the LOS link is considered in this paper, and the channel gain between VLC-AP $v$ and IoT device $j$ at time $t$ can be expressed as:

2.3 Energy harvesting model and work state of IoT devices

The harvested energy of the device is mainly determined by the DC part in the received signal. From Eq. (4), the energy harvested by device $j$ from VLC-AP $v$ can be expressed as [9]:

Furthermore, the remaining energy of device $j$ at time can be expressed as:

3. Problem formulation and solution method

3.1 Energy efficiency (EE) maximization and constraints

In this section, our goal is to achieve optimal EE in a VLC-IoT system while beneficially matching each subchannel with IoT devices and allocating system power to satisfy the QoS requirement, the maximum transmit power constraint, and the illumination constraint. On the other hand, the system also needs to optimize the DC bias and signal peak amplitude, subject to the LED linear constraint and maximum received energy constraint. Explicitly, the EE ${\eta _{EE}}$, can be defined as the ratio of the sum rate to the total power and the optimization problem over $\boldsymbol {B},\boldsymbol {A},\boldsymbol {P},\boldsymbol {a}$ can be formulated as:

Obviously, the EE optimization problem is a MINLFP problem that is difficult to obtain a solution directly, and there is no effective algorithm that can guarantee the optimal solution in polynomial time. As a result, in the following subsections, we reformulate the original problem in a more tractable form in terms of $a_{j,v}^{k,t}$ and $p_{j,v}^{k,t}$. Then the optimization problem is divided into two stages. The first stage called VCF-SA formulates cells and assigns subchannels. Furthermore, a heuristic power allocation algorithm named QTBPA is proposed in the second stage, resulting in a stable solution by a two-loop iterative approach. The above process is described in detail next.

3.2 Problem reformulation

In the original EE problem, C3 and C4 constrain the DC bias and the signal amplitude. It is worth noting that the DC bias $B_v^t$ of device $j$ at time $t$ must be less than or equal to $({I_H} + {I_L})/{2}$. This is because ${I_H} \ge B_v^t \ge ({I_H} + {I_L})/{2}$ and ${I_L} \le B_v^t \le ({I_H} + {I_L})/{2}$ are symmetric parts of the linear range that have the same limitation on signal amplitude. Assuming that the signal amplitude is constant, $B_v^t$ less than or equal to $({I_H} + {I_L})/{2}$ results in decreasing energy consumption of the LED array which leads to an increase in the EE. C3, therefore, can be rewritten as:

On the other hand, the signal transmitted by AP must be positive and meet the constraints of the maximum and minimum range of current according to C4, which can be expressed as:

With the definition of $A_v^t$, (20) can be rewritten equivalently as:

According to Eq. (2) and Eq. (16), the energy consumption of a VLC-AP depends on the DC part. And the maximum signal amplitude can be set to equal $B_v^t - {I_L}$ with determinative energy consumption, thus achieving the highest communication rate that leads to improved EE. In other words, the inequality signs in Eq. (17) can be replaced by equal signs:

Based on the above transform and the definition of $x_v^t$, the signal power at VLC-AP $v$ at time $t$ equals the sum of the power of all subchannels occupied by the devices associated with the VLC-AP:

Equation (18) and Eq. (19) indicate that the relationship between $p_{j,v}^{k,t}$, $B_v^t$, and $A_v^t$. Specifically, a unique DC bias $B_v^t$ or a unique signal amplitude $A_v^t$ can be calculated for a given set of transmit power $p_{j,v}^{k,t}$. Therefore, we can substitute Eq. (18) and Eq. (19) in the EE problem and obtain the reformulated EE problem in terms of $\boldsymbol {P}$ and $\boldsymbol {a}$ as follows:

3.3 Virtual cell formation and subchannel assignment (VCF-SA)

In the first stage, we propose a device-oriented VCF-SA algorithm to obtain $a_{j,v}^{k,t}$. Firstly, the system formulates VCs with known working state indicator and channel state information (CSI). And CT is adopted to enhance SINR, which means that all APs within the VC transmit the same signal in the same subchannel to increase the received signal power and reduce interference. Secondly, only the devices in the working state can send a matching request for subchannels to the CCU, and the system accepts or rejects devices based on QoS requirements.

To elaborate, according to CSI, the device is allocated to the corresponding VC while the SINR threshold is satisfied. After determining the device at the working state, subchannels are allocated to devices with the greatest channel gain until the QoS requirement is met. Then, the remaining subchannels are allocated to devices in sub-optimal channels. Repeat the above process until all subchannels are allocated or the QoS requirements of all devices are met. In this case, if there exist unallocated subchannels, they are all allocated to the device with the greatest channel gain to improve resource utilization. As a result, the subchannel assignment indicator $a_{j,v}^{k,t}$ is determined. The steps of the VCF-SA algorithm are summarized in Algorithm 1.

Compared with the VCF-SA method, although the exhaustive method can find the optimal, it needs to search all possible combinations of cell formation and subchannel assignment, so the calculation will be complicated and time-consuming. Although the proposed VCF-SA algorithm is suboptimal, it is simpler and can determine $a_{j,v}^{k,t}$ more quickly. Moreover, compared with other subchannel assignment strategies such as the strongest channel gain (SCG) assignment and random subchannel assignment (RCA), VCF-SA can achieve better EE performance, which will be shown and analyzed in simulation part.

Therefore, the total rate of the system at time can be rewritten as:

Algorithm 1. Virtual Cell Formation and Subchannel Assignment (VCF-SA)

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3.4 Quadratic transform-based power allocation (QTBPA)

In the previous subsection, we obtained the results of VCF and subchannel assignment. At the second stage, $a_{j,v}^{k,t}$ can be regarded as constants in the optimization problem, leaving only the variables $p_{j,v}^{k,t}$. The EE problem can be restated as:

Since the EE problem in Eq. (22) is non-convex and the objective function is in fraction form, we propose a QTBPA algorithm with a two-layer iteration. Firstly, we preprocess C5 which means substituting the updated DC part in Eq. (11). Specifically, a feasible $\boldsymbol {P}$ is set to obtain initial $\mathop {B_v^t}^ \wedge$. Thus, Eq. (11) is simplified by substituting $\mathop {B_v^t}^ \wedge$ for $B_v^t$ in the logarithmic function term. In the subsequent iterations, $B_v^t$ of the logarithmic function term is updated based on $\boldsymbol {P}$ obtained in the current iteration. Secondly, the fractional objective function in Eq. (22)) is equivalently transformed into subtractions with a variable $\chi$ [22]:

The optimal objective function value of Eq. (22) is equal to the solution $\chi$ of Eq. (23). For a fixed $\chi$, problem in Eq. (22) can be rewritten as:

Here, the problem in Eq. (24) is still a non-convex EE problem since the objective function is non-concave and C1 is non-convex. By introducing the auxiliary variable $y_j^{k,t}$, the quadratic transform technology in [23] is applied to transform each SINR term into a quadratic form with a given $\chi$:

And the optimal $y_j^{k,t}$ for fixed $p_{j,v}^{k,t}$ is:

We arrive at the following reformulation of the problem in Eq. (24):

Algorithm 2. Quadratic transformation-based power allocation (QTBPA)

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Hence, the QTBPA algorithm is proposed and summarized in Algorithm 2, which is designed in a two-loop iterative fashion. In the outer iteration, a feasible $\boldsymbol {A}$ and $\chi$ are initialized, then $y_j^{k,t}$ is calculated using Eq. (26). Then in the inner-iteration, for given $y_j^{k,t}$ and $\chi$, the convex problem in Eq. (27) can be solved efficiently by the CVX solver, and the value of $\mathop {B_v^t}^ \wedge$ and $\chi$ can be updated with the solution while $y_j^{k,t}$ is also updated by Eq. (26). This process repeats until converge to the optimal solution. Since each $SINR{_j^{k,t,*}}$ resides inside the nondecreasing logarithm function, the algorithm converges to a stationary point with a nondecreasing sum-of-functions-of-ratio value after every iteration [23].

4. Simulation results

In this section, we simulate and analyze the EE performance of the proposed VCF-SA-QTBPA method in an indoor VLC system. Without loss of generality, a 10m $\times$ 10m $\times$ 3m room model is considered in which 4 $\times$ 4 VLC-APs are uniformly distributed. Each LED array containing 225 LED beads has 15 available subchannels, each with a bandwidth of 1MHz. IoT devices are distributed randomly in the indoor environment, and the power in the working state $P_j^{self}$ is set as 100mW. The minimum rate threshold ${R_{\min }}$ is chosen to be 10Mbps, and the maximum illumination ${\Phi _{\max }}$ is $800lux$. Moreover, the maximum transmit power of VLC-AP $P^{\max }$, RF-AP power ${P_{RF - AP}}$, and CCU power ${P_{CCU}}$ are assumed as 20W, 1W, and 5W, respectively. Besides, 50 consecutive epochs of 0.2s each are considered to observe the energy harvesting process. The Monte Carlo method is used to evaluate performance where each data point of the simulation is the average result of 100 different device distributions. Other parameters adopted in the simulation part can be found in [5,9,12,19,25–27] and some key parameters are given in Table 2. For comparison purposes, we set SCG, RCA, and equal power allocation (EPA) as benchmarks. In addition, we also commence by investigating the EE for different bandwidth, FOV, and room sizes, followed by studying the effect of different maximum transmitting power constraints and the number of subchannels.

Table 2. Default simulation parameters

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In order to illustrate the convergence of the proposed VCF-SA-QTBPA algorithm, Fig. 4 depicts the average number of iterations versus the number of IoT devices. It can be observed that the number of iterations initially improves with the number of IoT devices, then remains fixed when the number exceeds 15. The reason is that an increase in the number of IoT devices, especially in the same cell, will enlarge the competition for subchannels, requiring more precise power allocation to achieve better EE. Moreover, the figure also indicates that the proposed method has a fast convergence speed (less than or equal to 10) when the number of IoT devices is less than or equal to 10, and it also has a determined convergence speed when the number of users is greater than 10.

 

Fig. 4. Average number of iterations versus the number of IoT devices

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Figure 5 reveals the average EE versus the number of IoT devices. By setting lower and upper bounds of the EE, we compare the results of the proposed scheme and benchmarks to demonstrate their feasibility and effectiveness. The lower bound takes RCA as the access scheme and allocates power to meet the minimum rate threshold. Since the distribution of IoT devices will also affect the energy efficiency of the system, we select the better EE obtained when IoT devices are centrally distributed at 9m $\times$ 9m as the upper bound to compare the results of other schemes. From this figure, we can obtain that the VCF-SA-QTBPA scheme increases more pronounced compared with other benchmarks. When the number of IoT devices is greater than 5, the proposed scheme always has the best EE performance. The reason for this phenomenon is that the proposed scheme allocates the power more rationally under the constraints of satisfying the QoS requirements, illumination requirements, maximum power budget, etc. Compared with the VCF-SA scheme, the device selects the VLC-AP with the best channel conditions in the SCG scheme. Although it obtains the largest received power from a specific VLC-AP, all the signals of other APs within the FOV become interference. And the RCA scheme randomly assigns subchannels to the device, so this scheme has the worst EE performance. Meanwhile, SCG-QTBPA and SCG-EPA curves also demonstrate that the QBTPA scheme outperforms the EPA scheme when the SCG scheme is adopted, since some energy is wasted when each AP distributes the total power equally to all available subchannels. Due to the difference in channel gain, it is inevitably to have a decrease in the sum rate. Furthermore, SCG-QTBPA is suboptimal, and the EE of SCG-EPA and RCA-EPA schemes initially increases with the number of devices, but gradually decreases when the number of users exceeds 17. Another insight from Fig. 5 is that the system EE begins to decline when the number of IoT decvices becomes excessively large, i.e., $|{\rm {J}}|$ > 30, since increasing the number of devices leads to increased interference between devices, resulting in lower EE. Another reason is that some IoT devices cannot obtain subchannels for data transmission, so the EE of the system will also decrease.

 

Fig. 5. Comparison of EE versus the number of IoT devices

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For the VLC-IoT system, there are multiple parameters that affect EE. In the following content, the influence of several key parameters will be discussed. Figure 6 shows the EE versus the bandwidth of subchannels with 10 IoT devices. We can find that the EE of all schemes will improve with the subchannel bandwidth because a larger bandwidth means a higher achievable rate. And we observe that the VCF-SA-QTBPA scheme always outperforms the benchmarks with different bandwidths. It further demonstrates the effectiveness of the proposed scheme.

 

Fig. 6. Comparison of EE versus subchannel bandwidth

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In Fig. 7, we compare the EE of the proposed scheme and benchmarks with different maximum transmit power per LED array. This figure shows that the EE of the four schemes initially increases with the maximum transmit power per LED array. Although the total power consumed increases, the additional power contributes more to the total rate, thus the EE increases. However, the EE begins to decline in turn after arriving at the peak. This is because when QoS, illumination, and energy storage requirements are satisfied, excessive power may mean that the illumination of some locations exceeds the maximum luminous flux or the harvested energy exceeds the maximum storage constraint and is wasted. Hence, it can be observed that monotonously increasing the maximum transmit power per LED array does not lead to better EE. In addition, it is also clear that the VCF-SA-QTBPA scheme is always superior to three benchmarks under different maximum power. Notably, Fig. 6 and Fig. 7 show that increasing bandwidth and total power are potential solutions to improve system EE. However, in actual VLC systems, there is a trade-off between LED power and bandwidth. As a result, we can conclude that the relationship between the two parameters needs to investigate comprehensively to increase system EE. We also take it as part of future research.

 

Fig. 7. Comparison of EE versus maximum transmit power per LED array

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Figure 8 depicts the impact of room size on the EE where $S$ denotes the width of the square room. In general, larger rooms require higher power to meet the luminous requirement, which increases DC power. In the simulation part, VLC-APs are not fixed since the fixed VLC-AP arrangement in an enlarged room result in more areas with poor lighting conditions. Therefore, VLC-AP positions change with the room size and still maintain a uniform distribution of 4 $\times$ 4. Consistent with the analysis in Fig. 8, for given room size, we can observe that higher transmission power per LED array does not lead to higher EE. Also, as the room size increases, the EE of the system decreases because more power is required to meet the luminous requirement. On the other hand, some VLC-APs that were in the FOV of a device may disappear as the room size enlarge, resulting in reduced achievable rate and ultimately affecting system EE. Hence, the maximum EE of different room sizes may be obtained at different maximum transmit power budgets. For example, the maximum EE occurs at 20W in a 10 $\times$ 10 room, and 25W in 14 $\times$ 14 and 16 $\times$ 16 rooms.

 

Fig. 8. EE versus maximum transmit power per LED array with different room size

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Figure 9(a) demonstrates the EE with different FOVs of the proposed scheme and benchmarks. As can be observed, the EE declined with the rise of FOV, and the proposed scheme always achieves the best EE. This can be explained by the fact that an increase in FOV means an increase in interference from other unassociated VLC-APs. Furthermore, to meet the QoS requirements, increasing signal power will lead to a rise in DC bias, which enlarges the system energy consumption. To this end, we investigate the Rate-FOV and Power-FOV relationship of the VCF-SA-QTBPA scheme as shown in Fig. 9(b). As anticipated, with increased FOV, the sum rate decreases monotonically while more power is consumed to satisfy QoS.

 

Fig. 9. (a) Comparison of EE versus FOVs (b) Sum rate and consumed power versus FOVs

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Finally, we investigate the impact of the available subchannels in Fig. 10. In this paper, outage devices refer to IoT devices that are not allocated to any subchannel or do not meet the achievable rate threshold in at least one of the considered epochs. It does not mean that these devices are interrupted during the entire energy reception process. It can be observed that the number of outage devices improves with the number of total devices due to the fiercer competition of subchannels. Moreover, the result of increasing the subchannel number to 20 indicates that the number of outage devices does decrease since more subchannels are available.

 

Fig. 10. Average IoT devices in outage versus the total number of IoT devices

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5. Conclusion

In this paper, we investigated the EE optimization problem for the OFDMA-based VLC-IoT system consisting of multiple self-power IoT devices and VLC-APs with SLIPT. Subchannel assignment and power allocation are jointly studied to optimize the EE with the consideration of the limited transmit power, QoS requirement, maximum luminous constraint, and maximum energy storage constraint. The proposed VCF-SA algorithm formulated VCs based on the location of IoT devices and assigned subchannels based on the working state and QoS requirements. Then the proposed QTBPA algorithm transformed the fractional non-convex problem into a convex problem based on quadratic transformation technology and obtained the optimal power allocation through two-loop iteration. The presented simulation results demonstrated that the VCF-SA-QTBPA scheme can significantly improve the EE compared to the benchmarks. It’s worth noting that VLC is expected to play a major role in developing the next generation of energy-efficient IoT networks, and the corresponding resource allocation will be a very important topic.

In future work, we plan to investigate the resource allocation of a more realistic VLC-IoT system, considering different modulation schemes, specific distribution and mobility of IoT devices, and the tradeoff between power and bandwidth of LEDs.