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

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## Abstract

**:**

## 1. Introduction

## 2. System Model

#### 2.1. Downlink Communication

_{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

#### 2.1.1. VLC Channel Model

_{l}and user u is

_{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.

_{e}is satisfied with the average emitted optical power P

_{o}:

_{l}in time slot t, and ${b}_{k}^{\left(u,l\right)}\left(t\right)=1$ indicates that AP

_{l}assigns subcarrier k to the user for communication in time slot t; otherwise, ${b}_{k}^{\left(u,l\right)}\left(t\right)=0$.

_{l}is

_{l}to user u on the subcarrier k.

_{l}and user u on the subcarrier k of the time slot t is

_{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:

_{l}and user u in the t timeslot is

_{l}is

_{l}can be set to

_{ave,VLC}represents the maximum average power consumption on VLC AP

_{l}.

#### 2.1.2. RF Channel Model

^{(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.

_{l}assigns RBi to user u; otherwise, ${x}_{i}^{\left(u,0\right)}\left(t\right)=0$. 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 ${p}_{i}^{\left(u,0\right)}\left(t\right)$, the signal-to-noise ratio between user u and the RF AP is

_{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

_{ave,RF}is the maximum average power consumption on the RF AP.

#### 2.2. Uplink Communication

^{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.

_{RF}is the power of the response signal, ${\chi}_{RF}\left(t\right)$ is the normalized signal, and ${\chi}_{RF}\left(t\right)\in \left[-1,1\right]$, $E\left[{\left|{\chi}_{RF}\left(t\right)\right|}^{2}\right]=1$. The signal at the RF receiver can be expressed as

_{RF}(t) is additive white Gaussian noise and obeys a complex Gaussian distribution with a mean of 0 and a variance of ${\sigma}_{RF}^{2}$.

#### 2.3. OFDMA System Model

_{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

_{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.

#### 2.4. Queue Model

_{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):

_{u}is a bounded variable that guarantees the stability of the system. According to the above analysis, Q

_{u}(t) can be expressed as

_{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

## 3. Optimization of the Problem Description

_{1}(t),···, Z

_{l}(t),···,Z

_{L}(t)},Z

_{l}(t) and evolved as follows:

_{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].

#### 3.1. AP Allocation

^{(u,l)}(t) in the system can be obtained by solving the following subproblems:

^{(u,l)}(t) = (Q

_{u}(t) + V)v

^{(u,l)}. Since (43) is a linear optimization problem, its solution is as follows:

^{(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.

#### 3.2. VLC AP Joint Subcarrier and Power Allocation

_{VLC}| subproblems, and each subproblem is expressed as

_{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 ${b}_{k}^{\left(u,l\right)}\left(t\right)\in \left\{0,1\right\}$ to ${\tilde{b}}_{k}^{\left(u,l\right)}\left(t\right)\in \left[0,1\right]$, the optimization problem is reformulated as

_{l}| linear combination of convex functions. Let $\mathbb{L}\left(P\right)={\displaystyle \sum _{k\in K}{\displaystyle \sum _{u\in {U}_{l}}{\tilde{b}}_{k}^{\left(u,l\right)}\left(t\right)\left({Q}_{u}\left(t\right)+V\right){B}_{VLC}{\mathrm{log}}_{2}\left(1+\frac{{p}_{k}^{\left(u,l\right)}\left(t\right){\left|\epsilon {h}_{k}^{\left(u,l\right)}\left(t\right)\right|}^{2}}{{\tilde{b}}_{k}^{\left(u,l\right)}\left(t\right){\sigma}_{VLC}^{2}}\right)}}-{Z}_{l}\left(t\right){\displaystyle \sum _{k\in K}{\displaystyle \sum _{u\in U}{p}_{k}^{\left(u,l\right)}\left(t\right)}}$ be the objective function and find the partial derivative of $\text{}{p}_{k}^{\left(u,l\right)}\left(t\right)$ for $\mathbb{L}\left(P\right)$:

#### 3.3. RF AP Joint Resource Block and Power Allocation

## 4. Analysis of Algorithm Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Zhou, Y.; Liu, L.; Wang, L.; Hui, N.; Cui, X.; Wu, J.; Peng, Y.; Qi, Y.; Xing, C. Service-aware 6G: An intelligent and open network based on the convergence of communication, computing, and caching. Digit. Commun. Netw.
**2020**, 6, 253–260. [Google Scholar] [CrossRef] - Ke, X.; Ding, D. Wireless Optical Communication, 2nd ed.; Science Press: Beijing, China, 2022. [Google Scholar]
- Arfaoui, M.A.; Soltani, M.D.; Tavakkolnia, I.; Ghrayeb, A.; Majid Safari, M.; Assi, C.; Haas, H. Physical layer security for visible light communication systems: A survey. IEEE Commun. Surv. Tutor.
**2020**, 22, 1887–1908. [Google Scholar] [CrossRef] - Wu, W.H.; Zhou, F.; Yang, Q.H. Adaptive Network Resource Optimization for Heterogeneous VLC/RF Wireless Networks. IEEE Trans. Commun.
**2018**, 66, 5568–5581. [Google Scholar] [CrossRef] - Papanikolaou, V.K.; Diamantoulakis, P.D.; Sofotasios, P.C.; Muhaidat, S.; Karagiannidis, G.K. On optimal resource allocation for hybrid VLC/RF networks with common backhaul. IEEE Trans. Cogn. Commun. Netw.
**2020**, 6, 352–365. [Google Scholar] [CrossRef] - Abdelhady, A.M.; Amin, O.; Chaaban, A.; Shihada, B.; Alouini, M.S. Downlink resource allocation for dynamic TDMA-based VLC systems. IEEE Trans. Wirel. Commun.
**2019**, 18, 108–120. [Google Scholar] [CrossRef] - Kashef, M.; Abdallah, M.; Al-Dhahir, N. Transmit power optimization for a hybrid PLC/VLC/RF communication system. IEEE Trans. Green Commun. Netw.
**2018**, 2, 234–245. [Google Scholar] [CrossRef] - Aboagye, S.; Ibrahim, A.; Ngatched, T.M.N.; Ndjiongue, A.R.; Dobre, O.A. Design of Energy Efficient Hybrid VLC/RF/PLC Communication System for Indoor Networks. IEEE Wirel. Commun. Lett.
**2020**, 9, 143–147. [Google Scholar] [CrossRef] - Ma, S.; Zhang, F.; Li, H.Z.; Mohamed, S.A.; Li, S.Y. Aggregated VLC-RF Systems: Achievable Rates, Optimal Power Allocation, and Energy Efficiency. IEEE Trans. Wirel. Commun.
**2020**, 19, 7265–7278. [Google Scholar] [CrossRef] - Obeed, M.; Salhab, A.M.; Zummo, S.A.; Alouini, M. Joint optimization of power allocation and load balancing for hybrid VLC/RF networks. J. Opt. Commun. Netw.
**2018**, 10, 553–562. [Google Scholar] [CrossRef] - Pratama, Y.S.M.; Choi, K.W. Bandwidth Aggregation Protocol and Throughput-Optimal Scheduler for Hybrid RF and Visible Light Communication Systems. IEEE Access
**2018**, 6, 32173–32187. [Google Scholar] [CrossRef] - Kahn, J.M.; Barry, J.R. Wireless infrared communications. Proc. IEEE
**1997**, 85, 265–298. [Google Scholar] [CrossRef] - Kashef, M.; Ismail, M.; Abdallah, M.; Mohamed; Qaraqe, K.A.; Serpedin, E. Energy Efficient Resource Allocation for Mixed RF/VLC Heterogeneous Wireless Networks. IEEE J. Sel. Areas Commun.
**2016**, 34, 883–893. [Google Scholar] [CrossRef] - Dakhli, C.M.; Zayani, R.; Belkacem, B.O.; Bouallegue, R. Theoretical analysis and compensation for the joint effects of HPA nonlinearity and RF crosstalk in VBLAST MIMO-OFDM systems over Rayleigh fading channel. EURASIP J. Wirel. Commun. Netw.
**2014**, 2014, 61. [Google Scholar] [CrossRef] - Hammouda, M.; Vegni, A.M.; Haas, H.; Peissig, J. Resource Allocation and Interference Management in OFDMA-based VLC Networks. Phys. Commun.
**2018**, 31, 169–180. [Google Scholar] [CrossRef] - Armstrong, J.; Schmidt, B.J.C. Comparison of Asymmetrically Clipped Optical OFDM and DC-Biased Optical OFDM in AWGN. IEEE Commun. Lett.
**2008**, 12, 343–345. [Google Scholar] [CrossRef] - Wang, Y.H.; He, Y.H.; Xu, C.; Zhou, Z.Y.; Pervaiz, H. Joint rate control and power allocation for low-latency reliable D2D-based relay network. EURASIP J. Wirel. Commun. Netw.
**2019**, 2019, 111. [Google Scholar] [CrossRef] - Bao, W.; Chen, H.; Li, Y.; Vucetic, B. Joint rate control and power allocation for non-orthogonal multiple access systems. IEEE J. Sel. Areas Commun.
**2017**, 35, 2798–2811. [Google Scholar] [CrossRef] - Guo, Y.; Yang, Q.; Kwak, K.S.; Fu, F. Quality-oriented rate control and resource allocation in time-varying OFDMA networks. IEEE Trans. Veh. Technol.
**2017**, 66, 2324–2338. [Google Scholar] [CrossRef] - Zhang, R.; Claussen, H.; Haas, H.; Hanzo, L. Energy efficient visible light communications relying on amorphous cells. IEEE J. Sel. Areas Commun.
**2016**, 34, 894–906. [Google Scholar] [CrossRef] - Valencia-Estrada, J.C.; García-Marquez, J.; Chassagne, L.; Topsu, S. Catadioptric interfaces for designing VLC antennae. Appl. Opt.
**2017**, 56, 7559. [Google Scholar] [CrossRef] [PubMed] - AlQahtani, S.A.; Alhassany, M. Comparing Different LTE Scheduling Schemes. In Proceedings of the IEEE 9th International Wireless Communications and Mobile Computing Conference (IWCMC 2013), Sardinia, Italy, 1–5 July 2013; pp. 264–269. [Google Scholar]

**Figure 4.**(

**a**) Relationship between average queue length Q and control parameter V; (

**b**) relationship between average transmission rate R and control parameter V.

**Figure 5.**The instantaneous transmission rate and queue length of each user change under different V values. (

**a**) V = 50; (

**b**) V = 150; (

**c**) V = 300.

**Figure 6.**(

**a**) The relationship between the average queue length Q and the number of users under the three algorithms; (

**b**) the relationship between the average transmission rate R and the number of users under the three algorithms.

**Figure 7.**(

**a**) The relationship between the average queue length Q of the outage probability and the number of users is considered under the three algorithms; (

**b**) the relationship between the average transmission rate R of the outage probability and the number of users is considered under the three algorithms.

**Figure 8.**(

**a**) The relationship between the average queue length Q and the penalty parameter V under different numbers of users in the uplink RF link; (

**b**) the relationship between the average transmission rate R and the penalty parameter V of the uplink RF link under different number of users.

**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.

**Table 1.**The relationship between SINR and modulation, coding rate, and SE [16].

SINRmin [dB] | Modulation Mode | Encoding Rate | SE [bit/Hz] |
---|---|---|---|

1 | QPSK | 0.44 | 0.8770 |

3 | QPSK | 0.59 | 1.1758 |

5 | 16QAM | 0.37 | 1.4766 |

8 | 16QAM | 0.48 | 1.9141 |

9 | 16QAM | 0.60 | 2.4063 |

11 | 64QAM | 0.45 | 2.7305 |

12 | 64QAM | 0.55 | 3.3223 |

14 | 64QAM | 0.65 | 3.9023 |

16 | 64QAM | 0.75 | 4.5234 |

18 | 64QAM | 0.85 | 5.1152 |

20 | 64QAM | 0.93 | 5.5547 |

Parameter | Meaning | Value |
---|---|---|

L × W × H | Room size | 8 m × 8 m × 3 m |

Φ_{1/2} | Power half angle | 70° |

FOV | Field of view | 60° |

n | Number of LEDs | 5 |

P_{ave} | LED transmit power | 4 W |

Ap | The effective receiving area of PD | 1 cm^{2} |

T_{l} | Optical filter gain | 1 |

G_{l} | Concentrator gain | 1 |

ε | Photoelectric conversion factor | 0.52 A/W |

n_{re} | The refractive index of PD | 1.5 |

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**MDPI and ACS Style**

Ke, X.; Xu, Y.; Qin, H.; Liang, J.
Research on Resource Allocation Strategy of Indoor Visible Light Communication and Radio Frequency Systems Integrating Orthogonal Frequency-Division Multiple Access Technology. *Photonics* **2023**, *10*, 1016.
https://doi.org/10.3390/photonics10091016

**AMA Style**

Ke X, Xu Y, Qin H, Liang J.
Research on Resource Allocation Strategy of Indoor Visible Light Communication and Radio Frequency Systems Integrating Orthogonal Frequency-Division Multiple Access Technology. *Photonics*. 2023; 10(9):1016.
https://doi.org/10.3390/photonics10091016

**Chicago/Turabian Style**

Ke, Xizheng, Yaxin Xu, Huanhuan Qin, and Jingyuan Liang.
2023. "Research on Resource Allocation Strategy of Indoor Visible Light Communication and Radio Frequency Systems Integrating Orthogonal Frequency-Division Multiple Access Technology" *Photonics* 10, no. 9: 1016.
https://doi.org/10.3390/photonics10091016