Capacity Maximization for Reconfigurable Intelligent SurfaceAided MISO Visible Light Communications
Abstract
:1. Introduction
 A controllable mirror array is used intelligently as RIS, and therefore, we model the RISaided MISOVLC channel. An optimization problem is formulated for this system model to reconfigure the direction on each element of RIS.
 For this system model, we regard the asymptotic capacity in high SNR of the RISaided MISOVLC system employing IM/DD with peakpower constraints as a goal. The optimization problem is formulated with the rotation angle of each mirror in RIS as the decision variable and the asymptotic capacity maximation as the goal. As for this nonconvex optimization problem, we convert it into a quadratic programming (QP) problem with hemispherical constraints, and prove that the problem can be solved by calculating the maximum eigenvalue of an equivalent matrix.
 Simulation results indicate that the asymptotic capacity of the MISOVLC channel can be improved with RIS. Additionally, the impact of the distance between the receiver and RIS, the deployment scheme of RIS, are considered in the last part of this paper, which may guide our deployment of RIS in the future.
2. Channel Model
2.1. Channel Gain of the LoS Paths
2.2. Channel Gain of the NLoS Paths
3. Problem Formulation and Solution
3.1. Primary Problem
3.2. Equivalent Problem
Algorithm 1: The Cyclic Search Algorithm. 
Input:
The equivalent matrix $\frac{{\mathcal{A}}_{k}+{\mathcal{A}}_{k}^{\mathrm{T}}}{2}$; The dimension of the equivalent matrix $dim$; The cyclic variable $i=1$; Output: The maximum eigenvalue ${\lambda}_{\mathrm{max}}$; the normalized eigenvector $\mathbf{v}$ corresponding to ${\lambda}_{\mathrm{max}}$;

4. Simulation Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Parameter  Value 

${\mathsf{\Phi}}_{1/2}$  ${70}^{\circ}$ 
a  $1.5$ 
${\mathsf{\Psi}}_{\mathrm{C}}$  ${85}^{\circ}$ 
${T}_{of}$  1 
${A}_{PD}$  $1\mathrm{c}{\mathrm{m}}^{2}$ 
${\sigma}^{2}$  1 
${\rho}_{\mathrm{RIS}}$  $0.95$ 
n  2 
LoS Channel Gain  NLoS Channel Gain  K  Proportion 

$0.79$  $0.09$  $\mathrm{K}=15$  $11.4\%$ 
$0.79$  $0.17$  $\mathrm{K}=60$  $21.5\%$ 
$0.79$  $0.19$  $\mathrm{K}=135$  $24.1\%$ 
$0.79$  $0.20$  $\mathrm{K}=240$  $25.3\%$ 
$0.79$  $0.21$  $\mathrm{K}=375$  $26.6\%$ 
$0.79$  $0.22$  $\mathrm{K}=1500$  $27.8\%$ 
LoS Channel Gain  NLoS Channel Gain  Way of Deployment  Proportion 

$0.80$  $0.90$  $\mathrm{K}=50\times 3$  $12.5\%$ 
$0.80$  $0.18$  $\mathrm{K}=25\times 6$  $22.5\%$ 
$0.80$  $0.20$  $\mathrm{K}=10\times 15$  $25\%$ 
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Wu, Q.; Zhang, J.; Guo, J. Capacity Maximization for Reconfigurable Intelligent SurfaceAided MISO Visible Light Communications. Photonics 2022, 9, 487. https://doi.org/10.3390/photonics9070487
Wu Q, Zhang J, Guo J. Capacity Maximization for Reconfigurable Intelligent SurfaceAided MISO Visible Light Communications. Photonics. 2022; 9(7):487. https://doi.org/10.3390/photonics9070487
Chicago/Turabian StyleWu, Qi, Jian Zhang, and Jianing Guo. 2022. "Capacity Maximization for Reconfigurable Intelligent SurfaceAided MISO Visible Light Communications" Photonics 9, no. 7: 487. https://doi.org/10.3390/photonics9070487