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Secrecy Capacity Analysis and Beamforming Optimization for MIMO-VLC Wiretap Channels

Sufang Yang, Longguang Li, Jintao Wang, Ya Li, Liang Xia, Hongjun He, Qixing Wang, Guangyi Liu

TL;DR

To enhance transmission confidentiality, a fully-connected beamforming scheme is proposed, along with a low-complexity sub-connected alternative, and Numerical results demonstrate that the proposed schemes achieve significant secrecy performance improvements compared with the benchmark scheme.

Abstract

This paper investigates a multiple-input multipleoutput (MIMO) visible light communication (VLC) wiretap channel consisting of a transmitter, a legitimate receiver, and an eavesdropper. The optical input is subject to both peakand average-intensity constraints. By applying the generalized entropy-power inequality to truncated exponential inputs, we derive a novel closed-form expression for the achievable secrecy rate for general MIMO VLC configurations. To enhance transmission confidentiality, a fully-connected beamforming scheme is proposed, along with a low-complexity sub-connected alternative. Although the resulting beamforming design problems are nonconvex, they are efficiently addressed by transforming them into a sequence of convex subproblems solvable via the successive convex approximation framework. Numerical results demonstrate that the proposed schemes achieve significant secrecy performance improvements compared with the benchmark scheme.

Secrecy Capacity Analysis and Beamforming Optimization for MIMO-VLC Wiretap Channels

TL;DR

To enhance transmission confidentiality, a fully-connected beamforming scheme is proposed, along with a low-complexity sub-connected alternative, and Numerical results demonstrate that the proposed schemes achieve significant secrecy performance improvements compared with the benchmark scheme.

Abstract

This paper investigates a multiple-input multipleoutput (MIMO) visible light communication (VLC) wiretap channel consisting of a transmitter, a legitimate receiver, and an eavesdropper. The optical input is subject to both peakand average-intensity constraints. By applying the generalized entropy-power inequality to truncated exponential inputs, we derive a novel closed-form expression for the achievable secrecy rate for general MIMO VLC configurations. To enhance transmission confidentiality, a fully-connected beamforming scheme is proposed, along with a low-complexity sub-connected alternative. Although the resulting beamforming design problems are nonconvex, they are efficiently addressed by transforming them into a sequence of convex subproblems solvable via the successive convex approximation framework. Numerical results demonstrate that the proposed schemes achieve significant secrecy performance improvements compared with the benchmark scheme.
Paper Structure (26 sections, 5 theorems, 13 equations, 11 figures, 3 algorithms)

This paper contains 26 sections, 5 theorems, 13 equations, 11 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Channel Model
  3. Achievable Secrecy Rate Characterization
  4. Proof of Achievable Secrecy Rate for Case I
  5. Proof of Achievable Secrecy Rate for Case II
  6. MIMO-VLC Wiretap Channel Beamforming Design
  7. Beamforming Design for Case I
  8. Fully-connected Beamforming Design
  9. Sub-connected Beamforming Design
  10. Beamforming Design for Case II
  11. Secrecy Rate Maximization Algorithm
  12. Preliminary
  13. Algorithm for Case I
  14. Fully-connected Beamforming Optimization Algorithm
  15. Sub-connected Beamforming Optimization Algorithm
  16. ...and 11 more sections

Key Result

Lemma 1

The secrecy capacity for the wiretap channel in channel model is given by where $\mathbf{U}$ is an auxiliary variable and $\mathbf{U} \rightarrow \mathbf{X} \rightarrow ( \mathbf{Y}_\textnormal{B},\mathbf{Y}_\textnormal{E} )$ form a Markov chain. $\blacksquare$

Figures (11)

  • Figure 1: Architectures of two beamforming schemes: (a) Direct-connected beamformer: the $j$-th LED is only connected to the $j$-th input $X_j$; (b) Fully-connected beamformer: each LED is connected to all inputs $X_j$s, $j\in\{1,\cdots,n_\textnormal{T}\}$.
  • Figure 2: Architecture of sub-connected beamforming scheme: the $\CMcal{I}_j$-th LED is only connected to the $\CMcal{I}_j$-th input $X_{\CMcal{I}_j}$, while the $\CMcal{I}^\textnormal{c}_k$-th LED is connected to all inputs $X_{\CMcal{I}_j}$s, where $\CMcal{I}_j\in\CMcal{I}$, $j\in \{ 1,\cdots,n_\textnormal{B} \}$, $\CMcal{I}^\textnormal{c}_k\in\CMcal{I}^\textnormal{c}$, and $k\in \{ 1,\cdots,n_\textnormal{T}-n_\textnormal{B} \}$.
  • Figure 3: Comparison of achievable secrecy rates: (a). $\mathbb{H}_\textnormal{B}=\mathbb{H}_\textnormal{B}^{1\times4}$ and $\mathbb{H}_\textnormal{E}=\mathbb{H}_\textnormal{E}^{1\times4}$; (b). $\mathbb{H}_\textnormal{B}=(\mathbb{H}_\textnormal{B}^{2\times4})^\mathsf{T}$ and $\mathbb{H}_\textnormal{E}=(\mathbb{H}_\textnormal{E}^{2\times4})^\mathsf{T}$.
  • Figure 4: Achievable secrecy rates of fully-connected beamformer when $\mathbb{H}_\textnormal{B}=\mathbb{H}_\textnormal{B}^{1\times4}$, $\mathbb{H}_\textnormal{E}=\mathbb{H}_\textnormal{E}^{1\times4}$, and $\bm{\alpha}=\alpha\mathbf{1}_{4}$.
  • Figure 5: Achievable secrecy rates of fully-connected beamformer when $\mathbb{H}_\textnormal{B}=\mathbb{H}_\textnormal{B}^{2\times4}$, $\mathbb{H}_\textnormal{E}=\mathbb{H}_\textnormal{E}^{2\times4}$, and $\bm{\alpha}=\alpha\mathbf{1}_{4}$.
  • ...and 6 more figures

Theorems & Definitions (5)

  • Lemma 1: Csiszár1978, Gamal2011
  • Theorem 2
  • Lemma 3
  • Lemma 4
  • Lemma 5