We study in this paper the secrecy performance of the multiple-input multiple-output (MIMO) visible light communication (VLC) wiretap channel. The underlying system model comprises three nodes: one transmitter, equipped with multiple fixtures of LEDs, one legitimate receiver and one eavesdropper, each equipped with multiple photo-diodes (PDs). The VLC channel is modeled as a real-valued amplitude-constrained Gaussian channel and the eavesdropper is assumed to be randomly located in the coverage area. We propose a low-complexity precoding scheme that aims at enhancing the secrecy performance of the system. Specifically, assuming discrete input signaling, we derive an average achievable secrecy rate for the underlying system in a closed-form, and the derived expression is a function of the precoding matrix and the input distribution using stochastic geometry. Then, we propose a low-complexity design of the precoding matrix based on the generalized singular value decomposition (GSVD) of the channel matrices of the system. We examine the resulting average achievable secrecy rate using the truncated discrete generalized normal (TDGN) distribution, which is the best-known discrete distribution available in the literature. Finally, we validate the proposed scheme through extensive simulations and we demonstrate its superiority when compared to other schemes reported in the literature.

中文翻译：

---

具有随机定位窃听者的 MIMO VLC 窃听信道的保密性能

我们在本文中研究了多输入多输出 (MIMO) 可见光通信 (VLC) 窃听通道的保密性能。底层系统模型包括三个节点：一个发射器，配备多个 LED 固定装置，一个合法接收器和一个窃听者，每个节点配备多个光电二极管 (PD)。VLC 信道被建模为实值幅度约束高斯信道，假设窃听者随机位于覆盖区域。我们提出了一种低复杂度的预编码方案，旨在提高系统的保密性能。具体来说，假设离散输入信号，我们以封闭形式推导出底层系统的平均可实现保密率，导出的表达式是预编码矩阵和使用随机几何的输入分布的函数。然后，我们提出了一种基于系统信道矩阵的广义奇异值分解 (GSVD) 的预编码矩阵的低复杂度设计。我们使用截断离散广义正态 (TDGN) 分布来检查所得的平均可实现保密率，这是文献中最知名的离散分布。最后，我们通过广泛的模拟验证了所提出的方案，并且与文献中报道的其他方案相比，我们证明了其优越性。我们使用截断离散广义正态 (TDGN) 分布来检查所得的平均可实现保密率，这是文献中最知名的离散分布。最后，我们通过广泛的模拟验证了所提出的方案，并且与文献中报道的其他方案相比，我们证明了其优越性。我们使用截断离散广义正态 (TDGN) 分布来检查所得的平均可实现保密率，这是文献中最知名的离散分布。最后，我们通过广泛的模拟验证了所提出的方案，并且与文献中报道的其他方案相比，我们证明了其优越性。