Secrecy Performance of the MIMO VLC Wiretap Channel with Randomly Located Eavesdropper

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.