Achievable Secrecy Sum-Rate of the MISO VLC Broadcast Channel with Confidential Messages

We investigate in this paper the achievable secrecy sum-rate of the multiple-input single- output (MISO) visible light communication (VLC) broadcast Gaussian channel with confidential messages. We consider a system model comprising (K+1) nodes: a transmitter (Alice) equipped with N fixtures of LEDs and K (K ≤ N) spatially dispersed users, each equipped with a single photo-diode (PD). The channel is modeled as deterministic and real-valued, subject to amplitude and power constraints, through which Alice wants to transmit in one channel use K confidential messages. We propose a new precoding scheme based on the eigenvalues of the pencils of the different K MISO VLC channels in order to maximize the achievable secrecy sum-rate of the overall system. The motivation behind this scheme is based on the fact that the optimal precoding scheme maximizing the achievable secrecy rate of the single user MISO VLC wiretap channel is expressed through the eigenvector associated to the largest eigenvalue of the wiretap channel's pencil. We investigate both cases, namely, when the locations of users are known, i.e., perfect channel state information (CSI) is available to Alice, or unknown, i.e., imperfect CSI. Furthermore, we adopt the truncated generalized normal (TGN) distribution as input signaling. We present several examples which demonstrate the substantial improvements in the secrecy sum-rates achieved by the proposed techniques compared to those achieved by zero-forcing (ZF) precoding.