Power Minimization-Based Secure Beamforming for MISO VLC Having Both Perfect and Imperfect CSI

The majority of research on visible light communications (VLC) neglects the non-line-of-sight (NLoS) channel gains, which cannot be ignored for physical-layer security analysis. Moreover, the commonly used semidefinite relaxation technique for power minimization problems may not always yield an optimal solution due to the removal of the rank-one constraint. In this letter, we investigate a power minimization-based secure beamforming problem for a multiple-input single-output VLC system having both LoS and NLoS components. Assuming perfect channel state information (CSI), we formulate an optimal secure beamforming problem with a worst-case secrecy rate constraint and a per-lamp power constraint. Instead of removing the rank-one constraint, we incorporate such a constraint into the objective function and treat it as a penalty term. Then, we propose a semidefinite programming and penalty function (SDPPF) algorithm to solve the non-convex problem. To enhance practicality, we also consider the case of imperfect CSI and explore a robust beamforming scheme. Numerical results demonstrate that the proposed SDPPF algorithm can achieve a power gain of at least 3 dB compared to existing algorithms. Moreover, the necessity of considering the NLoS channel gains is also verified.