Optimal and Robust Secure Beamformer for Indoor MISO Visible Light Communication

Abstract

In this paper, the physical-layer secrecy problem is investigated for the indoor multiple-input single-output (MISO) visible light communication systems. First, when the channel state information (CSI) of eavesdroppers is perfect, two kinds of optimal secure beamformers are, respectively, designed to minimize the transmit power and to maximize the secrecy rate. Moreover, it is shown that the secrecy rate maximization problem can be decomposed into a sequence of convex feasibility problems, which can be efficiently solved by using interior point methods. Second, when the CSI of eavesdroppers is imperfect, an ellipsoidal region model is applied to characterize the CSI uncertainty. This model leads to an infinite number of complicated constraints for the design of robust secure beamformers. By using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {S}$</tex-math></inline-formula> -lemma and semidefinite relaxation, this nonconvex problem is transformed into the convex semidefinite program. Finally, numerical results demonstrate the optimality and robustness of the proposed methods.