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Journal of Lightwave Technology

Optimal and Robust Secure Beamformer for Indoor MISO Visible Light Communication

Shuai Ma, Zhi‐Long Dong, Hang Li, Zhaolin Lu, Shiyin Li

Published Aug 31, 2016• 61 citations
Publisher

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$\mathcal {S}$-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.

DOI
10.1109/jlt.2016.2605000

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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 theS\mathcal {S}S-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.
For simplicity, most works on visible light communications (VLC) neglect the non-line-of-sight (NLoS) channel gain and the inter-symbol interference (ISI). This letter investigates the optimal and robust secure beamforming problems for multiple-input single-output VLC systems, where both the NLoS channel gain and ISI are considered. Under perfect channel state information (CSI), we formulate an optimal beamforming problem to maximize the secrecy rate under amplitude constraints on beamformers. The problem is shown to be nonconvex. We transform it into multiple tractable quasiconvex subproblems, and propose an iterative algorithm to solve it. To be more practical, we then consider the imperfect CSI and design the robust secure beamformers. Numerical results verify the efficiency of the proposed beamforming schemes. Moreover, it is also shown that the NLoS channel gain can improve the secrecy rate and well-designed beamformers can reverse the effect of ISI.
This work considers secure downlink transmission in indoor multiple-input, single-output visible-light communication (VLC) links. In particular, we study the design of transmit beamformers that maximize the achievable secrecy rate subject to amplitude constraints imposed by the limited dynamic range of the light-emitting diodes (LEDs). Such constraints render the design problem nonconvex and difficult to solve. We show, however, that this nonconvex problem can be transformed into a solvable quasiconvex line search problem. We also consider the more realistic case of imperfect channel information regarding the receiver's and eavesdropper's links. We tackle the worst-case secrecy rate maximization problem, again subject to amplitude constraints. In our treatment, uncertainty in the receiver's channel is due to limited feedback, and is modeled by spherical sets. On the other hand, there is no feedback from the eavesdropper, and the transmitter shall utilize the line-of-sight channel gain equation to map the eavesdropper's nominal location and orientation into an estimate of the channel gain. Thus, we derive uncertainty sets based on inaccurate information regarding the eavesdropper's location and orientation, as well as the emission pattern of the LEDs. We also consider channel mismatches caused by the uncertain non-line-of-sight components. We provide numerical examples to demonstrate the performance gain of the optimal beamformer compared with the suboptimal schemes, and the robust beamformer compared with its nonrobust counterparts. We also evaluate the worst-case secrecy rate performance of the robust beamformer in a typical VLC scenario along with the aforementioned uncertainty sources.
This paper analyzes the secrecy rate and designs the secure beamforming for an indoor visible light communication (VLC) network consisting of one transmitter, one legitimate receiver, one eavesdropper, and several friendly jammers. In the VLC network, both the main and wiretapping channels have a uniformly distributed signal input and corrupted with additive white Gaussian noise. The imperfect channel state information (CSI) is considered by using the ellipsoidal approximation method. Under the amplitude constraints of the data and the interfering signal, the secrecy rate for the VLC network is analyzed. A beamforming optimization problem is proposed to maximize the secrecy rate with the given constraints. It is shown that the optimization problem is non-convex. In this paper, it is transformed into a solvable quasi-convex linear search problem. Numerical results demonstrate the performance gain of the optimal beamformer compared to the zero-forcing scheme. Moreover, the secrecy performance under different CSI uncertainties is also provided.
In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. Specifically, we address the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario. The challenge of this problem is that it is a nonconvex optimization problem. This paper shows that the SRM problem can actually be solved in a convex and tractable fashion, by recasting the SRM problem as a semidefinite program (SDP). The SRM problem we solve is under the premise of perfect channel state information (CSI). This paper also deals with the imperfect CSI case. We consider a worst-case robust SRM formulation under spherical CSI uncertainties, and we develop an optimal solution to it, again via SDP. Moreover, our analysis reveals that transmit beamforming is generally the optimal transmit strategy for SRM of the considered scenario, for both the perfect and imperfect CSI cases. Simulation results are provided to illustrate the secrecy-rate performance gains of the proposed SDP solutions compared to some suboptimal transmit designs.
This paper studies the robust beamforming design problem for a multiple-input single-output (MISO) secrecy channel with a single-antenna eavesdropper. Due to the illegal nature, the eavesdropper may try to hide itself from being caught; thus, it could be difficult for the secrecy transmitter (S-Tx) to obtain accurate channel state information (CSI) of the eavesdropping link between S-Tx and the eavesdropper. Assuming that the CSI of the eavesdropping link belongs to a known uncertain set, this paper designs the optimal transmit strategy for the secrecy user to maximize the transmit rate under the condition that the eavesdropper cannot decode the secrecy message for all possible channel realizations of the eavesdropping link. This robust design problem is non-convex and cannot be solved by existing algorithms in the literature. By exploiting the relationship between the secrecy MISO channel and the cognitive radio (CR) MISO channel, this problem is transformed into a robust CR beamforming design problem, which can be solved efficiently by the interior point method. Numerical examples are provided to illustrate the effectiveness of the proposed algorithm.
In this letter, we investigate the secure beamforming design for multiuser multiple-input single-output interference channel with an eavesdropper. The robust secrecy rate optimization problem is studied with the imperfect channel state information. We consider the beamforming design to maximize the minimum worst case secrecy rate subject to the transmit power constraints with norm-bounded channel uncertainty. The problem is non-convex and hard to solve. We propose an effective method to reformulate this non-convex problem as a series of tractable convex program problems with linear matrix inequality and second-order cone constraints by exploiting the conservative approximation and the sequential convex approximation methods. The simulation results demonstrate the effectiveness of the proposed algorithm.