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IEEE Transactions on Signal Processing

Optimal and Robust Beamforming for Secure Transmission in MISO Visible-Light Communication Links

Ayman Mostafa, Lutz Lampe

Published Aug 29, 2016• 118 citations
Publisher

Abstract

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.

DOI
10.1109/tsp.2016.2603964

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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.
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.
Visible-light communication (VLC) is an enabling technology that exploits the lighting infrastructure to provide ubiquitous indoor broadband coverage via high-speed short-range wireless communication links. On the other hand, physical-layer security has the potential to supplement conventional encryption methods with an additional secrecy measure that is provably unbreakable regardless of the computational power of the eavesdropper. The lack of wave-guiding transmission media in VLC channels makes the communication link inherently susceptible to eavesdropping by unauthorized users existing in areas illuminated by the data transmitters. In this thesis, we study transmission techniques that enhance the secrecy of VLC links within the framework of physical-layer security. Due to linearity limitations of typical light-emitting diodes (LEDs), the VLC channel is more accurately modelled with amplitude constraints on the channel input, rather than the conventional average power constraint. Such amplitude constraints render the prevalent Gaussian input distribution infeasible for VLC channels, making it difficult to obtain closed-form secrecy capacity expressions. Thus, we begin with deriving lower bounds on the secrecy capacity of the Gaussian wiretap channel subject to amplitude constraints. We then consider the design of optimal beamformers for secrecy rate maximization in the multiple-input single-output (MISO) wiretap channel under amplitude constraints. We show that the design problem is nonconvex and difficult to solve, however it can be recast as a solvable quasiconvex line search problem. We also consider the design of robust beamformers for worst-case secrecy rate maximization when channel uncertainty is taken into account. Finally, we study the design of linear precoders for the two-user MISO broadcast channel with confidential messages. We consider not only amplitude constraints, but also total and per-antenna average power constraints. We formulate the design problem as a nonconvex weighted secrecy sum rate maximization problem, and provide an efficient search algorithm to obtain a solution for such a nonconvex problem. We extend our approach to handle uncertainty in channel information. The design techniques developed throughout the thesis provide valuable tools for tackling real-world problems in which channel uncertainty is almost always inevitable and amplitude constraints are often necessary to accurately model hardware limitations.
This paper considers improving the confidentiality of visible light communication (VLC) links within the framework of physical-layer security. We study a VLC scenario with one transmitter, one legitimate receiver, and one eavesdropper. The transmitter has multiple light sources, while the legitimate and unauthorized receivers have a single photodetector, each. We characterize secrecy rates achievable via transmit beamforming over the multiple-input, single-output (MISO) VLC wiretap channel. For VLC systems, intensity modulation (IM) via light-emitting diodes (LEDs) is the most practical transmission scheme. Because of the limited dynamic range of typical LEDs, the modulating signal must satisfy certain amplitude constraints. Hence, we begin with deriving lower and upper bounds on the secrecy capacity of the scalar Gaussian wiretap channel subject to amplitude constraints. Then, we utilize beamforming to obtain a closed-form secrecy rate expression for the MISO wiretap channel. Finally, we propose a robust beamforming scheme to consider the scenario wherein information about the eavesdropper's channel is imperfect due to location uncertainty. A typical application of the proposed scheme is to secure the communication link when the eavesdropper is expected to exist within a specified area. The performance is measured in terms of the worst-case secrecy rate guaranteed under all admissible realizations of the eavesdropper's channel.
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.
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.
Despite offering higher security than radio frequency (RF) channels, the broadcast nature of the visible light communication (VLC) channel makes VLC links inherently susceptible to eavesdropping by unauthorized users. In this work, we consider the physical-layer security of VLC links aided by friendly jamming. The jammer has multiple light sources, but does not have access to the data transmitted. The eavesdropper's reception is degraded by a jamming signal that causes no interference to the legitimate receiver. Due to the limited dynamic range of typical light-emitting diodes (LEDs), both the data and jamming signals are subject to amplitude constraints. Therefore, we begin with deriving a closed-form secrecy rate expression for the corresponding wiretap channel, and adopt secrecy rate as the performance measure. Then, we formulate a linear programming problem to maximize the secrecy rate when the eavesdropper's channel is accurately known to the jammer. Finally, we consider robust beamforming to maximize the worst-case secrecy rate when information about the eavesdropper's channel is uncertain due to location uncertainty. The robust scheme makes use of simple linear programming, making real-time implementation feasible in a variety of real-world scenarios.