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Artificial Noise Aided Secure Multicasting Design under the Secrecy Outage Probability Constraint

Bo Wang, Pengcheng Mu, Weile Zhang, Hui‐Ming Wang

Published Dec 1, 2017• 3 citations
Publisher

Abstract

This paper studies the artificial noise (AN) aided secure transmission design in a multiple-input- single-output multicast channel where a common message is transmitted to multiple receivers and only statistical channel state information of the eavesdropper is available. In this scenario, there may be no valid null space which allows the AN not to affect the legitimate receivers, and the traditional null-space AN scheme may not be applicable. To find the optimal design, we formulate a secrecy outage probability (SOP) constrained secrecy rate maximization problem which applies to an arbitrary number of the receivers. We adopt a novel approximation of the intractable SOP constraint and establish an efficient algorithm which solves the approximated problem to global optimality. The effectiveness of AN as well as the proposed solution is confirmed by simulation results. It is shown that the AN aided approach performs much better than pure beamforming even when there is no valid null space.

DOI
10.1109/glocom.2017.8254497

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This paper studies the artificial noise (AN) aided secure transmission design in a multiple-input- single-output multicast channel where a common message is transmitted to multiple receivers and only statistical channel state information of the eavesdropper is available. In this scenario, there may be no valid null space which allows the AN not to affect the legitimate receivers, and the traditional null-space AN scheme may not be applicable. To find the optimal design, we formulate a secrecy outage probability (SOP) constrained secrecy rate maximization problem which applies to an arbitrary number of the receivers. We adopt a novel approximation of the intractable SOP constraint and establish an efficient algorithm which solves the approximated problem to global optimality. The effectiveness of AN as well as the proposed solution is confirmed by simulation results. It is shown that the AN aided approach performs much better than pure beamforming even when there is no valid null space.
This paper investigates the physical layer security in a multiple-input-single-output multicast channel, where a common message is transmitted to multiple receivers and only statistical channel state information of the eavesdropper is available. We consider transmitting some artificial noise (AN) along with the information-bearing signal to improve secrecy. To find the optimal AN design, we formulate a secrecy outage probability (SOP) constrained secrecy rate maximization problem. For solving this problem, we adopt a novel transformation of the intractable SOP constraint and establish an efficient algorithm which solves the transformed problem to global optimality. We also propose a low-complexity refinement method to reduce the conservatism incurred by the transformation and an efficient algorithm to find a suboptimal solution when the information-bearing signal is transmitted using single-stream beamforming. Our solution is found to be a valuable generalization of the traditional null-space AN scheme. According to our simulation results, when the number of receivers is less than that of transmit antennas, distributing AN uniformly in the null space of the legitimate channel vectors is near-optimal. When there is no valid null space, transmitting AN will interfere with some legitimate receivers, and the secrecy performance can also be improved with carefully designed AN.
This paper studies the artificial noise (AN) aided beamforming design in the multiple-input, single-output, and multiple-eavesdropper wiretap channel from the perspective of secrecy outage. Unlike many existing works, which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper’s antennas from the perspective of secrecy outage. Furthermore, the optimal power allocation between the information-bearing signal and the AN is found under both general conditions and the conservative assumption that the eavesdropper can be arbitrarily close to the transmitter or his receiver noise power can be arbitrarily low. It is also found that the increase in the eavesdropper’s antenna number is equivalent to requiring a smaller SOP under the conservative assumption. The results in this paper can help generalize existing design solutions for single-antenna eavesdroppers to multi-antenna eavesdroppers.
The artificial noise (AN) aided beamforming design in the MISOME (multiple-input, single-output, multiple-eavesdropper) wiretap channel is studied from the perspective of secrecy outage. Unlike many existing works which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper's antennas from the perspective of secrecy outage. The power allocation problem is also studied and the closed-form optimal solution is obtained. It is found that the increase in the eavesdropper's antenna number is equivalent to requiring a smaller SOP.
In this letter, we investigate a robust transmit optimization design based on an artificial noise (AN)-aided precoding scheme for maximizing secrecy rate in a multiple-input multiple-output multiple-eavesdropper multicast network where a transmitter sends confidential information to multiple intended users and provides energy for multiple idle nodes while multiple passive eavesdroppers try to overhear the secret information. Supposing Gaussian CSI uncertainties, the proposed outage-constrained secrecy rate maximization (OC-SRM) problem is nonconvex and its analytical analysis is more challenging than several existing OC-SRM schemes. Technically, to circumvent this mathematically intractable secrecy problem, we resort to low SNR approximation and some conservative approximations (e.g., Bernstein-type inequality and sphere bounding) to reformulate the OC-SRM problem into two convex subproblems which can be efficiently solved by the off-the-shelf optimization solver. Simulation results are provided to validate the security performance of the robust AN-aided precoding design.
The secrecy rate maximization with the artificial noise (AN) aided beamforming for the multipel-input-single-output (MISO) wiretap channel is addressed in this paper under the constraint of secrecy outage probability. The channel state information (CSI) of the main channel is assumed to be perfectly known while the CSI of the eavesdropper is modeled as a complex Gaussian random vector. The generalized AN scheme where the AN is not constrained to be orthogonal to the information-bearing signal is considered. The complete solution to the maximum achievable secrecy rate and the corresponding optimal power allocation between the information-bearing signal and the AN is obtained without making any approximation of the secrecy outage probability constraint. The result shows that the optimal AN is always orthogonal to the information-bearing signal.
This paper considers artificial noise (AN) aided transmit designs for multiuser MISO systems in the eyes of service integration. Specifically, we combine two sorts of services, and serve them simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver. The confidential message is kept perfectly secure from all the unauthorized receivers. Our goal is to jointly design the optimal input covariances for the multicast message, confidential message, and AN, such that the achievable secrecy rate region is maximized subject to the sum power constraint. This secrecy rate region maximization (SRRM) problem is a nonconvex vector maximization problem. To handle it, we reformulate the SRRM problem into a provably equivalent scalar optimization problem and propose a searching method to find all of its Pareto optimal points. The equivalent scalar optimization problem is identified as a secrecy rate maximization (SRM) problem with the quality of multicast service (QoMS) constraints. Further, we show that this equivalent QoMS-constrained SRM problem, albeit nonconvex, can be efficiently handled based on a two-stage optimization approach, including solving a sequence of semidefinite programs (SDPs). Moreover, we also extend the SRRM problem to an imperfect channel state information (CSI) case where a worst case robust formulation is considered. In particular, while transmit beamforming is generally a suboptimal technique to the SRRM problem, we prove that it is optimal for the confidential message transmission whether in the perfect CSI scenario or in the imperfect CSI scenario. For implementation efficiency, we also analyze the computational complexity of our proposed methods and put forward two suboptimal schemes and two possible extensions. Finally, numerical results demonstrate that the AN-aided transmit designs are effective in expanding the achievable secrecy rate regions, and that the suboptimal strategies can achieve near-optimal performance.