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arXiv:1705.07337 · IEEE Transactions on Signal Processing

Full-Duplex Bidirectional Secure Communications Under Perfect and Distributionally Ambiguous Eavesdropper's CSI

Qiang Li, Ying Zhang, Jingran Lin, Sissi Xiaoxiao Wu

Published May 26, 2017• 20 citations
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Abstract

Consider a full-duplex (FD) bidirectional secure communication system, where two communication nodes, named Alice and Bob, simultaneously transmit and receive confidential information from each other, and an eavesdropper, named Eve, overhears the transmissions. Our goal is to maximize the sum secrecy rate (SSR) of the bidirectional transmissions by optimizing the transmit covariance matrices at Alice and Bob. To tackle this SSR maximization (SSRM) problem, we develop an alternating difference-of-concave (ADC) programming approach to alternately optimize the transmit covariance matrices at Alice and Bob. We show that the ADC iteration has a semiclosed form beamforming solution, and is guaranteed to converge to a stationary solution of the SSRM problem. Besides the SSRM design, this paper also deals with a robust SSRM transmit design under a moment-based random channel state information (CSI) model, where only some roughly estimated first- and second-order statistics of Eve's CSI are available, but the exact distribution or other high-order statistics is not known. This moment-based error model is different from the widely used bounded-sphere error model and the Gaussian random error model. Under the considered CSI error model, the robust SSRM is formulated as an outage probability-constrained SSRM problem. By leveraging the Lagrangian duality theory and difference-of-concave (DC) programming, a tractable safe solution to the robust SSRM problem is derived. The effectiveness and the robustness of the proposed designs are demonstrated through simulations.

DOI
10.1109/tsp.2017.2709270

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Consider a full-duplex (FD) bidirectional secure communication system, where two communication nodes, named Alice and Bob, simultaneously transmit and receive confidential information from each other, and an eavesdropper, named Eve, overhears the transmissions. Our goal is to maximize the sum secrecy rate (SSR) of the bidirectional transmissions by optimizing the transmit covariance matrices at Alice and Bob. To tackle this SSR maximization (SSRM) problem, we develop an alternating difference-of-concave (ADC) programming approach to alternately optimize the transmit covariance matrices at Alice and Bob. We show that the ADC iteration has a semiclosed form beamforming solution, and is guaranteed to converge to a stationary solution of the SSRM problem. Besides the SSRM design, this paper also deals with a robust SSRM transmit design under a moment-based random channel state information (CSI) model, where only some roughly estimated first- and second-order statistics of Eve's CSI are available, but the exact distribution or other high-order statistics is not known. This moment-based error model is different from the widely used bounded-sphere error model and the Gaussian random error model. Under the considered CSI error model, the robust SSRM is formulated as an outage probability-constrained SSRM problem. By leveraging the Lagrangian duality theory and difference-of-concave (DC) programming, a tractable safe solution to the robust SSRM problem is derived. The effectiveness and the robustness of the proposed designs are demonstrated through simulations.
This paper considers the physical-layer secrecy design for full-duplex (FD) bidirectional communications in the presence of an eavesdropper (Eve). The goal of this work is to maximize the sum secrecy rate (SSR) of the bidirectional transmissions via appropriately designing the transmit covariance matrices at the legitimate nodes. To this end, we propose an alternating difference-of-concave (ADC) approach to iteratively optimizing the transmit covariance matrices. We show that each ADC iteration can be carried out efficiently with a semi-closed- form solution, and that every limit point of ADC iterations is a stationary solution of the SSR maximization problem. Besides the SSR maximization, this paper also deals with a robust SSR maximization problem to account for imperfect CSI of Eve. Assuming a moment-based random CSI error model (i.e., only mean and covariance of the error are known, but the exact distribution is not known), robust transmit designs based on Markov's inequality and the robust conic reformulation are developed. The efficacy of the proposed designs is demonstrated through simulations.
This paper considers multiple-input multiple-output (MIMO) full-duplex (FD) two-way secrecy systems. Specifically, both multi-antenna FD legitimate nodes exchange their own confidential message in the presence of an eavesdropper. Taking into account the imperfect channel state information (CSI) of the eavesdropper, we formulate a robust sum secrecy rate maximization (RSSRM) problem subject to the outage probability constraint of the achievable sum secrecy rate and the transmit power constraint. Unlike other existing channel uncertainty models, e.g., norm- bounded and Gaussian-distribution, we exploit a moment-based random distributed CSI uncertainty model to recast our formulate RSSRM problem into convex optimization frameworks based on a Markov's inequality and robust conic reformulation, i.e., semidefinite programming (SDP). In addition, difference-of-concave (DC) approximation is employed to iteratively tackle the transmit covariance matrices of these legitimate nodes. Simulation results are provided to validate our proposed FD approaches.
This paper deals with the physical-layer (PHY) security problem for a full-duplex (FD) two-way relay system, where two FD sources exchange confidential information through an FD relay. Assuming imperfect channel state information (CSI) of the eavesdropper (Eve), we aim for a robust amplify-andforward (AF) relaying scheme that maximizes the sum secrecy rate of the two-way transmissions. Different from the widely used norm-bounded deterministic error model and the Gaussian random error model, we adopt a moment-based random error model to capture the imperfection of Eve's CSI. Specifically, the CSI error is assumed to be randomly distributed with given mean and covariance, but the exact distribution or other highorder statistics are not known. Under this moment-based error model, we formulate an outage-constrained sum secrecy rate maximization (OC-SRM) problem, which guarantees the outage sum secrecy rate is kept below certain threshold for arbitrary distributions fulfilling the mean and covariance. To tackle this OC-SRM problem, we first reexpress the outage probability into a more explicit form, and then develop a semidefinite relaxation (SDR)-based alternating difference-of-concave (DC) programming approach to computing a safe solution. Simulation results corroborate the robustness of the proposed design when varying the Eve's CSI error distribution.
Consider a full-duplex two-way relay network, where two legitimate nodes simultaneously transmit and receive confidential information through a full-duplex multiantenna relay, in the presence of an eavesdropper. To secure the communications, an artificial-noise (AN)-aided amplify-and-forward (AF) strategy is employed at the relay, with a goal of maximizing the sum secrecy rate of the two-way transmissions. This sum secrecy rate maximization (SSRM) problem is nonconvex by nature, but can be converted into the form of the difference-of-concave (DC) functions after the semidefinite relaxation (SDR). Thus, the classical DC programming naturally applies. We prove that the SDR is tight and give a specific way to recover a stationary solution of the SSRM problem from the relaxed DC problem. Moreover, to reduce the iteration complexity of DC, we proposed an inexact DC framework, which uses an approximate solution to iterate, rather than a globally optimal one. The convergence of the inexact DC to a stationary solution of the SSRM problem is also established.
This paper investigates an energy-constrained relay-assisted secure communication system in the presence of a legitimate source-destination pair and a passive eavesdropper with imperfect channel state information (CSI). The energy-constrained relay exploits a power splitting (PS) protocol to simultaneously harvest energy and decode information from the received signal from the source, and then forwards the confidential signal to the full-duplex (FD) destination while it simultaneously transmits artificial noise (AN) to confuse the passive eavesdropper. This robust beamforming design is developed by maximizing the secrecy rate under the constraints of energy harvesting (EH) requirement at the relay and AN transmit power at the destination. Specifically, we formulate the joint relay beamforming and PS ratio as well as the AN power optimization as a non-convex quadratically-constrained problem. In order to circumvent this non-convexity issue, we decompose the original problem into three subproblems which can be determined by the proposed semidefinite relaxation (SDR) and successive convex optimization methods. Furthermore, we derive closed-form expressions for the optimal solutions of each subproblem. Finally, the original non-convex problem can be solved through a convergence guaranteed iterative algorithm. Simulation results are provided to demonstrate the effectiveness and superior performance of the proposed robust design compared with the benchmark schemes.
Consider a two-way communication scenario where two single-antenna nodes, operating under full-duplex mode, exchange information to one another through the aid of a (full-duplex) multiantenna relay, and there is another single-antenna node who intends to eavesdrop. The relay employs artificial noise (AN) to interfere the eavesdropper's channel, and amplify-forward Alamouti-based rank-two beamforming to establish the two-way communication links of the legitimate nodes. Our problem is to optimize the rank-two beamformer and AN covariance for sum secrecy rate maximization (SSRM). This SSRM problem is nonconvex, and we develop an efficient solution approach using semidefinite relaxation (SDR) and minorization-maximization (MM). We prove that SDR is tight for the SSRM problem and, thus, introduces no loss. Also, we consider an inexact MM method where an approximate but computationally cheap MM solution update is used in place of the exact update in conventional MM. We show that this inexact MM method guarantees convergence to a stationary solution to the SSRM problem. The effectiveness of our proposed approach is further demonstrated by an energy-harvesting scenario extension, and by extensive simulation results.