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.
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.
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.
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.
Considering existing eavesdroppers, this paper analyzes the secrecy outage probability (SOP) of the full-duplex (FD) relaying network with imperfect channel state information (CSI), where the decode-and-forward relay protocol is adopted. To enhance the physical-layer security, two relay selection schemes are proposed. The first scheme uses the maximum-minimum principle to select the optimal relay. The other selection scheme is based on partial signal-to-interference-plus-noise ratio. Then, the tight closed-form approximations of the SOP are obtained for three special CSI cases, respectively. Moreover, based on these approximated results, the effects of some system parameters are analyzed for the SOP of the relay system, including the CSI error, the number of relays, the signal-to-noise ratio (SNR) of the eavesdropper, and the residual self-interference caused by the FD model. The numerical results show that at low SNR of the eavesdropper, residual self-interference has a significantly impact on SOP, while at high SNR of the eavesdropper, this effect is negligible. In addition, the SOP of FD model is always superior to the half-duplex (HD) model when the number of relays changes.
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 studies robust transmit design for secure AF relay networks with imperfect channel state information (CSI). Two CSI error models, deterministically bounded error model and stochastic error model, are considered. In order to use the power at relays more efficiently, a joint cooperative relaying and jamming scheme is considered, where relays cooperate to forward the source signal and simultaneously they cooperate to send jamming signals to confuse the eavesdroppers. In this joint cooperative relaying and jamming framework, we address the robust joint optimization of the relay weights and the input covariance matrix of jamming signals for secrecy rate maximization (SRM), under both total and individual relay power constraints. Specifically, for the case of deterministically bounded error model, where the CSI error can be specified by an uncertainty set, we maximize the worst-case secrecy rate. While for the case of stochastic error model, where the probability distribution of the CSI error is Gaussian, we maximize the outage constrained secrecy rate. The challenge of these considered SRM-based optimizations lies in their non-convexity. This paper shows that such SRM-based optimization can be solved in a convex fashion and via solving a sequence of semidefinite programs (SDPs). Numerical results are presented to show the efficacy of the proposed scheme.