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.
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.
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.
In this letter, a joint design of cooperative beamforming (CB) and artificial noise (AN) is proposed for two-way amplify-and-forward (AF) relay networks to improve the security of the date exchange. Based on secrecy sum rate maximization (SSRM) criterion, such joint design problem under individual relay power constraints is mathematically hard due to the non-convex objective function. By utilizing the semidefinite relaxation (SDR) technique and successive convex approximation (SCA) algorithm, we efficiently develop a stationary point for the original SSRM design problem. Proof is also given to show that SDR is always tight and yields a rank-one solution. Simulations are presented to validate the efficiency and merits of our proposed joint CB and AN design in enhancing the secrecy sum rate.
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 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.
Owing to the vulnerability of relay-assisted communications, improving wireless security from a physical layer signal processing perspective is attracting increasing interest. Hence, we address the problem of secure transmission in a relay-assisted network, where a pair of legitimate user equipments (UEs) communicate with the aid of a multiple-input multiple output (MIMO) relay in the presence of multiple eavesdroppers (eves). Assuming imperfect knowledge of the eves' channels, we jointly optimize the power of the source UE, the amplify-and-forward relaying matrix, and the covariance of the artificial noise transmitted by the relay, in order to maximize the received signal-to-interference-plus-noise ratio at the destination, while imposing a set of robust secrecy constraints. To tackle the resultant non-convex optimization problem with tractable complexity, a new penalized difference-of-convex (DC) algorithm is proposed, which is specifically designed for solving a class of non-convex semidefinite programs. We show how this penalized DC framework can be invoked for solving our robust secure relaying problem with proven convergence. In addition, to benchmark the proposed algorithm, we subsequently propose a semidefinite relaxation-based exhaustive search approach, which yields an upper bound of the secure relaying problem, however, with significantly higher complexity. Our simulation results show that the proposed solution is capable of ensuring the secrecy of the relay-aided transmission and significantly improving the robustness toward the eves' channel uncertainties as compared with the non-robust counterparts. It is also demonstrated the penalized DC-based method advocated yields a performance close to the upper bound.