In this paper, we study the physical layer security in a two-way relay system consisting of two transceivers, one eavesdropper, and multiple relays. We study the system in case of the channel state information (CSI) of the eavesdropper is unknown, and hence artificial noise is used to degrade the signal to noise ratio at the eavesdropper. In order to reserve the maximum possible power for artificial noise, we consider the problem of minimizing the total power of the information signal transmitted by the relays, under quality of service constraints at the legitimate transceivers. This problem has been solved using semidefinite programming (SDP) and second order cone programming (SOCP) methods. Here, aiming to significantly decrease the complexity, we propose a novel approach to find the optimal solution using the generalized eigenvalue. We show that in most cases, we can provide a closed-form expression of the optimal solution. In addition, our proposed solution can be used for all quadratically constrained quadratic programs (QCQPs) with positive definite objective function and two constraints. Simulation results demonstrate the effectiveness of our algorithm in terms of optimality and low complexity compared to SDP.
In this paper, we study the physical layer security in a two-way relay system consisting of two transceivers, one eavesdropper, and multiple relays. We study the system in case of the channel state information (CSI) of the eavesdropper is unknown, and hence artificial noise is used to degrade the signal to noise ratio at the eavesdropper. In order to reserve the maximum possible power for artificial noise, we consider the problem of minimizing the total power of the information signal transmitted by the relays, under quality of service constraints at the legitimate transceivers. This problem has been solved using semidefinite programming (SDP) and second order cone programming (SOCP) methods. Here, aiming to significantly decrease the complexity, we propose a novel approach to find the optimal solution using the generalized eigenvalue. We show that in most cases, we can provide a closed-form expression of the optimal solution. In addition, our proposed solution can be used for all quadratically constrained quadratic programs (QCQPs) with positive definite objective function and two constraints. Simulation results demonstrate the effectiveness of our algorithm in terms of optimality and low complexity compared to SDP.
Ahstract- This paper studies the physical layer security in a two-way relay system (TWRS) consisting of two transceivers, one eavesdropper, and multiple relays when the channel state information (CSI) of the eavesdropper is available. We consider the problem of maximizing the secrecy sum rate by optimizing the relay beamforming vector under relays' total power constraint. The optimization problem has been formulated in the literature as a product of three Rayleigh quotients, which is very difficult to solve, and the best proposed solution was a suboptimal solution to the null space beamforming. Here, we propose two approaches: 1) Optimal solution to the null space beamforming approach, and 2) Ignoring one Rayleigh quotient (IORQ) approach (which has not been proposed before). In the first approach, we convert the nonconvex product of two Rayleigh quotients into a convex problem with one dimensional search using semidefinite programming (SDP). Then we significantly reduce the complexity of solving the problem using the generalized eigenvalues. In the second approach, we look for the beamforming vector that does not eliminate the complete information signal at the eavesdropper aiming to increase the whole secrecy sum rate. Numerical results show that the proposed algorithms provide higher secrecy sum rates than the existing algorithms.
This paper studies the problem of secure information exchange between two sources via multiple relays in the presence of an eavesdropper.To this end, we propose a relay beamforming scheme, i.e., relay beamforming with artificial noise (RBwA), where the relay beamforming vector and the artificial noise vector are jointly designed to maintain the received signal-to-interference-ratio (SINR) at the two sources over a predefined Quality of Service (QoS) threshold while limiting the received SINR at the eavesdropper under a predefined secure threshold.For comparsion, the relay beamforming without artificial noise (RBoA) is also considered.We formulate two optimization problems for the two schemes, where our goal is to seek the optimal beamforming vector to minimize the total power consumed by relay nodes such that the secrecy of the information exchange between the two sources can be protected.Since both optimization problems are nonconvex, we solve them by semidefinite program (SDP) relaxation theory.Simulation results show that, via beamforming design, physical layer secrecy of two-way relay networks can be greatly improved and our proposed RBwA outperforms the RBoA in terms of both low power consumption and low infeasibility rate.
This paper considers a two-way relay network, where two source nodes exchange messages through several relays in the presence of an eavesdropper, and the channel state information (CSI) of the eavesdropper is imperfectly known. The amplify-and-forward relay protocol is used and the relay beamforming weights are designed. The model is built up to minimize the total relay transmit power while guaranteeing the quality of service at users and preventing the eavesdropper from decoding the signals. Due to the imperfect CSI, a semi-infinite programming problem is obtained. An algorithm is proposed to solve the problem, and the iterative points are updated through the linesearch technique, where the feasibility are preserved during iterations. The optimality property is analyzed. The obtained subproblems are quadratic constrained quadratic programming problems, either with less than 4 constraints or with only one variable, which are solved optimally. Simulation results demonstrate the importance of the proposed model, and imply that the proposed algorithm is efficient and converges very fast, where more than 85% of the problems are solved optimally.
In this paper, we propose a hybrid cooperative beamforming and jamming scheme to enhance the physical-layer security of a single-antenna-equipped two-way relay network in the presence of an eavesdropper. The basic idea is that in both cooperative transmission phases, some intermediate nodes help to relay signals to the legitimate destination adopting distributed beamforming, while the remaining nodes jam the eavesdropper, simultaneously, which takes the data transmissions in both phases under protection. Two different schemes are proposed, with and without the instantaneous channel state information of the eavesdropper, respectively, and both are subjected to the more practical individual power constraint of each cooperative node. Under the general channel model, it is shown that both problems can be transformed into a semi-definite programming (SDP) problem with an additional rank-1 constraint. A current state of the art technique for handling such a problem is the semi-definite relaxation (SDR) and randomization techniques. In this paper, however, we propose a penalty function method incorporating the rank-1 constraint into the objective function. Although the so-obtained problem is not convex, we develop an efficient iterative algorithm to solve it. Each iteration is a convex SDP problem, thus it can be efficiently solved using the interior point method. When the channels are reciprocal such as in TDD mode, we show that the problems become second-order convex cone programming ones. Numerical evaluation results are provided and analyzed to show the properties and efficiency of the proposed hybrid security scheme, and also demonstrate that our optimization algorithms outperform the SDR technique.
We consider an amplify-and-forward (AF) relay network with multiple source-destination pairs in the presence of an eavesdropper. This paper studies the robust artificial noise (AN) assisted joint transceiver optimization for secure communication with imperfect channel state information (CSI) of legitimate users and no CSI regarding the eavesdropper. The goal is to design the linear precoding matrix of the relay and the linear equalizer of each destination, such that the transmit power for the information-bearing signals and forwarded background noises at the relay can be minimized subject to the quality of service (QoS) constraints at the destinations. The remainder of the constrained total power is used to generate the AN for jamming the eavesdropper. Although such a power minimization problem is nonconvex, we recast it into two semidefinite programming (SDP) subproblems which can be solved using interior-point methods. Then this problem can be solved with the alternating iterative optimization algorithm. Simulations demonstrate that the proposed algorithm can significantly reduce the sensitivity to imperfect CSI, while degrading the eavesdropper's capability of intercepting.
In this paper, we address the security of a two-way relay network in the presence of an eavesdropper, where each node is only equipped with single antenna. We propose two-phase distributed analog network coding, or distributed beamforming and power allocation to enhance the secrecy sum rate of the data exchange. In the first phase, the two terminals broadcast their information data simultaneously to all the relay nodes. In the second phase, three different security schemes are proposed: optimal beamforming, null-space beamforming, and artificial noise beamforming. In the first scheme, the objective is to achieve the maximum secrecy sum rate of the two terminals. Mathematically, the objective function is difficult to optimize. In the second scheme, we maximize the total information exchanged while we eliminate the information leakage completely, subject to the total transmission power constraint. We show that the problem has a unique and global optimum, which can be solved using bisection method. When the instantaneous channel state information of the eavesdropper is not available, we propose an artificial noise beamforming in the third scheme. We minimize the information transmission power so that the artificial noise power is maximized to eliminate information leakage, under the constraints of quality of service (QoS) required by terminals. It is a second-order convex cone programming (SOCP) problem, thus can be efficiently solved using interior point methods. Numerical results are provided and analyzed to show the properties and efficiency of the proposed designs.