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.
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.
In this paper, we consider a two-way relay network with two sources and multiple cooperative relays in the presence of an eavesdropper. To guarantee the secrecy, a null space beamforming scheme is applied, where the relay beamforming vector lies in the nullspace of the equivalent channel of relay link from two sources to the eavesdropper. Our goal is to obtain the optimal beamforming vector as well as two sources' transmit power subject to various criteria. We propose three different approaches and solve them in an alternating iterative way, where subproblems for solving beamforming and sources' power are formulated in each iteration, respectively. First, we minimize the total transmit power under secrecy rate constraint at two sources. For beamforming vector subproblem, two different methods, semi-definite programming (SDP) and sequential quadratic programming (SQP), are proposed, where we analyze and verify SQP has lower complexity than SDP. Second, we maximize the secrecy sum rate, subject to total transmit power constraint. The beamforming vector subproblem is equivalent to a generalized Rayleigh quotient problem with rank constraint. Third, the problem of minimum per-user secrecy rate maximization under the total power constraint is investigated for user fairness. An iterative procedure utilizing the SDP with bisection search method is proposed to solve beamforming subproblem. In each approach the subproblem with two sources' power is formulated as a single variable problem and solved by Newton's method with line search. Simulation results demonstrate the validity of proposed approaches and algorithms for both symmetric and asymmetric scenarios.
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 two-way multiantenna relay systems, confidential information can be easily intercepted by eavesdroppers. To overcome this problem, two secure beamforming schemes are proposed: secrecy sum rate maximization beamforming (SSRMB) and null space beamforming (NSB). For the SSRMB scheme, the nonconvex secrecy sum rate maximization problem is solved using a successive convex approximation strategy, which is convergent. The obtained beamforming solution is locally optimal to the original problem. For the special scenario where the number of antennas at the relay is more than the number of eavesdroppers, the NSB scheme with a low complexity is proposed. The beamforming solution is obtained by solving a generalized Rayleigh quotient problem. Simulation results demonstrate that the proposed schemes can effectively improve the security performance, and the SSRMB scheme has a fast convergence rate.
In this paper, we investigate a two-way relay networks consisted of two sources, multiple cooperative relays, and an eavesdropper. To guarantee the secure communication, a null space beamforming strategy is applied, where the relay beamforming vector is design to lie in the null space of the equivalent channel from two sources to the eavesdropper. Aiming to minimize the total transmit power under individual secrecy rate constraint at two sources, an alternating iteration method is proposed to calculate the relay beamforming vector as well as sources' transmit power. For relay beamforming vector optimization subproblem, two different approaches, semi-definite programming (SDP) relaxation and sequential quadratic programming (SQP) method, are proposed. Subproblem with two sources' transmit power optimization is formulated as a single variable problem and solved by Newton method with line search effectively. Through the numerical simulations, we verify the effectiveness of proposed algorithm. Moreover, with computational complexity analysis, we show that the SQP method has lower complexity than SDP, and further verify it in terms of executing time.
In this paper, secure wideband beamforming design is investigated for two-way multiple-input multiple-output (MIMO) relaying systems with one eavesdropper. Due to the wideband signals exchanged by two sources via the relay, inter-symbol-interference (ISI) occurs inevitably and makes the beamforming design more challenging than the narrowband beamforming design. To sufficiently combat the ISI, the tapped delay lines are deployed at the relay. Besides, to reduce the computational complexity at the tapped delay lines based relay, the analog beamforming structure is also considered, and thus the MIMO relay beamforming can be distinctly partitioned into a transmit beamforming and a receive beamforming bridged by a single link. Joint optimization of the transmit and receive beamformings at both the relay and two sources is considered to maximize the secrecy sum rate (SSR) of the two-way MIMO relaying systems. Since the joint optimization is nonconvex and intractable, an iterative algorithm is proposed to decompose the original SSR maximization problem into four individual subproblems that can be reformulated as three types of convex problems, i.e., the generalized Rayleigh quotient problems, the polynomial time differential convex problem, and the semidefinite programming problem. A suboptimal solution for the secure transmit and receive beamformings at all nodes can then be obtained iteratively. Finally, numerical experiments are conducted to corroborate the effectiveness of our proposed iterative algorithm in terms of the achievable maximum SSR and ISI suppression.
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.