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 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 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, we consider a two-way relay network system which contains multiple cooperative relays transmitting information between two sources with attendance of an eavesdropper. A null space beamforming scheme is applied to ensure the secrecy in system. Our goal is achieving maximal secrecy sum rate with a certain level power transmit. In [1], authors propose an approach to solve Secrecy Sum Rate Maximization (SSRM) problem, whereas we use another approach based on Different of Convex Functions Algorithm (DCA).
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 letter studies cooperative secure beamforming for amplify-and-forward (AF) relay networks in the presence of multiple eavesdroppers. Under both total and individual relay power constraints, we propose two schemes, namely secrecy rate maximization (SRM) beamforming and null-space beamforming. In the first scheme, our design problem is based on SRM. Using a suboptimal, but convex, technique-semidefinite relaxation (SDR), we show that this problem can be handled by performing a one-dimensional search which involves solving a sequence of semidefinite programs (SDPs). To reduce the complexity, in the second scheme, we instead maximize the information rate at the destination while completely eliminating the information leakage to all eavesdroppers. We prove that this problem can be exactly solved by SDR with one SDP only. Simulation results demonstrate the performance gains of the two proposed designs.
This paper investigates the physical-layer security of a multiuser peer-to-peer (MUP2P) relay network for amplify-and-forward (AF) protocol, where a secure user and other unclassified users coexist with a multi-antenna eavesdropper and the eavesdropper can wiretap the confidential information in both two cooperative phases. Our goal is to optimize the transmit power of the source and the beamforming weights of the relays jointly for secrecy rate maximization subject to the minimum signal-to-interference-noise-ratio (SINR) constraint at each user, and the individual and total power constraints. Mathematically, the optimization problem is non-linear and non-convex, which does not facilitate an efficient resource allocation algorithm design. As an alternative, a null space beamforming scheme is adopted at the relays for simplifying the joint optimization and eliminating the confidential information leakage in the second cooperative phase, where the relay beamforming vector lies in the null space of the equivalent channel of the relay to eavesdropper links. Although the null space beamforming scheme simplifies the design of resource allocation algorithm, the considered problem is still non-convex and obtaining the global optimum is very difficult, if not impossible. Employing a sequential parametric convex approximation (SPCA) method, we propose an iterative algorithm to obtain an efficient solution of the non-convex problem. Besides, the proposed joint design algorithm requires a feasible starting point, we also propose a low complexity feasible initial points searching algorithm. Simulations demonstrate the validity of the proposed strategy.