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 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 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.
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, 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.
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.
A secure downlink transmission system which is exposed to multiple eavesdroppers and is appropriate for Internet of Things (IoT) applications is considered. A worst case scenario is assumed, in the sense that, in order to enhance their interception ability all eavesdroppers are located close to each other, near the controller and collude to form joint receive beamforming. For such a system, a novel cooperative nonorthogonal multiple access (NOMA) secure transmission scheme for which an IoT device with a stronger channel condition acts as an energy harvesting relay in order to assist a second IoT device operating under weaker channel conditions, is proposed and its performance is analyzed and evaluated. A secrecy sum rate (SSR) maximization problem is formulated and solved under three constraints: 1) transmit power; 2) successive interference cancellation; and 3) quality of service. By considering both passive and active eavesdroppers scenarios, two optimization schemes are proposed to improve the overall system SSR. On the one hand, for the passive eavesdropper scenario, an artificial noise-aided secure beamforming scheme is proposed. Since this optimization problem is nonconvex, instead of using traditional but highly complex, brute-force 2-D search, it is conveniently transformed into a convex one by using an epigraph reformulation. On the other hand, for the active multiantennas eavesdroppers’ scenario, the orthogonal-projection-based beamforming scheme is considered, and by employing the successive convex approximation method, a suboptimal solution is proposed. Furthermore, since for single antenna transmission the orthogonal-projection-based scheme may not be applicable a simple power control scheme is proposed. Various performance evaluation results obtained by means of computer simulations have verified that the proposed schemes outperform other benchmark schemes in terms of SSR performance.