This paper studies the secure beamforming design in a multiple-antenna three-node system where two source nodes exchange messages with the help of an untrusted relay node. The relay acts as both an essential signal forwarder and a potential eavesdropper. Both two-phase and three-phase two-way relay strategies are considered. Our goal is to jointly optimize the source and relay beamformers for maximizing the secrecy sum rate of the two-way communications. We first derive the optimal relay beamformer structures. Then, iterative algorithms are proposed to find source and relay beamformers jointly based on alternating optimization. Furthermore, we conduct asymptotic analysis on the maximum secrecy sum-rate. Our analysis shows that when all transmit powers approach infinity, the two-phase two-way relay scheme achieves the maximum secrecy sum rate if the source beamformers are designed such that the received signals at the relay align in the same direction. This reveals an important advantage of signal alignment technique in against eavesdropping. It is also shown that if the source powers approach zero, the three-phase scheme performs the best while the two-phase scheme is even worse than direct transmission. Simulation results have verified the efficiency of the proposed secure beamforming algorithms as well as the analytical findings.
This paper studies the secure beamforming design in a multiple-antenna three-node system where two source nodes exchange messages with the help of an untrusted relay node. The relay acts as both an essential signal forwarder and a potential eavesdropper. Both two-phase and three-phase two-way relay strategies are considered. Our goal is to jointly optimize the source and relay beamformers for maximizing the secrecy sum rate of the two-way communications. We first derive the optimal relay beamformer structures. Then, iterative algorithms are proposed to find source and relay beamformers jointly based on alternating optimization. Furthermore, we conduct asymptotic analysis on the maximum secrecy sum-rate. Our analysis shows that when all transmit powers approach infinity, the two-phase two-way relay scheme achieves the maximum secrecy sum rate if the source beamformers are designed such that the received signals at the relay align in the same direction. This reveals an important advantage of signal alignment technique in against eavesdropping. It is also shown that if the source powers approach zero, the three-phase scheme performs the best while the two-phase scheme is even worse than direct transmission. Simulation results have verified the efficiency of the proposed secure beamforming algorithms as well as the analytical findings.
From security perspective, a friendly relay may help to keep the confidential messages from being eavesdropped, while an untrusted relay may intentionally eavesdrop the messages when relaying. This paper studies the secure beamforming for multiple-input multiple-output (MIMO) two-way communications, where two source nodes exchange information with the help of an untrusted relay node. The relay adopts amplify-and-forward (AF) strategy and acts as both an essential helper and a potential eavesdropper. Our goal is to maximize the secrecy sum rate of the bidirectional links by jointly optimizing the source and relay beamformers. For the two-phase two-way relay scheme, we first derive the optimal structure of the relay beamformer and then propose an iterative algorithm to jointly optimize the source and relay beamformers. Then, a comprehensive study on the asymptotical performance is conducted by letting the source and relay powers approach zero or infinity. In particular, we show that when all powers approach infinity, the two-way relay scheme achieves the maximum secrecy rate if the transceiver beamformers are designed such that the received signals at the relay can be aligned to be parallel.
In this paper, we investigate energy-efficient secure communications in an untrusted two-way relay network, where two source nodes exchange messages via an untrusted relay. Considering both security threats and energy limitation, the performance metric secure energy efficiency is defined as the ratio of the secrecy sum rate to the total power consumption. Our objective is to maximize the secure energy efficiency by jointly designing the source and relay beamformers. We first derive the expression of secure energy efficiency under a general beamforming configuration. Then, an iterative algorithm based on the techniques of alternate optimization, fractional programming, barrier function method and semi-definite programming, is proposed to find the optimal solutions of the source and relay beamformers. Our analysis shows that the proposed scheme can not only solve the problem of secure energy efficiency maximization but also be applicable for solving the problem of secrecy sum rate maximization. Simulation results demonstrate that the proposed scheme achieves a good gain in terms of secure energy efficiency.
Full-duplex (FD) technique is very promising to support enormous data for 5G networks since it can greatly improve the spectrum efficiency. However, the secrecy performance of FD communication systems still remains largely unknown. As an initial step towards this end, this paper studies the physical layer security-based beamforming design in a FD two-way amplify-and-forward relay system, where two source nodes exchange messages with the assistance of an untrusted relay. The untrusted relay is willing to forward the messages and may also work as an eavesdropper to intercept the confidential messages. Our objective is to optimize the source and relay beamformers for maximizing the secrecy sum rate of the two-way communications with imperfect self-interference cancellation. For a specific system configuration, we first derive the expression of secrecy sum rate. By utilizing signal alignment technique and gradient method, we then propose two iterative algorithms to find the optimal source and relay beamforming matrices, respectively. Simulation results demonstrate that when the number of antennas at the relay is appropriate and the interference-to-noise ratio is in a low region the proposed FD scheme significantly improves the secrecy sum rate over conventional schemes.
An amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network composed of a source, a relay, and a destination is considered, where transmit beamforming is employed both at the source and at the relay. The relay is a user who is willing to help the communication from the source to the destination. In our paper, however, the relay is untrusted in the sense that it may make a passive security attack; that is, it may decode messages of the source. We consider two ways to transmit confidential information of the source to the destination: noncooperative secure beamforming and cooperative secure beamforming. In the noncooperative scheme, the relay is simply treated as an eavesdropper, and does not participate in communication. In the cooperative scheme, the relay is asked to relay signals from the source to the destination. In this paper, the source and relay beamforming is jointly designed to maximize the secrecy rate in the cooperative scheme. The conditions under which the cooperative scheme achieves a higher secrecy rate than the noncooperative scheme are derived in the low and high signal-to-noise ratio (SNR) regimes of the source-relay and relay-destination links. The performance of the secure beamforming schemes is compared through extensive numerical simulations.
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.
Abstract Here, the issue of physical layer security in a two‐way multi‐antenna relay network) is studied. In such a network, two multi‐antenna transceivers attempt to exchange their secret messages via a multi‐antenna relay node in the presence of an eavesdropper. Throughout the first hop, two sources send their messages to the relay node, while an eavesdropper tries to overhear these messages. Then, in the second hop, the relay attempts to send its signal in the null‐space direction of relay‐to‐eavesdropper channel to prevent eavesdropping. The main goal is to obtain effective receive and transmit beamforming vectors at transceivers as well as the beamforming matrix at the relay node to address the secrecy rate balancing problem. The underlying problem is not convex in general. To overcome this issue, the original problem is divided into three subproblems. In the first subproblem the beamforming design at the relay is optimized while in the second subproblem the receive beamforming in a closed form solution is obtained. Finally, in the last subproblem the transmit beamforming is solved using the semi‐definite relaxation and Taylor series expansion. Numerical results represent the effectiveness of the proposed method compared to the previous works in the literature.