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IEEE Transactions on Information Forensics and Security

Secure Beamforming for Full-Duplex MIMO Two-Way Untrusted Relay Systems

Shuangrui Zhao, Jia Liu, Yulong Shen, Xiaohong Jiang, Norio Shiratori

Published Jan 1, 2020• 43 citations
Publisher

Abstract

This paper focuses on a full-duplex multiple-input multiple-output two-way untrusted relay system, and investigates the optimal beamforming design of such system to maximize its secrecy sum rate (SSR) based on the physical layer security technology. We first provide the modeling of SSR under a general beamforming setting as well as the theoretical formulation of the optimal beamforming design problem. Based on the ideal assumption that the full channel state information is available, we then develop a novel theoretical framework to solve the optimal design problem and thus establish an upper bound on SSR, where the techniques of alternate optimization, fractional programming, semi-definite programming and barrier function method are jointly employed. With the consideration of the constraints in practical implementations, we further propose two sub-optimal beamforming design solutions based on either Wiener prediction or asymptotic approximation. The issue of how to reduce the computational complexity in the optimal relay beamforming design is also discussed in this paper. Finally, we present extensive numerical results to illustrate our theoretical findings and to demonstrate the performance of the proposed sub-optimal beamforming design solutions.

DOI
10.1109/tifs.2020.3001733

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This paper focuses on a full-duplex multiple-input multiple-output two-way untrusted relay system, and investigates the optimal beamforming design of such system to maximize its secrecy sum rate (SSR) based on the physical layer security technology. We first provide the modeling of SSR under a general beamforming setting as well as the theoretical formulation of the optimal beamforming design problem. Based on the ideal assumption that the full channel state information is available, we then develop a novel theoretical framework to solve the optimal design problem and thus establish an upper bound on SSR, where the techniques of alternate optimization, fractional programming, semi-definite programming and barrier function method are jointly employed. With the consideration of the constraints in practical implementations, we further propose two sub-optimal beamforming design solutions based on either Wiener prediction or asymptotic approximation. The issue of how to reduce the computational complexity in the optimal relay beamforming design is also discussed in this paper. Finally, we present extensive numerical results to illustrate our theoretical findings and to demonstrate the performance of the proposed sub-optimal beamforming design solutions.
This paper focuses on the multiple-input-multiple-output (MIMO) two-way relay system with an untrusted relay and investigates its secure and energy-efficient precoding design issue based on the physical layer security technology. We first provide theoretical modeling for the index of secrecy energy efficiency (SEE) and formulate the optimal precoding design for SEE maximization (SEEM) as a high-dimensional non-convex programming problem. By exploring the techniques like fractional programming, alternate optimization and semi-definite programming, we then develop a hierarchical theoretical framework to solve the SEEM problem and thus to identify the optimal precoding designs for the source and relay. Furthermore, we demonstrate the proposed theoretical framework is also applicable to the problem of precoding design for secrecy sum rate maximization. Finally, with the help of generalized singular value decomposition, we propose a sub-optimal relay precoding design scheme with significantly lower computational complexity. Extensive numerical results provided in the paper indicate that the proposed schemes can remarkably improve the SEE performance in MIMO two-way untrusted relay systems.
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.
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.
Physical-layer secure is an important issue for untrusted relay systems. In this paper, we investigate secure precoding design for non-regenerative multiple-input multiple-output untrusted two-way relay systems, where artificial noise (AN) is applied at the source and the relay is untrusted. We aim to maximize the secrecy sum rate by jointly designing the source's signal and AN precoders and the relay's precoder, under the sources and relay transmit power constraints. We consider two scenarios that perfect and imperfect channel state information of all the channels is available. For the former, we convert the secure precoding problem to a difference of convex programming and develop a constrained concave convex procedure based iterative algorithm which can obtain a local optimal solution. We also provide asymptotic analysis on the maximum secrecy sum rate when the relay transmit power approaches infinity, and propose alternating optimization method to compute asymptotic optimal precoders. For the latter, we model the channel uncertainties by using worst-case criterion and propose the weighted minimum mean square error based method to solve the robust secure precoding problem. Numerical simulations are presented to show the effectiveness of our proposed schemes.
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.