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IEEE Transactions on Information Forensics and Security

Artificial Noise Aided Secure Precoding for MIMO Untrusted Two-Way Relay Systems With Perfect and Imperfect Channel State Information

Quanzhong Li, Liang Yang

Published Apr 11, 2018• 79 citations
Publisher

Abstract

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.

DOI
10.1109/tifs.2018.2825944

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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.
Robust artificial noise (AN) aided secure precoding for an amplify-and-forward multiple-input multiple-output untrusted relay system is studied, where the relay is untrusted and willing to help forwarding multiple data streams from the source to destination. We consider that the available channel state information is imperfect and modeled by the worst case model. Our objective is to maximize the worst case secrecy rate under the robust transmit power constraints at the source and relay, by jointly designing the signal and AN precoding matrices at the source and the precoding matrix at the relay. The robust secure precoding problem is nonconvex and hard to solve. To overcome this difficulty, we propose the weighted minimum mean square error based method, where the signdefiniteness lemma is used to eliminate the channel uncertainties and an effective iterative optimization algorithm is developed. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.
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 propose a novel secure precoding scheme for the full-duplex multiple-input multiple-output (MIMO) untrusted relay network. To ensure security, the source uses a fraction of power to send artificial noise and the destination collaboratively transmits jamming signal with the harvested energy to the relay. Aiming at improving the power efficiency and keeping security simultaneously, we jointly maximize the achievable secrecy rate by optimizing the precoders of the information signal, jamming signal, artificial noise, amplification matrix, and power splitting ratio subject to the power constraints. Furthermore, to make the optimization problem solvable, we propose an iterative algorithm and deal with the non-convex constraints through concave convex procedure (CCCP). Simulation results show that the proposed precoding scheme has significantly improved the secrecy performance and power efficiency compared with the typical direct link (DL) scheme and non-cooperative jamming (No-CJ) scheme.
This paper investigates the artificial noise (AN)-aided robust secure beamforming design for multiple-input multiple-output (MIMO) two-way relaying (TWR) systems based on physical layer network coding (PNC). In terms of signal-to-interference-and-noise ratio (SINR), we propose two robust beamforming designs to optimize worst-case secrecy sum rate in the presence of an eavesdropper, where the eavesdropper's channel state information (ECSI) is imperfect. In low SINR regime, we give a robust joint beamforming design. Since the optimization problem is non-convex, we use a zero-forcing (ZF) constraint on AN beamforming, and after approximating the objective function, the non-convex problem is formulated into a semidefinite programming (SDP). On the other hand, in high SINR regime, we provide a quality-of-service (QoS)-based robust beamforming design, in which the optimal solution can be efficiently obtained by employing an iterative algorithm based on Taylor expansion and semidefinite relaxation (SDR) techniques. Numerical results show the efficiency of the proposed schemes.
Owing to the vulnerability of relay-assisted and device-to-device (D2D) communications, improving wireless security from a physical layer signal processing perspective is attracting increasing interest. Hence we address the problem of secure transmission in a relay-assisted network, where a pair of legitimate user equipments (UEs) communicate with the aid of a multiple-input multiple output (MIMO) relay in the presence of multiple eavesdroppers (eves). Assuming imperfect knowledge of the eves' channels, we jointly optimize the power of the source UE, the amplify-and-forward (AF) relaying matrix and the covariance of the artificial noise (AN) transmitted by the relay, in order to maximize the received signal-to-interference-plus-noise ratio (SINR) at the destination, while imposing a set of robust secrecy constraints. To tackle the resultant nonconvex optimization problem, a globally optimal solution based on a bi-level optimization framework is proposed, but with high complexity. Then a low-complexity sub-optimal method relying on a new penalized difference-of-convex (DC) algorithmic framework is proposed, which is specifically designed for non-convex semidefinite programs (SDPs). We show how this penalized DC framework can be invoked for solving our robust secure relaying problem with proven convergence. Our extensive simulation results show that both proposed solutions are capable of ensuring the secrecy of the relay-aided transmission and significantly improve the robustness towards the eves' channel uncertainties as compared to the non-robust counterparts. It is also demonstrated the penalized DC-based method advocated yields a performance close to the globally optimal solution.
In this paper, we investigate the physical layer security of a full-duplex decode-and-forward relay-aided system in the worst case, where all channel state informations are realistic imperfect. For the sake of confidentiality of signals transmitted from source to destination, a robust artificial noise (AN)-aided beamforming scheme is proposed. Explicitly, our objective function is that of maximizing the worst-case secrecy rate under the transmit power constraints, by jointly optimizing the beamforming matrix and AN at the source and the relay. To overcome the non-convexity of the robust AN-aided secure beamforming problem, we transform it into multi-block convex problems, where the semi-infinite linear matrix inequality is applied to eliminate the channel uncertainties. As a benefit, our proposed robust AN -aided secure beamforming scheme obtains substantial secrecy performance gains, which verifies the efficiency of the proposed scheme.