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IET Communications

Non‐linear transceiver design for secure communications with artificial noise‐assisted MIMO relay

Lei Zhang, Yunlong Cai, Benoı̂t Champagne, Minjian Zhao

Published Jan 12, 2017• 4 citations
Publisher

Abstract

This study investigates the problem of physical layer security for amplify‐and‐forward (AF) multiple‐input multiple‐output (MIMO) relay systems operating in the presence of a passive eavesdropper. Specifically, the authors consider the robust design of an artificial noise (AN)‐assisted non‐linear transceiver employing Tomlinson–Harashima precoding (THP), with imperfect knowledge of the legitimate channel states. The design problem can be reformulated as a two‐level optimisation, where the outer problem aims to optimise the source precoder as a function of the relay precoder, while the inner problem at the relay aims to jointly optimise the relay precoder as well as the power allocation between the AN and the information‐bearing signals. To solve the inner problem, the authors adopt a bisection method which attempts to maximise the AN power level, to confuse the eavesdropper, while satisfying the mean‐squared‐error requirement for the intended user. Some relaxation for the objective function is applied to transform the problem into a standard convex optimisation one. Regarding the outer problem, closed‐form solutions for the precoders can be derived by an iterative method based on the Karush–Kuhn–Tucker conditions. Simulation results illustrate the superior secrecy performance provided by the proposed non‐linear transceiver design with AN and THP.

DOI
10.1049/iet-com.2016.0617

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This study investigates the problem of physical layer security for amplify‐and‐forward (AF) multiple‐input multiple‐output (MIMO) relay systems operating in the presence of a passive eavesdropper. Specifically, the authors consider the robust design of an artificial noise (AN)‐assisted non‐linear transceiver employing Tomlinson–Harashima precoding (THP), with imperfect knowledge of the legitimate channel states. The design problem can be reformulated as a two‐level optimisation, where the outer problem aims to optimise the source precoder as a function of the relay precoder, while the inner problem at the relay aims to jointly optimise the relay precoder as well as the power allocation between the AN and the information‐bearing signals. To solve the inner problem, the authors adopt a bisection method which attempts to maximise the AN power level, to confuse the eavesdropper, while satisfying the mean‐squared‐error requirement for the intended user. Some relaxation for the objective function is applied to transform the problem into a standard convex optimisation one. Regarding the outer problem, closed‐form solutions for the precoders can be derived by an iterative method based on the Karush–Kuhn–Tucker conditions. Simulation results illustrate the superior secrecy performance provided by the proposed non‐linear transceiver design with AN and THP.
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.
We consider an amplify-and-forward (AF) relay network with multiple source-destination pairs in the presence of an eavesdropper. This paper studies the robust artificial noise (AN) assisted joint transceiver optimization for secure communication with imperfect channel state information (CSI) of legitimate users and no CSI regarding the eavesdropper. The goal is to design the linear precoding matrix of the relay and the linear equalizer of each destination, such that the transmit power for the information-bearing signals and forwarded background noises at the relay can be minimized subject to the quality of service (QoS) constraints at the destinations. The remainder of the constrained total power is used to generate the AN for jamming the eavesdropper. Although such a power minimization problem is nonconvex, we recast it into two semidefinite programming (SDP) subproblems which can be solved using interior-point methods. Then this problem can be solved with the alternating iterative optimization algorithm. Simulations demonstrate that the proposed algorithm can significantly reduce the sensitivity to imperfect CSI, while degrading the eavesdropper's capability of intercepting.
In this study, security schemes at the physical layer are proposed for an amplify‐and‐forward relay system in the presence of a passive eavesdropper. We focus on maximising the transmit power of the artificial noise (AN) to degrade the minimum mean square error (MMSE) level at the eavesdropper, while achieving MMSE constraint for the desired receiver. Assuming that the desired receiver and the passive eavesdropper possess perfect channel state information (CSI), AN is designed to lie in the null space of legitimate channels. However, the available CSI is impossible to be perfect in practice. Therefore the authors present a robust beamforming scheme which maximises the worst‐case transmit power of the AN under the condition of imperfect CSI and recovers a large fraction of the performance in the perfect CSI case. A classical alternating optimisation algorithm is proposed to obtain the relay beamforming weights, and simulation results show the benefit of proposed schemes.
This paper addresses joint transceiver design for secure downlink communications over a multiple-input multiple-output relay system in the presence of multiple legitimate users and malicious eavesdroppers. Specifically, we jointly optimize the base station (BS) beamforming matrix, the relay station (RS) amplify-and-forward transformation matrix, and the covariance matrix of artificial noise, so as to maximize the system worst-case secrecy rate in the presence of the colluding eavesdroppers under power constraints at the BS and the RS, as well as quality of service constraints for the legitimate users. This problem is very challenging due to the highly coupled design variables in the objective function and constraints. By adopting a series of transformation, we first derive an equivalent problem that is more tractable than the original one. Then, we propose and fully develop a novel algorithm based on the penalty concave-convex procedure (penalty-CCCP) to solve the equivalent problem, where the difficult coupled constraint is penalized into the objective and the resulting nonconvex problem is solved at each iteration by resorting to the CCCP method. It is shown that the proposed joint transceiver design algorithm converges to a stationary solution of the original problem. Finally, our simulation results reveal that the proposed algorithm achieves better performance than other recently proposed transceiver designs.
In this study, physical layer security techniques are studied for multi‐user peer‐to‐peer relay networks using amplify‐and‐forward protocol in the presence of an eavesdropper. Two system designs are considered: the minimum achievable secrecy rate maximisation and the total transmit power minimisation. First, considering user fairness, the authors study the max–min achievable secrecy rate problem subject to a total transmit power constraint. Mathematically, the optimisation problem is non‐linear and non‐convex. They propose a polynomial time algorithm based on the bisection technique to solve it. Second, they study the total transmit power minimisation problem which aims at minimising the total transmit power at relays such that individual secrecy rate for each user is satisfied. The total power optimisation problem is also non‐convex, so they use the relaxation technique to transform it into a convex problem which can be efficiently solved by the gradient‐based algorithms. Numerical evaluation of the obtained secrecy rate and transmit power results shows that the proposed designs can significantly improve the performance of secure wireless communications.
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.