In this letter, we propose a secure beamforming scheme for physical layer network coding (PNC)-based multiple-input multiple-output (MIMO) two-way relaying system. The relay node performs PNC mapping. An eavesdropper is attempting to intercept the user information. The channel state information (CSI) of the user-to-eavesdropper channel is imperfect at the user nodes. A robust optimization problem is formulated to design beamforming vectors at the user nodes and relay. The problem is non-convex, and an algorithm is proposed to solve that. In the numerical analysis, we discuss the convergence of the proposed algorithm and the impact of the CSI error on the performance.
In this letter, we propose a secure beamforming scheme for physical layer network coding (PNC)-based multiple-input multiple-output (MIMO) two-way relaying system. The relay node performs PNC mapping. An eavesdropper is attempting to intercept the user information. The channel state information (CSI) of the user-to-eavesdropper channel is imperfect at the user nodes. A robust optimization problem is formulated to design beamforming vectors at the user nodes and relay. The problem is non-convex, and an algorithm is proposed to solve that. In the numerical analysis, we discuss the convergence of the proposed algorithm and the impact of the CSI error on the performance.
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.
In this paper, we study a two-way relay network (TWRN), in which eavesdroppers' channel state information is imperfect, and all the eavesdroppers collude to form joint receive beamforming for enhanced receptions. To ensure the robustness of the TWRN, we design the transmit beamforming and establish two secure beamforming design formulations, which combines the physical layer network coding with artificial noise technique at the relay. One secure beamforming design formulation is to minimize the total transmit power in the TWRN, and the other one is to guarantee a maximum secrecy sum rate (SSR) in the worst-case. With the help of approximation techniques, the former optimization problem is converted into a convex problem, whose semidefinite relaxation solution is rank-one. However, due to the maximum available power limit of the system, the power optimization problem may be infeasible. To overcome this problem, the SSR optimization formulation is presented, and the optimization problem is decoupled into two subproblems that can be transformed into the convex forms. Finally, it is verified by the numerical results that the proposed schemes are effective.
In this paper, physical layer security is studied for multiuser peer-to-peer (MUP2P) relay networks using amplify-and-forward (AF) protocol, where a secure user and other unclassified users coexist with an eavesdropper. Though the beamforming design has been previously investigated with perfect channel state information (CSI) in the presence of an eavesdropper, this paper focuses on researching the robust relay beamforming mechanism for MUP2P relay networks. The worst-case secrecy rate is maximized, while subject to the worst-case signal-to-interference-noise ratio constraint at each user and the total power constraint at relays under a bounded spherical region for the norm of the CSI error vector from the relays to the destination. Mathematically, the optimization problem is nonlinear and nonconvex. We propose an iterative algorithm to obtain an efficient solution of the nonconvex problem by employing S-Procedure and rank relaxation techniques. The convergence of the proposed robust algorithm is proved and its complexity is analyzed. Simulations show that the proposed design can significantly improve the performance of secure wireless communications.
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.
This work investigates the vulnerability of analog network coding (ANC) to physical layer attacks from adversarial users, when all nodes are equipped with multiple antennas. Specifically, we examine the MIMO two way relay channel (TWRC) with two users trying to communicate with each other via a relay node in the presence of a passive eavesdropper. We propose a new performance metric, namely the secrecy sum rate of the MIMO TWRC, to quantify performance. We then consider secure transmission strategies for the scenarios of no eavesdropper channel state information at the transmitters (ECSIT) and complete ECSIT, respectively. Finally, numerical results are presented to illustrate the improvement in secrecy obtained with the proposed transmission 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.