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.
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.
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.
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.
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.
In this paper, energy-efficient secure communications via untrusted two-way relaying are investigated considering physical layer security to prevent the relays from intercepting the confidential information of users. The performance metric of secure energy efficiency (EE), defined as the ratio of the secrecy sum rate to the total power consumption, is maximized by jointly optimizing power allocation for all nodes, with the constraints of the maximum allowed power and the minimum target secrecy rate. To deal with this intractable nonconvex optimization problem, some optimization methods termed as fractional programming, alternate optimization, penalty function method, and difference of convex functions programming, are jointly applied to address a solution scheme with comparatively lower complexity. With these above-mentioned optimization methods, the primal problem is transformed into simple subproblems hierarchically so as to adopt the corresponding optimization algorithm. By simulations, the achievable secure EE, the secrecy sum rate and the total transmission power of the proposed scheme are compared with those of secrecy sum rate maximization. It is demonstrated that the proposed scheme can improve secure EE remarkably yet at the cost of secrecy sum rate loss. This fact also reveals the inherent tradeoff between energy and security.
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.
In this paper, we investigate the security issue of a two-hop amplify-and-forward multiple-input multiple-output wireless relay network in the existence of a multiantenna eavesdropper. The optimal scheme to achieve the secrecy capacity involves a nonconvex optimization and is still an open problem. Aiming to find an efficient way to enhance the secrecy rate with a tractable complexity, we propose a suboptimal joint source and relay linear precoding and power allocation scheme. In the scheme, the source node adopts a generalized singular value decomposition (SVD)-based precoding to transmit the signal in the first phase, and the relay node forwards the received signal based on the SVD precoding in the null-space of the wiretap channel in the second phase. Power allocations in both phases are optimized to maximize the secrecy rate by an alternating iterative optimization algorithm. Each iteration involves two subproblems. One has a water-filling solution and the other has a closed-form solution or a water-filling-like solution as well, both of which are computationally very efficient. The iteration converges fast and we prove that it guarantees to find a stationary optimum. Furthermore, we show that when the eavesdropper has equal or more antennas than the source does, the secrecy rate is a quasi-concave function of the source power so that allocating all the source power is generally not optimal. Numerical evaluation results are provided to show the effectiveness of the iterative algorithm and the proposed secrecy scheme.