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.
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.
In this paper, we investigate the security issue of a two-hop amplify-and-forward MIMO wireless relay networks in the existence of a multi-antenna eavesdropper. The optimal scheme to achieve the secrecy capacity involves a non-convex optimization and is still an open problem. Aiming to find an efficient way to enhance the secrecy rate, we propose a suboptimal joint source and relay linear precoding scheme. In the scheme, the source node adopt a generalized singular value decomposition (GSVD) based precoding to transmit the signal in the first phase, and the relay node forwards the received signal based on SVD in the null-space of the wiretap channel in the second phase. Power allocations in both phases are optimized to maximize the secrecy rate. An alternating iterative optimization algorithm is proposed to solve the problem. The algorithm is computationally efficient and guarantees to converge to a local optimum. Numerical evaluation results are provided to show the effectiveness of the iterative algorithm and the proposed secrecy scheme.
Simultaneous wireless information and power transfer (SWIPT) is able to prolong the lifetime of energy-constrained wireless networks. In this paper, we study the security issue of a nonregenerative multiple-input multiple-out (MIMO) relay system with SWIPT. When the full channel state information (CSI) of the eavesdropper is available, we aim to maximize the secrecy rate under the source and relay transmit power constraints and energy-harvesting (EH) constraints at the multiple EH receivers by jointly designing the source and relay beamforming matrices, which is a nonconvex optimization and is still an open problem. In order to enhance the secrecy rate effectively, we first transform the optimization into a difference of convex programming and propose a sequential parametric convex approximation-based iterative algorithm which is able to achieve a local optimum. To reduce the complexity, we also propose a singular value decomposition (SVD)-generalized SVD-based method to simplify the optimization into a joint source and relay power allocation problem. The alternating optimization is employed to find a suboptimal solution of the joint power allocation problem. When the CSI of the eavesdropper is unknown, we propose an artificial-noise (AN) aided joint source and relay beamforming scheme, which can maximize the AN power to jam the eavesdropper under the limited source and relay transmit power and satisfy the quality of service of the receiver. Simulation results have shown the effectiveness of our proposed schemes.
In this paper, we propose a joint source-relay precoding scheme to secure an amplify-and-forward multiple-input multiple-output wireless relay network in the existence of a multi-antenna eavesdropper. Different from existing works that only consider some specific signal design to simplify the problem, we take both the direct links from the source to the destination and to the eavesdropper into account, and investigate the general joint signal covariance matrices optimization problem to maximize the secrecy rate, which leads to a difficult non-convex optimization problem. To handle it, we propose a group alternating optimization algorithm to find a solution, which alternately optimizes the signal covariance matrix and the linear precoding matrix at the source and the relay, respectively. For optimizing the linear precoding matrix at the relay, the problem is still non-convex, and we propose a minorization-maximization (MM) method to handle it. The MM method transforms the original non-convex problem into a series of convex problems and guarantees the convergence of a local optimum. For optimizing the signal covariance matrix at the source, we reveal the convex-concave property of the problem, and find its global optimum using a barrier method combined with the Newton iteration. We also provide an initialization method to trigger the algorithm and analyze the convergence and complexity. The numerical results show the computational efficiency and the prominent performance of the proposed algorithm.
In this paper, we consider a dual-hop amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay network, where the source, relay, and destination are each equipped with multiple antennas. The relay is untrusted if it is willing to forward the signal to the destination and, at the same time, acts as a potential eavesdropper to interpret the message from the source. Since there exists no direct link between the source and the destination, a positive secrecy rate cannot be obtained. Addressing this issue, we propose a joint destination-aided cooperative jamming and precoding at both the source and the relay scheme: joint source, relay, and destination precoding (JP). We target at maximizing the secrecy rate by jointly designing the source, relay, and destination precoding matrices and propose an alternating iterative optimization algorithm to tackle the nonconvex problem. Then, a comprehensive study on the asymptotic performance is conducted in a high signal-to-noise ratio (SNR) regime. In particular, we present simple closed-form expressions for the two key performance parameters in the asymptotic secrecy rate, i.e., the high-SNR slope and the high-SNR power offset. Finally, numerical results are conducted to demonstrate the validity of the proposed secure scheme and its performance analysis.
This paper investigates the physical-layer security of a multiuser peer-to-peer (MUP2P) relay network for amplify-and-forward (AF) protocol, where a secure user and other unclassified users coexist with a multi-antenna eavesdropper and the eavesdropper can wiretap the confidential information in both two cooperative phases. Our goal is to optimize the transmit power of the source and the beamforming weights of the relays jointly for secrecy rate maximization subject to the minimum signal-to-interference-noise-ratio (SINR) constraint at each user, and the individual and total power constraints. Mathematically, the optimization problem is non-linear and non-convex, which does not facilitate an efficient resource allocation algorithm design. As an alternative, a null space beamforming scheme is adopted at the relays for simplifying the joint optimization and eliminating the confidential information leakage in the second cooperative phase, where the relay beamforming vector lies in the null space of the equivalent channel of the relay to eavesdropper links. Although the null space beamforming scheme simplifies the design of resource allocation algorithm, the considered problem is still non-convex and obtaining the global optimum is very difficult, if not impossible. Employing a sequential parametric convex approximation (SPCA) method, we propose an iterative algorithm to obtain an efficient solution of the non-convex problem. Besides, the proposed joint design algorithm requires a feasible starting point, we also propose a low complexity feasible initial points searching algorithm. Simulations demonstrate the validity of the proposed strategy.
In this paper, we study the precoder design problem for secrecy rate maximization in a decode-and-forward (DF)-based multiple-input multiple-output (MIMO) relay network. The system model considered here consists of a source, a trusted relay, a legitimate receiver and an eavesdropper, all mounted with multiple antennas. Our objective is to maximize the achievable secrecy rate of this DF-based MIMO relay wiretap system subject to a total transmit power constraint. Since the formulated secrecy rate maximization (SRM) problem is nonconvex in general, we solve it by employing a successive convex approximation (SCA) method. With the SCA method, the nonconvex part of the formulated problem is linearized to its first-order Taylor expansion. Then, the nonconvex SRM problem can be iteratively solved through successive convex programming of its convexified version, and thus an iterative precoding algorithm is developed. Moreover, the theoretical result is further extended to the case when multiple eavesdroppers are simultaneously present. Finally, numerical simulations are provided to evaluate the performance of the proposed algorithm. Results show that our algorithm can converge fast to a near-optimal solution.