A MIMO secure two-hop wireless communication system is considered in this paper. In this model, there are no direct links between the source-destination and the source-eavesdropper. The problem is maximizing the secrecy capacity of the system over all possible amplify and forward (AF) relay strategies, such that the power consumption at the source node and the relay node is limited. When all the nodes are equipped with single antenna, this non-convex optimization problem is fully characterized. When all the nodes (except the intended receiver) are equipped with multiple antennas, the optimization problem is characterized based on the generalized eigenvalues-eigenvectors of the channel gain matrices.
A MIMO secure two-hop wireless communication system is considered in this paper. In this model, there are no direct links between the source-destination and the source-eavesdropper. The problem is maximizing the secrecy capacity of the system over all possible amplify and forward (AF) relay strategies, such that the power consumption at the source node and the relay node is limited. When all the nodes are equipped with single antenna, this non-convex optimization problem is fully characterized. When all the nodes (except the intended receiver) are equipped with multiple antennas, the optimization problem is characterized based on the generalized eigenvalues-eigenvectors of the channel gain matrices.
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.
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.
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.
The problem of secure unicast communication over multihop wireless relay networks with directed links in the presence of an eavesdropper is considered. In the existing literature this problem has been considered in one or both of the following two scenarios: (A) relay nodes employ relaying schemes, such as Decode-and-Forward (DF), (B) the source communicates with the destination over a two-hop relay network. We argue that computationally complex relaying schemes such as DF render end-to-end performance characterization intractable, without providing any performance guarantee in general channel and network scenarios. Therefore, we consider one of the simplest relaying scheme: Amplify-and-Forward (AF) that allows us to provide guarantees on the optimal performance over a wide range of channel conditions. A node performing AF-relaying scales and forwards the signal received at its input. Further, with AF-relaying the end-to-end performance characterization problem remains tractable for much larger class of networks than those that can be considered with other relaying schemes. The key contribution of this work is twofold. We first provide the optimal vector of scaling factors that maximizes the achievable AF secrecy rate, no matter which relay the eavesdropper listens to. Further, we prove that in high-SNR regime, the optimal AF secrecy rate thus achieved is within a constant gap from the cutset upper bound on the secrecy capacity.
Cooperative communication in wireless relay systems can improve the physical layer security, and the relay selection has great impacts on the security performances. In this paper the relay selection in Amplify-and-Forward (AF) cooperative networks is investigated. The system model constitutes of a source, an eavesdropper, a destination, and a number of intermediate nodes with secrecy constraints. The proposed optimal selection (OS) algorithm is based on the instantaneous channel state information (CSI) of two hops, jointly protects the target destination against eavesdropping and interference. To simplify the complexity of OS, the suboptimal selection (SS) algorithm is also presented, which is based on the instantaneous of the first hop and the statistical CSI of the second hop respectively. The secrecy capacity and secrecy outage probability of these two relay selection algorithms are analyzed. Simulation results of OS and SS validate our theoretical analysis and show enhancement in the secrecy rate over the direct transmission.