In this article, the authors focus on a correlated channel model for secure relay beamforming in the relayeavesdropper network. In this network, a single-antenna sourcedestination pair transmits secure information with the help of a amplify-and-forward (AF) relay equipped with multiple antennas. The relay cannot obtain the instantaneous channel state information (CSI) of the eavesdropper. The relay only have the knowledge of correlation information between the legitimate and eavesdropping channels. Depending on this information, we derived the conditional distribution of the eavesdropping channel. Three beamformers at the relay are studied: the zero-forcing (ZF) beamformer, the generalized match-forward (GMF) beamformer and the general-rank beamformer (GRBF). The authors found that the ZF beamformer is invalid in this system, and the GMF beamformer is the optimal rank-1 beamformer, and the GRBF is the iteratively optimal beamformer. Numerical results are presented to illustrate three beamformers' performance, and the impacts of different parameters, especially the channel correlation, on the system performance are analyzed.
In this article, the authors focus on a correlated channel model for secure relay beamforming in the relayeavesdropper network. In this network, a single-antenna sourcedestination pair transmits secure information with the help of a amplify-and-forward (AF) relay equipped with multiple antennas. The relay cannot obtain the instantaneous channel state information (CSI) of the eavesdropper. The relay only have the knowledge of correlation information between the legitimate and eavesdropping channels. Depending on this information, we derived the conditional distribution of the eavesdropping channel. Three beamformers at the relay are studied: the zero-forcing (ZF) beamformer, the generalized match-forward (GMF) beamformer and the general-rank beamformer (GRBF). The authors found that the ZF beamformer is invalid in this system, and the GMF beamformer is the optimal rank-1 beamformer, and the GRBF is the iteratively optimal beamformer. Numerical results are presented to illustrate three beamformers' performance, and the impacts of different parameters, especially the channel correlation, on the system performance are analyzed.
This article is focused on secure relay beamformer design with a correlated channel model in the relay-eavesdropper network. In this network, a single-antenna source-destination pair transmits secure information with the help of an amplify-and-forward (AF) relay equipped with multiple antennas, and the legitimate and eavesdropping channels are correlated. The relay cannot obtain the instantaneous channel state information (CSI) of the eavesdropper, and has only the knowledge of correlation information between the legitimate and eavesdropping channels. Depending on this information, we derive the conditional distribution of the eavesdropping channel. Two beamformers at the relay are studied for the approximate ergodic secrecy rate: (1) the generalized match-and-forward (GMF) beamformer to maximize the legitimate channel rate, and (2) the general-rank beamformer (GRBF). In addition, one lower-bound-maximizing (LBM) beamformer at the relay is discussed for maximizing the lower bound of the ergodic secrecy rate. We find that the GMF beamformer is the optimal rank-one beamformer, that the GRBF is the iteratively optimal beamformer, and that the performance of the LBM beamformer for the ergodic secrecy rate gets close to that of the GRBF for the approximate secrecy rate. It can also be observed that when the relay has lower power or the channel gain of the second hop is low, the performance of the GMF beamformer surpasses that of the GRBF. Numerical results are presented to illustrate the beamformers’ performance.
In this paper, we study the robust relay beamformer design problem in the relay-eavesdropper network with imperfect knowledge of the eavesdropper's channel. In this network, the half-duplexing relay is equipped with multiple antennas and employs the amplify-and-forward (AF) relaying protocol. Assuming static legitimate links, we consider the relay beamforming problem under two models for the eavesdropper's channel: 1) the Rician fading channel model, where only statistical information of the eavesdropper's channel is known by the legitimate nodes; and 2) the deterministic uncertainty model, where the uncertainty region of the eavesdropper's channel vector is modeled as a sphere. As for the optimization criteria, we use an approximation of the ergodic secrecy rate under the Rician fading model and the worst-case secrecy rate under the deterministic uncertainty model. Under both models, the optimal rank-1, match-and-forward (MF), and zero-forcing (ZF) beamformers are developed, and the equivalence of the optimal rank-1 beamformer and the optimal MF beamformer is also established. Under the Rician fading model, it is shown that the optimal ZF beamformer may have a rank greater than 1 and, therefore, could outperform the optimal MF beamformer, whereas under the deterministic uncertainty model, the optimal ZF beamformer must be rank-1. Numerical results are presented to verify the effectiveness of the proposed relay beamformers.
This paper quantifies the impact of correlated fading on secure communication of multiple amplify-and-forward (AF) relaying networks. In such a network, the base station (BS) is equipped with multiple antennas and communicates with the destination through multiple AF relays, while the message from the relays can be overheard by an eavesdropper. We focus on the practical communication scenario, where the main and eavesdropper's channels are correlated. In order to enhance the transmission security, transmit antenna selection is performed at the BS, and the best relay is chosen according to the full- or partial-relay selection criterion, which relies on the dual-hop relay channels or the second-hop relay channels, respectively. For these criteria, we study the impact of correlated fading on the network secrecy performance, by deriving an analytical approximation for the secrecy outage probability and an asymptotic expression for the high main-to-eavesdropper ratio. From these results, it is concluded that the channel correlation is always beneficial to the secrecy performance of full relay selection. However, it deteriorates the secrecy performance if partial-relay selection is used, when the number of antennas at the BS is less than the number of relays.
In this paper, we investigate the secure relay beamforming problem for simultaneous wireless information and power transfer (SWIPT) in an amplify-and-forward (AF) two-way relay network. We consider scenarios that the eavesdropper's channel state information (CSI) is and is not available. When the eavesdropper's CSI is available, our objective is to maximize the achievable secrecy sum rate under transmit power constraint and energy harvesting constraint. Since the optimization problem is nonconvex, we derive its performance upper bound, which requires 2-D search, where a semidefinite programming is solved in each step. We also propose an upper bound-based rank-one solution by employing the Gaussian randomization method. To reduce computational complexity, we transform the optimization problem into a difference-of-convex programming and propose a sequential parametric convex approximation (SPCA)-based iterative algorithm to find a locally optimal solution. Furthermore, we also propose a zero-forcing (ZF)-based suboptimal solution. Simulation results demonstrate that the upper bound-based rank-one solution archives the performance almost the same as the upper bound that has high computational complexity. The low-complexity SPCA-based locally optimal solution performs close to the upper bound. The ZF-based suboptimal solution has the lowest computational complexity among the proposed solutions. When the eavesdropper's CSI is not available, we propose an artificial noise-aided secure relay beamforming scheme.
In this paper, we investigate the secure relay beamforming problems for the amplify-and-forward (AF) relay network, where the transmitter sends the information to the receiver with the help of a multiple-antenna relay in the presence of an eavesdropper. We first study the secrecy rate maximization (SRM) problem in the case of complete channel state information (CSI). The rank-1 relay beamformer, which has been solved in our previous work in “Secure relay beamforming with imperfect channel side information,” IEEE Trans. Veh. Technol., vol. 62, no. 5, pp. 2140-2155, June 2013, is rigorously proved to be globally optimal. Then, we turn to the case of partial eavesdropper's CSI (ECSI), where the uncertainty of ECSI is characterized as a bounded region, and study the worst-case secrecy rate maximization (WCSRM) problem. Different from the common spherical uncertainty region, the uncertainty region adopted in our paper imposes independent constraints on the channel gain and direction. With the proposed uncertainty region, we give an in-depth analysis of the WCSRM problem. We solve the rank-1 relay beamformer in an explicit form and move a step further by establishing the sufficient conditions for the global optimality of the rank-1 solution. Besides, the rank-2 relay beamformer with a special singular value decomposition (SVD) structure is also considered. By reducing the optimization variables into single variable, we show that the proposed rank-2 solution can be solved by simple line search. The asymptotic optimality of the proposed rank-2 relay beamformer in the high relay power region is also proved under mild conditions. Finally, numerical results are presented to verify the analysis in the paper.
The problem of robust relay beamforming for the multiple-antenna amplify-and-forward (AF) relay network in the presence of an eavesdropper is studied in the paper, with the partial eavesdropper's channel side information (ECSI) scenario being considered. In our work, the uncertainty of ECSI is modeled by using a bounded region, which imposes independent constraints on the channel gain and direction. We propose a new rank-2 relay beamformer with a special singular value decomposition (SVD) structure, whose optimal solution for the worst-case secrecy rate maximization problem can be derived via simple line searching. Furthermore, the asymptotic optimality of the proposed rank-2 beamformer is proved in the high-relay-power region under certain condition, with the performance of the proposed beamformer being verified by using numerical experiments.