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IEEE International Conference on Acoustics Speech and Signal Processing

Robust relay beamforming for multiple-antenna amplify-and-forward relay system in the presence of eavesdropper

Xiyuan Wang, Zhongshan Zhang, Keping Long

Published May 1, 2014• 5 citations
Publisher

Abstract

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.

DOI
10.1109/icassp.2014.6854697

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IEEE International Conference on Acoustics Speech and Signal Processing•Apr 1, 2015•4 citations
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.
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.
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 addresses the problem of secure amplify-and-forward (AF) relaying for multiple-input multiple output (MIMO) relaying networks in the presence of multiple eavesdroppers. Assuming practical imperfect eavesdroppers' channel state information (ECSI), we propose a robust approach to optimize the relay AF matrix, subject to power constraint, in order to maximize the received signal-to-interference-plus-noise ratio (SINR) at the destination while satisfying a set of secrecy constraints. The ECSI errors are assumed to fall within some predefined bounded sets. Since the resultant optimization problem is non-convex and semi-infinite, we transform it into a form constituted by the differences of convex functions (DC) using suitable matrix transformation techniques. Then an algorithmic solution with proven convergence is proposed by resorting to the penalty-DC algorithm (P-DCA). Experimental results show the security of the proposed transceiver design against eavesdropping and the robustness against the channel uncertainties.
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.
This letter studies the secure cooperative transmission for an amplify-and-forward (AF) relay network in the presence of multiple multi-antenna eavesdroppers. Since the perfect channel state information (CSI) of the eavesdroppers are not available, we propose a robust joint distributed beamforming and artificial noise scheme to maximize the worst-case secrecy rate of the network, under the total power constraint of all the relay nodes. With the semidefinite relaxation (SDR) technique, the design can be solved by a one-dimension search which involves a sequence of semidefinite programming (SDP). Simulation results demonstrate the validity of the proposed strategy.
In this paper, we address physical layer security for amplify-and-forward (AF) multi-antenna relay systems in the presence of multiple eavesdroppers. A robust joint design of cooperative beamforming (CB) and artificial noise (AN) is proposed with imperfect channel state information (CSI) of both the destination and the eavesdroppers. We aim to maximize the worst-case secrecy rate subject to the sum power and the per-antenna power constraints at the relay. Such joint design problem is non-convex. By utilizing the semidefinite relaxation (SDR) technique, S-procedure and the successive convex approximation (SCA) algorithm, the original non-convex optimization problem is recast into a series of semidefinite programs (SDPs) which can be efficiently solved using interior-methods. Simulation results are presented to verify the effectiveness of the proposed design.