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International Symposium on Telecommunications

The achievable secrecy rate of multi-antenna AF relaying using joint transmit and receive beamforming

Meysam Mirzaee, Soroush Akhlaghi

Published Sep 1, 2014• 3 citations
Publisher

Abstract

Physical layer security has attracted a great deal of attentions in recent years. This is achieved through using the physical layer characteristics to help sender to transfer data reliably with perfect secrecy. Using multiple-antenna relay node can improve the secrecy capacity of such channel. In this paper, we study the cooperative wiretap channel in which secure data transmission is achieved with the help of a MIMO Amplify and Forward (AF) relay. In such network, it is assumed multiple eavesdroppers attempt to listen to the relay transmitted signal and try to decode the source message. We assume the relay makes use of separated transmit/receive beamforming vectors, dubbed rank-one beamforming matrix. The beamforming vectors are computed such that the achievable secrecy rate is maximized, assuming the relay is subject to a maximum transmit power constraint. Accordingly, it is shown that the problem of finding proper receive beamforming vector can be translated into a scalar optimization problem, where using that the transmit beamforming vector can be obtained through solving a Semi-Definite Programming (SDP) problem.

DOI
10.1109/istel.2014.7000872

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Physical layer security has attracted a great deal of attentions in recent years. This is achieved through using the physical layer characteristics to help sender to transfer data reliably with perfect secrecy. Using multiple-antenna relay node can improve the secrecy capacity of such channel. In this paper, we study the cooperative wiretap channel in which secure data transmission is achieved with the help of a MIMO Amplify and Forward (AF) relay. In such network, it is assumed multiple eavesdroppers attempt to listen to the relay transmitted signal and try to decode the source message. We assume the relay makes use of separated transmit/receive beamforming vectors, dubbed rank-one beamforming matrix. The beamforming vectors are computed such that the achievable secrecy rate is maximized, assuming the relay is subject to a maximum transmit power constraint. Accordingly, it is shown that the problem of finding proper receive beamforming vector can be translated into a scalar optimization problem, where using that the transmit beamforming vector can be obtained through solving a Semi-Definite Programming (SDP) problem.
Secure communications using physical layer characteristics has attracted many attentions in recent years. Secrecy capacity of communication systems can be increased by using multiple-antenna nodes. In this paper, we concentrate on the cooperative wiretap channel in which confidential messages are sent from a source to a legitimate receiver with the help of a relay in the presence of an eavesdropper. We study the secrecy capacity of Amplify and Forward (AF) relaying under peak power constraint at the relay node. To this end, we first evaluate an achievable secrecy rate for Gaussian input by solving a nonconvex optimization problem. Then, we prove the converse by using the secrecy capacity of genie-aided channel as an upper bound of the secrecy capacity of interested channel. We show that this upper bound is achievable and equal to achievable secrecy rate of Gaussian input.
In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers PSand PR, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.
This paper considers secure communication for amplify-and-forward (AF) relay networks with finite alphabet input. The joint optimization of power selection and beamforming design for improving the physical layer security of AF relay networks with single and multiple eavesdroppers is investigated. For the case with one eavesdropper, we transform the problem of multi-variable beamforming design into a single-variable optimization problem through semi-definite programming and solve it with one-dimensional optimization techniques. Moreover, the corresponding source power is obtained by utilizing the relation between the mutual information and minimum mean square error. Then, an iterative two-step algorithm is proposed to maximize the achievable secrecy rate. In the presence of multiple eavesdroppers, a zero-forcing beamforming scheme, where the confidential signal is nulled out in the direction of all eavesdroppers, is proposed to enhance the physical layer security. We decouple the source power and the beamforming vector by transforming the achievable secrecy rate into a single-variable function of the source power. Then, the suboptimal source power and the corresponding beamforming vector with low-complexity are derived. Numerical examples show that the proposed schemes significantly enhance the secrecy performance of the AF relay networks.
In this paper, we study robust joint beamforming and cooperative jamming (CJ) in a secure decode-and-forward (DF) relay system in the presence of multiple eavesdroppers, in which a multi-antenna DF relay employs transmit beamforming to help the source deliver information to the destination and simultaneously generates Gaussian artificial noise to confuse these eavesdroppers. We assume that all the channel state information (CSI) is imperfectly known at the relay subject to norm-bounded CSI errors. Our objective is to maximize the achievable secrecy rate at the destination by jointly optimizing the transmit beamforming vector of information signals and the covariance matrix of jamming signals at the relay subject to its total transmit power constraint. Although this problem is non-convex and in general difficult to be solved, we obtain its optimal solution via the technique of semi-definite relaxation (SDR) together with a one-dimensional (1-D) search. Specifically, we prove that the SDR is tight for the problem of our interest. Finally, numerical results are provided to validate our proposed scheme.
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.
The idea of multiuser (nodes) cooperation is an efficient way to improve the physical-layer security of a wireless transmission in the presence of passive eavesdroppers. However, due to the half-duplex constraint of the practical transceivers, two phases are required for one round of data transmission, which grants the eavesdroppers two opportunities to wiretap the information. Therefore, protecting the data transmissions in both phases is critical. Toward this end, we propose a joint cooperative beamforming, jamming, and power-allocation scheme to enhance the security of an amplify-and-forward (AF) cooperative relay network in this paper. Different from the existing works assuming that the source node always uses its total power, we show that the secrecy rate is a quasi-concave function of the power of the source node so that allocating its total power may not be optimal. The beamformer design and power optimization problem can be solved by a bisection method together with a generalized eigenvalue decomposition, which has a semiclosed form and is computationally very convenient. Simulations show that the joint scheme greatly improves the security.