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IET Communications

Achievable secrecy rate of wiretap channels incorporating multi‐input–multi‐output amplify and forward relaying

Meysam Mirzaee, Soroush Akhlaghi

Published Feb 1, 2016• 9 citations
Publisher

Abstract

This study discusses the secrecy rate of two‐hop relay‐assisted cooperative wiretap channels, incorporating multi‐antenna amplify and forward relaying in the middle of transmission. In this regard, under the Gaussian code book assumption, three main scenarios including null‐space beamforming (NSBF), rank‐1 beamforming (RBF), and the so‐called general rank beamforming (GRBF) are proposed to be employed at the relay where their achievable secrecy rates are studied. Accordingly, for NSBF, a closed‐form solution is derived, whereas the corresponding optimisation problems are formulated for the remaining cases as a standard semi‐definite programming problem. Though GRBF ranks the first in terms of the achievable secrecy rate, RBF exhibits favourable results with a much lower complexity, as the corresponding optimisation problem runs over a reduced dimension. Moreover, NSBF has a much lower complexity, as it provides an analytical solution at the expense of a decrease in the secrecy rate, and interestingly, it performs quite well when the number of eavesdroppers is less than that of the relay antennas.

DOI
10.1049/iet-com.2015.0208

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IEEE Transactions on Wireless Communications•Dec 1, 2015•55 citations
This study discusses the secrecy rate of two‐hop relay‐assisted cooperative wiretap channels, incorporating multi‐antenna amplify and forward relaying in the middle of transmission. In this regard, under the Gaussian code book assumption, three main scenarios including null‐space beamforming (NSBF), rank‐1 beamforming (RBF), and the so‐called general rank beamforming (GRBF) are proposed to be employed at the relay where their achievable secrecy rates are studied. Accordingly, for NSBF, a closed‐form solution is derived, whereas the corresponding optimisation problems are formulated for the remaining cases as a standard semi‐definite programming problem. Though GRBF ranks the first in terms of the achievable secrecy rate, RBF exhibits favourable results with a much lower complexity, as the corresponding optimisation problem runs over a reduced dimension. Moreover, NSBF has a much lower complexity, as it provides an analytical solution at the expense of a decrease in the secrecy rate, and interestingly, it performs quite well when the number of eavesdroppers is less than that of the relay antennas.
Physical layer security has received considerable attentions in recent years. Moreover, cooperative communications using some nodes of network as relays make use of the benefit of multi‐antenna systems such as increasing the secrecy capacity. This study studies a communication network incorporating some multi‐input–multi‐output amplify and forward relays in the presence of some eavesdroppers. The objective persuaded in the current work is to find the beamforming matrices at the relays to maximise the achievable secrecy rate under either individual or total power constraint at these nodes. Accordingly, three main approaches including general rank beamforming (GRBF), rank‐1 beamforming (RBF) and null‐space beamforming (NSBF) are developed. For the NSBF under the total power constraint, a closed‐form solution is obtained, while for the remaining scenarios the corresponding optimisation problem is expressed as a semi‐definite programming problem. Numerical results indicate that the RBF and NSBF methods follow GRBF in some cases and degraded from GRBF in the others. However, it is shown that these two methods have much lower complexity than GRBF.
This study investigates the achievable secrecy rate of two‐way relay‐assisted networks. It is assumed that there is no direct link between transceiver ends and the communication is carried out in two hops through the use of multi‐antenna relays in the middle of transmission, where the relays employ amplify‐and‐forward strategies. To increase the bandwidth efficiency, intending nodes exchange their confidential messages in two hops. First, both nodes simultaneously send their messages to the relay nodes. Then, throughout the second hop, the relays make use of cooperative beamforming to send their incoming information in such a way that the achievable secrecy sum rate is maximised, considering each node is subject to a minimum secrecy rate constraint. Accordingly, two beamforming strategies, named as null‐space beamforming and information leakage alignment beamforming are proposed, where their achievable secrecy sum rates are investigated and compared to existing works addressed in the literature.
This study concerns maximising the minimum achievable secrecy rate (ASR) of a two‐way relay network in the presence of an eavesdropper, in which two nodes aim to exchange messages in two hops, using a multi‐antenna relay. Throughout the first hop, the two nodes simultaneously transmit their messages to the relay. In the second hop, the relay broadcasts a combination of the received information to the users such that the transmitted signal lies in the null space of the eavesdropper's channel; this is called null space beamforming (NSBF). The best NSBF matrix for maximising the minimum ASR is studied, showing that the problem is not convex in general. To address this issue, the problem is divided into three sub‐problems: a close‐to‐optimal solution is derived by using the semi‐definite relaxation technique. Simulation results demonstrate the superiority of the proposed method w.r.t. the most well‐known method addressed in the literature.
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.
Abstract Here, the issue of physical layer security in a two‐way multi‐antenna relay network) is studied. In such a network, two multi‐antenna transceivers attempt to exchange their secret messages via a multi‐antenna relay node in the presence of an eavesdropper. Throughout the first hop, two sources send their messages to the relay node, while an eavesdropper tries to overhear these messages. Then, in the second hop, the relay attempts to send its signal in the null‐space direction of relay‐to‐eavesdropper channel to prevent eavesdropping. The main goal is to obtain effective receive and transmit beamforming vectors at transceivers as well as the beamforming matrix at the relay node to address the secrecy rate balancing problem. The underlying problem is not convex in general. To overcome this issue, the original problem is divided into three subproblems. In the first subproblem the beamforming design at the relay is optimized while in the second subproblem the receive beamforming in a closed form solution is obtained. Finally, in the last subproblem the transmit beamforming is solved using the semi‐definite relaxation and Taylor series expansion. Numerical results represent the effectiveness of the proposed method compared to the previous works in the literature.
This paper investigates the ergodic achievable secrecy rate (EASR) of multiple-antenna amplify-and-forward relay systems, where one eavesdropper can wiretap the relay. To reveal the capability of the multiple-antenna relay in improving the secrecy performance, we derive new tight closed-form expressions of the EASR for three secure transmission schemes: artificial noise aided precoding (ANP), destination based jamming (DBJ) and eigen-beamforming (EB). We also derive the lower bounds of the EASR for ANP and DBJ with a large antenna array at the relay, and investigate their corresponding asymptotic performance in the high SNR and low SNR regimes to show valuable intrinsic insights as well. Based on the asymptotic analysis, we optimally allocate the power to the information signal and the artificial noise. Both the analysis and simulation results indicate that, in the moderate-to-high SNR regime, ANP achieves considerable performance gain over DBJ and EB, while in the low SNR regime, EB outperforms the other two schemes with equal power allocation. As SNR grows large, the EASR of EB approaches a constant independent of the first hop channel. Moreover, in the high SNR regime, it is optimal to allocate around half of total power to artificial noise for ANP and most of the power to artificial noise for DBJ.