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IEEE Transactions on Vehicular Technology

Destination-Aided Cooperative Jamming for Dual-Hop Amplify-and-Forward MIMO Untrusted Relay Systems

Jun Xiong, Longwang Cheng, Dongtang Ma, Jibo Wei

Published Oct 13, 2015• 74 citations
Publisher

Abstract

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.

DOI
10.1109/tvt.2015.2490099

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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.
We consider a secrecy dual-hop amplify-and-forward (AF) untrusted relay network, where the relay is willing to forward the signal to the destination while acting as a potential eavesdropper. Assuming that all these nodes are equipped with multiple antennas, we propose a joint destination aided cooperative jamming and precoding at both the source and the relay scheme, with the objective to maximize the worst case secrecy rate. The formulated problem is highly non-convex due to the maximization of the difference of several logarithmic determinant (log-det) functions in the CSI uncertainty region. To handle this challenge, we propose to linearize these log-det terms. After linearization, we tackle the CSI uncertainty based on epigraph reformulation and the sign-definiteness lemma. Finally, an alternating optimization (AO) algorithm is proposed to solve the reformulated problem. Numerical results are provided to demonstrate the performance of the proposed scheme.
An amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network composed of a source, a relay, and a destination is considered, where transmit beamforming is employed both at the source and at the relay. The relay is a user who is willing to help the communication from the source to the destination. In our paper, however, the relay is untrusted in the sense that it may make a passive security attack; that is, it may decode messages of the source. We consider two ways to transmit confidential information of the source to the destination: noncooperative secure beamforming and cooperative secure beamforming. In the noncooperative scheme, the relay is simply treated as an eavesdropper, and does not participate in communication. In the cooperative scheme, the relay is asked to relay signals from the source to the destination. In this paper, the source and relay beamforming is jointly designed to maximize the secrecy rate in the cooperative scheme. The conditions under which the cooperative scheme achieves a higher secrecy rate than the noncooperative scheme are derived in the low and high signal-to-noise ratio (SNR) regimes of the source-relay and relay-destination links. The performance of the secure beamforming schemes is compared through extensive numerical simulations.
Abstract—In this paper, the problem of secure transmission in two-hop amplify-and-forward (AF) systems with an untrusted relay is investigated. To prevent the untrusted relay from intercepting the source message and to achieve positive secrecy rate, the destination-based cooperative jamming (DBCJ) technique is used. In this method the destination sends an intended jamming signal to the relay. This jamming signal helps protecting the source message from being captured reliably at the untrusted relay, while the destination cancels itself intended jamming signal. The optimal power allocation (OPA) technique is considered for the presented system. It is observed that the objective function is a quasiconcave function at high signal-to-noise-ratio (SNR) regimes. Based on this OPA technique, we study the ergodic secrecy rate (ESR) and the secrecy outage probability (SOP) of the system when the source and relay are equipped with a single antenna while the destination is equipped with largescale antenna arrays (LSA). Using the achieved closed-form expressions, one can evaluate the performance of the secure system easily and fast and also, they provide significant insight for system design. Finally, simulation results indicate the accuracy of the derived expressions.
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.
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 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.