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Ergodic Secrecy Capacity of Dual-Hop Multiple-Antenna AF Relaying Systems

Rui Zhao, Yongming Huang, Wei Wang, Vincent K. N. Lau

Published Dec 1, 2015• 3 citations
Publisher

Abstract

This paper investigates the ergodic secrecy capacity (ESC) 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 lower bounds of the ESC for two secure transmission schemes: artificial noise aided precoding (ANP) and eigen-beamforming (EB). We also derive the lower bound of the ESC for ANP with a large antenna array at the relay, and investigate their corresponding asymptotic performance in the high and low SNR regimes. 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 EB, while in the low SNR regime, EB outperforms ANP with equal power allocation. As SNR grows large, the ESC of EB approaches a constant only related to the number of relay antennas. Moreover, in the high SNR regime, it is optimal to allocate around half of total power to artificial noise for ANP.

DOI
10.1109/glocom.2015.7417212

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This paper investigates the ergodic secrecy capacity (ESC) 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 lower bounds of the ESC for two secure transmission schemes: artificial noise aided precoding (ANP) and eigen-beamforming (EB). We also derive the lower bound of the ESC for ANP with a large antenna array at the relay, and investigate their corresponding asymptotic performance in the high and low SNR regimes. 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 EB, while in the low SNR regime, EB outperforms ANP with equal power allocation. As SNR grows large, the ESC of EB approaches a constant only related to the number of relay antennas. Moreover, in the high SNR regime, it is optimal to allocate around half of total power to artificial noise for ANP.
This paper investigates the ergodic secrecy capacity (ESC) 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 lower bounds of the ESC for two secure transmission schemes: artificial noise aided precoding (ANP) and eigen-beamforming (EB). We also derive the lower bound of the ESC for ANP with a large antenna array at the relay, and investigate their corresponding asymptotic performance in the high and low SNR regimes. 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 EB, while in the low SNR regime, EB outperforms ANP with equal power allocation. As SNR grows large, the ESC of EB approaches a constant only related to the number of relay antennas. Moreover, in the high SNR regime, it is optimal to allocate around half of total power to artificial noise for ANP.
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 correspondence, we consider an amplify-and-forward relay network in which relayed information is overheard by an eavesdropper. In order to confound the eavesdropper, a wireless-powered jammer is also considered which harvests energy from a multiple-antenna source. We proposed a new secure beamforming scheme in which beamforming vector is a linear combination of the energy beamforming (EB) and information beamforming (IB) vectors. In particular, we present a new closed-form solution for the proposed beamforming vector which is shown to achieve a near-optimal secrecy capacity for asymptotic regime of a large number of antennas at the source. Moreover, it is also demonstrated that the proposed beamforming vector achieves significantly higher secrecy rate as compared to the trivial EB and IB vectors. A tight closed-form approximation for the ergodic secrecy rate is also derived for a large number of antennas. Finally, numerical examples and simulations are provided which validate our analytical results.
In Rayleigh fading channels, we investigate the secrecy performance of a full-duplex relay secure transmission system. To improve the secrecy capacity of the system and efficiently interfere the interception of the eavesdropper, the multiple-antenna source applies the artificial noise aided precoding (ANP) scheme to broadcast the intended signal and the artificial noise simultaneously, and the decode-and-forward relay operates in full- duplex mode. To improve the received signal-to-noise ratio (SNR), the multiple-antenna destination applies maximum ratio combining (MRC) strategy. In the presence of self-interference at the relay, the approximate closed-form expression of ergodic achievable secrecy rate (EASR) for any values of antenna number and the exact closed-form expression of EASR for large-scale antennas array were derived respectively. Both the theoretical analysis and numerical simulations show that the ANP combined with full-duplex scheme can achieve considerable secrecy performance gain.
We consider the problem of secure transmission in two-hop amplify-and-forward untrusted relay networks. We analyze the ergodic secrecy capacity (ESC) and present compact expressions for the ESC in the high signal-to-noise ratio regime. We also examine the impact of large scale antenna arrays at either the source or the destination. For large antenna arrays at the source, we confirm that the ESC is solely determined by the channel between the relay and the destination. For very large antenna arrays at the destination, we confirm that the ESC is solely determined by the channel between the source and the relay.
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.