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arXiv:1808.02993

Secrecy Outage Performance of Multi-antenna Wiretap Channels With Diversity Combinings Over Correlated Rayleigh Fading Channels

Jiangbo Si, Zan Li, Julian Cheng, Caijun Zhong

Published Aug 9, 2018• 0 citations
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Abstract

This paper presents a detailed secrecy outage performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single input multiple output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U), where det(U) is the determinant of correlation matrix U. In contrast, in the high signal-to-noise ratio regime at the legitimate receiver, correlation between the main channels and the eavesdropper channels has a positive effect on SOP. Moreover, for multiple input and multiple output wiretap channels, the SOP of two transmit antenna selection (TAS) schemes are analyzed for the considered correlated channel model. The SOP relationship of the both TAS schemes is quantified by the secrecy array gain. Finally, numerical simulations are conducted to corroborate the analytical results.

DOI
10.48550/arxiv.1808.02993

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This paper presents a detailed secrecy outage performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single input multiple output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U), where det(U) is the determinant of correlation matrix U. In contrast, in the high signal-to-noise ratio regime at the legitimate receiver, correlation between the main channels and the eavesdropper channels has a positive effect on SOP. Moreover, for multiple input and multiple output wiretap channels, the SOP of two transmit antenna selection (TAS) schemes are analyzed for the considered correlated channel model. The SOP relationship of the both TAS schemes is quantified by the secrecy array gain. Finally, numerical simulations are conducted to corroborate the analytical results.
This paper presents a detailed secrecy performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single-input multiple-output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U), where det(U) is the determinant of correlation matrix U. In contrast, when the average SNR at the legitimate receiver is much larger than that at the eavesdropper, correlation between the main channels and the eavesdropper channels has a positive effect on SOP. Moreover, in the case of multiple-input and multiple-output wiretap channels, two transmit antenna selection schemes with or without the eavesdropper's channel state information are evaluated by the SOP and the average secrecy capacity for the considered correlated channel model, respectively. Finally, numerical simulations are conducted to corroborate the analytical results.
Asymptotic Secrecy Outage Performance for TAS/MRC Over Correlated Nakagami-m{m}m Fading Channels
In this paper, considering both the antenna correlation and the channel correlation between the legitimate receiver and the eavesdropper, we comprehensively investigate the secrecy performance for transmit antenna selection and maximal ratio combining (TAS/MRC) scheme in a multi-input multi-output multi-antenna eavesdropper (MIMOME) system. Different from the existing works, the correlated legitimate channels and correlated eavesdropper channels experience Nakagmai-m{m}mfading with distinct fading parameters, and are modeled as a combination of conditionally independent channel gains and independent channel gains. By this novel correlation representation, the combined effect of antenna correlation and channel correlation between the legitimate receiver and the eavesdropper on secrecy performance is quantified via the secrecy outage probability (SOP) under a more general fading circumstance. In addition, two special cases of correlated channels are addressed in detail. Finally, simulations are performed to verify our analysis. The analysis and simulation results show that at high signal-to-noise ratio (SNR), antenna correlation at the legitimate receiver can improve the SOP performance for the correlated MIMOME wiretap channels, and this finding is contrary to the conventional wisdom that antenna correlation degrades the SOP performance.
In this paper, the joint effect of multiple jamming signals and noise at the eavesdropper in wiretap channels is studied in terms of the secrecy outage probability, where all nodes are deployed with multiple antennas. Specifically, the transmitter employs a transmit antenna selection (TAS) technique; the legitimate receiver uses either a selection combining (SC) or a maximal-ratio combining (MRC) scheme; and the eavesdropper adopts the MRC technique. Exact closed-form expressions for the secrecy outage probability are derived for both SC and MRC schemes at the legitimate receiver, which are applicable for arbitrary number of power distributed jamming signals. An asymptotic secrecy outage analysis is conducted, which shows that the diversity gains for all combining schemes equal to the product of the number of antennas at the transmitter and the legitimate receiver. Representative numerical examples are presented to illustrate the effects of the key system parameters on the secrecy outage performance. Finally, the proposed analysis is validated through Monte Carlo simulation results.
In this paper, when transmit antenna selection (TAS) and maximal ratio combining (MRC) schemes are deployed for secrecy enhancement, the impact of channel correlation on secrecy performance is investigated over Rayleigh fading channels. Specially, both the exact and asymptotic secrecy outage probability (SOP) for TAS/MRC are derived based on a novel correlation model, where the correlated legitimate channels and eavesdropper channels are modeled as a set of conditional independent channel gains. Moreover, the lower bound of SOP is obtained in high signal-to-noise ratio (SNR) region. Finally, simulation results verify our analysis, and show that the channel correlation between the legitimate receiver and the eavesdropper is beneficial to the SOP at high SNR.
This paper investigates the secrecy outage performance of multiple-input multiple-output (MIMO) wiretap channels, where a generalized selection combining (GSC) scheme is assumed at the legitimate receiver, while the transmitter employs a transmit antenna selection (TAS) technique and the eavesdropper adopts a maximal-ratio combining (MRC) scheme.Assuming that the eavesdropper is subject to noise and jamming, a closed-form expression for the secrecy outage probability is derived, based on which the diversity and array gains are determined after performing an asymptotic analysis.The derived expression allows for arbitrary power distributed jamming signals, and are simplified to two special cases, i.e., distinct and equal power distributed jamming signals.Some representative numerical results are depicted to show the effects of the key system parameters on the secrecy performance.Finally, the proposed analysis is corroborated through Monte Carlo simulations.
Transmit antenna selection (TAS) is an emerging technology in physical layer security. To provide new insights into the achievable secrecy performance of TAS in practical communication systems, this paper investigates the average secrecy rate (ASR) and secrecy outage probability (SOP) under practical modulation schemes in TAS aided multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) wiretap channels over Rayleigh fading. Particularly, this research concentrates more on the square M-ary quadrature amplitude modulation (M-QAM). Furthermore, in the considered MIMOME channel, a single antenna is selected to transmit the secret message, and selection combining (SC) or maximal-ratio combining (MRC) is utilized at the legitimate receiver and the eavesdropper. Based on this system model, novel expressions for the ASR and SOP are formulated to characterize the secrecy performance of the finite-alphabet driven MIMOME channel. Besides exact analysis, an asymptotic analysis is performed using the considered performance metrics in high signal-to-noise ratio (SNR) regime. Theoretical analyses suggest that the asymptotic ASR and SOP converge to finite constants in high SNR regime due to the discrete constellation constraint, and we find that the asymptotic behaviour of discrete inputs differs from that of Gaussian inputs. Furthermore, we derive concise expressions to characterize the rate of convergence (ROC) of the ASR and SOP, respectively. To unveil more system design insights, we discuss the relationship between the ROC and several important system parameters such as the antenna number and the modulation order.