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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Secrecy Outage Probability and Secrecy Diversity Order of Alamouti STBC with Decision Feedback Detection over Time-Selective Fading Channels

Gyulim KIM, Hoojin Lee, Xinrong Li, Seong Ho Chae

Published Sep 18, 2023• 0 citations
Publisher

Abstract

This letter studies the secrecy outage probability (SOP) and the secrecy diversity order of Alamouti STBC with decision feedback (DF) detection over the time-selective fading channels. For given temporal correlations, we have derived the exact SOPs and their asymptotic approximations for all possible combinations of detection schemes including joint maximum likehood (JML), zero-forcing (ZF), and DF at Bob and Eve. We reveal that the SOP is mainly influenced by the detection scheme of the legitimate receiver rather than eavesdropper and the achievable secrecy diversity order converges to two and one for JML only at Bob (i.e., JML-JML/ZF/DF) and for the other cases (i.e., ZF-JML/ZF/DF, DF-JML/ZF/DF), respectively. Here, p-q combination pair indicates that Bob and Eve adopt the detection method p ∈ {JML, ZF, DF} and q ∈ {JML, ZF, DF}, respectively.

DOI
10.1587/transfun.2023eal2080

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This paper studies physical layer security for Alamouti space–time block code (STBC) with joint maximum likelihood (JML) or zero forcing (ZF) detection techniques particularly over multi-input single-output (MISO) wiretap time-selective Rayleigh fading channels. Specifically, we derive the secrecy outage probabilities (SOPs) and their concise but effective approximations for various combinations of JML and ZF at the legitimate receiver and eavesdropper. We also investigate the secrecy diversity gain by applying the high signal-to-noise ratio (SNR) approximation of SOP and prove that the corresponding asymptotic diversity order of two, two, one, and one can be achieved for JML-JML, JML-ZF, ZF-JML, and ZF-ZF, respectively. Our asymptotic analytical results corroborate that the secrecy diversity order is dominantly affected by the detection strategy of the legitimate receiver rather than that of the eavesdropper.
This letter studies the secrecy outage probability of diversity schemes (i.e., antenna-user selection with maximal ratio combining (AUS-MRC) scheme and the user selection with space-time block coding (US-STBC)) over arbitrary (i.e., integer and real valued) Nakagami fading channels. The exact secrecy expressions of the diversity schemes is derived for integer-valued fading index expressed as a finite sum and for real-valued fading index expressed as an infinite sum. Also, the secrecy diversity order and the secrecy SNR gain of the secrecy performance for the diversity schemes are quantified for arbitrary Nakagami fading channels. The first new insight provided by this letter is that the secrecy diversity order of the diversity schemes is proportional to the fading index for arbitrary fading parameters. Also, this letter shows that the secrecy diversity order of the diversity schemes is only affected by the parameters of the diversity scheme, not by eavesdropper’s parameters for arbitrary Nakagami fading channels.
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.
The amount of sensitive data, which is transmitted wirelessly will increase with future technologies. This raises many questions about secure data transmission. Besides cryptography, information-theoretic security gained increasing attention over the recent years. Among others, it deals with the problem of secure data transmission on the physical layer to a legitimate receiver (Bob) in the presence of an eavesdropper (Eve). In this work, we investigate upper and lower bounds on the secrecy outage probability for slowly-fading wiretap channels with an arbitrary dependency structure between the fading channels to Bob and Eve. Both cases of absence of channel-state information at the transmitter (CSI-T) and availability of CSI-T of only the main channel to the legitimate receiver are considered. Furthermore, we derive explicit expressions for the upper and lower bounds for Rayleigh fading and compare them to the case of independent channels. The joint distribution of the legitimate and eavesdropper channels has a tremendous impact on the achievable secrecy outage probability. The bounds enable developing guaranteed secrecy schemes by only measuring the marginal channel distributions.