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IEEE Wireless Communications Letters

Secrecy Outage Probability of MIMO Diversity Schemes Over Integer and Real-Valued Nakagami Fading Channels

Donghun Lee

Published Jan 11, 2022• 9 citations
Publisher

Abstract

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.

DOI
10.1109/lwc.2022.3141711

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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 considers transmit antenna selection (TAS) and receive generalized selection combining (GSC) for secure communication in MIMO wiretap channel, where confidential messages transmitted from an NA-antenna transmitter to an NB-antenna legitimate receiver are overheard by an NE-antenna eavesdropper. We assume that the main channel and the eavesdropper's channel undergo Nakagami-m fading with fading parameters mBand mE, respectively. In an effort to assess the secrecy performance, we present a closed-form expression for the secrecy outage probability. We then derive closed-form expressions for the secrecy outage probability at high signal-to-noise ratio (SNR) for two realistic scenarios: 1) the legitimate receiver is located close to the transmitter, and 2) the legitimate receiver and the eavesdropper are located close to the transmitter. In the first scenario, we confirm that the secrecy diversity order is mBNBNA. In the second scenario, we confirm that the secrecy diversity order collapses to zero. While this may appear discouraging at a first glance, we show that low secrecy outage probability can still be achieved.
This paper considers transmit antenna selection (TAS) and receive generalized selection combining (GSC) for secure communication in the multiple-input-multiple-output wiretap channel, where confidential messages transmitted from an NA-antenna transmitter to an NB-antenna legitimate receiver are overheard by an NE-antenna eavesdropper. We assume that the main channel and the eavesdropper's channel undergo Nakagami-m fading with fading parameters mB and mE, respectively. In order to assess the secrecy performance, we present a new unifying framework for the average secrecy rate and the secrecy outage probability. We first derive expressions for the probability density function and the cumulative distribution function of the signal-to-noise ratio with TAS/GSC, from which we derive exact expressions for the average secrecy rate and the secrecy outage probability. We then derive compact expressions for the asymptotic average secrecy rate and the asymptotic secrecy outage probability for two distinct scenarios: 1) the legitimate receiver is located close to the transmitter, and 2) the legitimate receiver and the eavesdropper are located close to the transmitter. For these scenarios, we present new closed-form expressions for several key performance indicators: 1) the capacity slope and the power offset of the asymptotic average secrecy rate, and 2) the secrecy diversity order and the secrecy array gain of the asymptotic secrecy outage probability. For the first scenario, we confirm that the capacity slope is one and the secrecy diversity order is mBNBNA. For the second scenario, we confirm that the capacity slope and the secrecy diversity order collapse to zero.
In the perspective of information-theoretical security, inspired by the heterogeneity between legal and illegal channels, we consider the physical layer secrecy performance of a novel system model with a single antenna employed for both the transmitter and legal receiver, in the presence of a multiple antennas passive eavesdropper over dissimilar fading channels, where the legal/illegal channels are subject to Rayleigh/Nakagami-m and Nakagami-m/Rayleigh fading, respectively. We assume that the eavesdropper employs either maximal-ratio combining or selection combining reception in order to benefit from space diversity. Specifically, the exact closed-form expressions of the probability of existence of secrecy capacity and the secrecy outage probability are derived by utilizing statistical characteristics of the signal-to-noise ratio. Moreover, the delightful results reveal that the secrecy performance achieves a greater level when the Nakagami-m fading is supposed on the main link due to the line of sight component. In final, the analytical results are verified by Monte-Carlo simulation.
Secrecy performance based on TAS/MRC scheme with Nakagami-m antenna correlation was investigated in MIMO wiretap channels. New closed-form expressions of the exact secrecy outage probability and the probability of positive secrecy were presented. For further insights, the asymptotic secrecy outage probability in the high SNR region was also derived. It is confirmed that antenna correlation has no effects on diversity order. Most importantly, we concluded that higher antenna correlation at receiver offers more beneficial effects on secrecy performance when average SNR of the main channel is at low level, but it imposes more detrimental effects when average SNR of the main channel is at medium and high level. Finally, we provide Monte Carlo simulations to verify the analytical results.
This paper investigates the role of the Maximum Ratio Combining (MRC) diversity scheme in enhancing security for multicast communications over a Nakagami-0.5 fading channel in the presence of multiple eavesdroppers. The considered scenario involves a singleantenna transmitter communicating confidentially with multiple legitimate receivers, while multiple eavesdroppers attempt to intercept the transmission. Explicit mathematical formulation have been established to evaluate the likelihood of achieving a positive secrecy multicast capacity and the probability of a secure outage, providing a theoretical framework to evaluate the secrecy performance. The analysis highlights the impact of critical system parameters, including the number of legitimate receivers, the number of eavesdroppers and the number of antennas employed at both legitimate receivers and eavesdroppers. By employing MRC, which coherently combines signals from multiple antennas to maximize the received signal-to-noise ratio, the study demonstrates significant improvements in the secrecy performance of multicast systems. The findings contribute valuable insights into designing more secure multicast communication networks in the presence of severe fading and adversarial interception.