Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1808.03343 · IEEE Transactions on Vehicular Technology

On Physical Layer Security Over Fox's $H$-Function Wiretap Fading Channels

Long Kong, Georges Kaddoum, Hatim Chergui

Published Jul 1, 2019• 53 citations
arXivHTMLPDF

Abstract

Most of the well-known fading distributions, if not all of them, could be encompassed by the Fox's H-function fading. Consequently, we investigate the physical layer security over Fox's H-function fading wiretap channels, in the presence of non-colluding and colluding eavesdroppers. In particular, for the non-colluding scenario, closed-form expressions are derived for the secrecy outage probability (SOP), the probability of non-zero secrecy capacity, and the average secrecy capacity. These expressions are given in terms of either univariate or bivariate Fox's H-function. In order to show the effectiveness of our derivations, three metrics are respectively listed over the following frequently used fading channels, including Rayleigh, Weibull, Nakagami-m, α - μ, Fisher-Snedecor (F-S) F, and extended generalized-K. Our tractable results are not only straightforward and general, but also feasible and applicable, especially the SOP, which is usually limited to the lower bound in the literature due to the difficulty of deriving closed-from analytical expressions. For the colluding scenario, a super eavesdropper equipped with maximal ratio combining (MRC) or selection-combining (SC) schemes is characterized. The lower bound of SOP and exact PNZ are thereafter derived with closed-form expressions in terms of the multivariate Fox's H-function. In order to validate the accuracy of our analytical results, Monte Carlo simulations are subsequently conducted for the aforementioned fading channels. One can observe that for the former non-colluding scenario, we have perfect agreement between the exact analytical and simulation results, and highly accurate approximations between the exact and asymptotic analytical results. On the contrary, the SOP and PNZ of colluding eavesdropper is greatly degraded with the increase of the number of eavesdroppers. Also, the so-called super eavesdropper with MRC is much powerful to wiretap the main channel than the one with SC.

DOI
10.1109/tvt.2019.2915017

Related papers

Exact closed‐form capacity and outage probability of physical layer security in shadowed fading channels

Hussien Al‐Hmood, Hamed Saffa Al-Raweshidy

In this study, the secrecy performance of physical layer when both the main and wiretap channels undergo shadowed fading conditions is analysed. In particular, the average secrecy capacity, secure outage probability (SOP), the lower bound of SOP (SOP ), and the probability of strictly positive secrecy capacity are derived by using the classic Wyner's wiretap model. Two different scenarios for the fading parameters, namely, and m , which represent the real extension of the number of the multipath clusters and the shadowing index, respectively, have been studied. These parameters are chosen first as arbitrary numbers, thus the performance metrics are given in exact closed‐form in terms of the extended generalised bivariate Fox's H ‐function that has been widely implemented in the open literature using various software packages. In the second scenario, both the fading parameters are assumed to be integer numbers to obtain the derived results in simple exact closed‐form mathematically tractable expressions in terms of some analytic functions. The numerical results of this analysis are verified via the Monte Carlo simulations.

IET Communications•Aug 29, 2019•8 citations

An Overview of Generic Tools for Information-Theoretic Secrecy Performance Analysis over Wiretap Fading Channels

Long Kong, Yun Ai, Lei, Lei +3 more

An alternative or supplementary approach named as physical layer security has been proposed to afford an extra security layer on top of the conventional cryptography technique. In this paper, an overview of secrecy performance investigations over the classic Alice-Bob-Eve wiretap fading channels is conducted. On the basis of the classic wiretap channel model, we have comprehensively listed and thereafter compared the existing works on physical layer secrecy analysis considering the small-scale, large-scale, composite, and cascaded fading channel models. Exact secrecy metrics expressions, including secrecy outage probability (SOP), the probability of non-zero secrecy capacity (PNZ), average secrecy capacity (ASC), and secrecy bounds, including the lower bound of SOP and ergodic secrecy capacity, are presented. In order to encompass the aforementioned four kinds of fading channel models with a more generic and flexible distribution, the mixture gamma (MG), mixture of Gaussian (MoG), and Fox's $H$-function distributions are three useful candidates to largely include the above-mentioned four kinds of fading channel models. It is shown that they are flexible and general when assisting the secrecy analysis to obtain closed-form expressions. Their advantages and limitations are also highlighted. Conclusively, these three approaches are proven to provide a unified secrecy analysis framework and can cover all types of independent wiretap fading channel models. Apart from those, revisiting the existing secrecy enhancement techniques based on our system configuration, the on-off transmission scheme, jamming approach (including artificial noise (AN) & artificial fast fading (AFF)), antenna selection, and security region are presented.

arXiv:2009.05976•Sep 13, 2020•0 citations

Secrecy Analysis of Physical Layer over $κ-μ$ Shadowed Fading Scenarios

Hussien Al‐Hmood, Hamed Saffa Al-Raweshidy

In this paper, the secrecy analysis of physical layer when both the main and wiretap channels undergo $κ-μ$ shadowed fading channel is investigated. In particular, the average secrecy capacity (ASC), secure outage probability (SOP), the lower bound of SOP (SOP$^L$), and the probability of strictly positive secrecy capacity (SPSC) are derived by using the classic Wyner's wiretap model. Two different scenarios for the fading parameters, i.e., $μ$ and $m$ which represents the shadowing impact have been studied. These parameters are chosen first as arbitrary numbers, thus the performance metrics are expressed in single infinite series with multivariate Meijer $G$-function. In the second scenario, both the aforementioned fading parameters are assumed to be integer numbers in order to obtain the derived results in simple exact closed-form analytic mathematically tractable expressions. The numerical results of this analysis are verified via Monte Carlo simulations.

arXiv:1804.09208•Apr 24, 2018•1 citation

Wireless physical-layer security with multiple receivers and eavesdroppers: Outage probability and average secrecy capacity

Yongjue Chen, Wei Li, Huixi Shu

The wiretap channel model in a wireless scenario is analyzed where there is a transmitter, multiple legitimate receivers, non-colluding and colluding eavesdroppers; each of them is equipped with one antenna. Furthermore, all the channels are mutually independent and experiencing quasi-static Nakagami-m fading. We derive closed-form expressions for the exact secrecy outage probability as well as the average secrecy capacity with both non-colluding and colluding eavesdroppers. Such performance metrics are used to analyze the impacts of the number of receivers and eavesdroppers on the system. Remarkably, our results reveal that, for non-colluding eavesdroppers, increasing the number of users will cause greater secrecy degradation than the number of eavesdroppers, especially when the main channel is far superior to the wiretap channel or the value of the fading parameter is high. And for the colluding case, it turns out to be the opposite.

IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)•Aug 1, 2015•10 citations

Achievable Physical-Layer Security Over Composite Fading Channels

Osamah S. Badarneh, Paschalis C. Sofotasios, Sami Muhaidat +3 more

We investigate the physical layer security limits of Wyner's wiretap model over Fisher-Snedecor .T composite fading channels. .T fading conditions have been recently shown to provide an accurate characterization of multipath fading and shadowing effects in emerging wireless transmission scenarios such as body centric, cellular and vehicular communications. To this end, we utilize a redefined analytic expression for the Fisher-Snedecor .T distribution in order to ensure unconstrained validity and reliability when used in the analysis of various performance metrics of interest. In this context, we assume that the main channel (i.e., between the source and the legitimate destination) and the eavesdropper's channel (i.e., between the source and the illegitimate destination) undergo independent quasi-static Fisher-Snedecor .T composite fading. Novel exact analytic expressions are then derived for the corresponding average secrecy capacity (ASC), secure outage probability (SOP) and probability of strictly positive secrecy capacity (SPSC) along with their insightful asymptotic representations. In addition, analytical expressions for the ASC, SOP and SPSC over mixed fading channels such as Nakagami-m/Nakagami-m, Nakagami-m/Fisher-Snedecor .T and Fisher-Snedecor .T/Nakagami-m are derived. The new formulations are validated through comparisons with Monte-Carlo simulations and analyzed to gain useful insights into the impact of the fading parameters on the achievable accuracy and the overall system performance.

IEEE Access•Jan 1, 2020•28 citations

Cascaded κ-µ Fading Channels with Colluding Eavesdroppers: Physical-Layer Security Analysis

Deemah H. Tashman, Walaa Hamouda

This paper studies the physical-layer security (PLS) of a system model consisting of a transmitter, a receiver, and multiple eavesdroppers. Cascaded general fading channel, which is the κ-μ distribution is assumed at the main and the wiretap links of the network. The impacts of the cascade level, the number of eavesdroppers attempting to overhear the confidential information, and the wiretap channel's parameters on the system's secrecy are investigated. Two of the main secrecy metrics are used to evaluate the secrecy level of the system, which are the secrecy outage probability (OPsec) and the probability of non-zero secrecy capacity (Pnsc). Exact and asymptotic form expressions for (OPsec) and (Pnsc) are derived. Asymptotic analysis is performed to gain a clear vision about the impact of some key parameters over the secrecy. The results show that the fading channel cascade level has a significant effect on the system's secrecy. Also, the results show that the system is less protected when increasing the number of eavesdroppers or when improving the wiretap channel's conditions. Analytical results are validated using Monte-Carlo simulations.

International Conference on Communications, Signal Processing, and their Applications (ICCSPA)•Mar 16, 2021•7 citations
On Physical Layer Security Over Fox's HHH-Function Wiretap Fading Channels
Most of the well-known fading distributions, if not all of them, could be encompassed by the Fox's H-function fading. Consequently, we investigate the physical layer security over Fox's H-function fading wiretap channels, in the presence of non-colluding and colluding eavesdroppers. In particular, for the non-colluding scenario, closed-form expressions are derived for the secrecy outage probability (SOP), the probability of non-zero secrecy capacity, and the average secrecy capacity. These expressions are given in terms of either univariate or bivariate Fox's H-function. In order to show the effectiveness of our derivations, three metrics are respectively listed over the following frequently used fading channels, including Rayleigh, Weibull, Nakagami-m, α - μ, Fisher-Snedecor (F-S) F, and extended generalized-K. Our tractable results are not only straightforward and general, but also feasible and applicable, especially the SOP, which is usually limited to the lower bound in the literature due to the difficulty of deriving closed-from analytical expressions. For the colluding scenario, a super eavesdropper equipped with maximal ratio combining (MRC) or selection-combining (SC) schemes is characterized. The lower bound of SOP and exact PNZ are thereafter derived with closed-form expressions in terms of the multivariate Fox's H-function. In order to validate the accuracy of our analytical results, Monte Carlo simulations are subsequently conducted for the aforementioned fading channels. One can observe that for the former non-colluding scenario, we have perfect agreement between the exact analytical and simulation results, and highly accurate approximations between the exact and asymptotic analytical results. On the contrary, the SOP and PNZ of colluding eavesdropper is greatly degraded with the increase of the number of eavesdroppers. Also, the so-called super eavesdropper with MRC is much powerful to wiretap the main channel than the one with SC.
In this study, the secrecy performance of physical layer when both the main and wiretap channels undergo shadowed fading conditions is analysed. In particular, the average secrecy capacity, secure outage probability (SOP), the lower bound of SOP (SOP ), and the probability of strictly positive secrecy capacity are derived by using the classic Wyner's wiretap model. Two different scenarios for the fading parameters, namely, and m , which represent the real extension of the number of the multipath clusters and the shadowing index, respectively, have been studied. These parameters are chosen first as arbitrary numbers, thus the performance metrics are given in exact closed‐form in terms of the extended generalised bivariate Fox's H ‐function that has been widely implemented in the open literature using various software packages. In the second scenario, both the fading parameters are assumed to be integer numbers to obtain the derived results in simple exact closed‐form mathematically tractable expressions in terms of some analytic functions. The numerical results of this analysis are verified via the Monte Carlo simulations.
An alternative or supplementary approach named as physical layer security has been proposed to afford an extra security layer on top of the conventional cryptography technique. In this paper, an overview of secrecy performance investigations over the classic Alice-Bob-Eve wiretap fading channels is conducted. On the basis of the classic wiretap channel model, we have comprehensively listed and thereafter compared the existing works on physical layer secrecy analysis considering the small-scale, large-scale, composite, and cascaded fading channel models. Exact secrecy metrics expressions, including secrecy outage probability (SOP), the probability of non-zero secrecy capacity (PNZ), average secrecy capacity (ASC), and secrecy bounds, including the lower bound of SOP and ergodic secrecy capacity, are presented. In order to encompass the aforementioned four kinds of fading channel models with a more generic and flexible distribution, the mixture gamma (MG), mixture of Gaussian (MoG), and Fox's HHH-function distributions are three useful candidates to largely include the above-mentioned four kinds of fading channel models. It is shown that they are flexible and general when assisting the secrecy analysis to obtain closed-form expressions. Their advantages and limitations are also highlighted. Conclusively, these three approaches are proven to provide a unified secrecy analysis framework and can cover all types of independent wiretap fading channel models. Apart from those, revisiting the existing secrecy enhancement techniques based on our system configuration, the on-off transmission scheme, jamming approach (including artificial noise (AN) & artificial fast fading (AFF)), antenna selection, and security region are presented.
Secrecy Analysis of Physical Layer over κ−μκ-μκ−μ Shadowed Fading Scenarios
In this paper, the secrecy analysis of physical layer when both the main and wiretap channels undergo κ−μκ-μκ−μ shadowed fading channel is investigated. In particular, the average secrecy capacity (ASC), secure outage probability (SOP), the lower bound of SOP (SOPL^LL), and the probability of strictly positive secrecy capacity (SPSC) are derived by using the classic Wyner's wiretap model. Two different scenarios for the fading parameters, i.e., μμμ and mmm which represents the shadowing impact have been studied. These parameters are chosen first as arbitrary numbers, thus the performance metrics are expressed in single infinite series with multivariate Meijer GGG-function. In the second scenario, both the aforementioned fading parameters are assumed to be integer numbers in order to obtain the derived results in simple exact closed-form analytic mathematically tractable expressions. The numerical results of this analysis are verified via Monte Carlo simulations.
The wiretap channel model in a wireless scenario is analyzed where there is a transmitter, multiple legitimate receivers, non-colluding and colluding eavesdroppers; each of them is equipped with one antenna. Furthermore, all the channels are mutually independent and experiencing quasi-static Nakagami-m fading. We derive closed-form expressions for the exact secrecy outage probability as well as the average secrecy capacity with both non-colluding and colluding eavesdroppers. Such performance metrics are used to analyze the impacts of the number of receivers and eavesdroppers on the system. Remarkably, our results reveal that, for non-colluding eavesdroppers, increasing the number of users will cause greater secrecy degradation than the number of eavesdroppers, especially when the main channel is far superior to the wiretap channel or the value of the fading parameter is high. And for the colluding case, it turns out to be the opposite.
We investigate the physical layer security limits of Wyner's wiretap model over Fisher-Snedecor .T composite fading channels. .T fading conditions have been recently shown to provide an accurate characterization of multipath fading and shadowing effects in emerging wireless transmission scenarios such as body centric, cellular and vehicular communications. To this end, we utilize a redefined analytic expression for the Fisher-Snedecor .T distribution in order to ensure unconstrained validity and reliability when used in the analysis of various performance metrics of interest. In this context, we assume that the main channel (i.e., between the source and the legitimate destination) and the eavesdropper's channel (i.e., between the source and the illegitimate destination) undergo independent quasi-static Fisher-Snedecor .T composite fading. Novel exact analytic expressions are then derived for the corresponding average secrecy capacity (ASC), secure outage probability (SOP) and probability of strictly positive secrecy capacity (SPSC) along with their insightful asymptotic representations. In addition, analytical expressions for the ASC, SOP and SPSC over mixed fading channels such as Nakagami-m/Nakagami-m, Nakagami-m/Fisher-Snedecor .T and Fisher-Snedecor .T/Nakagami-m are derived. The new formulations are validated through comparisons with Monte-Carlo simulations and analyzed to gain useful insights into the impact of the fading parameters on the achievable accuracy and the overall system performance.
This paper studies the physical-layer security (PLS) of a system model consisting of a transmitter, a receiver, and multiple eavesdroppers. Cascaded general fading channel, which is the κ-μ distribution is assumed at the main and the wiretap links of the network. The impacts of the cascade level, the number of eavesdroppers attempting to overhear the confidential information, and the wiretap channel's parameters on the system's secrecy are investigated. Two of the main secrecy metrics are used to evaluate the secrecy level of the system, which are the secrecy outage probability (OPsec) and the probability of non-zero secrecy capacity (Pnsc). Exact and asymptotic form expressions for (OPsec) and (Pnsc) are derived. Asymptotic analysis is performed to gain a clear vision about the impact of some key parameters over the secrecy. The results show that the fading channel cascade level has a significant effect on the system's secrecy. Also, the results show that the system is less protected when increasing the number of eavesdroppers or when improving the wiretap channel's conditions. Analytical results are validated using Monte-Carlo simulations.