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IET Communications

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

Hussien Al‐Hmood, Hamed Saffa Al-Raweshidy

Published Aug 29, 2019• 8 citations
Publisher

Abstract

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.

DOI
10.1049/iet-com.2019.0325

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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.
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.
In this study, the secrecy performance of the classic Wyner's wiretap model over generalised‐ K fading channels is studied. The closed‐form expressions for the average secrecy capacity, the lower bound of secure outage probability, and the probability of strictly positive secrecy capacity are derived. The new expressions provide a unified form, which can handle several of the well‐known composite fading environments as special or limiting cases. Moreover, all the derived expressions are given in terms of Meijer's G ‐function, which can be simply realised in MATLAB and MATHEMATICA. Monte‐Carlo simulations are performed to verify the proposed analysis models.
In this study, the secrecy performance of the classic Wyner's wiretap model over shadowed fading channels is studied. More specifically, the authors derive two analytical expressions for the lower bound of secure outage probability at high signal‐to‐noise ratio regime and the probability of strictly positive secrecy capacity over shadowed fading channels, respectively. As there exist infinite series in the two derived expressions, they further obtain two simple and explicit approximate expressions for the lower bound of secure outage probability and the probability of strictly positive secrecy capacity with the aid of the moment matching method. It is shown that the match between the analytical results and simulations is very excellent for all parameters under considerations.
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.
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.