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

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 (PLS) 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 nonzero secrecy capacity (PNZ), and the average secrecy capacity (ASC). 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 (EGK). 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.Index Terms-Physical layer security, Fox's H-function wiretap fading channels, Mellin transform, secrecy outage probability, probability of non-zero secrecy capacity, average secrecy capacity.

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

“…To write the confluent Lauricella hypergeometric function Φ 2 (.) in (22) in terms of the FHF, we use the following identity [28, 1.ii, pp. 259]…”

“…is the bivariate FHF. After inserting (23), (24), (25) and (31) in (22) and utilising the definition of the FHF, we obtain (32) that is shown at the bottom of this page in terms of the multiple closed contours R i in the complex r i -plane for i ∈ {1, 2, 3, 4}.…”

“…To compute the integral in (22) in exact closed-form, we express ln(.) and the hypergeometric functions in terms of the Meijer Gfunction.…”

Unified Framework for Secrecy Characteristics With Mixture of Gaussian (MoG) Distribution

“…The absence of secret keys makes it outperform the conventional cryptography technique from the information-theoretic viewpoint. In recent decades, plenty of works have studied the PLS over various fading channels, e.g., Rayleigh [1], Rician (Nakagami-n) [2], Hoyt (Nakagami-q) [3], α − µ [4]- [6], cascaded α − µ [7], κ − µ [8], Lognormal [9], Fisher-Snedecor F [10], generalized-K [11], extended generalized-K (EGK) [12], α − η − κ − µ [13], Málaga [14], etc.…”

“…L. Kong, S. Chatzinotas, and B. Ottersten are with the Interdisciplinary Centre for Security Reliability and Trust (SnT), University of Luxembourg, L-1855 Luxembourg (email: {long.kong, symeon.chatzinotas, bjorn.ottersten}@uni.lu) utilizing the Fox's H-function distribution was explored in [12], which provides a unified secrecy analysis framework, and the analytical results therein indicates that simple transformation of the fading channel characteristics in the manner of Fox's H-function distribution can largely encompass the existing works [1], [5]- [7], [10].…”