Performance Analysis of Physical-Layer Security Over Fluctuating Beckmann Fading Channels

In this paper, we analyse the performance of physical layer security over Fluctuating Beckmann (FB) fading channel, which is an extended model of both the <inline-formula> <tex-math notation="LaTeX">$\kappa -\mu $ </tex-math></inline-formula> shadowed and the classical Beckmann distributions. Specifically, the average secrecy capacity (ASC), secure outage probability (SOP), the lower bound of SOP (SOP<inline-formula> <tex-math notation="LaTeX">$^{L}$ </tex-math></inline-formula>), and the probability of strictly positive secrecy capacity (SPSC) are derived using two different values of the fading parameters, namely, <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> which represent the multipath and shadowing severity impacts, respectively. Firstly, when the fading parameters are arbitrary values, the performance metrics are derived in exact expressions in terms of the extended generalised bivariate Fox’s <inline-formula> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula>-function (EGBFHF) that has been widely implemented in the open literature. In the second case, to obtain simple mathematically tractable expressions in terms of analytic functions as well as to gain more insight on the behaviour of the physical layer security over Fluctuating Beckmann fading channel models, <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> are assumed to be integer and even numbers, respectively. In addition, the asymptotic behaviour for all the studied performance metrics has been provided. The numerical results of this analysis are verified via Monte Carlo simulations.

[1]  Hamed S. Al-Raweshidy,et al.  Effective rate analysis over Fluctuating Beckmann fading channels , 2019, ArXiv.

[2]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[3]  Kerstin Vogler,et al.  Table Of Integrals Series And Products , 2016 .

[4]  Matthieu R. Bloch,et al.  Wireless Information-Theoretic Security , 2008, IEEE Transactions on Information Theory.

[5]  Jaehoon Jung,et al.  Capacity and Error Probability Analysis of Diversity Reception Schemes Over Generalized- $K$ Fading Channels Using a Mixture Gamma Distribution , 2014, IEEE Transactions on Wireless Communications.

[6]  Imran Shafique Ansari,et al.  On Physical-Layer Security Over SIMO Generalized-$K$ Fading Channels , 2016, IEEE Transactions on Vehicular Technology.

[7]  Moataz M. H. El Ayadi,et al.  Closed-Form Exact and Asymptotic Expressions for the Symbol Error Rate and Capacity of the $H$-Function Fading Channel , 2016, IEEE Transactions on Vehicular Technology.

[8]  Jin Jin,et al.  Performance analysis of physical layer security over k - μ shadowed fading channels , 2018, IET Commun..

[9]  Hamed S. Al-Raweshidy,et al.  Exact closed-form capacity and outage probability of physical layer security in κ - μ shadowed fading channels , 2019, IET Commun..

[10]  Georges Kaddoum,et al.  Performance analysis of physical layer security over α–μ fading channel , 2016 .

[11]  Hamed S. Al-Raweshidy,et al.  Secrecy Analysis of Physical Layer over κ-μ Shadowed Fading Scenarios , 2018, ArXiv.

[12]  Imran Shafique Ansari,et al.  Physical-layer security over generalised-K fading channels , 2016, IET Commun..

[13]  Simon L. Cotton,et al.  Secrecy capacity analysis for α-μ/κ-μ and κ-μ/α-μ fading scenarios , 2016, 2016 IEEE 27th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC).

[14]  Georges Kaddoum,et al.  On Physical Layer Security Over the Fisher-Snedecor ${\mathcal{F}}$ Wiretap Fading Channels , 2018, IEEE Access.

[15]  A. W. Kemp,et al.  A treatise on generating functions , 1984 .

[16]  Simon L. Cotton,et al.  Secrecy Capacity Analysis Over κ-μ Fading Channels: Theory and Applications , 2015, IEEE Trans. Commun..

[17]  Xian Liu,et al.  Probability of strictly positive secrecy capacity of the Weibull fading channel , 2013, 2013 IEEE Global Communications Conference (GLOBECOM).

[18]  José F. Paris,et al.  On the Calculation of the Incomplete MGF With Applications to Wireless Communications , 2016, IEEE Transactions on Communications.

[19]  Huan Zhang,et al.  Performance Analysis of Physical Layer Security Over Generalized-$K$ Fading Channels Using a Mixture Gamma Distribution , 2016, IEEE Communications Letters.

[20]  Tomoaki Ohtsuki,et al.  Performance Analysis of Physical Layer Security over Rician/Nakagami-m Fading Channels , 2017, 2017 IEEE 85th Vehicular Technology Conference (VTC Spring).

[21]  Michel Daoud Yacoub,et al.  An Extension of the $\kappa$ -$\mu$ Shadowed Fading Model: Statistical Characterization and Applications , 2017, IEEE Transactions on Vehicular Technology.

[22]  George C. Alexandropoulos,et al.  Secrecy Outage Analysis Over Correlated Composite Nakagami- $m$ /Gamma Fading Channels , 2017, IEEE Communications Letters.

[23]  Manav R. Bhatnagar,et al.  On Physical Layer Security of α-η-κ-μ Fading Channels , 2018, IEEE Commun. Lett..

[24]  Liu,et al.  Enhancing the Physical Layer Security of Non-Orthogonal Multiple Access in Large-Scale Networks , 2016, IEEE Transactions on Wireless Communications.

[25]  Georges Kaddoum,et al.  On Physical Layer Security Over Fox's $H$-Function Wiretap Fading Channels , 2018, IEEE Transactions on Vehicular Technology.

[26]  Chaowei Yuan,et al.  Coverage and Rate Analysis in Downlink ${L}$ -Tier HetNets With Fluctuating Beckmann Fading , 2019, IEEE Wireless Communications Letters.

[27]  Hussien Al-Hmood,et al.  Secrecy Analysis of Physical Layer over κ-μ Shadowed Fading Scenarios , 2018, ArXiv.

[28]  Xian Liu.  Average secrecy capacity of the Weibull fading channel , 2016, 2016 13th IEEE Annual Consumer Communications & Networking Conference (CCNC).

[29]  Miguel R. D. Rodrigues,et al.  Secrecy Capacity of Wireless Channels , 2006, 2006 IEEE International Symposium on Information Theory.

[30]  Xian Liu,et al.  Probability of Strictly Positive Secrecy Capacity of the Rician-Rician Fading Channel , 2013, IEEE Wireless Communications Letters.

[31]  Mohamed-Slim Alouini,et al.  Rician ${K}$ -Factor-Based Analysis of XLOS Service Probability in 5G Outdoor Ultra-Dense Networks , 2019, IEEE Wireless Communications Letters.

[32]  I. S. Ansari,et al.  Secrecy Capacity Analysis Over $\alpha - \mu $ Fading Channels , 2017, IEEE Communications Letters.

[33]  Mohamed-Slim Alouini,et al.  Secrecy Capacity Analysis Over α-μ Fading Channels , 2017, IEEE Commun. Lett..