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Journal ArticleDOI

On Physical Layer Security of $\alpha$ - $\eta$ - $\kappa$ - $\mu$ Fading Channels

26 Jul 2018-IEEE Communications Letters (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 22, Iss: 10, pp 2168-2171
TL;DR: In this paper, the secrecy performance of the classic Wyner's wiretap model, where the main and eavesdropper channels are modeled by a general and versatile $\alpha $ - $\eta$ - $\kappa $ - ''mu $ fading model'' was analyzed.
Abstract: In this letter, we study the secrecy performance of the classic Wyner’s wiretap model, where the main and eavesdropper channels are modeled by a general and versatile $\alpha $ - $\eta $ - $\kappa $ - $\mu $ fading model. Novel and exact expressions of the average secrecy capacity and secrecy outage probability have been derived. Previous results on physical layer security can be obtained through our newly derived expressions by specializing the model parameters. More importantly, the derived results are also applicable for the secrecy performance analysis of some field measurements (e.g., in millimeter wave communications), which cannot be analyzed by previous results.
Citations
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Journal ArticleDOI
TL;DR: The results show that when the eavesdropper is placed near the transmitter, atmospheric condition imposes a less significant impact on secrecy performance; certain level of correlation can potentially enhance the secrecy performance for FSO communications; and the correlation imposes opposite impacts on the ASC and SOP of FSOcommunications.
Abstract: In this article, we study the physical layer security of free-space optical (FSO) communications under different eavesdropping scenarios. More specifically, the secrecy performance of FSO communication employing intensity modulation/direct detection detection is analyzed for the well-established Malaga channels. Three different realistic scenarios of eavesdropping are considered by assuming different placement locations for the eavesdropper in the paper. Novel expressions for the average secrecy capacity (ASC) and secrecy outage probability (SOP) are derived for the considered scenarios, and useful insights are also provided through asymptotic analysis. The results show: (1) When the eavesdropper is placed near the transmitter, atmospheric condition imposes a less significant impact on secrecy performance; (2) Certain level of correlation can potentially enhance the secrecy performance for FSO communications; (3) The correlation imposes opposite impacts on the ASC and SOP of FSO communications; and the secrecy performance metrics exhibit a non-monotonic impact with the increase of correlation; (5) When the correlation of the FSO links is too small or too large (i.e., the correlation parameter around 0 or 1), the correlation plays a more significant impact on secrecy performance; and (6) The asymptotic slope of the SOP is 0.5 for all eavesdropping scenarios under practical FSO channels.

45 citations

Journal ArticleDOI
TL;DR: This work introduces a comprehensive review of the main information-theoretic metrics used to measure the secrecy performance in physical layer security, and a theoretical framework related to the most commonly used physical layerSecurity techniques to improve secrecy performance is provided.
Abstract: Physical layer security is a promising approach that can benefit traditional encryption methods. The idea of physical layer security is to take advantage of the propagation medium’s features and impairments to ensure secure communication in the physical layer. This work introduces a comprehensive review of the main information-theoretic metrics used to measure the secrecy performance in physical layer security. Furthermore, a theoretical framework related to the most commonly used physical layer security techniques to improve secrecy performance is provided. Finally, our work surveys physical layer security research over several enabling 5G technologies, such as massive multiple-input multiple-output, millimeter-wave communications, heterogeneous networks, non-orthogonal multiple access, and full-duplex. We also include the key concepts of each of the technologies mentioned above. Also identified are future fields of research and technical challenges of physical layer security.

35 citations

Journal ArticleDOI
TL;DR: The effect of randomness caused by the Beaulieu-Xie fading channel on the performance of physical layer security and the closed-form expressions for lower-bound of secrecy outage probability and strictly positive secrecy capacity for the said channel are studied.
Abstract: With the expansion of IoT and device-to-device communication applications, the security and privacy of the information have been kept at the forefront. The existence of a secondary eavesdropper, which attempts to access the confidential information of the legitimate partners, makes the data communication insecure. In this regard, we study the effect of randomness caused by the Beaulieu-Xie fading channel on the performance of physical layer security. To this end, the analysis for the secrecy outage probability (SOP) and average secrecy capacity (ASC) is carried out. Further, we derived the closed-form expressions for lower-bound of secrecy outage probability and strictly positive secrecy capacity (SPSC) for the said channel. To get more insight into the system, the high-power and low-power analysis of the ASC are also provided. Besides, the impact of different fading parameters on the system matrices is also investigated. Finally, the theoretical results are verified via extensive Monte Carlo simulations.

31 citations

Journal ArticleDOI
TL;DR: The physical layer security over Fox's fading wiretap channels is investigated, and closed-form expressions are derived for the secrecy outage probability (SOP), the probability of non-zero secrecy capacity, and the average secrecy capacity for the non-colluding scenario.
Abstract: Most of the well-known fading distributions, if not all of them, could be encompassed by Fox's $H$-function fading. Consequently, we investigate the exact and asymptotic behavior of physical layer security (PLS) over Fox's $H$-function fading wiretap channels. In particular, closed-form expressions are derived for secrecy outage probability (SOP), probability of non-zero secrecy capacity (PNZ), and average secrecy capacity (ASC). These expressions are given in terms of either univariate or bivariate Fox's $H$-function. In order to show the comprehensive effectiveness of our derivations, three metrics are respectively listed over the following frequently used fading channels, including Rayleigh, Weibull, Nakagami-$m$, $\alpha-\mu$, Fisher-Snedecor (F-S) $\mathcal{F}$, and extended generalized-$\mathcal{K}$ (EGK). Our tractable results are more straightforward and general, besides that, they are feasible and applicable, especially the SOP, which was mostly limited to the lower bound in literature due to the difficulty of achieving closed-from expressions. In order to validate the accuracy of our analytical results, Monte-Carlo simulations are subsequently performed for the special case $\alpha-\mu$ fading channels. One can observe perfect agreements between the exact analytical and simulation results, and highly accurate approximations between the exact and asymptotic analytical results.

24 citations

References
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Proceedings ArticleDOI
01 Jul 1990
TL;DR: This algorithm allows us to calculate definite and indefinite integrals of the products of elementary and special functions of hypergeometric type and its realization in the REDUCE system during the process of creation of INTEGRATOR system.
Abstract: The most voluminous bibliography of the analytical methods for calculating of integrals is represented in the article [19]. It is shown there that the most effective and the simplest algorithm of analytical integration was made by O.I. Marichev [8, 9, 12]. Later it was realized in the reference-books [16-18, 20]. This algorithm allows us to calculate definite and indefinite integrals of the products of elementary and special functions of hypergeometric type. It embraces about 70 per cent of integrals which are included in the world reference-literature. It allows to calculate many other integrals too.The present article contains short description of this algorithm and its realization in the REDUCE system during the process of creation of INTEGRATOR system. Only one general method of integration is known to be realized on the computers, i.e. criterion algorithm for calculating of indefinite integrals of elementary functions through elementary functions by themselves (the authors of it are M. Bronstein and other).The idea of our algorithm is in the following. The initial integrals is transformed to contour integral from the ratio of products of gamma-functions by means of Mellin transform and parseval equality. The residue theorem is used for the calculating of the received integral which due to the strict rules results in sums of hypergeometric series. The value of integral itself and the integrand functions are the special cases of the well-known Meijer's G-function [4, 7, 8, 12, 14, 18].Programming packet is realized in programming languages PASCAL and REDUCE. It also offers the opportunity of finding the values for some classical integral transforms (Laplace, Hankel, Fourier, Mellin and etc.). The REDUCE's part of packet contains the main properties of the well-known special functions, such as the Bessel and gamma-functions and kindred functions, Anger function, Weber function, Whittaker functions, generalized hypergeometric functions. Special place in the packet is occupied by Meijers's G-function for which the main properties such as finding the particular cases and representation by means of hypergeometric series are realized.

1,028 citations

Journal ArticleDOI
TL;DR: This article examines security, a pivotal issue in the 5G network where wireless transmissions are inherently vulnerable to security breaches, and focuses on physical layer security, which safeguards data confidentiality by exploiting the intrinsic randomness of the communications medium.
Abstract: The fifth generation (5G) network will serve as a key enabler in meeting the continuously increasing demands for future wireless applications, including an ultra-high data rate, an ultrawide radio coverage, an ultra-large number of devices, and an ultra-low latency. This article examines security, a pivotal issue in the 5G network where wireless transmissions are inherently vulnerable to security breaches. Specifically, we focus on physical layer security, which safeguards data confidentiality by exploiting the intrinsic randomness of the communications medium and reaping the benefits offered by the disruptive technologies to 5G. Among various technologies, the three most promising ones are discussed: heterogenous networks, massive multiple-input multiple-output, and millimeter wave. On the basis of the key principles of each technology, we identify the rich opportunities and the outstanding challenges that security designers must tackle. Such an identification is expected to decisively advance the understanding of future physical layer security.

848 citations

Book
01 Jan 1979

635 citations

Journal ArticleDOI
01 Mar 1972
TL;DR: In this article, the authors evaluate an infinite integral whose integrand is a product of the H-function and a double Mellin-Barnes type contour integral, which is one of the most general integrals known so far and includes a large number of new and recently obtained interesting integrals as its particular cases.
Abstract: The aim of the present paper is to evaluate an infinite integral whose integrand is a product of the H-function and a double Mellin-Barnes type contour integral. The integral evaluated here is one of the most general integrals known so far and includes a large number of new and recently obtained interesting integrals as its particular cases. The Laplace-transform of the double Mellin-Barnes type contour integral has also been obtained as a special case of our main result and is likely to prove quite useful in solving certain boundary value problems.

246 citations