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Electronics Letters

Performance analysis of physical layer security over α – μ fading channel

Long Kong, Hung Tran, Georges Kaddoum

Published Nov 18, 2015• 49 citations
Publisher

Abstract

Recently, many works have focused on analysing the metrics of physical layer security over different wireless channels such as additive white Gaussian noise, Rayleigh, Rician and Nakagami‐ m fading distributions. To extend the analysis to the general case, the α – μ fading channel is considered, which can span the aforementioned cases. For this purpose, the physical layer security over the α – μ fading channel is presented. The closed‐form expressions for the probability of positive secrecy capacity and upper bound of the secrecy outage probability are derived. Their accuracies are assessed through comparison of theoretical analysis and simulations results.

DOI
10.1049/el.2015.2160

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Intrigued by the rapid growth and expand of wireless devices, data security is increasingly playing a significant role in our daily transactions and interactions with different entities. Possible examples, including e-healthcare information and online shopping, are becoming vulnerable due to the intrinsic nature of wireless transmission medium and the widespread open access of wireless links. Traditionally, the communication security is mainly regarded as the tasks at the upper layers of layered protocol stack, security techniques, including personal access control, password protection, and end-to-end encryption, have been widely studied in the open literature. More recently, plenty of research interests have been drawn to the physical layer forms of secrecy. 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Recently, many works have focused on analysing the metrics of physical layer security over different wireless channels such as additive white Gaussian noise, Rayleigh, Rician and Nakagami‐ m fading distributions. To extend the analysis to the general case, the α – μ fading channel is considered, which can span the aforementioned cases. For this purpose, the physical layer security over the α – μ fading channel is presented. The closed‐form expressions for the probability of positive secrecy capacity and upper bound of the secrecy outage probability are derived. Their accuracies are assessed through comparison of theoretical analysis and simulations results.
In this paper, the physical layer security aspects of a wireless framework over α−κ−μ shadowed (AKMS) fading channel are examined by acquiring closed-form novel expressions of average secrecy capacity, secure outage probability (SOP), and strictly positive secrecy capacity. The lower bound of SOP is derived along with the asymptotic expression of SOP at the high signal-to-noise ratio regime in order to achieve secrecy diversity gain. Capitalizing on these expressions, the consequences due to the simultaneous occurrence of fading and shadowing are quantified. Finally, Monte-Carlo simulations are demonstrated to assess the correctness of the expressions.
Abstract Physical layer security is a feasible solution to improve wireless communication secrecy against eavesdropping threats. Within this framework, this work examines the secrecy performance of a wireless link subjected to eavesdropping over generalized composite fading environments, specifically using the α-η-µ/Lognormal and α-κ-µ/Lognormal distributions. Closed-form results are derived for key secrecy performance metrics, including the average secrecy capacity (ASC), a lower bound on the secrecy outage probability SOPL, and the probability of strictly positive secrecy capacity (SPSC). Additionally, asymptotic analyses of ASC, SOPL, and SPSC are presented in the high-SNR regime to yield simplified insights into system behavior. The analysis accommodates arbitrary and independent fading conditions for the main and eavesdropper channels, thereby enabling a comprehensive evaluation of the impact of various channel parameters. Ultimately, all analytical outcomes are corroborated using comprehensive Monte Carlo simulations, affirming their precision and relevance.
In this study, the authors investigate the secrecy performance at the physical layer of wireless communication systems where the channels are modelled as cascaded fading channels, in which the fading effects are worse than those in the cellular communication channels like Rayleigh and Nakagami‐ m . Analytic results are derived for the cascaded Nakagami‐ m fading channel model comprising the cascaded Rayleigh, 2*Nakagami‐ m , the generalised‐ K , and the conventional cellular channel models as well. By evaluating the information‐theoretic physical layer security performance, they obtain the closed‐form expressions of the average secrecy capacity and probability of the positive secrecy capacity in case of that channel‐state‐information of the eavesdropper is known by the source. Then they obtain the exact closed‐form secrecy outage probability (SOP) when the eavesdropper is passive. Analytic results are computed in terms of the bivariate and univariate Meijer's G functions and later on are successfully validated through Monte Carlo simulations. The simulation results show that the secrecy performance worsens with the increasing cascading degree of the fading channels. For example, in 2*Nakagami‐ m fading channels where the cascading degree is 2, extra 4 dB signal‐to‐noise ratio is required to achieve the same SOP value in comparison with the classical Nakagami‐ m fading channels.
Intrigued by the rapid growth and expand of wireless devices, data security is increasingly playing a significant role in our daily transactions and interactions with different entities. Possible examples, including e-healthcare information and online shopping, are becoming vulnerable due to the intrinsic nature of wireless transmission medium and the widespread open access of wireless links. Traditionally, the communication security is mainly regarded as the tasks at the upper layers of layered protocol stack, security techniques, including personal access control, password protection, and end-to-end encryption, have been widely studied in the open literature. More recently, plenty of research interests have been drawn to the physical layer forms of secrecy. As a new but appealing paradigm at physical layer, physical layer security is based on two pioneering works: (i) Shannon’s information-theoretic formulation and (ii) Wyner’s wiretap formulation. \n \nOn account of the fundamental of physical layer security and the different nature of various wireless network, this dissertation is supposed to further fill the lacking of the existing research outcomes. To be specific, the contributions of this dissertation can be summarized as three-fold:(i) exploration of secrecy metrics to more general fading channels; (ii) characterization a new fading channel model and its reliability and security analysis in digital communication systems; and (iii) investigation of physical layer security over the random multiple-input multiple-output (MIMO) α −μ fading channels. \n \nTaking into account the classic Alice-Bob-Eve wiretap model, the first contribution can be divided into four aspects: (i) we have investigated the secrecy performance over single-input single-output (SISO) α −μ fading channels. The probability of non-zero (PNZ) secrecy capacity and the lower bound of secrecy outage probability (SOP) are derived for the special case when the main channel and wiretap channel undergo the same non-linearity fading parameter, i.e., α. Later on, for the purpose of filling the gap of lacking closed-form expression of SOP in the open literature and extending the obtained results in chapter 2 to the single-input multiple-output (SIMO) α − μ wiretap fading channels, utilizing the fact that the received signal-tonoise ratios (SNRs) at the legitimate receiver and eavesdropper can be approximated as new α −μ distributed random variables (RVs), the SOP metric is therefore derived, and given in terms of the bivariate Fox’s H-function; (ii) the secrecy performance over the Fisher-Snedecor F wiretap fading channels is initially considered. The SOP, PNZ, and ASC are finalized in terms of Meijer’s G-function; (iii) in order to generalize the obtained results over α −μ and Fisher-Snedecor F wiretap fading channels, a more flexible and general fading channel, i.e., Fox’s H-function fading model, are taken into consideration. Both the exact and asymptotic analysis of SOP, PNZ, and average secrecy capacity (ASC), are developed with closed-form expressions; and (iv) finally, motivated by the fact that the mixture gamma (MG) distribution is an appealing tool, which can be used to model the received instantaneous SNRs over wireless fading channels, the secrecy metrics over wiretap fading channels are derived based on the MG approach. \n \nDue to the limited transmission power and communication range, cooperative relays or multi-hop wireless networks are usually regarded as two promising means to address these concerns. Inspired by the obtained results in Chapters 2 and 3, the second main contribution is to propose a novel but simple fading channel model, namely, the cascaded α −μ. This new distribution is advantageous since it encompasses the existing cascaded Rayleigh, cascaded Nakagami-m, and cascaded Weibull with ease. Based on this, both the reliability and secrecy performance of a digital system over cascaded α −μ fading channels are further evaluated. Closed-form expressions of reliability metrics (including amount of fading (AF), outage probability, average channel capacity, and average symbol error probability (ABEP).) and secrecy metrics (including SOP, PNZ, and ASC) are respectively provided. Besides, their asymptotic behaviors are also performed and compared with the exact results. \n \nConsidering the impacts of users’ densities, spatial distribution, and the path-loss exponent on secrecy issue, the third aspect of this thesis is detailed in Chapter 8 as the secrecy investigation of stochastic MIMO system over α −μ wiretap fading channels. Both the stochastic geometry and conventional space-time transmission (STT) scheme are used in the system configuration. The secrecy issue is mathematically evaluated by three metrics, i.e., connection outage, the probability of non-zero secrecy capacity and the ergodic secrecy capacity. Those three metrics are later on derived regarding two ordering scheme, and further compared with Monte-Carlo simulations.
Physical Layer Security Over α\alphaα - κ\kappaκ - μ\muμ and α\alphaα - η\etaη - μ\muμ Fading Channels
In this correspondence, the physical layer security of wireless systems under generalized α-κ-μ and α-η-μ fading with arbitrary fading parameters is analyzed in terms of the secrecy outage probability (SOP). To this end, novel analytical expressions for the lower bound of the SOP are derived. Moreover, an asymptotic secrecy analysis is investigated for each corresponding SOP to get the secrecy diversity gain. Monte Carlo simulations are provided to assess the accuracy of the proposed analytical framework.
In this letter, physical layer secrecy/security performance analysis has been investigated over cascaded fading channels where the fading effects are worse than those in the cellular communication channels like Rayleigh and Nakagami-m. Analytic results are derived for the double Rayleigh fading channel model. As the analysis are evaluated, first the closed-form expression of the probability of the positive secrecy capacity is obtained, then the exact secrecy outage probability is obtained in the closed-form. Finally, the analytic results are verified by comparing with the computer simulations.