Closed-Form Exact and Asymptotic Expressions for the Symbol Error Rate and Capacity of the -Function Fading Channel

Alhennawi, Husam R.; Ayadi, Moataz M. H. El; Ismail, Mahmoud H.; Mourad, Hebat-Allah M.

doi:10.1109/tvt.2015.2424591

Cited by 113 publications

(79 citation statements)

References 21 publications

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“…• When the fading parameters, namely, µ and m which represent the real extension of multipath clusters and shadowing severity index, respectively are arbitrary numbers, the secrecy performance metrics are obtained in terms of the extended generalised bivariate Fox's H-function (EGBFHF). Although, this function is not available in the popular mathematical software packages such as MATLAB and MATHEMATICA, it has been implemented by several works such as [10] and [24].…”

Section: Introductionmentioning

confidence: 99%

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

Al‐Hmood

Al-Raweshidy

2019

IEEE Access

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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 κ − µ shadowed and the classical Beckmann distributions.Specifically, the average secrecy capacity (ASC), secure outage probability (SOP), the lower bound of SOP (SOP L ), and the probability of strictly positive secrecy capacity (SPSC) are derived in exact closed-form expressions using two different values of the fading parameters, namely, m and µ which represent the multipath and shadowing severity impacts, respectively. Firstly, when the fading parameters are arbitrary values, the performance metrics are derived in exact closed-form in terms of the extended generalised bivariate Fox's H-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, m and µ are assumed to be integer and even numbers, respectively. The numerical results of this analysis are verified via Monte Carlo simulations. Index TermsFluctuating Beckmann fading channel, average secrecy capacity, secure outage probability, probability of strictly positive secrecy capacity.to the additive white Gaussian noise (AWGN) and Rayleigh fading channel are given in [2] and [3], respectively. In [4], the SPSC when both the main and eavesdropper channels undergo Rician fading channel is derived. The SOP and the SPSC of the physical layer using Rician and Nakagami-m fading conditions for the Bob and the eavesdropper wireless channels are given in [5]. The Weibull fading channel model is used in [6] and [7] to study the SPSC and ASC, respectively.Recently, many works have been implemented using various generalized fading distributions that unify most of the well-known channel models. In addition, they provide results closer to the practical data than the conventional distributions, namely, Rayleigh, Nakagami-m, and Nakagami-n. In [8], the ASC over κ − µ fading channel that is used to model the line-of-sight (LoS) communication environment is derived. The performance of the physical layer security in non-linear communication scenario is analysed in [9] and [10] via utilising the α − µ fading condition. Moreover, the ASC, the SOP, the SOP L , and the SPSC of the physical layer over α − µ fading using the Fox's H-function channel model which is a unified framework for a variety of distributions are presented in [11]. The ASC using the κ − µ/α − µ and α − µ/κ − µ fading scenarios for the main/eavesdropper channels is given in [12]. The more generalised fading channels α − κ − µ and α − η − µ are used in [13] to derive the SOP L and its asymptotic value. These fading distributions are provided in a single model which is α − η − κ − µ that is also used to represent both the main channel and the eavesdropper's channel of the classic Wyner's wiretap model in [14].The wi...

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Section: Introductionmentioning

confidence: 99%

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

Al‐Hmood

Al-Raweshidy

2019

IEEE Access

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“…Although the numerical evaluation for multivariate Foxs H-function is not available in popular mathematical packages such as MATLAB and Mathematica, its efficient implementations have been reported. For example, two Mathematica implementations of the single Foxs H-function are provided in [14] and [15], a Python implementation for the multivariable Foxs H-function is presented in [16], and an efficient GPUoriented MATLAB routine for the multivariate Foxs H-function is introduced in [17]. In the following, we will utilize these novel implementations to evaluate our results.…”

Section: B Multivariable Fox's H-functionmentioning

confidence: 99%

“…The asymptotic expansions of the OP for high SNRs can be obtained by computing the residue [16]. Let us consider the residue at the points ζ = (ζ 1 , .…”

Section: Propositionmentioning

confidence: 99%

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Sum of Fisher-Snedecor F Random Variables and Its Applications

Zhang

Cheng

et al. 2020

IEEE Open J. Commun. Soc.

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The statistical characterization of the sum of random variables (RVs) are useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of a sum of independent but not identically distributed (i.n.i.d.)Fisher-Snedecor F RVs. Both PDF and CDF are given in terms of the multivariate Fox's H-function. Besides, a simple and accurate approximation to the sum of i.n.i.d. Fisher-Snedecor F variates is presented using the moment matching method. The obtained PDF and CDF are used to evaluate the performance of wireless communication applications including the outage probability, the effective capacity and the channel capacities under four different adaptive transmission strtegies. Moreover, the corresponding approximate expressions are obtained to provide useful insights for the design and deployment of wireless communication systems. In addition, we derive simple asymptotic expressions for the proposed mathematical analysis in the high signal-to-noise ratio regime. Finally, the numerical results demonstrate the accuracy of the derived expressions. Index TermsChannel capacity, effective capacity, Fisher-Snedecor F -distribution, sum of random variables, Recently, the Fisher-Snedecor F distribution was proposed [1] as a tractable fading model to describe the combined effects of shadowing and multipath fading. This distribution can be reduced to some common ). 2 fading models, such as Nakagami-m and Rayleigh fading channels. Furthermore, it is found in [1] that the F distribution can provide a better fit to the experimental data obtained for device-to-device (D2D) and wearable communication links, especially at 5.8 GHz, as compared with the well established generalized-K (GK) distribution. In addition, its probability density function (PDF) consists of only elementary functions and it leads to more tractable analysis than the GK model [1]. Due to its promising properties, the performance of digital communication systems over F distributed fading channels has been analyzed in [2]-[5] and the references therein. The sum of random variables (RVs) has a wide range of important applications in the performance analysis of wireless communication systems. For example, to enhance the quality of the received signal, maximal-ratio combining (MRC) can be deployed at the receiver to maximize the combiner output signalto-noise ratio (SNR) [6]. The system with MRC receiver operating over different fading channels has been extensively studied [7]-[12]. The PDF and CDF of the sum of Fisher-Snedecor F RVs has been derived in terms of Lauricella multivariate hypergeometric function [13]. However, there results are difficult to be used in the performance analysis of MRC systems over Fisher-Snedecor F fading channels due to the complex of the Lauricella multivariate hypergeometric function. Moreover, authors in [13] obtain outage probability (OP) and outage capacity expressions involving L-fold Mellin-Barnes...

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“…It is worth mentioning here that efficient implementations of the bivariate H-function using Python and MAT-LAB have already been presented in [16,22], respectively. To the best of the authors' knowledge, (14) is the most general expression for P m ever presented in the literature.…”

Section: Application To the Fox's H -Function Fading Channelmentioning

confidence: 99%

Unified approach for probability of detection evaluation over generalised fading channels

2016

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In this paper, we revisit energy detection-based spectrum sensing cognitive radio systems operating over generalised fading channels. In particular, we derive closed-form exact expressions as well as lowand high-signal-to-noise ratio asymptotic expansions for the misdetection probability over the Fox's H-function fading channel. The closed-form expression is given in terms of the bivariate Fox's Hfunction and subsumes most of the expressions previously presented in the literature. Also, the obtained asymptotic expressions are very easy to compute and can be used to get various performance insights.We verified, theoretically and numerically, the validity of the exact expression for important special cases previously reported in the literature, namely the Nakagami-m and the extended generalised-K (EGK) fading distributions. Numerical results also demonstrate the high accuracy of the asymptotic expansions.

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Closed-Form Exact and Asymptotic Expressions for the Symbol Error Rate and Capacity of the -Function Fading Channel

Cited by 113 publications

References 21 publications

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

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

Sum of Fisher-Snedecor F Random Variables and Its Applications

Unified approach for probability of detection evaluation over generalised fading channels

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