On the Fluctuating Beckmann Shadowed Composite Fading Model and Its Applications to Wireless Communications

Abstract

In this paper, the fundamental statistics of fluctuating Beckmann shadowed (FBS) fading model which is composite of fluctuating Beckmann (FB) and inverse Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> distributions, are provided. Accordingly, a wide range of composite generalized fading distributions can be obtained as special cases of the proposed distribution, such as, double shadowed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa -\mu$</tex-math></inline-formula> fading Type I. To this effect, mathematically tractable expressions of both the exact and asymptotic at high signal-to-noise (SNR) regime of the probability density function (PDF), cumulative distribution function (CDF), and generalised-moment generating function (G-MGF) are derived. In addition, the fundamental statistics for integer <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> and even value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> that represent the shadowing of the dominant components and real extension of the number of the multipath clusters, respectively, are given in simple closed-from formats. These statistical characterizations are then used to evaluate the performance of the wireless communications in terms of the outage probability (OP), average bit error probability (ABEP), amount-of-fading (AF), channel quality estimation index (CQEI), error vector magnitude (EVM), average channel capacity (ACC), and effective throughput (ET). Furthermore, the area under the receiver operating characteristics (AUC) curve of the energy detection based spectrum sensing and the secure outage probability (SOP) as well as the lower bound of SOP (SOP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{L}$</tex-math></inline-formula> ) of the physical layer are also analysed. The validation of the derived expressions is verified via comparing the numerical results with the Monte-Carlo simulations for different values of the fading parameters.