A Comprehensible Form of the Product of Two Gaussian Q Functions and its Usefulness in κ-μ Shadowed Fading Distribution

Abstract In 2007, contrary to other approximations, Karagiannidis et al. proposed a more accurate approximation of the Gaussian Q function and its integer powers, for all the positive arguments. However, when it is used to compute the symbol error probability (SEP) of various coherent digital modulation techniques over parametric fading distributions like the κ − μ shadowed fading, it loses its analytical tractability. In this paper, using Taylor series approximation of the exponential function, we comprehend the approximation of interest (with accuracy intact) which facilitates in the simplification of the key integrals used in the SEP computation of digital modulation techniques over κ − μ shadowed fading distribution. Apart from various applications, the significance of the κ − μ shadowed fading statistics lies in the fact that it unifies most of the popular fading models like one sided Gaussian, Rayleigh, Nakagami-m, Nakagami-q, Rician, Rician-shadowed, η − μ and κ − μ , under one umbrella. In order to show the utility of the proposed work, the SEP of hexagonal-QAM is calculated over Rayleigh fading channel which is one of the widely used cases of the κ − μ shadowed fading distribution. Monte Carlo simulations have also been carried out to justify the accuracy of the analysis.

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