Unified Composite Distribution With Applications to Double Shadowed $\kappa$-$\mu$ Fading Channels

Abstract

In this paper, a mixture Gamma shadowed (MGS) model is proposed as a unified composite distribution via representing the shadowing impact by an 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> . The exact expression and the asymptotic behaviour at high average signal-to-noise ratio (SNR) regime of the fundamental statistics of a MGS distribution are derived first. These statistics are then applied to analyze the performance of the wireless communication systems over 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">$\kappa$</tex-math></inline-formula> - <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> fading channels. In particular, the outage probability (OP), average bit error probability (ABEP), average channel capacity (ACC), effective capacity (EC) and average area under the receiver operating characteristics curve (AUC) of energy detection (ED) are provided. The numerical and simulation results as well as a comparison with previous exact works are presented to verify the validation of our analysis.