Copula – to model multi‐channel fading by correlated but arbitrary Weibull marginals, giving a closed‐form outage probability of selection‐combining reception

Abstract

This study introduces the mathematical paradigm of 'copula' to the technical field of channel modelling. Copulabased modelling allows each sensor of its distinct set of fading parameters, and allows cross-correlation among various sensors' parameter sets. Hence, the branch statistics may be non-identical over various branches, yet cross-correlated between branches. This scenario is realistic especially for sensors of different polarisations/constructions and/or for sensors at widely separate locationsas increasingly common for wireless transceivers. Despite such versatility in modelling, this copula-based multivariate fading distribution may yet be so simple in mathematical form that the system's outage probability can be analytically derived in a closed form, free of any infinite-term summation and free of any unsolved integration.

Copula function‐based analysis of outage probability and coverage region for wireless multiple access communications with correlated fading channels

“…normal, Clayton, and t Copula for estimation of channel parameters, where, the Clayton Copula accounts for only positive dependence values and can not justify the negative dependence structure. In [18], studying the performance of correlated fading channels under Weibull distribution using the Copula concept, a closed-form expression for outage probability exploiting the survival-Gumbel Copula function has been obtained.…”

The Impact of Side Information on Physical Layer Security under Correlated Fading Channels

“…Thus, by exploiting (70), W η can be computed, and then the proof is completed. Proof of C2 s : By applying Lemma 2 to ASC definition in (23) and exploiting the linearity rules of integration, (23) can be decomposed as: (75)…”

Copula based performance analysis for one‐hoping relay channel in wireless ad hoc network with correlated fading channels

“…Some works have also been done by the applications of Copula theory in the correlated wireless fading channels. In [20 ], the authors considered the correlated Weibull fading channels and obtained a closed‐form expression for outage probability by exploiting the survival Gumbel Copula. In contrast, Ghadi and Hodtani [21 ] derived the closed‐form expressions for outage probability and coverage region under correlated Rayleigh fading multiple access channels by utilising the Farlie–Gumbel–Morgenstern (FGM) Copula.…”