University of Oulu

Vega Sánchez, JD, Moya Osorio, DP, Benitez Olivo, EE, Alves, H, Paredes Paredes, MC, Urquiza Aguiar, L. On the statistics of the ratio of nonconstrained arbitrary α‐μ random variables: A general framework and applications. Trans Emerging Tel Tech. 2019;e3832. https://doi.org/10.1002/ett.3832

On the statistics of the ratio of nonconstrained arbitrary α ‐ μ random variables : a general framework and applications

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Author: Vega Sánchez, José David1; Moya Osorio, Diana Pamela2; Benitez Olivo, Edgar Eduardo3;
Organizations: 1Departamento de Electrónica, Telecomunicaciones y Redes de Información, Escuela Politécnica Nacional (EPN), Quito, 170525, Ecuador
2Department of Electrical Engineering, Federal University of São Carlos, São Carlos, SP, 13565-905 Brazil
3São Paulo State University (UNESP), Campus of São João da Boa Vista, São João da Boa Vista, SP, 13876-750, Brazil
4Centre for Wireless Communications (CWC), University of Oulu, Oulu, 90014, Finland
Format: article
Version: accepted version
Access: embargoed
Online Access: PDF Full Text (PDF, 0.5 MB)
Persistent link: http://urn.fi/urn:nbn:fi-fe202001071337
Language: English
Published: John Wiley & Sons, 2019
Publish Date: 2021-12-17
Description:

Abstract

In this paper, we derive closed‐form exact expressions for the main statistics of the ratio of two squared α‐μ random variables, which are of interest in many scenarios for future wireless networks where generalized distributions are more suitable to fit with field data. Importantly, different from previous proposals, our expressions are general in the sense that are valid for nonconstrained arbitrary values of the parameters of the α‐μ distribution. Thus, the probability density function, cumulative distribution function, moment generating function, and higher‐order moments are given in terms of both (i) the Fox H‐function for which we provide a portable and efficient Wolfram Mathematica code and (ii) easily computable series expansions. Our expressions can be used straightforwardly in the performance analysis of a number of wireless communication systems, including either interference‐limited scenarios, spectrum sharing, full‐duplex, or physical‐layer security networks, for which we present the application of the proposed framework. Moreover, closed‐form expressions for some classical distributions, derived as special cases from the α‐μ distribution, are provided as byproducts. The validity of the proposed expressions is confirmed via Monte Carlo simulations.

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Series: Transactions on emerging telecommunications technologies
ISSN: 2161-5748
ISSN-E: 2161-3915
ISSN-L: 2161-5748
Volume: Online First
Issue: Online First
Pages: 1 - 20
DOI: 10.1002/ett.3832
OADOI: https://oadoi.org/10.1002/ett.3832
Type of Publication: A1 Journal article – refereed
Field of Science: 213 Electronic, automation and communications engineering, electronics
Subjects:
Copyright information: © 2019 John Wiley & Sons, Ltd. This is the peer reviewed version of the following article: Vega Sánchez, JD, Moya Osorio, DP, Benitez Olivo, EE, Alves, H, Paredes Paredes, MC, Urquiza Aguiar, L. On the statistics of the ratio of nonconstrained arbitrary α‐μ random variables: A general framework and applications. Trans Emerging Tel Tech. 2019;e3832. https://doi.org/10.1002/ett.3832, which has been published in final form at https://doi.org/10.1002/ett.3832. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.