Efficient Numerical Methods for Analysis of Square Ratio of κ-μ And η-μ Random Processes with Their Applications in Telecommunications

Gradimir V. Milovanović, Suad Suljović, Stefan R. Panić, Ismet Kalčo, Mihajlo Stefanović

Research output: Contribution to journalArticle

Abstract

We will provide statistical analysis of the square ratio of -μ and η-μ random processes and its application in the signal-to-interference ratio (SIR) based performance analysis of wireless transmission subjected to the influence of multipath fading, modelled by -μ fading model, and undesired occurrence of co-channel interference (CCI), distributed as η-μ random process. First contribution of the paper is deriving exact closed expressions for the probability density function (PDF) and cumulative distribution function (CDF) of square ratio of -μ and η-μ random processes. Further, a verification of accuracy of these PDF and CDF expressions was given by comparison with the corresponding approximations obtained by the high-precision quadrature formulas of Gaussian type with respect to the weight functions on (0,+∞). The computational procedure of such quadrature rules is provided by using the constructive theory of orthogonal polynomials and the Mathematica package OrthogonalPolynomials created by Cvetković and Milovanović (2004). Capitalizing on obtained expression, important wireless performance criteria, namely, outage probability (OP), have been obtained, as functions of transmission parameters. Also, possible performance improvement is observed through a glance at SC (selection combining) reception employment based on obtained expressions.

Original languageEnglish
Article number4967613
JournalMathematical Problems in Engineering
Volume2018
DOIs
Publication statusPublished - 1 Jan 2018
Externally publishedYes

Fingerprint

Random process
Random processes
Telecommunications
Telecommunication
Numerical methods
Numerical Methods
Probability density function
Distribution functions
Cumulative distribution function
Fading
Fading (radio)
Multipath fading
Outages
Co-channel Interference
Outage Probability
Statistical methods
Quadrature Rules
Mathematica
Quadrature Formula
Multipath

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Efficient Numerical Methods for Analysis of Square Ratio of κ-μ And η-μ Random Processes with Their Applications in Telecommunications. / Milovanović, Gradimir V.; Suljović, Suad; Panić, Stefan R.; Kalčo, Ismet; Stefanović, Mihajlo.

In: Mathematical Problems in Engineering, Vol. 2018, 4967613, 01.01.2018.

Research output: Contribution to journalArticle

@article{0778a64509a945f396e224da226935f9,
title = "Efficient Numerical Methods for Analysis of Square Ratio of κ-μ And η-μ Random Processes with Their Applications in Telecommunications",
abstract = "We will provide statistical analysis of the square ratio of -μ and η-μ random processes and its application in the signal-to-interference ratio (SIR) based performance analysis of wireless transmission subjected to the influence of multipath fading, modelled by -μ fading model, and undesired occurrence of co-channel interference (CCI), distributed as η-μ random process. First contribution of the paper is deriving exact closed expressions for the probability density function (PDF) and cumulative distribution function (CDF) of square ratio of -μ and η-μ random processes. Further, a verification of accuracy of these PDF and CDF expressions was given by comparison with the corresponding approximations obtained by the high-precision quadrature formulas of Gaussian type with respect to the weight functions on (0,+∞). The computational procedure of such quadrature rules is provided by using the constructive theory of orthogonal polynomials and the Mathematica package OrthogonalPolynomials created by Cvetković and Milovanović (2004). Capitalizing on obtained expression, important wireless performance criteria, namely, outage probability (OP), have been obtained, as functions of transmission parameters. Also, possible performance improvement is observed through a glance at SC (selection combining) reception employment based on obtained expressions.",
author = "Milovanović, {Gradimir V.} and Suad Suljović and Panić, {Stefan R.} and Ismet Kalčo and Mihajlo Stefanović",
year = "2018",
month = "1",
day = "1",
doi = "10.1155/2018/4967613",
language = "English",
volume = "2018",
journal = "Mathematical Problems in Engineering",
issn = "1024-123X",
publisher = "Hindawi Publishing Corporation",

}

TY - JOUR

T1 - Efficient Numerical Methods for Analysis of Square Ratio of κ-μ And η-μ Random Processes with Their Applications in Telecommunications

AU - Milovanović, Gradimir V.

AU - Suljović, Suad

AU - Panić, Stefan R.

AU - Kalčo, Ismet

AU - Stefanović, Mihajlo

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We will provide statistical analysis of the square ratio of -μ and η-μ random processes and its application in the signal-to-interference ratio (SIR) based performance analysis of wireless transmission subjected to the influence of multipath fading, modelled by -μ fading model, and undesired occurrence of co-channel interference (CCI), distributed as η-μ random process. First contribution of the paper is deriving exact closed expressions for the probability density function (PDF) and cumulative distribution function (CDF) of square ratio of -μ and η-μ random processes. Further, a verification of accuracy of these PDF and CDF expressions was given by comparison with the corresponding approximations obtained by the high-precision quadrature formulas of Gaussian type with respect to the weight functions on (0,+∞). The computational procedure of such quadrature rules is provided by using the constructive theory of orthogonal polynomials and the Mathematica package OrthogonalPolynomials created by Cvetković and Milovanović (2004). Capitalizing on obtained expression, important wireless performance criteria, namely, outage probability (OP), have been obtained, as functions of transmission parameters. Also, possible performance improvement is observed through a glance at SC (selection combining) reception employment based on obtained expressions.

AB - We will provide statistical analysis of the square ratio of -μ and η-μ random processes and its application in the signal-to-interference ratio (SIR) based performance analysis of wireless transmission subjected to the influence of multipath fading, modelled by -μ fading model, and undesired occurrence of co-channel interference (CCI), distributed as η-μ random process. First contribution of the paper is deriving exact closed expressions for the probability density function (PDF) and cumulative distribution function (CDF) of square ratio of -μ and η-μ random processes. Further, a verification of accuracy of these PDF and CDF expressions was given by comparison with the corresponding approximations obtained by the high-precision quadrature formulas of Gaussian type with respect to the weight functions on (0,+∞). The computational procedure of such quadrature rules is provided by using the constructive theory of orthogonal polynomials and the Mathematica package OrthogonalPolynomials created by Cvetković and Milovanović (2004). Capitalizing on obtained expression, important wireless performance criteria, namely, outage probability (OP), have been obtained, as functions of transmission parameters. Also, possible performance improvement is observed through a glance at SC (selection combining) reception employment based on obtained expressions.

UR - http://www.scopus.com/inward/record.url?scp=85045050653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045050653&partnerID=8YFLogxK

U2 - 10.1155/2018/4967613

DO - 10.1155/2018/4967613

M3 - Article

AN - SCOPUS:85045050653

VL - 2018

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

M1 - 4967613

ER -