On the approximation of the generalized- distribution by a gamma distribution for modeling composite fading channels

Saad Al-Ahmadi; Halim Yanikomeroglu

doi:10.1109/TWC.2010.02.081266

On the approximation of the generalized- distribution by a gamma distribution for modeling composite fading channels

Saad Al-Ahmadi^*
, Halim Yanikomeroglu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

188 Scopus citations

Abstract

In wireless channels, multipath fading and shadowing occur simultaneously leading to the phenomenon referred to as composite fading. The use of the Nakagami probability density function (PDF) to model multipath fading and the Gamma PDF to model shadowing has led to the generalized-K model for composite fading. However, further derivations using the generalized-K PDF are quite involved due to the computational and analytical difficulties associated with the arising special functions. In this paper, the approximation of the generalized-K PDF by a Gamma PDF using the moment matching method is explored. Subsequently, an adjustable form of the expressions obtained by matching the first two positive moments, to overcome the arising numerical and/or analytical limitations of higher order moment matching, is proposed. The optimal values of the adjustment factor for different integer and non-integer values of the multipath fading and shadowing parameters are given. Moreover, the approach introduced in this paper can be used to well-approximate the distribution of the sum of independent generalized-K random variables by a Gamma distribution; the need for such results arises in various emerging distributed communication technologies and systems such as coordinated multipoint transmission and reception schemes including distributed antenna systems and cooperative relay networks.

Original language	English
Article number	5403551
Pages (from-to)	706-713
Number of pages	8
Journal	IEEE Transactions on Wireless Communications
Volume	9
Issue number	2
DOIs	https://doi.org/10.1109/TWC.2010.02.081266
State	Published - Feb 2010
Externally published	Yes

Bibliographical note

Funding Information:
Manuscript received September 20, 2008; revised March 19, 2009 and May 28, 2009; accepted July 27, 2009. The associate editor coordinating the review of this paper and approving it for publication was S. Gassemzadeh. The authors are with the Department of Systems and Computer Engineering, Carleton University, Ottawa, Canada (e-mail: {saahmadi, halim}@sce.carleton.ca). S. Al-Ahmadi’s work was supported by King Fahd University of Petroleum and Minerals, Saudi Arabia. Digital Object Identifier 10.1109/TWC.2010.02.081266

Keywords

Composite fading
Distributed antenna systems
Gamma distribution
Generalized-K distribution
Lower and upper tails
Moment matching
Network MIMO
Positive and negative moments
Radar and sonar

ASJC Scopus subject areas

Computer Science Applications
Electrical and Electronic Engineering
Applied Mathematics

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10.1109/TWC.2010.02.081266

Cite this

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abstract = "In wireless channels, multipath fading and shadowing occur simultaneously leading to the phenomenon referred to as composite fading. The use of the Nakagami probability density function (PDF) to model multipath fading and the Gamma PDF to model shadowing has led to the generalized-K model for composite fading. However, further derivations using the generalized-K PDF are quite involved due to the computational and analytical difficulties associated with the arising special functions. In this paper, the approximation of the generalized-K PDF by a Gamma PDF using the moment matching method is explored. Subsequently, an adjustable form of the expressions obtained by matching the first two positive moments, to overcome the arising numerical and/or analytical limitations of higher order moment matching, is proposed. The optimal values of the adjustment factor for different integer and non-integer values of the multipath fading and shadowing parameters are given. Moreover, the approach introduced in this paper can be used to well-approximate the distribution of the sum of independent generalized-K random variables by a Gamma distribution; the need for such results arises in various emerging distributed communication technologies and systems such as coordinated multipoint transmission and reception schemes including distributed antenna systems and cooperative relay networks.",

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author = "Saad Al-Ahmadi and Halim Yanikomeroglu",

note = "Funding Information: Manuscript received September 20, 2008; revised March 19, 2009 and May 28, 2009; accepted July 27, 2009. The associate editor coordinating the review of this paper and approving it for publication was S. Gassemzadeh. The authors are with the Department of Systems and Computer Engineering, Carleton University, Ottawa, Canada (e-mail: \{saahmadi, halim\}@sce.carleton.ca). S. Al-Ahmadi{\textquoteright}s work was supported by King Fahd University of Petroleum and Minerals, Saudi Arabia. Digital Object Identifier 10.1109/TWC.2010.02.081266",

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N2 - In wireless channels, multipath fading and shadowing occur simultaneously leading to the phenomenon referred to as composite fading. The use of the Nakagami probability density function (PDF) to model multipath fading and the Gamma PDF to model shadowing has led to the generalized-K model for composite fading. However, further derivations using the generalized-K PDF are quite involved due to the computational and analytical difficulties associated with the arising special functions. In this paper, the approximation of the generalized-K PDF by a Gamma PDF using the moment matching method is explored. Subsequently, an adjustable form of the expressions obtained by matching the first two positive moments, to overcome the arising numerical and/or analytical limitations of higher order moment matching, is proposed. The optimal values of the adjustment factor for different integer and non-integer values of the multipath fading and shadowing parameters are given. Moreover, the approach introduced in this paper can be used to well-approximate the distribution of the sum of independent generalized-K random variables by a Gamma distribution; the need for such results arises in various emerging distributed communication technologies and systems such as coordinated multipoint transmission and reception schemes including distributed antenna systems and cooperative relay networks.

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On the approximation of the generalized- distribution by a gamma distribution for modeling composite fading channels

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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