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Wireless Personal Communications
Published in: Wireless Personal Communications 2/2019

15-10-2019

Some New Results for Integrals Involving Gaussian Q-function and Their Applications to α–µ and η–µ Fading Channels

Author: Mehmet Bilim

Published in: Wireless Personal Communications | Issue 2/2019

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Abstract

This paper presents new analytical solutions for integrals that involve exponential functions, Gaussian Q- function and arbitrary powers. The offered expressions are both simple and convenient which are useful in applications for the derivation of the average error probability in different wireless communication environments such as α–µ and η–µ fading channels. To this end, the derived closed-form solutions are validated by computer simulations.
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Literature
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Beaulieu, N. C. (2006). A useful integral for wireless communication theory and its application to rectangular signaling constellation error rates. IEEE Transactions on Communications, 54(5), 802–805.CrossRef
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Chen, Y., & Beaulieu, N. C. (2007). Solutions to infinite integrals of Gaussian Q-function products and some applications. IEEE Communications Letters, 11(11), 853–855.CrossRef
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Lopez-Martinez, F. J., Pawula, R. F., Martos-Naya, E., & Paris, J. F. (2014). A clarification of the proper-integral form for the Gaussian Q-function and some new results involving the F-function. IEEE Communications Letters, 18(9), 1495–1498.CrossRef
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Simon, M. K. (2002). Single integral representations of certain integer powers of the Gaussian Q-function and their application. IEEE Communications Letters, 6(12), 532–534.CrossRef
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Li, R., & Kam, P. Y. (2007). Averages of the product of two Gaussian Q-functions over fading statistics and applications. IEEE Communications Letters, 11(1), 58–62.CrossRef
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Simon, M. K., & Alouini, M. S. (2005). Digital communication over fading channels. Hoboken: Wiley.
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Prudnikov, A. P., Brychkov, Y. A., & Marichev, O. I. (1986). Integrals, and series: special functions (Vol. 2). New York: Gordon and Breach Sci.MATH
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Magableh, A. M., & Matalgah, M. M. (2009). Moment generating function of the generalized α–μ distribution with applications. IEEE Communications Letters, 13(6), 411–413.CrossRef
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Yacoub, M. D. (2007). The η − μ distribution and the κ − μ distribution. IEEE Antennas and Propagation Magazine, 49(1), 68–81.CrossRef
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Metadata
Title
Some New Results for Integrals Involving Gaussian Q-function and Their Applications to α–µ and η–µ Fading Channels
Author
Mehmet Bilim
Publication date
15-10-2019
Publisher
Springer US
Published in
Wireless Personal Communications / Issue 2/2019
Print ISSN: 0929-6212
Electronic ISSN: 1572-834X
DOI
https://doi.org/10.1007/s11277-019-06901-1

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