AUTHOR(S): Dragana Krstic, Mihajlo Stefanovic, Vesad Doljak, Zoran Popovic, Radmila Gerov
|
TITLE Distribution of Maximum and Minimum of K-µ-g Random Variables |
ABSTRACT In this paper, the distributions of the maximum and the minimum of ?-µ-g random variables are derived. The ?-µ-g random variable was obtained from ?-µ random variable whose power has Gamma distribution. The expressions for probability density functions (PDF) of the maximum of two ?-µ-g random variables and minimum of two ?-µ-g random variables are performed and analyzed. Using these expressions, performance analysis of wireless communication systems in the presence of ?-µ-g multipath fading and ?-µ-g cochannel interference can be made. |
KEYWORDS κ-µ-g distribution, random variable, probability density function, maximum, minimum, short term fading, shadowing |
REFERENCES [1] P. M. Shankar, Fading and Shadowing in Wireless Systems, Springer, Dec 7, 2011. DOI 10.1007/978-1-4614-0367-8 [2] M. K. Simon, M. S. Alouini, Digital Communication over Fading Channels, USA: John Wiley & Sons. 2000. [3] P. C. Sofotasios, S. Freear, On the κ-µ/Gamma Generalized Multipath/ Shadowing Fading Distribution, https://arxiv.org/pdf/1505.04186.pdf [4] D. Krstic, M. Stefanovic, V. Doljak, Z. Popovic, E. Leitgeb, The Κ-µ-g Random Variable and the Κ-µ-g Random Process, in press [5] D. H. Pavlović, N. M. Sekulović, G. V. Milovanović, A. S. Panajotović, M. C. Stefanović, Z. J. Popović, Statistics for Ratios of Rayleigh, Rician, Nakagami-??, and Weibull Distributed Random Variables, Mathematical Problems in Engineering, Vol. 2013, Article ID 252804, http://dx.doi.org/10.1155/2013/252804 [6] E. Mekić, M. Stefanović, P. Spalević, N. Sekulović, A. Stanković, Statistical analysis of ratio of random variables and its application in performance analysis of multi-hop wireless transmissions, Mathematical Problems in Engineering, Vol. 2012, Article ID 841092 [7] S. Suljović, D. Krstić, S. Maričić, S. Zdravković, V. Milenković, M. Stefanović, Level Crossing Rate of SC Receiver Over Gamma Shadowed Weibull Multipath Fading Channel, to be published towards the end of December 2016. in Tehnički vjesnik/ Technical Gazette, Vol. 23, No. 6. [8] A. Stanković, Č. Stefanović, N. Sekulović, Z. Popović, M. Stefanović, The Distribution of Minimum of Ratios of Two Random Variables and Its Application in Analysis of Multi-hop Systems, Radioengineering, Vol. 21, No. 4, Dec. 2012. [9] Modified Bessel Function of the Second Kind, http://mathworld.wolfram.com/ModifiedBessel FunctionoftheSecondKind.html [10] Gauss hypergeometric function, http://mathworld.wolfram.com/Hypergeometric Function.html [11] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th edition, New York: Academic, 2007. |
Cite this paper Dragana Krstic, Mihajlo Stefanovic, Vesad Doljak, Zoran Popovic, Radmila Gerov. (2016) Distribution of Maximum and Minimum of K-µ-g Random Variables. International Journal of Communications, 1, 194-198 |
|