Dragana Krstić, Siniša Minić, Suad Suljović, Mihajlo Stefanović



The Second Order Performance of Macrodiversity Reception in the Presence of Weibull Fading, Gamma Fading and α-κ-μ Co-channel Interference

pdf PDF


In this paper, the wireless system consisting of macrodiversity selection combining (SC) receiver and two microdiversity SC receivers under the influence of small scale fading and large scale fading, as well as co-channel interference is observed. Small scale fading has Weibull distribution. Correlated large scale fading is described by Gamma distribution. Co-channel interference is disturbed by α-κ-μ fading and Gamma large scale fading. Probability density function (PDF) and cumulative distribution function (CDF) of the ratio of Weibull random variable and α-κ-μ random variable are given. The formula for CDF of macrodiversity SC receiver output signal to interference ratio (SIR) is also presented. Level crossing rates at the outputs of microdiversity SC receivers are determined. Then, the level crossing rate (LCR) of wireless system output signal to interference ratio is derived and shown in some figures. Based on them, the influence of Weibull fading nonlinearity parameter, α-κ-μ fading severity parameter, α-κ-μ fading nonlinearity parameter, Rician factor, Gamma long term fading severity parameter and Gamma long term fading correlation coefficient is studied.


macrodiversity receiver; microdiversity receiver; selection combining (SC); Gamma fading; Weibull fading; α-κ-μ fading; level crossing rate


[1] S. Panic, M. Stefanovic, J. Anastasov, P. Spalevic, Fading and Interference Mitigation in Wireless Communications. CRC Press, USA, 2013.

[2] M. K. Simon, M. S. Alouini, Digital Communication over Fading Channels, USA: John Wiley & Sons. 2000.

[3] W.C.Y. Lee, Mobile communications engineering, Mc-Graw-Hill, NewYork, USA, 2003.

[4] G. Fraidenraich, M. D. Yacoub, “The α-η-μ and α-κ-μ Fading distributions”, in Proc. of the 2006 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications (ISSSTA), Aug. 2006, pp. 16-20.

[5] W. Weibull, ”A statistical distribution function of wide applicability”, J. Appl. Mech.-Trans. ASME, 1951, 18 (3): 293–297.

[6] P. C. Sofotasios, S. Freear, “The α-κ-μ/ gamma distribution: A generalized non-linear multipath/shadowing fading model”, 2011 IEEE Annual India Conference (INDICON), 16-18 Dec. 2011, Hyderabad, ISBN: 978-1- 4577-1110-7, DOI:10.1109/INDCON.2011.6139442, pp. 1-6.

[7] P. C. Sofotasios, S. Freear, “The α-κ-μ Extreme distribution: Characterizing non- linear severe fading conditions”, Proc. of Australasian Telecommunication Networks and Applications Conference (ATNAC), 2011, Melbourne, Australia, Nov. 2011, pp. 1-4.

[8] S. Panic, P. Spalevic, A. Markovic, M. Stefanovic, “Performance analysis of wireless communication system in α-k-μ environment subjected to shadowing”, International Conference «Mathematical and Informational Technologies, MIT-2013», (X Conference «Computational and Informational Technologies for Science, Engineering and Education»), Vrnjacka Banja, Serbia, September, 5-8, 2013, Budva, Montenegro, September, 9-14, 2013.

[9] A. K. Papazafeiropoulos, S. A. Kotsopoulos, “Second-Order Statistics for the Envelope of α- κ-μ Fading Channels”, IEEE Communications Letters, Vol. 14, Issue: 4, April 2010, pp. 291- 293.

[10] D. Aleksić, D. Krstić, Z. Popović, M. Stefanović, “Level Crossing Rate of Macrodiversity SC Receiver Output Process in the Presence of Weibull Short Term Fading, Gamma Long Term Fading and Weibull Cochanell Interference”, WSEAS Transactions on Communications, ISSN / E-ISSN: 1109- 2742 / 2224-2864, Volume 15, 2016, Art. #31, pp. 285-291.

[11] D. Krstic, S. Minić, S. Milosavljević, B. Milosavljević, M. Stefanović, “Macrodiversity Outage Performance in the Presence of Weibull Short Term Fading, Gamma Long Term Fading and α-κ-µ Co-channel Interference”, International Journal of Communications, Vol. 11, 2017, pp. 14-21.

[12] M. D. Yacoub, “The κ-μ distribution and the η- μ distribution”, IEEE Antennas and Propagation Magazine, Volume: 49 Issue: 1, 11 June 2007, pp: 68 – 81, DOI: 10.1109/MAP.2007.370983

[13] U. S. Dias, M. D. Yacoub, “The κ-μ phaseenvelope joint distribution“, IEEE Transactions on Communications, 2010, Vol. 58, Issue: 1, pp. 40 – 45, DOI: 10.1109/TCOMM.2010.01.080175

[14] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series, eds. (1983)

[June 1964]. “Chapter 6.5”, 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications, ISBN 978-0- 486-61272-0. LCCN 64- 60036, MR 0167642, LCCN 65-12253, "Incomplete Gamma function", §6.5.

[15] I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products. Academic Press, USA San Diego, 2000.

[16] A. P. Prudnikov, Y. A. Brychkov, O. I. Marichev, Integrals and Series, Volume 3: More Special Functions. 1st ed., Gordon and Breach Science Publishers, New York, 1986.

[17] C. F. Gauss, “Disquisitiones generales circa seriem infinitam”, Societas Regia Scientiarum Gottingensis, Burndy Library

[18] E. W. Barnes, “A New Development in the Theory of the Hypergeometric Functions”, Proc. London Math. Soc. 6, 141- 177, 1908.

Cite this paper

Dragana Krstić, Siniša Minić, Suad Suljović, Mihajlo Stefanović. (2017) The Second Order Performance of Macrodiversity Reception in the Presence of Weibull Fading, Gamma Fading and α-κ-μ Co-channel Interference. International Journal of Communications, 2, 41-50


Copyright © 2017 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0