Abstract
In this paper, a closed-form expression for the moment generating function (MGF) of the instantaneous signal to noise ratio (SNR) per symbol is derived for Weibull fading channels. The derived MGF is valid for the rational values of fading parameter and it is shown to be useful for analyzing the symbol error rate for the case of M-ary phase shift keying and M-ary quadrature amplitude modulation schemes. Also, the outage probability can be accurately evaluated by using the probability density function of instantaneous SNR considered in this work.
References
Hashemi, H. (1993). The indoor radio propagation channel. Proceedings of IEEE, 81(7), 943–968.
Tzeremes, G., & Christodoulou, C. G. (2002 June). Use of Weibull distribution for describing outdoor multipath fading. In Proceedings of IEEE antennas, propagation society international symposium (vol. 1, pp. 232–235). San Antonio, TX.
Sagias, N. C., Mathiopoulos, P. T., & Tombras, G. S. (Dec. 2003). Selection diversity receivers in Weibull fading: Outage probability and average signal-to-noise ratio. Electronics Letters, 39(25), 1859–1860.
Bithas, P. S., et al. (Nov. 2005). Performance analysis of a class of GSC receivers over nonidentical Weibull fading channels. IEEE Transactions on Vehicular Technology, 54(6), 1963–1970.
Hemachandra, K. T., & Beaulieu, N. C. (Oct. 2011). New representations for the gaussian class multivariate Weibull distribution with constant correlation and applications. IEEE Transactions on Communications, 59(10), 2648–2653.
Sagias, N. C., et al. (2004). Channel capacity and second-order statistics in Weibull fading. IEEE Communications Letters, 8(6), 377–379.
Ismail, M. H., & Matalgah, M. M. (Mar. 2006). Performance of dual maximal ratio combining diversity in nonidentical correlated Weibull fading channels using Pade approximation. IEEE Transactions on Communications, 54(3), 397–402.
Simon, M. K., & Alouini, M.-S. (2000). Digital communication over fading channels (2nd ed.). New York: Wiley.
Cheng, J., Tellambura, C., & Beaulieu, N. C. (Aug. 2004). Performance of digital linear modulations on Weibull slow-fading channels. IEEE Transactions on Communications, 52(8), 1265–1268.
Ismail, M. H., & Matalgah, M. M. (2007). Exact and approximate error-rate analysis of BPSK in Weibull fading with cochannel interference. IET Communications, 1(2), 203–208.
Karagiannidis, G. K., Zogas, D. A., Sagias, N. C., Kotsopoulos, S. A., & Tombras, G. S. (2005). Equal-Gain and Maximal-Ratio combining over nonidentical Weibull fading channels. IEEE Transactions on Wireless Communications, 4(3), 841–846.
Magableh, A. M., & Matalgah, M. M. (2009). Moment generating function of the generalized \(\alpha -\mu \) distribution with applications. IEEE Communications Letters, 13(6), 411–413.
Aalo, V. A., Piboongungon, T., & Iskander, C. D. (Feb. 2005). Bit-Error rate of binary digital modulation schemes in generalized Gamma fading channels. IEEE Communications Letters, 9(2), 139–141.
Nadarajah, S., & Kotz, S. (July 2007). On the Weibull MGF. IEEE Transactions on Communications, 55(7), 1287.
Prudnikov, A. P., Brychkov, Y. A., & Marichev, O. I. (1986). Integrals and series (Vol. 1). London: Gordon and Breach.
Gradshteyn, I. S., & Rzyhik, I. M. (2007). Table of integrals, series and products (7th ed.). London: Academic Press.
Kapucu, N. (2012). Derivation of new mathematical expressions for performance analysis of cooperative communication systems over different fading channels. Master’s thesis, Graduate School of Natural and Applied Sciences, Erciyes University (in Turkish).
Acknowledgments
This work was supported by the Scientific Research Projects Coordinating Office of Erciyes University (EU-BAP, Project No: FBY-11-3682).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kapucu, N., Bilim, M. & Develi, I. A Closed-Form MGF Expression of Instantaneous SNR for Weibull Fading Channels. Wireless Pers Commun 77, 1605–1613 (2014). https://doi.org/10.1007/s11277-014-1599-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-014-1599-0