# Error Probability Distribution and Density Functions for Weibull Fading Channels With and Without Diversity Combining

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## Abstract

In this letter, a detailed theoretical analysis of probability distribution and density functions of probability of error in a wireless system is considered. Closed form expressions for distribution and density functions of the probability of error are derived for Weibull fading channels for the cases of (i) No Diversity (ND), (ii) Selection Combining (SC) diversity, and (iii) Switch and Stay Combining (SSC) diversity. Numerical results are plotted and discussed in detail for the various cases.

## Keywords

Distribution and density functions Weibull fading Selection combining diversity Switch and stay combining diversity## References

- 1.W. C. Jakes,
*Microwave Mobile Communications*, 1st edn, Wiley & Sons, Inc, MA, 1974.Google Scholar - 2.N. Sagias, G. Karagiannidis, and G. Tombras, Error-rate analysis of switched diversity receivers in Weibull fading,
*Electronic letters*, Vol. 40, No. 11, pp. 681–682, 2004.CrossRefGoogle Scholar - 3.M. Ismail and M. Matalgah, Performance of selection combining diversity in Weibull fading with cochannel interference,
*EURASIP Journal on Wireless Communications and Networking*, Vol. 2007, No. 1, pp. 10–15, 2007.Google Scholar - 4.N. Sagias and N. Tombras, On the cascaded Weibull fading channel model,
*Journal of the Franklin Institute*, Vol. 344, No. 1, pp. 1–11, 2007.MATHCrossRefMathSciNetGoogle Scholar - 5.P. Sahu and A. Chaturvedi, Performance analysis of predetection EGC receiver in Weibull fading channel,
*Electronic Letters*, Vol. 41, No. 2, pp. 85–86, 2005.CrossRefGoogle Scholar - 6.N. Sagias, G. Karagiannidis, D. Zogas, P. Mathiopoulos, and G. Tombras, Performance analysis of dual selection diversity in correlated Weibull fading channels,
*IEEE Transactions on Communications*, Vol. 52, No. 7, pp. 1063–1067, 2004.CrossRefGoogle Scholar - 7.H. Samimi and P. Azmi, An approximate analytical framework for performance analysis of equal gain combining technique over independent Nakagami, Rician, and Weibull fading channels,
*An International Journal of Wireless Personal Communications*, Vol. 43, No. 4, pp. 1399–1408, 2007.CrossRefGoogle Scholar - 8.G. Karagiannidis, D. Zogas, N. Sagias, S. Kotsopoulos, and G. Tombras, Equal-gain and maximal ratio combining over nonidentical Weibull fading channels,
*IEEE Transactions on Wireless Communications*, Vol. 4, No. 3, pp. 841–846, 2005.CrossRefGoogle Scholar - 9.S. Ikki and M. Ahmed,
*Performance of multi-hop relaying systems over Weibull fading channels*, Springer, Netherlands, 2007.Google Scholar - 10.N. Sagias, P. Varzakas, G. Tombras, and G. Karagiannidis, Spectral efficiency for selection combining RAKE receivers over Weibull fading channels,
*Journal of the Franklin Institute*, Vol. 342, No. 1, pp. 7–13, 2005.MATHCrossRefGoogle Scholar - 11.W. Karner, O. Nemethova, and M. Rupp, Link error prediction in wireless communication systems with quality based power control”
*International Conference on Communications, 2007*, pp. 5076–5081, 2007, doi: 10.1109/ICC.2007.838. - 12.M. Ismail and M. Matalgah, Exact and approximate error-rate analysis of BPSK in Weibull fading with co-channel interference,
*Institute of Engineering and Technology*, Vol. 1, No. 2, pp. 203–208, 2007.Google Scholar - 13.Q. Zhang, A simple approach to probability of error for equal gain combiners over Rayleigh fading channels,
*IEEE Transactions on Vehicular Technology*, Vol. 48, No. 4, pp. 1151–1154, 1999.CrossRefGoogle Scholar - 14.C. Jie and V. Bhaskar, Error probability distribution and density functions for Rayleigh and Rician fading channels with diversity,
*International Journal of Wireless Information Networks*, Vol. 15, No. 1, pp. 53–60, 2008.CrossRefGoogle Scholar - 15.M. Simon and M. Alouini, A unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels,
*IEEE Transactions on Communications*, Vol. 46, No. 12, pp. 1625–1638, 1998.CrossRefGoogle Scholar - 16.A. Poncet, Asymptotic probability density of the generalization error,
*Proceedings of the 1996 International Workshop on Neural networks for Identification, Control, Robotics, and Signal/Image processing (NICROSP), IEEE Computer Society*, p. 66, 1996.Google Scholar - 17.W. Liggett, Estimation of the error probability density from replicate measurements on several items,
*Biometrika Oxford Journal*, Vol. 75, No. 3, pp. 557–567, 1988.MATHCrossRefMathSciNetGoogle Scholar - 18.G. Lieberman, Adaptive digital communication for a slowly varying channel,
*IEEE Transactions on Communication and Electronics*, Vol. 82, No. 65, pp. 44–51, 1963.Google Scholar - 19.A. Papoulis,
*Probability, Random Variables and Stochastic Processes*, 3rd edn, McGraw Hill Companies, New York, 1991.Google Scholar - 20.V. Bhaskar and L. Joiner, Variable energy adaptation for asynchronous CDMA communications over slowly fading channels,
*Journal of Computers and Electrical Engineering*, Vol. 31, pp. 33–55, 2005.MATHCrossRefGoogle Scholar - 21.J. G. Proakis,
*Digital Communications*,4th edn, McGraw Hill, New York, 2001.Google Scholar - 22.I. Gradshteyn and I. Ryzhik,
*Table of Integrals, Series, and Products*, 5th edn, Academic Press, San Diego, CA, 1994.Google Scholar

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