Wireless Personal Communications

, Volume 70, Issue 2, pp 695–708 | Cite as

Outage Probability Analysis of Cooperative Diversity Networks Over Weibull and Weibull-Lognormal Channels

  • Abdelrahman H. Gaber
  • Mahmoud H. Ismail
  • Hebat-Allah M. Mourad
Article

Abstract

This paper presents the analysis of outage probability for a cooperative diversity wireless network using amplify-and-forward relays over independent non-identical distributed Weibull and Weibull-lognormal fading channels for single as well as multiple relays. To reach that end, a closed-from expression for the moment-generating function of the total signal-to-noise-ratio (SNR) at the destination is derived in terms of the tabulated Meijer’s G-function. Since it is hard to determine the exact probability distribution function of the SNR, a tight lower bound approximation is proposed. Simulation results are presented that show that the outage probability lower bound tends to be tight at high SNR values thus verifying the analytical results. The results also show the potential gain of relaying on the outage probability.

Keywords

Outage probability Cooperative diversity Amplify-and-forward Weibull fading Weibull-lognormal fading 

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References

  1. 1.
    Laneman J. N., Tse D. N. C., Wornell G. W. (2004) Cooperative diversity in wireless networks efficient protocols and outage behaviour. IEEE Transactions on Information Theory 50(12): 3062–3080MathSciNetCrossRefGoogle Scholar
  2. 2.
    Laneman, J. N., & Wornell, G. (2000). Energy-efficient antenna sharing and relaying for wireless networks. In Proceedings of wireless communications and networking conference (Vol. 1, pp. 3062–3080).Google Scholar
  3. 3.
    Laneman, J. N., & Wornell, G. (2002). Distributed space-time coded protocols for exploiting cooperative diversity in wireless networks. In Proceedings of global telecommunication conference (Vol. 1, pp. 77–81).Google Scholar
  4. 4.
    Mark J. W., Zhuang W. (2003) Wireless communications and networking. Prentice-Hall, Upper Saddle River, NJGoogle Scholar
  5. 5.
    Jiang H., Zhuang W., Shen X., Bi Q. (2006) Quality-of-service provisioning and efficient resource utilization in CDMA cellular communications. IEEE Journal on Selected Areas in Communications 24(1): 4–15CrossRefGoogle Scholar
  6. 6.
    Patel C., Stuber G., Pratt T. (2006) Statistical properties of amplify and forward relay fading channels. IEEE Transactions on Vehicular Technology 55(1): 1–9CrossRefGoogle Scholar
  7. 7.
    Kwasinski A., Liu K. (2008) Source-channel-cooperation tradeoffs for adaptive coded communications. IEEE Transactions on Wireless Communications 7(9): 3347–3358CrossRefGoogle Scholar
  8. 8.
    Karagiannidis G. K. (2006) Performance bounds of multihop wireless communications with blind relays over generalized fading channels. IEEE Transactions on Wireless Communications 5: 498–503Google Scholar
  9. 9.
    Karagiannidis G. K. (2004) Moments-based approach to the performance analysis of equal-gain diversity in Nakagami-m fading. IEEE Transactions on Communications 52: 685–690CrossRefGoogle Scholar
  10. 10.
    Hasna M. O., Alouini M.-S. (2003) End-to-end performance of transmission systems with relays over Rayleigh-fading channels. IEEE Transactions on Wirless Communications 2: 1126–1131CrossRefGoogle Scholar
  11. 11.
    Hasna M. O., Alouini M.-S. (2003) Outage probability of multihop transmission over Nakagami fading channels. IEEE Communications Letters 7: 216–218CrossRefGoogle Scholar
  12. 12.
    Boyer, J. (2001). Multihopwireless communications channels. M.Sc. thesis, Carleton University, Ottawa, ON, Canada.Google Scholar
  13. 13.
    Ding H., Ge J., da Costa D. B., Guo Y. (2011) Outage analysis for multiuser two-way relaying in mixed Rayleigh and Rician fading. IEEE Communications Letters 15: 410–412CrossRefGoogle Scholar
  14. 14.
    Gao Y., Ge J., Han C. (2011) Performance analysis of differential modulation and relay selection with detect-and-forward cooperative relaying. IEEE Communications Letters 15: 323–325CrossRefGoogle Scholar
  15. 15.
    Chu S.-I. (2011) Performance of amplify-and-forward cooperative communications with the Nth best-relay selection scheme over Nakagami-m fading channels. IEEE Communications Letters 15: 172–174CrossRefGoogle Scholar
  16. 16.
    Sagias N. C., Karagiannidis G. K. (2005) Gaussian class multivariate Weibull distributions: Theory and applications in fading channels. IEEE Transactions on Information Theory 51: 3608–3619MathSciNetCrossRefGoogle Scholar
  17. 17.
    Alouini, M. S., & Simon, M. K. (2001). Performance of generalized selection combining over Weibull fading channels. In Proceedings of IEEE vehicuar technology conference, Atlantic City, NJ (pp. 1735–1739).Google Scholar
  18. 18.
    Sagias N. C., Zogas D. A., Karagiannidis G. K., Tombras G. S. (2003) Performance analysis of switched diversity receivers in Weibull fading. Electronics Letters 39: 1472–1474CrossRefGoogle Scholar
  19. 19.
    Sagias N. C., Mathiopoulos P. T., Tombras G. S. (2003) Selection diversity receivers signal-to-noise ratio. Electronics Letters 39: 1859–1860CrossRefGoogle Scholar
  20. 20.
    Ikki, S. S., & Ahmed, M. H. (2009). Performance analysis of dual hop relaying over non-identical Weibull fading channels. IEEE 69th Vehicular Technology Conference, 2009. VTC Spring 2009. 26–29 April 2009, 1–5.Google Scholar
  21. 21.
    Ribeiro, A., Cai, X., & Giannakis, G. B. (2005). Symbol error probabilities for general cooperative links. IEEE Transactions on Wireless Communications, 4(3), 1264–1273.Google Scholar
  22. 22.
    Ikki S., Ahmed M. H. (2007) Performance analysis of cooperative diversity wireless networks over Nakagami-m fading channel. IEEE Communications Letters 11(4): 334–336CrossRefGoogle Scholar
  23. 23.
    Laneman, J. N. (2002). Cooperative diversity in wireless networks: Algorithms and architectures. Ph.D. dissertation, Mass. Inst. Technol., Cambridge, MA.Google Scholar
  24. 24.
    Sendonaris A., Erkip E., Aazhang B. (2003) User cooperation diversity—part I: System description. IEEE Transactions on Communications 51(11): 1927–1938CrossRefGoogle Scholar
  25. 25.
    Karagiannidis G. K., Tsiftsis T. A., Mallik R. K. (2006) Bounds of multihop relayed communications in Nakagami-m fading. IEEE Transactions on Communications 54: 18–22CrossRefGoogle Scholar
  26. 26.
    Hasna, M. O., & Alouini, M.-S. (2004). Harmonic mean and end-to-end performance of transmission systems with relays. IEEE Transactions on Communications 52(1), 130–135.Google Scholar
  27. 27.
    Tsiftsis, T. A., Karagiannidis, G. K., Kotsopoulos, S. A., & Pavlidou, F.-N. (2004). BER analysis of collaborative dual-hop wireless transmissions. IEE Electronics Letters, 40(11), 679–681.Google Scholar
  28. 28.
    Simon M. K., Alouini M.-S. (2005) Digital communication over fading channels (2nd ed.). Wiley, New YorkGoogle Scholar
  29. 29.
    Bletsas, A., Khisti, A., Reed, D. P., & Lippman, A. (2006). A simple cooperative diversity method based on network path selection. IEEE Journal on Selected Areas in Communications, 24(3), 659–672.Google Scholar
  30. 30.
    Wang, T., Cano, A., Giannakis, G. B., & Laneman, N. (2007). Highperformance cooperative demodulation with decode-and-forward relays. IEEE Transactions on Communications (accepted for publication).Google Scholar
  31. 31.
    Cheng J., Tellambura C., Beaulieu N. C. (2004) Performance of digital linear modulations on Weibull slow-fading channels. IEEE Transactions on Communications 52(8): 1265–1268CrossRefGoogle Scholar
  32. 32.
    Gradshteyn I. S., Ryzhik I. M. (2007) Table of integrals, series and products (7th ed.). Academic Press, San DiegoMATHGoogle Scholar
  33. 33.
    Abate, J., & Whitt, W. (1995). Numerical inversion of Laplace transform of probability distribution. ORSA Journal on Computing, 7(1), 36–43.Google Scholar
  34. 34.
    Ko, Y.-C., Alouini, M.-S., & Simon, M. K. (2000). Outage probability of diversity systems over generalized fading channels. IEEE Transactions on Communications, 48(11), 1783–1787.Google Scholar
  35. 35.
    Adamchik, V. S., & Marichev, O. I. (1990). The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system. In Proceedings of international conference on symbolic and algebraic computing, Tokyo, Japan (pp. 212–224).Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  • Abdelrahman H. Gaber
    • 1
  • Mahmoud H. Ismail
    • 1
  • Hebat-Allah M. Mourad
    • 1
  1. 1.Department of Electronics and Communications Engineering, Faculty of EngineeringCairo UniversityGizaEgypt

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