Skip to main content
SpringerLink
Log in

Performance Evaluation of Wireless Communication Systems over Weibull/q-Lognormal Shadowed Fading Using Tsallis’ Entropy Framework

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

In wireless communication channels, the signals arriving at the receiver may be of stochastic nature or be superpositioned due to non-uniform scattering and shadowing. For the ease of computation, we generally assume the mean ergodic property of communication channels which is error prone. The well known lognormal model fails to capture the extreme tail fluctuations in the presence of shadowing. In this setting, we exploit the importance of Tsallis non-extensive parameter ‘q’ to characterize various fading channels. The q-lognormal distribution captures the tail phenomena due to presence of non-extensive parameter ‘q’. In this paper, we provide an excellent agreement between the generated synthetic signal and the proposed q-Lognormal distribution for different values of parameter ‘q’. This paper also presents the analytical expression for the superstatistics Weibull/q-lognormal model to capture both fading and shadowing effects. It is observed that the Weibull/q-Lognormal model provides a better fit to the generated signal for \(q=1.8\) in comparison to the well known Weibull/Lognormal model. Finally, we provide an excellent agreement between the derived measures viz., amount of fading, outage probability, average channel capacity with extensive Monte-Carlo simulation scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Simon, M. K., & Alouini, M. S. (2005). Digital communication over fading channels (Vol. 95). Hoboken: Wiley.

    Google Scholar 

  2. Shankar, P. M. (2017). Fading and shadowing in wireless systems. Berlin: Springer.

    Book  MATH  Google Scholar 

  3. Rappaport, T. S. (1996). Wireless communications: Principles and practice (Vol. 2). Upper Saddle River: Prentice Hall PTR.

    MATH  Google Scholar 

  4. Sagias, N. C., & Karagiannidis, G. K. (2005). Gaussian class multivariate Weibull distributions: Theory and applications in fading channels. IEEE Transactions on Information Theory, 51(10), 3608–3619.

    Article  MathSciNet  MATH  Google Scholar 

  5. Shankar, P. M. (2004). Error rates in generalized shadowed fading channels. Wireless Personal Communications, 28(3), 233–238.

    Article  Google Scholar 

  6. Bithas, P. S., Sagias, N. C., Mathiopoulos, P. T., Karagiannidis, G. K., & Rontogiannis, A. A. (2006). On the performance analysis of digital communications over generalized-K fading channels. IEEE Communications Letters, 10(5), 353–355.

    Article  Google Scholar 

  7. Laourine, A., Alouini, M. S., Affes, S., & Stphenne, A. (2009). On the performance analysis of composite multipath/shadowing channels using the G-distribution. IEEE Transactions on Communications, 57(4), 1162–1170.

    Article  Google Scholar 

  8. Hashemi, H. (1993). The indoor radio propagation channel. Proceedings of the IEEE, 81(7), 943–968.

    Article  Google Scholar 

  9. Adawi, N. S. (1988). Coverage prediction for cellular mobile radio system operating in the 800/900 MHz frequency band. IEEE Transaction on Vehicular Technology, 37(1), 3–72.

    Article  Google Scholar 

  10. Sagias, N. C., Zogas, D. A., Karagiannidis, G. K., & Tombras, G. S. (2004). Channel capacity and second-order statistics in Weibull fading. IEEE Communications Letters, 8(6), 377–379.

    Article  Google Scholar 

  11. El Bouanani, F., Ben-Azza, H., & Belkasmi, M. (2012). New results for Shannon capacity over generalized multipath fading channels with MRC diversity. EURASIP Journal on Wireless Communications and Networking, 2012(1), 336.

    Article  Google Scholar 

  12. Karadimas, P., & Kotsopoulos, S. A. (2009). The Weibulllognormal fading channel: Analysis, simulation, and validation. IEEE Transactions on Vehicular Technology, 58(7), 3808–3813.

    Article  Google Scholar 

  13. Singh, R., Soni, S. K., Raw, R. S., & Kumar, S. (2017). A new approximate closed-form distribution and performance analysis of a composite Weibull/log-normal fading channel. Wireless Personal Communications, 92(3), 883–900.

    Article  Google Scholar 

  14. Beck, C., & Cohen, E. G. D. (2003). Superstatistics. Physica A: Statistical Mechanics and its Applications, 322, 267–275.

    Article  MathSciNet  MATH  Google Scholar 

  15. Senapati, D. (2016). Generation of cubic power-law for high frequency intra-day returns: Maximum Tsallis entropy framework. Digital Signal Processing, 48, 276–284.

    Article  MathSciNet  Google Scholar 

  16. Tsallis, C. (2004). Nonextensive statistical mechanics: construction and physical interpretation. Nonextensive Entropy, Interdisciplinary Applications, 1–53.

  17. Singh, A. K., & Singh, H. P. (2015). Analysis of finite buffer queue: maximum entropy probability distribution with shifted fractional geometric and arithmetic means. IEEE Communications Letters, 19(2), 163–166.

    Article  Google Scholar 

  18. Rajput, N. K., Ahuja, B., & Riyal, M. K. (2018). A novel approach towards deriving vocabulary quotient. Digital Scholarship in the Humanities, 33(4), 894–901.

    Article  Google Scholar 

  19. Picoli, S, Jr., Mendes, R. S., Malacarne, L. C., & Santos, R. P. B. (2009). q-distributions in complex systems: A brief review. Brazilian Journal of Physics, 39(2A), 468–474.

    Article  Google Scholar 

  20. Holtzman, J. M. (1992). A simple, accurate method to calculate spread-spectrum multiple-access error probabilities. IEEE Transactions on Communications, 40(3), 461–464.

    Article  MATH  Google Scholar 

  21. Mathai, A. M., & Haubold, H. J. (2008). Special functions for applied scientists (Vol. 4). New York: Springer.

    Book  MATH  Google Scholar 

  22. Abe, S., & Bagci, G. B. (2005). Necessity of q-expectation value in nonextensive statistical mechanics. Physical Review E, 71(1), 016139.

    Article  Google Scholar 

  23. Namaki, A., Lai, Z. K., Jafari, G. R., Raei, R., & Tehrani, R. (2013). Comparing emerging and mature markets during times of crises: A non-extensive statistical approach. Physica A: Statistical Mechanics and its Applications, 392(14), 3039–3044.

    Article  Google Scholar 

  24. Shankar, P. M. (2011). Statistical models for fading and shadowed fading channels in wireless systems: A pedagogical perspective. Wireless Personal Communications, 60(2), 191–213.

    Article  Google Scholar 

  25. Lieblein, J. (1955). On moments of order statistics from the Weibull distribution. The Annals of Mathematical Statistics, 1, 330–333.

    Article  MathSciNet  MATH  Google Scholar 

  26. Chauhan, P. S., Tiwari, D., & Soni, S. K. (2017). New analytical expressions for the performance metrics of wireless communication system over Weibull/Lognormal composite fading. AEU-International Journal of Electronics and Communications, 82, 397–405.

    Article  Google Scholar 

  27. Shannon, C. E. (2001). A mathematical theory of communication. ACM SIGMOBILE Mobile Computing and Communications Review, 5(1), 3–55.

    Article  MathSciNet  Google Scholar 

  28. Tiwari, D., Soni, S., & Chauhan, P. S. (2017). A new closed-form expressions of channel capacity with MRC, EGC and SC over lognormal fading channel. Wireless Personal Communications, 97(3), 4183–4197.

    Article  Google Scholar 

  29. Adamchik, V. S., & Marichev, O. I. (1990, July). The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system. In Proceedings of the international symposium on Symbolic and algebraic computation(pp. 212–224). ACM.

  30. Gradshteyn, I. S., & Ryzhik, I. M. (2014). Table of integrals, series, and products. New York: Academic press.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Ravenshaw University, Cuttack, Odisha, 753003, India

    Tanmay Mukherjee & Dilip Senapati

  2. Department of Computer Science, Ramanujan College, University of Delhi, New Delhi, 110019, India

    Amit Kumar Singh

Authors
  1. Tanmay Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amit Kumar Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dilip Senapati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dilip Senapati.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mukherjee, T., Singh, A.K. & Senapati, D. Performance Evaluation of Wireless Communication Systems over Weibull/q-Lognormal Shadowed Fading Using Tsallis’ Entropy Framework. Wireless Pers Commun 106, 789–803 (2019). https://doi.org/10.1007/s11277-019-06190-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-019-06190-8

Keywords

Search

Navigation