Skip to main content
SpringerLink
Log in

A Nakagami-N-gamma Model for Shadowed Fading Channels

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

Wireless channels are subject to short term fading and shadowing. Such shadowed fading channels are described using a Nakagami-lognormal process, with the Nakagami-m (short term fading) and lognormal distributions (shadowing). This approach does not result in a closed form solution for the density function of the signal-to-noise ratio (SNR) making wireless systems analysis difficult. It was suggested that a gamma or an inverse Gaussian distribution can be used in place of the lognormal distribution providing an analytical framework. The match of these two distributions to the lognormal was less than ideal. Invoking shadowing as multiplicative process, the distribution of the product of N gamma variables is proposed in place of the lognormal pdf resulting in the Nakagami-N-gamma model. It is shown that this model leads to simple solutions to the density and distribution functions as well as error rates for coherent phase shift keying modems. The outage probabilities and error rates based on the Nakagami-lognormal (NL) and Nakagami-N-gamma (NNG) models were compared. Results showed excellent match at levels of shadowing generally observed in wireless systems. While values of N as low as 3 was sufficient for low values of m and weak to moderate shadowing, values of N in the range of 7–9 provided better match for higher levels of shadowing and higher values of m. By varying N, it is also possible to get the NNG pdf to move closer to the NL pdf making the new model an ideal one for the shadowed fading channels with its flexibility and availability of analytical expressions.

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

Similar content being viewed by others

References

  1. Nakagami M. (1960) The m-distribution—A general formula of intensity distribution of rapid fading. In: Hoffman W. C. (eds) Statistical methods in radio wave propagation. Pergamon Press, Elmsford, NY

    Google Scholar 

  2. Suzuki H. (1975) A statistical model for urban radio propagation. IEEE Transactions on Communications 25(7): 673–679

    Article  Google Scholar 

  3. Coulson A. J., Williamson A. G., Vaughan R. G. (1998) A statistical basis for lognormal shadowing effects in multipath fading channels. IEEE Transactions on Communications 46(4): 494–502

    Article  Google Scholar 

  4. Abdi A., Kaveh M. K. (1998) Distribution: An approximate substitute for Rayleigh-lognormal distribution in fading-shadowing wireless channels. Electronics Letters 34: 851–852

    Article  Google Scholar 

  5. Shankar P. M. (2004) Error rates in generalized shadowed fading channels. Wireless Personal Communication 28: 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-Kfading channels. IEEE Communications Letters 10: 353–355

    Article  Google Scholar 

  7. Karmeshu R. A. (2007) On the efficacy of Rayleigh-inverse Gaussian distribution over K-distribution for wireless fading channels. Wireless Communications Mobile Computer 7: 1–7

    Article  Google Scholar 

  8. Laourine A., Alouini M.-S., Affes S., Stéphenne 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 

  9. Andersen, J. B. (2002). Statistical distributions in mobile communications using multiple scattering. In Proceedings 27th URSI general assembly. Netherlands: Maastricht.

  10. Erceg V., Fortune S. J., Ling J., Rustako A. J. Jr., Valenzuela R. A. (1997) Comparisons of a computer-based propagation prediction tool with experimental data collected in urban microcellular environments. IEEE Journal Selected areas in Communications 15(4): 677–684

    Article  Google Scholar 

  11. Salo J., El-Sallabi H. M., Vainikainen P. (2006) The distribution of the product of independent Rayleigh random variables. IEEE Transactions on Antennas and Propagation 54: 639–643

    Article  MathSciNet  Google Scholar 

  12. Clark J. R., Karp S. (1970) Approximations for lognormally fading optical signals. Proceedings IEEE 58: 1964–1965

    Article  Google Scholar 

  13. Gradshteyn I. S., Ryzhik I. M. (1994) Table of integrals, series, and products (5th ed.). Academic, San Diego, CA

    MATH  Google Scholar 

  14. Asplund, H., Molisch, A. F., Steinbauer, M. & Mehta, N. B. (2002). Clustering of scatterers in mobile radio channels—Evaluation and modeling in the COST259 directional channel model. In Proceedings IEEE ICC (pp. 901–905). New York.

  15. Papoulis A. (2002) Probability, random variables and stochastic processes (4th ed.). McGraw-Hill, New York

    Google Scholar 

  16. Mathai A. M. (1993) A handbook of generalized special functions for statistical and physical sciences. Oxford University Press, Oxford, UK, pp 82–83

    MATH  Google Scholar 

  17. Karagiannidis G. K., Tsiftsis T. A., Mullik R. K. (2006) Bounds for multihop relayed communications in Nakagami–m fading. IEEE Transactions on Communications 54(1): 18–22

    Article  Google Scholar 

  18. Shankar P. M. (2006) Performance analysis of diversity combining algorithms in shadowed fading channels. Wireless Personal Communication 37: 61–72

    Article  Google Scholar 

  19. Molisch A. (2005) Wireless communications. John Wiley & Sons, Hoboken, N. J., USA

    Google Scholar 

  20. Nee R., Prasad R. (2000) OFDM for wireless multimedia communications. Artech House, Boston, MA

    Google Scholar 

  21. Ma, X., Kobayashi, H., & Schwartz, S. C. (2003). In Proceedings of the 14th IEEE international symposium on personal, indoor and mobile radio Communication (pp. 2239–2243).

  22. Hou, L., Huijie, L., & Xiaokang, L. (2007). BER calculation of an OFDM system with phase nonlinearity. In Proceedings international symposium on intelligent signal processing and communication systems (pp. 633–636). China: Xiamen

  23. Santhanathan K., Tellambura C. (2001) Probability of error calculations of OFDM systems with frequency offset. IEEE Transactions Communications 49: 1884–1887

    Article  Google Scholar 

  24. Weeraddana P. C., Rajatheva N., Minn H. (2009) Probability of error analysis of BPSK OFDM systems with random residual frequency offset. IEEE Transactions Communications 57: 106–116

    Article  Google Scholar 

  25. Le K. N. (2010) BER of OFDM in Rayleigh fading environments with selective diversity. Wireless Communications and Mobile Computing 10: 306–311

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical & Computer Engineering, Drexel University, Philadelphia, PA, 19104, USA

    P. M. Shankar

Authors
  1. P. M. Shankar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. M. Shankar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shankar, P.M. A Nakagami-N-gamma Model for Shadowed Fading Channels. Wireless Pers Commun 64, 665–680 (2012). https://doi.org/10.1007/s11277-010-0211-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-010-0211-5

Keywords

Search

Navigation