Finite-state Markov Model for Lognormal, Chi-square (Central), Chi-square (Non-central), and K-distributions

Article

Abstract

This paper formulates a finite-state Markov channel model to represent received signal-to-noise (SNR) ratios having lognormal, K-distribution, chi-square (central) and chi-square (non-central) distributions in a slow fading channel. The range of the SNRs is partitioned into a finite number of states following earlier works in literature. Performance measures like level crossing rates, steady-state probabilities, transition probabilities, and state-time durations are derived, and numerical results are plotted and discussed for the FSMC models for all the distributions.

Key words

Lognormal distribution K-distribution Chi-square (central) distribution Chi-square (non-central) distribution Level crossing rate Average fade duration 

References

  1. 1.
    W. Turin, Digital Transmission Systems: Performance, Analysis, and Modelling, 2nd ed. McGraw-Hill, NY, 1999.Google Scholar
  2. 2.
    W. Tranter, K. Shanmugan, T. Rappaport, and K. Kosbar, Principles of Communication Systems Simulation with Wireless Applications, Prentice Hall, Inc., July, 2003.Google Scholar
  3. 3.
    S. Kundu, K. Basu, and S. Das, Finite-state Markov model for effective bandwidth calculation in wireless packet networks, Third International Symposium on Modeling and Optimization in Mobile, Ad hoc, and Wireless Networks (WiOpt ’05), pp. 351–357, 2005.Google Scholar
  4. 4.
    W. Tang, Finite-state Markov models for correlated fading channels in wireless communications. Technical report, University of Pennsylvania, 2001.Google Scholar
  5. 5.
    R. Chen, K. Chua, B. Tan, and C. Ng, Adaptive error coding using channel prediction, Journal of Wireless Networks, Vol. 5, No. 1, pp. 23–32, 1999.Google Scholar
  6. 6.
    C. Iskander and P. Mathiopoulos, Fast simulation of diversity Nakagami fading channels using finite-state Markov models. IEEE Transactions on Broadcasting, Vol. 49, No. 3, 2003.Google Scholar
  7. 7.
    J. Yun and M. Kavehrad, Markov error structure for throughput analysis of adaptive systems combined with ARQ over correlated fading channels, IEEE Transactions on Vehicular Technology, Vol. 54, No. 1, pp. 235–245, 2005.CrossRefGoogle Scholar
  8. 8.
    A. Ramesh, A. Chockalingam, and L. Milstein, A first-order Markov model for correlated Nakagami-m fading channels. Proc. IEEE GLOBECOM ’02, 2002.Google Scholar
  9. 9.
    P. Sadeghi and P. Rapajic, Capacity analysis for finite-state Markov mapping of flat-fading channels, IEEE Transactions on Communications, Vol. 53, No. 5, pp. 833–840, 2005.CrossRefGoogle Scholar
  10. 10.
    H. Rutagemwa and X. Shen, Modeling and analysis of WAP performance over wireless links. IEEE Transactions on Mobile Computing, Vol. 2, No. 3, pp. 221–232, 2003.CrossRefGoogle Scholar
  11. 11.
    H. S. Wang and P. Chang, On verifying the first-order Markovian assumption for a Rayleigh fading channel, IEEE Transactions on Vehicular Technology, Vol. 45, No. 2, pp. 353–357, 1996.CrossRefGoogle Scholar
  12. 12.
    M. Zorzi, R. Rao, and L. Milstein, On the accuracy of a first-order Markov model for data transmission on fading channels. Fourth IEEE Conference on Universal Personal Communications, pp. 211–215, 1995.Google Scholar
  13. 13.
    J. G. Proakis, Digital Communications, 4th ed. McGraw Hill, NY, 2001.Google Scholar
  14. 14.
    T. Moulsley and E. Vilar, Experimental and theoretical statistics of microwave amplitude scintillations on satellite downlinks, IEEE Transactions on Antenna Propagation, Vol. 30, pp. 1099–1106, 1982.CrossRefGoogle Scholar
  15. 15.
    J. Parsons, The Mobile Radio Propagation Channel, Wiley, Inc., NY, 1992.Google Scholar
  16. 16.
    L. Kanal, A. Sastry, Models for channels with memory and their applications to error control, Proceedings of the IEEE, Vol. 66, No. 7, pp. 724–744, 1978.MathSciNetCrossRefGoogle Scholar
  17. 17.
    G. L. Stuber, Principles of Mobile Communication, Kluwer Academic Publishers, Dordrecht, Netherlands, 1996.Google Scholar
  18. 18.
    Q. Zhang and S. Kassam, Finite-state Markov model for Rayleigh fading channels, IEEE Transactions on Communications, Vol. 47, No. 11, pp. 1688–1692, 1999.CrossRefGoogle Scholar
  19. 19.
    W. C. Jakes, Microwave Mobile Communications, 1st edn. John Wiley & Sons, Inc., MA, 1974.Google Scholar
  20. 20.
    H. S. Wang and N. Moayeri, Finite-state Markov channel—a useful model for Radio communication channels, IEEE Transactions on Vehicular Technology, Vol. 44, No. 1, pp. 163–171, 1995.CrossRefGoogle Scholar
  21. 21.
    C. D. Iskander and P. Mathiopoulos, Finite-state Markov modeling of diversity Nakagami channels. Proceedings of the 7th Canadian Workshop on Information Theory, 2001.Google Scholar
  22. 22.
    A. Abdi and M. Kaveh, Comparison of DPSK and MSK bit error rates for K and Rayleigh–lognormal fading distributions, IEEE Communication Letters, Vol. 4, pp. 122–124, 2000.CrossRefGoogle Scholar
  23. 23.
    I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, 5th ed. Academic Press, San Diego, CA, 1994.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Electronics and Communication EngineeringSRM UniversityKancheepuramIndia

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