Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지
DOI QR코드

DOI QR Code

Tight Bounds and Invertible Average Error Probability Expressions over Composite Fading Channels

  • Wang, Qian (Department of Electrical and Computer Engineering, National University of Singapore) ;
  • Lin, Hai (Department of Electrical and Information Systems, Graduate School of Engineering, Osaka Prefecture University) ;
  • Kam, Pooi-Yuen (Department of Electrical and Computer Engineering, National University of Singapore)
  • Received : 2014.07.21
  • Accepted : 2015.11.16
  • Published : 2016.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

Keywords

References

  1. J. G. Proakis, Digital Communications. 5th ed. New-York: McGraw-Hill, 2007.
  2. M. K. Simon and M.-S. Alouini, Digital Communication over Fading Channels. John Wiley & Sons, 2005.
  3. M. K. Simon and M.-S. Alouini, "A unified approach to the performance analysis of digital communication over generalized fading channels," in Proc. IEEE, vol. 86, no. 9, pp. 1860-1877, 1998. https://doi.org/10.1109/5.705532
  4. P. Loskot and N. C. Beaulieu, "Prony and polynomial approximations for evaluation of the average probability of error over slow-fading channels," IEEE Trans. Veh. Tech., vol. 58, no. 3, pp. 1269-1280, 2009. https://doi.org/10.1109/TVT.2008.926072
  5. P. Mary, M. Dohler, J.-M. Gorce, G. Villemaud, and M. Arndt, "M-ary symbol error outage over Nakagami-m fading channels in shadowing environments," IEEE Trans. Commun., vol. 57, no. 10, pp. 2876-2879, 2009. https://doi.org/10.1109/TCOMM.2009.10.080031
  6. Q. Shi and Y. Karasawa, "An accurate and efficient approximation to the Gaussian Q-function and its applications in performance analysis in Nakagami-m fading," IEEE Commun. Lett., vol. 15, no. 5, pp. 479-481, 2011. https://doi.org/10.1109/LCOMM.2011.032111.102440
  7. H. Shin and J. H. Lee, "On the error probability of binary and M-ary signals in Nakagami-m fading channels," IEEE Trans. Commun., vol. 52, no. 4, pp. 536-539, 2004. https://doi.org/10.1109/TCOMM.2004.826373
  8. A. Laourine, M.-S. Alouini, S. Affes, and A. Stephenne, "On the performance analysis of composite multipath/shadowing channels using the G-distribution," IEEE Trans. Commun., vol. 57, no. 4, pp. 1162-1170, 2009. https://doi.org/10.1109/TCOMM.2009.04.070258
  9. S. Atapattu, C. Tellambura, and H. Jiang, "A mixture gamma distribution to model the SNR of wireless channels," IEEE Trans. Wireless Commun., vol. 10, no. 12, pp. 4193-4203, 2011. https://doi.org/10.1109/TWC.2011.111210.102115
  10. O. Alhussein, S.Muhaidat, J. Liang, and P.D. Yoo, "A unified approach for representing wireless channels using EM-based finite mixture of gamma distributions," in Proc. IEEE GLOBECOM Workshops, 2014, pp. 1008-1013.
  11. B. Selim, O. Alhussein, S. Muhaidat, G. K. Karagiannidis, and J. Liang, "Modeling and analysis of wireless channels via the mixture of gaussian distribution," arXiv preprint arXiv:1503.00877, 2015.
  12. Y. Jeong, H. Shin, and M. Z.Win, "H-fading: Towards H-transform theory for wireless communication," in Proc. EuCNC, 2015, pp. 26-30.
  13. W. Cheng, "Performance analysis and comparison of dual-hop amplify-and-forward relaying over mixture gamma and generalized-k fading channels," in Proc. WCSP, 2013.
  14. J. Jung, S.-R. Lee, H. Park, S. Lee, and I. Lee, "Capacity and error probability analysis of diversity reception schemes over generalized-K fading channels using a mixture gamma distribution," IEEE Trans. Wireless Commun., vol. 13, no. 9, pp. 4721-4730, 2014. https://doi.org/10.1109/TWC.2014.2331691
  15. J. Jung, S.-R. Lee, H. Park, H. Lee, and I. Lee, "A PDF-based capacity analysis of diversity reception schemes over composite fading channels using a mixture gamma distribution," in Proc. IEEE VTC, 2014.
  16. A. A. Hammadi et al., "Unified analysis of cooperative spectrum sensing over composite and generalized fading channels," arXiv preprint arXiv:1503.01415, 2015.
  17. A. Agrawal and R. S. Kshetrimayum, "Analysis of UWB communication over IEEE 802.15. 3a channel by superseding lognormal shadowing by mixture of gamma distributions," AEU-International J. Electron. Commun., 2015.
  18. H. Fu, M.-W. Wu, and P.-Y. Kam, "Explicit, closed-form performance analysis in fading via new bound on Gaussian Q-function," in Proc. IEEE ICC, 2013, pp. 5819-5823.
  19. H. Fu, M.-W. Wu, and P.-Y. Kam, "Lower bound on averages of the product of L Gaussian Q-functions over Nakagami-m fading," in Proc. IEEE VTC, 2013.
  20. Z. Wang and G. B. Giannakis, "A simple and general parameterization quantifying performance in fading channels," IEEE Trans. Commun., vol. 51, no. 8, pp. 1389-1398, 2003. https://doi.org/10.1109/TCOMM.2003.815053
  21. J. Jung, S.-R. Lee, H. Park, and I. Lee, "Diversity analysis over composite fading channels using a mixture gamma distribution," in Proc. IEEE ICC, 2013, pp. 5824-5828.
  22. P. Mary, M. Dohler, J.-M. Gorce, G. Villemaud, and M. Arndt, "BPSK bit error outage over Nakagami-m fading channels in lognormal shadowing environments," IEEE Commun. Lett., vol. 11, no. 7, pp. 565-567, 2007. https://doi.org/10.1109/LCOMM.2007.070241
  23. A. Conti, M. Z. Win, and M. Chiani, "On the inverse symbol-error probability for diversity reception," IEEE Trans. Commun., vol. 51, no. 5, pp. 753-756, 2003. https://doi.org/10.1109/TCOMM.2003.811433
  24. A. Goldsmith, Wireless Communications. Cambridge university press, 2005.
  25. P. S. Bithas et al., "On the performance analysis of digital communications over generalized-k fading channels," IEEE Commun. Lett., vol. 10, no. 5, pp. 353-355, 2006. https://doi.org/10.1109/LCOMM.2006.1633320
  26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Courier Corporation, 1964.
  27. J. Lu, K. B. Letaief, J. C. Chuang, and M. L. Liou, "M-PSK and M-QAM BER computation using signal-space concepts," IEEE Trans. Commun., vol. 47, no. 2, pp. 181-184, 1999. https://doi.org/10.1109/26.752121