Wireless Networks

, Volume 25, Issue 7, pp 4359–4369 | Cite as

Bit error probability of the M-QAM scheme subject to multilevel (double) gated additive white Gaussian noise and Nakagami-m fading

  • Hugerles S. SilvaEmail author
  • Marcelo S. Alencar
  • Wamberto J. L. Queiroz
  • Danilo B. T. Almeida
  • Francisco Madeiro


In this paper, noise models called multilevel gated additive white Gaussian noise (GAWGN) and multilevel double gated additive white Gaussian noise (\(\hbox {G}^{2}\)AWGN) are adopted, corresponding to the sum of a white Gaussian component of variance \(\sigma _{g}^{2}\) and a white Gaussian noise component of variance \(\sigma _{i}^2\) gated by a discrete random process defined in continuous time, C(t), which takes values into a finite discrete set. A channel subject to this noise combined with the Nakagami-m fading can be used to characterize links in several environments subject to noise caused by different sources and with different intensities. In this work, new exact and closed-form expressions are presented for the bit error probability (BEP) of the M-ary quadrature amplitude modulation scheme (M-QAM) subject to Nakagami-m fading and multilevel GAWGN or multilevel \(\hbox {G}^{2}\)AWGN. The BEP curves are presented for different parameters that characterize mathematically the channel, corroborated by simulations performed with the Monte Carlo method.


Bit error probability Impulsive noise Nakagami-m fading 



This study was funded in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001 and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).


  1. 1.
    Haykin, S. (2001). Communication systems (4th ed.). New York, NY: Wiley.Google Scholar
  2. 2.
    Cohen, L. (2005). The history of noise [on the 100th anniversary of its birth]. IEEE Signal Processing Magazine, 22(6), 20–45.Google Scholar
  3. 3.
    Araújo, E. R., Queiroz, W. J. L., Madeiro, F., Lopes, W. T. A., & Alencar, M. S. (2015). On gated Gaussian impulsive noise in M-QAM with optimum receivers. Journal of Communication and Information Systems, 30(1), 10–20.Google Scholar
  4. 4.
    Lago-Fernández, J., & Salter, J. (2004). Modelling impulsive interference in DVB-T. R&D White Paper, WHP, 080(299), 1–51.Google Scholar
  5. 5.
    Sanchez, M. G., Haro, L., Ramon, M. C., Mansilla, A., Ortega, C. M., & Oliver, D. (1999). Impulsive noise measurements and characterization in a UHF digital TV channel. IEEE Transactions on Electromagnetic Compatibility, 41(2), 124–136.Google Scholar
  6. 6.
    Shongwe, T., Vinck, A. J. H., & Ferreira, H. C. (2015). The effects of periodic impulsive noise on OFDM. In Proceedings of the IEEE international symposium on powerline communications and its applications, pp. 29–31.Google Scholar
  7. 7.
    Cheffena, M. (2012). Industrial wireless sensor networks: Channel modeling and performance evaluation. EURASIP Journal on Wireless Communications and Networking, 2012(1), 1–8.Google Scholar
  8. 8.
    Stenumgaard, P., Chilo, J., Ferrer-Coll, P., & Angskog, P. (2013). Challenges and conditions for wireless machine-to-machine communications in industrial environments. IEEE Communications Magazine, 51(6), 187–192.Google Scholar
  9. 9.
    Kim, D., Ingram, M. A., & Smith, W. W. (2001). Small-scale fading for an indoor wireless channel with modulated backscatter. In Proceedings of the IEEE Vehicular Technology Conference (Vol. 3, pp. 1616–1620).Google Scholar
  10. 10.
    Karedal, J., Wyne, S., Almers, P., Tufvesson, F., & Molisch, A. F. (2004). Statistical analysis of the UWB channel in an industrial environment. In Proceedings of the IEEE Vehicular Technology Conference (Vol. 1, pp. 81–85).Google Scholar
  11. 11.
    Sexton, D., Mahony, M., Lapinski, M., & Werb, J. (2005). Radio channel quality in industrial wireless sensor networks. In Proceedings of the Sensors for Industry Conference (pp. 88–94).Google Scholar
  12. 12.
    Agrawal, P., Ahlén, A., Olofsson, T., & Gidlund, M. (2014). Characterization of long term channel variations in industrial wireless sensor networks. In Proceedings of the IEEE International Conference on Communications (ICC) (pp. 1–6).Google Scholar
  13. 13.
    Cheffena, M. (2016). Propagation channel characteristics of industrial wireless sensor networks. IEEE Antennas and Propagation Magazine, 58(1), 66–73.Google Scholar
  14. 14.
    Tuan, N. T., Kim, D., & Lee, J. (2018). On the performance of cooperative transmission schemes in industrial wireless sensor networks. IEEE Transactions on Industrial Informatics, 14(9), 4007–4018.Google Scholar
  15. 15.
    Nakagami, M. (1960) The \(m\)-distribution—a general formula of intensity distribution of rapid fading. Statistical Method of Radio Propagation, September.Google Scholar
  16. 16.
    Amzucu, D. M., Li, H., & Fledderus, E. (2014). Indoor radio propagation and interference in 2.4 GHz wireless sensor networks: Measurements and analysis. Wireless Personal Communications, 76(2), 245–269.Google Scholar
  17. 17.
    Ding, G., Wu, Q., Zhang, L., Lin, Y., Tsiftsis, T. A., & Yao, Y. (2018). An amateur drone surveillance system based on the cognitive internet of things. IEEE Communications Magazine, 56(1), 28–35.Google Scholar
  18. 18.
    Silva, H. S., Alencar, M. S., de Queiroz, W. J. L., Teixeira, D. B. A., & Madeiro, F. (2018). Bit error probability of \(M\)-QAM under impulsive noise and fading modeled by using Markov chains. Radioengineering, 27(4), 1183–1190.Google Scholar
  19. 19.
    Silva, H. S., Alencar, M. S., de Queiroz, W. J. L., Teixeira, D. B. A., & Madeiro, F. (2018). Closed-form expression for the bit error probability of the \(M\)-QAM for a channel subjected to impulsive noise and Nakagami fading. Wireless Communications and Mobile Computing, 2018, 1–9.Google Scholar
  20. 20.
    Silva, H. S., Alencar, M. S., de Queiroz, W. J. L., Teixeira, D. B. A., & Madeiro, F. (2019). Bit error probability of the \(M\)-QAM scheme under \(\eta\)-\(\mu\) fading and impulsive noise in a communication system using spatial diversity. International Journal of Communication Systems, 2019, 1–15.Google Scholar
  21. 21.
    Lopes, W. T. A., & Alencar, M. S. (2002). QPSK detection schemes for Rayleigh fading channels. In  Proceedings of the International Telecommunications Symposium (pp. 1–5).Google Scholar
  22. 22.
    Lopes, W. T. A., Madeiro, F., & Alencar, M. S. (2007). Closed-form expression for the bit error probability of rectangular QAM subject to Rayleigh fading. In Proceedings of the IEEE Vehicular Technology Conference (pp. 1–5).Google Scholar
  23. 23.
    de Queiroz, W. J. L., Lopes, W. T. A., Madeiro, F., & Alencar, M. S. (2010). An alternative method to compute the bit error probability of modulation schemes subject to Nakagami-\(m\) fading. EURASIP Journal on Advances in Signal Processing, 2010, 1–12.Google Scholar
  24. 24.
    Goldsmith, A. (2005). Wireless communications (1st ed.). New York, NY: Cambridge University Press.Google Scholar
  25. 25.
    Cho, K., & Yoon, D. (2002). On the general BER expression of one- and two-dimensional amplitude modulations. IEEE Transactions on Communications, 50(7), 1074–1080.Google Scholar
  26. 26.
    Gradshteyn, I. S., & Ryzhik, I . M. (2007). Table of integrals, series and products (7th ed.). New York, NY: Academic Express.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Federal University of Paraíba – UFPBJoão PessoaBrazil
  2. 2.Federal University of Bahia – UFBASalvadorBrazil
  3. 3.Federal University of Campina Grande – UFCGCampina GrandeBrazil
  4. 4.University of Pernambuco – UPERecifeBrazil

Personalised recommendations