Wireless Personal Communications

, Volume 104, Issue 2, pp 727–738 | Cite as

PAPR Distribution for Single Carrier M-QAM Modulations

  • Kouakou Kouassi
  • Guillaume AndrieuxEmail author
  • Jean-François Diouris


Single carrier modulations such as quadrature amplitude modulation (QAM) are recently becoming an attractive and complementary alternative to multiple carrier modulations. High order QAM provides spectral efficiency advantage at the price of larger dynamic range. This characteristic leads to enlarge the peak-to-average power ratio (PAPR) and so, to reduce the energy efficiency. This study provides an analysis of the PAPR distribution for QAM based systems. We focus on the distribution of the PAPR since it is the main evaluation means of PAPR reduction techniques. We present an analytic expression of the probability density function of the PAPR for limited length frames. The analysis shows that the expression of the PAPR usually found in the literature is valid only for long frames and is the asymptotic limit of the formula we propose. According to the simulation results, the distribution we suggest accurately describes the PAPR for long frames and is a good approximation for short frames.


Single carrier modulation Quadrature amplitude modulation (QAM) Peak-to-average power ratio (PAPR) Energy efficiency Central limit theorem (CLT) 



  1. 1.
    Sanjay Singh, M . H., & Sathish Kumar, M. (2009). Effect of peak-to-average power ratio reduction on the multicarrier communication system performance parameters. International Journal of Electrical and Computer Engineering (IJECE), 4, 779–786.Google Scholar
  2. 2.
    Jiang, T., Guizani, M., Chen, H.-H., Xiang, W., & Wu, Y. (2008). Derivation of PAPR distribution for OFDM wireless systems based on extreme value theory. IEEE Transactions on Wireless Communications, 7(4), 1298–1305.CrossRefGoogle Scholar
  3. 3.
    Ochiai, H., & Imai, H. (2001). On the distribution of the peak-to-average power ratio in OFDM signals. IEEE Transactions on Communications, 49(2), 282–289.CrossRefzbMATHGoogle Scholar
  4. 4.
    Litsyn, S., & Wunder, G. (2006). Generalized bounds on the crest-factor distribution of OFDM signals with applications to code design. IEEE Transactions on Information Theory, 52(3), 992–1006.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Jiang, T., & Wu, Y. (2008). An overview: Peak-to-average power ratio reduction techniques for OFDM signals. IEEE Transactions on Broadcasting, 54(2), 257–268.CrossRefGoogle Scholar
  6. 6.
    Pedrosa, P., Dinis, R., & Nunes, F. (2010). Iterative frequency domain equalization and carrier synchronization for multi-resolution constellations. IEEE Transactions on Broadcasting, 56(4), 551–557.CrossRefGoogle Scholar
  7. 7.
    Benvenuto, N., Dinis, R., Falconer, D., & Tomasin, S. (2010). Single carrier modulation with nonlinear frequency domain equalization: An idea whose time has come - again. Proceedings of the IEEE, 98(1), 69–96.CrossRefGoogle Scholar
  8. 8.
    Pancaldi, F., Vitetta, G., Kalbasi, R., Al-Dhahir, N., Uysal, M., & Mheidat, H. (2008). Single-carrier frequency domain equalization. IEEE Signal Processing Magazine, 25(5), 37–56.CrossRefGoogle Scholar
  9. 9.
    Talonen, M., & Lindfors, S. (2007) Power consumption model for linear RF power amplifiers with rectangular M-QAM modulation. In 4th International Symposium on Wireless Communication Systems, 2007. ISWCS 2007., (pp. 682–685).Google Scholar
  10. 10.
    Prabhu, R. S., & Daneshrad, B. (2008). Energy minimization of a QAM system with fading. IEEE Transactions on Wireless Communications, 7(12), 4837–4842.CrossRefGoogle Scholar
  11. 11.
    Cui, S., Goldsmith, A., & Bahai, A. (2005). Energy-constrained modulation optimization. IEEE Transactions on Wireless Communications, 4(5), 2349–2360.CrossRefGoogle Scholar
  12. 12.
    Wei, S., Goeckel, D., & Kelly, P. (2002). A modern extreme value theory approach to calculating the distribution of the peak-to-average power ratio in OFDM systems. In IEEE International Conference on Communications. ICC 2002. (2002), (Vol. 3, pp. 1686–1690).Google Scholar
  13. 13.
    Gnedenko, B. V. (1948). On a local limit theorem of the theory of probability. Uspekhi Mat. Nauk, 3(25), 187–194.MathSciNetGoogle Scholar
  14. 14.
    Marsaglia, G. (1965). Ratios of normal variables and ratios of sums of uniform variables. Journal of the American Statistical Association, 60(309), 193–204. [Online]. Available:

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université Bretagne Loire, Université de NantesUMR CNRS 6164 - Institute of Electronics and Telecommunications of Rennes (IETR), Polytech NantesNantesFrance

Personalised recommendations