Analytical Models for Distribution of the Envelope and Phase of Linearly Modulated Signals in AWGN Channel

Taleb Moazzeni, Yingtao Jiang, Henry Selvaraj, Tianding Chen


In this paper, analytical expressions for the distribution of the envelope and phase of linearly modulated signals such as BPSK,M-PSK, andM-QAM in AWGN are presented.We perform numerical simulations for different orders of signal constellations. The results show that the proposed theoretical models are in excellent agreement with the estimated distributions from various numerical experiments.


Full Text:



H. Ch. Cho, M. S. Fadali, and K. S. Lee, “Online probability density estimation of nonstationary random signal using dynamic Bayesian networks,” International Journal of Control, Automation, and Systems, vol. 6, no. 1, pp. 109–118, February 2008.

Y. Yang, Ch.-H Liu, and Ta-W. Soong, “A log-likelihood function-based algorithm for QAM signal classification,” Signal Processing, vol. 70, pp. 61–71, October 1998.

R. J. Achatz et al., “Estimating and graphing the amplitude probability distribution function of complex-baseband signals,” US DoC, NTIA/ITS, IEEE 802.15 Working Group for Wireless Personal Area Networks, 2004.

A. D. Whalen, Detection of Signals in Noise. New York: Academic Press, 1971.

F. Yusheng, R. Chunhui, and H. Wei, “QAM signals recognition based on amplitude distribution,” Journal of Electronics (China), vol. 28, no. 1, January 2011.

I. T. Monroy, “On analytical expressions for the distribution of the filtered output of square envelope receivers with signal and colored Gaussian noise input,” IEEE Transactions on Communications, vol. 49, no. 1, pp. 19–23, January 2001.

F. Bellili, A. St´ephenne, and S. Affes, “Cram´er-Rao bounds for SNR estimates in multicarrier transmissions,” in Proc. IEEE Vehicular Technology Conference VTC, Montreal, Canada, April 2009, pp. 1–5.

F. Bellili, A. St´ephenne, and S. Affes, “Cram´er-Rao lower bounds for NDA SNR estimates of square QAM modulated transmissions,” IEEE Transactions on Communications, vol. 58, no. 11, pp. 3211–3218, November 2010.

D. V. Hinkley, “On the ratio of two correlated normal random variables,” Biometrika, vol. 56, no. 3, pp. 635–639, December 1969.


  • There are currently no refbacks.

International Journal of Electronics and Telecommunications
is a periodical of Electronics and Telecommunications Committee
of Polish Academy of Sciences

eISSN: 2300-1933