TR2006-010

Approximating the Sum of Correlated Lognormal or Lognormal-Rice Random Variables


    •  Mehta, N.B.; Molisch, A.F.; Wu, J.; Zhang, J., "Approximating the Sum of Correlated Lognormal or Lognormal-Rice Random Variables", IEEE International Conference on Communications (ICC), ISSN: 8164-9547, June 2006, vol. 4, pp. 1605-1610.
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      • @inproceedings{Mehta2006jun,
      • author = {Mehta, N.B. and Molisch, A.F. and Wu, J. and Zhang, J.},
      • title = {Approximating the Sum of Correlated Lognormal or Lognormal-Rice Random Variables},
      • booktitle = {IEEE International Conference on Communications (ICC)},
      • year = 2006,
      • volume = 4,
      • pages = {1605--1610},
      • month = jun,
      • issn = {8164-9547},
      • url = {http://www.merl.com/publications/TR2006-010}
      • }
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    Electronics & Communications


A simple and novel method is presented to approximate by the lognormal distribution the probability density function of the sum of correlated lognormal random variables. The method is also shown to work well for approximating the distribution of the sum of lognormal-Rice or Suzuki random variables by the lognormal distribution. The method is based on matching a low-order Gauss-Hermite approximation of the moment-generating function of the sum of random variables with that of a lognormal distribution at a small number of points. Compared with methods available in the literature such as the Fenton-Wilkinson method, Schwartz-Yeh method, and their extensions, the proposed method provides the parametric flexibility to address the inevitable trade-off that needs to be made in approximating different regions of the probability distribution function.