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80 Years of Research on Sum of Lognormal Random Variables: Recent Breakthroughs and Applications in Wireless Communications

主讲人 :Julian Cheng教授(Senior Member) 地点 :教三811 开始时间 : 2019-07-12 14:00 结束时间 : 2019-07-12 16:00

摘要: The distribution for the sum of lognormal random variables finds applications in many science and engineering disciplines, and it is particularly important for wireless communication engineers. However, the distribution for the simplistic sum of independent lognormal random variables is analytically intractable, and it is more so for a sum of correlated lognormal random variables with non-identical parameters. In 1934, Wilkinson from Bell Telephone Labs first studied this problem in an unpublished work. Since then, various approximations have been proposed in the literature. All these approximations fail to accurately quantify the left tail (or right tail) behavior of the distribution function of a sum of lognormal random variables. In this talk, in the context of diversity receptions over lognormal fading channels, we first present that the left tail distribution of the sum of independent lognormal random variables can be accurately represented by a Marcum Q-function. The proposed analytical result outperforms all existing well-known sum of lognormal approximations. Using a different approach, we then extend the problem to a sum of correlated and non-identically lognormal random variables, and show that its left-tail distribution can again be represented by another Marcum Q-function. Our study reveals a number of new and surprising engineering insights into the transmission characteristics over the lognormal fading channels. For example, for the dual-branch case, we show that the outage performance of negatively correlated lognormal channels is better than that of independent lognormal channels. We also show that under certain parameter conditions, one of the two lognormal channels can contribute no performance gain to the diversity reception systems. This implies that one link can be discarded without causing asymptotic performance loss. These new findings can guide the communication engineers to design better systems for transmission over the lognormal fading channels.

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