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A Novel Accurate Approximation Method of Lognormal Sum Random Variables

Li, Xue
http://rave.ohiolink.edu/etdc/view?acc_num=wright1229358144

Abstract Details

2008, Master of Science in Engineering (MSEgr), Wright State University, Electrical Engineering.
Sums of lognormal random variables occur in many problems in wireless communications due to large-scale signal shadowing from multiple transmitters. With the emerging of cognitive radio technology, accurate analysis of interferences from multiple primary users and multiple secondary users is required. Such interferences are well modeled by the lognormal sum distribution. The lognormal sum distribution is known to have no close-form and is di±cult to compute numerically. Several approximations to the lognormal sum distribution have been proposed and employed in literature. However, these approximation methods are not without their drawbacks. Some widely used approximation methods are not accurate at the lower region, while some other approximation methods require the CDF (cumulative distribution function) curve from the Monte Carlo Simulation which is very computational demanding. In this master's thesis, we propose a novel approximation method, namely the Log Skew Normal (LSN) approximation, to accurately model the sum of M lognormal distributed random variables. The LSN approximation has good accuracy in the entire PDF (probability density function) region, especially in the lower PDF region. Furthermore, the proposed LSN approximation does not require the CDF curve. The close-form PDF of the resultingLSN random variable (RV) is presented and its parameters derived from those of the M individual lognormal RVs by using the moment matching technique. Simulation results on the CDF of sum of M lognormal random variables in di®erent conditions are used as reference curves to compare various approximation techniques. Simulation results con¯rm that the proposed LSN approximation provides better accuracy over a wide CDF range with no computational complexity increase.
Zhiqiang Wu, PhD (Advisor)
Zhiqiang Wu, PhD (Committee Chair)
Bin Wang, PhD (Committee Member)
Xiaodong Zhang, PhD (Committee Member)
47 p.
Electrical Engineering
lognormal sum; LSN; Log Skew Normal

Recommended Citations

Citations

  • Li, X. (2008). A Novel Accurate Approximation Method of Lognormal Sum Random Variables [Master's thesis, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1229358144

    APA Style (7th edition)

  • Li, Xue. A Novel Accurate Approximation Method of Lognormal Sum Random Variables. 2008. Wright State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=wright1229358144.

    MLA Style (8th edition)

  • Li, Xue. "A Novel Accurate Approximation Method of Lognormal Sum Random Variables." Master's thesis, Wright State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=wright1229358144

    Chicago Manual of Style (17th edition)

wright1229358144
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© 2008, all rights reserved.
This open access ETD is published by Wright State University and OhioLINK.