A Novel Accurate Approximation Method of Lognormal Sum Random Variables

Xue Li. M.S. Egr Department of Electrical Engineering, Wright State University, 2008. A Novel Accurate Approximation Method of Lognormal Sum Random Variables 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 difficult 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 resulting LSN 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 different conditions are used as reference curves to compare various approximation techniques. Simulation results confirm that the proposed LSN approximation provides better accuracy over a wide CDF range with no computational complexity increase.