Comparison of methods of computing lognormal sum distributions and outages for digital wireless applications

Four methods that can be used to approximate the distribution function (DF) of a sum of independent lognormal random variables (RVs) are investigated and compared. The aim is to determine the best method to compute the DF considering both accuracy and computational effort. The investigation focuses on values of the dB spread, σ, valid for practical problems in wireless transmission (6 dB⩽σ⩽12 dB). Similarly, we emphasize values of the DF which represent practical values of outage for current and future wireless systems. Contrary to some previous reports, our results show that the simpler Wilkinson´s approach gives a more accurate estimate, in some cases of interest, than Schwartz and Yeh´s (1982) approach. Overall, it is found that the Schleher´s (1977) cumulants matching approach is a good method for small to medium dB spreads (σ=6 dB), and Farley´s approach is a good method for large dB spreads (σ=12 dB)