On the Bivariate Nakagami-Lognormal Distribution and Its Correlation Properties

Abstract

The bivariate Nakagami-lognormal distribution used to model the composite fast fading and shadowing has been examined exhaustively. In particular, we have derived the joint probability density function, the cross-moments, and the correlation coefficient in power terms. Also, two procedures to generate two correlated Nakagami-lognormal random variables are described. These procedures can be used to evaluate the robustness of the sample correlation coefficient distribution in both macro- and microdiversity scenarios. It is shown that the bias and the standard deviation of this sample correlation coefficient are substantially high for large shadowing standard deviations found in wireless communication measurements, even if the number of observations is considerable.