On the Probability Density Function of the Signal Strength in Free-Space Optical Communications Systems with Diversity Reception

Abstract

We investigate the statistical characteristics of the signal power in a diversity reception (DR) free-space optics (FSO) communications systems. In this paper, the inverse-Gaussian (IG) probability density function (pdf) is proposed as a candidate pdf for modeling the statistical behavior of the sum of independent lognormal random variables, which is observed in DR-FSO systems under weak turbulence condition. It is shown here that the IG pdf offers a highly-accurate approximation of the lognormal sum (LNS) while offering a simple form factor, which leads to tractable error rate analysis of communication systems. This pdf requires the estimation of only 2 parameters, whereas the competing pdf models often require the estimation of 5 parameters. The previously proposed pdfs are often studied for the lognormal sum of large number of lognormal random variables $N (> 10)$. Furthermore, for small N, the accuracy of the previously proposed pdfs becomes suspect, whereas the IG pdf is shown to be very accurate for small values of N. The accuracy of the IG pdf is established using Hellinger distance (H- D), Kolmogorov-Smirnov (K-S) test, and Bhattacharyya distance (B-D). It is shown that the proposed pdf achieves a distance metric that remains less than $ 2\times 10^{-2}$ for values of $N\leq 5.$