PDF models for uplink to space in the presence of beam wander

Abstract

In this paper we discuss several models for the probability density function (pdf) of the irradiance of a Gaussian-beam wave from ground to space. We consider cases of tracked beams and untracked beams, both of which involve a certain amount of beam wander. The various pdf models that we introduce are all compared with simulation data over a broad range of beam diameters. We find that certain well-known models fit the simulation data in one of the regimes defined by the ratio of beam radius W₀ to Fried's parameter r₀ (<i>W</i>₀/r₀ <<1, <i>W</i>₀/r₀ ~ 1, <i>W</i>₀/r₀ >> 1), but not generally in the other regimes. This is true for tracked beams as well as untracked beams. Two new pdf models, developed here as a modulation of either the gamma-gamma pdf or the gamma pdf, are shown to provide excellent fits to the simulation data over all three regimes defined above.