Optical downlink propagation from space-to-earth: aperture-averaged power fluctuations, temporal covariance and power spectrum

In this work, we consider optical downlink from space-based laser sources and develop a consistent quantitative analysis of the collected power fluctuations by finite receiving apertures, and both the corresponding temporal covariance and power spectral density (PSD). Here we assume weak to moderate scintillation conditions where lognormal statistics are valid. We derive both exact solutions and highly accurate engineering easy to implement approximations for the downlink aperture-averaging factor, and both the corresponding aperture-averaged signal temporal covariance and PSD. Additionally, highly accurate elementary analytic scaling relations are derived for the corresponding aperture-averaged characteristic correlation time and scintillation bandwidth, which are in good agreement with available experimental observations. Finally closed form expressions for the so-called quasi-frequency that is central to the determination of level crossing rates and duration of fades and surges in a propagation channel are derived. Wherever possible, we endeavor to derive "user friendly" accurate engineering approximations for the various statistical quantities of interest.