Statistical Profile of Hermite–Gaussian Beam in the Presence of Residual Spatial Jitter in FSO Communications

In this letter, the statistics of the beam profile of a free-space optical (FSO) system is studied when the optical beam possesses a Hermite-Gaussian profile and the beam is subject to random pointing jitter. In particular, it is assumed that the received signal is impaired by the residual pointing error cause by the spatial tracking loop responsible for tracking the atmospheric beam wander and platform sway. The residual pointing jitter is assumed to have a Gaussian probability density function (pdf) with independent components in the two dimensions of the detector. The mean and variance of the beam profile along with the impact of spatial error on the signal-to-noise (SNR) loss and channel cross-talk are obtained assuming that the pointing jitter has a variance that is substantially smaller than the beam waist.