Robust Beam Position Estimation with Photon Counting Detector Arrays in
Free-Space Optical Communications
Optical beam center position on an array of detectors is an important
parameter that is essential for estimating the angle-of-arrival of the
incoming signal beam. In this paper, we have examined the beam position
estimation problem for photon-counting detector arrays, and to this end,
we have derived and analyzed the Cramer-Rao lower bounds on the
mean-square error of the unbiased estimators of the beam position.
Furthermore, we have also derived the Cramer-Rao lower bounds of other
beam parameters such as peak intensity, and the intensity of background
radiation on the array. In this sense, we have considered a robust
estimation of the beam position in which none of the parameters are
assumed to be known beforehand. Additionally, we have derived the
Cramer-Rao lower bounds of beam parameters for observations based on
both pilot and data symbols of a pulse position modulation (PPM) scheme.
Finally, we have considered a two-step estimation problem in which the
peak intensity and background radiation are estimated using a method of
moments estimator, and the beam center position is estimated with the
help of a maximum likelihood estimator.