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Robust Beam Position Estimation with Photon Counting Detector Arrays in Free-Space Optical Communications




angle-of-arrival, beam center position, Cramer-Rao lower bounds, free-space optical communications, maximum likelihood estimator, method of moments estimator, photon counting detector arrays, pulse position modulation


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.


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2020-09-21 — Updated on 2020-09-21