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Optical beam center position on an array of detectors is an important(hidden) parameter that is essential not only from a tracking perspective, butis also important for optimal detection of Pulse Position Modulation symbols infree-space optical communications. In this paper, we have examined the beamposition estimation problem for photon-counting detector arrays, and to thisend, we have proposed and analyzed a number of non-Bayesian beam positionestimators. These estimators are compared in terms of their mean-square error,bias and the probability of error performance. Additionally, the Cramer-RaoLower Bounds (CRLB) of the tracking error is also derived, and the CRLB curvesgive us additional insights concerning the effect of number of detectors andthe beam radius on mean-square error performance. Finally, the effect of beamposition estimation on the probability of error performance is investigated,and our study concludes that the probability of error of the system isminimized when the beam position on the array is estimated as accurately aspossible.

Beam Tracking with Photon-Counting Detector Arrays in Free-Space Optical Communications