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\begin{document}

\title{Signal Acquisition with Photon-Counting Detector Arrays in Free-Space
Optical Communications}



\author[1]{Muhammad Salman Bashir }%
\author[2]{Mohamed-Slim Alouini }%
\affil[1]{King Abdullah University of Science and Technology}%
\affil[2]{Affiliation not available}%


\vspace{-1em}



  
  \date{June 18, 2024}


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\begin{abstract}
Pointing and acquisition are an important aspect of free-space optical
communications because of the narrow beamwidth associated with the
optical signal. In this paper, we have analyzed the pointing and
acquisition problem in free-space optical communications for
photon-counting detector arrays and Gaussian beams. In this regard, we
have considered the maximum likelihood detection for detecting the
location of the array, and analyzed the one-shot probabilities of missed
detection and false alarm using the scaled Poisson approximation.
Moreover, the upper/lower bounds on the probabilities of missed
detection and false alarm for one complete scan are also derived, and
these probabilities are compared with Monte Carlo approximations for a
few cases. Additionally, the upper bounds on the acquisition time and
the mean acquisition time are also derived. The upper bound on mean
acquisition time is minimized numerically with respect to the beam
radius for a constant signal-to-noise ratio scenario. Finally, the
complementary distribution function of an upper bound on acquisition
time is also calculated in a closed form. Our study concludes that an
array of smaller detectors gives a better acquisition performance (in
terms of acquisition time) as compared to one large detector of similar
dimensions as the array.\\%
\end{abstract}%



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