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.

中文翻译：

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在自由空间光通信中使用光子计数探测器阵列进行信号采集

由于与光信号相关的窄波束宽度，指向和捕获是自由空间光通信的一个重要方面。在本文中，我们分析了光子计数探测器阵列和高斯光束在自由空间光通信中的指向和采集问题。在这方面，我们考虑了用于检测阵列位置的最大似然检测，并使用缩放泊松近似分析了漏检和误报的一次性概率。此外，还导出了一次完整扫描的漏检和误报概率的上限/下限，并将这些概率与一些情况下的蒙特卡罗近似进行了比较。此外，还导出了采集时间和平均采集时间的上限。对于恒定信噪比情况，平均采集时间的上限相对于波束半径在数值上最小化。最后，采集时间上界的互补分布函数也以封闭形式计算。我们的研究得出的结论是，与一个与阵列尺寸相似的大型探测器相比，较小探测器阵列提供了更好的采集性能（就采集时间而言）。