Adaptive optics wavefront sensors based on photon-counting detector arrays

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.

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Cramér-Rao Bounds for Beam Tracking With Photon Counting Detector Arrays in Free-Space Optical Communications

IEEE Open Journal of the Communications Society ◽

10.1109/ojcoms.2021.3078091 ◽

2021 ◽

pp. 1-1

Author(s):

Muhammad Salman Bashir ◽

Ming-Cheng Tsai ◽

Mohamed-Slim Alouini

Keyword(s):

Optical Communications ◽

Free Space ◽

Photon Counting ◽

Free Space Optical ◽

Detector Arrays ◽

Photon Counting Detector ◽

Beam Tracking

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

10.36227/techrxiv.12980309.v2 ◽

2020 ◽

Author(s):

Muhammad Salman Bashir ◽

Ming-Cheng Tsai ◽

Mohamed-Slim Alouini

Keyword(s):

Lower Bounds ◽

Background Radiation ◽

Photon Counting ◽

Position Estimation ◽

Beam Position ◽

Detector Arrays ◽

Photon Counting Detector ◽

Center Position ◽

Beam Center ◽

Beam Parameters

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

10.36227/techrxiv.12980309.v1 ◽

2020 ◽

Author(s):

Muhammad Salman Bashir ◽

Ming-Cheng Tsai ◽

Mohamed-Slim Alouini

Keyword(s):

Lower Bounds ◽

Background Radiation ◽

Photon Counting ◽

Position Estimation ◽

Beam Position ◽

Detector Arrays ◽

Photon Counting Detector ◽

Center Position ◽

Beam Center ◽

Beam Parameters

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

10.31224/osf.io/nqf3y ◽

2020 ◽

Author(s):

Muhammad Salman Bashir ◽

Ming-Cheng Tsai ◽

Mohamed-Slim Alouini

Keyword(s):

Lower Bounds ◽

Background Radiation ◽

Photon Counting ◽

Position Estimation ◽

Beam Position ◽

Detector Arrays ◽

Photon Counting Detector ◽

Center Position ◽

Beam Center ◽

Beam Parameters

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.

Download Full-text