Free-Space Optical Communications With Detector Arrays: A Mathematical Analysis

Bashir, Muhammad Salman

doi:10.1109/taes.2019.2944574

“…The authors in [8] inspect the relationship between the probability of error and the estimation of beam position on the detector array, and using an argument based on Chernoff bounds, they show that precise estimation of beam center on the array is necessary in order to minimize the probability of error. Additionally, the author in [9] presents a mathematical argument to show that the probability of error decreases monotonically as the number of detectors in the array is increased. Furthermore, the authors in [10] analyze the acquisition performance of an FSO system that employs an array of detectors at the receiver.…”

Section: L R C /O T P a Background Literature Reviewmentioning

confidence: 99%

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

Bashir¹,

Tsai²,

Alouini³

2020

Preprint

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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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“…The authors in [8] inspect the relationship between the probability of error and the estimation of beam position on the detector array, and using an argument based on Chernoff bounds, they show that precise estimation of beam center on the array is necessary in order to minimize the probability of error. Additionally, the author in [9] presents a mathematical argument to show that the probability of error decreases monotonically as the number of detectors in the array is increased. Furthermore, the authors in [10] analyze the acquisition performance of an FSO system that employs an array of detectors at the 1 Typically, a quadrant photodetector is employed in the tracking assembly in order to track the beam position.…”

Section: Literature Review and Contributions/organization Of Thismentioning

confidence: 99%

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

Bashir¹,

Tsai²,

Alouini³

2020

Preprint

Self Cite

0

View full text Add to dashboard Cite

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. <br><br>

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“…If the intensity profile of the beam is known (or approximately known) at the receiver, an array of smaller detectors is more useful in terms of minimizing the probability of error as compared to one large detector which has the same size as the entire array [16]. We can think of Fig.…”

Section: B Communications With An Array Of Detectorsmentioning

confidence: 99%

“…where the probability of failure p is defined in (16). Moreover, in terms of the probability density…”

Section: F Complementary Distribution Function Of T Umentioning

confidence: 99%

“…Integrated Circuit (ROIC) design, especially for significantly faster data-rates. Furthermore, for a large number of elements in the array, custom microlens arrays are required for increased optical coupling in order to compensate for the reduction in the optical fill factors [16]. Finally, the storage complexity also goes up as a factor of N 2 (we need to store N 2 photon count values in order to compute the sufficient statistic for the evaluation of (7)).…”

Section: A B C Amentioning

confidence: 99%

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Signal Acquisition with Photon-Counting Detector Arrays in Free-Space Optical Communications

Bashir¹,

Alouini²

2019

Preprint

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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. <br>

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Free-Space Optical Communications With Detector Arrays: A Mathematical Analysis

Cited by 30 publications

References 10 publications

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

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

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

Signal Acquisition with Photon-Counting Detector Arrays in Free-Space Optical Communications

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