TY - JOUR
T1 - Cramér-Rao Bounds for Beam Tracking with Photon Counting Detector Arrays in Free-Space Optical Communications
AU - Bashir, Muhammad Salman
AU - Tsai, Ming Cheng
AU - Alouini, Mohamed Slim
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2021/5/18
Y1 - 2021/5/18
N2 - 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 Cramér-Rao lower bounds on the mean-square error of unbiased estimators of beam position. Furthermore, we have also derived the Cramér-Rao lower bounds of other system parameters such as signal peak intensity, and dark current noise power, on the array. In this sense, we have considered robust estimation of beam position in which none of the parameters are assumed to be known beforehand. Additionally, we have derived the Cramér-Rao lower bounds of beam and noise 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 signal peak and dark current noise intensities are estimated using a method of moments estimator, and the beam center position is estimated with the help of a maximum likelihood estimator.
AB - 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 Cramér-Rao lower bounds on the mean-square error of unbiased estimators of beam position. Furthermore, we have also derived the Cramér-Rao lower bounds of other system parameters such as signal peak intensity, and dark current noise power, on the array. In this sense, we have considered robust estimation of beam position in which none of the parameters are assumed to be known beforehand. Additionally, we have derived the Cramér-Rao lower bounds of beam and noise 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 signal peak and dark current noise intensities are estimated using a method of moments estimator, and the beam center position is estimated with the help of a maximum likelihood estimator.
KW - Angle-of-arrival
KW - beam center position
KW - Cramèr-Rao lower bound
KW - dark current
KW - maximum likelihood estimator
KW - method of moments estimator
KW - photon-counting detector arrays
KW - pulse position modulation
UR - http://www.scopus.com/inward/record.url?scp=85107942229&partnerID=8YFLogxK
U2 - 10.1109/OJCOMS.2021.3078091
DO - 10.1109/OJCOMS.2021.3078091
M3 - Article
AN - SCOPUS:85107942229
VL - 2
SP - 1065
EP - 1081
JO - IEEE Open Journal of the Communications Society
JF - IEEE Open Journal of the Communications Society
SN - 2644-125X
M1 - 9427053
ER -