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

Abstract

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.

Optical Wireless Communications: Illuminating the Path for Cooper's Law

“…At the receiver, the beam energy is divided optimally between the beam tracking and data detection channels to maximize the error performance of the receiver [309]. To reduce the computational complexity of the tracking subsystems further, photon-counting detector arrays-based on the closed-loop data-aided tracking principle-that act as both tracking and symbol detection devices are discussed in [310]- [313]. The data detection performance of detector arrays, under precise pointing, is discussed in [314], [315] where equal gain combining and maximal ratio combining principles are deployed to fuse the outputs of array elements.…”

Optimal Power Allocation Between Beam Tracking and Symbol Detection Channels in a Free-Space Optical Communications Receiver

“…We wrap up the literature review section with the mention of some references on detector array receivers in free-space optical communications. The authors consider detector arrays for joint beam tracking and symbol detection in [31]- [34], whereas the studies [35], [36] consider FSO acquisition algorithms based on detector array receiver. The article [37] consider time synchronization of pulse position modulation signals based on an array of detectors.…”

“…2 which consists of a signal intensity estimation block, a selection block and three photodetectors of different areas. The intensity estimation block operates on pilot symbols to estimate signal intensity with the help of an array of detectors [34]. The intensity estimate is then fed into a selection block that selects the best photodetector to maximize channel capacity for incoming data symbols.…”

Retrofitting FSO Systems in Existing RF Infrastructure: A Non-Zero Sum Game Technology

“…FSO can be further beneficial for the downlink from the energy efficiency standpoint due to the reduced energy consumption [87], [88]. However, more efforts are required to develop advanced pointing, acquisition, and tracking mechanisms (PAT) for FSO systems for near-Earth application [89]- [92]. We note that many satellite and aerial network configurations based on hybrid RF/FSO links have been proposed in the literature, such as the following:…”