Time Synchronization in Photon-Limited Deep Space Optical Communications

Abstract

Random jitter or offset between the transmitter/receiver clocks is an important parameter that has to be accurately estimated for optimal detection of Pulse Position Modulation (PPM) symbols for high data-rate optical communications. This parameter in general is modeled as an unknown random quantity that depends on the clock drift between the transmitter/receiver clocks, and the random motion between the transmitter and receiver stations. In this paper, we have modeled the time jitter for two scenarios-phase modulation jitter and frequency modulation jitter. The phase modulation jitter is modeled as a Gaussian random variable which is estimated with the help of a maximum a posteriori probability (MAP) estimator. The frequency modulation jitter is characterized as a random walk, and this leads to the jitter modeling as a state space variable in the context of a dynamical system. Since the observations are the photon counts in each slot of a PPM symbol (for both MAP estimation and tracking), the resulting dynamical model is highly nonlinear, and therefore, particle filters are employed for tracking the frequency modulation jitter. We evaluate the performance of the maximum a posteriori estimators and particle filters both in terms of the relative mean-square error and probability of error, and for various signal-to-noise ratios. Furthermore, this evaluation is also carried out for low photon rates that are typical for deep space communications. We conclude that with MAP estimation and particle filters that estimate/track the time offset, we achieve a significant performance gain in terms of probability of error as compared to systems that do not have a time synchronization system in place.

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

“…Furthermore, the authors in [8] analyze the acquisition performance of an FSO system that employs an array of detectors at the receiver, and they demonstrated that the acquisition performance in terms of mean acquisition time can be significantly enhanced by employing a large number of detectors in the receiver array. In the same vein, the study in [9] considers time synchronization schemes based on an array of detectors, and this study showed that the synchronization performance improves significantly by using an array of detectors at the receiver.…”

A Single Detector Versus an Array of Detectors Receiver in Free-Space Optical Communications: A Performance Comparison

“…The authors in [7] analyze the probability of error in detail for the joint beam position tracking and symbol detection system, and show that the probability of error of a maximal ratio combining scheme is minimized if the beam is tracked accurately enough in time. The authors in [8] consider time synchronization schemes for a detector array receiver in a photon-counting channel in deep space optical communications. The authors in [9] have considered the communications performance for an array of detectors and discussed the effects of the number of detectors and the beam parameter information on the performance.…”

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

“…Furthermore, the authors in [10] analyze the acquisition performance of an FSO system that employs an array of detectors at the receiver. Finally, the authors in [11] consider time synchronization schemes based on an array of detectors.…”