Maximum-Likelihood Estimation for Frequency-Modulated Continuous-Wave Laser Ranging Using Photon-Counting Detectors.

摘要

We analyze the minimum achievable mean-square error in frequency- modulated continuous-wave (FMCW) range estimation of a single stationary target when photon counting detectors are employed. Starting from the probability density function for the photon arrival times, we derive the Cramer-Rao bound (CRB) and highlight three important regimes: the dark-noise-dominated regime wherein the CRB improves quadratically with the mean received photon number, the shot-noise-dominated regime (i.e., the standard quantum limit) in which the improvement is linear, and the dead-time-dominated regime wherein the CRB is constant. We show that if both signal and reference photons cost equal, the shot-noise-limited CRB is minimized when the local field strength is equal to that of the target-return field, and the average frequency-modulation energy determines the performance. Simulation of the maximum-likelihood (ML) estimator shows that its performance approaches the standard quantum limit only when the mean received photons are between two thresholds. We provide analytic approximations to these thresholds for linear frequency modulation. Finally, we report on a proof-of-concept experiment in which ML estimation outperforms conventional beat-frequency estimation.