Enhanced timing of a 113 km O-TWTFT link with complex maximum likelihood estimation process

Optical two-way time-frequency transfer (O-TWTFT), utilizing optical frequency comb carriers and linear optical sampling, effectively enables space-to-ground optical frequency standard comparisons. Previously reported detection sensitivities of O-TWTFTs were typically in the nanoWatt level, necessitating high-power optical frequency combs to compensate for significant losses in high-orbit satellite-to-ground passes. Such hardware-based solutions, while effective, tend to be costly. This paper presents a novel data post-processing algorithm to enhance sensitivity. Unlike previous timing methods, which depend solely on optical phase data and discard intensity information — resulting in elevated errors, especially under low-reception power, our approach employs complex least squares (CLS) estimation in the complex frequency domain. By preserving all intermediate data and avoiding noise from phase unwrapping, it achieves superior sensitivity and accuracy. Experiments over a 113-kilometer free-space link validate the algorithm’s robustness, delivering a detection sensitivity of 0.1 nanoWatts — over tenfold better than prior techniques — despite a 100-decibel link loss, comparable to Earth–Moon optical links.