Coherent fiber links operated for years: effect of missing data

Abstract

Aiming at delivering a highly available service, the French national optical fiber link network is run mostly unmanned and automatically, with the help of a global supervision. However, at a year scale, missing data are seemingly unavoidable. Here, we present a first study of the uncertainty of coherent fiber links with missing data. We present the tools to assess statistical properties for processes which are not strictly stationary, and a simulation of optical fiber links depending only on a handful of parameters. We show how missing data affects the phase-coherent optical fiber links, and how to mitigate the issue with a fill-in procedure that preserves the statistical properties. We apply the method for a 5 years-long data set of a 1410 km long fiber link. Second, we apply the method to the case of optical clock comparisons, where the downtimes of the optical clocks degrade the coherence of the links. We show that our methodology of processing the missing data is robust and converges to consistent mean values, even with very low uptimes. We present an offset and uncertainty contribution from the French fiber network of 2.4 (9.0) × 10−20, that is an improvement by a factor 5 as compared to a processing without taking the effect of missing data into account.