Precision of spacecraft Doppler tracking at low signal-to-noise ratios

The signal-to-noise ratio received at Earth is typically larger than 10 dB-Hz for radio tracking of a spacecraft in deep space, allowing a phase-locked loop to execute reliable carrier tracking. Recently, missions have been proposed to utilize low-gain antennas for Doppler tracking where the signal-to-noise ratio may be at the single-digit (dB-Hz) level. In this work, we discuss spacecraft Doppler tracking at these low signal-to-noise ratios through an analysis of thermal noise on the radio link, results from ground testing with the Deep Space Network, and demonstrations with an active spacecraft. We show that by utilizing an open-loop receiver to capture the carrier signal and by applying post-processing techniques, radio data with the signal-to-noise ratio as low as 4 dB-Hz can be used to derive Doppler data with precision sufficient for tracking a spacecraft in deep space.