The Tunka-Radio extension (Tunka-Rex) is a radio detector for air showers in
Siberia. From 2012 to 2014, Tunka-Rex operated exclusively together with its
host experiment, the air-Cherenkov array Tunka-133, which provided trigger,
data acquisition, and an independent air-shower reconstruction. It was shown
that the air-shower energy can be reconstructed by Tunka-Rex with a precision
of 15\% for events with signal in at least 3 antennas, using the radio
amplitude at a distance of 120\,m from the shower axis as an energy estimator.
Using the reconstruction from the host experiment Tunka-133 for the air-shower
geometry (shower core and direction), the energy estimator can in principle
already be obtained with measurements from a single antenna, close to the
reference distance. We present a method for event selection and energy
reconstruction, requiring only one antenna, and achieving a precision of about
20\%. This method increases the effective detector area and lowers thresholds
for zenith angle and energy, resulting in three times more events than in the
standard reconstruction
