  Tunka-Rex is a radio detector for cosmic-ray air showers in Siberia,
triggered by Tunka-133, a co-located air-Cherenkov detector. The main goal of
Tunka-Rex is the cross-calibration of the two detectors by measuring the
air-Cherenkov light and the radio signal emitted by the same air showers. This
way we can explore the precision of the radio-detection technique, especially
for the reconstruction of the primary energy and the depth of the shower
maximum. The latter is sensitive to the mass of the primary cosmic-ray
particles. In this paper we describe the detector setup and explain how
electronics and antennas have been calibrated. The analysis of data of the
first season proves the detection of cosmic-ray air showers and therefore, the
functionality of the detector. We confirm the expected dependence of the
detection threshold on the geomagnetic angle and the correlation between the
energy of the primary cosmic-ray particle and the radio amplitude. Furthermore,
we compare reconstructed amplitudes of radio pulses with predictions from
CoREAS simulations, finding agreement within the uncertainties.
