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 cosmicray 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.

The EAS Cherenkov light array Tunka-133, with $ 3 km 2 geometric area, is taking data since 2009. The array permits a detailed study of cosmic ray energy spectrum and mass composition in the PeV energy range. After a short description of the methods of EAS parameter reconstruction, we present the allparticle energy spectrum and results of studying CR composition, based on 3 seasons of array operation. In the last part of the paper, we discuss possible interpretations of the obtained results.

We reconstructed the energy and the position of the shower maximum of air showers with energies E 100 PeV applying a method using radio measurements performed with Tunka-Rex. An event-to-event comparison to air-Cherenkov measurements of the same air showers with the Tunka-133 photomultiplier array confirms that the radio reconstruction works reliably. The Tunka-Rex reconstruction methods and absolute scales have been tuned on CoREAS simulations and yield energy and X max values consistent with the Tunka-133 measurements. The results of two independent measurement seasons agree within statistical uncertainties, which gives additional confidence in the radio reconstruction. The energy precision of Tunka-Rex is comparable to the Tunka-133 precision of 15 %, and exhibits a 20 % uncertainty on the absolute scale dominated by the amplitude calibration of the antennas. For X max , this is the first direct experimental correlation of radio measurements with a different, established method. At the moment, the X max resolution of Tunka-Rex is approximately 40 g/cm 2 . This resolution can probably be improved by deploying additional antennas and by further development of the reconstruction methods, since the present analysis does not yet reveal any principle limitations.