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.

a b s t r a c tA new EAS Cherenkov light array, Tunka-133, with $ 1 km 2 geometrical area has been installed at the Tunka Valley (50 km from Lake Baikal) in 2009. The array permits a detailed study of cosmic ray energy spectrum and mass composition in the energy range 10 16-10 18 eV with a uniform method. We describe the array construction, DAQ and methods of the array calibration. The method of energy reconstruction and absolute calibration of measurements are discussed. The analysis of spatial and time structure of EAS Cherenkov light allows to estimate the depth of the EAS maximum X max .The results on the all particles energy spectrum and the mean depth of the EAS maximum X max vs. primary energy derived from the data of two winter seasons (2009)(2010)(2011) are presented. Preliminary results of joint operation of the Cherenkov array with antennas for the detection of EAS radio signals are shown. Plans for future upgrades -deployment of remote clusters, radioantennas and a scintillator detector network and a prototype of the HiSCORE gamma-telescope -are discussed.

We present an improved method for the precise reconstruction of cosmic-ray air showers above 10 17 eV with sparse radio arrays. The method is based on the comparison of measured pulses to predictions for radio pulse shapes by CoREAS simulations. We applied our method to the data of Tunka-Rex, a 1 km 2 radio array in Siberia operating in the frequency band of 30-80 MHz. Tunka-Rex is triggered by the air-Cherenkov detector Tunka-133 and by scintillators (Tunka-Grande). The instrument collects air-shower data since 2012. The present paper describes an updated data analysis of Tunka-Rex and details of the new method applied. After quality cuts, when Tunka-Rex reaches its full efficiency, the energy resolution of about 10% given by the new method has reached the limit of systematic uncertainties due to the calibration uncertainty and shower-to-shower fluctuations. At the same time the shower maximum reconstruction has improved compared to the previous method based on the slope of the lateral distribution and reaches a precision of better than 35 g/cm 2 . We also define conditions of the measurements at which the shower maximum resolution of Tunka-Rex reaches a value of 25 g/cm 2 and becomes competitive to optical detectors. To check and validate our reconstruction and efficiency cuts we compare individual events to the reconstruction of Tunka-133. Furthermore, we compare the mean of the shower maximum as a function of primary energy to the measurements of other experiments.PACS numbers: 96.50.sd, 95.55.Jz, 07.50.Qx,