Instruments and Methods for the Radio Detection of High Energy Cosmic RaysCosmic rays at energies above 10 15 eV cannot be measured directly due to the low flux. Instead, the properties of the primary cosmic ray particles (arrival direction, energy, mass) have to be reconstructed from measurements of secondary particles forming an air shower. For this, digital radio antenna arrays, like LOPES at the Karlsruhe Institute of Technology (KIT), are a relatively new instrument. The radio emission mainly originates from the deflection of secondary air shower electrons and positrons in the Earth's magnetic field. The radio technique aims at achieving a similar quality in the reconstruction of air shower parameters as the established Cherenkov or fluorescence light detection methods, which in contrast to the radio technique are limited to dark, moonless nights.The present studies aim to advance the air shower radio detection in technological aspects and analysis methods. The developments are mainly applied to LOPES, but also provide a useful set of tools, which will soon be applied on the analysis of first AERA measurements. AERA is a next generation digital radio array at the Pierre Auger Observatory in Argentina. Moreover, this thesis reflects the recent progress in the understanding of the radio emission by air showers. The main results of the studies are:• A new method for time calibration with a reference beacon has been developed.It allows a time resolution of ∼ 1 ns even with large antenna arrays. This is necessary for digital radio interferometry which improves the signal-to-noise ratio and the reconstruction accuracy of the primary particle properties. This method is essential for the measurement of cosmic rays with LOPES, and is going to be applied at AERA.• A per-event comparison of lateral distributions measured with LOPES and REAS3 simulations reflects a significantly improved understanding of the radio emission mechanisms. For the first time a Monte Carlo simulation of the radio emission by air showers can in average reproduce measured data. A detailed investigation of systematic effects was performed to accurately reconstruct LOPES lateral distributions. In particular, a method has been developed to appropriately treat the influence of radio noise on measured lateral distributions.• It is shown that a conical radio wavefront fits LOPES measurements and REAS3 simulations better than a spherical wavefront, which up to now has been assumed for LOPES beamforming analyses. Furthermore, the atmospheric depth of the shower maximum X max can be reconstructed by determining the opening angle of the conical wavefront. However, due to the small lateral extension of LOPES of about 200 m and the high radio background at KIT, the measurement uncertainty (∆X max ≈ 200 g/cm 2 ) is too large for a per-event reconstruction of the primary mass. This will improve at AERA, but could not be examined in detail because of a delay in the construction. • Eine neue Methode zur Zeitkalibration mit einen Rerefenzsender (Beaco...