  Tunka-Rex (Tunka Radio Extension) is an antenna array for cosmic-ray
detection located in Siberia. Previous studies of cosmic rays with Tunka-Rex
have shown high precision in determining the energy of the primary particle and
the possibility to reconstruct the depth of the shower maximum. The next step
is the reconstruction of the mass composition and the energy spectrum of cosmic
rays. One of the main problems appearing within this task is to estimate the
detection efficiency of the instrument, and the exposure of the observations.
The detection efficiency depends on properties of the primary cosmic rays, such
as energy and arrival direction, as well as on many parameters of the
instrument: density of the array, efficiency of the receiving antennas,
signal-detection threshold, data-acquisition acceptance, and trigger
properties. More than that, the configuration of detector changes with time.
During the measurements some parts of the detector can provide corrupted data
or sometimes do not operate. All these features should be taken into account
for an estimation of the detection efficiency. For each energy and arrival
direction we estimate the detection probability and effective area of the
instrument. To estimate the detection probability of a shower we use a simple
Monte Carlo model, which predicts the size of the footprint of the radio
emission as function of the primary energy and arrival direction (taking into
account the geometry of Earth's magnetic field). Combining these approaches we
calculate the event statistics and exposure for each run. This is the first
accurate study of the exposure for irregular large-scale radio arrays taking
into account most important features of detection, which will be used for the
measurement of primary cosmic-ray spectra with Tunka-Rex.
