  The recent progress in the radio detection technique for air showers paves
the path to future cosmic-ray radio detectors. Digital radio arrays allow for a
measurement of the air-shower energy and depth of its maximum with a resolution
comparable to those of the leading optical detection methods. One of the
remaining challenges regarding cosmic-ray radio instrumentation is an accurate
estimation of their efficiency and aperture. We present a probabilistic model
to address this challenge. We use the model to estimate the efficiency and
aperture of the Tunka-Rex radio array. The basis of the model is a
parametrization of the radio footprint and a probabilistic treatment of the
detection process on both the antenna and array levels. In this way, we can
estimate the detection efficiency for air showers as function of their arrival
direction, energy, and impact point on the ground. In addition, the transparent
internal relationships between the different stages of the air-shower detection
process in our probabilistic approach enable to estimate the uncertainty of the
efficiency and, consequently, of the aperture of radio arrays. The details of
the model will be presented in the contribution.
