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Sparse digital antenna arrays constitute a promising detection technique forfuture large-scale cosmic-ray observatories. It has recently been shown thatthis kind of instrumentation can provide a resolution of the energy and of theshower maximum on the level of other cosmic-ray detection methods. Due to thedominant geomagnetic nature of the air-shower radio emission in the traditionalfrequency band of 30 to 80 MHz, the amplitude and polarization of the radiosignal strongly depend on the azimuth and zenith angle of the arrivaldirection. Thus, the estimation of the efficiency and subsequently of theaperture of an antenna array is more complex than for particle orCherenkov-light detectors. We have built a new efficiency model based onutilizing a lateral distribution function as a shower model, and aprobabilistic treatment of the detection process. The model is compared to thedata measured by the Tunka Radio Extension (Tunka-Rex), a digital antenna arraywith an area of about 1 km$^2$ located in Siberia at the Tunka AdvancedInstrument for Cosmic rays and Gamma Ray Astronomy (TAIGA). Tunka-Rex detectsradio emission of air showers using trigger from air-Cherenkov and particledetectors. The present study is an essential step towards the measurement ofthe cosmic-ray flux with Tunka-Rex, and is important for radio measurements ofair showers in general.

Modeling the Aperture of Radio Instruments for Air-Shower Detection