  In this paper we explore the possibility to complement the cosmic ray physics
program of the IceCube observatory with an extended surface array of radio
antennas. The combination of air-shower sampling on the surface and muon
calorimetry underground offers significant scientifc potential: the neutrino
sensitivity above the horizon can be enhanced by vetoing air-showers on the
ground, photon-induced air-showers can be identifed by their small muon
component and the coincident measurement of the particle density on the surface
and the muon component gives useful information on the composition of the
primary flux. All of these analyses are pursued with the existing IceTop array.
However, the IceTop footprint is small compared to the acceptance of the InIce
sensor array, which severely limits the solid angle for coincident
measurements, calling for an extended surface air-shower detector. As
demonstrated by the LOPES experiment, measuring air-showers through their
geosynchrotron emission has become a viable and cost-efficient method. The
science case for the RASTA project - a dedicated radio array seeking to exploit
this method at the South Pole - is presented.
