We describe a CubeSat constellation integrated with ultrawideband (UWB) multiple input and multiple output (MIMO) radars operating over the frequency range of 50–600 MHz for remote sensing of large ice sheets on the Earth, as well as distant planets and moons. It can be used for measurements of ice thickness and basal conditions of Antarctica and Greenland ice sheets, the mapping of lunar lava tubes, and sub-surface detection/characterization of volatiles on Mars. In this paper we provide a short discussion of the science requirements and conceptual design of a constellation of CubeSats with UWB MIMO radars for sounding ice and mapping of lava tubes.