The MIMOSA radar is a spaceborne unfocused nadir looking synthetic aperture P-Band radar designed to penetrate the Earth superficial layers and proposed in the frame of the Earth Explorer Opportunity Missions (ESA). This paper reviews all the mission aspects. The scientific objectives are presented: 3D mapping of Antarctic ice sheet, biomass monitoring, and prospective objectives. The instrument concept is developed. The physics of the measurement is analyzed to show that the expected signal is a mixture of deep echoes-and surface clutter. A clutter rejection processing is proposed and some results of signal simulation are given for typical ice surfaces. A preliminary instrument design is described, based on the physics analysis and simulations results.