A full polarimetric antenna system on board the ExoMars rover is part of the Experiment “Water Ice and Subsurface Deposit Observations on Mars” (WISDOM). The WISDOM-Experiment is a Ground Penetrating Radar (GPR) selected to be part of the Pasteur payload aboard the rover of the ExoMars mission. The Pasteur Panoramic Instruments (wide angle camera PANCAM, infrared spectrometer MIMA and WISDOM) will perform large-scale scientific investigations at the sites the Rover will visit. Among these instruments, WISDOM is the only that can provide a view of the subsurface structure prior to drilling. WISDOM has been designed to characterize the shallow subsurface structure of Mars. WISDOM will for the first time give access to the geological structure, electromagnetic nature, and, possibly, hydrological state of the shallow subsurface by retrieving the layering and properties of the buried reflectors. It will address important scientific questions regarding the planet's present state and past evolution. The measured data will also be used to determine the most promising locations to obtain underground samples with the drilling system mounted on board the rover. The instrument's objective is to get high-resolution measurements down to 2 m depth in the Martian crust. The radar is a gated step frequency system covering a frequency range from 500 MHz to 3 GHz. The radar is fully polarimetric and makes use of an ultra wideband antenna system based on Vivaldi antenna elements. The paper describes requirements, design and realization of the WISDOM antenna system accommodated on the ExoMars rover. Simulated and measured antenna performance is compared in this paper. Test measurements performed in permafrost regions on earth will be shown in the presentation.