The paper discusses various aspects of the system design for a satellite in a highly elliptical inclined orbit, and presents a number of antenna design options for the proposed Archimedes mission. A satellite constellation was studied for the provision of multi media communication services in the L and S Band for northern latitudes. The inclined elliptical orbit would allow coverage of Europe, America, and East Asia. Using Canada and North America as the baseline coverage area, this paper addresses system considerations such as the satellite configuration and pointing, beam configuration, and requirements for antennas. A trade-off is performed among several antenna candidates including a direct radiating array, a focal-fed reflector, and a single reflector imaging system. Antenna geometry, performance, and beam forming methods are described. The impact of the designs on the antenna deployment is discussed. more...