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The ground link in the European Data Relay System (DRS) will be established via a single feeder-link antenna assembly forming part of the DRS satellite payload. The antenna will operate in the Ka band and radiate a single high-gain beam to cover several ground stations in Europe. The results of a study carried out to investigate the design of the feeder antenna using the reflector shaping are presented. The basic approach consists of shaping the profile of an offset parabolic such that the gain performance within the two coverage sectors is optimized simultaneously when the reflector is illuminated by a dedicated feed for each coverage. Compared to the conventional multielement-fed parabolic reflector solution, this approach avoids the need for complicated beam forming networks, has a lower mass and, since large aperture feed elements can be used, offers a wider bandwidth potential.