The invention relates to an antenna system (1) having a housing (2), in which a printed circuit board is provided, and at least one antenna element (8), the at least one antenna element (8) being arranged inside a cover. A motherboard (11) without an antenna element (8) is preferably arranged inside the housing (2), an antenna circuit board (12) is provided at a distance from the motherboard (11), outside the housing (2), and the at least one antenna element (8) is arranged on the antenna circuit board (12).