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This paper describes the design and the optimization performed for the elements of the MWR antenna system, a microwave radiometer embarked on the ENVISAT-1 platform of the European Space Agency. This instrument provides, through the Earth atmosphere analysis, a scientific support to the radar altimeter RA-2 positioned on the same spacecraft. The MWR radiometer antenna system is composed by a parabolic offset reflector antenna called the "measurement antenna" pointed toward the Earth and by a corrugated feed called the "sky horn" pointed toward the cold sky for calibration purposes. The parabola is illuminated by two feedhorns, FH-24 and FH-37, to provide an analysis capability in two frequency bands from 23.6 to 24.0 GHz and from 36.3 to 36.7 GHz and the sky horn supports simultaneously these two bands. An analogous radiometer was embarked on the ERS-1 and ERS-2 satellites and the MWR instrument for the ENVISAT-I platform must be similar to the precedent versions. For this reason the parabolic antenna optic is a fixed and the inherited parameter which can not be changed but must be taken into account for the design and optimization activity. Starting from the electrical requirements that the antenna system must satisfy, a description of the design and optimization activity are given for all the elements and parameters which do not affect the antenna optic but are "degrees of freedom" useful to reach the required electrical performance.