The present invention relates to an antenna array adapted to radiate or receive electromagnetic waves of one or two polarizations with very low cross polarization and low side lobes. An antenna array comprising many antenna elements, e.g. more than ten antenna elements, is provided in which formation of grating lobes are inhibited in selected directions of the radiation and cross polarization within the main lobe is suppressed at least 30 dB below the main lobe peak value. According to a preferred embodiment of the invention, the antenna elements of the antenna array comprise probe-fed patches, preferably rectangular patches, more preferred square patches. Further, it is preferred that the feed probes are positioned at the axis of symmetry of the square or rectangular patches.