A device with a substrate lens antenna uses a lens shaped dielectric body located on top of a planar feed antenna. A leaky wave antenna structure is used as feed antenna. The leaky wave antenna structure has a feed input and a first and second wave propagation branch extending from the feed input. The lens shaped dielectric body has a plane surface containing a focal point of the lens shaped dielectric body, the plane surface located adjacent the first plane, with the focal point adjacent the position of the feed input. Preferably the lens shaped dielectric body is spaced from the leaky wave structure at a sufficient distance to remove most of the propagation speed reduction effect of the dielectric on wave propagation along the leaky wave antenna. This helps to suppress undesirable side-lobes.