In a communications network served by a high altitude platform, the antenna beams illuminating each cell require minimized sidelobe powers. Asymmetric beams are advantageous so that cell footprints remain circular. At millimeter wavelengths a lens antenna can have the desired properties. We have chosen a 6 km diameter cell at 32 degrees elevation angle and shown how the required beam asymmetry can be implemented using an optimized polynomial for describing the lens profile. The measured average sidelobe level is below -42 dB
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