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Using a single offset cylindrical parabolic reflector and a parallel-plate Luneburg lens, a novel high-gain and high-efficiency antenna is developed for automotive radar at mm-wave frequencies. Particularly, a pair of small corrugated extensions is added to the lens for a cylindrical wave. Thus, by feeding a cylindrical wave to the reflector, especially the performance in elevation is enhanced, keeping the complete antenna compact. For verification, a prototype antenna for an adaptive cruise control radar at 76.5 GHz is designed and measured. The theoretical results are verified with good agreement.