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Using a single offset cylindrical parabolic reflector and an improved parallel-plate Luneburg lens, a novel antenna is developed for automotive radar in the mm-wave range. By adding linearly- or circularly-corrugated extensions to the parallel-plate Luneburg lens, a cylindrical wave illuminates the reflector, and hence good performances are achieved. Using GO, the aperture field of the antenna is found and then far-fields of the entire antenna are derived using the aperture field integration method. Design procedures of the entire antenna are presented. For verification of design rules and simulation, a prototype antenna for an adaptive cruise control (ACC) radar at 76.5 GHz is designed and measured. The antenna has properties of a relatively wide scan angle and multiple beams.