Dual-shaped-reflector directivity pattern synthesis using the successive projections method

The successive projections method is extended to apply to specifying shapes for the surfaces of both reflectors in a dual-reflector antenna so that its directivity pattern is within specified upper and lower bounds. The extension is enabled by deriving a good approximate formula for the projections. The technique is through studying the ordering, relaxing and weighting of the projections. The technique is used to design a satellite antenna providing a regional coverage on the Earth. The results show that the method can be two orders of magnitude faster than a gradient search, and that the coverage directivity is significantly greater than that obtained by shaping only the main reflector of the dual-reflector system