Pattern synthesis for antennas with multiple primary beams by minimax optimisation

Increasingly stringent requirements are evolving for selective illumination of irregularly shaped geographical areas by communication-satellite antennas. The desirability of minimising spillover illumination near borders, and the technical requirement to conserve transmitter power, constrains the shape of the main beam of the antenna and the sidelobe levels. We describe a minimax optimisation algorithm for designing the required shaped-beam antennas. A 1-dimensional example is given to demonstrate the features of the method.