Design of shaped-beam antennas through minimax gain optimization

An essential part of realizing a shaped beam by using a multiple-beam antenna is determining the excitation coefficient for each individual port. An algorithm which optimizes the power gain in a minimax sense is described. This criterion, although not as mathematically tractable as least squares, is necessary when the specifications prescribe that the worst case be as good as possible. It will be shown how the basic algorithm is very efficient and how it permits simple modifications to allow the specification of one-sided errors for the pattern, and direct optimization of gain slopes. A design of a C-band shaped-beam satellite antenna provides an example.