Power synthesis of shaped beam antenna patterns

The authors present a variational method for the synthesis of planar array antennas with separable variables. The element pattern is taken into account to optimize both the amplitude and the phase of each radiating element or subarray. In the power synthesis, the relaxation of the arbitrary hypothesis on the pattern phase leads to an improvement of the synthesized pattern. A new minimization criterion is obtained for the function relating the desired pattern to the obtained pattern. This makes it possible to easily take into account the constraints on the pattern. The specifications are given by a minimum and a maximum gain value at stations on the earth and are interpolated on the array period. The analytical development of the function considerably improves its computational efficiency. A synthesis example is presented.<>