A numerical method in power synthesis of aperture antennas

The synthesis of an aperture field radiating a prescribed radiation pattern has ben widely considered in the literature from both a theoretical and a numerical point of view. As known, a complete statement of the problem is strictly related to the choice of the functional of the radiated field to be minimized by the synthesis procedure . This functional allows the restriction of the set of all the possible solutions (which in general, at the expense of the superdirectivity gain, could reproduce as closely as desired.any prescribed pattern) to an appropriate subset. In this way, accounting for the physical realizability of the pattern,the synthesis problem, which is intrinsically an ill-posed problem, becomes a.stable one. When the functional to be minimized involves both amplitude and phase of the radiated field, the so called "field synthesis" problem is obtained. When only the amplitude of he radiated field is prescribed, the "power synthesis" problem is referred to. It is to be noted that, as shown by Voytovich €11, the freedom on the phase of the reconstructed pattern. in the power synthesis problem, leads to an improvement of the precision of the reconstruction of the prescribed amplitude. In the following the power synthesis problem is then considered.