In this paper a new method is described for multibeam antennas synthesis where both the amplitude and phase of each radiating element is a design variable. The developed optimization method made possible to solve the synthesis problem and to answer all the constraints imposed by the radiation pattern. Two approaches for visualizing satellite antenna radiation patterns are presented. Gain-level contours drawn over a geographical map gives clearest qualitative information. A three-dimensional (3D) surface plot displays the qualitative shape of the radiation pattern more naturally. The simulations results have shown power, precision and speed of the variational method with respect to the constraints imposed on radiation pattern of the of multibeam antennas network
