An iterative least-squares synthesis technique is presented for the optimization of the element excitation in conformal array antennas. This method allows the designer to have predefined goals for the shaped radiation pattern over a selected frequency band and for the polarization properties of the array. Linear or circular polarization can be used in the synthesis. Different kinds of synthesis goals can be set, whereby the copolarization or cross-polarization properties of the array are weighted or a narrowband or wideband design is sought. The amplitudes of the element excitations can be fixed. Several synthesis examples are presented for an array on a sphere with circular polarized elements. Broad-band and low cross-polarization designs are included.