Phase-Only Synthesis for Large Planar Arrays via Zernike Polynomials and Invasive Weed Optimization

A synthesis method for the design of large planar array antennas with phase-only control is here presented. The synthesis is based on the use of Zernike polynomials, as global basis function for the phase, to reduce the number of optimization variables with respect to the number of elements of the array. Invasive weed optimization (IWO) is applied to polynomial coefficients' optimization to circumvent nonlinearity and local trapping issues typical of phase-only problems. The periodicity of the array factor is exploited to reduce the optimization to a Voronoi cell of the grating-lobes' lattice and nonuniform meshing is introduced to best adapt the control stations to the beam shape requirements. The technique is applied to the design of shaped beams for continental coverage from geostationary satellites.