Synthesis of phased array antennas generating shaped patterns by exploiting phase tapering only is a challenging problem. A phase-only tapering permits maximizing the DC to RF power efficiency and results to be particularly useful in satellite applications with stringent constraints on the available power. Such a synthesis is a highly nonlinear problem most effectively addressed via stochastic optimization techniques. In this paper several basis functions to represent the phase distribution are traded-off and compared, within an invasive weed optimization paradigm.
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 non-linearity 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 non-uniform 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.
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