Fast phase-only synthesis of conformal reflectarrays

Phase-only synthesis (POS) techniques represent an important tool for reflectarray design. Indeed, although based on approximate scattering models, for planar antennas, they are numerically effective thanks to the use of fast Fourier transform (FFT) routines. Conformal reflectarrays are becoming of interest as they reduce the frequency dependence of the feed/elements path length. Although synthesis algorithms can be extended from planar to conformal geometries, improving computational efficiency is not trivial. We present a POS, power pattern synthesis technique of conformal, shaped-beam reflectarrays, based on the p-series approach, on non-uniform FFTs, and on fast implementations of the FFT and of matrix-vector and vector-vector multiplications. The approach allows modulating computational burden and accuracy, depending on the needs. The method faces crucial issues concerning the reliability of the solution, by adopting a multi-step strategy. At first, the unknown phase shifts are represented by few degrees of freedom and an efficient and effective global optimisation algorithm is applied. Then, assuming as a starting point the obtained solution, all the reflectarray degrees of freedom are taken into account. The computational performance of the approach and its capability in synthesising shaped-beam patterns are discussed against parabolic and faceted reflectarrays, also considering the coverage of an operative mission.