Single surface phaseless characterization of antennas via hierarchically-ordered optimizations

A new approach for determining the complex scalar field radiated by a finite-dimensional source starting from its modulus is proposed and assessed. First, by introducing a suitable relaxation, we show that the original problem can be conveniently tackled in terms of a finite number of different convex programming problems. Then, an effective procedure for dealing with a small number of hierarchically ordered optimizations is introduced and discussed. Numerical experiments, including consideration of an actual radiating source and of noisy data, are provided with reference to the canonical case of far-field data and array antennas.