Deterministic and stochastic methods for the synthesis of large-scale antenna arrays

Given a large antenna array of arbitrary geometry, the problem of synthesizing S desired patterns is considered, with two requirements: (a) each pattern can be transformed into any of the others by phase-only control, that is, the excitation amplitude applied to each array element holds constant during the reconfiguration process, although it can be different from the other excitation amplitudes; (b) the dynamic range ratio of the excitation amplitudes must be minimized, or reduced below a prescribed threshold. To this aim, we first propose the use of two deterministic methods: the first one minimizes a cost function, while the second one is based on an intersection approach and exploits the method of projections. A third approach is also considered, which minimizes a fitness function by a genetic algorithm. Numerical results of the three methods are mutually compared.