This papers discusses an effective framework for determining the number and direction of all possible grating lobes in the case of three-dimensional (3D) array antennas. Illustrating examples support the introduced theoretical concepts. The analysis highlights some intrinsic benefits of using 3D architectures, when compared with planar arrays. It also presents incentives for including the discussion of this class of conceptually relevant systems in (under)graduate curricula.

The (computational) complexity involved by beamforming in moving constellations of (nano) satellites is investigated by means of illustrative numerical experiments. While the number of radiators in such three-dimensional (3D) array antennas is not large, evaluating their radiation patterns entails challenging computational intricacies in view of the satellites being in motion and each satellite performing general 3D rotations. As a result, the relevant array radiation patterns become time-dependent, the elementary radiation patterns being themselves time-dependent. The discussed experiments will illustrate the time evolution of the radiation pattern for given individual satellite orbits and rotation laws. At the same time, they will provide a basis for estimating the computational complexity involved by predicting the complete beamforming in future space-bound remote sensing missions using constellations of (nano) satellites.