Investigation of beamforming patterns from volumetrically distributed phased arrays

This work presents distributed beamforming using three dimensional randomly distributed volumetric arrays. This work examines a statistical ensemble (mean-valued) of average beampattern behavior for canonical and non-canonical volumetrically bound distributed (random) antenna arrays. Cubical, cylindrical, and spherical topologies of isotropic elements are analyzed to show beamforming and scanning from zenith to meridian for canonical topologies. In addition, small amounts of work have previously been investigated and therefore this work helps to enlighten with illustrations of the beampattern phenomena of a select few non-conically bound distributed and volumetric structures. To validate the distributed array pattern behavior, the manifold is composed of one million isotropic radiators densely populated amongst geometrical bounds to examine characteristic pattern behavior. This provides faithful convergence of numerical beampatterns to their expected (mean) patterns. Last of all, results show an increasing complexity of pattern behavior for use in many spatial advancements in distributed beamforming.