A comparison of geometrically bound random arrays in euclidean space

Geometrically bound linear, planar, and volumetric random array topologies are analyzed through a probabilistic approach to study the topological impact on beam pattern. The analysis assumes randomly distributed elements with uniform distribution to evaluate the statistically averaged beam pattern for linear, planar (square and circular), and volumetric (cubical, cylindrical, and spherical) geometries used to bound the array. Results show that many simple geometries share analytical similarities due to symmetry. Numerical results of the average beam pattern show good agreement to analytical solution and are shown for comparison.