Uniform spherical distributions for adaptive array applications

This study investigates optimal three dimensional antennas for adaptive applications. The choice of the antenna element distribution on the spherical surface is governed by the desire to maintain a nearby constant pattern. Spherical arrays provide wide scan coverage with low grating lobe levels. We calculate the uniform distribution of a set of antennas on a sphere. Based on formulas of the spherical trigonometry, we show all the possible exact uniform distributions. It is astonishing, that only five possible solutions can be found. In this paper, the co-ordinates and the figures of these regular polyhedrons are shown. Because the number of possible uniform spherical distributions is limited, the number of elements that can be placed uniformly without approximation on a spherical surface is also limited to 20