Parameters of a spherical random antenna array

The shape of the beam of a spherical random antenna array - regarded as the simplest volume-array case for space applications - is discussed. A general expression for the array output, as related to a random receiving antenna array consisting of N antenna elements uniformly distributed over a sphere of given radius, is presented and examined. It is assumed that the sensitivity characteristic of each element is uniform. The discussion is not limited to the far-field case only, it is valid also for smaller focusing distances. Attention is given to deriving suitable formulas for the array bandwidth, beamwidth, and hyperfocal distance, which are considered important working parameters of a given array.