A Study Of Aperiodic (Random) Arrays of Various Geometries

The use of wireless communication techniques and network centric topologies for portable communication networks and platforms makes it important to investigate new distributed beamforming techniques. Platforms such as micro air vehicles (MAVs), unattended ground sensors (UGSs), and unpiloted aerial vehicles (UAVs) can all benefit from advances in this area by enabling advantages in stealth, enhanced survivability, and maximum maneuverability. Collaborative beamforming is an example of a new technique to utilize these systems which uses a randomly distributed antenna array with a fitting phase coefficient for the elements. In this example, the radiated signal power of each element is coherently added in the far-field region of a specified target direction with net destructive interference occurring in all other regions to suppress sidelobe behavior.

A wide variety of topologies can be used to confine geometrically these mobile random arrays for analysis. The distribution function for these topologies must be able to generalize the randomness within the geometry. Gaussian and Uniform distributions are investigated in this analysis, since they provide a way to calculate the statistically averaged beampattern for linear, planar (square and circular), and volumetric (cubical, cylindrical, and spherical) geometries. They are also of practical interest since the impact of array topology on the beampattern can typically be described in closed form. A rigorous analysis is presented first for disc-shaped topologies to motivate the discussion on random array properties and provide several new insights into their behavior. The analyses of volumetric geometries which are of interest to this work are drawn from this planar topology to provide a tractable and coherent discussion on the properties of more complex geometries. This analysis considers Normal and Gaussian distributed array element populations to derive the average beampattern, sidelobe behavior, beamwidth, and directivity. The beampattern is also examined in a similar manor for circular and spherical arrays with a truncated Gaussian distribution. A summary of the random array analysis and its results concludes this thesis.