Investigation of Randomly Populated Cylindrical, Spherical, and Cubical Arrays for Application in Space, Aerial, and Underwater Collaborative Beamforming

This work investigates and analyzes collaborative beamforming for a Swarm-enabled distributed sensing project. It investigates the use of a three-dimensional, randomly populated, and uniformly-distributed array in three configurations: spherical, cylindrical, and cubical. These topologies uniquely act like a practical bound to contain the elements in swarm-type applications. In addition, these topologies provide mathematical simplicity toward understanding the fundamental research problem of both surface and underwater swarm-based UUV sensor networks, and their constraints to implementing a physical system in a volumetric setting. Therefore, statistical, ensemble, mean-valued average beampatterns scanned at the meridian elevation plane are analyzed in closed form using a large population of one million elements densely populated amongst geometrical bounds. This large density profile applies the law of large numbers in which numerical beampatterns converge to their expected (mean) patterns. Faithful agreement of the solution is shown to validate the distributed array pattern behavior. Finally, additional simulations are provided in this work using a cylindrical manifold that comprises ten, fifty, and one hundred isotropic radiators to determine the feasibility of a small element population.