Trajectory Processes that Preserve Uniformity: A Stochastic Geometry Perspective

Stochastic geometry has been successfully applied for performance analysis of wireless networks. Performance of some emerging applications such as unmanned aircraft systems (UAS) relies heavily on unique mobility characteristics that are sometimes not fully captured by the current stochastic geometry results. This paper focuses on this issue by introducing families of trajectory processes that preserve uniformity within a cell in the framework of aerial base stations (ABS) networks. This means if the ABS move according to such trajectory processes, they will be distributed according to a binary point process (BPP) at any time snapshot. We propose two families of such processes, namely spiral and oval processes, and analytically prove our claim. We then focus on 2 special cases of such processes, namely, radial and ring processes and demonstrate their attractive properties as far as implementation is concerned.