3GPP-inspired Stochastic Geometry-based Mobility Model for a Drone Cellular Network

This paper deals with the stochastic geometry-based characterization of the time-varying performance of a drone cellular network in which the initial locations of drone base stations (DBSs) are modeled as a Poisson point process (PPP) and each DBS is assumed to move on a straight line in a random direction. This drone placement and trajectory model closely emulates the one used by the third generation partnership project (3GPP) for drone-related studies. Assuming the nearest neighbor association policy for a typical user equipment (UE) on the ground, we consider two models for the mobility of the serving DBS: (i) UE independent model, and (ii) UE dependent model. Using displacement theorem from stochastic geometry, we characterize the time-varying interference field as seen by the typical UE, using which we derive the time-varying coverage probability and data rate at the typical UE. We also compare our model with more sophisticated mobility models where the DBSs may move in nonlinear trajectories and demonstrate that the coverage probability and rate estimated by our model act as lower bounds to these more general models. To the best of our knowledge, this is the first work to perform a rigorous analysis of the 3GPP-inspired drone mobility model and establish connection between this model and the more general non-linear mobility models

Tight Lower Bounds on the Contact Distance Distribution in Poisson Hole Process

In this letter, we derive new lower bounds on the cumulative distribution function (CDF) of the contact distance in the Poisson Hole Process (PHP) for two cases: (i) reference point is selected uniformly at random from $\mathbb{R}^2$ independently of the PHP, and (ii) reference point is located at the center of a hole selected uniformly at random from the PHP. While one can derive upper bounds on the CDF of contact distance by simply ignoring the effect of holes, deriving lower bounds is known to be relatively more challenging. As a part of our proof, we introduce a tractable way of bounding the effect of all the holes in a PHP, which can be used to study other properties of a PHP as well.Comment: To appear in IEEE Wireless Communications Letter