Downlink Coverage Analysis for a Finite 3D Wireless Network of Unmanned Aerial Vehicles

TL;DR

This paper analyzes the downlink coverage probability in a finite 3D UAV network modeled as a binomial point process, deriving exact and approximate expressions considering Nakagami-m fading and LOS scenarios.

Contribution

It provides a novel exact expression for coverage probability in finite UAV networks and introduces an approximation method for LOS-dominant conditions.

Findings

Coverage probability varies with UAV height and receiver location.

Derived bounds for coverage probability using Berry-Esseen theorem.

Approximate coverage probability effectively captures dominant interferer effects.

Abstract

In this paper, we consider a finite network of unmanned aerial vehicles (UAVs) serving a given region. Modeling this network as a uniform binomial point process (BPP), we derive the downlink coverage probability of a reference receiver located at an arbitrary position on the ground assuming Nakagami-$m$ fading for all wireless links. The reference receiver is assumed to connect to its closest transmitting node as is usually the case in cellular systems. After deriving the distribution of distances from the reference receiver to the serving and interfering nodes, we derive an exact expression for downlink coverage probability in terms of the derivative of Laplace transform of interference power distribution. In the downlink of this system, it is not unusual to encounter scenarios in which the line-of-sight (LOS) component is significantly stronger than the reflected multipath components. To emulate such scenarios, we also derive the coverage probability in the absence of fading from the results of Nakagami-$m$ fading by taking the limit $m \to \infty$. Using asymptotic expansion of incomplete gamma function, we concretely show that this limit reduces to a redundant condition. Consequently, we derive an accurate coverage probability approximation for this case using dominant interferer-based approach in which the effect of dominant interferer is exactly captured and the residual interference from other interferers is carefully approximated. We then derive the bounds of the approximate coverage probability using Berry-Esseen theorem. Our analyses reveal several useful trends in coverage probability as a function of height of the transmitting nodes and the location of reference receiver on the ground.