Downlink Coverage Analysis for a Finite 3D Wireless Network of Unmanned Aerial Vehicles (1701.01212v1)

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.

• The paper analyzes downlink coverage in finite 3D UAV networks using stochastic geometry and a binomial point process model, deriving an exact expression for coverage probability.
• Empirical observations show that UAV altitude negatively impacts coverage, while a higher path-loss exponent improves it.
• This research offers a robust analytical foundation for deploying UAV-based networks and can be extended to other three-dimensional network modeling applications.

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

This paper, authored by Vishnu Vardhan Chetlur and Harpreet S. Dhillon, presents a detailed and rigorous analysis of downlink coverage in finite three-dimensional wireless networks formed by unmanned aerial vehicles (UAVs). The paper leverages a homogeneous binomial point process (BPP) to model the spatial distribution of UAVs and employs Nakagami-m fading to account for channel variations, offering significant insights into UAV network coverage probability and its reliance on network parameters.

Analytical Framework and Methodology

The authors extend the use of stochastic geometry, a mathematical tool commonly applied for infinite homogeneous networks, to analyze finite networks. They derive the distribution of distances from a reference receiver, located arbitrarily on the ground, to both the serving UAV and interfering UAVs. A notable achievement is the derivation of an exact expression for the downlink coverage probability, which hinges on the Laplace transform of the interference power distribution.

The paper further investigates scenarios devoid of small-scale fading, termed "no-fading" environments, using an asymptotic expansion of the incomplete gamma function. This exploration reveals that a direct computation approach yields a redundant condition, hence motivating the use of dominant interferer-based approaches. The effect of a dominant interferer is captured precisely while approximating residual interference using normal distribution assumptions under the central limit theorem (CLT).

Empirical Observations

Through theoretical derivations validated against simulations, the paper illustrates several critical trends:

• The altitude of UAVs significantly influences coverage probability: increasing UAV height generally deteriorates coverage due to larger propagation distances.
• The path-loss exponent also plays a crucial role: coverage probability enhances as the path-loss exponent increases, indicating sharper attenuation of interference relative to desired signals.
• Coverage probabilities fluctuate with receiver position, reaffirming the importance of considering arbitrary user locations.

Implications and Future Directions

This research illuminates both theoretical and practical implications for deploying UAV networks as supplementary infrastructure in environments where traditional base stations are impractical or insufficient. The methodologies developed here could extend to broader applications in three-dimensional network modeling, including hybrid terrestrial-UAV deployments. Future work might refine these models to incorporate earth curvature, more sophisticated spatial correlations, and realistic environmental obstructions.

The exploration of UAV network coexistence with terrestrial networks, as well as other performance metrics such as energy efficiency or throughput, could offer further value for evolving network architectures.

Conclusion

The paper provides a robust analytical foundation for understanding downlink coverage in UAV-based networks. It demonstrates how novel applications of stochastic geometry can capture the complexities of three-dimensional wireless communication scenarios, offering a pathway for more informed deployments of UAV-based networks and establishing a groundwork for subsequent advancements in this dynamic field.