[Paper Review] Downlink Coverage and Rate Analysis of an Aerial User in Integrated Aerial and Terrestrial Networks.

Nesrine Cherif, Mohamed Alzenad+2 more|arXiv (Cornell University)|May 24, 2019

UAV Applications and Optimization16 citations

TL;DR

This paper analyzes downlink coverage and rate performance for an aerial user in an integrated aerial-terrestrial network using stochastic geometry. It models terrestrial-BSs as a 2D Poisson point process and aerial-BSs as a 3D Binomial point process, assuming LoS for air-to-air links and simplified LoS probability for cellular-to-air links. The key finding is that directive beamforming at aerial-BSs significantly improves performance by reducing interference.

ABSTRACT

In this paper, the downlink coverage probability and average achievable rate of an aerial user in a vertical HetNet (VHetNet) comprising aerial base stations (aerial-BSs) and terrestrial-BSs are analyzed. The locations of terrestrial-BSs are modeled as an infinite 2-D Poisson point process (PPP) while the locations of aerial-BSs are modeled as a finite 3-D Binomial point process (BPP) deployed at a particular height. We adopt cellular-to-air (C2A) channel model that incorporates LoS and NLoS transmissions between the terrestrial-BSs and the typical aerial user while we assume LoS transmissions for the air-toair (A2A) channels separating the aerial user and aerial-BSs. For tractability reasons, we simplify the expression of the LoS probability provided by the International Telecommunications Union using curve fitting. We assume that the aerial user is associated with the BS (either an aerial-BS or terrestrial-BS) that provides the strongest average received power. Using tools from stochastic geometry, we derive analytical expressions of the coverage probability and achievable rate in terms of the Laplace transform of interference power. To simplify the derived analytical expressions, we assume that the C2A links are in LoS conditions. Although this approximation gives pessimistic results compared to the exact performance, the analytical approximations are easier to evaluate and quantify well the performance at high heights of the aerial user. Our findings reveal that using directive beamforming for the aerial-BSs improves the downlink performance substantially since it alleviates the strong interference signals received from the aerial-BSs.

Motivation & Objective

• To evaluate downlink coverage probability and achievable rate for an aerial user in a heterogeneous network combining aerial and terrestrial base stations.
• To model the spatial distribution of terrestrial-BSs as a 2D Poisson point process and aerial-BSs as a 3D Binomial point process at a fixed altitude.
• To analyze performance under a signal association rule based on strongest average received power, incorporating LoS and NLoS propagation models.
• To simplify the LoS probability expression using curve fitting for tractability in performance analysis.
• To evaluate the impact of directive beamforming at aerial-BSs on interference mitigation and system performance.

Proposed method

• Model terrestrial-BS locations as a homogeneous Poisson point process in 2D for spatial randomness and tractability.
• Model aerial-BS locations as a finite 3D Binomial point process at a fixed height to represent controlled deployment.
• Use a cellular-to-air (C2A) channel model that accounts for both LoS and NLoS propagation between terrestrial-BSs and the aerial user.
• Assume all air-to-air (A2A) links are in LoS condition between the aerial user and aerial-BSs for simplification.
• Apply curve fitting to the ITU-recommended LoS probability model to enable analytical tractability.
• Derive closed-form expressions for coverage probability and achievable rate using the Laplace transform of the interference power.

Experimental results

Research questions

• RQ1 What is the downlink coverage probability of an aerial user served by a heterogeneous network of aerial and terrestrial base stations?
• RQ2 How does the average achievable rate at the aerial user scale with network parameters such as BS density and altitude?
• RQ3 How does the assumption of LoS-only transmission in the air-to-air link affect the accuracy and tractability of performance analysis?
• RQ4 To what extent does directive beamforming at aerial-BSs improve coverage and rate by reducing interference?
• RQ5 How does the signal association rule based on strongest average received power influence system performance in a mixed aerial-terrestrial environment?

Key findings

• The use of directive beamforming at aerial-BSs leads to a substantial improvement in downlink coverage and achievable rate by suppressing interference from other aerial-BSs.
• Assuming LoS conditions for all C2A links yields pessimistic but analytically tractable performance bounds, especially at high altitudes.
• The derived analytical expressions for coverage probability and rate are simplified using the Laplace transform of interference power, enabling efficient numerical evaluation.
• The finite 3D Binomial point process model for aerial-BSs allows for realistic deployment modeling at a fixed altitude with controlled density.
• The performance analysis reveals that aerial-BSs significantly enhance coverage at high altitudes, particularly when beamforming is employed.
• The simplified LoS probability model based on curve fitting enables practical computation without sacrificing significant accuracy in high-altitude scenarios.