1 Dedicating Cellular Infrastructure for Aerial Users Advantages and Potential Impact on

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Dedicating Cellular Infrastructure for Aerial

Users: Advantages and Potential Impact on

Ground Users

Lin Chen, Mustafa A. Kishk, Member, IEEE, and Mohamed-Slim Alouini,

Fellow, IEEE

Abstract

A new generation of aerial vehicles is hopeful to be the next frontier for the transportation of

people and goods, becoming even as important as ground users in the communication systems. To

enhance the coverage of aerial users, appropriate adjustments should be made to the existing cellular

networks that mainly provide services for ground users by the down-tilted antennas of the terrestrial

base stations (BSs). It is promising to up-tilt the antennas of a subset of BSs for serving aerial users

through the mainlobe. With this motivation, in this work, we use tools from stochastic geometry to

analyze the coverage performance of the adjusted cellular network (consisting of the up-tilted BSs and

the down-tilted BSs). Correspondingly, we present exact and approximate expressions of the signal-to-

interference ratio (SIR)-based coverage probabilities for users in the sky and on the ground, respectively.

Numerical results verify the analysis accuracy and clarify the advantages of up-tilting BS antennas on

the communication connectivity of aerial users without the potential adverse impact on the quality of

service (QoS) of ground users. Moreover, it is unveiled that there exists an optimal value of the up-

tilted/down-tilted BS density ratio for maximizing the coverage probability of the aerial or ground users.

Index Terms

Stochastic geometry, aerial transportation, cellular networks, coverage probability, up-tilt angle.

Lin Chen is with the Department of Information Engineering, The Chinese University of Hong Kong (CUHK), Hong

Kong. Mustafa A. Kishk is with the Department of Electronic Engineering, National University of Ireland, Maynooth,

W23 F2H6, Ireland. Mohamed-Slim Alouini is with KAUST, CEMSE division, Thuwal 23955-6900, Saudi Arabia. (e-mail:

lin.chen@link.cuhk.edu.hk; mustafa.kishk@mu.ie; slim.alouini@kaust.edu.sa).

arXiv:2210.04030v1 [cs.IT] 8 Oct 2022

I. INTRODUCTION

In recent years, aerial transportation has seen unprecedented advances since the terrestrial

trafﬁc congestion and the constraints of public transportation infrastructure. Transportation of

(i) goods through unmanned aerial vehicles (UAVs) and (ii) people through ﬂying cars is not a

futuristic dream anymore [1], [2].

To become a reality, it is important to provide a strong and reliable connection for all kinds

of aerial transportation to ensure (i) safety and control of UAVs and (ii) coverage for mobile

users in ﬂying cars. However, the current cellular infrastructure is primarily designed to serve

users spatially distributed on the ground. In particular, the antennas of the terrestrial base stations

(BSs) are down-tilted and completely direct towards the ground users. Consequently, the aerial

users can only get sidelobe gain from the current cellular infrastructure, which might not be

enough to ensure the full coverage of such a new type of users. Therefore, there is an urgent

need to modify the current cellular network to meet the connectivity requirement of aerial users

(e.g., UAVs for delivery or surveillance and mobile equipment held by people in ﬂying cars).

A. Related Work

Aerial communication equipment-enabled communication systems have recently attracted much

research interest [3]–[8]. For example, by employing geographic information, the authors in [3]

jointly optimized the 3D position and power allocation of the UAV relay to improve communi-

cation capacity. In [4], UAVs were served as BSs, whose placement is based on the prediction of

the user equipment (UE) movement, to provide seamless communication services for the ﬂash

mobile crowds. Ref. [5] formulated an optimization problem to design the trajectory of a UAV

by maximizing the minimum rate of the downlink (from a UAV to a ground UE). However, in

the above works, UAVs either act as BSs or relays to enhance the quality of service (QoS) of

ground users, while the coverage probability of UAVs (regarded as UEs, i.e., UAV-UEs) is not

considered.

The QoS of aerial communication equipment served by the existing cellular network also

has some work. The authors in [9], [10] discussed the technical feasibility of leveraging the

established cellular network for supporting the connectivity of UAVs in a cost-effective manner.

Modeling the actual radiation pattern in the vertical plane of the BSs equipped with uniform linear

antennas (ULAs), Ref. [11] provided the uplink and downlink coverage performance analysis

for the UAV-UE in cellular networks composed of regularly-distributed BSs.

On the other hand, adjusting the current network structure to serve aerial users has been

investigated recently, e.g., [12]–[18]. The authors in [13] found an optimal value of the UAV

height to ensure connectivity. The height-dependent path-loss exponent and the small-scale fading

were further considered in [14] to analyze the coverage probability of the aerial users. In addition

to optimizing the height of the aerial users, the parameters of BSs have been modiﬁed to improve

the aerial coverage probability [15]–[18]. Ref. [15], [16] proposed to reduce the down-tilt angle

and scale the beamwidth of BS antennas to allow part of BSs to provide services through

mainlobes for both aerial users and ground users. However, once such BSs are associated with

ground users, they unavoidably interfere with aerial users from the mainlobes and vice versa. In

order to suppress interference, antenna patterns were designed in [17], [18].

It is worth noting that the existing literature on improving the QoS of aerial users mainly

focuses on optimizing the height of BSs/UAVs and the down-tilted angle/beamwidth. However,

in these solutions, the BSs tilting their antennas downward still aims at serving the ground

users. In fact, as a result of the on-growing set of applications of UAVs, it is anticipated to see

a continuous increase in the number of aerial users, even becoming comparable to the number

of ground users in the communication systems. Therefore, it is reasonable to design a cellular

network composed of two types of BSs for serving ground users and aerial users, respectively.

B. Contributions

Motivated by the above discussion, in the paper, we propose to up-tilt the antennas of a

fraction of BSs to ensure the coverage of aerial users. Intuitively, the up-tilted BSs enable aerial

users to receive higher power through the mainlobes and only interfere with ground users from

the sidelobes. This implies that the proposal can increase the received power at aerial users

and decrease the interference power at ground users. However, this proposal also involves some

new technical challenges related to characterizing the interference from both the sidelobes of

down-tiled BSs and the sidelobes/mainlobes of up-tilted BSs for aerial users and the opposite

for ground users. We use the signal-to-interference ratio (SIR)-based coverage probability as a

performance metric to quantify the impact of the coexistence of up-tilted BSs and down-tilted

BSs on aerial users and grounds users. Employing the stochastic geometry approach, we seek a

reasonable solution to improve the coverage probability of aerial users without deteriorating the

QoS of ground users. The main contributions of this paper are listed as follows:

•We propose a new method to ensure the connectivity of aerial users, i.e. converting a part

of the down-tilted BSs into up-tilted BSs, which makes it possible for the cellular network

to transmit signals to aerial users through mainlobes.

•Using stochastic geometry, we derive the expressions of the SIR-based coverage probabilities

of aerial users and ground users to evaluate the effectiveness of the proposed cellular

network. We also verify the analysis accuracy by extensive Monte Carlo simulations.

•With the improvement on the coverage probabilities in numerical results compared with the

current network comprising only down-tilted BSs, we show that the proposed network is

effective to increase the QoS of aerial users without lowering that of ground users.

•We further explore the impact of system parameters, including the up-tilted/down-tilted BS

density ratio, the up-tilted angle/beamwidth, and the heights of BSs and aerial users on the

coverage performance. These analyses provide insights into the design of future networks

to achieve wide coverage for both aerial users and ground users.

The rest of this paper is structured as follows. We introduce the proposed cellular network,

the corresponding stochastic geometry-based model, and the performance metrics in Sec. II. In

Sec. III, we derive the expressions of the performance metrics. Then, we present and discuss

the numerical results in Sec. IV. Finally, we conclude our work in Sec. V. Table I summarizes

the notations in this paper.

TABLE I: Table of notations

Notation Description

hT;ha;hgThe altitude of the terrestrial BSs; the aerial users; the ground users

ΨT;Ψa;ΨgThe PPP modeling the locations of the terrestrial BSs; the aerial users; the ground users

λT;λa;λgThe density of ΨT;Ψa;Ψg

GM;GSMainlobe gain; sidelobe gain provided by BSs

ΨU;ΨDThe PPP modeling the locations of BSs with the up-tilted antennas; the down-tilted antennas

θU;θDThe up-tilt angle; the down-tilt angle of the BS antenna

ϕU;ϕDThe vertical antenna beamwidth of the up-tilted BSs; the down-tilted BSs

δThe fraction of the BSs that direct their antennas towards aerial users by up-tilting.

λU;λDThe density of ΨU;ΨD. Note that λU=δλTand λD= (1 −δ)λT

PL(r)The probability that a link with horizontal distance ris clear of any blockage

PN(r)The probability that a link is obstructed by at least one blockage, where PN(r)=1− PL(r)

UML;UMN;USL;USN The BS using up-tilted antenna provides mainlobe gain or sidelobe gain with LoS or NLoS transmission

DML;DMN;DSL;DSN The BS using down-tilted antenna provides mainlobe gain or sidelobe gain with LoS or NLoS transmission

b;wThe type of serving BSs, where b=b1b2b3with b1∈ {U,D},b2∈ {M,S}, and b3∈ {L,N}; the type of interfering BSs

Fig. 1: Depiction of a fraction of the terrestrial BSs that direct their antennas towards aerial users.

II. SYSTEM MODEL

In this section, we introduce the idea of switching a subset of the cellular infrastructure into a

fully dedicated network for serving aerial users, followed by the channel model, the association

policy between the BSs and the users, and the performance metrics.

A. Network Model

We consider a cellular network consisting of terrestrial BSs, aerial users, and ground users

with particular altitudes hT,ha, and hg, respectively. We model their 2D locations as three

independently homogeneous PPPs (HPPPs): ΨT={ti} ∈ R2with density λT,Ψa={ai} ∈ R2

with density λa, and Ψg={gi} ∈ R2with density λg, respectively. In fact, the aerial users are

movable and have different altitudes. The 2D-PPP modelling of aerial users can be considered

as an approximation to a scenario in which the altitudes of aerial users are uniformly distributed

within a range of heights and hais the average altitude.1Each BS serves one single user

in a time-frequency slot. Besides, we assume that the antenna radiation patterns of BSs are

omnidirectional in the horizontal plane and directional in the vertical plane, while all users

employ omnidirectional antennas. As illustrated in Fig. 1, a fraction (δ) of terrestrial BSs are

dedicated to serving aerial users by up-tilting their beams with angle θUand vertical beamwidth

ϕU, where 0≤δ≤1. The density of the BSs with an up-tilt angle is denoted by λU=δλT. The

rest of BSs have down-tilt angle θDand vertical beamwidth ϕDwith density λD= (1 −δ)λT.

1The analysis of aerial communication devices with different altitudes matches that with the same altitude (equal to the average

altitudes of aerial communication devices) [19], [20].

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1DedicatingCellularInfrastructureforAerialUsers:AdvantagesandPotentialImpactonGroundUsersLinChen,MustafaA.Kishk,Member,IEEE,andMohamed-SlimAlouini,Fellow,IEEEAbstractAnewgenerationofaerialvehiclesishopefultobethenextfrontierforthetransportationofpeopleandgoods,becomingevenasimportantasgroundusersint...

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