Sum Capacity Maximization in Multi-Hop Mobile Networks with Flying Base Stations Mohammadsaleh Nikooroo1 Omid Esraﬁlian2 Zdenek Becvar1 David Gesbert2

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Sum Capacity Maximization in Multi-Hop Mobile

Networks with Flying Base Stations

Mohammadsaleh Nikooroo1, Omid Esraﬁlian2, Zdenek Becvar1, David Gesbert2

1Faculty of Electrical Engineering Czech Technical University in Prague, Prague, Czech Republic

2Communication Systems Department, EURECOM, Sophia Antipolis, France

1{nikoomoh,zdenek.becvar}@fel.cvut.cz, 2{esraﬁli,gesbert}@eurecom.fr

Abstract—Deployment of multi-hop network of unmanned

aerial vehicles (UAVs) acting as ﬂying base stations (FlyBSs)

presents a remarkable potential to effectively enhance the per-

formance of wireless networks. Such potential enhancement,

however, relies on an efﬁcient positioning of the FlyBSs as well

as a management of resources. In this paper, we study the

problem of sum capacity maximization in an extended model for

mobile networks where multiple FlyBSs are deployed between

the ground base station and the users. Due to an inclusion of

multiple hops, the existing solutions for two-hop networks cannot

be applied due to the incurred backhaul constraints for each

hop. To this end, we propose an analytical approach based on

an alternating optimization of the FlyBSs’ 3D positions as well

as the association of the users to the FlyBSs over time. The

proposed optimization is provided under practical constraints on

the FlyBS’s ﬂying speed and altitude as well as the constraints

on the achievable capacity at the backhaul link. The proposed

solution is of a low complexity and extends the sum capacity by

23%-38% comparing to state-of-the-art solutions.

Index Terms—Flying base station, wireless backhaul, relaying,

sum capacity, mobile users, mobile networks, 6G.

I. INTRODUCTION

Unmanned aerial vehicles (UAVs) have attracted an abun-

dance of research interest in wireless communications in the

last few years thanks to their high mobility and adaptability to

the environment. Deployed as ﬂying base stations (FlyBSs),

UAVs can potentially bring a great improvement in applica-

tions such as surveillance, emergency situations, or providing

user’s coverage in areas with unreliable connectivity [1], [2],

[3],[4]. Several challenges exist to enable an effective use

of FlyBSs, including an efﬁcient cooperation between the

FlyBSs’ via a management of the resources as well as FlyBSs’

positioning. An important case with cooperative FlyBSs is

relaying networks where FlyBSs either serve the ground users

directly (access link) or relay the data to establish a connection

between the users and the ground base station (GBS).

Several recent works target enhancing the performance

in networks with relaying FlyBSs. With respect to those

works only focusing on the communication at the access

link, relaying networks necessitate to consider the backhaul

This work was supported by the project No. LTT 20004 funded by Ministry

of Education, Youth and Sports, Czech Republic and by the grant of Czech

Technical University in Prague No. SGS20/169/OHK3/3T/13, and partially

by the HUAWEI France supported Chair on Future Wireless Networks at

EURECOM.

link connecting the users to the GBS. In particular, ﬂow

conservation constraints apply at each relay node to ensure

a sufﬁcient backhaul capacity for the fronthaul link. The basic

model for relaying FlyBS networks is a two-hop architecture

where all FlyBSs directly serve users at the access link and

also connect directly to the GBS via the backhaul link. A

majority of recent works target an enhancement in two-hop

relaying networks with a consideration of backhaul.

The problem of resource allocation and FlyBS’s positioning

is considered in many works targeting various objectives, in-

cluding optimization of minimum rate for delay-tolerant users

[5], energy consumption [6], network proﬁt gained from users

[7], sum capacity [8], network latency [9]. The mentioned

works [5]-[9] consider a single FlyBS, and an application of

those works to multiple-FlyBS scenario is not trivial.

Several works also consider multiple FlyBSs in two-hop

relaying networks. In [10] the authors study a joint place-

ment, resource allocation, and user association of FlyBSs

to maximize the network’s utility. Furthermore, the authors

in [11] maximize the sum capacity via FlyBS’s positioning,

user association, and transmission power allocation. In [12]

the minimum rate of the users is maximized via resource

allocation and positioning in wireless backhaul networks.

Furthermore, the authors in [13] investigate an optimization

the FlyBS’s position, user association, and resource allocation,

to maximize the utility in software-deﬁned cellular networks

with wireless backhaul. Due to the introduced ﬂow conser-

vation constraints, an extension of studies/solutions on two-

hop FlyBS networks to higher number of hops is often not

simple or straightforward. There are quite a limited number of

works that consider relaying FlyBSs in networks with more

than two hops. In [14] the minimum downlink throughput is

maximized by optimizing the FlyBSs’ positioning, bandwidth,

and power allocation. The provided solution, however, does

not address interference management as orthogonal transmis-

sions is assumed. Furthermore, the FlyBSs’ altitude is not

optimized. Then, in [15] the number of FlyBSs is optimized

while ensuring both coverage to all ground users as well as

backhaul connectivity to a terrestrial base station. The authors

in [16] investigate an interference management scheme based

on machine learning and a positioning based on K-means to

mitigate interference and FlyBSs’ power consumption.

In the view of existing works on relaying FlyBS networks,

arXiv:2210.11884v1 [eess.SY] 21 Oct 2022

we are motivated to take one step forward and to address

a maximization of sum capacity via a placement of FlyBSs

and an association of users in a multi-hop relaying FlyBS

architecture where the FlyBSs serving the users at the access

link connect to a GBS via another relaying FlyBS. Such an

extension from two-hop model would allow a vaster range

of user coverage to connect more remote users to the GBS.

Unlike the most of related works, in our model, also the

GBS and the relay are allowed to serve the users directly.

In contrast to most of related works, a reuse of channels from

the access link is enabled to establish the backhaul connection.

The solution is provided under backhaul constraints.

The main contribution of this paper is explained as follow.

We provide a framework based on a multi-hop FlyBS wireless

network where the FlyBSs at the access link communicate with

a ground base station through a relaying FlyBS. We formulate

the network’s sum capacity with a consideration of channel

resue for the backhaul link. We formulate the problem of sum

capacity maximization via an association of the users and a

positioning of the FlyBSs at the access link and the relay. In

our model, a direct serving of the users by the relaying FlyBS

as well as by the GBS is also possible. A heuristic iterative

solution is proposed based on an alternating optimization of

the FlyBSs’ positions at the access link, FlyBS’s position at

the relay, and then a reassociation of the users to the FlyBSs.

An approximation of the sum capacity is proposed to derive

a radial function to determine the FlyBSs’ optimal directions

of movement in the proposed iterative positioning.

The rest of this paper is organized as follows. In Section II

we elaborate the system model for multi-hop FlyBS network.

Next, the problem of sum capacity maximization is formulated

and our proposed solution to the FlyBS’s positioning and user

association is provided in Section III. Then, in section IV,

we specify our adopted simulation scenario and we show the

performance of our proposed solution and we compare it with

existing works. Last, we conclude the paper and outline the

potential extensions for the future work.

II. SYSTEM MODEL AND PROBLEM FORMULATION

In this section, we deﬁne the system model and provide

details about transmission power and channel capacity.

We consider a set of MFlyBSs and a ground base station

(GBS) serving Nground users. M−1of those FlyBSs

serve at the access link. The backhaul communication between

those M−1FlyBSs and the GBS is established via an

intermediate relay FlyBS. Fig. 1 illustrates the adopted model.

Let Q={q1,...,qM}be the set of the FlyBS’s positions

where qm[k] =[Xm[k], Ym[k], Hm[k]]Tdenote the location

of the m-th FlyBS at the time step k(1 ≤m≤M),

where the index m=Mindicates the relay. Let qM+1 =

[XM+1, YM+1, HM+1]Tdenote the GBS’s position. Next, let

dm1,m2[k]denote the Euclidean distance between the m1-

th and m2-th BSs’ receivers (we use the general term BS

when referring to both GBS and FlyBSs). Furthermore, let

vn[k] =[xn[k], yn[k], zn[k]]Tdenote the coordinates of the

n-th ground user at the time step k. Then, dn,m[k]denotes

Figure 1: System model with the FlyBSs at the access link,

relaying FlyBS, and the GBS serving moving users.

Euclidean distance of the n-th user to the m-th BS. As in

many related works, we assume that the current positions

of the users are known to the BSs. Also, the FlyBSs can

determine their own position [8], [10], [14], [18]. Let A=

(an,m)∈ {0,1}N×(M+1)be the association matrix where

an,m =1 indicates an association of the n-th user to the m-th

BS. Note that the users can be directly served by the relay or

the GBS as well. Every user cannot be associated to more than

one BS. Also, we assume the whole radio band is divided into

the set of channels L={l1, . . . , lC}, where channel lchas a

bandwidth of Bc(1 ≤c≤C). Note that the channels can

be of different bandwidth in our model. We adopt orthogonal

downlink channel allocation for all users associated to the

same BS. Furthermore, let gnbe the index of the channel

allocated to the n-th user. Also, we assume IMand IM+1

denote the set of indices of channels allocated to the users

served by the relay and by the GBS, respectively. Also, let

IM,m be the set of channels’ indices used between the relay

and the m-th FlyBS at the access link. The relay communicates

with users and other FlyBSs using orthogonal channels. Note

that, we do not target an optimization of channel allocation due

to space limit, and we leave that for future work. Nevertheless,

our model works with any channel allocation.

The received power from the m-th FlyBS at the n-th user

is denoted as pR

n,m and calculated as:

n,m = Γn,m(γ

γ+ 1 hn+1

γ+ 1 ˜

hn)d−αn,m

n,m =Qn,md−αn,m

n,m ,(1)

where Γn,m is a parameter depending on communication

frequency and gain of antennas. Furthermore, γis the Ri-

cian fading factor, hnis the line-of-sight (LoS) component

satisfying |hn|=1, and ˜

hndenotes the non-line-of-sight

(NLoS) component satisfying ˜

hn∼CN (0,1), and αn,m is

the pathloss exponent. Note that the coefﬁcient Γn,m(γ

γ+1 hn+

γ+1 ˜

hn)d−αn,m

n,m is substituted with Qn,m for an ease of presen-

tation in later discussions. Similar relation applies for backhaul

link as pR

m1,m2,k =Qm1,m2,kd−αm1,m2

m1,m2where pR

m1,m2,k is the

received power at m1-th BS from m2-th BS over k-th channel.

The downlink capacity of the n-th user is calculated as

Cn,m =an,mBgnlog2(1 + pR

n,m

σ2

n,m +Pm0∈{an,m0=0}pR

n,m0

)(2)

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SumCapacityMaximizationinMulti-HopMobileNetworkswithFlyingBaseStationsMohammadsalehNikooroo1,OmidEsralian2,ZdenekBecvar1,DavidGesbert21FacultyofElectricalEngineeringCzechTechnicalUniversityinPrague,Prague,CzechRepublic2CommunicationSystemsDepartment,EURECOM,SophiaAntipolis,France1{nikoomoh,zdenek.b...

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Sum Capacity Maximization in Multi-Hop Mobile Networks with Flying Base Stations Mohammadsaleh Nikooroo1 Omid Esraﬁlian2 Zdenek Becvar1 David Gesbert2

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