senso s
A icle
Modeling Op imal Loca ion Dis ibu ion o Deploymen o
Flying Base S a ions as On-Demand Connec i i y Enable s in
Real-Wo ld Scena ios
Ji i Poko ny 1,2,* , Pa el Seda 1, Milos Seda 3and Ji i Hosek 1


Ci a ion: Poko ny, J.; Seda, P.; Seda,
M.; Hosek, J. Modeling Op imal
Loca ion Dis ibu ion o Deploymen
o Flying Base S a ions as
On-Demand Connec i i y Enable s in
Real-Wo ld Scena ios. Senso s 2021,
21, 5580. h ps://doi.o g/10.3390/
s21165580
Academic Edi o s: En ico Na alizio
and Ma io Luca F a olini
Recei ed: 30 June 2021
Accep ed: 16 Augus 2021
Published: 19 Augus 2021
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
1Depa men o Telecommunica ions, Facul y o Elec ical Enginee ing and Communica ion,
B no Uni e si y o Technology, Technicka 12, 616 00 B no, Czech Republic; [email p o ec ed] (P.S.);
[email p o ec ed].cz (J.H.)
2Uni o Elec ical Enginee ing, Tampe e Uni e si y, Ko keakoulunka u 7, 337 20 Tampe e, Finland
3Ins i u e o Au oma ion and Compu e Science, B no Uni e si y o Technology,
Technicka 2, 616 69 B no, Czech Republic; [email p o ec ed].cz
*Co espondence: ji i.poko ny@ u b .cz
Abs ac :
The amoun o in e ne a ic gene a ed du ing mass public e en s is signi ican ly g owing
in a way ha equi es me hods o inc ease he o e all pe o mance o he wi eless ne wo k se ice.
Recen ly, legacy me hods in o m o mobile cell si es, equen ly called cells on wheels, we e used.
Howe e , mode n echnologies a e allowing he use o unmanned ae ial ehicles (UAV) as a pla o m
o ne wo k se ice ex ension ins ead o g ound-based echniques. This esul s in he de elopmen
o lying base s a ions (FBS) whe e he numbe o deployed FBSs depends on he demanded ne wo k
capaci y and speci ic use equi emen s. La ge-scale e en s, such as ou doo music es i als o
spo ing compe i ions, equi ing deploymen o mo e han one FBS need a me hod o op imally
dis ibu e hese ae ial ehicles o achie e high capaci y and minimize he cos . In his pape , we
p esen a ma hema ical model o FBS deploymen in la ge-scale scena ios. The model is based on a
loca ion se co e ing p oblem and he goal is o minimize he numbe o FBSs by inding hei op imal
loca ions. I is es ic ed by use s’ h oughpu equi emen s and FBSs’ a ailable h oughpu , also, all
use s ha equi e connec i i y mus be se ed. Two me a-heu is ic algo i hms (cuckoo sea ch and
di e en ial e olu ion) we e implemen ed and e i ied on a eal example o a music es i al scena io.
The esul s show ha bo h algo i hms a e capable o inding a solu ion. The majo di e ence is in he
pe o mance whe e di e en ial e olu ion sol es he p oblem six o eigh imes as e , hus i is mo e
sui able o epe i i e calcula ion. The ob ained esul s can be used in comme cial scena ios simila o
he one used in his pape whe e p o iding su icien connec i i y is c ucial o good use expe ience.
The designed algo i hms will se e o he ne wo k in as uc u e design and o assessing he cos s
and easibili y o he use-case.
Keywo ds:
UAV base s a ion; lying base s a ion; FBS; loca ion op imiza ion; ne wo k co e age
capaci y; on-demand; loca ion co e ing p oblem; 5G
1. In oduc ion
In e ne ubiqui y has become na u al in he mode n wo ld and he demand o i keeps
g owing signi ican ly. People use he in e ne o social ne wo king, s eaming mul imedia
da a, playing games, wo k, and many o he hings. Howe e , in some cases, he demand
exceeds he o e ing and use s a e no p o ided wi h enough h oughpu o sha ing
hei da a. This can be caused by obsole e elecommunica ion in as uc u e o when use
demands exceed, by mul iple imes, he in as uc u e capabili ies. Such a si ua ion is
ypical, especially du ing la ge-scale e en s, whe e he da a demand is empo a ily aised
abo e he in as uc u e limi s. Du ing such e en s, implemen a ion o suppo ing ne wo k
in as uc u e is manda o y o sa is y use equi emen s.
Senso s 2021,21, 5580. h ps://doi.o g/10.3390/s21165580 h ps://www.mdpi.com/jou nal/senso s
Senso s 2021,21, 5580 2 o 22
Recen ly, o cope wi h his imbalance, he e we e a ew solu ions in oduced as, e.g.,
Cell on Wheels (COW) o po able base s a ion ha was b ough o he a ec ed a ea.
Howe e , all hose echnologies a e limi ed especially in e ms o deploymen speed and
ope a ional cos s. The e o e, one o he al e na i e solu ions can be he u iliza ion o
unmanned ae ial ehicles and hei a ailabili y enabled h ough a apid de elopmen o
mode n echnologies. The unmanned ae ial ehicles can be applied in a ious sec o s like
pa olling, deli e y, ideo eco ding, and also as on-demand connec i i y p o ide s. In
ac , he e a e al eady many comme cial and esea ch concep s whe e unmanned ae ial
ehicles a e used as po able base s a ions. Unmanned Ae ial Vehicle (UAV) base s a ion,
o Flying Base S a ion (FBS) can bene i om he mos ad an ageous ea u es o UAV, e.g.,
as deploymen ime, mobili y, and low cos .
When i comes o size, COWs a e a leas en o wen y imes bigge and hea ie , o
possibly e en mo e, han a high olume FBS. Tha also means ha he FBS can p o ide
a lowe da a- a e han a COW. In la ge-scale scena ios, i is hen e y likely o equi e
mo e han a single FBS. The dis ibu ion o use s can be andom o clus e ed in o g oups o
di e en sizes. Each use can equi e di e en da a h oughpu . This aises he ques ion
o how o op imally dis ibu e mul iple FBSs o e a la ge a ea o p o ide he equi ed
da a- a e o all use s.
The desc ibed esea ch ollows ou p e ious wo k [
1
], whe e we made a p oo o he
concep o he di ec ional backhaul link o pu poses o ne wo k h oughpu imp o emen s
in dense a eas. In ou wo k, he FBSs a e used o assis ing cu en in as uc u e o ex end
ne wo k h oughpu o on-demand scena ios. The idea is demons a ed in Figu e 1. The e
is an e en wi h la ge amoun o use s ha equi es much highe ne wo k h oughpu han
he cu en in as uc u e can p o ide. The numbe o FBSs is de e mined om he use s’
demand and om he a ailable h oughpu om he local in as uc u e. The p oblem
desc ibed in his wo k is a ype o co e age p oblem.
FBS
Ru al a ea
FBS
Dense a ea
BTS
Backhaul
Backhaul
DR 1 DR 2
DR 3
DR 6
DR 5
DR 4
DR 1
DR 1 DR 2
Web b owsing low Web b owsing high DR 3
DR 4
Video s eaming 720p
Video s eaming 1080p DR 6
DR 5 Videocha s Gaming
Figu e 1. Use-cases wi h FBSs assis ing cu en in as uc u e o ex end he co e age in he a ea.
This pape p esen s a ma hema ical model o FBS dis ibu ion o e an a ea. Use
demands and FBS h oughpu capaci ies a e u ilized as es ic ing aspec s. The model is
e i ied on a ealis ic music es i al scena io. Heu is ic algo i hms we e used o implemen
he model since i s compu a ional complexi y, which is de i ed om he Se Co e ing
P oblem (SCP) p oblem is a leas
O(n2)
. I is known om he no ee lunch heo em [
2
] ha
no heu is ic can be conside ed as be e han o he s o all he p oblems and hei da ase s.
Senso s 2021,21, 5580 3 o 22
Howe e , in he ecen esea ch on he p oblem o se co e ing-based opics he di e en ial
e olu ion algo i hm seems p omising [
3
]. The o he p omising algo i hm om he a ailable
me a-heu is ic algo i hms is he cuckoo sea ch ha is widely used in ecen li e a u e o
a wide a ea o op imiza ion p oblems as is: (i) o es co e
classi ica ion [4]
, (ii) load
balanced da a ga he ing [
5
], (iii) pe mu a ion low shop scheduling
p oblem [6]
, and many
o he s [7,8]
. Fo ha eason, he cuckoo sea ch and di e en ial e olu ion algo i hms we e
used including he cus om modi ica ion ha con ains he
epai Ope a o
(see
Algo i hm 3)
,
o p o ide an e icien FBS placemen .
The main con ibu ions o his pape a e as ollows:
•
Design o a no el model o FBS dis ibu ion o e a selec ed a ea: This model is
de i ed om SCP. Due o he high demand o da a- a es, ou main es ic ing
aspec s a e conside ed, (i) use and base s a ion capaci ies ( o bo h downlink and
uplink), (ii) FBS backhaul link h oughpu , (iii) conside a ion o exis ing base s a ion
nodes in he a ea o co e , (i ) he possibili y o selec loca ions wi h lowe p io i y in
he gi en a ea. This model p o ides he minimum numbe o equi ed FBSs and hei
op imal loca ions. This knowledge is o be used in comme cial applica ions;
•
Implemen a ion o wo modi ied heu is ic algo i hms: di e en ial e olu ion and
cuckoo sea ch we e used o ob ain a solu ion o he designed model. Di e en ial
e olu ion is well sui ed o se co e ing-based p oblems. Cuckoo sea ch is a mo e
ecen algo i hm widely used in op imiza ion p oblems. Algo i hms can be se o
ob aining esul s whe e all use s a e p o ided wi h he in e ne co e age o he
pe cen age o all use s in case he numbe o FBS exceeds he maximum
a ailable limi ;
•
Ve i ica ion o he model on eal li e scena io: o e all easibili y o he wo imple-
men ed algo i hms was e i ied on a speci ic eal-wo ld scena io. Resul ing numbe
o FBSs and calcula ion ime we e used as he key pe o mance iden i ie s.
2. Li e a u e Re iew and S a e o he A Discussion
FBSs can be u ilized in a numbe o di e en use-cases, e.g., pos -disas e , co e age/ca-
paci y suppo o local in as uc u e, IoT da a collec ion, e c. In all use-cases, he FBSs a e
used as an access poin o elays o UEs on he g ound. Depending on a ious pa ame e s
o he use-case, FBSs ha e di e en equi emen s o ul ill. Mos o he esea ch wo ks in
he opic o FBS loca ion op imiza ion ha e simila objec i es wi h a common goal o ei he
minimize o maximize he desi ed pa ame e in o de o op imize he pe o mance. The
objec i es can be summa ized in o wo ollowing a eas:(i) maximiza ion o UE co e age,
powe e iciency (endu ance o UAVs), spec al e iciency, and (ii) minimiza ion o he
numbe o UAVs, and in e e ences. In ou wo k, we ocus on op imal UAV dis ibu ion
o e an a ea wi h he goal o minimizing he numbe o FBSs. This will lead o lowe
cos and complexi y o he solu ion. This esea ch can be used o bo h 2D and 3D FBS
dis ibu ion. FBS ajec o y op imiza ion p oblems a e no a pa o he scope o his wo k,
i.e., a e FBSs a e placed in he designa ed loca ion, hey con inuously ho e wi hou
mo ing o ano he loca ion.
FBSs we e discussed in nume ous esea ch wo ks. Fo ouhi e al. in [
9
] in es iga e a
new mobili y model o FBSs o imp o ing he pe o mance o cellula ne wo ks. The same
au ho s p opose, in [
10
], a mobili y con ol algo i hm o posi ion FBSs o a be e loca ion o
imp o e da a h oughpu . In [
11
], Migna di e al. p opose a ajec o y design o an FBS in
o de o imp o e he e es ial base s a ion pe o mance. The numbe o s udies conce ning
FBS inc eased apidly om 2016. UAV loca ion op imiza ion is a p oblem ha needs o
be sol ed in any FBS use case. Co e age con ol p oblems o mul iple UAV scena ios
a e discussed in [
12
], a e iew ocusing on co e age me hods o collec i e beha io o
UAVs. Ano he e iew on loca ion op imiza ion p oblems was made by
Cicek e al. [13]
whe e he au ho s speci ically a ge op imiza ion me hods o FBSs. To he bes o au ho ’s
knowledge, hese a e he only wo ele an o e iews on his opic. Acco ding o he
second o e iew, esea ch s udies can be di ided in o h ee main b anches—s a ic, semi-
dynamic, and dynamic. S a ic is whe e UAVs and Use Equipmen (UE)s a e s a iona y,
Senso s 2021,21, 5580 4 o 22
semi-dynamic whe e UAVs can mo e eely bu UEs a e s a iona y, and dynamic, whe e
UAVs and UEs can dynamically change hei loca ion. These can be u he di ided in o
scena ios wi h single o mul iple UAVs. Ou esea ch ocuses on a dynamic scena io wi h
mul iple UAVs.
UAV loca ion can be op imized by means o di e en algo i hms. Au ho s in [
13
]
di ided hese algo i hms in o i e g oups: (i) exac — he algo i hm is capable o inding
he global op imum; (ii) well known heu is ic algo i hms, such as Dynamic P og am-
ming (DP), Pa icle Swa m Op imiza ion (PSO), Gene ic Algo i hm (GA), o G adien
Algo i hm (GDA); (iii) lea ning algo i hms— hese algo i hms use lea ning p ocedu es;
(i ) enume a ion— inding
he bes solu ion using exhaus i e sea ch; and ( ) P oblem Spe-
ci ic Heu is ic (PSH)—a heu is ic algo i hm modi ied acco ding o he p oblem p ope ies.
PSH algo i hms a e he mos used om he lis o s udies, because hey a e mos likely o
gi e be e esul s since hey a e always sui ed o a speci ic case. PSH algo i hm is also
used in ou wo k, speci ically Cuckoo Sea ch (CUCKS) and Di e en ial E olu ion (DE)
algo i hms in modi ied e sion o se e ou models.
DE is a heu is ic algo i hm ha was de eloped in 1997 [
14
]. Di e en ial e olu ion
was used in many p e ious wo ks o UAV pa h planning, e.g., in [
15
] he au ho s p o-
pose a UAV co e ing me hod wi h di e en ial e olu ion as a cos op imiza ion algo i hm.
A me hod o imp o ing ene gy e iciency and op imize pa h planning was p oposed
in [
16
] and in [
17
]. CUCKS [
18
] is a ela i ely new algo i hm in oduced in 2009. I is a
me a-heu is ic algo i hm inspi ed by cuckoo bi ds beha io . Th ee esea ch wo ks we e
ound ela ed o UAV dis ibu ion ha used cuckoo sea ch. In [
19
] he au ho s p oposed
an imp o ed disc ee cuckoo sea ch algo i hm o econnaissance mission planning. T a-
jec o y planning based on CUCKS was p oposed in [
20
], whe e he au ho s ocused on
ene gy e iciency and h oughpu op imiza ion. CUCKS was compa ed o pa icle swa m
op imiza ion in [21], he goal he e was o e alua e online ou e planning me hods.
In addi ion, he pape s summa ized in he o e iew [
13
], a summa y o mos ecen
pape s is p o ided in his sec ion, aking in o accoun pape s be ween he yea s 2018
and 2021. All pape s ocus on he loca ion op imiza ion p oblem wi h FBSs, i.e., how o
op imally dis ibu e he FBSs in o de o minimize o maximize one o mo e pa ame e s.
Twel e pape s om he pas ou yea s we e selec ed and hey a e summa ized in
Table 1
.
The pape s o m ou g oups acco ding o hei goals. In he i s g oup, he au ho s aim
o minimize he numbe o equi ed FBSs [
22
–
26
], in he second, o achie e maximum
co e age o UEs [
26
–
30
], in he hi d, o maximize he ne wo k h oughpu [
31
,
32
], and,
in he ou h, o maximize he spec al e iciency [
33
]. The op imiza ion p oblem is ei he
sol ed by exis ing algo i hms o hei combina ion [
24
,
27
,
28
,
32
,
33
] o a new algo i hm is
de eloped o de i ed om a p e ious algo i hm [22,23,25,29,31].
In ou esea ch, he op imiza ion p oblem is sol ed by he CUCKS and DE algo i hms.
Nei he o he algo i hms we e used o he op imiza ion simila o ou s, i.e., minimiza ion
o he numbe o FBSs. The algo i hms we e selec ed as p omising algo i hms ecen ly
used o a wide a ea o op imiza ion p oblems.
Table 1. Summa y o he mos ecen pape s on loca ion op imiza ion p oblem in FBSs use-cases.
Used Algo i hms Use-Case Objec i e Published
Mul i-Popula ion GA o ho izon al
dimensions placemen , Mixed In e-
ge Second O de Cone P oblem o
al i ude placemen .
Conges ed a ea con aining a se o
use s. The e es ial Base S a ion
(BS) canno p o ide se ice o use s.
A UAV BS is deployed in o de o
p o ide se ice o as many use s
as possible. The use s ha e di e -
en Quali y o Se ice (QoS) equi e-
men s.
Max. no. o co -
e ed UEs wi h di e -
en QoS.
2018 [27]
No el alg.: Adap i e Mul iple d one
base S a ion placemen .
UAV BS se e as elays in ho spo
a ea o assis o he mac o BS
Min. no. o UAVs
and sa is y he QoS o
UEs.
2018 [22]
Senso s 2021,21, 5580 5 o 22
Table 1. Con .
Used Algo i hms Use-Case Objec i e Published
Geome ic elaxa ion, K-means de-
ploymen , Powe e icien K-means
deploymen , Robus Deploymen
wi h impe ec use loca ion in o -
ma ion.
Te es ial in as uc u e is una ail-
able. Requi ed suppo om UAV
BS.
Max. no. o co e ed
UEs.
2018 [28]
Cen alized deploymen algo i hm,
dis ibu ed mo ion con ol algo-
i hm.
UEs a e dis ibu ed andomly and in
clus e s, also, s a ic and dynamic sce-
na ios a e conside ed. Two en i on-
men s – wi h and wi hou obs acles.
Two di e en ini ial s a es o FBSs.
Min. numbe o
UAVs, co e all UEs.
Max. no. o co e ed
UEs.
2018 [26]
No el alg. based on GA.
Real en i onmen wi h di e en UE
densi ies.
Max. no. o co e ed
UEs.
2019 [29]
No el alg.: Edge-p io .
Random use dis ibu ion wi h
known posi ions.
Min. numbe o
UAVs, co e all UEs.
2019 [23]
No el alg. based on GA.
Exis ing deploymen o s a ic base
s a ions
Max. UE h oughpu
and min. consump-
ion.
2019 [31]
Hyb id alg.: Cen alized g eedy
sea ch alg. o de e mining he no.
o FBSs. Dis ibu ed mo ion alg. o
enabling each FBS o au onomously
con ol i s mo ion owa d he op i-
mal posi ion.
UAVs wi h o wi hou he suppo
o g ound BS. Dis ibu ion o UEs is
unknown.
Min. no. o UAVs,
max. load balance.
2019 [24]
UAV-a i icial bee colony.
Deploymen o UAV BS in pos dis-
as e scena io.
Max. ne wo k
h oughpu .
2019 [32]
No el alg.
mmWa e ne wo k, se ing all
g ound use s, p ede ined se o
loca ions.
Min. numbe o
UAVs, co e all UEs.
2020 [25]
K-means clus e ing and s able ma -
iage app oach o ind 2D posi ions.
Space cons ained exhaus i e sea ch
and PSO o ind he op imal al i udes
o he FBSs.
UEs a e dis ibu ed wi h homoge-
nous Poisson poin p ocess. When a
g ound s a ion is damaged and s ops
ansmi ing, UAVs a e deployed in
he a ea wi h los connec i i y.
Max. spec al e i-
ciency, main ain QoS.
2020 [33]
Sequen ial Exhaus i e Sea ch, Se-
quen ial Maximal Weigh ed A ea.
Ta ge a ea wi h wo se s o use s de-
manding ei he he same o di e en
QoS equi emen s.
Max. no. o co e ed
UEs wi h he same
and di e en QoS.
2021 [30]
3. Design o Ma hema ical Model and I s Implemen a ion
The e ec i e deploymen o UAV ac oss a selec ed a ea is a di icul ask. In his
wo k, he enhancemen o loca ion co e ing models is p esen ed (see Sec ion 3.4) o he
UAV deploymen o on-demand connec i i y scena ios. To ease he ma hema ical model
eadiness, in Table 2we p o ide he e minology used in he emaining pa o his pape
adap ed o he e ms used in he li e a u e.

Senso s 2021,21, 5580 6 o 22
Table 2. Mapping ma hema ical e minology o communica ion ne wo ks e minology.
Ma hema ical Te minology Wi eless Ne wo ks Te minology
Facili y UAV o base s a ion node
Demand A use in a gi en a ea
Capaci y
Th oughpu ha is eques ed by sum o use e-
qui emen s in a gi en a ea o co e
Mul iple se ice
A use equi es o be po en ially co e ed by he
x
UAV o base s a ion nodes.
Exis ing se ice
Usually base s a ion nodes ha al eady exis s in he
a ea o co e and should emain a e he econ ig-
u a ion o deploymen phase
3.1. Deploymen Model
The design o ou models is based on he so-called Loca ion Se Co e ing P oblem
(LSCP) [
34
] and Maximal Co e ing Loca ion P oblem (MCLP) [
35
] models om he a ea o
acili y loca ion p oblems. These models ha e many ex ensions p esen ed in he li e a u e,
howe e , none o hese models and ex ensions i in o ou use-case. The gap in he
li e a u e ha we encoun e is ha he models a e no conside ing he combina ion o he
ollowing ac o s:
• (i) each demand capaci y is assigned o jus one acili y a a gi en momen ;
•
(ii) conside a ion o exis ing se ices ( he capaci y o exis ing BTS nodes in a gi en
a ea mus be aken in o accoun );
•
(iii) he acili y capaci ies and demand capaci ies should be ep esen ed sepa a ely o
downlink and uplink and no as jus a numbe al oge he because he ese ed a io
o uplink and downlink may di e o each node sepa a ely;
•
(i ) he possibili y o selec loca ions om he o iginal da ase ha may no be co e ed.
This is impo an when we ind ou ha o co e he whole a ea we need mo e acili ies
(UAVs) han is a ailable. We can educe he less impo an a eas and p obably sa e
some acili ies.
Implici ly we assume ha he equi emen o he co e age a ailabili y (dis ance o
su icien signal powe in ou case including in e e ence conside a ion) om acili y o
demand is always me . Fu he in his pa ag aph, we e e ence he abo e-men ioned model
equi emen s when discussing he a ailable op imiza ion models in he li e a u e. The
ma hema ical model and he need o he i s equi emen (i) was o iginally discussed
in [36,37]
bu his need was no de ined in he model, only discussed. Fu he ,
in [38]
, he
model included ha equi emen . The second equi emen (ii) is ma hema ically de ined
in [39]
o LSCP and u he ex ended o MCLP model
in [40]
. The hi d aspec (iii) is, o
he bes o ou knowledge, no co e ed in he li e a u e, e en he ecen a icle [
41
] on ha
opic does no conside i . The las equi emen (i ) is a special e sion o he so-called
Mul i-Se ice Loca ion Se Co e ing P oblem (MS-LSCP) ha is conside ing mul iple
co e ages o speci ic demands [
42
] bu always se o ze o since he co e age equi emen
om he demand o a acili y is always ze o. Based on ha , we de eloped a new model
ha a ge s all he abo e-men ioned equi emen s al oge he .
To de i e a ma hema ical model le us se he ollowing no a ion:
•I= a se o acili y si es (UAV) 1, 2, . . . , m;
•J= a se o demand a eas (cus ome s) 1, 2, . . . , n;
•dij = he sho es dis ance be ween acili y iand demand j;
•Dmax
= maximum dis ance which will be accep ed o ope a ion be ween he acili ies
and demands;
•lj= numbe o acili ies equi ed o se icing demand j;
•xi∈ {
0, 1
}
, whe e
xi=
1 means ha acili y
i
is selec ed, while
xi=
0 means ha i is
no selec ed;
Senso s 2021,21, 5580 7 o 22
•Nj={i|dij ≤Dmax}.
Fo he sake o simplici y, he acili y si es will be e e ed as acili y and demand a eas
as demand.
The MS-LSCP can be o mula ed as ollows: minimize he numbe o acili ies needed
o co e he whole a ea, and loca e hem in such a manne o p o ide co e age o each
demand by a eques ed numbe o acili ies o a speci ic demand. In p ac ice, his is
impo an o back-up co e age o especially impo an demands o educe he cases when
some o he acili ies ail and he impo an demand loses he connec ion. Fo mally:
Minimize
∑
i∈I
xi(1)
subjec o
∀j∈J:∑
i∈Nj
xi≥lj(2)
∀i∈I:xi∈ {0, 1}(3)
I
lj=
1 o each demand
j
, hen he abo e model is simpli ied o a single case, known
as he classical LSCP. I lj=0 hen demand jdoes no need o be co e ed.
Howe e , in eal si ua ions besides (o ins ead o ) he MS-LSCP wi hin he p ede ined
ange, i is mo e impo an o conside capaci ies o acili ies. Since in ou conside ed
scena io we ha e o deal wi h he high densi y o use s ha a e simul aneously connec ed,
we assume he ollowing addi ional no a ions:
•Ci= capaci y o acili y i;
•aj= amoun o demand a j;
•yij ∈ {
0, 1
}
= non- agmen ed demand om loca ion
j
is assigned (1) o is no assigned
(0) o acili y i.
Fu he , he e is a se o exis ing acili ies
E
(exis ing base s a ion nodes in he a ea),
and i s co esponding decision a iables
xi
,
i∈E
a e se o 1. Now, assume ha capaci ies
and demands a e di ided in o uploads and downloads. Fo example, om he use ’s poin
o iew, he demand o 100 Mbi /s may be di ided in o 80 Mbi /sec o download and 20
Mbi /s o upload. To each ha expec a ions assume he ollowing:
•Cu
i= upload capaci y o acili y i;
•Cd
i= download capaci y o acili y i;
•au
j= upload amoun o demand a j;
•ad
j= download amoun o demand a j.
Howe e , i s ill mus be sa is ied ha he demand
j
( o download and upload a he
same ime) is di ec ed o jus one acili y
i
, and he meaning o
yij
emains he same as
men ioned abo e. Now, le us combine all hese assump ions in o he ollowing model:
Minimize
(1+ε)∑
i/∈E
xi+∑
i∈E
xi(4)
subjec o
∀j∈J:∑
i∈Nj
xi≥lj(5)
∀j∈J:∑
i∈Nj
yij =1 (6)
Senso s 2021,21, 5580 8 o 22
∀i∈Nj:Cu
ixi≥∑
j∈J
yijau
j(7)
∀i∈Nj:Cd
ixi≥∑
j∈J
yijad
j(8)
(∀i∈I)(∀j∈J):yij ≤xi(9)
(∀i∈I)(∀j∈I)(i6=j):dij ≥dminxixj(10)
∀i∈E :xi=1 (11)
∀i∈I:xi∈ {0, 1}(12)
(∀i∈I)(∀j∈J):yij ∈ {0, 1}, (13)
whe e
ε
is he addi ional cos o building a new acili y as compa ed o keeping an exis ing
one. The cos canno be easily calcula ed as i depends on many a iables, e.g., BS loca ion,
di icul y o ins alla ion o emo al, building, and law p ocessing. The se ice p o ide
mus es ima e his pa ame e o each pa icula loca ion.
Since cons ain (10) is non-linea , we eplace i by he ollowing equa ion wi hou he
p oduc o bina y a iables xiand xj o ob ain a mixed in ege p og amming model.
(∀i∈I)(∀j∈I)(i6=j):dij ≥(xi+xj−1)dmin (14)
Cons ain (6) gua an ees ha he demand
j
is assigned o jus one acili y a a gi en
momen . All selec ed acili ies mus ha e a su icien sum o hei capaci ies o uploads
and downloads o co e all upload and download demands (in p ac ice, his is an ideal
case, ne wo k ope a o s a e ying o each ha s a e wi h he a ailable esou ces). This
is gua an eed by cons ain s (7) and (8). I a acili y is selec ed o be emo ed om he
ne wo k in as uc u e, none o he demand should be assigned o i , his is gi en by
cons ain (9). To educe he possible in e e ences we include he cons ain ep esen ed
by cons ain (10). The
dij
,
i∈I
,
j∈I
is he dis ance be ween cen es
i
and
j
. Fo all UAV
pai s he dis ance will be g ea e o equal han a ce ain h eshold ha can signi ican ly
educe he signal o e laps ha usually inc eases he in e e ences.
Fu he , as i is ypical in loca ion co e ing pape s whe e he model enhancemen s a e
p esen ed, we p o ide an al e na i e in e ms o a maximiza ion model. This maximiza ion
model conside s a p ede ined numbe o new acili ies (deno ed as
p
) o be loca ed wi h
he aim o co e as much as possible, deno ed by p:
Maximize
∑
i∈Nj
∑
j∈J
yijaj(15)
subjec o
∀j∈J:∑
i∈Nj
xi≥lj(16)
∀j∈J:∑
i∈Nj
yij =1 (17)
∀i∈Nj:Cu
ixi≥∑
j∈J
yijau
j(18)
∀i∈Nj:Cd
ixi≥∑
j∈J
yijad
j(19)
(∀i∈I)(∀j∈J):yij ≤xi(20)
(∀i∈I)(∀j∈I)(i6=j):dij ≥(xi+xj−1)dmin (21)
Senso s 2021,21, 5580 9 o 22
∀i∈E :xi=1 (22)
∑
i/∈E
xi=p(23)
∀i∈I:xi∈ {0, 1}(24)
(∀i∈I)(∀j∈J):yij ∈ {0, 1}. (25)
3.2. Model Limi a ions
The p oposed model has se e al limi a ions ha should be add essed when adop ing
he model. In he ollowing lis o limi a ions we would like o highligh wha should be
imp o ed in u u e esea ch wo k.
•
The model does no modi y he FBSs’ con igu a ions. The model uses he op imal con-
igu a ion o e e y single FBS, howe e , in he inal s ep, he FBS can modi y some
pa ame e s, e.g., he ansmission powe o sa e ene gy o o op imize spec al e i-
ciency. In his model, we decided no o exceed he eal compu a ion complexi y o he
model, because i would lead o wo NP-ha d p oblems in one model. We sugges he
adop e s o he model o op imize hese con igu a ions in he nex p ocessing phase.
Fo example, he ein o cemen lea ning echniques can be applied o op imiza ion
o he FBS’s pa ame e s o p o ide a sui able solu ion.
•
The model conside s one way o educe he in e e ences. In he model, he in e e ences
can be educed by se ing he minimal dis ance be ween any wo FBSs. Howe e ,
he model can also include addi ional ways o educe he in e e ences, e.g., o add
ano he objec i e o ind he highes dis ance be ween he BS loca ions;
•
The model is de ined o s a ic scena ios. I he use s unexpec edly change hei loca ions,
he cu en op imal loca ions ha e o be e-compu ed. In p ac ice, i may no p esen a
p oblem since he da a can be p epa ed be o ehand wi h sui able es ima es o use
equi emen s om he pa icula loca ions. I necessa y, he compu a ion e- un
o new equi emen s is a ask ha can be un pe iodically, e.g., e e y 3, 5, 10 min,
acco ding o he equi emen s.
3.3. Model Compu a ional Complexi y Conside a ions
The size o he sea ch space is de e mined by he numbe o all possible selec ions o
acili ies. Fo m acili ies, acco ding o he binomial heo em, i is equal o
m
1+m
2+m
3+· · · +m
m= (1+1)m−1=O(2m). (26)
Fu he mo e, we need o ind he mos complex condi ion in ex ended models o
m<n
(whe e
n
is he numbe o demand a eas) o ind he esul ing compu a ional com-
plexi y. In he minimiza ion model hese a e cons ain (9), and (13) in he co esponding
cons ain s o he maximiza ion model, which equi e
m·n
ope a ions. Based on ha he
esul ing ime complexi y o hese models is O(2mmn).
3.4. Designa ed Implemen a ion
The ma hema ical model om he Sec ion 3.1, enhancing he LSCP and MCLP models
ha a e o iginally e ol ed om SCP, alls in o
N P − comple e
class o p oblems. In his
sec ion, we p oposed he implemen a ion o a designed model p esen ed in cons ain s (4)
o Equa ion (13) using wo heu is ic algo i hms ha ease he in eg a ion and ep oducibili y
o he p oposed solu ion in o a so wa e solu ion ha may use hem.
Since he o iginal model SCP is
N P − comple e
, i is sui able o employ heu is ic
algo i hms o sol e such asks o la ge da ase s (mo e han 55-60 UAVs), o each a solu ion
in a easonable ime. Fo he UAV deploymen use-case o his pape , wo p omising me a-
heu is ic algo i hms we e chosen. Fi s , he CUCKS algo i hm wi h Lé y Fligh s [
43
,
44
],
and he DE [15,45], ha can p o ide a sui able solu ion o his p oblem.
Senso s 2021,21, 5580 16 o 22
o each algo i hm. In hese uns, he esul ing numbe o FBSs a ied om he bes esul
o plus one o wo mo e loca ions. The esul s a e shown in Table 7.
Table 6. Tes ing en i onmen pa ame e s.
OS Sys em Type CPU RAM
Windows 10 PRO 64-bi Ope a ing Sys em,
x64-based p ocesso
In el(R) Co e(TM) i7-7700
CPU @ 3.60 GHz 3.60 GHz
16.0 GB
Two cases o FBS deploymen we e in es iga ed, one whe e FBSs a e dis ibu ed
e enly in a g id inside he whole a ea and second whe e he FBSs a e also dis ibu ed
e enly bu on he edges o he a ea. The second deploymen was in es iga ed o cases
when FBSs a e no allowed o ly o e c owded a eas o sa e y easons. The o iginal
dis ibu ion o he i s case o da ase C is shown in Figu e 3, he FBSs a e deployed
in a g id wi h dis ances o 100 m. This lead o he o al numbe o 70 ini ial deploymen
loca ions. The ini ial loca ions o he second case o da ase G a e shown in Figu e 6. He e,
he dis ances be ween FBSs we e sho ened o 50m o each simila numbe o o iginal
loca ions as in case one. The numbe o ini ial loca ions plays a big ole in calcula ion ime o
he minimized solu ion. Acco ding o he esul s om Table 7, i was p o en ha numbe s
be ween 60 and 70 symbolize a ce ain h eshold o calcula ion complexi y, because o
he da ase s D and H whe e he numbe s o ini ial loca ions we e 90 and 85 p olonged he
calcula ion ime adically. Longe ime would comp omise he use ulness o he algo i hms
o epea ed use in sho pe iods o ime, o ins ance in case o high use mobili y. On he
o he hand, i would make he esul mo e accu a e.
Figu e 3. O iginal dis ibu ion g id wi h FBSs placed inside o he a ea o da ase C.
The p ocessing o he algo i hms akes ce ain amoun o ime. Speci ically o da ase s
C and G, p ocessing o he CUCKS ook 2274 s o he case wi h he BS inside o he a ea
and 1856 s o he BS ou side o he a ea. These alues a e app oxima ely ou o six imes
highe han hose o DE: 373 s o he case wi h he BS inside o he a ea and 387 s o he BS
ou side o he a ea. The numbe o esul ing loca ions in all ou cases was en. The eason
o his was likely ha he equi ed a e age da a- a e o all use s combined a each momen
was 29,610 Mb/s. I his alue is di ided by he a ailable h oughpu on each FBS (3 Gb/s),

Senso s 2021,21, 5580 17 o 22
we achie e en. This means ha he esul ing numbe o loca ions is highly a ec ed by he
h oughpu limi o he FBSs a he han by he adius o hei wi eless de ices.
Figu e 4. Cuckoo sea ch esul ing g id o da ase C.
Figu e 5. Di e en ial e olu ion esul ing g id o da ase C.
The dis ibu ion o FBSs seems logical o bo h algo i hms and bo h cases. The
algo i hms alida e he expec ed esul ha mo e loca ions will be selec ed o e a eas wi h
highe use densi ies. I is isible mo e in he cases wi h loca ions inside o he a ea, i.e.,
Figu es 4and 5. Clea ly, he use densi y o ces he algo i hms o selec mo e loca ions in
he dense a eas. Bo h algo i hms gi e simila esul s in e ms o FBS dis ibu ion, howe e
i he p e e ence was he calcula ion ime, he DE should be he a o able op ion. The
sho e calcula ion ime would be app ecia ed in scena ios whe e he FBSs’ posi ion would
Senso s 2021,21, 5580 18 o 22
be cons an ly upda ed. The eason why DE is so much as e han CUCKS is ha he DE
algo i hm is no gene a ing he new pool o solu ions o each gene a ion in opposi e o he
CUCKS algo i hm.
Figu e 6. O iginal dis ibu ion wi h use s ou side o he a ea o da ase G.
Table 7. Calcula ion esul s o CUCKS and DE algo i hms using 10,000 i e a ions.
Theo . No. o Candida e
Loca ions o Deploy UAVs
CS DE CS DE Da ase
Numbe o FBS Calc. Time, s
FBS gene a ed inside o he a ea
30 10 10 1019 329 A
50 10 10 1850 358 B
70 10 10 2274 373 C
90 10 10 3156 554 D
FBS gene a ed ou side o he a ea
25 10 10 918 302 E
45 10 10 1530 369 F
65 10 10 1856 387 G
85 10 10 2844 523 H
The da a- a e and adius pa ame e s used in he scena io we e de i ed om heo e i-
cal capabili ies o wo echnologies—IEEE 802.11ac and IEEE 802.11ad. E en hough he
esul s suppo he heo e ical alues, i is di icul o p edic he ou come o a eal imple-
men a ion because he e a e s ill a g ea numbe o a iables du ing li e es , e.g., wea he
condi ions, in e -BS and in e -use in e e ence, and apid use mobili y. Tha means, eal
measu emen s a e equi ed o suppo he heo e ical alues. E en hough he measu e-
men s would show much lowe pe o mance, u u e o mmWa e communica ions migh
p o ide e en g ea e and mo e s able pa ame e s wi h he new IEEE 802.11ay s anda d. I
is an upda ed IEEE 802.11ad s anda d p omising ex ended ange and highe h oughpu
p o ided by newly implemen ed mul iple-inpu and mul iple-ou pu (MIMO) ea u e.
Senso s 2021,21, 5580 19 o 22
Figu e 7. Cuckoo sea ch esul ing g id o da ase G.
Figu e 8. Di e en ial e olu ion esul ing g id o da ase G.
Le us now discuss he limi a ions o used me hods in his esea ch. The limi a ions
lie in he ini ial numbe o FBSs loca ions, since inc easing his numbe would ex end
d ama ically he calcula ion ime. As i was es ablished o ou case, his would no be
such a c i ical issue because o he high numbe o use s in he a ea. In some o he cases
howe e , i migh be c ucial o posi ion he FBSs in o mo e p ecise spo s. Fu he , in ou
scena io, he e is heo e ically unlimi ed numbe o FBSs a ailable o co e he a ea. I
he use equi emen s would ise o i he FBS capabili ies would be lowe , he numbe o
FBSs could ise o he poin whe e he o al implemen a ion p ice would make he solu ion
un easible. This condi ion can be implemen ed in he algo i hm, howe e i is no o he
eason ha au ho s wan ed o keep he decision making unde hei con ol.
Senso s 2021,21, 5580 20 o 22
Fo u u e esea ch di ec ions we expec o implemen and e i y mo e heu is ic
algo i hms and also p o ide addi ional models a ge ing a si ua ion in which he e is a
speci ic numbe o d ones (signi ican ly limi ed esou ces). The ocus will be mo e on how
o co e as mos as possible loca ions using he op imized heu is ic pa ame e s, wi h a
de ailed ocus on scena ios whe e he use s a e quickly mo ing o di e en loca ions.
One o he impo an ac o s o be conside ed is bo h in e -BS and in e -use in e e -
ence. Including in e e ence educ ion in o desc ibed algo i hms would adically inc ease
complexi y o he solu ion in he way ha i would become e en mo e di icul o ob ain
a solu ion wi h ega ds o calcula ion ime and compu a ional complexi y. One op ion o
add ess he in e e ences p oblem is in he nex s age a e ob aining he solu ion om he
algo i hms. This is planned as he nex s ep in his esea ch. The e a e a ious app oaches
o add ess he in e e ence p oblem om which he ollowing app oaches a e planned by
he au ho s:
• Se ing minimum dis ance om one FBS o ano he ;
•
Using ma hema ical model wi h mul i-objec i e unc ion–minimize numbe o FBSs
and maximize dis ance be ween BSs;
• Reducing adius o he FBSs by educing an enna gain;
• Using di e en adio equencies among neighbo ing FBSs.
5. Conclusions
The key objec i e o his pape was he op imal FBS dis ibu ion o e a desi ed a ea
while minimizing he numbe o necessa y FBSs. Two no el ma hema ical models we e
designed o his pu pose. The models ake in o accoun se e al aspec s ha a e c ucial
in he p esen ed scena io. I includes he capaci ies o bo h downlink and uplink, he
conside a ion o exis ing base s a ion nodes in he UAV deploymen a ea, and he possibili y
o selec lowe p io i y loca ions ha may be excluded om he co e age. Fu he , we
conside he compu a ional complexi y o hese models o e y la ge da ase s, which a e
de ined by ens o housands o use s and ens o FBSs. We employ cuckoo sea ch and
di e en ial e olu ion algo i hms wi h he de eloped
epai Ope a o
p o iding a easible
solu ion o his p oblem.
To e i y he iabili y o he models, da a om a eal-li e scena io we e used. The
P esen ed scena io was a c owded music es i al wi h a ious use densi ies. Two use-cases
o FBS dis ibu ion we e es ed. Fi s wi h FBSs dis ibu ed inside he a ea and second
wi h FBSs ou side he a ea. The wo algo i hms we e implemen ed and he op imal solu ion
was ob ained ia ex ensi e simula ions wi h eigh da ase s. Bo h o he algo i hms we e
able o ind a solu ion. Majo di e ence was in he compu a ion ime whe e he CUCKS
ob ained esul s in ime h ee o six imes highe o he wo use-cases han he DE. I is
howe e impo an o conside ha e en hough he highe numbe o candida e loca ions
can p o ide highe accu acy o he inal solu ion, i can lead o unnecessa y wai ing ime.
I is ecommended o u u e model adop e s o ind an op imal numbe o he candida e
loca ions sui able o hei speci ic use-case.
The da a used as inpu s o he implemen ed algo i hms we e mos ly based on heo e -
ical alues, and he esea ch would bene i g ea ly om suppo o eal-li e measu emen s.
The measu emen s migh e eal some de iciency in da a- a es and FBSs’ adii. One cause o
he de iciency migh be signal in e e ences, ha ha e no been add essed in his esea ch.
Howe e , as discussed in Sec ion 4.2, including in e e ences migh make ou models
excessi ely complex, hence he issue o in e e ences will be add essed in de ail in ou
u u e esea ch.
Au ho Con ibu ions:
Concep ualiza ion, J.P., P.S., J.H; me hodology, J.P., P.S.; so wa e, J.P., P.S.;
alida ion, J.P., P.S., M.S.; o mal analysis, P.S.; da a cu a ion, J.P., P.S., M.S.; w i ing—o iginal d a
p epa a ion, J.P., P.S.; w i ing— e iew and edi ing, J.H; isualiza ion, J.P.; supe ision, M.S., J.H. All
au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Senso s 2021,21, 5580 21 o 22
Funding:
The desc ibed esea ch was inanced by he Minis y o Indus y and T ade o Czech
Republic p ojec No. FV40309.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : No applicable.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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