Modeling Optimal Location Distribution for Deployment of Flying Base Stations as On-Demand Connectivity Enablers in Real-World Scenarios

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 . Re e ences 1. Ge asimenko, M.; Poko ny, J.; Schneide , T.; Si jo , J.; And ee , S.; Hosek, J. P o o yping Di ec ional UAV-Based Wi eless Access and Backhaul Sys ems. In P oceedings o he 2019 IEEE Global Communica ions Con e ence (GLOBECOM), Big Island, HI, USA, 9–13 Decembe 2019; IEEE: Pisca away, NJ, USA, 2019; pp. 1–6. 2. Wolpe , D.H.; Mac eady, W.G. No ee lunch heo ems o op imiza ion. IEEE T ans. E ol. Compu . 1997,1, 67–82. [C ossRe ] 3. K i e , J.; B é illie s, M.; Lepagno , J.; Idoumgha , L. On he op imal placemen o came as o su eillance and he unde lying se co e p oblem. Appl. So Compu . 2019,74, 133–153. [C ossRe ] 4. Shan hasheela, A.; Shanmuga adi u, P. Cuckoo Sea ch Based Fo es Co e Classi ica ion. J. Compu . Theo . Nanosci. 2019 , 16, 3550–3553. [C ossRe ] 5. Sadeghi, F.; A okh, A. Load-balanced da a ga he ing in In e ne o Things using an ene gy-awa e cuckoo-sea ch algo i hm. In . J. Commun. Sys . 2020,33, e4385. [C ossRe ] 6. Zhang, Y.; Yu, Y.; Zhang, S.; Luo, Y.; Zhang, L. An colony op imiza ion o Cuckoo Sea ch algo i hm o pe mu a ion low shop scheduling p oblem. Sys . Sci. Con ol. Eng. 2019,7, 20–27. [C ossRe ] 7. Thi ugnanasambandam, K.; P akash, S.; Sub amanian, V.; Po hula, S.; Thi umal, V. Rein o ced cuckoo sea ch algo i hm-based mul imodal op imiza ion. Appl. In ell. 2019,49, 2059–2083. [C ossRe ] 8. Cai, X.; Niu, Y.; Geng, S.; Zhang, J.; Cui, Z.; Li, J.; Chen, J. An unde -sampled so wa e de ec p edic ion me hod based on hyb id mul i-objec i e cuckoo sea ch. Concu . Compu . P ac . Exp. 2020,32, e5478. [C ossRe ] 9. Fo ouhi, A.; Ding, M.; Hassan, M. Se ice on demand: D one base s a ions c uising in he cellula ne wo k. In P oceedings o he 2017 IEEE Globecom Wo kshops (GC Wkshps), Singapo e, 4–8 Decembe 2017; IEEE: Pisca away, NJ, USA, 2017; pp. 1–6. 10. Fo ouhi, A.; Ding, M.; Hassan, M. Flying d one base s a ions o mac o ho spo s. IEEE Access 2018,6, 19530–19539. [C ossRe ] 11. Migna di, S.; Ve done, R. On he pe o mance imp o emen o a cellula ne wo k suppo ed by an unmanned ae ial base s a ion. In P oceedings o he 2017 29 h In e na ional Tele a ic Cong ess (ITC 29), Genoa, I aly, 4–8 Sep embe 2017; IEEE: Pisca away, NJ, USA, 2017; Volume 2, pp. 7–12. 12. Huang, S.; Teo, R.S.H.; Leong, W.L.; Ma inel, N.; Fo es , G.L.; Micheloni, C. Co e age Con ol o Mul i-Unmanned Ae ial Vehicles: A Sho Re iew. Unmanned Sys . 2018,6, 1–14. 13. Cicek, C.T.; Gul ekin, H.; Ta li, B.; Yanikome oglu, H. UAV base s a ion loca ion op imiza ion o nex gene a ion wi eless ne wo ks: O e iew and u u e esea ch di ec ions. In P oceedings o he 2019 1s In e na ional Con e ence on Unmanned Vehicle Sys ems-Oman (UVS), Musca , Oman, 5–7 Feb ua y 2019; IEEE: Pisca away, NJ, USA, 2019; pp. 1–6. 14. S o n, R.; P ice, K. Di e en ial e olu ion—A simple and e icien heu is ic o global op imiza ion o e con inuous spaces. J. Glob. Op im. 1997,11, 341–359. [C ossRe ] 15. Gonzalez, V.; Monje, C.A.; Ga ido, S.; Mo eno, L.; Balague , C. Co e age Mission o UAVs Using Di e en ial E olu ion and Fas Ma ching Squa e Me hods. IEEE Ae osp. Elec on. Sys . Mag. 2020,35, 18–29. [C ossRe ] 16. Wang, Z.; Liu, R.; Liu, Q.; Thompson, J.S.; Kadoch, M. Ene gy E icien Da a Collec ion and De ice Posi ioning in UAV-Assis ed IoT. IEEE In e ne Things J. 2019,7, 1122–1139. [C ossRe ] 17. Adhika i, D.; Kim, E.; Reza, H. A uzzy adap i e di e en ial e olu ion o mul i-objec i e 3D UAV pa h op imiza ion. In P oceedings o he 2017 IEEE Cong ess on E olu iona y Compu a ion (CEC), San Sebas ián, Spain, 5–8 June 2017; IEEE: Pisca away, NJ, USA, 2017; pp. 2258–2265. 18. Yang, X.S.; Deb, S. Cuckoo sea ch ia Lé y ligh s. In P oceedings o he 2009 Wo ld Cong ess on Na u e & Biologically Inspi ed Compu ing (NaBIC), Coimba o e, India, 9–11 Decembe 2009; IEEE: Pisca away, NJ, USA, 2009; pp. 210–214. 19. Zhang, Y.Z.; Li, H.; Ma, Y.H.; Zhang, J.D.; He, J.L. Coope a i e econnaissance mission planning o he e ogeneous UAVs wi h DCSA. In P oceedings o he 2019 IEEE 15 h In e na ional Con e ence on Con ol and Au oma ion (ICCA), Edinbu gh, UK, 16–19 July 2019; IEEE: Pisca away, NJ, USA, 2019; pp. 417–422. 20. Zhu, K.; Xu, X.; Han, S. Ene gy-e icien UAV ajec o y planning o da a collec ion and compu a ion in mMTC ne wo ks. In P oceedings o he 2018 IEEE Globecom Wo kshops (GC Wkshps), Abu Dhabi, UAE, 9–13 Decembe 2018; IEEE: Pisca away, NJ, USA, 2018; pp. 1–6. 21. Góez-Sánchez, G.D.; Ja amillo-Ga zón, J.A.; Velásquez, R.A. Pe o mance compa ison o pa icle swa m op imiza ion and Cuckoo sea ch o online ou e planning. IEEE Ae osp. Elec on. Sys . Mag. 2018,33, 40–50. [C ossRe ] 22. Zhang, S.; Sun, X.; Ansa i, N. Placing mul iple d one base s a ions in ho spo s. In P oceedings o he 2018 IEEE 39 h Sa no Symposium, Newa k, NJ, USA, 24–25 Sep embe 2018; IEEE: Pisca away, NJ, USA, 2018; pp. 1–6. Senso s 2021,21, 5580 22 o 22 23. Qin, J.; Wei, Z.; Qiu, C.; Feng, Z. Edge-P io Placemen Algo i hm o UAV-Moun ed Base S a ions. In P oceedings o he 2019 IEEE Wi eless Communica ions and Ne wo king Con e ence (WCNC), Ma akech, Mo occo, 15–18 Ap il 2019; IEEE: Pisca away, NJ, USA, 2019; pp. 1–6. 24. Wang, H.; Zhao, H.; Wu, W.; Xiong, J.; Ma, D.; Wei, J. Deploymen algo i hms o lying base s a ions: 5G and beyond wi h UAVs. IEEE In e ne Things J. 2019,6, 10009–10027. [C ossRe ] 25. Si alingam, T.; Manosha, K.S.; Raja he a, N.; La a-aho, M.; Dissanayake, M.B. Posi ioning o Mul iple Unmanned Ae ial Vehicle Base S a ions in u u e Wi eless Ne wo k. In P oceedings o he 2020 IEEE 91s Vehicula Technology Con e ence (VTC2020-Sp ing), An we p, Belgium, 25–28 May 2020; IEEE: Pisca away, NJ, USA, 2020; pp. 1–6. 26. Zhao, H.; Wang, H.; Wu, W.; Wei, J. Deploymen algo i hms o UAV ai bo ne ne wo ks owa d on-demand co e age. IEEE J. Sel. A eas Commun. 2018,36, 2015–2031. [C ossRe ] 27. Chen, Y.; Li, N.; Wang, C.; Xie, W.; X , J. A 3D placemen o unmanned ae ial ehicle base s a ion based on mul i-popula ion gene ic algo i hm o maximizing use s wi h di e en QoS equi emen s. In P oceedings o he 2018 IEEE 18 h In e na ional Con e ence on Communica ion Technology (ICCT), Chongqing, China, 8–11 Oc obe 2018; IEEE: Pisca away, NJ, USA, 2018; pp. 967–972. 28. Sun, J.; Masou os, C. Deploymen s a egies o mul iple ae ial BSs o use co e age and powe e iciency maximiza ion. IEEE T ans. Commun. 2018,67, 2981–2994. [C ossRe ] 29. Lai, C.C.; Chen, C.T.; Wang, L.C. On-demand densi y-awa e UAV base s a ion 3D placemen o a bi a ily dis ibu ed use s wi h gua an eed da a a es. IEEE Wi el. Commun. Le . 2019,8, 913–916. [C ossRe ] 30. Adam, N.; Tappa ello, C.; Heinzelman, W.; Yanikome oglu, H. Placemen op imiza ion o mul iple UAV base s a ions. In P oceedings o he 2021 IEEE Wi eless Communica ions and Ne wo king Con e ence (WCNC), Nanjing, China, 29 Ma ch 2021 ; IEEE: Pisca away, NJ, USA, 2021; pp. 1–7. 31. Bec a , Z.; Mach, P.; Plachy, J.; de Tudela, M.F.P. Posi ioning o Flying Base S a ions o Op imize Th oughpu and Ene gy Consump ion o Mobile De ices. In P oceedings o he 2019 IEEE 89 h Vehicula Technology Con e ence (VTC2019-Sp ing), Kuala Lumpu , Malaysia, 28 Ap il–1 May 2019; IEEE: Pisca away, NJ, USA, 2019; pp. 1–7. 32. Li, J.; Lu, D.; Zhang, G.; Tian, J.; Pang, Y. Pos -Disas e Unmanned Ae ial Vehicle Base S a ion Deploymen Me hod Based on A i icial Bee Colony Algo i hm. IEEE Access 2019,7, 168327–168336. [C ossRe ] 33. Hydhe , H.; Jayakody, D.N.K.; Hemachand a, K.T.; Sama asinghe, T. In elligen UAV deploymen o a disas e - esilien wi eless ne wo k. Senso s 2020,20, 6140. [C ossRe ] 34. ReVelle, C.; To egas, C.; Falkson, L. Applica ions o he loca ion se -co e ing p oblem. Geog . Anal. 1976,8, 65–76. [C ossRe ] 35. Chu ch, R.; ReVelle, C. The maximal co e ing loca ion p oblem. Pap. Reg. Sci. 1974,32, 101–118. [C ossRe ] 36. Cu en , J.R.; S o beck, J.E. Capaci a ed co e ing models. En i on. Plan. B Plan. Des. 1988,15, 153–163. [C ossRe ] 37. Ge a d, R.A. The Loca ion o Se ice Facili ies Using Models Sensi i e o Response Dis ance, Facili y Wo kload, and Demand Alloca ion. Ph.D. Thesis, Uni e si y o Cali o nia, San a Ba ba a, CA, USA, 1995. 38. Seda, P.; Seda, M.; Hosek, J. On Ma hema ical Modelling o Au oma ed Co e age Op imiza ion in Wi eless 5G and beyond Deploymen s. Appl. Sci. 2020,10, 8853. [C ossRe ] 39. Plane, D.R.; Hend ick, T.E. Ma hema ical p og amming and he loca ion o i e companies o he Den e i e depa men . Ope . Res. 1977,25, 563–578. [C ossRe ] 40. Mu ay, A.T. Op imising he spa ial loca ion o u ban i e s a ions. Fi e Sa . J. 2013,62, 64–71. [C ossRe ] 41. Chauhan, D.; Unnik ishnan, A.; Figliozzi, M. Maximum co e age capaci a ed acili y loca ion p oblem wi h ange cons ained d ones. T ansp. Res. Pa C Eme g. Technol. 2019,99, 1–18. [C ossRe ] 42. Chu ch, R.L.; Ge a d, R.A. The mul i-le el loca ion se co e ing model. Geog . Anal. 2003,35, 277–289. [C ossRe ] 43. Yang, W.; Yang, H.; Tang, S. Op imiza ion and con ol applica ion o senso placemen in ae ose oelas ic o UAV. Ae osp. Sci. Technol. 2019,85, 61–74. [C ossRe ] 44. Song, P.C.; Pan, J.S.; Chu, S.C. A pa allel compac cuckoo sea ch algo i hm o h ee-dimensional pa h planning. Appl. So Compu . 2020,94 , 106443. [C ossRe ] 45. Huang, P.Q.; Wang, Y.; Wang, K.; Yang, K. Di e en ial E olu ion Wi h a Va iable Popula ion Size o Deploymen Op imiza ion in a UAV-Assis ed IoT Da a Collec ion Sys em. IEEE T ans. Eme g. Top. Compu . In ell. 2019,4, 324–335. [C ossRe ] 46. Alliance, N. Radio access pe o mance e alua ion me hodology. NGMN Whi e Pap. 2008,1, 36. 47. Rochim, A.F.; Ha ijadi, B.; Pu banug aha, Y.P.; Fuad, S.; Nug oho, K.A. Pe o mance compa ison o wi eless p o ocol IEEE 802.11 ax s 802.11 ac. In P oceedings o he 2020 In e na ional Con e ence on Sma Technology and Applica ions (ICoSTA), Su abaya, Indonesia, 20 Feb ua y 2020; IEEE: Pisca away, NJ, USA, 2020; pp. 1–5. 48. Zhu, X.; Dou exi, A.; Kocak, T. Th oughpu and co e age pe o mance o IEEE 802.11 ad millime e -wa e WPANs. In P oceedings o he 2011 IEEE 73 d Vehicula Technology Con e ence (VTC Sp ing), Budapes , Hunga y, 15–18 May 2011; IEEE: Pisca away, NJ, USA, 2011; pp. 1–5. 49. 3GPP. Requi emen s o Fu he Ad ancemen s o E ol ed Uni e sal Te es ial Radio Access (E-UTRA) (LTE-Ad anced); Technical Repo (TR) 36.913; Ve sion 15.0.0; 3 d Gene a ion Pa ne ship P ojec (3GPP): Valbonne, F ance, 2018. 50. Ho nyák, J.; Skˇ i ánek, P.; Mikuláš ík, K.; Radek, Z. In e ac i e Map o Deployed BTS in Czech Republic. A ailable online: h p://gsmweb.cz/ (accessed on 30 June 2021).