Tampere University of Technology

Flexible and Reliable UAV-Assisted Backhaul Operation in 5G mmWave CellularNetworks

CitationGapeyenko, M., Petrov, V., Moltchanov, D., Andreev, S., Himayat, N., & Koucheryavy, Y. (2018). Flexible andReliable UAV-Assisted Backhaul Operation in 5G mmWave Cellular Networks. IEEE Journal on Selected Areasin Communications, 36(11), 2486-2496. https://doi.org/10.1109/JSAC.2018.2874145Year2018

VersionPeer reviewed version (post-print)

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Published inIEEE Journal on Selected Areas in Communications

DOI10.1109/JSAC.2018.2874145

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1

Flexible and Reliable UAV-Assisted BackhaulOperation in 5G mmWave Cellular Networks

Margarita Gapeyenko, Vitaly Petrov, Dmitri Moltchanov,Sergey Andreev, Nageen Himayat, and Yevgeni Koucheryavy

Abstract—To satisfy the stringent capacity and scalabilityrequirements in the fifth generation (5G) mobile networks, bothwireless access and backhaul links are envisioned to exploitmillimeter wave (mmWave) spectrum. Here, similar to the designof access links, mmWave backhaul connections must also addressmany challenges such as multipath propagation and dynamic linkblockage, which calls for advanced solutions to improve theirreliability. To address these challenges, 3GPP New Radio (NR)technology is considering a flexible and reconfigurable backhaularchitecture, which includes dynamic link rerouting to alternativepaths. In this paper, we investigate the use of aerial relay nodescarried by e.g., unmanned aerial vehicles (UAVs) to allow for suchdynamic routing, while mitigating the impact of occlusions on theterrestrial links. This novel concept requires an understandingof mmWave backhaul dynamics that accounts for: (i) realistic3D multipath mmWave propagation; (ii) dynamic blockage ofmmWave backhaul links; and (iii) heterogeneous mobility ofblockers and UAV-based assisting relays. We contribute the re-quired mathematical framework that captures these phenomenato analyze the mmWave backhaul operation in characteristicurban environments. We also utilize this framework for a newassessment of mmWave backhaul performance by studying itsspatial and temporal characteristics. We finally quantify thebenefits of utilizing UAV assistance for more reliable mmWavebackhaul. The numerical results are confirmed with 3GPP-calibrated simulations, while the framework itself can aid in thedesign of robust UAV-assisted backhaul infrastructures in future5G mmWave cellular.

Index Terms—5G New Radio; millimeter wave; multipath3D channel model; UAV communications; integrated access andbackhaul; dynamic human body blockage; moving cells.

I. INTRODUCTION

Over the past years, the work on fifth-generation (5G)networks has achieved impressive results [1], [2]. 3GPP hasrecently ratified non-standalone 5G New Radio (NR) technol-ogy to augment further LTE evolution. Currently, the standard-ization has completed the standalone 5G NR specifications toallow for independent NR-based deployments [3]. Cateringfor high-rate and reliable wireless connectivity, the 5G cel-lular paradigm aims to densify the network with terrestrialbase stations [4] by additionally employing moving (e.g.,car-mounted) small cells for on-demand capacity boost aswell as harnessing more abundant millimeter-wave (mmWave)spectrum for both access and backhaul radio links [5], [6].

Manuscript received April 16, 2018; revised September 15, 2018; acceptedSeptember 28, 2018. This work was supported by Intel Corporation, andthe Academy of Finland (projects WiFiUS and PRISMA). The work of M.Gapeyenko was supported by Nokia Foundation. V. Petrov acknowledges thesupport of HPY Research Foundation funded by Elisa. (Corresponding author:Margarita Gapeyenko.)

M. Gapeyenko, V. Petrov, D. Moltchanov, S. Andreev, and Y. Kouch-eryavy are with Tampere University of Technology, Tampere, Finland (e-mail:{firstname.lastname, evgeni.kucheryavy}@tut.fi).

N. Himayat is with Intel Corporation, Santa Clara, CA, USA (e-mail:nageen.himayat@intel.com).

Despite the notable benefits of the mmWave band, it alsoposes new challenges due to highly directional mmWavelinks subject to complex multipath propagation, which issusceptible to link blockage phenomena because of a widerange of obstacles [7]–[9]. There has been a surge in researchwork on reliability analysis of mmWave access to outlinetechniques for mitigating the inherent limitations of mmWave-based communication [10]–[14].

As that work matures, provisioning of high-rate back-haul capabilities for 5G has attracted recent attention, asmmWave backhaul links remain vulnerable to similar block-age issues [15]. Aiming to assess and improve reliabilityof mmWave backhaul operation in 5G NR systems, 3GPPhas initiated a new study on integrated access and backhaul,which specifies the respective challenges and requirements.The panned specifications target to construct a flexible andreconfigurable system architecture with dynamic backhaulconnections. In this context, the capability to reroute backhaullinks in case of their blockage by moving humans and carbodies becomes essential [16]. Extending the 3GPP studies onthe matter, the utilization of unmanned aerial vehicles (UAVs)equipped with radio capabilities and acting as mobile relaynodes may be considered to further improve flexibility andreliability of backhaul operation.

The recent acceleration in user traffic fluctuations calls formore flexible and reliable backhaul solutions in 5G mmWavecellular, which may require dynamic rerouting. Therefore, theintegration of both terrestrial and aerial network components toachieve this goal is essential. The corresponding performanceassessment requires an appropriate evaluation methodologythat may capture the dynamics of backhaul links, mmWaveradio propagation properties, and blockage phenomena causedby moving objects. Different from mmWave access, the re-search literature on 5G mmWave backhaul is scarce. In [17],the authors propose an analytical model for coexistence ofaccess and backhaul links, while in [18] the capacity eval-uation of cellular networks with in-band wireless backhaulwas proposed. In [19], a performance evaluation of mmWavebackhaul links is conducted.

To the best of our knowledge, an integrated methodologyfor flexible mmWave backhaul operation with dynamic linksthat reroute subject to the channel conditions has not beenavailable as of yet. Addressing that gap, this work offers a newmethodology that can assess complex scenarios with multipleterrestrial and aerial base stations. These are equipped withmmWave backhaul capabilities and can reroute their links tomaintain uninterrupted connectivity over unreliable blockage-prone channels, while leveraging UAV-based relay assistanceas illustrated in Fig. 1.

Our considered scenario captures three important compo-

2

UAV-BS

hC

hB

NR-BS

hAhD

Blocker

COW-BS

UAV flight

Blocker's

path

Time

Time

TimeTo NR-BS

To UAV-BS

Outage

COW-BSbackhaulconnectivity

NR-BS isin outage

UAV-BSselected

NR-BS linkrestored

UAV-BS isin outage

NR-BS isin outage

NR-BS linkrestored

Backhau

l link

Fig. 1. Scenario of interest with UAV-BS assistance.

nents of future 5G mmWave backhaul solutions: (i) dynamicblockage of mmWave links; (ii) complex multipath propa-gation in urban environments; and (iii) flexible mobility ofassisting UAV relays. A range of simpler scenarios can also beassessed by applying the relevant components of our developedframework with opportunistic UAV mobility model (e.g., thosewith static deployment of UAV-based relays [20]–[22]). Thecontributions of this work are therefore as follows.• A novel mathematical framework that captures the es-

sential features of mmWave backhaul operation underdynamic blockage by moving humans as well as possiblelink rerouting to UAV-based relay nodes in realisticscenarios under 3D multipath propagation. This analyticalframework is further verified with detailed system-levelsimulations (SLS) that explicitly model the 3GPP 3Dmultipath propagation channel.

• A performance assessment of flexible mmWave backhauloperation in crowded urban deployments that includesboth time-averaged and time-dependent metrics of in-terest, such as outage probability and spectral efficiencytogether with outage and non-outage duration distribu-tions. A highlight of our methodology is characterizationof uninterrupted connectivity duration, which accountsfor tolerable outage time subject to application-specificrequirements.

• An understanding of benefits made available with UAVrelay assistance to mmWave backhaul reliability in re-alistic city scenarios. We demonstrate that under certainspeed, intensity, and service capacity, the use of UAV-based relays enables significant gains for the systemperformance. In particular, outage probability and out-age duration in the considered scenario become notablyreduced, while spectral efficiency increases substantially.

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

our system model of the target urban scenario is introduced.The analytical framework for time-averaged performance eval-uation of mmWave backhaul operation is outlined in Sec-tion III. Further, an analytical model to assess temporal metricsof interest in mmWave backhaul is contributed by Section IV.The corresponding numerical results that explore the spatialand temporal characteristics of flexible mmWave backhaulby leveraging assistance of UAV relay nodes are offered inSection V. Conclusions are drawn in the last section.

II. SYSTEM MODEL

A. Network deployment and COW-BSs

We consider a circular area with the radius of R, whereseveral “Cell on Wheels” base stations (COW-BSs) are dis-tributed uniformly according to a Poisson Point Process (PPP)with the density of λC . These COW-BSs provide connectivityto the human users in their vicinity and are equipped withmmWave backhaul links to the terrestrial New Radio basestations (NR-BSs) as well as aerial UAV-carried base stations(UAV-BSs) as illustrated in Fig. 2. In the scenarios whereover-provisioning leads to increased operator expenses (e.g.,temporary and unexpected events), on-demand network den-sification with COW-BSs might become a viable option. Theheight of a COW-BS is hC . A terrestrial NR-BS is located atthe circumference of the circle area at the height of hA. Sincethe height of a consumer vehicle is generally lower than thatof a pedestrian, the latter may act as a potential blocker tothe mmWave signal [23]. We assume that walking pedestriansform a PPP with the density of λB and the height of hB ,where hA > hB > hC .

The human blockers in our scenario are dynamic and theirtravel patterns are assumed to follow the Random DirectionMobility (RDM) model. The angle of movement in thisformulation is chosen uniformly within [0, 2π), while the timeof travel until the subsequent turn is distributed exponentially.The UAV-BSs may fly through the center of the circle byentering and leaving it at random points that are distributeduniformly across its circumference [24]. This work considers

NR-BS

COW-BS to NR-BS linkCOW-BS to UAV-BS link

UAV-BS trajectory

Clusters path

Blocker

COW-BS

UAV-BS

COW-BS

R

D0

D1

(vD, hD)

Blockers trajectory

(v, hB)

Fig. 2. Geometrical 2D illustration of target setup.

3

mobility of the UAV-BS as it becomes a distinguishing featurefor this new type of BSs. In [25], the authors demonstratethe benefits of dynamic over static UAV deployments. There-fore, mobility modeling is important to assess system-levelperformance in the scenarios where several types of BSs maycoexist. The speed of the UAV-BSs is vD and their altitudeis hD. The process of entering the circle by the UAV-BSs isassumed to be Poisson in time with the intensity of λD. Theremaining important notation is summarized in Table I.

B. 3D channel model and dynamic blockage of backhaul links

In order to model the mmWave backhaul links, we em-ploy the current 3GPP 3D multipath channel model [11]by taking into account all of the key features of mmWavecommunication. The model assumes that there are multiplealternative paths (named clusters) between the Tx and the Rx(see Fig. 3), each featured by its own delay, pathloss, andzenith of arrival/departure angles. Each of these paths can beblocked or non-blocked by the moving human blockers usingthe analytical model from [8].

The COW-BSs utilize beamsteering mechanisms to alwaysuse the best path, which is currently non-blocked and has thestrongest signal. Beamsteering employed at all the communi-cating nodes also minimizes the level of interference betweenthe backhaul links, thus making the considered mmWaveregime noise-limited [26]. Signal blockage by buildings isnot modeled, as none occlude the backhaul links between theCOW-BSs and the NR-BSs/UAV-BSs in the target scenario.

While the employed 3GPP model is sufficiently detailedand accurate [27], the complexity of the used algorithms [11]challenges its analytical tractability. Therefore, in our math-ematical study, we utilize a statistical approximation of thekey modeling parameters [28], such as power of every clustertransmitted by the NR-BS and the UAV-BS, PA,i and PD,i,and zenith angle of arrival (ZOA) for every cluster, θA,i andθD,i, where i = 1, 2, . . . , N is the cluster number.

C. mmWave backhaul connectivity model

The radio channel conditions of the backhaul links are dy-namic in nature due to temporal variations of the propagationenvironment. These are captured by the utilized propagationmodel [28], while the mobility of human blockers surroundingthe COW-BSs is modeled explicitly in our work. The NR-BSis assumed as the primary option for the backhaul links ofCOW-BSs (see Fig. 1). When COW-BS is currently in outage

UAV-BS

θD,iθA,1

NR-BS

COW-BS

LoS cluster

Reflected clus

terPA,i

PD,iPA,1 PD,1

Fig. 3. 3GPP-driven 3D multipath channel model.

TABLE ISUMMARY OF NOTATION AND PARAMETERS

Notation DescriptionDeployment

hA, hC , hD Heights of NR-BS, COW-BS, UAV-BSλC , λB Density of COW-BSs and blockers per unit arearB , v, hB Radius, speed, and height of a blockerR Radius of the service areaλD Temporal intensity of UAV-BSs entering the service

areaTD , vD Time and speed of UAV-BSs traversing the service

areaKD UAV-BS service capacity

TechnologyN Number of 3D multipath propagation clustersθA,i and θD,i ZOA of i-th cluster from NR-BS and UAV-BSfθA,i

and fθD,iPdf of ZOA of i-th cluster from NR-BS and UAV-BS

C and E[C] Spectral efficiency and its mean valuepO Outage probability∆O Tolerable outage durationTU and E[TU ] Uninterrupted connectivity time and its mean value

Mathematical frameworkpD,av Probability of UAV-BS availabilityPA and PD Received power at NR-BS to COW-BS and UAV-BS

to COW-BS linksfPA

and fPDPdf of received power at NR-BS to COW-BS andUAV-BS to COW-BS links

fPA,iand fPD,i

Pdf of power of i-th cluster arriving from NR-BSand UAV-BS

un Pmf of number of UAV-BSs available for COW-BSpA,i and pD,i Blockage probability of i-th cluster arriving from

NR-BS and UAV-BSλB,T Temporal intensity of blockers crossing the blockage

zoneTB and LB Time and distance walked inside the blockage zone

by a single blockerfη , fω Pdf of blocked and unblocked intervalsfO and fG Pdf of outage and non-outage duration

with respect to NR-BS (i.e., the signal received from NR-BSis too weak), COW-BS may temporarily reroute its backhaultraffic to UAV-BS traversing the area. Once the radio link toNR-BS recovers, COW-BS reconnects to the terrestrial NR-BSand reroutes its backhaul traffic back to it. Hence, the UAV-BSs are employed in unfavorable conditions to improve thecontinuity of backhaul links.

We measure the capacity of UAV-BS in terms of themaximum number of simultaneously supported backhaul links,which we denote as KD. This consideration reflects thepotential limitations of the mmWave radio equipment carriedby the UAV-BS as well as the specifics of the employednetwork architecture and connectivity protocols. In its turn,the connection between the UAV-BS and the core network isinherently characterized by unobstructed line-of-sight propa-gation without obstacles [29]. Therefore, this link is modeledas always reliable.

D. Illustrative metrics of interest

To assess the performance quality of the mmWave backhaullinks in the described scenario, we concentrate on two typesof metrics, namely, time-averaged and time-dependent. In theformer case, we address (i) outage probability, pO, and (ii)spectral efficiency, C. In the latter, we assume that the systemmay tolerate a certain fixed outage duration ∆O and thusderive (iii) the mean uninterrupted connectivity time, E[TU ].As intermediate parameters, we also obtain (iv) the outage andnon-outage duration distributions, fO and fG, respectively.

4

III. TIME AVERAGED ANALYSIS

In this section, we address the time-averaged system met-rics, including outage probability and spectral efficiency.

A. Outage ProbabilityThe outage probability pO for a randomly chosen COW-

BS in the area of interest is obtained as follows. Observe thatthe COW-BS is always associated with the NR-BS when thelatter is in non-outage conditions. Otherwise, the COW-BS isconnected to a randomly chosen UAV-BS that is available,provided that there is at least one UAV-BS in non-outageconditions having fewer than KD COW-BSs connected to it.Hence, the outage probability is produced as

pO = pA,O(u0 + (1− u0)(u0,n + (1− u0,n)pD,nav)), (1)

where u0 is the probability of having no UAV-BS traversingthe area at the moment, u0,n is the probability of havingno UAV-BS in non-outage conditions, pA,O and pD,nav arethe outage probability on the COW-BS to NR-BS link andthe probability that the UAV-BS is currently unavailable,respectively. In what follows, we derive these unknown terms.

1) Outage probability on COW-BS to NR-BS and COW-BSto UAV-BS links: Consider a randomly chosen COW-BS. LetpA,i be the probability that i-th cluster between the NR-BS andthe COW-BS is blocked and first consider blockage of the LoSpath, pA,1. Fixing the distance x between NR-BS and COW-BS, we observe that there is always a so-called blockage zoneas shown in Fig. 4. At any given instant of time t, the numberof blockers moving according to the RDM model within theservice zone follows a Poisson distribution [30]. Hence, theprobability that the LoS path is blocked is given by

pA,1(x) = 1− e(−2λBrB

[x

hB−hChA−hC

+rB]). (2)

Let D0 be a random variable (RV) denoting the 2D distancebetween the NR-BS and a randomly chosen COW-BS, and letfD0

(x) be its probability density function (pdf). Noticing thatthe COW-BSs are uniformly distributed within a service areacircle, the sought distance is [31]

fD0(x) =2x

πR2cos−1

( x

2R

), 0 < x < 2R. (3)

COW-BS

NR-BS

Blockagezone

Blocker

hC

hB

hA

D0

LB

rB

d

M1M2 M3

M4

M5

M6

M7

vt

vt

vt

vtξ2

2rB

Blockage on backhaul link, hC<hB

Fig. 4. Illustration of dynamic blockage process.

The LoS path blockage probability is then

pA,1 =

∫ 2R

0

fD0(x)pA,1(x)dx. (4)

Consider now the blockage probability for i-th cluster, i =2, 3, . . . , N . As opposed to the LoS path, the 3GPP model doesnot explicitly specify where the reflected cluster comes from.Instead, it provides the ZOA, θA,i and θD,i, i = 2, 3, . . . , N .In [28], it was shown that the ZOA for all clusters follows aLaplace distribution and we denote it as the pdf fθA,i

(y;x).The blockage probability pA,i(x) of every cluster is then

pA,i =

∫ π

−π

∫ 2R

0

fθA,i(y;x)pA,i(y)dxdy, (5)

where pA,i(y) is the blockage probability as a function of theZOA, derived as

pA,i(y) = 1− e[−2λBrB(tan y(hB−hC)+rB)]. (6)

Substituting (6) and pdf of ZOA from [28], we obtain

pA,i =

π∫−π

2R∫0

1− e−2λBrB(tan y(hB−hC)+rB)

2bzey−az(x)

bz

dxdy, (7)

where az(x) = π2 −arctan

(hA−hC

x

)and bz , z = 2, 3, . . . , N ,

are the parameters estimated from the statistical data (see [28]for details) and bz is given as

b1 =0, b2 =0.3146, b3 =0.3529, b4 =0.4056, b5 =0.4897. (8)

After characterizing the blockage probabilities of individ-ual clusters on the COW-BS to NR-BS link, we derive anexpression for the received power. As shown in [28], thefraction of power of i-th cluster between the NR-BS and theCOW-BS separated by the distance of x follows a Log-normaldistribution with the pdf fPA,i

(y;x).Once the fraction of power distributions is obtained, the

received power from every cluster is calculated as

PA,z = Ps,z10(PT−30−L)/10, z = 1, 2, . . . , (9)

where PT is the transmit power in dBm and L is the pathloss in dB. Then, PA,z is given as

PA,z = Ps,z10(Ap−21.0 log10(D3,0))/10, (10)

where Ap = PT − 30− 32.4− 20 log10 fc.As one may observe, PA,z is a function of two RVs, Ps,z

and D3,0, and fD3,0(x) is the pdf of the 3D distance between

the NR-BS and the COW-BS in the form

fD3,0=

2x

πR2cos−1

(√x2 − (hA − hC)2

2R

), (11)

where x ∈ (hA − hC ,√

4R2 + (hA − hC)2).Since D3,0 and Ps,z are independent, their joint pdf is

fPs,z,D3,0(x1, x2) =

1

x1dz√

2πe

(− (ln x1−cz)2

2d2z

)×

2x2

πR2cos−1

(√x2

2 − (hA − hC)2

2R

), (12)

5

where cz and dz , z = 2, 3, . . . , are the parameters derivedfrom the statistical data (see [28] for details) and given as

c1 = −2.88, c2 = −3.55, c3 = −4.1, c4 = −4.98, c5 = −6.2,

d1 = 1.2, d2 = 1.1, d3 = 1.3, d4 = 1.8, d5 = 2.51. (13)

Finally, the pdf of PA,z is

fPA,z(y) =

∫ x2,max

x2,min

fPs,z,D3,0

(y

10(Ap−21.0 log10(x2))/10, x2

)×

1

10(Ap−21.0 log10(x2))/10dx2, (14)

where x2,min = hA−hC and x2,max =√

4R2 + (hA − hC)2.Assuming mutual independence in the cluster blockage, the

pdf of the received power is produced as

fPA(y) =

N∑k=1

(1− pA,k)

k−1∏j=1

pA,j

fPA,k(y), (15)

where the weights are the probabilities of choosing cluster i.Finally, the outage probability with the NR-BS is

pA,O = Pr{PA(y) ≤ N0TS} =

∫ N0TS

0

fPA(y)dy, (16)

where N0 is the Johnson-Nyquist noise at the receiver and TSis the SNR threshold. Note that due to the complex structure ofthe conditional received power fPA

(y), the outage probabilitypA,O can only be produced with numerical integration.

The LoS path and i-th cluster blockage probability on a linkbetween the UAV-BS and the COW-BS are obtained similarlyexcept for the 2D distance between UAV-BS and COW-BS,D1, with the pdf given as

fD1(x) =4x

πR2

[cos−1

( x

2R

)− x

2R

√1− x2

4R2

], (17)

where x ∈ (0, 2R). Using this result, the corresponding 3Ddistance between the UAV-BS and the COW-BS constitutes

fD3,1=

4x

πR2

[cos−1

(√x2 − (hD − hC)2

2R

)−

−√x2 − (hD − hC)2

2R

√1− x2 − (hD − hC)2

4R2

], (18)

where x ∈ (hD − hC < x <√

4R2 + (hD − hC)2).2) Availability probability of UAV-BS: To complete the

derivation of pO, we find the probability that at least one UAV-BS in non-outage conditions is available for service, pD,av.

The time spent by each UAV-BS within the service area isconstant and equals TD = 2RvD, where vD is the speed ofUAV-BS. Hence, the number of UAV-BSs that are availablein the service zone is captured by the M/G/∞ queuingsystem with a constant service time. It is known that thenumber of customers in M/G/∞ queue coincides with thenumber of customers in M/M/∞ queue and follows a Poissondistribution with the parameter λDTD [32]1.

1To ensure a certain number of UAV-BSs above the area one may directlyuse a mean number of UAV-BSs.

Note that the availability of UAV-BSs is not sufficient for theCOW-BS to be able to associate with them. In addition, thereshould be at least one UAV-BS in non-outage conditions. Theintensity of such UAV-BSs is λDTD(1 − pD,O), where pD,Ois the probability that a randomly selected UAV-BS resides inthe outage conditions. Therefore, the number of UAV-BSs thatare available for the COW-BS U follows a Poisson distributionwith the probability mass function (pmf) of

un =[λDTD(1− pD,O)]n

n!e−λDTD(1−pD,O), (19)

where n = 0, 1, . . . .Let W denote the number of COW-BSs in the outage

conditions. The number of COW-BSs in the service areafollows a Poisson distribution with the density of λC . Hence,the number of COW-BSs in the outage conditions also followsa Poisson distribution with the parameter of λCpA,OπR2. Theprobability that the UAV-BS remains available for service is

pD,av = Pr{KDU −W > 0} =

∞∑i=1

Pr{Z = i}, (20)

where Z = KDU −W .Observe that KDU is a scaled Poisson RV in (21), which

implies that pD,av can be evaluated numerically for any valueof KD. The pmf of Z is then established as

Pr{Z = z} =

∞∑x=0

|KDx− 1|KD

[λCpA,OπR2](KDx−z)

(KDx− z)!×

e

(−λCpA,OπR

2−λDTD(1−pD,O))[λDTD(1− pD,O)]x/KD

(x/KD)!. (21)

B. Spectral efficiencyConsider now spectral efficiency of an arbitrarily chosen

COW-BS. Observe that this COW-BS spends a fraction oftime, pA, connected to the NR-BS and a fraction of time,pD, connected to the UAV-BS. The rest of the time, pO, thisCOW-BS resides in outage. Hence, the spectral efficiency is

C = pA log2

[1 +

PAN0

]+ pD log2

[1 +

PDN0

], (22)

where PA and PD are the received powers whenever associ-ated with NR-BS and UAV-BS.

Observe that pA,O = 1 − pA is the outage probabilitywhen only NR-BS is available. Recalling that UAV-BS areonly employed when the NR-BS to COW-BS link experiencesoutage conditions, the fraction of time that the COW-BS isassociated with the UAV-BS is pD = pA,OpD,av. Therefore,the mean spectral efficiency is provided by

E[C] = (1− pA,O)

∫ ∞0

fPA(x) log2

[1 +

PAN0

]dx+

+ pA,OpD,av

∫ ∞0

fPD(x) log2

[1 +

PDN0

]dx, (23)

which can be evaluated numerically.In addition to the mean value, the form of (22) enables us to

determine the distribution of the spectral efficiency. Observethat the spectral efficiencies associated with the UAV-BS to

6

COW-BS and the NR-BS to COW-BS links are independentRVs. The resulting pdf takes the following form

fC(x) =

∫ ∞

0

(2fPA(y) − 1)(2fPA

(x−y) − 1)

(N40 2x log2 2)−1

dy, x > 0,

pO, x = 0,

(24)

where the convolution integral can be evaluated numerically.

IV. TIME DEPENDENT ANALYSIS

In this section, we continue by quantifying uninterruptedconnectivity performance, including the outage and non-outage duration distributions as well as the uninterruptedconnectivity duration.

A. Dynamics of cluster blockage process

To capture the temporal dynamics of the blockage processfor a single cluster, we need to track the blockers that arecrossing the blockage zone, see Fig. 4. We begin by consider-ing the dynamics of the LoS blockage process and concentrateon the temporal properties of the process when the blockersare entering the blockage zone and occluding the LoS.

We specify the area around the blockage zone as shownin Fig. 4, where the moving blockers may cross the blockagezone by occluding the LoS between the COW-BS and the NR-BS. To specify these conditions, the area around the blockagezone is further divided into i, i = 1, 2, ...7, zones. The intensityof blockers crossing the blockage zone of the COW-BS locatedat the distance of x from the NR-BS is approximated as

λB,T (z) =

7∑i=1

∫∫Mi

gi(x, y)Pr{AB}Pr{TB > t}(λBMi)−1

dxdy, (25)

where the event AB is when a blocker moves towards theblockage zone (see Fig. 4), Mi is the area of zone i, gi(x, y)is the pdf of the blocker locations in zone i. Here, gi(x, y) =1/Mi as the blockers move according to the RDM modeland at every instant of time their coordinates are distributeduniformly within the area [30], while Pr{TB > t} = e−1/E[τ ]

is the probability that such movement is longer than t seconds.Observe that the probability for a blocker to move towards

CDEF is Pr{AB} = ξi(x, y)/2π, where ξi(x, y) is a rangeof movement angles within zone i that lead to crossing theblockage zone. We thus simplify (25) as

λB,T (z) =λBe

−1/E[τ ]

2π

7∑i=1

∫∫Mi

ξi(x, y) dx dy, (26)

where ξi(x, y) are calculated as

ξ1(x, y)=ξ3(x, y)=ξ5(x, y)=ξ7(x, y)=cos−1( xvt

)+tan−1

(yx

),

ξ2(x, y) = ξ6(x, y) = 2 cos−1(x/vt),

ξ4(x, y) = 2 tan−1(x/y), (27)

and M1 = M3 = M5 = M7 with x-coordinate within therange of (0, vt) and y-coordinate within the range of (0, vt/2),M2 = M6 with x-coordinate within the range of (0, vt)and y-coordinate within the range of (0, d − 2vt), M4 withx-coordinate within the range of (0, 2rB) and y-coordinatewithin the range of (0, vt), where 2rB < vt.

It has been shown in [33] that the process of meetingsbetween a stationary node and a node moving inside a boundedarea according to the RDM is approximately Poisson. We buildon this result to approximate the nature of the process ofblockers meeting the blockage zone. Due to the properties ofthe RDM model, the entry point is distributed uniformly overthe three sides of the blockage zone [30].

Let η and ω be the RVs denoting the blocked and non-blocked periods, respectively. Since blockers enter the zonein question according to a Poisson process with the intensityof λB,T (x), the time spent in the unblocked part, ω, followsan exponential distribution with the parameter of λB,T (x),Fω(t;x) = 1− e−λB,T (x)t, as demonstrated in [8]. The pdf ofη, fη(t;x), is the same as the distribution of the busy period inthe M/GI/∞ queuing system [34] given by (28), where FTB

is the CDF of time that one blocker spends in the blockagezone, which is provided in [8].

The pdfs of the blocked and non-blocked intervals, fη(t;x)and fω(t;x), are conditioned on the distance between COW-BS and NR-BS. Deconditioning with (3), we obtain the pdfsof the blocked and non-blocked intervals when associated withthe NR-BS as

fη(t) =

∫ 2R

0

fη(t;x)fD0(x;R)dx,

fω(t) =

∫ 2R

0

fω(t;x)fD0(x;R)dx, (29)

which can be calculated numerically.To capture the dynamics of the cluster blockage process,

we can represent it by using a continuous-time Markov chain(CTMC) process with two states, which is defined by theinfinitesimal generator in the following form

Λ1,A =

[−α1,A α1,A

β1,A −β1,A

], (30)

where the subscript (1, A) shows that the model is built forthe LoS cluster of the NR-BS to COW-BS link, while α1,A =1/E[η] and β1,A = 1/E[ω] are the means of blocked andnon-blocked intervals of the LoS cluster given in (29).

The process of blockage for other clusters on the NR-BS to COW-BS link is analyzed similarly. The key differ-ence is that the blockage zone is specified by the ZOAinstead of the heights of NR-BS and COW-BS as well asthe distance between them. Let us denote the generatorsof all clusters associated with the NR-BS to COW-BS linkby Λi,A, i = 1, 2, . . . , N . Assuming independence betweenthe cluster blockage processes, the associated CTMC model,{SA(t), t > 0}, SA(t) ∈ {1, 2, . . . , 2N}, is a superposition ofthe individual blockage processes. The infinitesimal generatorof {SA(t), t > 0} is then given by the Kronecker product ofΛi,A, i = 1, 2, . . . , N .

The blockage dynamics of the UAV-BS to COW-BS linkis represented similarly by leading to the Markov process ap-proximation {SD(t), t > 0}, SD(t) ∈ {1, 2, . . . , 2N}. Finally,the aggregate blockage model of both links is represented bya superposition of the blockage processes that characterize theNR-BS to COW-BS and the UAV-BS to COW-BS links. Theresulting infinitesimal generator is Λ = ΛA ⊗ ΛD.

7

Fη(x) = 1−

[[1− FTB

(x)]

1−x∫

0

(1− Fη(x− z)) exp(−λB,TFTB(z))λB,T dz

+

x∫0

(1− Fη(x− z))|de−λB,TFTB(z)|

]. (28)

B. Performance measures of interest1) Outage and non-outage duration distribution: Having

the CTMC representation of the outage process, we cannow calculate time-dependent performance metrics of interest,including the distributions of consecutive intervals spent inoutage and non-outage conditions, the corresponding distribu-tions of residual time, as well as the distribution and the meanduration of uninterrupted connectivity.

Let RVs G and O denote the non-outage and outage time du-rations, respectively. The distribution of time spent in outage,fO(x), x > 0, is directly given by the sojourn time in the statewhere all clusters are blocked. For our model, it is always state1. The distribution of time spent in the non-outage state can befound by modifying the CTMC to have an absorption state inoutage. Then, the sought distribution is the first-passage time(FPT) to the outage state that can be established by using [35].Particularly, let fG(t) be the pdf of the FPT from the set ofnon-blockage states, {2, 3, . . . , 2×2N}, to the blockage state.

It is easy to see that the sought distribution is of the phase-type nature [36] with the representation (~α, S), where ~α is theinitial state distribution defined over {2, 3, . . . , 2 × 2N} andS is obtained from the infinitesimal generator Λ by excludingthe first row and column. The pdf is then given by [37] as

fG(t) = ~αeSt~s0, t > 0, (31)

where ~s0 = −S~1, ~1 is the vector of ones with size 2N −1, while eSt is the matrix exponential defined as eSt =∑∞k=0

1k! (St)

k.The initial state distribution, ~α, is determined by the nor-

malized rates out of the outage state e.g.,

αi =

{0, i = 1,

πi/∑2N

j=2 πj , i = 2, 3, . . . , 2N .(32)

2) Uninterrupted connectivity time: Consider now an appli-cation that may tolerate at most ∆O in the outage conditions,which implies that all of the outages whose durations areless than ∆O do not cause connectivity interruptions. Theprobability that a session is interrupted is

pI =

∫ ∆O

0

xfO(x)dx. (33)

As one may observe, the duration of uninterrupted con-nectivity is produced by a geometrical distribution with theparameter pI , which is scaled with the aggregate durations ofnon-outage and outage intervals conditioned on the event thatit is smaller than ∆O. Hence, we have

E[TU ] =1

pI(E[G] + E[O|O ≤ ∆O]), (34)

where the means are readily given by

E[G] =

∞∫0

xfG(x)dx, E[O|O ≤ ∆O] =

∆O∫0

xfO(x)

1− pIdx. (35)

V. NUMERICAL RESULTS

In this section, the obtained analytical findings are illus-trated, explained, and compared with the results producedwith our SLS framework. Below is an illustrative exampleto demonstrate the capabilities of our proposed framework,which is applicable for a range of comprehensive and realisticdeployment models currently under investigation.

We address a typical crowded urban deployment, wherea pedestrian plaza (e.g., St. Peter’s Square, Vatican City) ismodeled. The area of interest is assumed to be of circularshape with the radius of 50 m. The terrestrial NR-BS is locatedat a side of the square on the wall of one of the buildings atthe height of 10 m. Pedestrians move around the square byfollowing their travel patterns as described in Section II withthe fixed speed of 3 km/h. UAV-BSs are assumed to traversethe pedestrian plaza at the height of 20 m with the fixed speedthat varies from 5 km/h to 40 km/h. The remaining modelingparameters are summarized in Table II. Our simulation param-eters partially follow the guidelines in [24] with respect to theheight and the speed of the UAV-BS, as well as refer to [11]for modeling the radio part.

To validate the assumptions of our developed analyticalframework, we utilize an in-house SLS tool that incorporatesall of the relevant procedures considered by our study. ThemmWave-specific physical layer was designed by followingthe corresponding 3GPP guidelines; particularly, the 3GPP’s3D multipath channel model outlined in [11] was employed.This simulation tool captures the following key procedures:session arrival process, UAV-BS arrival and departure pro-cesses, UAV-BS and pedestrian mobility, and dynamic back-haul link rerouting between the UAV-BS and the NR-BSenhanced with multi-connectivity operation [38].

The tool operates in a time-driven manner with the step of0.01 s. To match the capabilities of our analytical framework,idealistic and reliable signaling at all the connections has beenassumed: if the current connection is interrupted, the COW-BS immediately attempts to reconnect via a UAV-BS and doesnot spend any additional resources for this migration. Forthe sake of better accuracy in the output results, all of the

TABLE IIDEPLOYMENT AND TECHNOLOGY PARAMETERS

Parameter ValueDeploymentArea radius, R 50 mHeight of NR-BS, hA 10 mHeight of UAV-BS, hD 20 mHeight of COW-BS, hC 1.5 mHeight of blocker, hB 1.7 mRadius of blocker, rB 0.2 mSpeed of blocker, v 1 m/sTechnologyNR-BS transmit power 35 dBmUAV-BS transmit power 23 dBmTarget SNR for non-outage conditions 3 dBCOW-BS antenna gain 5 dBUAV-BS antenna gain 7 dBNR-BS antenna gain 10 dBCarrier frequency 28 GHz

8

0 2 4 6 8 10Temporal intensity of UAV-BSs entering the service area, λD [min−1 ]

0

2

4

6

8

10

Out

age

prob

abili

ty, p

O [%

]

7.0

7.5

8.0

8.5

9.0

9.5

Mea

n sp

ectra

l eff

icie

ncy,

E[C

] [bi

t/s/H

z]pO (λB=0.1)

pO (λB=0.3)

pO (λB=0.5)

pO (λB=0.7)

Sim. - pO (λB=0.1)

Sim. - pO (λB=0.7)

E[C] (λB=0.1)

E[C] (λB=0.3)

E[C] (λB=0.5)

E[C] (λB=0.7)

Sim. - E[C] (λB=0.1)

Sim. - E[C] (λB=0.1)

Fig. 5. Outage probability and mean spectral efficiency. Effect of crowddensity and intensity of UAV-BS flights.

collected intermediate data are averaged over 100 replications,each starting with a re-deployment of the layout. Each ofsuch replications corresponds to 10 min of real-time operation.Hence, approximately 17 hours of real-time system operationhave been modeled.

1) Effect of UAV-BS flight intensity: The UAV-BSs areassumed to move at a moderate speed of 10 km/h. The point 0on the OX axis represents the baseline scenario with no UAV-BS assistance. Analyzing Fig. 5, we notice that both the outageprobability and the spectral efficiency are improved with thegrowth in the intensity of UAV-BS traversals. Specifically, forλB = 0.7 the outage probability decreases from 7.5% for thebaseline scenario to 1.5% for 10 UAV-BSs per minute. Mean-while, the corresponding increase in the spectral efficiency isfrom 6.5 bit/s/Hz to 8 bit/s/Hz, which is around 25%.

Going further, we observe that the benefits of UAV-BSassistance for performance are more visible in challengingconditions (high density of humans, such as 0.7) rather thanat low blocker densities (such as 0.1 or 0.3). Moreover, Fig. 5clearly indicates that two UAV-BSs traversing the area of in-terest per minute with λB = 0.7 reduce the outage probabilitydown to 5.3%, which is close to 5.2% observed with λB = 0.5in the baseline scenario (no UAV-BSs, λD = 0).

We finally note that the results of our mathematical analy-sis match well with those obtained via the simulation tool,which confirms the accuracy of the analytical findings. Aslight difference between them is due to several simplifyingassumptions introduced by the mathematical framework for

5 10 15 20 25 30 35 40Speed of UAV-BS, vD [km/h]

0

2

4

6

8

10

12

Out

age

prob

abili

ty, p

O [%

]

6.5

7.0

7.5

8.0

8.5

9.0

9.5

Mea

n sp

ectra

l eff

icie

ncy,

E[C

] [bi

t/s/H

z]pO (KD=1)

pO (KD=3)

pO (KD=5)

Sim. - pO (KD=1)

Sim. - pO (KD=5)

E[C] (KD=1)

E[C] (KD=3)

E[C] (KD=5)

Sim. - E[C] (KD=1)

Sim. - E[C] (KD=5)

Fig. 6. Outage probability and mean spectral efficiency. Effect of UAV-BSspeed and its capabilities.

0 50 100 150 200 250 300Outage duration, O [ms]

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

Prob

abili

ty d

ensi

ty fu

nctio

n, fO

With UAV-BSs (vD =10 km/h, KD=10)

With UAV-BSs (vD=10 km/h, KD=5)

With UAV-BSs (vD=20 km/h, KD=10)

With UAV-BSs (vD=20 km/h, KD=5)

With UAV-BSs (vD=40 km/h, KD=10)

With UAV-BSs (vD=40 km/h, KD=5)

No UAV-BSs

Sim. - With UAV-BSs (vD=10 km/h, KD=5)

Sim. - No UAV-BSs

Fig. 7. Distribution of outage duration. Effect of UAV-BS speed and itscapabilities.

the sake of analytical tractability: e.g., an approximation of the3GPP’s multipath propagation model as detailed in Section IIIand [28].

2) Effect of UAV-BS flight speed: The intensity of UAV-BSs traversing the area, λD, is fixed and set to 10 UAV-BSsper min. We model a crowded scenario with λB = 0.7, whilethe maximum number of simultaneous backhaul connectionsper UAV-BS, KD, varies from 1 to 5. We observe that adecrease in the UAV-BS speeds has a notable positive effecton performance. As an example, lowering UAV-BS speedsfrom 40 km/h down to 10 km/h for KD = 1 results in reducedoutage probability from 7.1% to 3.5%, which is over 2 times.The corresponding gain in the mean spectral efficiency, E[C],is smaller but still visible: from 6.9 bit/s/Hz to 7.7 bit/s/Hz.

We continue by evaluating the effect of the UAV-BS speedsin Fig. 7, which presents the pdf of the outage duration forcertain values of vD and KD. The UAV-BS intensity, λD, isset to 10 per min, while the density of humans in the area,λB , equals 0.7. There is a notable decrease in the mean outageduration, E[O], when UAV-BSs are utilized. Particularly, thesaid parameter decreases from 276 ms for the baseline deploy-ment down to as low as 88 ms for (vD = 10 km/h, KD = 10)case. Finally, we notice that increasing the UAV-BS capacity,KD, by two times (from 5 to 10 simultaneous connections)brings a notable decrease in the mean outage duration.

3) Effect of service capacity of UAV-BSs, KD: To thisaim, we analyze the primary backhaul session continuityrelated parameter – the average duration of the uninterruptedconnectivity subject to a certain tolerable outage duration. Inother words, a connection is assumed to be interrupted if andonly if the outage duration is longer than a certain value, ∆O.We illustrate these results in Fig. 8 for two UAV-BS intensities(λD = 1 and 10 UAV-BSs per min).

Studying Fig. 8, we notice that for 100 ms of tolerableoutage, the average duration of uninterrupted connectivitygrows from 7 s for the baseline scenario to 46 s for 10 UAV-BSs per min, KD = 10. We then observe that the impactof an increased UAV-BS capacity, KD, is notable but weakerthan that of the intensity of UAV-BS traversals: the curve for(10 UAV-BSs per min, KD = 1) is much higher than the onefor (1 UAV-BS per min, KD = 10). This is mainly due tothe fact that at least one out of 10 UAV-BSs is much morelikely to reside in non-outage conditions with respect to theCOW-BS than a single UAV-BS, regardless of the capacity.

9

10 20 30 40 50 60 70 80 90 100Tolerable outage duration, ∆O [ms]

0

10

20

30

40

50

Mea

n un

inte

rrup

ted

conn

ectiv

ity ti

me,

E[TU] [

s]λD=10 min−1 , KD=10

λD=10 min−1 , KD=5

λD=10 min−1 , KD=1

λD=1 min−1 , KD=10

λD=1 min−1 , KD=5

λD=1 min−1 , KD=1

No UAV-BSs

Sim. - λD=10 min−1 , KD=10

Sim. - λD=1 min−1 , KD=10

Sim. - No UAV-BSs

Fig. 8. Mean uninterrupted connectivity time. Effect of UAV-BS traversalintensity and its capabilities.

Finally, we observe that the relative impact of KD on thesaid parameter depends on the intensity of UAV-BS flightsacross the area. Particularly, the improvement brought byKD = 5 and KD = 10 vs. KD = 1 is significant for1 UAV-BS per min and marginal for 10 UAV-BSs per min. Insummary, for high intensity of UAV-BS traversals, there is noneed for higher capacity of the UAV-BSs. Meanwhile, if theintensity of UAV-BS flights is lower than required from theconnectivity perspective, there is a driver to invest resourcesinto advanced radio units on the UAV-BSs.

VI. CONCLUSION

Dynamic and reconfigurable system architectures aiming tosupport backhaul operation in mmWave bands are one of therecent focus items in the ongoing 3GPP standardization. Theycan be further augmented by an emerging element in the 5Glandscape – UAVs with flexible mobility and capability tocarry radio equipment. These may become efficient backhaulconnectivity providers in 5G and beyond networks, especiallyin case of highly dynamic traffic fluctuations to avoid excessiveover-provisioning of network resources.

To this aim, we contribute a new analytical framework thatincorporates 3GPP’s multipath channel model, heterogeneousmobility of UAVs and humans, as well as human bodyblockage effects, which are identified by 3GPP as one of themain sources of performance degradation for the prospectiveNR operation. Our methodology allows to produce both time-averaged and continuous-time metrics in dependence on UAV-BS speed and traversal intensity, heights of the communicatingentities within the scenario (NR-BS, UAV-BS, COW-BS, andhuman blockers), as well as blocker dimensions and speeds.

We demonstrate that UAV-BS assistance can offer signif-icant benefits to mmWave backhaul under certain systemparameters. For instance, the intensity of UAV-BS flights equalto 10 reduces the outage probability on a COW-BS backhaullink by 6 times. Moreover, by lowering the UAV-BS speedabove the service area from 40 km/h down to 10 km/h, the saidoutage probability drops by 2 times. Further, one may derivethe target intensity of UAV-BS traversals that is required tosupport the key performance indicators as a function of theblocker density. The contributed framework can be appliedto a wide range of practical scenarios, such as conventionallayouts with the near-static deployment of UAV-BSs by e.g.,adjusting the speed parameter.

REFERENCES

[1] M. Shafi, A. F. Molisch, P. J. Smith, T. Haustein, P. Zhu, P. D.Silva, F. Tufvesson, A. Benjebbour, and G. Wunder, “5G: A TutorialOverview of Standards, Trials, Challenges, Deployment, and Practice,”IEEE Journal on Selected Areas in Communications, vol. 35, no. 6, pp.1201–1221, June 2017.

[2] 5GPPP, “View on 5G Architecture,” White paper v2.0, December 2017.[3] 3GPP, “Report of 3GPP TSG RAN meeting #78,” 3GPP RP-180516,

December 2017.[4] J. Sachs, G. Wikstrom, T. Dudda, R. Baldemair, and K. Kittichokechai,

“5G Radio Network Design for Ultra-Reliable Low-Latency Communi-cation,” IEEE Network, vol. 32, no. 2, pp. 24–31, March 2018.

[5] U. Siddique, H. Tabassum, E. Hossain, and D. I. Kim, “Wirelessbackhauling of 5G small cells: Challenges and solution approaches,”IEEE Wireless Communications, vol. 22, no. 5, pp. 22–31, October 2015.

[6] C. Dehos, J. L. Gonzalez, A. D. Domenico, D. Ktenas, and L. Dussopt,“Millimeter-wave access and backhauling: The solution to the exponen-tial data traffic increase in 5G mobile communications systems?” IEEECommunications Magazine, vol. 52, no. 9, pp. 88–95, September 2014.

[7] T. Bai, R. Vaze, and R. W. Heath, “Analysis of blockage effects on urbancellular networks,” IEEE Transactions on Wireless Communications,vol. 13, no. 9, pp. 5070–5083, September 2014.

[8] M. Gapeyenko et al., “On the temporal effects of mobile blockersin urban millimeter-wave cellular scenarios,” IEEE Transactions onVehicular Technology, vol. 66, no. 11, pp. 10 124–10 138, November2017.

[9] V. Petrov, M. Komarov, D. Moltchanov, J. M. Jornet, and Y. Kouch-eryavy, “Interference and SINR in Millimeter Wave and TerahertzCommunication Systems With Blocking and Directional Antennas,”IEEE Transactions on Wireless Communications, vol. 16, no. 3, pp.1791–1808, March 2017.

[10] V. Petrov, M. A. Lema, M. Gapeyenko, K. Antonakoglou,D. Moltchanov, F. Sardis, A. Samuylov, S. Andreev, Y. Koucheryavy,and M. Dohler, “Achieving End-to-End Reliability of Mission-CriticalTraffic in Softwarized 5G Networks,” IEEE Journal on Selected Areasin Communications, vol. 36, no. 3, pp. 485–501, March 2018.

[11] 3GPP, “Study on channel model for frequencies from 0.5 to 100 GHz(Release 15),” 3GPP TR 38.901 V15.0.0, June 2018.

[12] F. B. Tesema, A. Awada, I. Viering, M. Simsek, and G. Fettweis, “Eval-uation of context-aware mobility robustness optimization and multi-connectivity in intra-frequency 5G ultra dense networks,” IEEE WirelessCommunications Letters, vol. 5, no. 6, pp. 608–611, December 2016.

[13] O. E. Ayach, S. Subramanian, J. E. Smee, A. Sampath, and J. Li,“Method and apparatus for connection point discovery and associationin a directional wireless network,” October 2016, US9474013B2.[Online]. Available: https://patents.google.com/patent/US9474013B2/en

[14] M. Mousaei and B. Smida, “Optimizing pilot overhead for ultra-reliable short-packet transmission,” in IEEE International Conferenceon Communications, May 2017.

[15] NGMN, “Small cell backhaul requirements,” White paper, June 2012.[16] 3GPP, “Study on integrated access and backhaul (Release 15),” 3GPP

TR 38.874 V0.4.0, August 2018.[17] C. Saha, M. Afshang, and H. S. Dhillon, “Integrated mmWave Access

and Backhaul in 5G: Bandwidth partitioning and downlink analysis,”Available: https://arxiv.org/pdf/1710.06255.pdf, 2018.

[18] K. Balachandran, J. Kang, K. Karakayali, and J. Singh, “Capacitybenefits of relays with in-band backhauling in cellular networks,” inIEEE International Conference on Communications, May 2008.

[19] M. Jaber, F. J. Lopez-Martinez, M. A. Imran, A. Sutton, A. Tukmanov,and R. Tafazolli, “Wireless backhaul: Performance modelling and impacton user association for 5G,” IEEE Transactions on Wireless Communi-cations, pp. 1–1, 2018.

[20] I. Bor-Yaliniz, A. El-Keyi, and H. Yanikomeroglu, “Efficient 3-Dplacement of an aerial base station in next generation cellular networks,”in IEEE International Conference on Communications, May 2016.

[21] E. Kalantari, M. Z. Shakir, H. Yanikomeroglu, and A. Yongacoglu,“Backhaul-aware robust 3D drone placement in 5G+ wireless networks,”in IEEE International Conference on Communications Workshops (ICCWkshps), May 2017, pp. 1–6.

[22] M. Mozaffari, W. Saad, M. Bennis, and M. Debbah, “Efficient de-ployment of multiple unmanned aerial vehicles for optimal wirelesscoverage,” IEEE Communications Letters, vol. 20, no. 8, pp. 1647–1650,August 2016.

[23] K. Haneda et al., “5G 3GPP-like channel models for outdoor urbanmicrocellular and macrocellular environments,” in IEEE 83rd VehicularTechnology Conference (VTC Spring), May 2016.

10

[24] 3GPP, “Study on enhanced LTE support for aerial vehicles, (Release15),” TR 36.777 V15.0.0, January 2018.

[25] A. Fotouhi, M. Ding, and M. Hassan, “Dynamic base station reposi-tioning to improve performance of drone small cells,” in 2016 IEEEGlobecom Workshops (GC Wkshps), December 2016, pp. 1–6.

[26] J. G. Andrews, T. Bai, M. Kulkarni, A. Alkhateeb, A. Gupta, and R. W.Heath, “Modeling and analyzing millimeter wave cellular systems,”IEEE Transactions on Communications, vol. 65, no. 1, pp. 403–430,January 2016.

[27] M. Zhang, M. Polese, M. Mezzavilla, S. Rangan, and M. Zorzi, “Ns-3 Implementation of the 3GPP MIMO Channel Model for FrequencySpectrum above 6 GHz,” in Workshop on ns-3, June 2017.

[28] M. Gapeyenko, V. Petrov, D. Moltchanov, S. Andreev, Y. Koucheryavy,M. Valkama, M. R. Akdeniz, and N. Himayat, “An Analytical Rep-resentation of the 3GPP 3D Channel Model Parameters for mmWaveBands,” in 2nd ACM Workshop on Millimeter-Wave Networks andSensing Systems, October 2018, pp. 1–6.

[29] Y. Zeng, R. Zhang, and T. J. Lim, “Wireless communications withunmanned aerial vehicles: Opportunities and challenges,” IEEE Com-munications Magazine, vol. 54, no. 5, pp. 36–42, May 2016.

[30] P. Nain, D. Towsley, B. Liu, and Z. Liu, “Properties of random directionmodels,” in IEEE INFOCOM, vol. 3, March 2005.

[31] A. M. Mathai, An introduction to geometrical probability: Distributionalaspects with applications. CRC Press, 1999, vol. 1.

[32] G. Newell, “The M/G/∞ queue,” SIAM Journal on Applied Mathemat-ics, vol. 14, no. 1, pp. 86–88, 1966.

[33] R. Groenevelt, “Stochastic models for mobile ad hoc networks,” INRIASophia-Antipolis, PhD thesis, 2005.

[34] D. J. Daley, “The busy period of the M/GI/∞ queue,” Queueing Systems:Theory and Applications, vol. 38, no. 2, pp. 195–204, 2001.

[35] J. G. Kemeny, J. L. Snell et al., Finite Markov chains. van NostrandPrinceton, NJ, 1960, vol. 356.

[36] T. Altiok, “On the phase-type approximations of general distributions,”IIE Transactions, vol. 17, no. 2, pp. 110–116, 1985.

[37] M. F. Neuts, Matrix-geometric solutions in stochastic models: an algo-rithmic approach. Courier Corporation, 1981.

[38] V. Petrov et al., “Dynamic multi-connectivity performance in ultra-dense urban mmWave deployments,” IEEE Journal on Selected Areasin Communications, vol. 35, no. 9, pp. 2038–2055, September 2017.

Margarita Gapeyenko (mar-garita.gapeyenko@tut.fi) is a Ph.D. candidate atthe Laboratory of Electronics and CommunicationsEngineering at Tampere University of Technology,Finland. She earned her M.Sc. degree inTelecommunication Engineering from University ofVaasa, Finland, in 2014, and B.Sc. degree in Radio-Engineering, Electronics, and Telecommunicationsfrom Karaganda State Technical University,Kazakhstan, in 2012. Her research interests includemathematical analysis, performance evaluation, and

optimization methods for mmWave networks, UAV communications, and(beyond-)5G heterogeneous systems.

Vitaly Petrov (vitaly.petrov@tut.fi) received theM.Sc. degree in information systems security fromthe Saint Petersburg State University of AerospaceInstrumentation, St Petersburg, Russia, in 2011, andthe M.Sc. degree in communications engineeringfrom the Tampere University of Technology, Tam-pere, Finland, in 2014, where he is currently pur-suing the Ph.D. degree. He was a Visiting Scholarwith the Georgia Institute of Technology, Atlanta,USA, in 2014 and a Strategic Intern with the NokiaResearch Center, Helsinki, Finland, in 2012. He is

the recipient of Best Student Paper Award at IEEE VTC-Fall’15 and BestStudent Poster Award at IEEE WCNC’17. His current research interests arein Internet-of-Things, mmWave/THz band communications, nanonetworks,cryptology, and network security.

Dmitri Moltchanov (dmitri.moltchanov@tut.fi) is aSenior Research Scientist in the Laboratory of Elec-tronics and Communications Engineering, TampereUniversity of Technology, Finland. He received hisM.Sc. and Cand.Sc. degrees from Saint-PetersburgState University of Telecommunications, Russia, in2000 and 2002, respectively, and Ph.D. degree fromTampere University of Technology in 2006. Hisresearch interests include performance evaluationand optimization issues of wired and wireless IPnetworks, Internet traffic dynamics, quality of user

experience of real-time applications, and traffic localization P2P networks.Dmitri Moltchanov serves as TPC member in a number of internationalconferences. He authored more than 50 publications.

Sergey Andreev (sergey.andreev@tut.fi) receivedthe Specialist and Cand.Sc. degrees from St. Pe-tersburg State University of Aerospace Instrumen-tation, St. Petersburg, Russia, in 2006 and 2009,respectively, and the Ph.D. degree from TampereUniversity of Technology, Finland, in 2012. Since2018, he has been a Visiting Senior Research Fellowwith the Centre for Telecommunications Research,Kings College London, U.K. He is currently a SeniorResearch Scientist with the Laboratory of Elec-tronics and Communications Engineering, Tampere

University of Technology. He has authored or co-authored over 150 publishedresearch works on wireless communications, energy efficiency, heterogeneousnetworking, cooperative communications, and machine-to-machine applica-tions.

Nageen Himayat is a Principal Engineer with IntelLabs, where she leads a team conducting research onseveral aspects of next generation (5G/5G+) of mo-bile broadband systems. Her research contributionsspan areas such as multi-radio heterogeneous net-works, mm-wave communication, energy-efficientdesigns, cross layer radio resource management,multi-antenna, and non-linear signal processing tech-niques. She has authored over 250 technical publi-cations, contributing to several IEEE peer-reviewedpublications, 3GPP/IEEE standards, as well as holds

numerous patents. Prior to Intel, Dr. Himayat was with Lucent Technologiesand General Instrument Corp, where she developed standards and systems forboth wireless and wire-line broadband access networks. Dr. Himayat obtainedher B.S.E.E degree from Rice University, and her Ph.D. degree from theUniversity of Pennsylvania. She also holds an MBA degree from the HaasSchool of Business at University of California, Berkeley.

Yevgeni Koucheryavy (evgeni.kucheryavy@tut.fi)received the Ph.D. degree from the Tampere Univer-sity of Technology, in 2004. He is a Professor withthe Laboratory of Electronics and CommunicationsEngineering, Tampere University of Technology,Finland. He is the author of numerous publications inthe field of advanced wired and wireless networkingand communications. His current research interestsinclude various aspects in heterogeneous wirelesscommunication networks and systems, the Internetof Things and its standardization, and nanocommu-

nications. He is an Associate Technical Editor of the IEEE CommunicationsMagazine and Editor of the IEEE Communications Surveys and Tutorials.