1

Energy-Efficient Massive IoT Shared Spectrum

Access over UAV-enabled Cellular Networks

Ghaith Hattab, Student Member, IEEE, Danijela Cabric, Senior Member, IEEE

Abstract

Data aggregation has become an emerging paradigm to support massive Internet-of-things (IoT),

a new and critical use case for fifth-generation new radio (5G-NR). Indeed, data aggregators can

complement cellular base stations and process IoT traffic to reduce network congestion. In this paper,

we consider using mobile data aggregators, e.g., drones, that collect IoT traffic and aggregate them

to the network. Specifically, we first discuss how the spectrum can be shared between cellular users

(UEs) and IoT devices in the presence of drones, proposing a time-division duplexing protocol. We

use stochastic geometry to analyze this protocol, comparing it to the standard spectrum sharing and

orthogonal allocation protocols. We then formulate a stochastic optimization problem to optimize the

nominal IoT transmit power, maximizing the average energy-efficiency (EE) of the IoT device subject

to interference constraints to protect UEs. Simulations are presented to validate the theoretical insights

and the effectiveness of the proposed protocol. It is shown that using drones, to aggregate IoT traffic,

improves the EE of IoT devices, yet the EE degrades as their altitudes increases. Equally important,

optimizing the transmit power is critical to further improve the EE, while ensuring fair coexistence with

UEs.

Index Terms

Cellular networks, massive IoT, spectrum sharing, stochastic geometry, UAVs.

I. INTRODUCTION

Fifth-generation new-radio (5G-NR) is set to unlock new application scenarios on different

fronts. One specific use case is the native support of a massive number of sensors and ma-

chines, collectively known as massive cellular Internet-of-things (IoT) or massive machine-type

communications (mMTC) [2]. Indeed, it is envisaged that billions of IoT devices will require

Internet-connectivity by 2020, creating transformative economic potentials for operators and

stakeholders [3] and spanning several vertical sectors such as smart cities and agriculture [4].

This paper was presented in part at the IEEE Int. Conf. on Wireless and Mobile Computing (WiMoB) [1]. G. Hattab and D.

Cabric are with the Department of Electrical and Computer Engineering, University of California, Los Angeles, CA 90095-1594

USA (email: ghattab@ucla.edu, danijela@ee.ucla.edu).

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Cellular networks have started to support new user categories tailored for IoT applications,

e.g., NB-IoT and NR-lite, in addition to enabling extended discontinuous reception to reduce

power consumption [5], [6]. Such IoT optimizations, however, are still limited to services that

do not require a large deployment of sensors and machines. Indeed, as the density of IoT devices

increases, several challenges emerge [7]. First, collisions among IoT devices increase due to the

increased number of access requests, making retransmissions more frequent, and thus affecting

their energy-efficiency (EE). Second, interference increases when IoT devices share the same

spectrum with cellular users (UE), degrading the coverage needed for the former and reducing

the spectral efficiency (SE) for the latter. In this paper, we propose a transmission protocol that

uses drones to aggregate IoT traffic, while ensuring fair shared spectrum access with existing

UEs.

A. Related work

The techniques toward the coexistence of IoT devices and UEs can be broadly classified into

orthogonal-based and sharing-based solutions [6]–[9]. In the former, resource blocks are split

among IoT devices and UEs as means to avoid interference and congestion. However, resource

partitioning inevitably leads to a spectral efficiency tradeoff between IoT devices and UEs. In

contrast, in spectrum sharing, all resource blocks are shared between UEs and IoT devices.

To control congestion, several techniques have emerged such as access class barring (ACB)

and randomized back-off schemes [10], [11]. These methods, nevertheless, do not address the

co-channel interference after access requests are granted. Alternative to these approaches, data

aggregation has emerged as an effective solution to handle the massive IoT traffic. An experimen-

tal study is discussed in [4] showing the benefits of IoT data aggregation on cellular networks.

In [12]–[15], stochastic geometry is used to analyze the coverage performance and/or the energy

consumption using single and/or multiple aggregators. These works, however, consider fixed

terrestrial aggregators and focus only on the performance of IoT devices, i.e., the coexistence

of IoT devices and UEs is not considered. In this paper, we consider using unmanned aerial

vehicles (UAVs) or drones that stop at optimized predetermined locations.

Integrating UAVs with cellular networks has attracted significant attention, e.g., it has become

a study item for recent and future 3GPP releases [16]. Indeed, UAVs are envisioned to become

data aggregators (relays) or even base stations (BSs) [17], as their mobility brings unparalleled

flexibility to cellular networks. For example, UAVs can help realize several IoT applications, e.g.,

3

smart cities, by extending the coverage of existing cellular infrastructure, enabling low-power

communications with low-cost sensors, and reducing network congestion via offloading some of

the traffic generated from massive IoT devices. Implementation and practical considerations for

UAV-based IoT platforms are presented in [18], [19], showing the feasibility of using UAVs for

IoT applications. Optimization and analysis of UAV-based aggregation are studied in [20]–[25].

For example, the authors in [20] focus on optimizing the throughput of a single link between a

source and a destination, assisted by a relaying UAV, whereas in our work we consider a large-

scale cellular network. In [21], the authors focus on minimizing the time it takes the drone to

aggregate data samples collected by IoT devices to estimate a field of interest. In [22], the authors

study optimizing the UAV’s trajectory and sensors’ wake-up schedules to minimize their energy

consumption. In [23], the locations and associations of the drones are optimized to minimize the

transmit powers of IoT devices. In [24], [25], the authors optimize the deployment of UAVs to

minimize the average nominal transmit power of ground users. Compared to the aforementioned

works, we mainly focus on the coexistence of UEs and IoT devices, using UAVs to enable a fair

shared spectrum access. We further optimize the average nominal transmit power of IoT devices

to maximize their EE.

B. Contributions

The main contributions in this paper are as follows.

• Shared spectrum-based transmission protocol: We present a time-division duplexing (TDD)

transmission protocol that provides a shared-spectrum access between massive IoT and UEs

over the cellular network using UAVs as data aggregators for IoT devices. We use stochastic

geometry [26] to characterize the average available resources for UEs and IoT devices and

compare the proposed protocol with a sharing-based protocol via ACB as well as resource

splitting via frequency partitioning. We also analyze the coverage of the UEs in the presence

of IoT devices transmitting to their associated drones.

• Energy-efficiency maximization: We then optimize the nominal transmit power of the IoT

device to maximize its average EE subject to a protection criterion to its nearest UE. For

tractable analysis, we first consider a single-cell single-drone (SC-SD) scenario, where the

average EE is derived in closed form. We further analyze the interference-to-signal ratio

(ISR) at the UE in the same cell with IoT devices and use its distribution as a protection

constraint. Convexity analysis and insights on the optimal transmit power are discussed.

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We also present extensions to the problem, where the BS power is optimized and multiple

drones per cell are considered.

We validate the theoretical expression of the EE and the effectiveness of optimizing the nominal

transmit power of IoT devices via Monte Carlo simulations, showing that the proposed scheme

provides significant EE improvements to IoT devices compared to transmitting at the maximum

power, which is typically done to extend coverage [5]. The proposed scheme is further compared

to ACB and orthogonal allocation in a large network. Simulations show that the EE is significantly

improved for practical drone altitudes, with minimal degradation to the UE’s spectral efficiency

in the UL and the DL. Such improvements are translated into an increased lifetime of IoT

devices, which is validated using the 3GPP evaluation methodology in [27].

II. SYSTEM MODEL

A. Cellular network model

We use stochastic geometry to model the cellular network since it provides tractable analysis

of large-scale networks [26]. Such analysis helps understand the impact of different network

parameters, gleaning useful design guidelines.

1) BSs and UEs: In stochastic geometry, the locations of BSs are commonly modeled using

the homogeneous Poisson Point process (HPPP) ΦB with density λB [15]. Each BS is equipped

with a multi-antenna array with MB antennas. We assume the BS can multiplex 1 ≤ UB ≤MB

users per resource block. During downlink (DL) data communications, the BS transmits at a

nominal power of PB, such that each multiplexed user is equally allocated a power of PB/UB.1

For UEs, we assume that they are also generated from an independent HPPP ΦU with density

λU, where each one is equipped with a single-antenna system and connects to the nearest BS.

During uplink (UL) data communications, the UE transmits at nominal power of PU.2 We remark

that we focus on a single-tier network for easier exposition in the subsequent analysis. However,

1In practice, the BS may optimize power allocation to UEs, e.g., using a water-filing algorithm that considers the BS-UE

channel quality. Note if there are a large number of UEs in the network, it is reasonable to assume that the BS can find a subset

of UEs with good channels, and so it can schedule them together and use equal power allocation.2We use the term nominal power here because, in general, the BS may request the UE to add an offset to the transmit power

depending on the UE’s estimated path loss. This scheme is known as fractional power control. The optimization of UE transmit

power is outside the scope of this work.

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it is straightforward to extend this work to multi-tier heterogeneous networks as we have done

in our prior work in [1].

2) Ground-to-ground channel model: For ground-to-ground links, e.g., BS-UE links, we

assume a power-law path loss model with a loss of L0 at a reference distance of 1m and a

decaying exponent of αG. For small-scale fading, we assume a Rayleigh fading channel, with

gamma distributed channel power gains, as they model a variety of multi-antenna transmission

modes [28]. Specifically, the channel power gains between the UE and the tagged BS and the

UE and an interfering BS are, respectively, modeled as gB ∼ Γ(∆B, 1) and fB ∼ Γ(ΨB, 1), e.g.,

for multi-user zero-forcing beamforming, we have ∆B = MB − UB + 1 and ΨB = UB [28].

B. IoT devices model

We primarily consider UL IoT connectivity, which is typically the bottleneck in massive IoT

communications [4]. Furthermore, we assume that IoT devices are clustered either inherently,

e.g., deploying sensors in hotspots to monitor the same physical phenomenon [15], or via a

clustering algorithm, as done in [23]. To this end, we model the locations of IoT devices using

an independent clustered HPPP process. In particular and similar to [15], we consider the Matern

cluster process, where the locations of cluster centers, i.e., parent points, is modeled by the

independent HPPP ΦCl with density λCl. In each cluster, IoT devices represent the daughter

points of the clustered process, denoted by ΦM, and they are uniformly distributed in a disk of

radius R and with density λM. Thus, the average density of IoT devices in the network is λMλCl.

Finally, we assume all IoT devices are single-antenna transmitters, and they transmit at a fixed

power of PM.

Applications where such IoT models are reasonable include the mass deployment of IoT

devices across a city, where sensors can be anchored on bridges for infrastructure monitoring,

on buildings for utility metering, or in a farm for water management [4]. Such applications are

delay tolerant, yet they require reliable coverage and a very long lifetime.

C. Using UAVs as data aggregators

We consider deploying UAVs, e.g., drones, as a middle layer between IoT devices and the

cellular infrastructure. The drone acts as a mobile data aggregator that is sent by a BS to provide

coverage for a cluster of IoT devices. We note that while drones can be used as BSs or relays

for UE traffic, as discussed in [17], in this work we primarily use them as aggregators for IoT

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devices that have delay-tolerant traffic. We assume the density of drones, λD, is equal to the

density of clusters, i.e., λD = λCl, and each one flies at an altitude of hD. We note that fewer

drones can be also used, e.g., a drone can serve multiple clusters by moving from one point

to another over time. Further, the drone is equipped with an omni-directional single-antenna

cellular transceiver. We discuss the case of a multi-tier drone network, where each tier is defined

by a different altitude, in Section IV-B.

1) Initial access phase: Since we focus on massive IoT applications with machines and

sensors anchored to fixed locations, it is reasonable to assume that the locations of IoT devices

in the cluster are registered in a server or a database, and hence they are known to the mobile

operator [4], [23]. In particular, the drone, which is sent by the BS, moves to predetermined

stop points for UL data aggregation. In this work and for tractable analysis, the stop point of

the l-th drone, (xD,l, yD,l, hD), is the centroid of its cluster of IoT devices. We note that such

location minimizes the distance to the typical IoT device, i.e., it can be shown that (xD,l, yD,l) =

argmin(x,y) EΦM[dM,l], where dM,l is the 3D distance between a typical IoT device and the drone.

Finally, we note that the trajectory of the drone and its mobility can be optimized to extend its

lifetime as discussed in [24], [29]. In this work, it suffices to assume that drones can manage to

hover around a cluster of IoT devices to collect data from them.

2) Ground-to-air channel model: We consider the following popular ground-to-air path loss

model for the link between an IoT device and the l-th drone [23], [30]–[32]

lM→D(dM,l) = PLOS(dM,l, hD)L0d−αAM,l +(1− PLOS(dM,l, hD))LNLOSL0d

−αAM,l , (1)

where PLOS(dM,l, hD) is the line-of-sight (LOS) probability, LNLOS is the excessive path loss

due to non-LOS, and αA is the ground-to-air path loss exponent. Note that, as investigated in

[32], the impact of multi-path fading is negligible in such links, and thus it is ignored. The LOS

probability is found using the 3GPP UMa-AV channel model, and it can be expressed as [16]

PLOS(dM,l, hD) = min

ξ1

rM,l

, 1

(1− e−rM,l/ξ2

)+ e−rM/ξ2 , (2)

where rM,l =√d2

M,l − h2D, and ξ1 and ξ2 are some constants as given in [16, Table B-1]. For

the link between the BS and the drone, we consider a similar model, which is expressed as

lB→D(dB,l) = LSTR ·(PLOS(dB,l, hD)L0d

−αAB,l +(1− PLOS(dB,l, hD))LNLOSL0d

−αAB,l

), (3)

where the attenuation LSTR is due to the fact that the BS’s antenna array steering direction

typically points horizontally or is tilted downwards when communicating with ground users [33].

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Cellular network(density )

Legacy UEs(density )IoT devices

(density )

Drone (UAV)

antennas

(a)

1

0.5

y-coord

00-1

0.01

-0.5

x-coord

-0.5

0.02

0

z-co

ord 0.03

0.5 -1

0.04

1

0.05

BSUEIoT DeviceDrone

(b)

Fig. 1: (a) The UAV-enabled cellular architecture; (b) A spatial realization of the network

topology (λU = 5λB, λD = λB, and λM = 20/cluster).

Such attenuation depends on the drone’s relative location with the array’s boresight. However,

we assume it to be constant for tractable analysis, which is reasonable when the drone is flying

at heights higher than the BS’s antenna height.

The UAV-enabled cellular network is shown in Fig. 1a, where a drone is sent by a BS to a

cluster of IoT devices, stops at (xD,l, yD,l) to collect data from IoT devices, and then aggregates

the traffic to the BS. An illustration of one realization of the network is also shown in Fig. 1b.

D. Performance Metrics

We consider two metrics: the spectral efficiency (SE) of a typical UE in the UL and DL and

the energy efficiency (EE) of a typical IoT device, which are defined next.

1) UE Spectral Efficiency: We consider the UE to employ a multi-modulation and coding

scheme, and thus the spectral efficiency of a typical UE in the DL/UL is defined as [34]

CU,ξ = βU,ξ

KU∑k=1

log2(1 + τU,k)1(τU,k+1 ≥ γU,ξ ≥ τU,k), (4)

where ξ ∈ DL,UL, γU,ξ is the signal-to-interference-plus-noise ratio (SINR), τU,k are the

SINR thresholds, 1(·) is the indicator function, and βU,ξ is a pre-log term that denotes the

UE long-term available resources in time, frequency, and space. This rate model assumes KU

possible thresholds, and it is a generalization of the single-rate model, i.e., KU = 1, that is

commonly used in the literature [28], [35]. We emphasize that the mean load approximation,

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i.e., the assumption that the load βU,ξ is independent of γU,ξ [34], [35], is used only for tractable

analysis, while we relax this assumption when we run Monte Carlo simulations in Section V.

2) IoT Energy Efficiency: We consider the EE of the IoT device, i.e., the ratio of the achieved

rate, r(PM), to the total power consumption, c(PM). More formally, the EE of a typical IoT device

is defined as [36]

EM ,r(PM)

c(PM)=βM

∑KM

k=1 log2(1 + τM,k)1(τM,k+1 ≥ γM ≥ τM,k)

PCP + η−1PM

, (5)

where PCP is a constant that quantifies the circuit power consumption, η is the power amplifier

efficiency, and βM and γM are the IoT device long-term resources and SINR, respectively. The

motivation behind using this particular metric is as follows. We aim to address two conflicting

objectives: maximizing the rate and minimizing the transmit power. Thus, one approach is to

formulate a scalarized multi-objective optimization problem [37], where the objective function

is a weighted sum of r(PM) and c(PM). In such a problem, different weights lead to different

Pareto optimal solutions, i.e., operating points that lie on the Pareto boundary, where improving

one objective value can only degrade the other objective value. It can be shown that the ratio of

the two objectives, in this case the EE, is one of the points on the Pareto boundary [37]. The

ratio here also has a physical interpretation, i.e., the efficiency of the communication protocol

measured in the output bps per unit power consumed. Moreover, the metric is also relevant

to applications where coverage is paramount. For example, the value of τM,1 determines the

minimum coverage needed since a zero rate, and hence zero EE, is achieved if γM < τM,1.

Third, the metric is also applicable to devices that only support a single modulation scheme,

where we would set KM = 1.

We note that in this paper, we focus on optimizing the link between the IoT device and the

drone. The link between the drone and the BS can be optimized separately, e.g., the drone can

get closer to the BS to ensure reliable aggregation [38], the drone can compress data generated

from devices performing a similar task [39], or the drone can itself be a BS [17]. Since this link

is studied in the aforementioned works, it is outside the scope of this paper. A summary of the

main parameters is given in Table I.

III. TDD PROTOCOL FOR SHARED SPECTRUM ACCESS

In this section, we present the proposed transmission protocol to enable shared spectrum access

between massive IoT and UEs over UAV-enabled cellular networks. We then analyze the average

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TABLE I: Main parameters and their values if applicable

Description Parameters Value(s) (if applicable)

Path loss parameters

αG: Path loss exponent for ground-to-ground links αG = 3.5

αA: Path loss exponent for ground-to-air links αA = 2.2 [16]

L0: Path loss at a reference distance of 1m (assuming 2GHz carrier frequency) L0 = −38dB

LNLOS: Additional non-LOS path loss LNLOS = −20dB [31]

LSTR: Additional path loss due to BS’s antenna array steering direction LSTR = −30dB [16]

BS parameters

PB : BS transmit power PB = 46, 32dBm

MB: Number of antennas at the BS MB = 32

UB: Number of spatially multiplexed users UB = 4

UE parametersPU: UE transmit power PU = 23dBm

τU,k : SINR threshold from −5 to 30dB

IoT device parameters

PmaxM and Pmin

M : Maximum and minimum allowable transmit powers PmaxM = 23dBm and Pmin

M = 1dBm

PCP : Circuit power consumption PCP = 90mW [27]

η: PA efficiency η = 0.44 [27]

τM,k : SINR threshold from −5 to 10dB

R: Cluster radius R = 50m [15]

allocated resources of the UE and the IoT device under the proposed protocol and compare it

to those achieved under existing transmission protocols.

We focus on TDD cellular networks, and thus the proposed protocol is divided into two slots:

T1 and T2. In the first time slot, the UE operates in the UL, communicating with its tagged BS.

Similarly, in this slot, we treat the drone as another UE, which aggregates previously collected

data from IoT devices and sends it to its tagged BS. In the second time slot, the UE operates in

the DL, whereas the IoT device operates in the UL, communicating with its associated drone,

as shown in Fig. 2a. The proposed protocol is motivated as follows.3

• Maximum bandwidth: The protocol allows the IoT device to share the same time-frequency

block with the UE, i.e., no resource splitting is used.

• Reducing congestion: When the UE operates in the UL, it competes for scheduling with

drones instead of IoT devices, and thus the channel congestion is significantly reduced.

• Limiting the impact of IoT interference: The shared access paradigm inevitability leads

to additional interference from IoT devices into UEs. However, when IoT devices transmit

data in the UL, UEs operate in the DL, where their tagged BSs transmit at much higher

3The proposed protocol differs from the reverse TDD protocol in [40]. The latter is developed to address the coexistence of

macro and small cells in the presence of wireless backhaul. In addition, in a given time slot, not all cells use the same spectrum

in reverese TDD, and further, small cells are divided into two groups. The first small cell group operates in the UL, i.e., from

small cell to macro cell, and the second one operates in DL, i.e., from small cell to UE.

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Time

Freq.

(a) Proposed TDD

Time

Freq.

(b) Sharing-based TDD

Time

Freq.

(c) Orthogonal-based TDD

Fig. 2: Comparison of the different TDD transmission protocols.

power than the transmit power of IoT devices as PB PM.

A. Characterization of average resources in the proposed and existing protocols

For tractable analysis, we assume that a proportional fair scheduler is used, e.g., round-robin,

and thus under the mean load approximation [35], the average load is inversely proportional to

the average number of devices connected to the same source.

1) Proposed protocol: Let βPU,UL denote the average allocated resources to a typical UE

operating in the UL under the proposed protocol. Then, it can be shown that

βPU,UL

(a)= W︸︷︷︸

Freq.

× UB︸︷︷︸Space

× T1

(1

NPB,UL

)︸ ︷︷ ︸

Time

(b)= W × UB × T1

(λB

λU + λD

),

(6)

where (a) follows since the entire bandwidth W is allocated to the UE, UB UEs can be spatially

multiplexed by the same BS, and the portion of the time allocated to the UE is inversely

proportional to the average number of devices connected to the BS, i.e., NPB,UL. Here, (b) follows

by showing that the average number of UEs (or drones) connected to the BS under the nearest

BS association is λU/λB (or λD/λB) [35]. Similarly, the average portion of resources of the UE

in the DL is expressed as βPU,DL = W × UB × T2

(λB

λU

), which follows since in the second time

slot, no IoT devices are connected to the BS under the proposed protocol. For the IoT device, it

can be shown that the average portion of resources is given as βPM = W ×T2λ

−1M , which follows

since the average number of IoT devices per cluster is λM, and the drone multiplexes one IoT

device per time-frequency slot. Note that for low-rate applications, the drone can divide the

bandwidth W into smaller frequency blocks and serve multiple IoT devices, one per frequency

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block. This does not change βPM since the decrease in frequency resources is equally compensated

by increased time resources.

2) Comparison with sharing-based protocol: In the sharing-based protocol, the IoT device

is registered as another UE, as shown in Fig. 2b. To control channel congestion, the 3GPP

standard proposes one mechanism, namely access class barring (ACB), which prioritizes UE

traffic over IoT devices [7]. More formally, each BS broadcasts a parameter 0 ≤ κ ≤ 1 to all IoT

devices in vicinity. The IoT device then generates a random number n ∈ [0, 1] before initiating

a channel access request. If n > κ, then the IoT device does not request access. Clearly, for

κ = 1, the protocol simplifies to a standard sharing protocol that is agnostic to the device type.

Let βSU,UL denote the average allocated resources to a typical UE operating in the UL under

the sharing-based protocol. Then, we have βSU,UL = W × UB × T1

(λB

λU+κλMλCl

), which follows

since the average number of IoT devices per BS is λMλCl/λB, yet only a fraction, κ, of them

request access. Clearly, for βSU,UL > βP

U,UL, we must have κ < λ−1M , yet this degrades the average

resources allocated to the IoT device. Indeed, the mean resources for the IoT device under the

sharing protocol is βSM = P(n > κ)βS

M|n>κ + P(n ≤ κ)βSM|n>κ, which can be simplified to

βSM = W × UB × κT1

(λB

λU + κλMλCl

)(a)

≤ βPM

(UBλB

λU + λCl

), (7)

where (a) follows using κ < λ−1M and assuming T1 = T2. Since the density of UEs is typically

higher than the density of BSs, i.e., λU UBλB, we get βSM < βP

M. Finally, for the second time

slot, we have βSU,DL = βP

U,DL for the UE.

3) Comparison with orthogonal-based protocol: Alternative to using ACB to resolve channel

congestion, 3GPP has also proposed the separation of frequency resources [7], as shown in Fig.

2c. Let WU ∈ [0,W ] be the portion of the spectrum allocated for UEs, then the average portion of

allocated resources for a typical UE in the UL under this protocol is βOU,UL = WU×UB×T1

(λB

λU

).

If WU/W > λU/(λU +λD), then we have βOU,UL > βP

U,UL. However, this comes at the expense of

reducing the resources allocated to the IoT device since we have βOM = WM×UB×T1

(λB

λMλCl

),

which is bounded by

βOM

(a)< W × UB ×

T1

λM

(λB

λU + λCl

)(b)< βP

M,

(8)

where (a) follows from the fact that WM = W −WU and thus WU

W> λU

λU+λCl⇐⇒ WM

W< λCl

λU+λCl.

In addition, (b) follows assuming T1 = T2 and the density of UEs is high. Finally and similar

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to the sharing-based protocol, we have βOU,DL = βP

U,DL for the UE.

To summarize, for the sharing protocol to outperform the proposed one in terms of resource

allocation for the UE, we must use aggressive ACB with very small values of κ, which inevitably

affects the IoT EE as the average portion of allocated resources is decreased. For the orthogonal

allocation to outperform the proposed protocol in terms of the UE performance, nearly all

resources should be allocated to the UE, i.e., WU → W , since λU λD, and this also limits the

resources allocated to the IoT device. We note that the derived theoretical allocated resources

for the proposed protocol, i.e., (βPU,UL, β

PU,DL, β

PM), are agnostic to the type of aggregator used.

Indeed, using drones versus terrestrial aggregators primarily affect the signal and interference

powers and not the number of resources allocated to devices.

B. Analysis of IoT Interference on UEs

While the proposed protocol improves the average allocated resources of a typical UE, in

comparison with existing protocols, the signal-to-interference ratio (SIR) of a typical UE degrades

due to the presence of an additional interference term generated from IoT devices (cf. Fig. 2a).

To study the coverage probability of the typical UE, we define the UE SIR as

γPU,DL =

PB

UBgBL0x

−αGB∑

yb∈Φ′B

PB

UBfbL0y

−αGb +

∑zm∈Φ′M

PMfmL0z−αGm

, (9)

where Φ′B is the set of interfering BSs, Φ′M is the set of interfering IoT devices, fm ∼ Γ(1, 1),

xB is the distance to the tagged BS, yb is the distance to the b-th interfering BS, and zm is the

distance to the m-th interfering IoT device.

The coverage probability is defined as CPU,DL(τ) , P(γP

U,DL ≥ τ), which can be rewritten as

CPU,DL(τ)

(a)= 2πλB

∫ ∞0

xEgB

[FIU

( gB

τxαG

)]e−πλBx

2

dx, (10)

where (a) follows from the distribution of the distance from the UE to the tagged BS [35] and

FIU(·) is the cumulative distribution function (CDF) of the interference. Using the Gil-Pelaez

Inversion theorem [41] to compute the interference CDF, we get the following theorem.

Theorem 1. The coverage probability of the UE under the proposed protocol is expressed as

CPU,DL(τ) =

1

2− Υ(τ, λB, λD, PB,M)

π, (11)

where PB,M = sinc−1(δG)PMUB/PB, δG = 2/αG, and

Υ(τ, λB, λD, PB,M) =∫∞

01t

Im

(1+jt/τ)−∆B

2F1(δG,ΨB;1−δG;jt)+λDλB

PδGB,M(−jt)δG

dt. (12)

13

-10 -5 0 5 10 15 20

(dB)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cov

erag

e P

roba

bilit

y Theo: No IoTTheo:

D=1

Theo: D

=2

Theo: D

=5

Sim: No IoTSim:

D=1

Sim: D

=2

Sim: D

=5

(a) Variations of SIR threshold

0 5 10 15 20 25

PM

(dBm)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cov

erag

e P

roba

bilit

y

Theo: No IoTTheo:

D=1

Theo: D

=2

Theo: D

=5

Sim: No IoTSim:

D=1

Sim: D

=2

Sim: D

=5

(b) Variations of IoT transmit power, PM

Fig. 3: The UE DL coverage performance with and without IoT devices.

Proof: See Appendix A.

The expression is given in a single integral form that can be efficiently evaluated using numer-

ical software. The key insight here is that the degradation of the UE coverage due to the presence

of IoT devices depends mainly on two factors: (i) the ratio of the transmit power of the IoT

device to the power allocated to the UE, i.e., PM/(PB/UB) and (ii) the average number of drones

per BS, i.e., λD/λB. To see this, note that the coverage probability in the absence of IoT devices

is CNU,DL(τ) = 1

2− 1

π

∫∞0

1t

Im

(1+jt/τ)−∆B

2F1(δG,ΨB;1−δG;jt)

dt, and thus using stochastic dominance, i.e.,

CNU,DL(τ) ≥ CP

U,DL(τ), we have∫∞

01t

Im

(1+jt/τ)−∆B

2F1(δG,ΨB;1−δG;jt)

dt ≤ Υ(τ, λB, λD, PB,M), where the

gap above decreases as λD/λB → 0 and/or PM/(PB/UB)→ 0.

We validate the theoretical expression with Monte Carlo simulations, using the same param-

eters in Table I. Fig. 3a shows the distribution of coverage in the presence and absence of IoT

devices. It is observed that increasing the number of drones decreases the coverage, yet the

degradation is not severe, e.g., the median SIR merely degrades by 1.7dB under the proposed

protocol with λD/λB = 5. Recall that here a drone is assigned to a single cluster. However, if a

single drone is assigned instead to serve multiple clusters, moving from one stop point to another,

then the interference on UEs from IoT transmission decreases, e.g., median SIR degradation is

less than 0.36dB when λD/λB = 1. Nevertheless, the cost of reducing this interference is the

increased delay on IoT devices, leading eventually to degradation of the IoT energy efficiency

when λMλCl 1. To this end, another approach to limit the interference is to reduce the IoT

transmit power, as shown in Fig. 3b. In the next section, we focus on optimizing the IoT transmit

14

power such that the IoT EE is maximized and the IoT interference is controlled.

IV. IOT ENERGY-EFFICIENCY MAXIMIZATION

In this section, we formulate a stochastic optimization problem to maximize the average EE

of an IoT device under the proposed protocol. The problem has the following form

maximizePM

E[EM]

subject to f(IU) ≤ ε,

PM ∈ P ,

(13)

where the f(·) is an interference constraint to protect UEs and P is the feasible set of transmit

powers. We have the following remarks about the problem in (13). First, it is a stochastic

optimization framework, as the objective function is the mean of a random variable, and the

expectation is taken with respect to spatial realizations. Second, such formulation aims to

mainly optimize the nominal transmit power, PM, significantly reducing the complexity of

implementation, i.e., the network or the drone only broadcasts the optimal value as a reference

power over a control channel4 to all of its IoT devices. Thus, all devices belonging to the same

cluster use the same transmit power, which maximizes on average the EE, i.e., this approach does

not necessarily maximize the EE of every device as a single value is used, yet it significantly

reduces the control overhead. Third, the constraint is a function of the interference from IoT

devices into UEs. We do not enforce a UE rate constraint because this would incur additional

overhead due to the necessary coordination between UEs and UAVs. There are two challenges

to solve (13). The first one is that the objective function is intractable due to the ground-to-air

channel model from interfering BSs and IoT devices into drones. The second one is that the

UE coverage probability in (11) is given in an integral form, making it not amenable to use

as a UE protection criterion. For these reasons, we focus on optimizing the EE in a single-cell

single-drone (SC-SD) setting, i.e., we ignore the interference from BSs and IoT devices outside

the cell of the typical IoT device. We discuss several extensions to this problem in Section IV-B.

4In LTE and 5G-NR, the BS sends power control commands via the downlink control information (DCI) over the physical

downlink control channel (PDCCH). In this case, the reference power, also known as open-loop transmit power, Po, is set to the

solution of the problem, i.e., Po = P ?M. Once the device successfully decodes the DCI, it follows the power control commands

on the uplink channel, possibly adding offsets to Po depending on the path loss or channel quality.

15

A. Optimization of the IoT EE in the SC-SD Case

1) Derivation of the average EE: Let EM and γM denote the IoT EE and IoT UL SINR in the

SC-SD case, respectively, and let p = PM for notational simplicity. Then, the average EE under

the proposed protocol, i.e., EM(p) , E[EM], can be written as EM(p) =βP

M

∑KMk=1 µkP(γM(p)≥τM,k)

PCP+η−1p,

where µ1 = log2(1 + τM,1) and µk = log2(1 + τM,k+1)− log2(1 + τM,k) for k > 1.

In a single cell, the drone receives signals from IoT devices in its cluster and receives

interference from the tagged BS, which operates in the DL. The next proposition presents the

distributions of the received desired signal and interference powers at the drone, which will be

useful to evaluate P(γM(p) ≥ τM,k).

Proposition 1. The distribution of the desired signal power, SM = PMlM→D(dM,l), at a typical

drone is expressed as

P(SM ≤ τ) = 1− (PMLM/τ)δA − h2D

R2, (14)

where δA = 2/αA, LM = L0((1−LNLOS)PLOS,M +LNLOS), PLOS,M is the average of (2), which is

computed numerically, and τ ∈ [PMLM(R2 +h2D)−1/δA , PMLMh

−αAD ]. In addition, the distribution

of the interference signal power IB = PBlB→D(dB,l) is given as

P(IB ≤ τ) = exp(πλBh2D) · exp

(−πλB(PBLB/τ)δA

), (15)

where LB = L0((1− LNLOSLSTR)PLOS,B + LNLOSLSTR) and τ ∈ [0, PBLBh−αAD ].

Proof: See Appendix B.

Remark: It is observed from (14) that as hD increases, the variations in SM reduces since

τ ∈ [PMLM(R2 +h2D)−1/δA , PMLMh

−αAD ], i.e., the distribution of SM becomes more concentrated

around the median. This follows because the drone location is optimized to reduce the average

2D distance to a typical IoT device, increasing the LOS probability particularly when hD ≥ R.

Similarly, it is observed from (15) that increasing the density of BSs increases the interference

as the average distance between the drone and its tagged BS decreases. Furthermore, it can be

shown that increasing the drone’s height decreases IB, but not as rapidly as the decrease in SM.

Using Proposition 1, we derive the coverage probability and the average EE of the IoT device.

Theorem 2. The coverage probability of an IoT device in the SC-SD case is given as

P(γM ≥ τ) ≈ eπλBh2D · exp

−πλB

(PMLM

τ− PN

PBLB

)−δA , (16)

16

where LM = LM(R2

2+ h2

D)−1/δA and PN is the noise power. In addition, the average EE of an

IoT device is expressed as

EM(p) =βP

MeπλBh

2D∑KM

k=1 µke− πλB

(PBLB)−δA

(pLMτk−PN

)−δAPCP + η−1p

.(17)

Proof: The coverage probability can be written as

P(γM ≥ τ) , P(

SM

IB + PN≥ τ

)≈ P

(IB ≤

SM

τ− PN

), (18)

where we have used the median received signal power SM computed from (14) to approximate

the coverage (recall that SM has small variations particularly when hD ≥ R). Thus, using (15),

we arrive at (16).

2) IoT Interference Constraint: We consider the distribution of the interference-to-signal ratio

(ISR) as a protection criterion. We note that in [42], the mean of ISR (MISR) has been used

as a metric to compare different interference mitigation techniques over cellular networks with

stochastic topologies. Yet, using the ISR distribution provides more flexibility compared to the

MISR, e.g., the protection criterion can be designed to limit the median, the 95th percentile, etc.

The ISR is defined as ISRU ,EfM [IU,M]

EgB [SB]=

PMz−αGM

∆BPBUB

z−αGB

, where IU,M is the interference from the

typical IoT device to its nearest UE and SB is the received desired signal power at the UE from

its tagged BS. We note, similar to the MISR metric, the expectation is first taken with respect

to channel realizations. The distribution is thus given as

P(ISRU ≥ ρ)(a)= EzM

[exp

(−πλBz

2M

(ρ

∆BPB

UBPM

)δG)]

(b)=

[1 +

λB

λU

(ρ

∆BPB

UBPM

)δG]−1

,

(19)

where (a) follows using the complementary CDF of the distance from the UE to its tagged BS

and (b) follows by taking the expectation with respect to the distance between the IoT device

and the nearest UE.

3) The SC-SD problem: Using (17) as an objective function and the ISR expression in (19)

as an interference constraint, i.e., f(IU) ≤ ε⇔ P(ISRU ≥ ρ) ≤ ε, we have

maximizePM

∑KMk=1 µk exp

(− πλB

(PBLB)−δA

(PMLMτk

−PN)−δA)

PCP+η−1PM

subject to PM ≤ ρ(

∆BPB

UB

)(λB

λU· ε

1−ε

)1/δG,

PminM ≤ PM ≤ Pmax

M ,

(20)

17

where PminM and Pmax

M are the minimum and maximum allowable transmit powers, respectively.

In what follows, we denote the numerator of the objective function, i.e., the rate, by r(PM), and

the denominator, i.e., power consumption, by c(PM). The following proposition shows that the

problem in (20) is quasiconcave, and thus a local maximum is a global one [43].

Proposition 2. The objective function in (20) is quasiconcave and unimodal, whereas the

constraints are all affine. Hence, the optimization problem is quasiconcave.

Proof: The proof follows from showing that r(p) is S-shaped in p (see Appendix C).

Since the problem has a single optimizing variable, a line search is sufficient to solve the

problem. A closed-form solution can be derived for the special case KM = 1 and αA = 2.

Specifically, the objective function, in this case, is maximized at

p?unconst =τM,1(PN + πλBPBLB)

LM

+

√πτM,1λBPBLB(PNτM,1 + LMηPCP)

LM

, (21)

and thus the optimal transmit power is P ?M = minPmax

M , ρ(∆BPB

UB)(λB

λU· ε

1−ε

)1/δG, p?unconst. It

is observed from (21) that the optimal power increases for: (i) higher target threshold τM,1 to

meet the new coverage requirement, (ii) higher BS transmit power PB or higher BS density λB

to combat the increased interference from the cellular network, or (iii) higher PA efficiency η

to utilize the decrease in power consumption.

B. Generalizations to the SC-SD problem

1) Optimizing BS transmit power: The BS transmit power can be optimized with PM. Indeed,

PB affects both the objective function and the interference constraint in (20). To this end, if the

optimized nominal transmit power P ?M satisfies the interference constraint with strict inequality,

then PB can be reduced so that the constraint is met with equality, reducing the interference

seen at the drone. In return, PM can be set lower due to the reduction in interference, and thus

the EE is further improved. This procedure can be done recursively, as summarized in Alg. 1,

until no further improvements are achieved. Here, PminB and Pmax

B determine the range of the

feasible BS transmit power.

2) Generalization to the single-cell multi-drone case: We consider the single-cell multi-drone

case (SC-MD), where each cell has multiple drones, each serving a cluster of IoT devices. We

can further assume each drone belongs to a different tier, i.e., we consider an N -tier drone

18

Algorithm 1 Optimizing BS transmit power1: procedure (PB,0 = Pmax

B ; ζ > 0 )

2: while∣∣E(PM,i+1)− E(PM,i)

∣∣ > ζ do

3: Update constraint: Iconst,i = ρ(

∆BPB,i

UB

)(λB

λU· ε

1−ε

)1/δG

4: Solve for PM,i+1 in (20) using line search

5: Update BS transmit power: PB,i+1 = min

(max

(PM,i+1

ρ∆BUB

(λBλU

· ε1−ε

)1/δG, Pmin

B

), Pmax

B

)6: i = i+ 1

7: end while

8: return P ?M = PM,i and P ?B = PB,i

9: end procedure

network such that the l-th tier drone flies at an altitude of hD,l and serves an IoT cluster of

radius Rl. The IoT device in a cluster served by the l-th drone transmits at power PM,l.

The challenge in the multi-drone is that the objective function can no longer be given in a

closed-form expression due to the complicated ground-to-air path loss model between multiple

interferers and the drone. Here, the interferers, with respect to a given drone, are the tagged BS

and the other IoT devices transmitting to their respective drones in the same cell. To this end, we

propose to model the different interference sources in the cell as one Poissonian source with a

transmit power equal to the sum of transmit powers of all interferers. Such an approach ensures

a tractable formulation and will be validated in the simulations section. Under this modeling

assumption, the EE of an IoT device served by the l-th drone tier can be written as

El(PM) ,βP

MeπλBh

2D∑KM

k=1 µke−

πλB

(PM,lLM,l

τk−PN

)−δA(PBLB+

∑n 6=l PM,nLM,n)−δA

PCP + η−1PM,l

, (22)

where PM is the vector of transmit powers. Next, we discuss two common formulations for the

EE optimization in the SC-MD case: the max-min and sum-EE formulations.

In the max-min approach, the objective is to maximize the minimum EE of a typical IoT

device, and thus the optimization problem is given as

maximizePM

minl

El(PM)

subject to∑

l PM,l ≤ ρ(

∆BPB

UB

)(λB

λU· ε

1−ε

)1/δG,

PminM ≤ PM,l ≤ Pmax

M ∀l.

(23)

19

In the sum-EE formulation, the objective is to maximize∑N

l=1 El(PM). The EE expression in

(23) is still quasiconcave, and since the objective function is the minimum of quasiconcave

functions, it remains quasiconcave. Thus, the max-min problem is quasiconcave. However, for

the total EE formulation, the objective function is not necessarily quasiconcave, as the sum of

quasiconcave functions does not preserve quasiconcavity. Both approaches can be solved using

the generalized Dinkelbach’s algorithm [44], which solves the max-min globally, whereas it has

become a popular algorithm to solve the sum of ratios, although it does not necessarily arrive

at the global optimal solution, if it exists [45].

C. Implementation and practical considerations

Solving the EE problem requires prior knowledge about ∆B and UB, which are determined

by the BS via the transmission mode in LTE or via BS DL precoding in NR. Further, the BS

needs to have prior estimates about the network load, i.e., λB and λU. Since IoT devices may

have varying PA efficiencies, a nominal value may be used for a given modulation and coding

scheme to estimate the total power consumption, i.e., c(p). Estimating the rate, i.e., r(p), is

easier as cellular networks already rely on rate-based metrics for link adaptation, e.g., using the

channel-equality indicator (CQI) tables, and thus existing methods can be applied. In terms of

computational complexity, solving the SC-SD problem has low complexity, and thus the drone

can solve it locally, yet the BS must relay the relevant information to the drone. For the multi-

drone case, it is more economical to solve the problem at the BS, eliminating the need for the

drones to communicate with each other.

Once each IoT cluster receives the nominal transmit power, each IoT device can individually

apply fractional power control (FPC) to adapt to the channel quality or path loss. Note that UEs

also use FPC, yet the value of PU does not affect the performance of IoT devices or the EE

optimization problem since IoT devices do not interfere with UL UEs in the proposed protocol.

Finally, there remain practical challenges related to deploying drones and synchronizing UEs

and IoT devices. For example, the authors in [18] have already developed an IoT platform that

uses drones for crowd surveillance, yet scaling such a platform requires innovative solutions

to enable extended hours of operations and autonomous control of a large number of drones.

Furthermore, similar to a BS synchronizing multiple UEs over the same time-frequency slot

for MIMO spatial-multiplexing, the BS must extend its capability to synchronize UEs and IoT

devices using UL scheduling grants in order to implement the proposed TDD protocol.

20

V. SIMULATION RESULTS

Unless otherwise stated, we use the simulation parameters given in Table I. In each spatial

realization of the network, we generate BSs, UEs, and IoT devices according to their distributions.

Each drone then moves to their predetermined stop points. We then generate the channel power

gains according to their distributions and compute the large-scale fading for all links to compute

their SINR, where a thermal noise power, with spectral density −174dBm/Hz, is considered at

all receivers. Then the SE of UEs is computed via (4) and the EE IoT devices is computed via

(5) for the different transmission protocols. We note that we use the actual load and the 3GPP

LOS probability, instead of their mean, to compute the performance metrics.

A. Validation of the theoretical analysis

We first validate the theoretical analysis and the stochastic optimization problem, focusing on

SC-SD and SC-MD scenarios. We compare the EE performance under the proposed nominal

transmit power with that achieved under a coverage-maximizing scheme, where the IoT device

transmits at a maximum power of PM = 23dBm [5].

1) Impact of IoT transmit power on the EE: We consider two IoT categories: CAT-0 and

NB-IoT. In the former, the IoT device shares the entire band with the UE, i.e., W = 20MHz

and PB = 46dBm. In the latter, the IoT only shares a single resource block, i.e., W = 180KHz

and PB = 32dBm. For interference protection, we assume ε = 0.5 and ρdB = −6dB, i.e., the

median ISR should not exceed −6dB. Note that this ISR threshold is commonly used as a

protection criterion in FCC’s regulations [46], and it corresponds to an SINR degradation of

1dB. The performance of EE under different transmit powers is shown in Fig. 4a. It is observed

that the theoretical expression in (17) matches well with Monte Carlo simulations. Further, the

EE is significantly improved using the proposed SC-SD framework compared to the max-power

scheme, e.g., the EE in CAT-0 of the proposed SC-SD framework is 4.5x and 3.3x that of max-

power for hD = 50m and hD = 120m, respectively. This follows because the drone’s location

is optimized to minimize the 2D distance to the IoT device, requiring low transmit power for

reliable coverage. Third, increasing the drone’s height has two effects: an increase in the optimal

transmit power and a decrease in the EE. These follow because as hD increases, the received

signal power decreases more rapidly than interference, degrading the coverage. Thus, the IoT

device must transmit at higher power to combat the degradation, decreasing its EE. Finally,

the NB-IoT operation is more efficient than CAT-0 since in the former the IoT device shares a

21

0 5 10 15 20IoT Transmit Power (dBm)

0

0.5

1

1.5

2

2.5

3

3.5

4

IoT

EE

(bp

s/H

z/J)

CAT-0

Theory (17)Sim.Theory: Solution of (20)Sim: Solution of (20)

0 5 10 15 20IoT Transmit Power (dBm)

0

0.5

1

1.5

2

2.5

3

3.5

4

IoT

EE

(bp

s/H

z/J)

NB-IoT

(a) Energy-efficiency performance

-10 -5 0 5 10 15 20 25 30

(dB)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cov

erag

e P

roba

bilit

y

Theory (16): 50mSim: 50mTheory (16): 120mSim: 120m

CAT-0

NB-IoT

(b) Coverage probability

Fig. 4: Validation of the theoretical EE and coverage.

smaller number of carriers with the UE, reducing the interference. In Fig. 4b, we validate the

coverage approximation in (16), which is shown to be in good agreement with Monte Carlo

simulations. It is evident that using drones at lower altitudes is critical to provide high coverage,

making it an alternative to IoT devices transmitting at a higher UL power.

2) Validation of BS transmit power optimization and the SC-MD case: We validate the

generalizations of the SC-SD. Here, we consider CAT-0 parameters (similar trends are observed

for NB-IoT and hence omitted).

Fig. 5a illustrates the impact of optimizing the BS transmit power using Alg. 1. It is shown

that the BS’s transmit power decreases at first since the ISR constraint is satisfied with strict

inequality. This allows the IoT device to further decrease its transmit power, which in return

improves its EE, until the constraint is satisfied with equality. For instance, the EE improves

approximately by 30% compared to the case without BS power optimization. We note that

optimizing PB may not be applicable in cases where stricter UE protections are required.

Next, we study the EE performance in the presence of multiple drones in the same cell, where

we assume they can fly at one of the these altitudes: hD = [50, 100, 150, 200, 250]m. Fig. 5b

shows the performance of Max-min and Sum-EE schemes, where power allocation is done using

the Generalized Dinkelbach’s algorithm. It is evident that the EE is improved compared to max-

power. We further show the EE of IoT devices that belong to the different drones. It is observed

that the Max-min solution aims to improve the EE of devices connected to the drone with the

highest altitude as this tier achieves the lowest EE. In contrast, the Sum-EE formulation favors

22

1 3 5 7 9

Iteration

2.8

3

3.2

3.4

3.6

3.8

IoT

EE

(bp

s/H

z/J)

Theo (17)Sim.

2 4 6 8 10

Iteration

-16

-14

-12

-10

-8

-6

Med

ian

ISR

(dB

)Theory (19)Sim.

1 2 3 4 5 6 7 8 9 10

Iteration

0

10

20

30

40

50

Tx

pow

er (

dBm

) IoT Tx power (sol. to Alg. 1)BS Tx power (sol. to Alg. 1)

(a) Impact of optimizing BS power (λM = 50m)

50m 100m 150m 200m 250m

Drone tiers (defined by altitude)

0

0.5

1

1.5

2

EE

(bp

s/H

z/J)

Average IoT EE per tier

0

1

2

3

4

5

EE

(bp

s/H

z/J)

Total EE per cell

Max-powerMax-minSum-EE

0

0.2

0.4

0.6

EE

(bp

s/H

z/J)

Minimum EE per cell

(b) EE performance in the SC-MD case

Fig. 5: Validation of generalizations to the SC-SD case (CAT-0 parameters and ρdB = −6dB).

the drones with lower altitudes as they provide higher EE for IoT devices. The disparity between

both formulations at the lowest and highest altitudes can increase with stricter ISR threshold.

B. Performance comparison with existing protocols

In this section, we compare the performance of the proposed protocol with other ones in large

networks, i.e., many cells, and hence the results are obtained via Monte Carlo simulations. To

evaluate the impact of IoT coexistence on the UEs’ spectral efficiency, we consider a benchmark

scheme without IoT devices. The proposed protocol is then compared to the following coexistence

schemes: (i) a standard spectrum sharing protocol, (ii) orthogonal-based protocol that uses

frequency partitioning, and (iii) the proposed protocol, but with terrestrial aggregators that are

deployed at the clusters’ centroid and IoT devices transmitting at maximum power. Further, we

also study the performance of the proposed protocol with the optimal PM that maximizes the

EE over the entire network, i.e., all cells and drones instead of just the SC-SD case. We obtain

PM using extensive exhaustive simulations. We consider CAT-0 IoT devices (similar trends are

observed for NB-IoT), λU = 50λB and λCl = λD = 5λB. Unless otherwise stated, we assume

δ = 1, WU = 0.5W , and hD = 50m.

1) UE performance comparison: We first study the performance of the UE in the DL and

the UL under different protocols. We note that both the orthogonal-based and the aggregator-

based protocols decouple the UE UL performance from the IoT density as in the former IoT

devices use different frequency blocks, and in the latter IoT devices connect to aggregators

23

10-2 10-1 100 101

DL Spectral Efficiency (bps/Hz)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CD

F

UE Benchmark (no IoT)Spectrum sharing [1.0]Orthog [1.0]Proposed [0.98]Terrestrial aggregators [0.88]Proposed with exhaustive search [0.98]

(a) Distribution of DL SE

10-2 10-1 100 101

UL Spectral Efficiency (bps/Hz)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CD

F

UE Benchmark (no IoT)Spectrum sharing with

m =10 [0.52]

Spectrum sharing with m

=30 [0.32]

Orthog [0.56]Proposed [0.88]Terrestrial aggregators [0.91]Proposed with exhaustive search [0.88]

(b) Distribution of UL SE

Fig. 6: UE spectral efficiency under different protocols (CAT-0 parameters and ρdB = −6dB).

instead of BSs. This is not the case for the sharing-based protocol, where we study the UE’s

performance for λM = 10 and λM = 30. Fig. 6a and Fig. 6b show the distribution of the DL

SE and UL SE across all UEs, respectively. We also show in the legend the mean SE relative

to the benchmark, i.e., the ratio of the mean SE under the given protocol to the mean SE in the

absence of IoT devices. Since our model considers IoT devices to only operate in the UL, the

DL SE of spectrum sharing and frequency partitioning protocols is the same as the benchmark.

For the proposed protocol, it is shown that the DL degradation is minimal since UAVs are

used and the transmit power is optimized to limit the IoT interference. More importantly, the

proposed protocol outperforms spectrum sharing and frequency partitioning in the UL, e.g., the

relative mean UL SE of the proposed protocol is improved by 2.7x compared to spectrum sharing

(λM = 30). Finally, using terrestrial aggregators improves the UL SE, similar to using drones,

yet the DL SE is still degraded by 10% compared to the proposed protocol.

2) IoT performance comparison: We then study the EE of the IoT device under the different

protocols. In Fig. 7a, the EE is shown for different densities of IoT devices. As expected, as

the number of IoT devices increases, the EE decreases under all protocols. Yet, the proposed

protocol achieves the highest EE and scales better with λM compared to existing ones. It is also

observed that it is beneficial to use UAVs over terrestrial aggregators as the former provides

higher LOS, i.e., the EE improves by 3x when aerial aggregators are used instead of terrestrial

ones. In Fig. 7b, we study the EE for different drone’s altitudes. We show the performance

under the existing protocols and the proposed one with terrestrial aggregators, which do not

24

5 10 15 20 25 30

M

10-1

100

101

IoT

EE

(bp

s/H

z/J)

Spectrum sharingOrthog.ProposedTerrestrial aggregatorsProposed with exhaustive search

(a) Variations of IoT density (hD = 50m)

50 100 150 200 250 300

Drone height, hD

(m)

10-2

10-1

100

101

IoT

EE

(bp

s/H

z/J)

Spectrum sharingOrthog.ProposedTerrestrial aggregatorsProposed with exhaustive search

maximum height by regulations

(b) Variations of drone’s height (λM = 10)

Fig. 7: IoT EE performance under different protocols.

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1UE Uplink SE (bps/Hz)

0

0.5

1

1.5

2

IoT

EE

(bp

s/H

z/J)

Spectrum sharingProposedTerrestrial aggregatorsProposed with exhaustive search

(a) Varisations of ACB threshold

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1UE Uplink SE (bps/Hz)

0

0.5

1

1.5

2

IoT

EE

(bp

s/H

z/J)

Orthog.ProposedTerrestrial aggregatorsProposed with exhaustive search

(b) Variations of frequency partitioning ratio

Fig. 8: IoT energy-efficiency vs. UE spectral efficiency (λM = 10 and hD = 50m).

depend on hD, for reference. It is observed that the proposed protocol is beneficial for lower

altitudes. At very high altitudes, the received signal power is lower, and the LOS probability

with interfering BSs, from different cells, increases. We note that in many regions, e.g., North

America, Europe, China, etc., the maximum legal altitude for drones is roughly 120m (400ft),

and thus the proposed solution is superior in practical scenarios.

Fig. 8 shows the IoT EE versus the UE SE in the UL under different ACB thresholds κ (Fig.

8a) and different frequency allocation ratios WU (Fig. 8b). The performance of the proposed

protocol, which does not depend on these parameters, is also shown for reference. It can be seen

that existing protocols have operating points with higher UE SE performance in comparison with

proposed ones. However, high ACB threshold and frequency partitioning ratio are needed, and

thus the IoT device will be limited with time and frequency resources, respectively. Finally, it

is shown that optimizing PM over the SC-SD case leads to a nearly identical performance to

exhaustive search, yet the latter requires extensive simulations to solve.

25

C. IoT device lifetime comparison

In this section, we follow the 3GPP evaluation methodology to compute the lifetime of IoT

devices for the different schemes [27], [47]. In particular, the IoT device sends Nrep reports per

day to the network. For each report, the device operates in the following stages: standby, idle,

transmission, and reception. Let PS, PI, and PRX denote the power consumption of the standby,

idle, and reception stages. Similarly, let TS, TI, and TRX be their durations. For a fair comparison,

we assume the energies consumed for these three stages are the same across the schemes, i.e.,

the schemes only differ in the energy consumed during the transmission stage as our focus is

on the UL. The transmission duration is

T(ν)TX =

B/β(ν)M∑KM

k=1 log2(1 + τM,k)1(τM,k+1 ≥ γ(ν)M ≥ τM,k)

, (24)

where B is the total size of the data transmitted per report, which includes the connection request,

the data packet, and the acknowledgment [27, Table 4]. The superscript ν denotes the scheme

used. Similarly, P (ν)TX = PCP +η−1P

(ν)M . Thus, the total energy consumed per day is given as [27]

E(ν)IoT = Nrep

(T

(ν)TXP

(ν)TX + TRXPRX + TIPI

)+ TSPS. (25)

Let the IoT battery’s capacity be CIoT Wh, then the device lifetime in years is given as Y (ν) =

CIoT

E(ν)IoT

× 3600365

. Note that increasing the IoT transmit power is expected to improve the SINR,

increasing the rate and decreasing T(ν)TX . Yet, this comes at the expense of increased power

consumption during the transmission stage, i.e., higher P (ν)TX .

For the simulation set-up, we use a more realistic deployment and channel model. Specifically,

we consider a hexagonal deployment of BSs, and consider the NR 3D-UMa channel model for

ground-to-ground links [48] and the UMa-AV model for ground-to-air links [33]. These models

assume multi-slope path loss with different attenuation, depending on whether the link is LOS

or non-LOS, as well as consider log-normal shadowing. We assume the antenna height of the

BS and IoT devices are 30m and 1.5m, respectively, and the operating channel is centered at

2GHz. We use the battery lifetime parameters given in Table II [27]. Finally, we allow each

IoT device to apply fractional power control on top of the optimized nominal transmit power to

compensate for path loss, where we consider a factor of 0.3.

Fig. 9 shows the CDF of the IoT device lifetime for each scheme. We have the following

observations. First, the improvements in EE under the proposed scheme are translated into

tangible enhancements to the IoT device lifetime, e.g., the median lifetime is increased by more

26

TABLE II: Battery lifetime parameters [5], [27]

Description Parameters

IoT device NB-IoT with W = 180KHz, CIoT = 5Wh, B = 229bytes [27, Table 4], and Nrep = 12

Powers PRX = 90mW, PI = 3mW, and PS = 0.015mW [27, Table 1]

Durations TRX = 565ms, TI = 22451ms, and TS = 86400s [27, Table 6]

8 10 12 14 16 18

IoT deivce lifetime (years)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CD

F

Spectrum sharingOrthogProposed (h

D=50m)

Proposed (hD

=100m)

Terrestrial aggregators

Fig. 9: Distribution of IoT device lifetime.

than three years compared to spectrum sharing and frequency partitioning schemes. Second,

due to the aggregators’ proximity to IoT devices, whether aerial or terrestrial, the variance in

lifetime across devices is lower under compared to schemes without aggregators. When UAVs are

used instead of terrestrial aggregators, the variance is further reduced thanks to the better LOS

conditions. Finally, as the drone altitude increases, the IoT device lifetime slightly decreases,

i.e., the performance gain of using drones over terrestrial aggregators is reduced.

VI. CONCLUSIONS

In this work, we have proposed a TDD protocol for a shared spectrum access between massive

IoT and cellular UEs with UAVs acting as data aggregators. Using stochastic geometry, it

is shown that the protocol improves the average allocated resources of IoT devices and UEs

compared to resource splitting and ACB, yet UEs experience additional interference from IoT

devices. Thus, we have optimized the nominal transmit power of the IoT device to maximize its

energy-efficiency while constraining the interference on UEs. The optimal nominal power can

be then biased by each IoT device individually using uplink power control when additional path

loss compensation is needed. Simulation results show that the proposed protocol significantly

improves the EE, and hence the IoT device lifetime, thanks to the drones proximity to the IoT

device, while still protecting the UEs thanks to the optimized IoT transmit power.

27

The key insights gleaned from this work are as follows. First, it is beneficial for drones to fly

at lower altitudes as higher altitudes increase the LOS with interferers, forcing the IoT device to

increase its transmit power and degrading its EE. In case drones, belonging to the same BS, fly

at different altitudes, then maximizing the minimum EE and the total EE amount to prioritizing

devices connected to drones at the highest and the lowest altitudes, respectively. Second, the

extended coverage mode, where IoT devices transmit at maximum power, is not necessarily

energy efficient as the gain in coverage does not outweigh the loss in power consumption.

APPENDIX

A. Proof of Theorem 1

Recall that the aggregate interference at the UE is given as

IU =∑yb∈Φ′B

fby−αGb︸ ︷︷ ︸

IU,B

+∑

zm∈Φ′M

PM

PB/UB

fmz−αGm︸ ︷︷ ︸

IU,M

, (26)

where we have normalized the interference by L0PB/UB. Using the Gil-Pelaez Inversion theorem

[41] to evaluate the interference CDF, we get FIU(

gB

τxαG

)= 1

2− 1

π

∫∞0

ImϕIU(xαGt)e−jtgB/τ

dt,

where ϕIU(xαGt) = EIU [exp (jtxαGIU)] is the characteristic function (CF), which is given as

ϕIU(xαGt)(a)= EIU,B

[e

(jtxαG

∑yb∈Φ′

Bfby−αGb

)]× EIU,M

[e

(jtxαG

∑zm∈Φ′

M

PMPB/UB

fmz−αGm

)], (27)

where (a) follows since interfering BSs are independent from the interfering IoT devices.

Using the probability-generating functional of the HPPP process [26], it can be shown that

ϕIU,B(xαGt) = exp (πλBx2(1− Efb [Ω(fb, δG, t)])), where Ω(fb, δG, t) = 1F1(−δG; 1 − δG; jtfb),

and 1F1(a; b; c) is the confluent hypergeometric function [49]. Similarly, we have

ϕIU,M(xαGt)(a)= e

−2πλD

∫∞0 y

1−Efm

ejt UBPMfmxαG

PByαG

dy(b)= exp

(−πλDx

2P δGB,M(−jt)δG

),

(28)

where (a) follows using the fact that the set of interfering IoT devices can be modeled as

a set of Poisson interferers with density of λD as one IoT device is scheduled per drone

per time-frequency slot, and (b) follows using the CF of fm and then using the substitution

l = xαGy−αG . Here, the integral lower limit is zero as the set of interfering IoT devices

is independent of the UE’s location, i.e., no protection zone is present unlike the case of

28

interfering BSs which cannot be closer than the tagged BS. To summarize, we have ϕIU(xαGt) =

exp(πλBx

2(

1− Ef [Ω(fb, δG, t)]− (λD/λB)P δGB,M(−jt)δG

)). Thus, the coverage becomes

CPU,DL(τ) =

1

2− 2λB

∫ ∞0

1

tIm ϕg(−t/τ)Ξ(t) dt, (29)

where ϕgB(−t/τ) = 1

(1+jt/τ)∆Bis the CF of gB and Ξ(t) = (2πλB)−1

Ef [Ω(fb,δG,t)]+(λD/λB)PδGB,M(−jt)δG

. Using

Ef [Ω(fb, δG, t)] = 2F1(ΨG, UB; 1− δG; jt) in (29), we arrive at (11).

B. Proof of Proposition 1

Let the IoT device be at a distance xM from the drone. Then, using the mean LOS probability,

the received signal power at the drone can be approximated as P(SM ≤ τ) ≈ P(PMLMx

−αAM ≤ τ

).

W can further simplify this expression to

P(PMLMx

−αAM ≤ τ

)= 1− FxM

((PMLM

τ

)1/αA

)

(a)=

1− (PMLM/τ)δA−h2D

R2 , PMLM

(R2+h2D)1/δA

≤ τ ≤ PMLM

h1/δAD

0, otherwise,

(30)

where (a) follows using the CDF of the distance between the typical IoT device and the

drone FxM(·), which is found using the fact that the IoT device is randomly distributed over

an area of radius R centered around the 2D coordinates of the drone. Further, let rB denote

the distance between the tagged BS and the drone, then P(IB ≤ τ) ≈ P(PBLBr

−αAB ≤ τ

)=

1−FrB((

PBLB

τ

)1/αA)

. Since the distance between a point in R2 and the nearest BS is distributed

as fyB(y) = 2πλBy exp(−2πλBy

2) [35]. Hence, the distribution of rB =√y2

B + h2D can be shown

to be frB(r) =2rfyB (

√r2−h2

D)√r2−h2

D

. Thus, we can compute FrB(r) =∫∞hDfrB(r)dr to arrive at (15).

C. Proof of Proposition 2

We first derive useful properties for r(p). In particular, r(p) is a non-negative sum of coverage

probabilities, each is non-decreasing with the transmit power, and thus r(p) is non-decreasing

with p. Thus, the t-sublevel sets, i.e., Rt,sub = p|r(p) ≤ t, and the t-superlevel sets, i.e.,

Rt,sup = p|r(p) ≥ t, are convex, and hence r(p) is quasilinear [43]. To show that r(p) is

S-shaped, we take the 2nd derivative with respect to p to get

d2r(p)

dp2= cBL

2M

KM∑k=1

µke−πλB

pLMτM,k

−PNPBLB

−δA

τ 2M,k

(pLM

τM,k− PN

)2(1+δA)×

cB − (1 + δA)

(pLM

τM,k

− PN

)δA,

(31)

29

where cB = δAπλB(PBLB)δA . Note that( pLMτM,k

−PNPBLB

)≥ 0 for any feasible τM,k and the derivative

is non-increasing with p. Furthermore, there exists a point p• such that d2r(p)dp2 ≥ 0 for p ≤ p•

and d2r(p)dp2 ≤ for p ≥ p•, and hence the function is S-shaped.

To prove that the objective function in (20) is quasiconcave, then it is sufficient to prove that

the superlevel sets Et,sup = p| r(p)c(p)≥ t are convex. Since the objective is non-negative, then we

only consider the case for t ≥ 0 and prove that p|r(p) − c(p)t ≥ 0 is convex. We consider

two cases. First, for p ≥ p•, r(p) is concave, and thus for p1, p2 ∈ Et,sup and β ∈ [0, 1] we have

r(βp1 + (1− β)p2)− c(βp1 + (1− β)p2)t(a)

≥ βr(p1) + (1− β)r(p2)− c(βp1 + (1− β)p2)t

(b)= β (r(p1)− c(p1)t) + (1− β) (r(p2)− c(p2)t)

≥ 0,(32)

where (a) follows because r(p) is concave and (b) follows because c(p) is affine, and thus, Et,sup

is convex. Second, for p ≤ p•, r(p) is convex. Taking the first derivative of E(p), we get

dE(p)

dp=η−1(pr′(p)− r(p)) + PCPr

′(p)

c2(p). (33)

The second sum term r′(p) ≥ 0 as r(p) is a non-decreasing function in p. In addition, the first

sum term pr′(p)− r(p) ≥ 0 because r(p) is convex, i.e., for any convex differentiable function

g(x) with g(0) = 0, we have g(y) ≥ g(x) + (y − x)g′(x) [43], and by setting y = 0 we get

xg′(x) ≥ g(x). Thus, the derivative is non-negative, i.e., it is a non-decreasing function in p ≤ p•,

and hence the superlevel sets are convex, which completes the proof that the objective function

is quasiconcave. To prove that the objective function is unimodal, note that E(0) = E(∞) = 0,

and since E(p) is quasiconcave, then it has to be unimodal.

REFERENCES

[1] G. Hattab and D. Cabric, “Energy-efficient massive cellular IoT shared spectrum access via mobile data aggregators,” in

IEEE 13th Int. Conf. Wireless and Mobile Computing(WiMob), Oct. 2017, pp. 1–6.

[2] ITU-R, “IMT Vision – framework and overall objectives of the future development of IMT for 2020 and beyond,” ITU-R,

M. 2083-0, Sep. 2015.

[3] Mckinsey Global Institute, “The internet of things: Mapping the value beyond the hype,” Mckinsey&Company, Tech. Rep.,

Jun. 2015.

[4] Z. Dawy, W. Saad, A. Ghosh et al., “Toward massive machine type cellular communications,” IEEE Wireless Commun.,

vol. 24, no. 1, pp. 120–128, Feb. 2017.

[5] 3GPP, “Cellular system support for ultra low complexity and low throughput internet of things, release 13,” TS 45.820,

Nov. 2015.

30

[6] A. Rico-Alvarino, M. Vajapeyam, H. Xu et al., “An overview of 3GPP enhancements on machine to machine

communications,” IEEE Commun. Mag., vol. 54, no. 6, pp. 14–21, Jun. 2016.

[7] E. Soltanmohammadi, K. Ghavami, and M. Naraghi-Pour, “A survey of traffic issues in machine-to-machine communica-

tions over LTE,” IEEE Internet Things J., vol. 3, no. 6, pp. 865–884, Dec. 2016.

[8] P. K. Wali, A. A. N, and D. Das, “Optimal time-spatial randomization techniques for energy efficient IoT access in

LTE-advanced,” IEEE Trans. Veh. Technol., vol. 66, no. 8, pp. 7346–7359, Aug. 2017.

[9] Z. Feng, Z. Feng, and T. A. Gulliver, “Biologically inspired two-stage resource management for machine-type communi-

cations in cellular networks,” IEEE Trans. Wireless Commun., vol. 16, no. 9, pp. 5897–5910, Sep. 2017.

[10] N. Jiang, Y. Deng, A. Nallanathan et al., “Analyzing random access collisions in massive IoT networks,” IEEE Trans.

Wireless Commun., vol. 17, no. 10, pp. 6853–6870, Oct. 2018.

[11] Z. Wang and V. W. S. Wong, “Optimal access class barring for stationary machine type communication devices with timing

advance information,” IEEE Trans. Wireless Commun., vol. 14, no. 10, pp. 5374–5387, Oct. 2015.

[12] T. Kwon and J. M. Cioffi, “Random deployment of data collectors for serving randomly-located sensors,” IEEE Trans.

Wireless Commun., vol. 12, no. 6, pp. 2556–2565, Jun. 2013.

[13] D. Malak, H. S. Dhillon, and J. G. Andrews, “Optimizing data aggregation for uplink machine-to-machine communication

networks,” IEEE Trans. Commun., vol. 64, no. 3, pp. 1274–1290, Mar. 2016.

[14] U. Tefek and T. J. Lim, “Relaying and radio resource partitioning for machine-type communications in cellular networks,”

IEEE Trans. Wireless Commun., vol. 16, no. 2, pp. 1344–1356, Feb. 2017.

[15] J. Guo, S. Durrani, X. Zhou et al., “Massive machine type communication with data aggregation and resource scheduling,”

IEEE Trans. Commun., vol. 65, no. 9, pp. 4012–4026, Sep. 2017.

[16] 3GPP, “Study on enhanced LTE support for aerial vehicles,” TR 36.777, Dec. 2017.

[17] I. Bor-Yaliniz and H. Yanikomeroglu, “The new frontier in RAN heterogeneity: Multi-tier drone-cells,” IEEE Commun.

Mag., vol. 54, no. 11, pp. 48–55, Nov. 2016.

[18] N. H. Motlagh, M. Bagaa, and T. Taleb, “UAV-based IoT platform: A crowd surveillance use case,” IEEE Commun. Mag.,

vol. 55, no. 2, pp. 128–134, Feb. 2017.

[19] Z. Yuan, J. Jin, L. Sun et al., “Ultra-reliable IoT communications with UAVs: A swarm use case,” IEEE Commun. Mag.,

vol. 56, no. 12, pp. 90–96, Dec. 2018.

[20] Y. Zeng, R. Zhang, and T. J. Lim, “Throughput maximization for UAV-enabled mobile relaying systems,” IEEE Trans.

Commun., vol. 64, no. 12, pp. 4983–4996, Dec. 2016.

[21] O. M. Bushnaq, A. Celik, H. ElSawy et al., “Aeronautical data aggregation and field estimation in IoT networks: Hovering

& traveling time dilemma of uavs,” arXiv preprint arXiv:1810.08035, Oct. 2018.

[22] C. Zhan, Y. Zeng, and R. Zhang, “Energy-efficient data collection in UAV enabled wireless sensor network,” IEEE Wireless

Commun. Lett., vol. 7, no. 3, pp. 328–331, Jun. 2018.

[23] M. Mozaffari, W. Saad, M. Bennis et al., “Mobile unmanned aerial vehicles (UAVs) for energy-efficient internet of things

communications,” IEEE Trans. Wireless Commun., vol. 16, no. 11, pp. 7574–7589, Nov. 2017.

[24] E. Koyuncu, M. Shabanighazikelayeh, and H. Seferoglu, “Deployment and trajectory optimization of UAVs: A quantization

theory approach,” IEEE Trans. Wireless Commun., vol. 17, no. 12, pp. 8531–8546, Dec. 2018.

[25] J. Guo, P. Walk, and H. Jafarkhani, “Optimal deployments of uavs with directional antennas for a power-efficient coverage,”

arXiv, Nov. 2019.

[26] M. Haenggi, Stochastic Geometry for Wireless Networks. Cambridge University Press, 2012.

[27] 3GPP, “NB-IoT: Battery lifetime evaluation,” R1-156006, Oct. 2015.

31

[28] L. H. Afify, H. ElSawy, T. Y. Al-Naffouri et al., “A unified stochastic geometry model for MIMO cellular networks with

retransmissions,” IEEE Trans. Wireless Commun., vol. 15, no. 12, pp. 8595–8609, Dec. 2016.

[29] Y. Zeng and R. Zhang, “Energy-efficient UAV communication with trajectory optimization,” IEEE Trans. Wireless Commun.,

vol. 16, no. 6, pp. 3747–3760, Jun. 2017.

[30] M. Mozaffari, W. Saad, M. Bennis et al., “Efficient deployment of multiple unmanned aerial vehicles for optimal wireless

coverage,” IEEE Commun. Lett., vol. 20, no. 8, pp. 1647–1650, Aug. 2016.

[31] ——, “Unmanned aerial vehicle with underlaid device-to-device communications: Performance and tradeoffs,” IEEE Trans.

Wireless Commun., vol. 15, no. 6, pp. 3949–3963, Jun. 2016.

[32] A. Al-Hourani, S. Kandeepan, and S. Lardner, “Optimal LAP altitude for maximum coverage,” IEEE Wireless Commun.

Lett., vol. 3, no. 6, pp. 569–572, Dec. 2014.

[33] 3GPP, “Study on 3D channel model for LTE,” TR 36.889, May 2017.

[34] W. Bao and B. Liang, “Rate maximization through structured spectrum allocation and user association in heterogeneous

cellular networks,” IEEE Trans. Commun., vol. 63, no. 11, pp. 4510–4524, Nov. 2015.

[35] Y. Lin, W. Bao, W. Yu et al., “Optimizing user association and spectrum allocation in HetNets: A utility perspective,”

IEEE J. Sel. Areas Commun., vol. 33, no. 6, pp. 1025–1039, Jun. 2015.

[36] A. Zappone, L. Sanguinetti, G. Bacci et al., “Energy-efficient power control: A look at 5G wireless technologies,” IEEE

Trans. Signal Process., vol. 64, no. 7, pp. 1668–1683, Apr. 2016.

[37] E. Bjornson, E. A. Jorswieck, M. Debbah et al., “Multiobjective signal processing optimization: The way to balance

conflicting metrics in 5G systems,” IEEE Signal. Proc. Mag., vol. 31, no. 6, pp. 14–23, Nov. 2014.

[38] W. Mei, Q. Wu, and R. Zhang, “Cellular-connected UAV: Uplink association, power control and interference coordination,”

arXiv preprint arXiv:1807.08218, Jul. 2018.

[39] A. Biason, C. Pielli, A. Zanella et al., “On the energy/distortion tradeoff in the IoT,” arXiv preprint arXiv:1702.03695,

Feb. 2017.

[40] L. Sanguinetti, A. L. Moustakas, and M. Debbah, “Interference management in 5g reverse tdd hetnets with wireless

backhaul: A large system analysis,” IEEE J. Sel. Areas Commun., vol. 33, no. 6, pp. 1187–1200, Jun. 2015.

[41] J. Gil-Pelaez, “Note on the inversion theorem,” Biometrika, vol. 38, no. 3-4, Dec. 1951.

[42] H. Wei, N. Deng, W. Zhou et al., “Approximate SIR analysis in general heterogeneous cellular networks,” IEEE Trans.

Commun., vol. 64, no. 3, pp. 1259–1273, Mar. 2016.

[43] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, 2004.

[44] A. Zappone and E. Jorswieck, “Energy efficiency in wireless networks via fractional programming theory,” Foundations

and Trends® in Communications and Information Theory, vol. 11, no. 3-4, pp. 185–396, 2015.

[45] S. Schaible and J. Shi, “Fractional programming: the sum-of-ratios case,” Optimization Methods and Software, vol. 18,

no. 2, pp. 219–229, 2003.

[46] “Title 47 of the code of federal regulations,” Federal Communications Commission (FCC), Tech. Rep. Section 101.115,

July 2017.

[47] G. Hattab and D. Cabric, “Performance analysis of uplink cellular IoT using different deployments of data aggregators,”

in Proc. IEEE Global Communications Conf. (GLOBECOM), Dec. 2018, pp. 1–6.

[48] 3GPP, “Study on channel model for frequencies from 0.5 to 100 GHz,” TS 38.901, Dec. 2017.

[49] A. Jeffrey and D. Zwillinger, Table of Integrals, Series, and Products. Elsevier LTD, Oxford, 2014.