# Resource Allocation for UAV Assisted Wireless Networks with QoS Constraints

Weihang Ding1, Zhaohui Yang1, Mingzhe Chen2, Jiancao Hou1 and Mohammad Shikh-
Bahaei1  1Centre for Telecommunications Research, Department of Engineering,
King’s College London, London WC2R 2LS, UK.  2Electrical Engineering
Department of Princeton University, USA,
The Chinese University of Hong Kong, Shenzhen, China.

###### Abstract

For crowded and hotspot area, unmanned aerial vehicles (UAVs) are usually
deployed to increase the coverage rate. In the considered model, there are
three types of services for UAV assisted communication: control message, non-
realtime communication, and real-time communication, which can cover most of
the actual demands of users in a UAV assisted communication system. A
bandwidth allocation problem is considered to minimize the total energy
consumption of this system while satisfying the requirements. Two techniques
are introduced to enhance the performance of the system. The first method is
to categorize the ground users into multiple user groups and offer each group
a unique RF channel with different bandwidth. The second method is to deploy
more than one UAVs in the system. Bandwidth optimization in each scheme is
proved to be a convex problem. Simulation results show the superiority of the
proposed schemes in terms of energy consumption.

###### Index Terms:

Resource allocation, UAV, Energy consumption

##  I Introduction

With the prevalent using of mobile communication devices, the conventional
wireless networks are greatly challenged nowadays. The normal ground base
stations may be inadequate if there are disasters or unexpected big crowds in
the region. Besides, some of the regions can hardly be served by ground base
stations because of hardness of facilities construction or huge obstacles such
as skyscrapers and mountains [1]. In these cases, unmanned aerial vehicles
(UAVs) assisted wireless communication platform is a rather promising
technology [2].

The major advantage of UAV-assisted wireless communication is that UAVs have
high altitudes, which result in the high qualities of the channels. The
probability that the channels between the ground users and the UAV are line of
sight (LoS) increases as the altitude of the UAV increases. The channel
quality also depends on ambient environmental parameters and the horizontal
distance between the user and the UAV [3, 4, 5]. Significant efforts have been
applied for this field based on the channel model. The optimal three-
dimensional (3D) position distribution of the UAVs is studied in [6, 7, 8].
Other aspects of UAV-assisted wireless communication network are also studied
previously such as coverage analysis [9], [10], cell partitions of the UAVs
[11], and spectrum sharing [12]. The second type of UAV-assisted wireless
communication employs mobile UAVs. These UAVs can serve as not only base
stations, but also relays [13]. As mobility is one of the most important
property of the second type of UAVs, their trajectories are needed to be
determined. The UAV’s trajectory can be periodic or non-periodic based on the
actual requirements to optimize the overall performance of the system [14],
[15]. Moreover, there are many previous works focusing on other parameters of
UAVs to optimize the performance of the communication system in slightly
different scenarios. These parameters include power [16], beamwidth [17],
bandwidth assignment [18], etc.

In order to optimize the performance of a UAV-assisted wireless communication
system, the overall energy consumption is one of the most critical issue owing
to the limited budget of the battery capacity. Apart from energy consumed by
wireless communication, certain amount of propulsion energy is used by the UAV
to support their movements. As a result, the whole system ought to be designed
differently from the ground system. The power consumption model for
helicopters is defined in the well known textbook [19]. In [20], the authors
studied the trade-off between the propulsion energy and communication related
energy consumed by the system to find the optimal transmit power of the fixed
ground users and the trajectory of the fixed-wing UAV. As the UAV gets closer
to the ground user groups, the energy cost to transmit messages can be
significantly reduced while additional propulsion energy is needed to enable
the UAV’s movement.The main aim of the UAV discussed in [20] is collecting
data from ground terminals. Quality of Service (QoS) is a significant issue to
be considered in UAV-assisted communication systems. The author in [21] and
[22] focused on the 3-D placement of UAVs to achieve the required QoS with the
help of multiple algorithms.

However, most of the previous works merely focused on the energy used for
transmitting signals and ignore the propulsion energy of the UAVs. The total
energy consumed by the same system when served by different numbers of UAVs
was rarely compared by previous works. Moreover, the above works ignore the
joint consideration of energy consumption for multiple UAVs and the bandwidth
allocation for multiple users. An iterative algorithm is proposed in [23]
which results in higher energy efficiency and lower delay compared to
conventional federated learning (FL) methods.

The objective of this paper is to study the bandwidth assignment and the UAV
deployment for this UAV assisted wireless communication network. We aim to
minimize the overall energy consumed by this whole system while the available
bandwidth is assigned to different radio frequency (RF) channels to satisfy
different types of QoS.

The main contributions of this paper are listed as follows:

  * •

The optimal assignments of bandwidth to different users and services under
energy limitations are obtained.

  * •

The users are categorized based on their channel qualities for the purpose of
saving energy.

  * •

The optimal UAV distribution is studied through the comparison between the
system served different amounts of UAVs.

The rest of this paper is organized as follows. The system model is described
in Section II. The problem formulation is described in Section III. Section IV
and V are the numerical results and conclusion of this paper.

##  II System Model

###  II-A RF Channel Model

Consider an UAV-assisted wireless communication system with $n$ ground users
uniformly distributed in a square area with length $R$. The horizontal
positions of the ground uses are denoted by the set
$\mathcal{X}=\\{\bm{x_{i}}\\}_{i=1}^{n}=\\{(x_{i},y_{i})\\}_{i=1}^{n}$. There
are $k$ UAVs deployed in this system. The 3-D positions of UAVs can be denoted
as set
$\mathcal{Y}=\\{\bm{y_{j}}\\}_{j=1}^{k}=\\{(x_{j}^{0},y_{j}^{0},h_{j}^{0})\\}_{j=1}^{k}$.
Let $\mathcal{I}_{j}$ denote the set of users served by UAV $j$. To avoid
collision among the UAVs, the distance between any two UAVs must not exceed
$R_{max}$, i.e., $\|\bm{y_{m}}-\bm{y_{n}}\|\geq R_{max}$, $\forall
m,n\in\\{1,\cdots,k\\}$.

The overall channel gain (expressed in dB) between user $i$ and UAV $j$ can be
modeled as:

$g_{i,j}=-\underbrace{\left(20\log{d}+20\log{f_{c}}+20\log{\frac{4\pi}{c}}\right)}_{\text{Free
space pass loss}}-\eta$ (1)

where $d=\sqrt{{h_{j}^{0}}^{2}+(x_{i}-x^{0}_{j})^{2}+(y_{i}-y^{0}_{j})^{2}}$,
$f_{c}$ is the carrier frequency of the RF channel, and $\eta$ here refers to
the excessive pass loss determined by whether the channel is LoS and the
ambient environment.

The probability of LoS, which is closely related to the ambient environment
and the density and distribution of large obstacles including high buildings
and mountains, can be defined as:

$P_{LoS,i,j}=\frac{1}{1+a\exp{\left(-b\left(\frac{180}{\pi}\tan^{-1}\left(\frac{h_{j}^{0}}{d_{H,i,j}}\right)-a\right)\right)}}$
(2)

where $d_{H,i,j}=\sqrt{(x_{i}-x_{j}^{0})^{2}+(y_{i}-y_{j}^{0})^{2}}$ denotes
the horizontal distance between user $i$ and UAV $j$, $a$ and $b$ are
environmental factors.[24] As the channel is either Los or non LoS (NLoS), the
probability of NLoS can be written as

$P_{NLoS,i,j}=1-P_{LoS,i,j}$ (3)

Accordingly, we can rewrite $g_{i,j}$ as:

$g_{i,j}=\left\\{\begin{aligned}
&\\-(20\log{d}+20\log{f_{c}}+20\log{\frac{4\pi}{c}})-\eta_{LoS}\text{,}\\\
&\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\text{if
the channel is LoS}\\\
&\\-(20\log{d}+20\log{f_{c}}+20\log{\frac{4\pi}{c}})-\eta_{NLoS}\text{,}\\\
&\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\>\text{if
the channel is NLoS}\end{aligned}\right.$ (4)

where $\eta_{LoS}$ and $\eta_{NLoS}$ are the excessive pass loss factor of LoS
and NLoS channels respectively [6].

The average expected channel gain of a user located at $(x_{i},y_{i})$ can be
given by:

$\displaystyle\mathbb{E}[g_{i,j}]$
$\displaystyle=P_{LoS,i,j}g_{LoS,i,j}+P_{NLoS,i,j}g_{NLoS,i,j}=\bar{g}_{i,j}$
(5)

The transmit power of messages depends on the channel quality, available
bandwidth, and required channel capacity. The average power and energy costed
by the wireless channel between user $i$ and UAV $j$ in this system can be
written as:

$P_{ij}=\left(2^{\frac{C}{b_{\xi}}}-1\right)\frac{N_{0}b_{\xi}}{\bar{g}_{i,j}}$
(6)

$E_{ij}=P_{ij}T_{tran}=\left(2^{\frac{C}{b_{\xi}}}-1\right)\frac{N_{0}b_{\xi}T_{tran}}{\bar{g}_{i,j}}$
(7)

where $C$ is the data rate between the UAV base station $j$ and the ground
user $i$, $b_{\xi}$ denotes the bandwidth allocated to the $\xi$th RF channel,
$N_{0}$ is the spectral density of Additive white Gaussian noise (AWGN), and
$T_{tran}$ is the overall transmission time.

###  II-B Propulsion Energy Model

According to textbooks [19] and [25], the UAV’s torque coefficient $q_{c}$
while hovering can be expressed as

$q_{c}=\frac{\delta}{8}\left(1+\frac{3V^{2}}{\Omega^{2}R_{u}^{2}}\right)+\left(1+k\right)\frac{T_{u}\lambda_{i}}{\rho
sA_{u}\Omega^{2}R_{u}^{2}}+\frac{1}{2}d_{0}\frac{V^{3}}{\Omega^{3}R_{u}^{3}}$
(8)

where $\delta$ is profile drag coefficient, $V$ is the UAV’s speed, $k$ is the
incremental correction factor to induced power, $\rho$ is the air density,
$R_{u}$ is the radius of the UAV’s rotor, $\Omega$ is the angular velocity of
the rotors, and $T_{u}$ is the rotor thrust of this UAV. $A_{u}$ denotes the
disc area covered by the UAV’s rotor which can be calculated from equation
$A_{u}=\pi R_{u}^{2}$. The rotor solidity $s$ is defined as the ratio of the
overall rotor area to the rotor disc area. In other words, it denotes how much
of the rotor disc area is covered by the rotor blades at a time. $s$ can be
expressed as $s=\frac{bc}{\pi R_{u}}$ where $b_{u}$ and $c_{u}$ are the number
of rotor blades and the chord length of the rotor blades. $\lambda_{i}$
denotes the mean induced velocity normalized by the UAV’s tip speed. It is
described more detailed later in this paper. $d_{0}$ is the UAV’s fuselage
drag ratio. While a UAV is moving at high speed, air resistance can be a
significant resource of energy cost. A UAV’s fuselage drag ratio $d_{0}$ in
this case is defined as $d_{0}=\frac{S_{FP}}{sA_{u}}$, where $S_{FP}$ is the
UAV’s property defined as the fuselage equivalent flat plate area.

The relationship between a UAV’s required power and torque coefficient is

$\displaystyle P_{0}$ $\displaystyle=q_{c}\rho sA_{u}\Omega^{3}R_{u}^{3}$ (9)
$\displaystyle=\frac{\delta}{8}\rho
sA_{u}\Omega^{3}R_{u}^{3}\left(1+\frac{3V^{2}}{\Omega^{2}R_{u}^{2}}\right)+(1+k)T_{u}v_{i0}$
$\displaystyle+\frac{1}{2}d_{0}\rho sA_{u}V^{3}$

where $v_{i0}$ is the mean induced velocity and it can be obtained by equation
$v_{i0}=\lambda_{i}\Omega R_{u}$. Furthermore, in the case where the UAV
operates with a speed $V$ and a rotor thrust $T_{u}$, the mean induced
velocity of this UAV $v_{i0}$ can be calculated as follows

$v_{i0}=\sqrt{\sqrt{\frac{T_{u}^{2}}{4\rho^{2}A_{u}^{2}}+\frac{V^{4}}{4}}-\frac{V^{2}}{2}}$
(10)

In our system model, we assume that the UAVs are static and, hence, their
velocity $V=0$, and its rotor thrust $T_{u}$ equals to the UAV’s weight, which
is denoted by $W$. Besides, in our system, the energy used by the UAVs to
reach their designated position is ignored. Therefore, the overall propulsion
power of this UAV assisted wireless communication system can be expressed as

$P_{UAV}=\frac{\delta}{8}\rho
sA_{u}\Omega^{3}R_{u}^{3}+(1+k)\frac{W^{3/2}}{\sqrt{2\rho A_{u}}}$ (11)

###  II-C Service Types

In order to improve the utilization of bandwidth and energy and avoid
excessive resources, all services provided by the UAV-assisted wireless
communication system are categorized based on their QoS requirements. There
are three types of services discussed in this paper, which can cover almost
all potential user needs.

  * •

Control message: This kind of messages are always quite short packets
containing only a few numbers or commands (typically a few hundred bits) but
require very low latency, which is used to transfer control messages like the
instructions to UAVs, the real-time information of the ambient environment and
so on. All control messages are transmitted by one single RF channel to
minimize the queuing latency.

  * •

Non-real-time message: This kind of messages are used to transfer delay-
tolerant files whose packets are much bigger than control messages. Therefore,
limitations like latency and block probability can be ignored in this case.
There are $k_{n}$ RF channels allocated to this kind of service.

  * •

Real-time communication: This type of service is like Public Switched
Telephone Network (PSTN). A user will occupy a channel during the connection
and the call request is rejected if there is no empty channel. The number of
RF channels $k_{r}$ used for this kind of service is based on the overall
traffic load and the maximum block probability.

####  II-C1 Control Message

It is assumed that the time that the packets from each user are transmitted is
Poisson distributed with an average transmission rate $\lambda$. The length of
the packets are assumed to be exponentially distributed with an expectation of
$L$. Therefore, this queuing network can be modeled as a M/M/1 queuing network
with infinite buffer size. If we split the whole channel into $k$ sub-channels
using Frequency Division Multiplexing (FDM) or Time Division Multiplexing
(TDM), the average queuing latency is $k$ times larger than it in the system
while only a whole channel is used. As our major objective is to reduce the
latency of this kind of messages, and the packets are so short that the
probability of collision is rather low, we will use a whole RF channel to
transmit control messages.

The data rate requirement of this channel can be calculated as

$C_{min}=\frac{1}{T_{req}}+n\lambda L$ (12)

where $T_{req}$ is the maximum allowed latency of control messages.

CSMA/CD (listen before and while talking) protocol is used. If the user finds
the channel busy, the transmission will be inhibited until the channel turns
idle. However, while collisions happen, an exponential back-off algorithm is
introduced to determine the re-transmission process. The major disadvantage of
using CSMA/CD in this system is that the delay is more variable and harder to
evaluate. But we still can find methods to find out the average delay and
throughput of a CSMA/CD protocol. The utilization of CSMA/CD is
$\frac{1}{1+3.44\frac{T_{prop}}{T_{tran}}}$, so the data rate requirement of
this channel can be expressed as

$C_{req}=\left(1+3.44\frac{T_{prop}}{T_{tran}}\right)C_{min}$ (13)

where $T_{tran}$ is the time needed for a packet to be transmitted through
this channel and is defined as $T_{tran}=\frac{L}{C_{min}}$, and $T_{prop}$ is
the time needed for the wireless signal to propagate to the correlated UAV
base station. However, the signal’s propagation speed in such a wireless
communication system is the speed of light which is $3*10^{8}$ meters per
second. Hence, the transmission time in this system is several hundred times
longer than the propagation time, so that $C_{req}$ is very close to
$C_{min}$, which means collisions in this system have got little effect. So we
can ignore the collisions of packets and use the value of $C_{min}$ as
$C_{req}$ in further studies.

The bandwidth that is allocated to control messages is $b_{c}$ and the
achievable data rate in practice is $C_{c}$, then, the energy consumed by the
channel between ground user $i$ and UAV $j$ to transmit control messages in
one second can be written as

$\displaystyle E_{i,j,c}$
$\displaystyle=P_{i,j,c}T_{tran}\lambda=\left(2^{\frac{C_{c}}{b_{c}}}-1\right)\frac{N_{0}b_{c}L\lambda}{g_{i,j}C_{c}}$
(14)

####  II-C2 Non-real-time Message

The multiple access technique used to transmit non-real-time messages is TDMA
combined with FDMA. We split the bandwidth used for this type of service into
multiple RF channels and divide each RF channel into multiple time slots. Each
user who wants to transmit non-real-time messages can use only one physical
channel at a time. It is assumed that $k_{n}$ RF channel is allocated for this
type of service and the minimum allowed data rate is $R_{n}$.

In the conventional cellular wireless communication system, the whole
bandwidth is evenly distributed into multiple RF channels. Each RF channel is
selected by users randomly.

However, in such a UAV assisted wireless communication system, the quality of
the channels can vary significantly depends on whether the channel is LoS or
NLoS. In this paper, we are trying to find a method to categorize the users
into several groups based on the channel quality between each user and the UAV
base station. The available bandwidth is distributed to each user group
depending on the channel quality of users in one group. The advantage of this
method compared with the traditional way can be reflected by the reduction of
energy consumed in a fixed amount of time.

The users that use the $\xi$th RF channel are belong to set
$\mathcal{R}_{\xi}$, which can be expressed as $i\in\mathcal{R}_{\xi}$.

The energy consumed by the transmission of non-real-time messages by the
channel between ground user $i$ and UAV $j$ in each second can be written as

$\displaystyle E_{i,j,n}$
$\displaystyle=P_{i,j,n}T_{tran}=\left(2^{\frac{C_{\xi}}{b_{\xi}}}-1\right)\frac{N_{0}b_{\xi}}{g_{i,j}}$
(15)

where $C_{\xi}$ denotes the actual data rate of user $i\in\mathcal{R}_{\xi}$
to transmit non-real-time messages, and $b_{\xi}$ is the bandwidth of the RF
channel that is used by user $i\in\mathcal{R}_{\xi}$.

####  II-C3 Real-time Communication

This type of service is like public switched telephone network (PSTN).
Whenever a user wants to initiate a real-time communication, an idle channel
will be selected and occupied during this communication. If all the channels
are unavailable at this time, then the user will fail to get a connection and
the communication is said to be blocked. The parameter Grade of Service (GoS)
$B_{l}$ is defined to measure the probability that a communication is failed
to set up.

It is assumed that the frequency that the communications are requested to
initiated are Poisson distributed with an expected value of $Q$. It means that
on average, $Q$ communications occur per unit time $t$, i.e. one hour. The
average duration of the connections is $T$. Therefore, it can be seen as a
M/M/m/m queuing system with no buffer size, where $m$ stands the total number
of available channels assigned to this type of service. The probability of the
last state in the Markov chain is the blocking probability $B_{l}$ in this
system.

The minimum required channels in the system can be obtained by the following
Equation (16) or Erlang-B tabular. Erlang is the unit of traffic load $A$ and
can be calculated by $A=\frac{QT}{t}$. The Erlang-B can be given by:

$B_{l}=\frac{A^{N}/N!}{A^{0}/0!+A^{1}/1!+A^{2}/2!+\cdots+A^{N}/N!}$ (16)

where $N$ denotes the number of physical channels used for this type of
service.

Each RF channel can be divided into ten subframes with burst data rate $R_{b}$
according to Long Term Evolution (LTE) frame structure, so the number of RF
channels required for real-time communication can be calculated by
$k_{r}=N/10$.

About 100 ms of latency is tolerable for real-time service. Therefore, latency
limitation can be ignored for real-time communication. The energy consumed by
the channel between ground user $i$ and UAV $j$ for real-time communication in
each second can be expressed as

$\displaystyle E_{i,j,r}$
$\displaystyle=P_{i,j,r}T_{tran}=\left(2^{\frac{C_{r}}{b_{r}}}-1\right)\frac{N_{0}b_{r}}{g_{i,j}}\frac{TQ}{60}$
(17)

where $b_{r}$ and $C_{r}$ are the bandwidth of each RF channel and the
achievable date rate allocated to real-time communication respectively.

##  III Problem formulation

###  III-A Single UAV System

In the case that all the ground users are served by one UAV base station, the
probability that a channel is QoS is decided by the elevation angle (or in
other words, the horizontal and vertical distance between the user and the UAV
base station) and the ambient environment. There is obviously a trade-off
between the free space path loss and the probability of LoS, so that we can
find an optimal altitude for the UAV base station to save energy.

In the conventional cellular wireless communication system, the whole
bandwidth is evenly distributed into multiple RF channels. In this project, we
are trying to find a method to categorize the users into several groups based
on the channel quality between each user and the UAV base station. The
available bandwidth is distributed to each user group depending on the channel
quality of users in each group.

The overall energy consumption in this system $E_{tot,1}$ which is the
summation of propulsion energy and communication related energy can be written
as (18).

$\displaystyle E_{tot,1}$ $\displaystyle=E_{c}+E_{n}+E_{r}+E_{UAV}$ (18)
$\displaystyle=\sum_{i=1}^{n}(2^{\frac{C_{c}}{b_{c}}}-1)\frac{N_{0}b_{c}Ln\lambda}{\overline{g}_{i,1}C_{c}}+\sum_{\xi=1}^{k_{n}}\sum_{i\in\mathcal{R}_{\xi}}(2^{\frac{C_{\xi}}{b_{\xi}}}-1)\frac{N_{0}b_{\xi}}{\overline{g}_{i,1}}+\sum_{i=1}^{n}(2^{\frac{C_{r}}{b_{r}}}-1)\frac{N_{0}b_{r}}{\overline{g}_{i,1}}\frac{TQ}{60}$
$\displaystyle+\frac{\delta}{8}\rho
sA_{u}\Omega^{3}R_{u}^{3}+(1+k)\frac{W^{3/2}}{\sqrt{2\rho A_{u}}}$

$\displaystyle E_{tot,2}$ $\displaystyle=E_{c}+E_{n}+E_{r}+E_{UAV}$ (19)
$\displaystyle=\sum_{j=1}^{2}\sum_{i\in\mathcal{X}_{j}}(2^{\frac{C_{c}}{b_{c}}}-1)\frac{N_{0}b_{c}Ln\lambda}{\overline{g}_{i,j}C_{c}}+\sum_{\xi=1}^{k_{n}/2}\sum_{i\in\mathcal{R}_{\xi}}(2^{\frac{C_{\xi}}{b_{\xi}}}-1)\frac{N_{0}b_{\xi}}{\overline{g}_{i,1}}+\sum_{\xi=\frac{k_{n}}{2}+1}^{k_{n}}\sum_{i\in\mathcal{R}_{\xi}}(2^{\frac{C_{\xi}}{b_{\xi}}}-1)\frac{N_{0}b_{\xi}}{\overline{g}_{i,2}}$
$\displaystyle+\sum_{j=1}^{2}\sum_{i\in\mathcal{X}_{j}}(2^{\frac{C_{r}}{b_{r}}}-1)\frac{N_{0}b_{r}}{\overline{g}_{i,j}}\frac{TQ}{60}+E_{UAV}+\frac{\delta}{4}\rho
sA_{u}\Omega^{3}R_{u}^{3}+(1+k)\frac{2W^{3/2}}{\sqrt{2\rho A_{u}}}$

For the purpose of minimizing the energy consumed by this system, the
optimization problem can be written mathematically as:

$\displaystyle\mathop{\min}\limits_{b_{c},b_{\xi},b_{r},C_{c},C_{\xi},C_{r}}$
$\displaystyle E_{tot,1}$ (20) $\displaystyle\rm{Subject\>to:}$
$\displaystyle\>\>b_{c}+\sum_{\xi=1}^{k_{n}}b_{\xi}+k_{r}b_{r}\leq B,$
$\displaystyle\>\>0<b_{c}<B,$ $\displaystyle\>\>0<b_{r}<B,$
$\displaystyle\>\>0<b_{\xi}<B,\>\>\>\forall\xi\in\\{1,2,\cdots,k_{n}\\}$
$\displaystyle\>\>C_{req}\leq C_{c},$ $\displaystyle\>\>R_{b}\leq C_{r},$
$\displaystyle\>\>R_{n}\leq C_{\xi},\>\>\>\forall\xi\in\\{1,2,\cdots,k_{n}\\}$

It can be proved that this optimization problem is convex. The optimal
solution can be obtained efficiently.

###### Theorem 1

Problem (20) is a convex problem.

Proof: Here, $b_{c}$ and $C_{c}$ are the only variables in $E_{C}$. Similarly,
$b_{\xi}$ and $C_{\xi}$ are the only variables in $E_{n}$, $b_{r}$ and $C_{r}$
are the only variables in $E_{r}$. The second derivatives of $E_{c}$, $E_{n}$
and $E_{r}$ are all positive. That is, $E_{c}$, $E_{n}$ and $E_{r}$ are all
convex. The summation of there three convex functions, $E_{tot,1}$, is still a
convex function. Meanwhile, all the inequality constraints in Problem (20) are
convex. Therefore, optimization problem (20) is a convex problem.

###  III-B Double UAV System

By deploying multiple UAVs instead of one single UAV, the quality of the
channels between the users and the UAV base station can be improved
significantly. Therefore, the energy used for transmitting messages is
reduced, which may cancel out the propulsion energy cost by additional UAVs.

The major problem is to find out the optimal matches between the ground users
and the UAVs. The difference of all the users’ channel gains to both UAVs,
i.e. $\overline{g}_{i,1}-\overline{g}_{i,2}$ are calculated and are sorted
from largest to smallest. The first half users, i.e. $\mathcal{X}_{1}$ in this
list are selected to be served by UAV $1$ while the second half, i.e.
$\mathcal{X}_{2}$ are chosen to be connected to UAV $2$.

The users are also needed to be categorized into multiple groups for the
purpose of transmitting non-real-time messages. If the number of user groups
$k_{n}$ remains unchanged, then the first $k_{n}/2$ sets, i.e.
$\mathcal{R}_{1}$ to $\mathcal{R}_{k_{n}/2}$ are all composed of the users
connecting to UAV $1$ and the second half of user sets, i.e.
$\mathcal{R}_{k_{n}/2+1}$ to $\mathcal{R}_{k_{n}}$ contains the ones that are
served by UAV $2$.

Simple to the single-UAV case, we can write the overall energy consumed by all
the users $E_{tot,2}$ as (19).

In order to minimize the energy consumed by this system, we can write the
optimization problem as follows:

$\displaystyle\mathop{\min}\limits_{b_{c},b_{\xi},b_{r},C_{c},C_{\xi},C_{r}}$
$\displaystyle E_{tot,2}$ (21) $\displaystyle\rm{Subject\>to:}$
$\displaystyle\>\>b_{c}+\sum_{\xi=1}^{k_{n}}b_{\xi}+k_{r}b_{r}\leq B,$
$\displaystyle\>\>0<b_{c}<B,$ $\displaystyle\>\>0<b_{r}<B,$
$\displaystyle\>\>0<b_{\xi}<B,\>\>\>\forall\xi\in\\{1,2,\cdots,k_{n}\\},$
$\displaystyle\>\>C_{req}\leq C_{c},$ $\displaystyle\>\>R_{b}\leq C_{r},$
$\displaystyle\>\>R_{n}\leq C_{\xi},\>\>\>\forall\xi\in\\{1,2,\cdots,k_{n}\\}$

Similar to Problem (20), Problem (21) can be proved to be a convex problem as
well. Hence, we can obtain the optimal solution of this problem efficiently by
using the conventional methods such as dual method in [26, 27].

##  IV Numerical Results

For our simulations, the side length of the region where the ground users are
distributed is set as $R=2000$m and the UAVs are assumed to be in the center
of their coverage. The average transmission rate, packet length and required
latency of control messages are set as $\lambda=10$, $L=200$bits, and
$T_{req}=1$ms respectively. The average data rate of non-real-time service is
$R=1$Mbps for each users. The average call duration and average number of
calls per hour of real-time communication are set as $T=2$minutes, and $Q=10$
respectively. We set maximum blocking probability $B_{l}=2\%$. The burst data
rate $R_{b}$ is set identical to the burst data rate of LTE network, which
equals to 270.8Kbps. The AWGN spectral density and carrier frequency are set
as $N_{0}=10^{-16}$W/Hz and $f_{c}=1$GHz. The UAV’s propulsion energy related
parameters are set as what is showed in table I.

(a) Energy save rate in percent

(b) Energy consumption comparison

Figure 1: Energy consumption in suburban region TABLE I: UAV’s propulsion energy related parameters Physical meaning | Notation | Simulation value
---|---|---
Aircraft weight in Newton | $W$ | 20
Air density in kg/m3 | $\rho$ | 1.225
Rotor radius in meter | $R_{u}$ | 0.4
Rotor disc area in m2 | $A_{u}$ | 0.503
Blade angular velocity in radians/s | $\Omega$ | 300
Rotor solidity | $s$ | 0.05
Incremental correction factor | $k$ | 0.1
Profile drag coefficient | $\delta$ | 0.012

(a) Energy save rate in percent

(b) Energy consumption comparison

Figure 2: Energy consumption in urban region

(a) Energy save rate in percent

(b) Energy consumption comparison

Figure 3: Energy consumption in dense urban region

Figs. 1-3 show the energy efficiency which can be calculated by the percentage
of energy saved by grouping users and the comparison between the system served
by one and two UAVs in three kinds of environments respectively.

We can observe from the graphs that more energy can be saved if the altitude
of the UAV is lower. This happens because the probability of LoS reduces as
the altitude of UAV reduces. The decreasing of LoS probability will further
leads to the larger differences between the qualities of the channels.

In suburban region, the quality of the channels is rather high so that the
communication related energy is much less than the propulsion energy consumed
in this system. Therefore, it is better to deploy only one UAV base station
for the purpose of saving energy.

It is remarkable that only when more than 700 users are served, deploying two
UAVs simultaneously can be more energy-efficient in urban region.

In dense urban regions, more energy is consumed by the users to transmit
messages. As long as more than 100 users are in the system, more than one UAVs
should be deployed in order to save energy.

##  V Conclusion

In this paper, we aim to allocate the overall bandwidth to multiple RF
channels to minimize the total energy consumption of this system while
satisfying all three services of the system. If the bandwidth resource is
limited, there are ways to enhance the energy efficiency of the system. The
first method is to categorize the users into multiple groups and offer each
user group a unique RF channel with different bandwidth. Numerical results
show that plenty of energy can be saved through using this technique.
Moreover, deploying multiple UAVs can sometime result in higher energy
efficiency compared with deploying one UAV only. It is proved through the
comparison between the same user sets served by one UAV and two UAVs.

## Acknowledgment

This work was supported by the Engineering and Physical Science Research
Council (EPSRC) through the Scalable Full Duplex Dense Wireless Networks
(SENSE) grant EP/P003486/1.

## References

  * [1] N. Zhao, W. Lu, M. Sheng, Y. Chen, J. Tang, F. R. Yu, and K. Wong, “Uav-assisted emergency networks in disasters,” _IEEE Wireless Communications_ , vol. 26, no. 1, pp. 45–51, February 2019.
  * [2] S. Chandrasekharan, K. Gomez, A. Al-Hourani, S. Kandeepan, T. Rasheed, L. Goratti, L. Reynaud, D. Grace, I. Bucaille, T. Wirth, and S. Allsopp, “Designing and implementing future aerial communication networks,” _IEEE Communications Magazine_ , vol. 54, no. 5, pp. 26–34, May 2016.
  * [3] A. Al-Hourani, S. Kandeepan, and A. Jamalipour, “Modeling air-to-ground path loss for low altitude platforms in urban environments,” in _2014 IEEE Global Communications Conference_ , Dec 2014, pp. 2898–2904.
  * [4] W. Khawaja, I. Guvenc, D. W. Matolak, U. Fiebig, and N. Schneckenberger, “A survey of air-to-ground propagation channel modeling for unmanned aerial vehicles,” _IEEE Communications Surveys Tutorials_ , pp. 1–1, 2019.
  * [5] D. W. Matolak and R. Sun, “Unmanned aircraft systems: Air-ground channel characterization for future applications,” _IEEE Vehicular Technology Magazine_ , vol. 10, no. 2, pp. 79–85, June 2015.
  * [6] S. L. S. Al-Hourani, Akrama Kandeepan, “Optimal lap altitude for maximum coverage,” Ph.D. dissertation, Deccember 2014.
  * [7] J. Lyu, Y. Zeng, R. Zhang, and T. J. Lim, “Placement optimization of uav-mounted mobile base stations,” _IEEE Communications Letters_ , vol. 21, no. 3, pp. 604–607, March 2017.
  * [8] J. Chen and D. Gesbert, “Optimal positioning of flying relays for wireless networks: A los map approach,” in _2017 IEEE International Conference on Communications (ICC)_ , May 2017, pp. 1–6.
  * [9] V. V. Chetlur and H. S. Dhillon, “Downlink coverage analysis for a finite 3-d wireless network of unmanned aerial vehicles,” _IEEE Transactions on Communications_ , vol. 65, no. 10, pp. 4543–4558, Oct 2017.
  * [10] A. AL-Hourani, S. Chandrasekharan, G. Kaandorp, W. Glenn, A. Jamalipour, and S. Kandeepan, “Coverage and rate analysis of aerial base stations [letter],” _IEEE Transactions on Aerospace and Electronic Systems_ , vol. 52, no. 6, pp. 3077–3081, December 2016.
  * [11] M. Mozaffari, W. Saad, M. Bennis, and M. Debbah, “Optimal transport theory for cell association in uav-enabled cellular networks,” _IEEE Communications Letters_ , vol. 21, no. 9, pp. 2053–2056, Sep. 2017.
  * [12] M. Chen, W. Saad, and C. Yin, “Liquid state machine learning for resource and cache management in lte-u unmanned aerial vehicle (uav) networks,” _IEEE Transactions on Wireless Communications_ , vol. 18, no. 3, pp. 1504–1517, March 2019.
  * [13] Y. Zeng, R. Zhang, and T. J. Lim, “Throughput maximization for uav-enabled mobile relaying systems,” _IEEE Transactions on Communications_ , vol. 64, no. 12, pp. 4983–4996, Dec 2016.
  * [14] Y. Zeng and R. Zhang, “Energy-efficient uav communication with trajectory optimization,” _IEEE Transactions on Wireless Communications_ , vol. 16, no. 6, pp. 3747–3760, June 2017.
  * [15] M. Chen, M. Mozaffari, W. Saad, C. Yin, M. Debbah, and C. S. Hong, “Caching in the sky: Proactive deployment of cache-enabled unmanned aerial vehicles for optimized quality-of-experience,” _IEEE Journal on Selected Areas in Communications_ , vol. 35, no. 5, pp. 1046–1061, May 2017.
  * [16] S. Zhang, H. Zhang, Q. He, K. Bian, and L. Song, “Joint trajectory and power optimization for uav relay networks,” _IEEE Communications Letters_ , vol. 22, no. 1, pp. 161–164, Jan 2018.
  * [17] H. He, S. Zhang, Y. Zeng, and R. Zhang, “Joint altitude and beamwidth optimization for uav-enabled multiuser communications,” _IEEE Communications Letters_ , vol. 22, no. 2, pp. 344–347, Feb 2018.
  * [18] W. Huang, Z. Yang, C. Pan, L. Pei, M. Chen, M. Shikh-Bahaei, M. Elkashlan, and A. Nallanathan, “Joint power, altitude, location and bandwidth optimization for uav with underlaid d2d communications,” _IEEE Wireless Communications Letters_ , vol. 8, no. 2, pp. 524–527, April 2019.
  * [19] G. A.R.S.Bramwell and D.Balmford, _Bramwell’s Helicopter Dynamics (Butterworth-Heinemann), 2nd ed._ Washington, DC, USA: AIAA, 2001.
  * [20] D. Yang, Q. Wu, Y. Zeng, and R. Zhang, “Energy tradeoff in ground-to-uav communication via trajectory design,” _IEEE Transactions on Vehicular Technology_ , vol. 67, no. 7, pp. 6721–6726, July 2018.
  * [21] M. Alzenad, A. El-Keyi, and H. Yanikomeroglu, “3-d placement of an unmanned aerial vehicle base station for maximum coverage of users with different qos requirements,” _IEEE Wireless Communications Letters_ , vol. 7, no. 1, pp. 38–41, Feb 2018.
  * [22] Z. Zhu, L. Li, and W. Zhou, “Qos-aware 3d deployment of uav base stations,” in _2018 10th International Conference on Wireless Communications and Signal Processing (WCSP)_ , Oct 2018, pp. 1–6.
  * [23] Z. Yang, M. Chen, W. Saad, C. S. Hong, and M. Shikh-Bahaei, “Energy efficient federated learning over wireless communication networks,” 2019.
  * [24] M. B. M. Mozaffari, W. Saad and M. Debbah, “Unmanned aerial vehicle with underlaid device-to-device communications: Performance and tradeoffs,” Ph.D. dissertation, University of Mars, June 2005.
  * [25] A.Filippone, _Flight Performance of Fixed and Rotary Wing Aircraft (Butterworth-Heinemann)_. Washington, DC, USA: AIAA, 2006.
  * [26] Z. Yang, C. Pan, M. Shikh-Bahaei, W. Xu, M. Chen, M. Elkashlan, and A. Nallanathan, “Joint altitude, beamwidth, location, and bandwidth optimization for uav-enabled communications,” _IEEE Communications Letters_ , vol. 22, no. 8, pp. 1716–1719, Aug 2018.
  * [27] Z. Yang, C. Pan, K. Wang, and M. Shikh-Bahaei, “Energy efficient resource allocation in uav-enabled mobile edge computing networks,” _IEEE Transactions on Wireless Communications_ , vol. 18, no. 9, pp. 4576–4589, Sep. 2019.


* [148] S. Dananjayan and G. M. Raj, “Artificial intelligence during a pandemic: The COVID-19 example,” _The International Journal of Health Planning and Management_ , 2020.
  * [149] AI Helps Doctors Diagnose the Coronavirus. [Online]. Available: https://news.developer.nvidia.com/ai-helps-doctors-diagnose-the-coronavirus/.
  * [150] D. Yang, Z. Xu, W. Li, A. Myronenko, H. R. Roth, S. Harmon, S. Xu, B. Turkbey, E. Turkbey, X. Wang, W. Zhu, G. Carrafiello, F. Patella, M. Cariati, H. Obinata, H. Mori, K. Tamura, P. An, B. J. Wood, and D. Xu, “Federated semi-supervised learning for COVID region segmentation in chest CT using multi-national data from China, Italy, Japan,” _Medical Image Analysis_ , vol. 70, p. 101992, May 2021.
  * [151] I. Fenemigho, E. Ukponmwan, E. C. Nnakwue, I. Udoete, C. Asuzu, A. Adaralegbe, and U. Effiong, “COVID-19, flattening the curve: recommendations towards control and managing a second wave,” _Journal of Global Health Reports_ , vol. 4, p. e2020074, 2020.
  * [152] Blockchain and AI Technologies Combined to Battle Coronavirus - COVID-19 as Immuno-Oncology Company Mateon Partners with Meridian IT to Fast Track Drug Manufacturing. [Online]. Available: https://www.the-blockchain.com/2020/03/19/blockchain-and-ai-technologies-combined-to-battle-coronavirus-COVID-19-as-immuno-oncology-company-mateon-partners-with-meridian-it-to-fast-track-drug-manufacturing/.
  * [153] Z. Che, Y. Cheng, S. Zhai, Z. Sun, and Y. Liu, “Boosting deep learning risk prediction with generative adversarial networks for electronic health records,” in _2017 IEEE International Conference on Data Mining (ICDM)_ , 2017, pp. 787–792.
  * [154] D. C. Nguyen, M. Ding, P. N. Pathirana, A. Seneviratne, J. Li, and H. V. Poor, “Federated learning for internet of things: A comprehensive survey,” _IEEE Communications Surveys & Tutorials_, 2021.
  * [155] N. Fabiano, “Internet of things and blockchain: legal issues and privacy. the challenge for a privacy standard,” in _2017 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData)_ , 2017, pp. 727–734.
  * [156] N. Ahmad and P. Chauhan, “State of data privacy during COVID-19,” _IEEE Annals of the History of Computing_ , vol. 53, no. 10, pp. 119–122, 2020.
  * [157] T. Sharma and M. Bashir, “Use of apps in the COVID-19 response and the loss of privacy protection,” _Nature Medicine_ , vol. 26, no. 8, pp. 1165–1167, 2020.
  * [158] X. Li, P. Jiang, T. Chen, X. Luo, and Q. Wen, “A survey on the security of blockchain systems,” _Future Generation Computer Systems_ , 2017.
  * [159] Q. Liu, T. Liu, Z. Liu, Y. Wang, Y. Jin, and W. Wen, “Security analysis and enhancement of model compressed deep learning systems under adversarial attacks,” in _2018 23rd Asia and South Pacific Design Automation Conference (ASP-DAC)_ , 2018, pp. 721–726.
  * [160] E. Chen, K. Lerman, and E. Ferrara, “COVID-19: The first public coronavirus twitter dataset,” _arXiv preprint arXiv:2003.07372_ , 2020.
  * [161] J. P. Cohen, P. Morrison, and L. Dao, “COVID-19 image data collection,” _arXiv preprint arXiv:2003.11597_ , 2020.
  * [162] W. Liu, P. T.-W. Yen, and S. A. Cheong, “Coronavirus disease 2019 (COVID-19) outbreak in China, spatial temporal dataset,” _arXiv preprint arXiv:2003.11716_ , 2020.
  * [163] J. A. Dev, “Bitcoin mining acceleration and performance quantification,” in _2014 IEEE 27th Canadian conference on electrical and computer engineering (CCECE)_ , 2014, pp. 1–6.
  * [164] H. R. Hasan, K. Salah, R. Jayaraman, J. Arshad, I. Yaqoob, M. Omar, and S. Ellahham, “Blockchain-based solution for COVID-19 digital medical passports and immunity certificates,” 2020.
  * [165] A. I. Sanka and R. C. Cheung, “Efficient high performance fpga based nosql caching system for blockchain scalability and throughput improvement,” in _2018 26th International Conference on Systems Engineering (ICSEng)_ , 2018, pp. 1–8.
  * [166] J. P. Costa, M. Grobelnik, F. Fuart, L. Stopar, G. Epelde, S. Fischaber, P. Poliwoda, D. Rankin, J. Wallace, M. Black _et al._ , “Meaningful big data integration for a global COVID-19 strategy,” _IEEE Computational Intelligence Magazine_ , vol. 15, no. 4, pp. 51–61, 2020.
  * [167] Y. Liu, K. Wang, Y. Lin, and W. Xu, “Lightchain: A lightweight blockchain system for industrial internet of things,” _IEEE Transactions on Industrial Informatics_ , vol. 15, no. 6, pp. 3571–3581, 2019.
  * [168] W. J. Gordon and C. Catalini, “Blockchain technology for healthcare: facilitating the transition to patient-driven interoperability,” _Computational and structural biotechnology journal_ , vol. 16, pp. 224–230, 2018.
  * [169] X. Li, P. Jiang, T. Chen, X. Luo, and Q. Wen, “A survey on the security of blockchain systems,” _Future Generation Computer Systems_ , vol. 107, pp. 841–853, 2020.
  * [170] H. Lee, M. Shin, K. S. Kim, Y. Kang, and J. Kim, “Recipient-oriented transaction for preventing double spending attacks in private blockchain,” in _2018 15th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON)_ , 2018, pp. 1–2.
  * [171] N. Liu, Z. Zhang, A. W. Ho, and M. E. H. Ong, “Artificial intelligence in emergency medicine,” _Journal of Emergency and Critical Care Medicine_ , vol. 2, p. 82, 2018.
  * [172] Y. Wang, T. Wang, Y. Cui, H. Mei, X. Wen, J. Lu, and W. Chen, “COVID-19 data visualization public welfare activity,” _Visual Informatics_ , vol. 4, no. 3, pp. 51–54, 2020.
  * [173] D. Chi-Nguyen, P. N. Pathirana, M. Ding, and A. Seneviratne, “Secrecy performance of the uav enabled cognitive relay network,” in _2018 IEEE 3rd International Conference on Communication and Information Systems (ICCIS)_ , 2018, pp. 117–121.
  * [174] A. Kumar, K. Sharma, H. Singh, S. G. Naugriya, S. S. Gill, and R. Buyya, “A drone-based networked system and methods for combating coronavirus disease (COVID-19) pandemic,” _Future Generation Computer Systems_ , vol. 115, pp. 1–19, 2021.

|  Dinh C. Nguyen (Graduate Student Member, IEEE) is currently pursuing the
Ph.D. degree at the School of Engineering, Deakin University, Victoria,
Australia. His research interests focus on blockchain, deep reinforcement
learning, mobile edge/cloud computing, network security and privacy. He is
currently working on blockchain and reinforcement learning for Internet of
Things and 5G networks. He has been a recipient of the prestigious Data61 PhD
scholarship, CSIRO, Australia.
---|---
|  Ming Ding (M’12-SM’17) received the B.S. and M.S. degrees (with first-class
Hons.) in electronics engineering from Shanghai Jiao Tong University (SJTU),
Shanghai, China, and the Doctor of Philosophy (Ph.D.) degree in signal and
information processing from SJTU, in 2004, 2007, and 2011, respectively. From
April 2007 to September 2014, he worked at Sharp Laboratories of China in
Shanghai, China as a Researcher/Senior Researcher/Principal Researcher.
Currently, he is a senior research scientist at Data61, CSIRO, in Sydney, NSW,
Australia. His research interests include information technology, data privacy
and security, machine learning and AI, etc. He has authored over 140 papers in
IEEE journals and conferences, all in recognized venues, and around 20 3GPP
standardization contributions, as well as a Springer book ”Multi-point
Cooperative Communication Systems: Theory and Applications”. Also, he holds 21
US patents and co-invented another 100+ patents on 4G/5G technologies in CN,
JP, KR, EU, etc. Currently, he is an editor of IEEE Transactions on Wireless
Communications and IEEE Wireless Communications Letters. Besides, he has
served as Guest Editor/Co-Chair/Co-Tutor/TPC member for many IEEE top-tier
journals/conferences and received several awards for his research work and
professional services.
---|---
|  Pubudu N. Pathirana (Senior Member, IEEE) was born in 1970 in Matara, Sri
Lanka, and was educated at Royal College Colombo. He received the B.E. degree
(first class honors) in electrical engineering and the B.Sc. degree in
mathematics in 1996, and the Ph.D. degree in electrical engineering in 2000
from the University of Western Australia, all sponsored by the government of
Australia on EMSS and IPRS scholarships, respectively. He was a Postdoctoral
Research Fellow at Oxford University, Oxford, a Research Fellow at the School
of Electrical Engineering and Telecommunications, University of New South
Wales, Sydney, Australia, and a Consultant to the Defence Science and
Technology Organization (DSTO), Australia, in 2002. He was a visiting
professor at Yale University in 2009. Currently, he is a full Professor and
the Director of Networked Sensing and Control group at the School of
Engineering, Deakin University, Geelong, Australia and his current research
interests include bio-medical assistive device design, human motion capture,
mobile/wireless networks, rehabilitation robotics and radar array signal
processing.
---|---
|  Aruna Seneviratne (Senior Member, IEEE) is currently a Foundation Professor
of telecommunications with the University of New South Wales, Australia, where
he holds the Mahanakorn Chair of telecommunications. He has also worked at a
number of other Universities in Australia, U.K., and France, and industrial
organizations, including Muirhead, Standard Telecommunication Labs, Avaya
Labs, and Telecom Australia (Telstra). In addition, he has held visiting
appointments at INRIA, France. His current research interests are in physical
analytics: technologies that enable applications to interact intelligently and
securely with their environment in real time. Most recently, his team has been
working on using these technologies in behavioral biometrics, optimizing the
performance of wearables, and the IoT system verification. He has been awarded
a number of fellowships, including one at British Telecom and one at Telecom
Australia Research Labs.
---|---