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QoS-Compliant 3D Deployment Optimization
Strategy for UAV Base Stations
Xukai Zhong, Yiming Huo, Member, IEEE, Xiaodai Dong, Senior Member, IEEE, and Zhonghua Liang, Senior
Member, IEEE
Abstract—Unmanned aerial vehicle (UAV) is being integrated
as an active element in 5G and beyond networks. Because of
its flexibility and mobility, UAV base stations (UAV-BSs) can be
deployed according to the ground user distributions and their
quality of service (QoS) requirement. Although there has been
quite some prior research on the UAV deployment, no work has
studied this problem in a 3 dimensional (3D) setting and taken
into account the UAV-BS capacity limit and the quality of service
(QoS) requirements of ground users. Therefore, in this paper, we
focus on the problem of deploying UAV-BSs to provide satisfac-
tory wireless communication services, with the aim to maximize
the total number of covered user equipment (UE) subject to user
data rate requirements and UAV-BSs’ capacity limit. First, we
model the relationship between the air-to-ground (A2G) path loss
(PL) and the location of UAV-BSs in both horizontal and vertical
dimensions which has not been considered in previous works.
Unlike the conventional UAV deployment problem formulation,
the 3D deployment problem is decoupled into a 2D horizontal
placement and altitude determination connected by path loss
requirement and minimization. Then, we propose a novel genetic
algorithm (GA) based 2D placement approach in which UAV-
BSs are placed to have maximum coverage of the users with
consideration of data rate distribution. Finally, numerical and
simulation results show that the proposed approach has enabled
a better coverage percentage comparing with other schemes.
Index Terms—Unmanned aerial vehicle (UAV), wireless com-
munications, broadcasting, user equipment (UE), air-to-ground
(A2G), channel models, 3D deployment, genetic algorithm (GA).
I. INTRODUCTION
UNMANNED aerial vehicle (UAV)-assisted communica-
tions have recently gained fast popularity as an effective
solution to complement traditional stationary base stations.
Unmanned aerial vehicle base stations (UAV-BSs) have the
rapid-deployment and reconfiguration advantages compared
to terrestrial ones [1]. The roadmap of telecommunication
infrastructure provider [2] and 3GPP technical reports [3]
have demonstrated promising field trials results of wireless
connectivity to the UAVs, and discussed the future ubiquitous
mobile broadband coverage both on the ground and in the
sky. The fifth generation (5G) and beyond wireless communi-
cations and Internet-of-Things (IoT) application scenarios can
X. Zhong, Y. Huo and X. Dong are with the Department of Electrical
and Computer Engineering, University of Victoria, Victoria, BC V8P 5C2,
Canada (e-mail: xukaiz@uvic.ca, ymhuo@uvic.ca, xdong@ece.uvic.ca). This
work was supported by Wighton Engineering Product Development Fund.
(Corresponding author: Xiaodai Dong)
Z. Liang is with School of Information Engineering, Changan University,
Xian, Shanxi Province, China (e-mail: lzhxjd@hotmail.com). Z. Liangs work
was supported in part by the Natural Science Basic Research Project in
Shaanxi Province of China under Grant 2020JM-242, and in part by the
National Natural Science Foundation of China under Grant 61871314, and in
part by the Fundamental Research Funds for the Central Universities, CHD
under Grant 300102249303.
be facilitated by the UAV communication or treat it as a critical
integral part [4], [5], [6]. The advantages of high mobility
and flexibility of UAVs as part of the high-performance
wireless communications network can also potentially serve
the broadcasting industry. For example, UAVs are used to
conduct object-oriented tracking during aerial filming [7] and
transmit the broadcasting streams simultaneously. Moreover,
a mathematical model was proposed to overcome the prob-
lem of sport event filming with connectivity constraints in
[8]. A taxonomy to formulate the concept of multiple-UAV
cinematography was proposed to enable the autonomous UAV
filming in [9].
Despite the benefits in enabling UAV-BSs in the broad-
casting and communications industry, there are significant
challenges in terms of UAV system design and deployment
strategies. For example, finding suitable UAV-BSs’ positions
when deploying the UAV-BSs network is particularly difficult
in terms of cost-efficiency. Since the life time of the battery
powering one UAV-BS is limited and the number of available
UAV-BSs is also constrained, UAV-BSs should be deployed in
a method which maximizes the number of covered users in
an energy-efficient way. Another critical challenge is that in
practical situations, different user equipment (UE) may have
different quality of service (QoS) requirements while each
UAV-BS has limited data rate capacity. Therefore, the rational
distribution of the radio resources needs to be considered.
Research on UAV-BSs development has focused on finding
horizontal positioning [10]-[12] and altitude optimization [13]-
[15]. In [10] and [11], an identical coverage radius is assumed
for all UAV-BSs. The work in [10] proposes an efficient spiral
placement algorithm aiming to minimize the required number
of UAVs, while [11] models the UAV deployment problem
based on circle packing theory and study the relationship
between the number of deployed UAV-BSs and the coverage
duration. In [12], the authors use a K-Means clustering method
to partition the ground users to ksubsets and users belonging
to the same subset are served by one UAV. All these works
have a fixed altitude assumption. The relationship between the
altitude of UAV-BSs and the coverage area is studied in [13]
and [14]. In [13], the method of finding the optimal altitude
of a single UAV placement for maximizing the coverage is
studied based on a channel model with probabilistic path
loss (PL). Reference [14] formulates an equivalent problem
based on the same channel model as [13] and proposes an
efficient solution. Moreover, [15] studies multiple UAV-BS
3D placements with a given radius taking into account energy
efficiency by decoupling the UAV-BS placement in the vertical
dimension from the horizontal dimension. In recent years,
arXiv:2008.03125v1 [eess.SP] 7 Aug 2020
2
artificial intelligence algorithms are exponentially developed
and applied in various research fields.
In this paper, we investigate multiple 3D UAV-BS deploy-
ment with the aim to maximize the number of UAV-served
UEs under realistic conditions where each UE has a QoS
compliance including a maximum tolerated path loss and a
unique data rate requirement and each UAV-BS has a limited
sum capacity. The novelty and contributions are summarized
as follows:
•First, in order to consider a more practical deployment
scenario, the QoS compliance of ground users is mea-
sured by taking into account the maximum allowed path
loss and a unique data rate requirement. It is worth
mentioning that the existing problems and results in
the literature ignore the QoS requirements, while QoS
compliance leads to different coverage radii of UAV-BSs.
•Second, the 3D placement problem is treated as a 2D
deployment by placing multiple circles of various sizes
in the horizontal dimension and then determining the al-
titude of UAV-BSs, which simplifies the original problem
without losing the accuracy.
•Last, a new genetic algorithm (GA) based UAVs deploy-
ment strategy and framework is proposed and proved to
provide an effective solution and performance in compar-
ison.
The remainder of this paper is organized as follows. Section
II conducts the problem formulation and provides the system
model. In Section III, we first analyze the 3D deployment
problem and then decouple it into a 2D problem, followed by
the determination of the UAVs altitudes. In Section IV, the
GA algorithm is investigated and analyzed for solving the 2D
placement problem. Section V presents the numerical results
and discussions. Finally, Section VI concludes the entire paper
with the future work.
II. SY ST EM MO DE L
Fig. 1 shows a communication network model where many
UEs are clustered to be served by multiple UAV-BSs. The
objective is to find the optimal locations for UAV-BSs so
that the ground users’ coverage ratio and the coverage radii
can be maximized. Let Pbe the set of all the UEs which
are labelled as i= 1,2, ... |P|. Each UE has a unique data
rate requirement ciand all UEs have a maximum tolerated
path loss P Lmax that serves the purpose to guarantee all
the data rate requirements from UEs are feasible, for QoS
compliance. Qdenotes the set of available UAV-BSs labelled
as j= 1,2, ... |Q| and each UAV-BS has a data rate capacity
Cj. In our system, we assume that no ground base station
is available but the locations and data rate requirement of all
users are pre-known. Furthermore, in spite of the well-known
interference issues in UAV-assisted networks, such as multi-
cell co-channel interference [16], [17], this work does not take
into account the said interference which can be mitigated by
various techniques such as, frequency planning, multi-beam
UAV communication scheme [18], mmWave multi-stream
multi-beam beamforming [19], non-orthogonal multiple access
(NOMA) technique [20], cooperative NOMA scheme [21],
Fig. 1. A communication system model of multiple UAV-BSs serving ground
users.
cooperative interference cancellation strategy [18], [22], and
other interference cancellation techniques.
The A2G channel modeling follows [13] where line-of-sight
(LoS) occurs with a certain probability, which falls into our
application scenarios. The probability of a LoS and non line-
of-sight (NLoS) channel between UAV jat the horizontal
position mj= (xj, yj)and user iat the horizontal location
ui= (˜xi,˜yi)are formulated as [13]
PLoS =1
1 + aexp(−b(180
πtan−1(Hj
rij )−a)),
PNLoS =1 −PLoS ,
(1)
where Hjis the altitude of UAV-BS j;aand bare environment
dependent variables; rij =p(xj−˜xi)2+ (yj−˜yi)2is the
horizontal euclidean distance between the ith user and jth
UAV. Then the path loss for LoS and NLoS can be written as
P LLoS = 20 log( 4πfcdij
c) + ηLoS ,
P LNLoS = 20 log( 4πfcdij
c) + ηNLoS
(2)
where fcis the carrier frequency, cis the speed of light and
dij denotes the distance between between the UE and UAV-
BS given by dij =qH2
j+r2
ij . Moreover, ηLoS and ηNLoS
are the environment dependent average additional path loss for
LoS and NLoS condition respectively. According to (1), (2),
the path loss (PL) can written as:
P L =P LLoS ×PLoS +P LNLoS ×PN LoS
=A
1 + aexp(−b(180
π(Hj
rij )−a)) + 20 log rij
cos(Hj
rij )+B
(3)
where A=ηLoS −ηNLoS and B= 20 log( 4πfc
c) + ηN LoS .
In order to show the effect of different P Lmax on the
radius-altitude curve, we have plotted this relation (3) in Fig. 2
3
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Altitude (H) (m)
0
1000
2000
3000
4000
5000
6000
Radius (R) (m)
PLmax = 117
PLmax = 114
PLmax = 110
PLmax = 105
Fig. 2. Radius vs. altitude curve for different maximum path loss.
where the coverage radius is a function of both, the altitude H
and the P Lmax, by keeping the urban environment statistical
parameter set as (9.61, 0.43, 0.1, 20).
III. UAV-BS 3D DEPLOYMENT PROBLEM
For the problem at hand, the 3D deployment of UAV-BSs
can be decomposed into the 2D horizontal locations opti-
mization and altitude determination. This is because the UAV
altitude only impacts the cell radius and path loss experienced
in the cell, while the horizontal location and a radius determine
which UEs are covered by the UAV. As clearly seen in Fig. 2,
for a given P Lmax, there is a maximum radius Rmax and a
corresponding altitude Hmax. If the altitude is smaller or larger
than Hmax, while maintaining the same radius, the path loss
on the cell edge will be larger than the given P Lmax. Since
the cell radius affects the total number of the covered UEs, we
want the cell radius to be maximized in order to potentially
cover more users. Hence the 3D deployment solution takes
the procedure as follows. First, a maximum cell radius upper
bound Rmax that guarantees the desired P Lmax requirement
is derived. Second, the 2D placements of |Q|UAVs and their
respective coverage radii bounded by Rmax that maximize the
total number of UEs supported while satisfying the individual
data rate requirements and the UAV capacity constraint are
formulated and solved. Finally, given the actual coverage
radius of each UAV obtained from the second step, the altitude
that leads to the achieved minimum cell edge path loss is
determined.
A. 2D UAV-BS Deployment Problem
Since we model the 2D deployment problem via placing
multiple circles of different sizes, unlike authors in [23] who
investigate a problem of solving for the least number of UAVs
to cover users in a region, this problem is equivalent to finding
the appropriate location and radius for each UAV-BS to cover
as many UEs as possible while simultaneously satisfying the
data rate requirements and the UAV capacity constraint.
A binary variable γij ∈ {0,1}is used to indicate whether or
not the user iis covered by UAV-BS j, 1 for service and 0 for
no coverage. The necessary condition for user ito be covered
by UAV-BS jis that the horizontal Euclidean distance between
them is less than the coverage radius of UAV-BS j,Rj, which
can be written as kmj−γij uik ≤ Rj. Following [11], the
constraint equation can be rewritten as kmj−γijuik ≤ Rj+
M(1 −γij ), where Mis a large constant which is larger than
the largest horizontal distance between a user and a UAV so
the constraint holds in any condition. As defined earlier, mj=
(xj, yj)and it stands for the horizontal position of UAV j
while ui= (˜xi,˜yi)represents the horizontal location of user
i.
If a user is within the serving area of a UAV-BS, the UAV-
BS can allocate certain data channels to the user which has
a unique data rate requirement ci. For simplicity, we assume
that for any UE, the allocated data rate equals what it requires.
Then the data rate allocation problem can be expressed as
P|P|
i=1 ciγij ≤Cj, j ∈ {1,2, ... |Q|}, where Cjis the data
capacity of UAV j.
At this stage, the UAV deployment problem becomes a
rucksack-like problem in combinatorial optimization, which
is a NP-hard problem. It can be expressed as
maximize
Rj,mj
|Q|
X
j=1
|P|
X
i=1
γij ,
s.t. C1 : kmj−γij uik ≤ Rj+M(1 −γij ),
i∈ {1,2, ... |P|} , j ∈ {1,2, ... |Q|} , γij ∈ {0,1}
C2 :
|P|
X
i=1
ciγij ≤Cj, j ∈ {1,2, ... |Q|}
C3 :
|Q|
X
j=1
γij ≤1, i ∈ {1,2, .. |P|}
C4 :Rj≤Rmax, j ∈ {1,2, ... |Q|} .
(4)
Our objective is to maximize the number of served users.
First, C1in (4), guarantees that a UE can be served by a
UAV-BS, when the horizontal distance between the UE and
the UAV-BS is less than UAV-BS’s coverage radius. Then
C2regulates that the total data rate of all covered users
served by one UAV-BS cannot exceed the data rate capacity
of the UAV-BS. Furthermore, C3ensures each user should be
served by at most one UAV-BS. Last, Fig. 2 shows that the
function of coverage radius respective to altitude for a given
P Lmax is a concave function so there exists a maximum radius
Rmax that any coverage radii R > Rmax does not have a
feasible solution. Thus, C4ensures that the radii of UAV-BSs
are no larger than Rmax. A genetic algorithm to solve this
optimization problem will be presented in the next section.
B. The Determination of UAV-BS Altitude
After Subsection III-A, the horizontal locations and cov-
erage radii of UAV-BSs have been determined and all the
4
500 1000 1500 2000 2500 3000
Altitude (H) (m)
32
34
36
38
40
42
44
46
48
50
52
Path Loss (db)
R = 1000
R = 1500
R = 5000
Fig. 3. Path loss vs. altitude for given radii in an urban environment.
coverage radii are less than Rmax. Therefore, for each UAV-
BS, the range of altitude which results in the P L value less
than P Lmax can be obtained from Fig. 2. The objective for
this step is to find the optimal altitude for each UAV-BS which
requires least transmit energy, ie., the minimum path loss, to
provide service for the coverage range derived in step 1.
As observed from (3), the path loss between a UAV-BS
and UE is a function of the horizontal distance rand the
altitude H, that is, P L =f(r, H ). Also, from Fig. 2, for
a given P Lmax, defining the elevation angle θ=H
R, there
exists an elevation angle θmax that maximizes the radius R
by solving ∂ R
∂H = 0. As derived in [13], θmax satisfies the
following equation:
π
9 ln(10) tan(θmax) + abA exp(−b(180
πθmax −a))
(aexp(−b(180
πθmax −a)) + 1)2= 0
(5)
where θmax is environment dependent so it is a constant
in a given environment. It has been proven by [15] that
this elevation angle provides the minimum PL of the users
in the boundary which is equivalent to the P L of all the
UEs within the covered range are minimized so the required
transmit power of the UAV-BS is minimized. Therefore, once
the actual coverage radius Rof each UAV-BS is obtained
in Subsection III-A, the UAV-BS altitude Hopt is given by
Hopt =Rtan(θmax). Fig. 3 shows the relationship between
P L and altitude for given radii. It can be observed that as long
as the radius is fixed, a minimum value of P L always exists.
IV. GEN ET IC AL GO RI TH M BASED 2D PLAC EM EN T
In order to solve complex optimization problems, there
have been a wide range of applications of swarm intelligence
algorithms [24], [25], [26], [27], [28] and evolutionary-based
metaheuristics [29], [30], [31]. For example, [24] presented
a detailed analysis on evolutionary algorithm based real-life
applications. In this section, we present a GA based UAV-BS
deployment strategy to provide wireless services for a group
of UEs. The objective is to solve the optimization problem (4).
The genetic algorithm is an efficient solution to the complex
optimization problems with multiple variables, widely appear-
ing in real-life optimization problems of a variety of fields.
For example, [32] introduced a method based on GA and deep
learning to predict financial behaviours. Moreover, the genetic
algorithm was indeed applied in the cellular communications
related research field such as facilitating terrestrial base station
placement and showed excellent efficiency [33].
GA works on a population which consists of some candidate
solutions and the population size is the total number of
solutions [34]. Each solution is considered to be a chromosome
and each chromosome has a set of genes where each gene
is represented by the features of the solutions. Then, each
individual chromosome has a fitness value which is computed
based on the fitness function representing the quality of the
chromosome. Moreover, a selection method called roulette
wheel method where the chromosome with higher fitness value
has a higher chance to survive the population.
However, the selection process can only assure in each
generation, a better solution has a higher chance to enter
the next generation. In order to ensure the diversity of the
solution to avoid falling into local optimal solutions, crossover
and selection are applied after the selection process. In the
crossover procedure, two chromosome are selected in a prob-
ability of crossover rate to exchange information so new
chromosomes are generated. Also, in the mutation procedure,
each chromosome has a probability of mutation rate to replace
a set of genes with new random values. The basic GA process
has various variables including population size, crossover
rate and mutation rate. The population size determines the
size of candidate solutions. The value of crossover rate and
mutation rate represent the diversity of the candidate solutions
throughout the iteration. The whole process repeats until the
time step reaches an iteration limit. Fig. 4 illustrates the whole
process of GA.
As illustrated in Algorithm 1, the horizontal location, and
the coverage radius of each UAV-BS are treated as a gene
in the GA model. Therefore, for UAV-BS j, the combination
(xj,yj,Rj) is a gene. Placing genes for all the available UAV-
BSs together, i.e., {xj, yj, Rj}j∈Q makes a chromosome. The
required inputs include K,D,P,Q,Rmax,{ci}i∈P ,{ui}i∈P ,
θopt,pm,pcwhere Kis the number of iterations for finding the
optimal result, D,pmand pcare the population size, mutation
rate and crossover rate for GA respectively. The outputs are
the horizontal locations, altitudes and coverage radii, denoted
by Oj, j = 1,2, ... |Q|, of all the UAV-BSs.
First, |Q| empty lists are created and each of them is to
store the covered UEs of the corresponding UAV-BSs. Also,
two arrays r,ˆrare created, respectively, to store the number of
covered UEs in each UAV-BS and the total number of covered
UEs of all UAV-BSs known as the fitness score. In step 3, the
first population ν1is generated by creating Dchromosomes
where the horizontal locations of all UAV-BSs are initialized
by assigning each of them with the equidistant point of 3
random UEs’ locations, and the coverage radius is initialized
5
Fig. 4. Genetic algorithm workflow.
by generating a random numbers in the range from 1 to Rmax.
Then, Kiterations are executed to find the 2D deployment
result from Step 4 to Step 20. In Step 5 and Step 6, if the
horizontal distance between a UE and a UAV-BS is less than
the coverage radius, the UE can be served by the UAV-BS.
Also, if a UE is within the coverage range of more than one
UAV-BS, it is assigned to the closest one. In the for loop from
Step 7 to Step 16, calculate the sum data rate Pˆp∈Ojcˆpof all
covered UEs for each UAV-BS. If the sum data rate is smaller
than the data capacity Cj, the number of covered UEs |Oj|
is stored to array r. Otherwise, a negative number is stored
to array ˆrand the algorithm breaks out the loop and goes
back to Step 5, which means the fitness of this chromosome
is negative. In Step 15, the fitness function of the chromosome
is the total number of covered UEs and it is saved into array
ˆr.
In Step 17, the roulette wheel method is applied to update
the current population νˆ
k. A random chromosome is selected
within the current population to be the competitor. Comparing
the fitness score of all the chromosomes with the competitor,
the chromosomes with less fitness scores are replaced by
the competitor. Afterward, in the crossover procedure, pcof
chromosomes are randomly selected and paired. Each pair is
considered to be the parent chromosomes. In each parent chro-
mosomes, the first half genes of one chromosome and second
half genes of the other chromosome are exchanged to produce
children chromosomes. In Step 19, all the chromosomes have
a probability of pmto perform mutation process in which one
gene of the mutated chromosome is selected to be replaced by
Algorithm 1 Genetic Algorithm Based 2D UAV-BS Placement Method
Input: K,D,P,Q,{ci}i∈P ,{ui}i∈P ,θmax,pm,pc
Output: {mj}j∈Q,{Hj}j∈Q ,{Rj}j∈Q
1: Create |Q| empty list {Oj}j∈Q.
2: Create two arrays r,ˆrwith size |Q| and Drespectively.
3: Initialize Population: Initialize first population ν1by creating Dsets of
chromosomes.
4: for ˆ
k= 1;ˆ
k≤K;ˆ
k+ + do
5: for ˆ
i= 1;ˆ
i≤D;ˆ
i+ + do
6: Perform UE assignments according to their distances to UAV-BSs
and store the results in {Oj}j∈Q.
7: for j= 1;j≤ |Q|;j+ + do
8: if Pˆp∈Ojcˆp≤Cjthen
9: r[j]← |Oj|
10: else
11: ˆr[ˆ
i]← −100
12: Continue and go back to step 5
13: end if
14: end for
15: Fitness Function: ˆr[ˆ
i] = sum(r)
16: end for
17: Selection: update νˆ
kusing roulette wheel method to select chromo-
somes
18: Crossover: Based on pc, update νˆ
kby exchanging information of
parent chromosomes to produce children chromosomes
19: Mutation: Based on pm, gene is selected randomly to replace new
random values
20: end for
21: Find the chromosome with maximum value in ˆrand obtain {mj}j∈Q
and {Rj}j∈Q from the chromosome.
22: Obtain {Hj}j∈Q by solving H=Rtan(θmax)
23: return {Hj}j∈Q,{Rj}j∈Q,{mj}j∈Q
random horizontal location and coverage radius.
Finally, in Step 21 and Step 22, we can obtain the result of
horizontal locations and coverage radii of UAV-BSs via choos-
ing the chromosome with the maximum fitness score. Finally,
the optimal altitudes are obtained by Hopt =Rtan(θmax).
Since we model our problem to be a rucksack problem and
put additional constraints on it, the computational complexity
is proportional to the search space. In our proposed algorithm,
Step 4 to Step 16 have complexity O(KLD)where Kis the
number of UAV-BSs, Lis the iteration time, Dis the number
of chromosomes. Step 17 to 19 perform the mathematical
operation and cost O(1), and similarly, step 21 and 22 also
cost O(1). Therefore, the time complexity of the GA UAV-BS
deployment method is O(KLD).
V. NUMERICAL RESULTS
In our simulations, we consider the UEs are uniformly
distributed in a 5000 m ×5000 m area. Referring to [13],
the environment parameters are set up as followed: fc= 2
GHz, P Lmax = 110 dB, (a,b,ηLoS ,ηNLoS ) is configured to
be (4.88, 0.43, 0.1, 21), (9.61, 0.43, 0.1, 20), (12.08, 0.11, 1.6,
23), (27.23, 0.08, 2.3, 34) corresponding to suburban, urban,
dense urban and high-rise urban environments, respectively.
Also, we assume there are three different data rate require-
ments of all UEs, c1= 5 ×106bps, c2= 2 ×106bps and
c3= 1 ×106bps, and each UE has one of these three data
rate requirements. Moreover, all the UAV-BSs have the same
data rate capacity C= 1 ×108bps. Fig. 5 illustrates the UE
distribution and the GA deployment result with 100% coverage
percentage.
6
-1000 0 1000 2000 3000 4000 5000 6000
x-dimension (m)
-1000
0
1000
2000
3000
4000
5000
6000
y-dimension (m)
UE c1
UE c2
UE c3
UAV-BS location
Fig. 5. The 100% coverage ratio result of GA deployment with 80 UEs in a
5000 m ×5000 m square region with different data rate requirements.
12345678910
Number of UAV-BSs
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Coverage Ratio
Dense Urban
Urban
Suburban
Highrise Urban
Fig. 6. The coverage ratio versus the number of UAV-BSs in four environ-
ments.
In our optimization problem, there are four variables which
we need to set up, which are population size, iteration time,
mutation rate and crossover rate. According to [35], the range
of crossover rate and mutation rate are within [0.5, 0.8] and
[0.01, 0.05], respectively. In our problem, in order to analyze
how those two parameters affect the algorithm efficiency, in
the simulation we fix the iteration size and the population size
to be 10000 and 100 respectively, and deploy 10 UAV-BSs to
cover 200 UEs. As a result, Fig. 7 and Fig. 8 show that in
our optimization problem those two parameters hardly have
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Iterations
20
30
40
50
60
70
80
90
Coverage Percentage
Crossover Rate 0.5
Crossover Rate 0.65
Crossover Rate 0.8
Fig. 7. GA iteration with different crossover rates.
impact on the efficiency of the convergence. Furthermore, the
parameters (pm,pc) are configured to be (0.01, 0.8). The time
complexity of GA is related to the multiplication of population
size and iteration size, as mentioned in Section IV. In other
words, these two parameters have a significant impact on the
algorithm efficiency where a smaller the multiplication results
in a higher GA efficiency. Thus, we conduct an analysis of
the relation between the population size and the minimum
required iteration number. The minimum required iteration
number is defined to be the number of iterations taken to get
the fitness value converged to a certain number for 15% of the
entire iteration number. Moreover, Table I shows that setting
population size to be 100 paired with a iteration number of
17000 can make the GA demonstrate good performance in
terms of efficiency. Therefore, the GA parameters set (K,D,
pm,pc) is configured to be (17000, 100, 0.01, 0.8).
TABLE I
MULTI PL ICATI ON O F THE P OP ULATI ON S IZE A ND T HE IT ER ATION
NUMBER.
Population Size Minimum Required Iteration Multiplication
50 35380 1769000
75 23031 1727325
100 16875 1687500
150 15984 2397600
200 16036 3207200
300 15944 4783200
500 16015 8007500
Fig. 6 shows the average coverage ratios of 80 UEs by
10 available UAV-BSs with 15 realizations in four different
environments when increasing the number of UAV-BSs. As
seen from Fig. 6, the coverage ratio varies significantly in
four deployment scenarios, particularly with high-rise urban
one much more challenging than others.
By applying Shannon Capacity Theorem, the required SN R
of each UAV-BS can be calculated through C=Blog2(1 +
Pr
Pn), where Bis the bandwidth of the channel, Prand Pn
7
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Iterations
20
30
40
50
60
70
80
90
Coverage Percentage
Mutation Rate 0.1
Mutation Rate 0.05
Mutation Rate 0.01
Fig. 8. GA iteration with different mutation rates.
denote the required received power and average noise power,
respectively. In our model, we assume that B= 1 ×107
Hz, Pr=−74 dBm and Pn=−100 dBm. Thus, we can
obtain the minimum required power for each UAV-BS by
Pt=Pr+P L(Rj, Hj). Fig. 9 further depicts the average
minimum required transmit power of all UAV-BSs when
increasing the number of UEs, in the urban environment,
with 15 available UAV-BSs, and 4 different approaches that
determine altitudes. In the fixed altitude approach, all the
UAV-BSs are deployed in the same altitude. In the random
altitude approach, each UAV-BS is deployed at an altitude that
is uniformly drawn from a feasible range. The altitudes from
both fixed altitude and random altitudes are selected from the
range where P Lmax requirement is met. As we can see, if the
UAV-BSs are deployed in the altitude in the way we proposed,
less average transmit power is required to provide wireless
service.
TABLE II
COVERAGE RATIO COMPARISON IN URBAN ENVIRONMENTS.
Methods–|P| 80 200 450
GA Deployment Method 99.2% 88.6% 75.3%
K-Means 98.6% 82.3% 69.4%
Branch and Cut 95.6% 83.1% 69.4%
Greedy Search 92.6% 79.1% 71.4%
Random 85.6% 72.1% 59.4%
For further performance comparison, when given 10 avail-
able UAV-BSs in urban environment parameters, we test 5
algorithms to obtain the coverage percentage of UEs. In
each algorithm test, we generated 15 times of uniform UE
distributions of 80, 200 and 450 UEs respectively in the same
square region. Besides the GA deployment strategy proposed,
we have simulated four other schemes for comparison. The
first one is random placement which randomly selects a
location in a uniform distribution within the square region and
a coverage radius. The second one is the K-means algorithm
80 100 120 140 160 180 200 220
Number of UEs
43
44
45
46
47
48
49
50
Average Transmit Power(dbm)
Altitude with Maximum Coverage
Fixed Altitude - 1200m,
Fixed Altitude - 1300m
Random Altitude
Fig. 9. The UAV’s average transmit power comparison of altitude with
maximum coverage, fixed altitude and random altitude in urban environments.
which partitions the UEs into ˆ
Kclusters to be covered by
ˆ
KUAV-BSs. The third one is a linear programming method
called branch and cut [36] which breaks down each UAV-BS
placing into sub-problems and optimizes each placement. The
fourth one is called greedy search which does the UAV-BS
placement one by one and maximizes the covered UEs in each
placement. Compared with four other algorithms as shown in
Table II., namely, K-Means, Branch and Cut, Greedy and Cut,
Greedy Search, Random, GA has demonstrated the significant
advantage of solving the optimization problem with many
variables involved. It is observed that the result of GA based
deployment has higher coverage percentage and this advantage
is more pronounced when the number of UEs increases, at the
cost of higher complexity and more computing resources.
Furthermore, the proposed GA algorithm can be potentially
applied to more application scenarios, such as, geoscience and
remote sensing [37], cloud computing [38], performing tasks
by self-sufficient autonomous robots [39], automatic voltage
regulator system design optimization [40], etc. Furthermore,
a wide range of real-time applications, such as biomedical
wireless power transfer (WPT) [41], multi-core systems [42],
real-time design of thinned array antennas [43], fault repair
scheme [44], automatic mode-locked fiber laser [45], traffic
surveillance [46], have been realized based on GA algorithms.
Last, in order to evaluate how the errors of detecting UEs’
precise and exact locations affect the numerical results, a sim-
ulation is performed in the same area when the UEs’ locations
have a maximum localization error of 5 meters (a normal
localization resolution of outdoor localization techniques, e.g.,
GPS), in uniform random directions. Consequently, the nu-
merical results of the average coverage ratio are given after
running the simulations 15 times, with UEs set to 80, 200 and
8
450, respectively. From Table III, it can be observed that the
5-meter localization error hardly affects the result. Therefore,
our proposed method maintains reliable performance even in
a practical and challenging application scenario.
TABLE III
COMPARISON OF THE COVERAGE WITH AND WITHOUT ERROR IN THE
UES’LOCATIONS.
Methods–|P| 80 200 450
GA Deployment Method (Without error) 99.2% 88.6% 75.3%
GA Deployment Method (With error) 99.1% 88.5% 75.1%
VI. CONCLUSIONS
This research has proposed and evaluated a cost-efficient 3D
UAV-BS deployment algorithm for providing real-life wireless
communication services when all the UEs are randomly dis-
tributed with various data rate requirements. A novel and prac-
tical GA-based UAVs deployment algorithm has been designed
to maximize the number of covered UEs while simultaneously
meeting the UEs’ individual data rate requirements under the
capacity limit of UAV-BSs, which have not been considered
in existing works. The proposed algorithm outperforms four
conventional approaches in terms of the coverage ratio, with
good tolerance to UEs’ localization errors.
A possible future work is to extend the GA-based deploy-
ment algorithm to the applications when A2G interference
model is involved. Also, a real experimental validation in-
volving both UAVs and ground users will be interesting to
implement to verify the original idea and algorithm proposed
in this paper.
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Xukai Zhong received his Bachelor degree of Ap-
plied Science from Simon Fraser University, Burn-
aby, BC, Canada, in 2018, and Master degree of
Engineering in Electrical and Computer Engineering
from University of Victoria, Victoria, BC, Canada, in
2020. He is currently working in Fortinet, Burnaby,
BC, Canada, as Software Developing Engineer. His
recent research interests include machine learning,
computer vision, robotics and UAV communications.
Yiming Huo (S’08–M’18) received his B.Eng de-
gree in information engineering from Southeast Uni-
versity, China, in 2006, and M.Sc. degree in System-
on-Chip (SoC) from Lund University, Sweden, in
2010, and Ph.D. in electrical engineering at Univer-
sity of Victoria, Canada, in 2017, and he is currently
a Post-Doctoral Research Fellow with the same
department. His recent research interests include 5G
and beyond wireless systems, terahertz technology,
space technology, Internet of Things, and machine
learning.
He has worked in several companies and institute including Ericsson, ST-
Ericsson, Chinese Academy of Sciences, STMicroelectronics, and Apple Inc.,
Cupertino, CA, USA. He is a member of several IEEE societies, and also a
member of the Massive MIMO Working Group of the IEEE Beyond 5G
Roadmap. He was a recipient of the Best Student Paper Award of the 2016
IEEE ICUWB, the Excellent Student Paper Award of the 2014 IEEE ICSICT,
and the Bronze Leaf Certificate of the 2010 IEEE PrimeAsia. He also received
the ISSCC-STGA Award from the IEEE Solid-State Circuits Society (SSCS),
in 2017. He has served as the Program Committee of the IEEE ICUWB 2017,
the TPC of the IEEE VTC 2018/2019/2020, the IEEE ICC 2019, the Session
Chair of the IEEE 5G World Forum 2018, the Publication Chair of the IEEE
PACRIM 2019, the Technical Reviewer for multiple premier IEEE conferences
and journals. He is currently an Associate Editor for IEEE Access.
Xiaodai Dong (S’97–M’00–SM’09) received the
B.Sc. degree in information and control engineering
from Xian Jiaotong University, China, in 1992, the
M.Sc. degree in electrical engineering from the
National University of Singapore in 1995, and the
Ph.D. degree in electrical and computer engineering
from Queens University, Kingston, ON, Canada, in
2000. From 1999 to 2002, she was with Nortel Net-
works, Ottawa, ON, Canada, and worked on the base
transceiver design of the third-generation mobile
communication systems. From 2002 to 2004, she
was an Assistant Professor with the Department of Electrical and Computer
Engineering, University of Alberta, Edmonton, AB, Canada. Since 2005,
she has been with the University of Victoria, Victoria, Canada, where she
is currently a Professor with the Department of Electrical and Computer
Engineering. She was the Canada Research Chair (Tier II) from 2005 to 2015.
Dr. Dong’s research interests include 5G, mmWave communications, radio
propagation, Internet of Things, machine learning, terahertz communications,
localization, wireless security, e-health, smart grid, and nano-communications.
She served as an Editor for IEEE Transactions on Wireless Communications
in 2009-2014, IEEE Transactions on Communications in 2001-2007, Journal
of Communications and Networks in 2006-2015, and is currently an Editor
for IEEE Transactions on Vehicular Technology and IEEE Open Journal of
the Communications Society.
Zhonghua Liang (S’07–M’08–SM’20) received the
B.Sc. degree in radio engineering and the M.Sc.
and Ph.D. degrees in information and communi-
cation engineering from Xi’an Jiaotong University,
Xi’an, China, in 1996, 2002, and 2007, respectively.
From July 1996 to August 1999, he was with the
Guilin Institute of Optical Communications (GIOC),
Guilin, China, where he was a System Engineer in
optical transmission systems. From 2008 to 2009, he
was a Postdoctoral Fellow with the Department of
Electrical and Computer Engineering, University of
Victoria, Victoria, BC, Canada. Since 2010, he has been with the School of
Information Engineering, Chang’an University, Xi’an, China, where he is cur-
rently a Professor. His research interests include ultra-wideband technology,
wireless communication theory, Internet of Things, wireless sensor networks,
and adaptive signal processing techniques for wireless communication sys-
tems.
