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1
Energy Efficient Resource Allocation in
UAV-Enabled Mobile Edge Computing Networks
Zhaohui Yang, Cunhua Pan, Kezhi Wang, and Mohammad Shikh-Bahaei
Abstract—In this paper, we consider the sum power mini-
mization problem via jointly optimizing user association, power
control, computation capacity allocation and location planning
in a mobile edge computing (MEC) network with multiple
unmanned aerial vehicles (UAVs). To solve the nonconvex prob-
lem, we propose a low-complexity algorithm with solving three
subproblems iteratively. For the user association subproblem, the
compressive sensing based algorithm is accordingly proposed.
For the computation capacity allocation subproblem, the optimal
solution is obtained in closed form. For the location planning
subproblem, the optimal solution is effectively obtained via one-
dimensional search method. To obtain a feasible solution for this
iterative algorithm, a fuzzy c-means clustering based algorithm
is proposed. Numerical results show that the proposed algorithm
achieves better performance than conventional approaches.
Index Terms—Unmanned aerial vehicle-enabled communica-
tion, mobile edge computing, resource allocation, user association,
location optimization.
I. INTRODUCTION
With high mobility and the explosive growth of data traffic,
unmanned aerial vehicles (UAVs) assisted wireless commu-
nications have attracted considerable attention [1]. Compared
to conventional wireless communications, UAV-enabled wire-
less communications can provide higher wireless connectiv-
ity in areas without infrastructure coverage. Besides, high
throughput can always be achieved in UAV-enabled wireless
communications due to the higher probability of line-of-sight
(LoS) communication links between user equipments (UEs)
and UAVs [2]–[5]. Due to the above distinctions, UAVs can
be utilized in many applications, such as relaying [6]–[8], data
collection [9]–[12], device-to-device communication networks
[13], wireless power transfer networks [14] and caching net-
works [15].
To fully exploit the design degrees of freedom for UAV-
enabled communications, it is crucial to investigate the lo-
cation and trajectory optimization. In [16], the altitude of
the UAV was optimized to provide maximum radio coverage
on the ground. To maximize the number of covered users
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. (Corresponding authors: Cunhua Pan; Kezhi
Wang.)
Z. Yang and M. Shikh-Bahaei are with the Centre for Telecommunications
Research, Department of Informatics, King’s College London, London WC2B
4BG, U.K. (e-mails: yang.zhaohui@kcl.ac.uk; m.sbahaei@kcl.ac.uk).
C. Pan is with School of Electronic Engineering and Computer Sci-
ence, Queen Mary University of London, London E1 4NS, U.K. (e-mail:
c.pan@qmul.ac.uk).
K. Wang is with the Department of Computer and Information
Sciences, Northumbria University, Newcastle NE2 1XE, U.K. (e-mail:
kezhi.wang@northumbria.ac.uk).
using the minimum transmit power, an optimal location and
altitude placement algorithm was investigated in [17] for
UAV-base stations (BSs). With different quality-of-service
(QoS) requirements of users, authors in [18] studied the
three-dimension (3D) UAV-BS placement that maximizes the
number of covered users. Considering the adjustable UAVs’
locations, the UAV number minimization was considered in
[19]. In [20] and [21], the UAV’s trajectory was optimized by
jointly considering both the communication throughput and
the UAV’s energy consumption. Further optimizing user-UAV
association, [22] investigated the sum power minimization
problem of the UAV. Different from [16]–[22] with fixed-
beamwidth antenna, the beamwidth of the directional antenna
was optimized in [23] with fixed bandwidth allocation to
improve the system throughput. Through jointly optimizing
beamwidth and bandwidth, the sum power was further mini-
mized in [24]. Deploying UAVs as users, [25] proposed a novel
concept of 3D cellular networks and developed an optimal 3D
cell association scheme [26].
Recently, mobile edge computing (MEC) has been pro-
posed as a promising technology for future communications
since it can improve the computation capacity of UEs with
computation-hungry applications, such as, augmented reality
(AR) [27]. With MEC, UEs can offload the tasks to the MEC
servers that locate at the edge of the network. Since MEC
servers can be deployed near to UEs, network with MEC
can provide UEs with low latency and save energy for UEs
[28]. There are two operation modes for MEC, i.e., partial
and binary computation offloading. In partial computation
offloading, the computation tasks can be divided into two
parts, where one part is locally executed and the other part
is offloaded to MEC servers [29]–[34]. In binary computation
offloading, the computation tasks are either locally executed
or offloaded to MEC servers [35], [36].
Due to the mobility of UAVs, the integration of UAV-
enabled communication with MEC can further improve the
computation performance [37]–[41]. The UAV-enabled MEC
architecture was first proposed in [37], which showed that the
computation performance can be improved with UAVs. Jointly
optimizing bit allocation and UAV’s trajectory, the authors in
[39] and [40] minimized the total mobile energy consumption
while satisfying QoS requirements of the offloaded mobile
application. Considering wireless power transfer, the computa-
tion rate maximization problem was studied in [41] for a UAV-
enabled MEC wireless powered system, subject to the energy
harvesting causal constraint and the UAV’s speed constraint.
In this paper, we consider resource allocation in a UAV-
enabled MEC network with multiple UAVs. The objective of
2
this paper is to minimize the sum power consumption of UEs
and UAVs including both communication related power and
mechanical power. Compared with references [39] and [40],
where only the total power of all the UEs is minimized, this
paper considers the total power minimization of both UEs and
UAVs since the UAVs are also power constrained. Although
the computation and communication power consumption of
the UAV is considered in [41], the mechanical power of the
UAV is ignored. Since the mechanical power of the UAV is
significant compared to the computation and communication
power, this paper considers both communication related power
and mechanical power of each UAV. Morover, the works in
[39]–[41] all considered only one UAV in the UAV-enabled
MEC network even though there always exist multiple UAVs
for practical applications.
The main contributions of this paper are summarized as
follows:
1) We formulate the sum power minimization problem with
latency and coverage constraints via jointly optimizing
user association, power control, computation capacity
allocation and location planning. To solve the noncon-
vex sum power minimization problem, an algorithm is
proposed by solving three subproblems iteratively. We
also provide the complexity analysis of the proposed
algorithm.
2) For user association problem with `
0
-norm, we apply the
compressive sensing based algorithm, where the closed-
form solution is given in each iteration.
3) For computation capacity allocation or location plan-
ning, we first decompose the original problem into
multiple small optimization problems. Then, the optimal
computation capacity allocation is derived in closed
form, while the optimal location planning is obtained
via one-dimensional search method.
The rest of the paper is organized as follows. In Section II,
we introduce the system model and sum power minimization
formulation. The proposed algorithm is addressed in Section
III. Some numerical results are shown in Section IV, and
conclusions are finally drawn in Section V.
The main notations used in the paper are summarized in
Table I.
II. SYSTEM MODEL
+
j
x
y
z
(X
j
,Y
j
,H
j
)
(x
i
,y
i,
0)
Fig. 1. A UAV-aided network.
TABLE I
LIST OF MAIN NOTATIONS.
Notation Description
N Number of UEs
M Number of UAVs
N Set of UEs
M Set of UAVs
M
0
Possible place for the tasks to be executed
a
ij
Offloading indicator of UE i
U
i
Computation task of UE i
F
i
Number of CPU cycles of task U
i
D
i
Data size of task U
i
T Latency requirement for all tasks
f
ij
Computation capacity of UAV j allocated to UE i
T
C
ij
Execution time of UAV j to compute UE i’s task
T
Tr
ij
Offloading time of UE i to UAV j
r
ij
Offloading transmission rate of UE i to UAV j
f
ue
i,max
Maximal computation capacity of UE i
p
ij
Transmission power of UE i to UAV j
p
E
i
Local execution power of UE i
p
ue
i
Power consumption of UE i
P
ue
i,max
Maximal power consumption of UE i
p
uav
j
Power consumption of UAV j
f
j
Total used computation capacity of UAV j
f
ue
j,max
Maximal computation capacity of UAV j
(x
i
, y
i
, 0) Coordinate of UE i
(X
j
, Y
j
, H
j
) Coordinate of UAV i
R
ij
Horizontal distance between UE i and UAV j
θ
j
Half-power beamwidth of antenna for UAV j
g
ij
Uplink channel gain between UE i and UAV j
U
j
Maximal number of associated UEs for UAV j
As shown in Fig. 1, we consider a UAV-aided network
with N UEs and M rotary-wing UAVs, which are able
to hover. The sets of the UEs and UAVs are denoted by
N = {1, 2, ..., N} and M = {1, 2, ..., M}, respectively. Each
UE has a computation task to be executed, which can be
offloaded to the UAVs. Define a new set M
0
= {0, 1, · · · , M}
to represent the possible place in which the tasks can be
executed, where 0 means that UE conducts task itself without
offloading. Then, define a
ij
as the offloading indicator variable
of UE i satisfying
a
ij
= {0, 1}, ∀i ∈ N , j ∈ M
0
,
(1)
where a
ij
= 1, j 6= 0 denotes that UE i decides to offload
the task to UAV j, while a
ij
= 0, j 6= 0 indicates that UE i
decides not to offload the task to UAV j, and a
ij
= 1, j = 0
denotes UE conducts the task itself. One has
M
X
j=0
a
ij
= 1, i ∈ N ,
(2)
which reflects that each task can only be executed at one place.
Similar to [42], we assume that UE i has the computation-
ally intensive task U
i
to be executed as follows
U
i
= (F
i
, D
i
, T ), ∀i ∈ N ,
(3)
where F
i
describes the total number of the central processing
unit (CPU) cycles of U
i
to be computed, D
i
denotes the data
size transmitting to the cloud if offloading action is decided
and T is the latency constraint or QoS requirement by this
task. In this paper, we consider that all tasks have the same
3
latency requirement T , without loss of generality. D
i
and F
i
can be obtained by using the approaches provided in [43].
Then, the execution time of the task can be calculated as
T
C
ij
=
F
i
f
ij
, ∀i ∈ N , j ∈ M
0
,
(4)
where f
ij
is the computation capacity of UAV j allocated to
UE i and j = 0 means the UE executes the task itself.
If the data is offloaded to the UAV, the time required to
offload the data is calculated as
T
Tr
ij
=
D
i
r
ij
, ∀i ∈ N , j ∈ M,
(5)
where r
ij
is the offloading transmission rate of UE i to UAV
j. Then, we can have
a
ij
D
i
r
ij
+
F
i
f
ij
≤ T, ∀i ∈ N , j ∈ M,
(6)
which means that each task executed in the UAV must meet
the latency requirement. Note that the downloading time
from the UAV is low and negligible [44]. In (6), we define
a
ij
D
i
r
ij
+
F
i
f
ij
= 0 for the case where a
ij
= 0 and f
ij
= 0.
If this task is executed in UE itself, one has
a
ij
F
i
f
ij
≤ T, ∀i ∈ N , j = 0.
(7)
The computation capacity for the UE i is constrained by
f
ij
≤ f
ue
i,max
, ∀i ∈ N , j = 0.
(8)
The power consumption at UE i is given by
p
ue
i
=
(
P
M
j=1
a
ij
p
ij
, if offloading,
p
E
i
, if local execution
(9)
where p
ij
is the transmitting power of UE i to the UAV j and
p
E
i
is the execution power in UE i if UE conducts the task
itself, which is given by
p
E
i
= κ
i
f
ν
i
ij
, i ∈ N , j = 0,
(10)
where κ
i
≥ 0 and ν
i
≥ 1 are positive coefficients specified in
the CPU model [45]. The UE power is constrained by
p
ue
i
≤ P
ue
i,max
, i ∈ N .
(11)
The computing power consumption for UAV j can be given
as
p
uav
j
= s
j
f
w
j
j
, ∀j ∈ M,
(12)
where s
j
and w
j
are constants. In (12), f
j
is the computation
capacity provided by UAV j to the associated UEs, which can
be given as
f
j
=
N
X
i=1
a
ij
f
ij
, ∀j ∈ M.
(13)
Due to limited computation capacity, the computation capacity
for UAV j is constrained by
f
j
≤ f
uav
j,max
, ∀j ∈ M.
(14)
Assume that the coordinates of UE i are (x
i
, y
i
, 0) and
the coordinates of UAV j are (X
j
, Y
j
, H
j
). The horizontal
distance between UE i and UAV j is calculated as
R
ij
=
q
(X
j
− x
i
)
2
+ (Y
j
− y
i
)
2
, ∀i ∈ N , j ∈ M.
(15)
It is assumed that each UAV is equipped with a directional
antenna of adjustable beamwidth. The azimuth and elevation
half-power beamwidths of antenna are equal for UAV j, which
are both denoted by 2θ
j
∈ (0, π). For UAV j, the antenna gain
in the direction with azimuth angle θ and elevation angle ψ
1
can be modelled as [46, Eq. (2-51)]
G =
(
G
0
θ
2
j
if 0 ≤ θ ≤ θ
j
and 0 ≤ ψ ≤ θ
j
g ≈ 0 otherwise,
(16)
where G
0
≈ 2.2846, and g means the channel gain outside
the beamwidth of the antenna. For simplicity, we set g = 0.
We consider the case that the UEs are located outdoors, and
the channel between each UE and UAV is mainly a LoS path.
The uplink channel gain between UE i and UAV j is
g
ij
=
g
0
H
2
j
+ R
2
ij
, (17)
where g
0
is the channel power gain at the reference distance
1 m, i.e., it is assumed that the communication is neglected
via the sidelobes.
If UE i wants to offload the task to UAV j, it has to be in
the coverage area of UAV j, i.e.,
R
ij
≤ H
j
tanθ
j
.
(18)
According to (16) and (17), if UE i decides to offload the
task to UAV j, the data rate is given by
r
ij
= Blog
2
1 +
αp
ij
θ
2
j
(H
2
j
+ R
2
ij
)
!
, ∀i ∈ N , j ∈ M,
(19)
where B is the system bandwidth, α = g
0
G
0
/σ
2
and σ
2
is the noise power. For UAVs with overlapped coverage
area, UAVs are allocated with orthogonal frequency resources,
which indicates that there is no interference among UAVs.
According to constraints (6) and (7), the latency constraints
can be combined as
M
X
j=1
a
ij
D
i
Blog
2
1 +
αp
ij
θ
2
j
(H
2
j
+R
2
ij
)
+
F
i
f
ij
+
a
i0
F
i
f
i0
≤ T.
(20)
According to (2), each UE either conducts the task locally or
uploads the task to one unique UAV. If UE i conducts the
task locally, i.e., a
i0
= 1 and a
ij
= 0, ∀j ∈ M, equation (20)
becomes
a
i0
F
i
f
i0
≤ T, (21)
1
The azimuth and elevation angles are defined with respect to three
reference axises, two orthogonal axises on the ground plane with intersection
(X
j
, Y
j
, 0), i.e., x axis and y axis, and one vertical axis across points
(X
j
, Y
j
, 0) and (X
j
, Y
j
, H
j
), i.e., z axis.
4
which is the same as equation (7). If UE i uploads the task
to one unique UAV j, i.e., a
ij
= 1, a
i0
= 0 and a
il
= 0,
l ∈ M \ {j}, equation (20) becomes
a
ij
D
i
Blog
2
1 +
αp
ij
θ
2
j
(H
2
j
+R
2
ij
)
+
F
i
f
ij
≤ T, (22)
which is the same as equation (6) since r
ij
in defined in (19).
In practice, the number of UEs associated with one UAV is
limited, i.e.,
N
X
i=1
a
ij
≤ U
j
, ∀j ∈ M,
(23)
where U
j
is the maximal allowed number of UEs associated
with UAV j.
Then, we can formulate the sum power minimization prob-
lem as follows:
min
A
A
A,F
F
F ,P
P
P ,Z
Z
Z
W
1
N
X
i=1
M
X
j=1
a
ij
p
ij
+ W
1
N
X
i=1
a
i0
κ
i
f
ν
i
i0
+ W
2
M
X
j=1
s
j
N
X
i=1
a
ij
f
ij
!
w
j
+ Q
j
N
X
i=1
a
ij
0
!
(24a)
s.t.
M
X
j=0
a
ij
= 1, i ∈ N (24b)
s
j
N
X
i=1
a
ij
f
ij
!
w
j
+ Q
j
N
X
i=1
a
ij
0
≤ P
uav
j,max
,
∀j ∈ M (24c)
M
X
j=1
a
ij
D
i
Blog
2
1 +
αp
ij
θ
2
j
(H
2
j
+R
2
ij
)
+
F
i
f
ij
+
a
i0
F
i
f
i0
≤ T, ∀i ∈ N (24d)
R
ij
=
q
(X
j
− x
i
)
2
+ (Y
j
− y
i
)
2
, ∀j ∈ N , j ∈ M
(24e)
a
ij
R
ij
≤ H
j
tanθ
j
, ∀i ∈ N , j ∈ M (24f)
M
X
j=1
a
ij
p
ij
+ a
i0
κ
i
f
ν
i
i0
≤ P
ue
i,max
, ∀i ∈ N (24g)
N
X
i=1
a
ij
f
ij
≤ f
uav
j,max
, ∀j ∈ M (24h)
N
X
i=1
a
ij
≤ U
j
, ∀j ∈ M (24i)
a
ij
= {0, 1}, f
i0
≤ f
ue
i,max
∀i ∈ N , j ∈ M
0
(24j)
f
ij
≥ 0, p
ij
≥ 0, H
min
j
≤ H ≤ H
max
j
,
θ
min
j
≤ θ
j
≤ θ
max
j
, ∀i ∈ N , j ∈ M, (24k)
where A
A
A = {a
ij
}
i∈N ,j∈M
0
, F
F
F = {f
ij
}
i∈N ,j∈M
0
, P
P
P =
{p
ij
}
i∈N ,j∈M
, Z
Z
Z = {X
j
, Y
j
, H
j
, θ
j
}
j∈M
, W
1
and W
2
are
respectively constant positive weights for UE power and UAV
power, Q
j
is the propulsion power for ensuring the UAV j to
remain aloft, k · k
0
is the `
0
-norm
2
, and P
uav
j,max
> Q
j
is the
maximal battery power of UAV j. [H
min
j
, H
max
j
] is the feasible
region of height H
j
determined by obstacle heights and
authority regulations, and [θ
min
j
, θ
max
j
] is the feasible region of
half-beamwidth θ
j
determined by practical antenna beamwidth
tuning technique. The term Q
j
P
N
j=1
a
ij
0
stands for the
propulsion power of UAV j if it serves at least one UE.
Objective function (24a) is the sum power of UEs and
UAVs including transmission power, execution power and
propulsion power. Constraints (24b) represent that the UE
either conducts the task locally or uploads the task to one
unique UAV. The maximal power constraint for each UAV
is shown in (24c). Since each UE executes the task itself or
uploads the task to one and only one UAV according to (24b),
the latency requirements for all UEs can be given in (24d).
Constraints (24e) and (24f) state that the offloaded UEs should
be in the coverage area of the associated UAVs. The maximal
transmission power constraints for UEs are given in (24g).
The maximal computation capacity and maximal associated
number of UEs for UAVs are given in (24h) and (24i),
respectively. There are two major differences with Problem
(24) and well-known MEC problems in the literature [12],
[39]–[41]. The first difference is that this paper considers the
UAV-enabled MEC with multiple UAVs, and the battery power
limit for each UAV is also involved. The other difference is
that Problem (24) optimizes the beamwidth and altitude of all
UAVs.
III. PROPOSED ALGORITHM
Due to the nonconvex objective function and discrete con-
straints, Problem (24) is a nonconvex problem. It is gen-
erally hard to effectively obtain a globally optimal solu-
tion for this nonconvex problem. In the following, a joint
optimization algorithm is proposed to obtain a suboptimal
solution with an iterative mechanism. Specifically, the user
association subproblem is first solved due to the fact that
the decision variables for user association are discrete. Based
on the obtained user association, the optimal conditions for
the transmission power of the UEs are obtained, which is
helpful in simplifying the original problem. According to the
optimal conditions for the transmission power of the UEs,
both computation capacity allocation subproblem and location
planning subproblem can be decoupled into multiple small-
size problems, which fortunately have the closed-form optimal
solutions. A clustering based algorithm is also provided to
obtain a feasible solution of the iterative algorithm.
A. User Association Optimization
Problem (24) is hard to be solved due to non-smooth `
0
-
norm, which can be approximately solved via a sequence
of weighted `
1
-norm minimizations in compressive sensing
2
`
0
-norm is usually used for vectors, and scalar can be viewed as a special
case of vector with one dimension.
