UAV-Assisted Relaying and Edge Computing:
Scheduling and Trajectory Optimization
Xiaoyan Hu, Student Member, IEEE, Kai-Kit Wong, Fellow, IEEE, Kun Yang, Senior Member, IEEE,
and Zhongbin Zheng
Abstract—In this paper, we study an unmanned aerial vehicle
(UAV)-assisted mobile edge computing (MEC) architecture, in
which a UAV roaming around the area may serve as a computing
server to help user equipment (UEs) compute their tasks or act
as a relay for further offloading their computation tasks to the
access point (AP). We aim to minimize the weighted sum energy
consumption of the UAV and UEs subject to the task constraints,
the information-causality constraints, the bandwidth allocation
constraints and the UAV’s trajectory constraints. The required
optimization is nonconvex, and an alternating optimization algo-
rithm is proposed to jointly optimize the computation resource
scheduling, bandwidth allocation, and the UAV’s trajectory in an
iterative fashion. Numerical results demonstrate that significant
performance gain is obtained over conventional methods. Also,
the advantages of the proposed algorithm are more prominent
when handling computation-intensive latency-critical tasks.
Index Terms—UAV, mobile edge computing, resource schedul-
ing, bandwidth allocation, trajectory optimization.
I. INTRODUCTION
A. Motivation and Prior Works
With the popularization of Internet of things (IoT) and the
increasingly complex mobile applications, such as virtual and
augmented reality, online gaming, automatic driving, etc., the
computing demands at user equipment (UEs) are reaching an
unprecedented level. Mobile edge computing (MEC), widely
regarded as the technology to help the resource-limited UEs
handle computation-intensive latency-critical tasks, has attract-
ed great attention from both the academia and the industry.
The standardization organizations and industry associations
such as ETSI and 5GAA have identified several use cases for
MEC, from the intelligent video acceleration and application-
aware performance optimization to vehicle-to-everything and
massive machine-type communications, etc. [1, 2].
Manuscript received December 5, 2018; revised April 13, 2019 and June 19,
2019; accepted June 28, 2019. This work was supported in part by the U.K.
Engineering and Physical Sciences Research Council (EPSRC) under Grant
EP/K015893/1 and in part by the Natural Science Foundation of China under
Grant 61620106011 and Grant 61572389. This work will be presented in part
at the IEEE Global Communications Conference (GLOBECOM), Waikoloa,
HI, USA, December 2019. The associate editor coordinating the review of
this paper and approving it for publication was N. Michelusi. (Corresponding
author: Xiaoyan Hu.)
X. Hu and K.-K. Wong are with the Department of Electronic and Electrical
Engineering, University College London, London WC1E 7JE, U.K. (e-mail:
{xiaoyan.hu.16, kai-kit.wong}@ucl.ac.uk).
K. Yang is with the School of Computer Science and Electronic Engineer-
ing, University of Essex, Colchester CO4 3SQ, U.K., and also with the School
of Communication Engineering, University of Electronic Science and Tech-
nology of China, Chengdu 611731, China (e-mail: kunyang@essex.ac.uk).
Z. Zheng is with the East China Institute of Telecommunications, China
Academy of Information and Communications Technology, Shanghai 200001,
China (e-mail: ben@ecit.org.cn).
The rationale behind MEC is that UEs’ computing tasks can
be offloaded and completed at the edge of wireless networks
by deploying cloud servers at the access points (APs), so as to
liberate the UEs from heavy computing workloads and prolong
their battery lifetime [3, 4]. Recently, MEC has been widely
used in cellular networks, focusing on improving the energy
efficiency or reducing the latency of various cellular-based
MEC systems [5–14]. A multicell MEC system was studied
in [5], where the total energy consumption was minimized by
jointly optimizing the radio and computational resources. In
[6], the resource allocation for minimizing the weighted sum
energy consumption of users was addressed with a derived
threshold-based optimal policy. Later in [7], the scenario of
a UE with multiple tasks was considered, where multiple
APs assisted the UE to reduce its total task execution latency
and energy consumption. A two-tier heterogeneous network
with the coexistence of edge and central cloud computing was
studied in [8], and the cloud selection was optimized to min-
imize the network’s energy consumption. In [9], a device-to-
device (D2D) fogging was explored to achieve energy-efficient
task completion by sharing computation and communication
resources amongst mobile devices. The sum of computation
efficiency defined as the calculated data bits divided by the
energy consumption was maximized in [10] with iterative and
gradient descent methods. In addition, the works in [11–14]
introduced the use of energy harvesting or wireless power
transfer (WPT) technologies into the cellular-based MEC
systems, which has enabled the UEs to have sustainable energy
support to their transmissions and computation, but at the cost
of increasing the computational complexity of the systems.
Due to the attractive advantages of unmanned aerial vehicle
(UAV) for its easy deployment, flexible movement, and line-
of-sight (LoS) connections, and so on, UAV-enabled wireless
communication networks have been much researched in recent
years [15–19]. For instance, an energy-efficient UAV commu-
nication was investigated in [16], in which an UAV flew at a
fixed altitude and had the initial and final locations preset on
its trajectory design. In [17], the UAV-enabled mobile relaying
systems were studied, where the throughput was maximized
by optimizing the transmit power allocation and the UAV’s
trajectory. Recently, [18] proposed a generic framework for the
analysis and optimization of the air-to-ground systems, and an
optimum altitude for UAV in maximizing the coverage region
with a guaranteed minimum outage performance was derived.
WPT technology was considered for UAV wireless networks
in [19], and the UAV trajectory was optimized to maximize
the sum energy or the minimum energy transferred to all the
UEs. It was revealed that UAV-enabled WPT can significantly
enhance the WPT performance over the traditional WPT
system with fixed energy transmitters.
It is a great attempt to leverage the technology of the UAV in
MEC systems, and the performance improvement of the UAV-
enabled MEC architecture has been shown to be substantial
[20–22]. A UAV-based MEC system was investigated in [20],
where a moving UAV equipped with a processing server was
considered to help UEs compute their offloaded tasks. The
total mobile energy consumption was minimized by jointly
optimizing the task-bit allocation and the UAV trajectory
using the successive convex approximation (SCA) methods.
Later in [21], a wireless-powered UAV-enabled MEC system
was studied, where the UAV was endowed with an energy
transmitter and an MEC server to provide energy as well as
MEC services for the UEs. The computation rate maximization
problems were addressed under both the partial and binary
computation offloading modes by alternating algorithms. In
another study [22], the UAV acted as a UE rather than an MEC
server, which was served by multiple cellular ground base
stations to compute its offloaded tasks. The UAV’s mission
completion time was minimized by optimizing the resource
allocation and the UAV trajectory through an SCA algorithm.
B. Our Contributions
The aforementioned MEC works concentrate either on the
cellular-based MEC networks, where the UEs’ tasks are com-
pleted by using the computing resources at the APs; or the
UAV-enabled MEC architectures by exploiting the computing
capability of the UAV processing server. However, for the UEs
with seriously degraded links to the AP due to severe blockage,
it is impossible to take full use of the computing resources at
the AP directly. Besides, due to the size-constrained resource-
limited property of the UAVs, it is risky to rely only on the
UAVs to assist the UEs for completing their computation-
intensive latency-critical tasks. For these reasons, this paper s-
tudies a UAV-assisted MEC architecture, where the computing
resources at the UAV and the AP are utilized at the same time.
In addition, the energy-efficient LoS transmissions of the UAV
have been fully exploited since the UAV is not only served as a
mobile computing server to help the UEs compute their tasks
but also as a relay to further offload UEs’ tasks to the AP
for computing. To our best knowledge, this is the first work
considering the UAV-assisted MEC architecture by letting the
UAV act as an MEC server and a relay simultaneously.
Our main contributions are summarized as follows:
• UAV-Assisted MEC Architecture—We consider a UAV-
assisted MEC architecture where the cellular-connected
UAV is served as a mobile computing server as well as a
relay to help the UEs complete their computing tasks or
further offload their tasks to the AP for computing. This
architecture takes full advantages of the UAV’s energy-
efficient LoS transmissions, and makes proper use of the
computing resources at both the UAV and AP.
• Problem Formulation with Joint Computation Re-
source Scheduling, Bandwidth Allocation and UAV’s
Trajectory Optimization—Our aim is to minimize the
weighted sum energy consumption (WSEC) of the UAV
and the UEs subject to the UEs’ task constraints, the
information-causality constraints, the bandwidth alloca-
tion constraints and the UAV’s trajectory constraints, by
jointly optimizing the computation resource scheduling,
the bandwidth allocation and UAV’s trajectory iteratively.
The formulated problem is complicated and non-convex
due to the coupled optimization variables.
• Alternating Algorithm with Guaranteed Convergence
—An alternating optimization algorithm is devised to
decouple the optimization variables, through which the
formulated problem can be properly solved by addressing
three subproblems iteratively. Note that the computation
resource scheduling parameters, including the offload-
ing/downloading task sizes and the CPU frequencies at
each UE and the UAV, as well as the bandwidth allocation
parameters are obtained in closed form by leveraging
the Lagrange duality method, and that the correspond-
ing Lagrange multipliers associated with the inequality
constraints can be obtained using the subgradient method
while those associated with the equality constraints can
be obtained through bi-section search. The subproblem
relating to the UAV’s trajectory optimization can be
efficiently solved by CVX [23] based on the SCA method.
Besides, the convergence of the proposed algorithm can
be guaranteed, and the required complexity appears to be
acceptable.
• Considerable Performance Improvement—Simulation
results are presented to show the optimized trajectories
of the UAV under different scenarios and the significant
performance enhancement by leveraging the proposed
algorithm when compared to existing schemes, such as
the one with a preset UAV trajectory, the scheme with
task offloading only, the scheme with equal bandwidth
allocation, and the local computing scheme without of-
floading. Moreover, the proposed algorithm is capable
of providing more stable performance in adapting to the
change in the operating environment, and its advantages
will become much more prominent when dealing with
the computation-intensive and latency-critical tasks.
The rest of this paper is organized as follows. In Section II,
we introduce our system model and then formulate the op-
timization problem. The proposed method that decouples the
problem into three subproblems then solving it iteratively is
presented in Section III. Section IV provides the simulation
results. Finally, we conclude the paper in Section V.
II. SYSTEM MODEL AND PROBLEM FORMULATION
As shown in Fig. 1, a UAV-assisted MEC system is consid-
ered, which consists of an AP, a cellular-connected UAV, and
K ground UEs, all being equipped with a single antenna. The
UAV and UEs are all assumed to have an on-board communi-
cation circuit and on-board computing processor powered by
their embedded battery, while the AP is capable of providing
high-speed transmission rate with grid power supply and is
endowed with an ultra-high performance processing server.
It is also assumed that each UE has a bit-wise-independent
AP
(x
k
,y
k
,0)
(x
0
,y
0
,0)
x
y
h
UE k
UAV
UEsϣoffloading links
APϣs downloading links
MEC
processor
MEC
server
UAVϣs downloading links
(x[n],y[n],H)
h
k
[n]
h
AP
[n]
UAV´ s offloading links
Fig. 1. An illustration of the UAV-assisted MEC architecture, where the UAV
serves as an MEC server to help the ground UEs compute their offloaded tasks
or as a possible relay to further forward the offloaded tasks to the AP with
more powerful computing resources.
computation-intensive task, and the UAV acts as an assistant
to help the UEs complete their computation tasks by providing
both MEC and relaying services. For providing MEC service,
the UAV shares its computing resources with the UEs to
help compute their tasks; while for the relaying service, the
UAV forwards part of the UEs’ offloaded tasks to the AP for
computing with the purpose of saving its own energy.
A. Channel Model and Coordinate System
A three-dimensional (3D) Euclidean coordinate system is
adopted, whose coordinates are measured in meters. We as-
sume that the locations of the AP and all the UEs are fixed
on the ground with zero altitude, with the location of the AP
being
v
0
= (x
0
, y
0
, 0). Let K = {1, . . . , K} denote the set of
the UEs, with
v
k
= (x
k
, y
k
, 0) representing the location of UE
k ∈ K. It is assumed that the locations of UEs are known to
the UAV for designing its trajectory [16]. We assume that the
UAV flies at a fixed altitude H > 0 during the task completion
time T , which corresponds to the minimum altitude that is
appropriate to the work terrain and can avoid buildings without
the requirement of frequent descending and ascending.
For ease of exposition, the finite task completion time T is
discretized into N equal time slots each with a duration of
τ = T/N , where τ is sufficiently small such that the UAV’s
location can be assumed to be unchanged during each slot.
The initial and final horizontal locations of the UAV are preset
as u
I
= (x
I
, y
I
) and u
F
= (x
F
, y
F
), respectively. Let N =
{1, . . . , N } denote the set of the N time slots. At the n-th
time slot, the UAV’s horizontal location is denoted as u[n] ≡
u(nτ) = (x[n], y[n]) with u[0] = u
I
and u[N ] = u
F
. It
is assumed that the UAV flies with a constant speed in each
time slot, denoted as v[n], which should satisfy the following
maximum speed constraint
v[n] =
∥u[n] − u[n − 1]∥
τ
≤ V
max
, n ∈ N , (1)
where V
max
is the predetermined maximum speed of the UAV,
and V
max
≥ ∥u
F
−u
I
∥/T establishes to make sure that at least
one feasible trajectory of the UAV exists.
Similar to [16], the wireless channels between the UAV and
the AP as well as the UEs are assumed to be dominated by
LoS links, which is verified by recent field experiments done
by Qualcomm [24].
1
Thus, the channel power gain between
the UAV and the AP and between the UAV and UE k at the
time slot n can be, respectively, given by
h
AP
[n] = h
0
d
−2
AP
=
h
0
∥u[n] − v
0
∥
2
+ H
2
, n ∈ N , (2)
h
k
[n] = h
0
d
−2
k
=
h
0
∥u[n] − v
k
∥
2
+ H
2
, k ∈ K, n ∈ N , (3)
where h
0
is the channel power gain at a reference distance of
d
0
= 1m; d
AP
and d
k
are respectively the distances between
the UAV and the AP as well as the UE k at the n-th time slot
with v
0
= (x
0
, y
0
) and v
k
= (x
k
, y
k
) denoting the horizontal
locations of the AP and UE k, k ∈ K. It is assumed that
the channel reciprocity establishes in our considered scenario,
and thus the offloading and downloading channels between the
UEs and the UAV are identical. In this paper, the direct links
between UEs and the AP are assumed to be negligible due
to e.g., severe blockage,
2
which means that the UEs cannot
directly offload their task-input bits to the AP unless with the
assistance of the UAV. The motivation behind this scenario
is based on the fact that it is more important to guarantee
the UEs’ computation tasks being completed within the given
limited time T with as little UEs’ energy as possible, than
dropping their tasks or letting the UEs compute their takes
locally at the cost of exhausting their energy.
B. Computation Task Model and Execution Methods
The computation task of UE k ∈ K is denoted as a positive
tuple [I
k
, C
k
, O
k
, T
k
], where I
k
denotes the size (in bits) of
the computation task-input data (e.g., the program codes and
input parameters), C
k
is the amount of required computing
resource for computing 1-bit of input data (i.e., the number
of CPU cycles required), O
k
∈ (0, 1) is the ratio of task-
output data size to that of the task-input data, i.e., the output
data size should be O
k
I
k
, and T
k
is the maximum tolerable
latency with T
k
≤ T, k ∈ K. In this paper, we only consider
the case that T
k
= T for all k ∈ K. It should be noted that
the UEs’ task-input bits are bit-wise independent and can be
arbitrarily divided to facilitate parallel trade-offs between local
computing at the UEs and computation offloading to the UAV
or further to the AP with the assistance of the UAV. In other
words, the UEs can accomplish their computation tasks in a
partial offloading fashion [4] with the following three ways.
1) Local Computing at UEs: Each UE can perform local
computing and computation offloading simultaneously since
local computing at the UEs does not need radio resources
such as bandwidth. To efficiently use the energy for local
computing, the UEs leverage a dynamic voltage and frequency
scaling (DVFS) technique, and thus the energy consumed for
local computing can be adaptively controlled by adjusting
1
It is of great value to extend our work on the probabilistic LoS and Rician
fading channel models when we consider the scenarios where the UAV’s flying
altitude changes according to the work terrain.
2
The general case with direct links between the UEs and the AP will be
considered as one of our future works.
the UEs’ CPU frequency during each time slot [25]. The
CPU frequency of UE k during time slot n is denoted as
f
k
[n] (cycles/second). Thus, the computation bits and energy
consumption of UE k during time slot n for local computing
can be, respectively, expressed as
3
L
local
k
[n] = τ f
k
[n]/C
k
, k ∈ K, n ∈ N , (4)
E
local
k
[n] = τ κ
k
f
3
k
[n], k ∈ K, n ∈ N , (5)
where κ
k
is the effective capacitance coefficient of UE k that
depends on its processor’s chip architecture.
2) Task Offloaded to the UAV for Computing: The UEs’
remaining task-input data should be computed remotely, first
by offloading to the UAV, and then one part of the data being
computed at the UAV while the other part further offloaded to
the AP for computing. In order to avoid interference among the
UEs during the offloading process, we adopt the time-division
multiple access (TDMA) protocol. Each slot is further divided
into K equal durations δ = T/(NK), and UE k offloads
its task-input data in the k-th duration. Let l
k
[n] denote the
offloaded bits of UE k in its allocated duration at time slot n,
and thus the corresponding energy consumption of UE k at
slot n for computation offloading can be calculated as
E
off
k
[n] = δp
k
[n]
≡
δN
0
h
k
[n]
2
l
k
[n]
δB
off
k
[n]
− 1
, k ∈ K, n ∈ N , (6)
where p
k
[n] is the transmit power of UE k for offloading l
k
[n]
computation bits to the UAV at time slot n, B
off
k
[n] is the
corresponding allocated bandwidth for UE k, and N
0
denotes
the noise power at the UAV.
4
Assume that the UAV also adopts the DVFS technique to
improve its energy efficiency for computing, and its adjustable
CPU frequency in the k-th duration of slot n for computing UE
k’s offloaded task is denoted as f
U,k
[n]. Hence, the completed
computation bits and the energy consumption of the UAV for
computing UE k’s task at slot n can be, respectively, given by
L
U,k
[n] = δf
U,k
[n]/C
k
, k ∈ K, n ∈ N , (7)
E
U,k
[n] = δκ
U
f
3
U,k
[n], k ∈ K, n ∈ N , (8)
where κ
U
is the effective capacitance coefficient of the UAV.
Note that computing L
U,k
[n] bits of UE k’s task-input data
will produce O
k
L
U,k
[n] bits of task-output data, which should
be downloaded from the UAV to the UE k later.
3) Task Offloaded to the AP for Computing: Part of the
UEs’ offloaded task-input data at the UAV will be offloaded to
the AP’s processing server for computing. To better distinguish
the offloading signals from different UEs, the TDMA protocol
with K equal time divisions (δ = T /(NK)) is also adopted in
this case. Let l
off
U,k
[n] denote the number of UE k’s task-input
bits being offloaded from the UAV to the AP at time slot n.
Thus, the corresponding energy consumption of the UAV for
offloading UE k’s task at slot n can be calculated as
E
off
U,k
[n] = δp
off
U,k
[n]
3
All the energy consumption in this paper uses the unit of Joule.
4
Without loss of generality, we assume that the noise power at any node
in the system is considered the same as N
0
.
≡
δN
0
h
AP
[n]
2
l
off
U,k
[n]
δB
off
U,k
[n]
− 1
, k ∈ K, n ∈ N , (9)
where p
off
U,k
[n] and B
off
U,k
[n] are respectively the transmit power
and the allocated bandwidth of the UAV for offloading UE
k’s task to the AP at time slot n. After computing the l
off
U,k
[n]
input bits at the AP, O
k
l
off
U,k
[n] bits of computation results
for UE k will be generated. As the AP is integrated with an
ultra-high-performance processing server, the computing time
is negligible. The AP will send the computation results back
to the UAV in the TDMA manner using a separate bandwidth.
Since the AP is supplied with grid power and can support
ultra-high transmission rate, the download transmission time
from the AP to the UAV is also assumed negligible.
5
For the later two offloading methods, the generated com-
putation results at the UAV (including the results from UAV’s
computing and received from the AP) will then be downloaded
back to the corresponding UEs. It is assumed that the UAV
is equipped with a data buffer with sufficiently large size,
and it is capable of storing each UE’s offloaded data and
the corresponding computation results separately. Besides, we
assume that the UAV operates in a frequency-division-duplex
(FDD) mode in each UE’s operation duration δ with separate
bandwidths allocated for task reception from UEs ({B
off
k
[n]}),
task offloading transmission to the AP ({B
off
U,k
[n]}), and task
results downloading transmission to the UEs ({B
down
U,k
[n]}),
with a total bandwidth B satisfying the constraint
B
off
k
[n] + B
off
U,k
[n] + B
down
U,k
[n] = B, k ∈ K, n ∈ N . (10)
The UEs’ computation results are subsequently transmitted
by the UAV using TDMA similar to the UEs’ offloading
process, each with an equal duration δ in each time slot. Let
l
down
U,k
[n] denote the bits of task-output data being downloaded
from the UAV to UE k at time slot n. Hence, the corresponding
energy consumption of the UAV can be calculated as
E
down
U,k
[n] = δp
down
U,k
[n]
≡
δN
0
h
k
[n]
2
l
down
U,k
[n]
δB
down
U,k
[n]
− 1
, k ∈ K, n ∈ N , (11)
where p
down
U,k
[n] is the transmit power of the UAV for down-
loading UE k’s task-output data at time slot n.
Note that at each time slot n, the UAV can only compute
or forward the task-input data that has already been received
from the UEs. By assuming that the processing delay, e.g., the
delay for decoding and computing preparation, at the UAV is
one time slot, then we have the following information-causality
constraint:
n
i=2
δf
U,k
[i]
C
k
+ l
off
U,k
[i]
≤
n−1
i=1
l
k
[i], (12)
5
Once the AP receives the forwarded l
off
U,k
[n] bits input data from the UAV
in the k-th duration of the n-th time slot, it will immediately decode, compute
the data, and then send the induced O
k
l
off
U,k
[n] bits of output data back to the
UAV, all with ultra-low latency that is negligible compared with the length of
each duration δ, which means that the UAV can receive the task-output data
from the AP in the same duration of its offloading process.
for n ∈ N
2
and k ∈ K where N
2
= {2, . . . , N −1}. Similarly,
at each time slot n, the UAV can only transmit the task-output
data corresponding to the task-input data that has already been
computed at the UAV or offloaded for computing at the AP.
Thus, we have another information-causality constraint:
n
i=3
l
down
U,k
[i] ≤ O
k
n−1
i=2
δf
U,k
[i]
C
k
+ l
off
U,k
[i]
, (13)
for n ∈ N
3
and k ∈ K where N
3
= {3, . . . , N}. It is clear
that the UEs should not offload at the last two slots, while the
UAV should not compute or forward the received input data of
UEs’ at the first and the last slots as well as not transmit the
output data to the UEs in the first two slots. Hence, we have
l
k
[N − 1] = l
k
[N] = 0, f
U,k
[1] = f
U,k
[N] = 0, l
off
U,k
[1] =
l
off
U,k
[N] = 0, and l
down
U,k
[1] = l
down
U,k
[2] = 0.
C. Problem Formulation
Considering the fact that the traditional battery-based UEs
and UAVs are usually power-limited, one major problem the
UAV-assisted MEC system faces will be energy. Hence, in this
paper, we try to minimize the WSEC of the UAV as well as
all the UEs during the whole task completion time T . In the
previous subsection, we have obtained the energy consumption
of the UEs and the UAV for task offloading/downloading
and computation. In fact, the energy consumption for UAV’s
propulsion is also considerable which is greatly affected by
the UAV’s trajectory, and hence should be taken into account.
With the assumption that the time slot duration τ is sufficiently
small, the UAV’s flying during each slot can be regarded as
straight-and-level flight with constant speed v[n]. Taking a
fixed-wing UAV as an example [16, 26], its propulsion energy
consumption at time slot n can be expressed as
E
fly
U
[n] = τ
θ
1
v
3
[n] +
θ
2
v[n]
, n ∈ N , (14)
where θ
1
and θ
2
are two parameters related to the UAV’s
weight, wing area, wing span efficiency, and air density, etc.
Combining with the above analysis, we obtain the total energy
consumption of UE k and the UAV in each time slot n as
E
k
[n] = E
local
k
[n] + E
off
k
[n], k ∈ K, n ∈ N , (15)
E
U
[n] =
K
k=1
E
U,k
[n] + E
off
U,k
[n] +
E
down
U,k
[n]
+ E
fly
U
[n], n ∈ N . (16)
In our considered scenario, the UEs’ CPU computing fre-
quencies {f
k
[n]}, their offloading task-input bits {l
k
[n]} and
the corresponding allocated bandwidth {B
off
k
[n]}; the UAV’s
CPU computing frequencies {f
U,k
[n]}, its forwarding (further
offloading) task-input bits {l
off
U,k
[n]} and downloading task-
output bits {l
down
U,k
[n]} as well as the corresponding allocated
bandwidths {B
off
U,k
[n]}, {B
down
U,k
[n]} for different UEs; along
with the UAV’s trajectory {u[n]} will be optimized to mini-
mize the WSEC. To this end, the WSEC minimization problem
can be formulated as problem (P1) given below
min
z,B,u
N
n=1
w
U
E
U
[n] +
K
k=1
w
k
E
k
[n]
(17a)
s.t.
n
i=2
δf
U,k
[i]
C
k
+ l
off
U,k
[i]
≤
n−1
i=1
l
k
[i], ∀n ∈ N
2
, ∀k ∈ K, (17b)
n
i=3
l
down
U,k
[i] ≤ O
k
n−1
i=2
δf
U,k
[i]
C
k
+ l
off
U,k
[i]
, ∀n ∈ N
3
, ∀k ∈ K,(17c)
N−1
n=2
δf
U,k
[n]
C
k
+ l
off
U,k
[n]
=
N−2
n=1
l
k
[n], ∀k ∈ K, (17d)
N
n=3
l
down
U,k
[n] = O
k
N−1
n=2
δf
U,k
[n]
C
k
+ l
off
U,k
[n]
, ∀k ∈ K, (17e)
N
n=1
τ
C
k
f
k
[n] +
N−2
n=1
l
k
[n] = I
k
, ∀k ∈ K, (17f)
B
off
k
[n] + B
off
U,k
[n] + B
down
U,k
[n] = B, ∀n ∈ N , ∀k ∈ K, (17g)
f
k
[n] ≥ 0, ∀n ∈ N , ∀k ∈ K, (17h)
l
k
[N − 1] = l
k
[N] = 0, l
k
[n] ≥ 0, ∀n ∈ N
1
, ∀k ∈ K, (17i)
f
U,k
[1] = f
U,k
[N] = 0, f
U,k
[n] ≥ 0, ∀n ∈ N
2
, ∀k ∈ K, (17j)
l
off
U,k
[1] = l
off
U,k
[N] = 0, l
off
U,k
[n] ≥ 0, ∀n ∈ N
2
, ∀k ∈ K, (17k)
l
down
U,k
[1] = l
down
U,k
[2] = 0, l
down
U,k
[n] ≥ 0, ∀n ∈ N
3
, ∀k ∈ K, (17l)
B
off
k
[N − 1] = B
off
k
[N] = 0, B
off
k
[n] ≥ 0, ∀n ∈ N
1
, ∀k ∈ K,(17m)
B
off
U,k
[1] = B
off
U,k
[N] = 0, B
off
U,k
[n] ≥ 0, ∀n ∈ N
2
, ∀k ∈ K, (17n)
B
down
U,k
[1] = B
down
U,k
[2] = 0, B
down
U,k
[n] ≥ 0, ∀n ∈ N
3
, ∀k ∈ K, (17o)
u[0] = u
I
, u[N] = u
F
, (17p)
∥u[n] − u[n − 1]∥ ≤ V
max
τ, ∀n ∈ N , (17q)
where z , {z
k
[n]}
k∈K,n∈N
and B , {B
k
[n]}
k∈K,n∈N
with z
k
[n] , {f
k
[n], l
k
[n], f
U,k
[n], l
off
U,k
[n], l
down
U,k
[n]} and
B
k
[n] , {B
off
k
[n], B
off
U,k
[n], B
down
U,k
[n]}, respectively, denote
the sets of the computational resource scheduling variables
and the bandwidth allocation variables for UE k in time slot
n, u , {u[n]}
n∈N
denotes the set of the UAV’s horizontal
locations for all the slots, i.e., the trajectory of the UAV, and
N
1
= {1, . . . , N − 2}. In (P1), (17a) is the objective function
for minimizing the WSEC where w
U
and {w
k
}
k∈K
represent
the weights of the UAV and UEs, respectively, which trade-offs
between the UAV and UEs, and the priority/fairness among the
UEs. Also, (17b) and (17c) are the two information-causality
constraints, while (17d)–(17f) are the UEs’ computation task
constraints to make sure that all the UEs’ computation task-
input data has been computed and the task-output data has
been received. The bandwidth constraints are in (17g), while
(17h)–(17o) ensure the non-negativeness of the optimization
variables. (17p) and (17q) specify the UAV’s initial and final
horizontal locations, and its maximum speed constraints.
III. ALGORITHM DESIGN
The problem (P1) is a complicated non-convex optimization
problem because of the non-convex objective function where
non-linear couplings exist among the variables l
k
[n] and
B
off
k
[n], l
off
U,k
[n] and B
off
U,k
[n], l
down
U,k
[n] and B
down
U,k
[n] for k ∈
K, n ∈ N , and these variables are also strongly coupled with
the trajectory of the UAV, i.e., u[n]. To address these issues,
we propose a three-step alternating optimization algorithm to
