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Citation: Mei, C.; Gao, C.; Wang, H.;
Xing, Y.; Ju, N.; Hu, B. Joint Task
Offloading and Resource Allocation
for Space–Air–Ground Collaborative
Network. Drones 2023,7, 482.
https://doi.org/10.3390/
drones7070482
Academic Editors: Peiying Zhang,
Sheng Wu, Zakarya Muhammad
and Guanjun Xu
Received: 13 June 2023
Revised: 17 July 2023
Accepted: 17 July 2023
Published: 21 July 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
drones
Article
Joint Task Offloading and Resource Allocation for
Space–Air–Ground Collaborative Network
Chengli Mei 1, Cheng Gao 2, Heng Wang 1, Yanxia Xing 1, Ningyao Ju 2and Bo Hu 2, *
1Chinatelecom Research Institute, Beijing 102209, China; meichl@chinatelecom.cn (C.M.);
wangh26@chinatelecom.cn (H.W.); xingyx@chinatelecom.cn (Y.X.)
2State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and
Telecommunications, Beijing 100876, China; gaoch@bupt.edu.cn (C.G.); juningyao@bupt.edu.cn (N.J.)
*Correspondence: hubo@bupt.edu.cn
Abstract:
The space–air–ground collaborative network can provide computing service for ground
users in remote areas by deploying edge servers on satellites and high-altitude platform (HAP)
drones. However, with the growing number of ground devices required to be severed, it becomes
imperative to address the issue of spectrum demand for the HAP drone to meet the access of a large
number of users. In addition, the long propagation distance between devices and the HAP drone, and
between the HAP drone and LEO satellites, will lead to high data transmission energy consumption.
Motivated by these factors, we introduce a space–air–ground collaborative network that employs
the non-orthogonal multiple access (NOMA) technique, enabling all ground devices to access the
HAP drone. Therefore, all devices can share the same communication spectrum. Furthermore, the
HAP drone can process part of the ground devices’ tasks locally, and offload the rest to satellites
within the visible range for processing. Based on this system, we formulate a weighted energy
consumption minimization problem considering power control, computing frequency allocation,
and task-offloading decision. The problem is solved by the proposed low-complexity iterative
algorithm. Specifically, the original problem is decomposed into interconnected coupled subproblems
using the block coordinate descent (BCD) method. The first subproblem is to optimize power
control and computing frequency allocation, which is solved by a convex algorithm after a series of
transformations. The second subproblem is to make an optimal task-offloading strategy, and we solve
it using the concave–convex procedure (CCP)-based algorithm after penalty-based transformation
on binary variables. Simulation results verify the convergence and performance of the proposed
iterative algorithm compared with the two benchmark algorithms.
Keywords:
space–ground–air collaborative network; mobile edge computing; drone communication;
non-orthogonal multiple access (NOMA); task offloading and resource allocation
1. Introduction
With the rapid development of emerging applications such as Internet of Things
(IOT) and Augmented Reality (AR)/Virtual Reality (VR), the fifth generation (5G) and
future wireless networks need to meet the connectivity needs of massive mobile
devices [1]
,
while ensuring low latency [
2
] and low energy consumption [
3
]. In recent years, significant
advancements have been made in low-earth orbit (LEO) satellite communication, with
the successful commercialization of satellite constellations such as Starlink and OneWeb.
Therefore, satellite communication is considered a crucial component of future networks.
By carrying edge servers, LEO satellites can provide offloading services for ground devices
(GDs) [
4
–
6
]. Although LEO satellites can directly provide services for ground devices,
severe path loss causes ground devices to consume a lot of energy to upload data to LEO
satellites, and satellite communication has a high communication delay. These have brought
many new challenges to meeting the GDs’ Quality of Service (QoS) requirements.
Drones 2023,7, 482. https://doi.org/10.3390/drones7070482 https://www.mdpi.com/journal/drones
Drones 2023,7, 482 2 of 19
Recently, the high-altitude platform (HAP) drone has attracted the attention of many
companies and researchers. Flying or hovering at an altitude of 20–50 km [
7
], the HAP
drone is an unmanned aerial vehicle (UAV) in which a base station is deployed. HAP
drones are mainly divided into solar stratospheric UAVs and floating air balloons. At
present, companies such as Softbank, DLR, and Facebook are conducting in-depth research
on HAP drones. The HAP drone can provide communication services by establishing
line-of-sight (LoS) links with GD [
8
]. Furthermore, due to the payload of the HAP drone
exceeding 100 kg [
9
,
10
], the HAP drone can also be equipped as an edge server to provide a
task-offloading service for GDs. Compared with LEO satellite constellations such as Iridium
and Starlink [
11
], the communication link between HAP drones and ground devices is more
stable, and a ground device needs to consume less energy to transmit the same amount
of data. Hence, space–air–ground collaborative networks are considered a promising
approach to meeting the access and task-processing needs of massive ground devices.
However, when orthogonal multiple access (OMA) techniques such as frequency-
division multiple access (FDMA) are used as the means of communication between the
HAP drone and GDs, due to the large number of connected devices, the bandwidth
available to each device is very limited [
12
]. Therefore, the non-orthogonal multiple access
(NOMA) technique can be used for communication between the HAP drone and ground
devices, and at this time, all devices can communicate with the HAP drone through the
same spectrum [
13
]. The process of task offloading from ground devices to the HAP
drone is the process of data uplink transmission. Using the NOMA technique in this
process, all devices transmit data on the same spectrum, and the receiver (i.e., HAP drone)
applies an advanced multi-user detection (MUD) technique such as successive interference
cancellation (SIC) to extract data from different users based on their respective channel
conditions [14].
Based on the above discussion, we propose a space–air–ground collaborative network
to make the HAP drone and LEO satellites cooperate for mobile edge computing. Further,
we formulate a weighted energy consumption minimization problem considering power
control, computing frequency allocation, and task-offloading decision. The main challenges
we face can be summarized as follows:
•
How to properly control the transmission power of ground devices and the HAP
drone? In this system, distinct communication methods are employed for the interac-
tions between devices and the HAP drone, as well as between the HAP drone and LEO
satellites. Consequently, it is imperative to develop specific power control strategies
tailored to each transmission method.
•
How to reasonably allocate the computing resources of each edge server? In this
system, the HAP drone can directly obtain the computing capability of edge nodes
(deployed on LEO satellites) and the computing requirements of GDs. Based on this
information, HAP drones need to allocate a reasonable size of computing resources
for each task.
•
How to make a task-offloading decision? Considering a partial offloading model, each
task can be split into two parts: the first part of it is processed at the HAP drone and
the rest of it is offloaded to LEO satellite for processing. Therefore, the task-splitting
strategy needs to be appropriately made. In addition, there are multiple LEO satellites
in the field view of the HAP drone, and it is necessary to determine the target LEO
satellite for each task offloading.
In this paper, we propose a space–air–ground collaborative network. Specifically,
considering the difference in the number of access devices, the communication between the
ground device and the HAP drone and the communication between the HAP drone and the
LEO satellite adopt the NOMA technique and FDMA technique, respectively. Subsequently,
the HAP drone can process all or part of the tasks locally, or offload device tasks to LEO
satellites within its visible range. The main contributions of this paper are summarized
as follows.
Drones 2023,7, 482 3 of 19
(1)
Considering the limited energy and resources of nodes in the system, we formulate
an optimization problem of joint task offloading and resource allocation, aiming to
minimize the weighted total energy consumption of the system. This problem is a
mixed-integer non-linear programming (MINLP) problem.
(2)
We propose a low-complexity iterative algorithm based on a block coordinate descent
(BCD) method to solve this MINLP problem, which reduces the complexity of the orig-
inal problem by converting the original problem into two subproblems for the iterative
solution. For the first subproblem, we transform the problem into a convex optimiza-
tion problem and solve it with the convex algorithm. For the second subproblem, we
convert this to a continuous variable problem by using a penalty-based transformation,
and then we solve it by a concave–convex procedure (CCP)-based algorithm.
(3)
The simulation experiments have verified the convergence of the proposed algorithm
in this paper. Furthermore, compared to the other two benchmark algorithms, the
algorithm proposed in this paper consistently achieves a smaller overall system-
weighted energy consumption under the same conditions.
The rest of this paper is structured as follows. The related works are discussed
in Section 2. The system model is introduced in Section 3, including communication
models, task offloading, and computation models. In Section 4, we formulate an energy
minimization problem. Section 5presents a proposed low-complexity iterative algorithm.
The convergence and performance of the proposed algorithm are proven in Section 6.
Finally, conclusions are given in Section 7.
2. Related Works
The related works of this paper include space–air–ground collaborative edge com-
puting and NOMA-assisted edge computing. In the following, we introduce their specific
research progress.
2.1. Space–Air–Ground Collaborative Edge Computing
Recently, several space–air–ground collaborative edge computings were intro-
duced [9,15–19].
Nan Cheng et al. [
15
] presented a space–air–ground integrated network (SAGIN)
edge/cloud computing architecture for offloading the computation-intensive applications
considering remote energy and computation constraints, where flying UAVs provide near-
user edge computing and satellites provide access to the cloud computing. In [
16
], the
authors proposed a framework of edge computing-enabled SAGINs to support various
Internet of Vehicles (EC-IoV) services for vehicles in remote areas whose main objective
of the framework is to minimize the task completion time and satellite resource usage. A
deep learning-driven offloading and caching algorithm is proposed to achieve real-time
decision-making. In [
17
], Bomin Mao et al. considered the UAVs and satellites to offer
wireless-powered IoT device edge computing and cloud computing services, respectively,
and focus on the computation offloading problem and consider deep learning techniques
to optimize the task success rate considering the energy dynamics and channel conditions.
A deep learning-based optimization strategy for offloading policies is proposed, employing
a long short-term memory (LSTM) model to effectively address the dynamic characteristics
of energy harvesting performance.
The authors in [
9
] conducted a study on a satellite–air-integrated edge computing net-
work to provide edge computing services for ground user (GUE) equipment by combining
LEO satellites and HAPs. The authors minimized the weighted total energy consumption
of GUEs, HAPs, and satellites in the network, including communication and calculation
energy consumption, through joint GUE association, multi-user multi-input multi-output
transmission precoding, calculation task allocation, and resource allocation. Ahmad Al-
sharoa and Mohamed-Slim Alouini [
18
] studied the goal of optimizing resource allocation
and the location of HAP under the framework of the integration of ground base stations,
high-altitude platforms, and satellite stations, and realized the improvement of the user
Drones 2023,7, 482 4 of 19
throughput. The authors divided the scene into two stages: the short-term stage and
long-term stage to formulate and solve the optimization problem. In the short-term stage,
user association and resource allocation are considered, and in the long-term stage, the
location optimization problem of HAP is considered. Long Zhang et al. [
19
] proposed
a satellite-to-air integrated computing (SAIC) architecture in a disaster environment, in
which the computing tasks from two layers of users (i.e., ground/air user equipment) were
either executed locally on HAPs or offloaded to LEO satellites for computing. Under SAIC
architecture, the problem of joint two-layer user association and unloading decisions with
the goal of maximizing the total rate is studied.
2.2. NOMA-Assisted Edge Computing
The authors in [
20
] integrated cloud-edge computing and NOMA to propose a net-
work communication model, which can provide users with energy-efficient and low-latency
services. The model considers the energy consumption, transmission delay, and quality of
service; the authors jointly optimized the offloading decision and its radio resource alloca-
tions for NOMA transmission to reduce the system cost (the weighted sum of consumed
energy and delay). Zhiguo Ding et al. [
21
] proposed a hybrid NOMA-MEC scheme, in
which a user first offloads parts of its task by using a time slot allocated to another user and
then offloads the remainder of its task during a time slot solely occupied by itself, where
the power and time allocation is jointly optimized to reduce the energy consumption of
computation offloading. In [
22
], the authors investigated the edge user allocation problem
in the NOMA-based MEC system. The authors introduced a decentralized game-theoretic
approach to allocating maximum users to edge servers in a specific area at the lowest
computing resource and transmit power costs. The authors in [
23
] proposed a novel coop-
erative MEC that exploits the combination of NOMA and multiple helpers. In the proposed
system featuring a user, multiple helpers, and a base station, the user can simultaneously
offload its computation-intensive tasks to the helpers using NOMA when there is no strong
direct transmission link between the user and the BS. Then, the helpers can compute and
offload these tasks through NOMA. Ming Zeng et al. [
24
] aimed to minimize the overall
delay for offloading in a multi-user NOMA-MEC network under maximum power con-
straint and maximum energy constraint for offloading users, and they proposed a NOMA
scheme that can achieve substantial delay reduction compared with time division multiple
access (TDMA). In [
25
], a NOMA-based vehicle edge computing (VEC) network model
is proposed, and the cost minimization problem is constructed. Under the premise of
ensuring the delay tolerance of all vehicle users (VUEs), the total system cost is minimized
through the joint optimization of offloading decision-making, VUE clustering, subchannel
and computation resource allocation, and transmission power control. The authors in [
26
]
proposed a general hybrid NOMA-MEC offloading strategy, which includes conventional
orthogonal multiple access (OMA) and pure NOMA-based offloading as special cases. A
multi-objective optimization problem is formulated to minimize the energy consumption
for MEC offloading.
3. System Model
In the space–air–ground collaborative network, there are multiple LEO satellites
equipped with mobile edge computing servers within the visual range of the HAP drone,
which can be denoted as
M={
1, 2,
. . .
,
M}
. All satellites can provide edge computing
services for ground devices (GDs). The computation capacity of LEO satellite
m
is
Fm
; this
means that the maximum number of CPU cycles per second for satellite
m
is
Fm
. In this
scenario, the HAP drone is also equipped with an edge computing server. The computation
capacity of the HAP drone is
Fh
. On the ground, there are
N
GDs, which can be denoted as
N={
1, 2,
. . .
,
N}
. For GD
n
, its task can be denoted as
{Dn
,
cn
,
Tn}
, where
Dn
is the input
data size of task
n
,
cn
represents the number of CPU cycles required to process 1bit task
n
,
and
Tn
represents the maximum delay to process the task
n
. The computation capacity of
GD ncan be denoted as Fn.
Drones 2023,7, 482 5 of 19
3.1. NOMA-Based Communication Model
3.1.1. GD-HAP Drone Uplink Communication Model
All GDs transmit data to the HAP drone based on the NOMA technique. The received
signal of the HAP drone from GD ncan be denoted as
yn=hh,n√pnsn
| {z }
desired sign al
+∑i∈N\{n}hh,i√pisi
| {z }
intra−inte r f erence
+ˆ
nn
|{z}
noise
(1)
where
hh,n
,
hh,i
are channel gains between the HAP drone and GD
n
, and between the HAP
drone and GD
i
.
pn
,
pi
are transmission power of GD
n
and GD
i
.
ˆ
nn
is the additional white
Gaussian noise (AWGN), which is considered to satisfy the distribution of ˆ
n∼CN(0, σ2).
The signal-to-interference-plus-noise-ratio (SINR) at HAP drone from GD nis
γn=
hh,n
2pn
∑i∈N\{n}
hh,i
2pi+σ2(2)
Then, we can get the data rate between HAP and GD n
Rn=Bhlog2(1+γn)(3)
where Bhis the bandwidth for each GD.
3.1.2. Consideration of SIC Decoding
In the stage of device upload data, all GDs transmit their tasks to the HAP drone
simultaneously based on the NOMA technique. All GDs are sorted by channel gains
hh,1
≥
hh,2
≥. . . ≥
hh,N
(4)
Then, the HAP drone utilizes the SIC technique to decode data from GDs. According to
the principles of SIC, the HAP drone first decodes the information from the GD with larger
channel gain, and then removes it from the interference terms of other GDs. Therefore, the
offloading rate of i-th GD can be expressed as [27]
Ri,h=Bhlog2(1+
hh,i
2pi
∑N
j=i+1
hh,j
2pj+σ2
)(5)
3.2. FDMA-Based Communication Model
The communication between the HAP drone and LEO satellites adopts the Frequency
Division Multiple Access (FDMA) technique; the data rate between the HAP drone and
LEO satellite mcan be denoted as
Rh,m=Bslog2(1+
hh,m
2ph,m
σ2)(6)
where
hh,m
is the channel gain between the HAP drone and LEO satellite
m
.
Bs
is the
allocated bandwidth for each LEO satellite. Assuming that the total available bandwidth is
Btotal, the bandwidth allocated to each LEO is Bs=Btotal
M.
Based on 3GPP specifications, the free space path loss (FSPL) in dB between GD and
HAP drone, and between HAP drone and LEO satellite can be expressed as [28].
FSPL(dh,i,f c) = 32.45 +20 log10(fc) + 20 log10(dh,i)(7)
where
dh,i=p(xh−xi)2+ (yh−yi)2+ (hh−hi)2
is the distance between the HAP drone
and LEO satellite, or between the HAP drone and GD.
{xh
,
yh
,
hh}
is the coordinate of the
Drones 2023,7, 482 6 of 19
HAP drone.
{xi
,
yi
,
hi}
is the coordinate of the LEO satellite or GD
i
(
i∈ M∪ N
).
fc
is the
carrier frequency in GHz of the transmitted signal. Therefore, the channel gain between
HAP and LEO or GD i∈ {M ∪ N} can be formulated as
hh,i
2=10−FSP L(dh,i,f c)
10 (8)
3.3. Task Offloading and Computation Model
3.3.1. GD-HAP Drone Task Offloading Model
In this system, all GDs offload their tasks to the HAP drone. For GD
n
, its task
transmission time from GD nto the HAP drone can be formulated as
ttrans
n=Dn
Rn,h
(9)
And the energy consumption of GD
n
to offload its task to HAP drone can be ex-
pressed as
Etrans
n=pn×ttrans
n=pnDn
Rn,h
(10)
3.3.2. HAP Drone Transmission and Computation Model
In this paper, we adopt a partial offloading protocol [
9
]. For GD
n
, the HAP and the
LEO satellite process different portions of its computation task. When the HAP drone
receives the task of GD, it can execute part of it on the local server. At the same time,
the HAP drone offloads the rest of the task to the LEO satellite, which is executed by the
LEO satellite server. GD
n
’s task can be divided into two parts:
δn(
0
≤δn≤Dn)
bits
are executed at the HAP drone’s MEC server, and
Dn−δn
bits are offloaded to the LEO
satellite for processing. Therefore, the time delay for executing GD
n
’s task at HAP can be
formulated as
tn,h=cnδn
fn,h
(11)
And the energy consumption for executing GD n’s task at HAP can be expressed as
En,h=κh(fn,h)2cnδn(12)
where
fn,h
is the computation resource allocated to GD
n
’s task by the HAP drone.
κh
is a
constant relative to the hardware architecture of the HAP drone.
When the HAP drone offloads the rest of the GD
n
’s task to the LEO satellite
m
, the
transmission delay of task offloading can be denoted as
tn,h,m=αn,mDn−δn
Rh,m
+Th,m(13)
where
αn,m∈ {
0, 1
}
,
∀n∈ N
,
m∈ M
is the offloading indicator of GD
n
by the HAP drone.
αn,m=
1 indicates that the HAP drone offloads GD
n
’s task to the LEO satellite
m
, and
αn,m=
0, otherwise.
Th,m
is the round-trip propagation delay between the HAP drone and
LEO satellite m, which can be formulated as
Th,m=2p(xh−xm)2+ (yh−ym)2+ (hh−hm)2
c(14)
where
c
is the speed of light. The energy consumption of task offloading can be expressed as
En,h,m=phm∗tn,h,m=ph,m(αn,mDn−δn
Rh,m
+Th,m)(15)
Drones 2023,7, 482 7 of 19
3.3.3. LEO Satellite Computation Model
In this paper, the LEO cannot offload the GD’s task to another LEO satellite. If the HAP
drone offloads GD
n
’s task to LEO satellite
m
, the computation delay of task
n
executed on
LEO mcan be denoted as
tn,m=αn,mcn(Dn−δn)
fn,m(16)
where
fn,m
is the computation resource allocated to GD
n
’s task by LEO satellite
m
. Further-
more, the energy consumption of task computation on LEO satellite
m
can be formulated as
En,m=αn,mκm(fn,m)2cn(Dn−δn)(17)
where κmis a constant relative to the hardware architecture of LEO satellite m.
3.4. Overall Delay and Energy Consumption
The processing delay of GD
n
’s task can be divided into two parts. The first part is the
time delay processed by the HAP drone, and the second part is the time delay processed by
the LEO satellite, which can be expressed as
Tall
n,h=Dn
Rn,h
+cnδn
fn,h
(18)
and
Tall
n,m,s=ttrans
n+tn,h,m+tn,m
=Dn
Rn,h
+αn,mDn−δn
Rh,m
+Th,m+αn,mcn(Dn−δn)
fn,m(19)
The weighted energy consumption of the system can be formulated as
Esys =ωgEtrans +ωhEh+ωsEs
=ωg
N
∑
n=1
(pnDn
Rn,h
) + ωh
N
∑
n=1
κh(fn,h)2cnδn
+ωh
N
∑
n=1
M
∑
m=1
(ph,mαn,m(Dn−δn
Rh,m
+Th,m))
+ωs
N
∑
n=1
M
∑
m=1
(αn,mκm(fn,m)2cn(Dn−δn))
(20)
4. Strategy Design and Problem Formulation
In this section, we first present the process of resource allocation and task offload-
ing. Then, we formulate the optimization problem of joint task offloading and resource
allocation to minimize the weight energy consumption of the system.
4.1. Strategy Design
This paper studies the space–air–ground collaborative network shown in Figure 1,
where the HAP drone directly connects with LEO satellites and ground devices through
Ka-band and C-band, respectively. The HAP drone serves as the control node in this system,
responsible for collecting information from all nodes in the system (user task information,
satellite computing resource information, etc.), and making and distributing task offloading
and resource allocation strategy. The implementation process of task offloading and
resource allocation strategy design can be divided into four steps:
Drones 2023,7, 482 8 of 19
•
Information collection: in this step, the HAP drone collects information from LEO
satellites
M
within its visual range, and information from GDs
N
connected to the
HAP drone (including computational resources, channel information, etc.).
•
Task-offloading request: In this step, the GDs connected to the HAP drone send a
task-offloading request to the HAP drone, which includes specific information about
the task, such as the data size, required CPU cycles per bit of data processing, and the
maximum processing tolerance delay.
•
Strategy-making and distribution: After the HAP drone collects information from
each node and receives task-offloading requests from the GDs, the HAP drone makes
an appropriate strategy for resource allocation and task offloading based on this
information. The resource allocation and task-offloading strategy will be sent to the
respective GDs and LEO satellites via C-band and Ka-band.
•
Task processing: After receiving the resource allocation and task-offloading strategy
from the HAP drone, the GDs send the task to the HAP drone according to the strategy,
and then the HAP drone and LEO satellites process the tasks based on the resource
allocation and task-offloading strategy.
GD - HAP drone link HAP drone - LEO link
FDMA
NOMA
GD HAP drone LEO satellite Edge server
Figure 1. The scenario of the space–air–ground collaborative network.
4.2. Problem Formulation
In the previous section, we defined the system’s weighted energy consumption as the
weighted sum of the energy consumption of each node. In order to minimize the system’s
Drones 2023,7, 482 9 of 19
weighted energy consumption, a joint optimization problem of task offloading and resource
allocation is formulated as follows:
OP : min
P,F,α,δEsys (21a)
s.t. 0 ≤pn≤Pmax
n,∀n∈ N (21b)
0≤ph,m≤Pmax
h,∀m∈ M (21c)
0≤fn,h,fn,m,∀n∈ N,m∈ M (21d)
N
∑
n=1
fn,h≤Fh(21e)
N
∑
n=1
fn,m≤Fm,∀m∈ M (21f)
0≤δn≤Dn,∀n∈ N (21g)
Tall
n,h≤Tn,∀n∈ N (21h)
Tall
n,m,s≤Tn,∀n∈ N,m∈ M (21i)
αn,m∈ {0, 1},∀n∈ N,m∈ M (21j)
M
∑
m=1
αn,m=1, ∀n∈ N (21k)
where
P={pn|∀n∈ N} ∪{ph,m|∀m∈ M} ∈ Z1×(M+N)
is the set of all transmit powers,
F∈ZN×(M+1)
is the set of total computation resources for the HAP drone and all LEO
satellites,
α={αn,m|∀n∈ N
,
m∈ M} ∈ ZN×M
and
δ={δn|∀n∈ N} ∈ Z1×N
are
collections of target access LEO satellite selection and task-splitting decisions.
Constraints (21b) and (21c) indicate that the transmit power cannot exceed the maxi-
mum power. Constraint (21d) represents that the CPU frequency allocation variables are
non-negative. Constraints (21e) and (21f) are constraints of the total computation capacity
for the HAP drone and each LEO satellite. Constraint (21g) is the constraint of task-splitting
variables. Constraints (21h) and (21i) ensure that the processing delay of the task cannot
exceed the maximum tolerable delay. Constraints (21j) and (21k) restrict the variables
αn,m
to binary integer variables, and each task cannot be offloaded to multiple LEO satellites.
5. Algorithm Design for OP
OP
OP
In this section, we propose a joint task-offloading and resource allocation optimization
scheme to solve the problem
OP
. First, we decouple the
OP
to two subproblems based
on the BCD method, one for the optimization of all devices’ transmission power and
computation resources with fixed task-offloading decisions
{α
,
δ}
, which can be denoted as
P1: min
P,FEsys (22a)
s.t. (21b)–(21f), (21h), (21i) (22b)
Furthermore, task-offloading decisions are optimized based on fixed transmission and
computation allocation strategy, and this subproblem can be denoted as
P2: min
α,δEsys (23a)
s.t. (21g)–(21k) (23b)
By alternately solving these two subproblems, we can obtain an optimized resource
allocation and task-offloading strategy.
Drones 2023,7, 482 10 of 19
5.1. Algorithm Design for P1
P1
P1
Problem
P1
is non-convex and thus difficult to solve directly. To solve the problem
P1
, in this subsection, we convert this to convex form and solve it by convex algorithm.
Considering that the transmit power allocation problem of the HAP drone is non-convex,
we can denote
f1(Ph) = min
Ph
N
∑
n=1
M
∑
m=1
(ph,mαn,m(Dn−δn
Rh,m
+Th,m))
=min
Ph
M
∑
m=1
(
N
∑
n=1
αn,m(Dn−δn)) ph,m
Bslog2(1+ph,m
hh,m
2
σ2)
+
M
∑
m=1
(
N
∑
n=1
αn,m)Th,mph,m(24a)
s.t. (21d) (24b)
where
Ph={ph,m|m∈ M} ∈ Z1×M
, which is the set of transmit power from the HAP
drone to LEO satellites. We introduce new variables
τh={τh,m|m∈ M} ∈ Z1×M
, which
can be denoted as
τh,m=1
Rh,m
=1
Bslog2(1+ph,m
hh,m
2
σ2)
,∀m∈ M (25)
then, Phcan be expressed as
ph,m=σ2
hh,m
2(21
Bsτh,m−1),∀m∈ M (26)
We can rewrite f1(Ph)as
g1(τh) = min
τh
M
∑
m=1
(
N
∑
n=1
αn,m(Dn−δn)) σ2
hh,m
2(21
Bsτh,m−1)τh,m
+
M
∑
m=1
(
N
∑
n=1
αn,m)Th,m
σ2
hh,m
2(21
Bsτh,m−1)(27a)
s.t. 1
Bslog2(1+pmax
h
hh,m
2
σ2)≤τh,m∀m∈ M (27b)
This is a convex optimization problem, which is easy to solve. Further, considering
the transmit power allocation problem of all GDs is also non-convex. Let
Pn={pn|∀n∈
N} ∈ Z1×N
be the set of all ground devices’ transmit power, and we can denote the GD’s
transmit power allocation problem as
f2(Pn) = min
Pn
N
∑
n=1
pn
Dn
Bhlog2(1+|hh,n|2pn
∑N
j=n+1|hh,j|2pj+σ2)
(28a)
s.t. (21c) (28b)
Drones 2023,7, 482 11 of 19
We introduce new variables
{t1,n|∀n∈ N } ∈ Z1×N
, which represent the transmission
delay for GDs to transmit the task data to the HAP. Furthermore, we can transform the
f2(Pn)to
g2(Pn,{t1,n}) = min
Pn,{t1,n}
N
∑
n=1
pnt1,n(29a)
s.t. Dn
Bhlog2(1+|hh,n|2pn
∑N
j=n+1|hh,j|2pj+σ2)≤t1,n,∀n∈ N (29b)
(21c) (29c)
Note that the constraint (29b) is non-convex, which can be rewritten as
Dn≤t1,nBhlog2(1+
hh,n
2pn
∑N
j=n+1
hh,j
2pj+σ2
)
=t1,nBhlog2(∑N
j=n
hh,n
2pj+σ2)−t1,nBhlog2(∑N
j=n+1
hh,n
2pj+σ2)(30)
To solve non-convex constraint, we introduce new variables
t2,n≤Bhlog2(∑N
j=n
hh,n
2pj+
σ2)
and
t3,n≥Bhlog2(∑N
j=n+1
hh,n
2pj+σ2)
. Thus, constraint (30) can be rewritten as
Dn≤t1,nt2,n−t1,nt3,n
,
∀n∈ N
. It is obvious that this is also non-convex. We can transform
it into the Difference of Convex (DC) program
0≥Dn−t1,nt2,n+t1,nt3,n
=Dn+t2
1,n+t2
2,n
2−(t1,n+t2,n)2
2+(t1,n+t3,n)2
2−t2
1,n+t2
3,n
2(31)
Further, we transform the above formula into a convex optimization form using the
Taylor expansion around current point {t0
1,n,t0
2,n,t0
3,n|∀n∈ N }.
0≥Dn+t2
1,n+t2
2,n
2−(t0
1,n+t0
2,n)2
2−(t0
1,n+t0
2,n)(t1,n−t0
1,n+t2,n−t0
2,n)
+(t1,n+t3,n)2
2−(t0
1,n)2+ (t0
3,n)2
2−t0
1,n(t1,n−t0
1,n)−t0
3,n(t3,n−t0
3,n)
(32)
Now, this constraint is convex. Furthermore, the Esys can be rewritten as
ˆ
Esys =ωg
N
∑
n=1
pnt1,n+ωh
N
∑
n=1
κh(fn,h)2cnδn
+ωh
M
∑
m=1
(
N
∑
n=1
αn,m(Dn−δn)) σ2
hh,m
2(21
Bsτh,m−1)τh,m
+ωh
M
∑
m=1
(
N
∑
n=1
αn,m)Th,m
σ2
hh,m
2(21
Bsτh,m−1)
+ωs
N
∑
n=1
M
∑
m=1
(αn,mκm(fn,m)2cn(Dn−δn))
(33)
Drones 2023,7, 482 12 of 19
Through the above transformation of problem
P1
, we can rewrite
P1
as problem
P3
, and
solving problem P3 can realize the solution of problem P1.P3can be formulated as
P3: min
F,τh,t
ˆ
Esys (34a)
s.t. 1
Bslog2(1+pmax
h
hh,m
2
σ2)≤τh,m∀m∈ M (34b)
Bhlog2(∑N
j=n
hh,n
2pj+σ2)≥t2,n,∀n∈ N (34c)
Bhlog2(∑N
j=n+1
hh,n
2pj+σ2)≤t3,n,∀n∈ N (34d)
t1,n+cnδn
fn,h≤Tn,∀n∈ N (34e)
t1,n+αn,m(Dn−δn)τh,m+Th,m
+αn,mcn(Dn−δn)
fn,m≤Tn,∀n∈ N (34f)
(21b), (21d)−(21f), (32) (34g)
where
t={t1,n
,
t2,n
,
t3,n|n∈ N}
. This is a convex optimization problem, and we can solve
it by using existing convex solvers, e.g., CVX toolbox [29].
5.2. Algorithm Design for P2
P2
P2
With fixed {
P
,
F
}, the optimization objective
Esys
is only related to
Eh
and
Es
. This also
means that
Etrans
in the objective function does not need to be optimized in this problem,
so the P2can be rewritten as
P4: min
α,δ(ωhEh+ωsEs)(35a)
s.t. (21g)–(21k) (35b)
The constraint (21j) shows that
α
are 0–1 integer variables in
P4
, so this is an integer
programming problem. The objective function (35a) and constraint (21i) are non-convex.
This is an MINLP problem, which is difficult to solve. To solve this problem, we introduce
the auxiliary variables
`α={`
αn,m|∀n∈ N
,
m∈ M} ∈ ZN×M
; the constraint
(
21
j)
can be
transformed to [30]
αn,m∗(1−`
αn,m) = 0, ∀n∈ N,m∈ M (36)
and
αn,m=`
αn,m,∀n∈ N,m∈ M (37)
To simplify the solution to the
P4
, we can add the constraints (36) and (37) as penalties
to the objective function of P4, at which point P4can be rewritten as problem P5
P5: min
α,δ(ωhEh+ωsEs) + λ
N
∑
n=1
M
∑
m=1
(|(αn,m−`
αn,m)|2+|αn,m(1−`
αn,m)|2)(38a)
s.t. 0 ≤αn,m≤1, ∀n∈ N,m∈ M (38b)
(21g)–(21i), (21k) (38c)
Note that
P5
is still non-convex because (35a) and (21i) are non-convex. To simplify
the problem-solving process, we begin by transforming the problem into a Difference of
Convex (DC) program problem. Based on the CCP method, we can find a non-convex
feasible set near the current feasible point by the iterative convex approximation method
and then solve a new convex approximation in each iteration [
31
]. We convert the non-
Drones 2023,7, 482 13 of 19
convex problem into a convex optimization problem by performing Taylor expansion on
the current point, and (ωhEh+ωsEs) can be rewritten as
E0=ωh
N
∑
n=1
κh(fn,h)2cnδn
+ωh
N
∑
n=1
M
∑
m=1
ph,m(Dn
Rh,m
+Th,m)αn,m
+ωh
N
∑
n=1
M
∑
m=1
ph,m
Rh,m
(1
2(α2
n,m+δ2
n)−(α0
n,m+δ0
n)2
2
−((αn,m−α0
n,m)((α0
n,m+δ0
n)−((δn−δ0
n)((α0
n,m+δ0
n))
+ωs
N
∑
n=1
M
∑
m=1
κm(fn,m)2cnDnαn,m
−ωs
N
∑
n=1
M
∑
m=1
κm(fn,m)2cn(1
2(α2
n,m+δ2
n)−(α0
n,m+δ0
n)2
2
−((αn,m−α0
n,m)((α0
n,m+δ0
n)−((δn−δ0
n)((α0
n,m+δ0
n))
(39)
where
{α0
n,m|∀n∈ N
,
m∈ M}
and
{δ0
n|∀n∈ N}
denote the current feasible point. Fur-
thermore, (21i) can be rewritten as
(Dn
Rn,h
+cnDn
fn,m
)αn,m+ ( Dn
Rn,h
+cn
fn,m
)θn,m+Th,m+Dn
Rn,h≤Tn,∀n∈ N,m∈ M (40)
where
θn,m≥α2
n,m+δ2
n
2−(α0
n,m+δ0
n)2
2−((α0
n,m+δ0
n))(αn,m−α0
n,m+δn−δ0
n)
. So, the problem
P5can be transformed to
P6: min
α,δE=E0+λ
N
∑
n=1
M
∑
m=1
(|(αn,m−`
αn,m)|2+|αn,m(1−`
αn,m)|2)(41a)
s.t. (21g), (21h), (21k), (38b), (40) (41b)
This is a standard convex optimization problem that can be solved by the CVX tool-
box. Throughout each iteration, solving problem
P6
is equivalent to solving problem
P2
. However, it is crucial to note that the solution obtained for
P6
may not adhere to the
constraints set by
P2
, as
P2
specifically requires
α
to be integers. Therefore, it is imperative
to continuously iterate and solve
P6
until the
α
values converge to integers, signifying the
completion of the solution for problem
P2
. To solve this problem, we need to update the
variables
`α
in each iteration according to the association strategy
α0
of the previous round,
and the closed form of `αcan be expressed as [30]
`
αn,m=α0
n,m+ (α0
n,m)2
1+ (α0
n,m)2,∀n∈ N,m∈ M (42)
Based on the above discussion, we can summarize the iterative algorithm as
Algorithm 1
.
In each iteration, the first step is to obtain new power control and computing resource
allocation strategies based on the previous round’s resource allocation and task-offloading
strategies. Next, based on the new power control and computing resource allocation
strategies, as well as the previous round’s task-offloading strategy, a new task-offloading
strategy is obtained by solving
P6
. Then, the penalty coefficient
λ
, i.e.,
λ=µλ
, is updated.
Finally, the iteration stops when the weighted system energy consumption of the current
iteration and the previous iteration does not exceed the maximum tolerance value e.
Drones 2023,7, 482 14 of 19
Algorithm 1:
Joint Task-Offloading and Resource Allocation Algorithm for solv-
ing OP
1: Input
: maximum tolerance
e
, constant parameter
µ
, where
µ>
1, the maximum
number of iterations I termax , initial feasible point {P0,t0,α0,δ0}.
2: for i=1 to I termax do
3: Update the communication and computation resource allocation strategy
{Pi,ti,Fi}by solving P3based on {Pi−1,ti−1,αi−1,δi−1}.
4: Update variables `αiwith fixed variables αi−1based on (42)
5: Obtain optimal {αi,δi}by solving P6with given {Fi,ti,αi−1,δi−1,`αi}.
6: Update penalizing coefficient λby λ=µλ
7: if |Ei−Ei−1|
Ei−1≤e
8: break.
9: end if
10: end for
11: Output: The optimal policy {Pi,Fi,αi,δi}and optimal energy system Ei
5.3. Complexity Analysis
In each iteration of Algorithm 1, the computational complexity is determined by the
computational complexities of
P3
and
P6
. The number of optimization variables in prob-
lem
P3
is
I1=MN +M+
4
N
, and the number of constraints is
I2=MN +
2
M+
6
N+
1.
We solve
P3
using the interior point method; according to [
32
,
33
], the computational
complexity is
O((I2
1I2+I3
1)I0.5
2)
. The number of optimization variables in problem
P6
is
I3=MN +N
, and the number of constraints is
I4=
2
MN +
3
N
. Similarly, the computa-
tional complexity for
P6
is
O((I2
3I4+I3
3)I0.5
4)
. Therefore, the computational complexity of
the proposed algorithm can be expressed as O((I2
1I2+I3
1)I0.5
2(I2
3I4+I3
3)I0.5
4L).
6. Numerical Result
In this section, numerical simulation results are provided to demonstrate the perfor-
mance of the proposed algorithm. We consider a square area of 2000 m
×
2000 m; the
HAP drone is located in the center of this area with an altitude of 20 km [
34
]. In this
system, multiple LEO satellites are randomly distributed at an altitude of 200 km, and
GDs are randomly distributed on the ground in this area. We use the MATLAB R2020b
(version 9.9.0.1467703) to simulate, and the cvx toolbox used is also installed on MATLAB.
Simulation results are obtained on the PC with the Intel Core i5-10505 CPU, 16G RAM, and
a 64-bit operating system x64-based processor.
In the proposed system, the NOMA communication scheme is adopted between GDs
and the HAP drone, and the FDMA communication scheme is adopted between the HAP
drone and LEO satellites. The HAP drone communicates with GDs using 5 GHz bands on
the C-band and adopts 31 GHz bands on Ka-band to communicate with LEO satellites. The
communication bandwidth between the GD and HAP drones and between the HAP drone
and LEO satellites is 100 MHz [
9
]. AWGN spectral density is
−
174 dBm/Hz [
35
]. All GDs
have the same maximum transmission power of 23 dBm [
36
], and the maximum transmit
power of the HAP drone is 43 dBm [
37
]. To simplify the experiment, we assume that the
delay constraints of all tasks are the same, which are 3 s, and the CPU cycles to compute
one-bit tasks are also the same (unless otherwise specified, it is 1000 cycle/bit [
38
]). The
computing capacity of the HAP drone is
Fh=
10 GHz. We consider that the HAP drone
has a stronger computing capacity than a single LEO satellite, so we set the computing
capacity of each LEO satellite to be Fm=2 GHz. We set ωg=1, ωh=0.5, and ωs=0.2.
For comparison, the following task-offloading and resource allocation algorithms
are employed in the simulations: (i) Pure HAP: all tasks are executed at the HAP drone,
and computing and communication resource allocation is obtained by solving
P3
(that
is
{αn,m=
0,
∀n∈ N
,
m∈ M}
and
{δn=Dn
,
∀n∈ N}
). (ii) OMA: the communication
scheme between the GD and HAP drones is FDMA. Computing and communication
Drones 2023,7, 482 15 of 19
resource optimization are solved by the convex optimization algorithm, and the task-
offloading strategy is obtained by solving
P6
. (iii) Proposed: the optimization algorithm
proposed in this paper.
Figure 2verifies the convergence of the proposed algorithm in this paper. We plot
two curves for the number of ground devices 20 and 40. From Figure 2, we found that the
proposed iterative algorithm can quickly converge to a stable solution, and this verifies
the convergence properties of our proposed algorithm. So, the algorithm we proposed
is an effective algorithm with rapid convergence. The proposed algorithm is based on
a single time slot, during which the LEO satellite is assumed to be quasi-static. When
considering satellite movement, we can update resource allocation and task scheduling
strategies according to multi-dimensional resource information of different time slots.
2 4 6 8 10 12 14
Iteration
60
70
80
90
100
110
120
130
140
150
160
Energy consumption (J)
Proposed algorithm, N=40
Proposed algorithm, N=20
Figure 2. Convergence process of proposed algorithm under a different number of ground devices.
Figure 3shows the sum of weighted energy consumption against the data size of GDs’
tasks, in which the time constraints of all GDs are 3 s. The number of LEO satellites is
M=
3, and the number of GDs is
N=
40. From Figure 3, we can obtain that as the data
size of GDs’ tasks increases, the sum weighted energy consumption of the system tends to
increase for all schemes because the required energy consumption of the GDs offloading
tasks to the edge server of the HAP drone or LEO satellite is positively related to the data
size of all tasks. Compared with the two types of benchmark algorithms, the proposed
algorithm can ensure the minimum weighted energy consumption, which shows that this
algorithm can reduce the weighted energy consumption of the system by optimizing task
offloading and resource allocation.
100~200 300~400 500~600 700~800 900~1000
The data size of task at each ground device (Kb)
0
100
200
300
400
500
600
700
Energy consumption (J)
Pure HAP
OMA
Proposed
4
6
8
10
Figure 3. Weighted energy consumption of the system versus different task data size.
Drones 2023,7, 482 16 of 19
Figure 4demonstrates the energy consumption of the system for the three algorithms
versus the different number of ground devices. In this figure, we set the number of LEO
satellites
M=
3. The performance is compared at different data sizes of tasks, between
300 Kb and 400 Kb, and between 900 Kb and 1000 Kb. From the figure, we can get that the
larger the number of ground devices, the more energy consumption for ground devices to
offload their tasks. In this figure, we can also see that the proposed iterative algorithm has
much lower energy consumption compared to the two benchmark algorithms. Moreover,
the greater the amount of task data, the more the performance of the proposed algorithm
will be improved.
10 15 20 25 30 35
The number of ground devices
100
101
102
103
Energy consumption (J)
300-400Kb pure HAP
300~400Kb OMA
300~400Kb Proposed
900~1000Kb pure HAP
900~1000Kb OMA
900~1000Kb Proposed
22
24
26
200
400
600
Figure 4. Weighted energy consumption of the system versus different number of ground devices.
Figure 5shows the energy consumption for the three algorithms versus different max-
imum tolerance delay, where
T={
2, 2.5, 3, 3.5, 4, 4.5, 5
}
(s). We set the number of ground
devices as 20, and there are three LEO satellites. Based on the analysis of
Figure 5
, it is
evident that the energy consumption of all algorithms decreases as the maximum tolerance
delay increases. This is because with the increasing of the maximum tolerance delay, the
transmit power of GDs and HAP drone can be smaller, and the CPU resource allocated to all
tasks can also be smaller, which results in lower system energy consumption. By comparing
the energy consumption of the three algorithms, we can get that the proposed algorithm
can obtain smaller system energy consumption, and the smaller the tolerance delay of tasks,
the more obvious the ability of the proposed algorithm to reduce energy consumption.
2 2.5 3 3.5 4 4.5 5
Maximum task tolerance delay (sec)
0
50
100
150
200
250
300
350
400
450
500
Energy consumption (J)
Pure HAP
OMA
Proposed
Figure 5. Weighted energy consumption of the system versus different maximum tolerance delay.
Drones 2023,7, 482 17 of 19
Figure 6displays the weighted energy consumption versus different required CPU
numbers for one-bit task data. In this figure, we set the number of ground devices as 40,
and we set the number of LEO satellites as 3. From Figure 6, we can see that, for a fixed
number of ground devices and LEO satellites, the energy consumption increases with the
required number of CPU cycles for one-bit data. The energy consumption is consistently
lower than the other two benchmark algorithms.
600 700 800 900 1000 1100 1200
Required CPU cycles for one bit data (cycles/bit)
0
50
100
150
200
250
300
350
Energy consumption (J)
Pure HAP
OMA
Proposed
Figure 6.
Weighted energy consumption of the system versus different CPU cycles for one-bit
task data.
Figure 7depicts the energy consumption of the system for three different algorithms
with a different number of LEO satellites. We compared the performance of three algorithms
in two scenarios where the number of ground devices is 20 and 40. Compared with the
other two algorithms, the energy consumption of the pure HAP algorithm is always the
highest and does not change with the number of LEO satellites. This is because the task-
offloading process of the pure HAP algorithm does not involve the participation of LEO
satellites. The energy consumption of the other two algorithms decreases with the increase
in the number of LEO satellites. This is because the weight of satellite energy consumption
is lower, and as the number of satellites increases, more task data can be allocated to LEO
satellites. The energy consumption of the proposed algorithm is always the lowest, which
further illustrates the performance of the proposed algorithm.
23456
Number of LEO satellites
50
100
150
200
250
300
350
400
Weight energy consumption (J)
N=20, pure HAP
N=20, OMA
N=20, proposed
N=40, pure HAP
N=40, OMA
N=40, proposed
Figure 7. Energy consumption of the system versus different number of LEO satellites.
7. Conclusions
In this paper, we focus on the space–air–ground collaborative network. Ground
devices communicate with the HAP drone based on the NOMA technique. The HAP
Drones 2023,7, 482 18 of 19
drone can process part of a GD’s task locally while offloading the rest of the task to LEO
satellites for processing. We formulate an optimization problem to jointly optimize multiple
resource allocation and task offloading to minimize the weighted energy consumption
of the system while ensuring the maximum task tolerance delay is met. We proposed
an iterative algorithm that can converge quickly to reduce the complexity of the original
problem. The simulation results verify the convergence and performance of the proposed
algorithm compared to the other two benchmark algorithms. There are two main research
directions in the future. In terms of scenarios, the research on scenarios involving multiple
HAP drones and multiple satellites, covering a broader range, will become a new research
trend. In terms of algorithms, distributed algorithms such as federated learning will receive
more in-depth research.
Author Contributions:
Conceptualization, C.M. and C.G.; methodology, C.G. and N.J.; validation,
N.J., C.G., and B.H.; formal analysis, C.G. and N.J.; investigation, H.W. and Y.X.;
writing—original
draft preparation, C.G.; writing—review and editing, C.M., H.W., and B.H.; supervision, C.M. and
H.W.; project administration, Y.X.; funding acquisition, C.M. All authors have read and agreed to the
published version of the manuscript.
Funding:
This work was supported by the 2020 National Key R&D Program “Broadband Communica-
tion and New Network” special “6G Network Architecture and Key Technologies” 2020YFB1806700.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflicts of interest.
References
1.
Lee, Y.L.; Qin, D.; Wang, L.-C.; Sim, G.H. 6G Massive Radio Access Networks: Key Applications, Requirements and Challenges.
IEEE Open J. Veh. Technol. 2021,2, 54–66. [CrossRef]
2.
Huynh, D.V.; Nguyen, V.-D.; Chatzinotas, S.; Khosravirad, S.R.; Poor, H.V.; Duong, T.Q. Joint Communication and Computation
Offloading for Ultra-Reliable and Low-Latency With Multi-Tier Computing. IEEE J. Sel. Areas Commun.
2023
,41, 521–537.
[CrossRef]
3.
Chen, Q.; Meng, W.; Quek, T.Q.S.; Chen, S. Multi-Tier Hybrid Offloading for Computation-Aware IoT Applications in Civil
Aircraft-Augmented SAGIN. IEEE J. Sel. Areas Commun. 2023,41, 399–417. [CrossRef]
4.
Centenaro, M.; Costa, C.E.; Granelli, F.; Sacchi, C.; Vangelista, L. A Survey on Technologies, Standards and Open Challenges in
Satellite IoT. IEEE Commun. Surv. Tutor. 2021,23, 1693–1720. [CrossRef]
5.
Xie, R.; Tang, Q.; Wang, Q.; Liu, X.; Yu, F.R.; Huang, T. Satellite-Terrestrial Integrated Edge Computing Networks: Architecture,
Challenges, and Open Issues. IEEE Netw. 2020,34, 224–231. [CrossRef]
6.
Kim, T.; Kwak, J.; Choi, J.P. Satellite Edge Computing Architecture and Network Slice Scheduling for IoT Support. IEEE Internet
Things J. 2022,9, 14938–14951. [CrossRef]
7.
Jia, Z.; Sheng, M.; Li, J.; Han, Z. Toward Data Collection and Transmission in 6G Space–Air–Ground Integrated Networks:
Cooperative HAP and LEO Satellite Schemes. IEEE Internet Things J. 2022,9, 10516–10528. [CrossRef]
8.
Sudheesh, P.G.; Mozaffari, M.; Magarini, M.; Saad, W.; Muthuchidambaranathan, P. Sum-Rate Analysis for High AltitudePlatform
(HAP) Drones With Tethered Balloon Relay. IEEE Commun. Lett. 2018,22, 1240–1243. [CrossRef]
9.
Ding, C.; Wang, J.-B.; Zhang, H.; Lin, M.; Li, G.Y. Joint Optimization of Transmission and Computation Resources for Satellite and
High Altitude Platform Assisted Edge Computing. IEEE Trans. Wirel. Commun. 2022,21, 1362–1377. [CrossRef]
10.
Qiu, J.; Grace, D.; Ding, G.; Zakaria, M.D.; Wu, Q. Air-ground heterogeneous networks for 5G and beyond via integrating high
and low altitude platforms. IEEE Wirel. Commun. 2019,26, 140–148. [CrossRef]
11.
Thompson, S.; Martin, S.; Bevly, D. Single Differenced Doppler Positioning with Low Earth Orbit Signals of Opportunity and
Angle of Arrival Estimation. In Proceedings of the ION International Technical Meeting, 25–28 January 2021; pp. 497–509.
Available online: https://www.ion.org/publications/abstract.cfm?articleID=17845 (accessed on 20 May 2023).
12.
Dai, L.; Wang, B.; Ding, Z.; Wang, Z.; Chen, S.; Hanzo, L. A Survey of Non-Orthogonal Multiple Access for 5G. IEEE Commun.
Surv. Tutor. 2018 ,20, 2294–2323. [CrossRef]
13.
Ding, Z.; Fan, P.; Poor, H.V. Impact of Non-Orthogonal Multiple Access on the Offloading of Mobile Edge Computing. IEEE Trans.
Commun. 2019,67, 375–390. [CrossRef]
14. Kiani, A.; Ansari, N. Edge Computing Aware NOMA for 5G Networks. IEEE Internet Things J. 2018,5, 1299–1306. [CrossRef]
15.
Cheng, N.; Lyu, F.; Quan, W.; Zhou, C.; He, H.; Shi, W.; Shen, X. Space/Aerial-Assisted Computing Offloading for IoT Applications:
A Learning-Based Approach. IEEE J. Sel. Areas Commun. 2019,37, 1117–1129. [CrossRef]
16.
Yu, S.; Gong, X.; Shi, Q.; Wang, X.; Chen, X. EC-SAGINs: Edge-Computing-Enhanced Space–Air–Ground-Integrated Networks
for Internet of Vehicles. IEEE Internet Things J. 2022,9, 5742–5754. [CrossRef]
Drones 2023,7, 482 19 of 19
17.
Mao, B.; Tang, F.; Kawamoto, Y.; Kato, N. Optimizing Computation Offloading in Satellite-UAV-Served 6G IoT: A Deep Learning
Approach. IEEE Netw. 2021,35, 102–108. [CrossRef]
18.
Alsharoa, A.; Alouini, M.-S. Improvement of the Global Connectivity Using Integrated Satellite-Airborne-Terrestrial Networks
With Resource Optimization. IEEE Trans. Wirel. Commun. 2020,19, 5088–5100. [CrossRef]
19.
Zhang, L.; Zhang, H.; Guo, C.; Xu, H.; Song, L.; Han, Z. Satellite-Aerial Integrated Computing in Disasters: User Association and
Offloading Decision. In Proceedings of the IEEE International Conference on Communications (ICC), Dublin, Ireland, 7–11 June
2020; pp. 554–559.
20.
Du, R.; Liu, C.; Gao, Y.; Hao, N.; Wang, Z. Collaborative Cloud-Edge-End Task Offloading in NOMA-Enabled Mobile Edge
Computing Using Deep Learning. J. Grid Comput. 2022,20, 14. [CrossRef]
21.
Ding, Z.; Xu, J.; Dobre, O.A.; Poor, H.V. Joint Power and Time Allocation for NOMA–MEC Offloading. IEEE Trans. Veh. Technol.
2019,68, 6207–6211. [CrossRef]
22.
Lai, P.; He, Q.; Cui, G.; Chen, F.; Grundy, J.; Abdelrazek, M.; Hosking, J.; Yang, Y. Cost-Effective User Allocation in 5G
NOMA-Based Mobile Edge Computing Systems. IEEE. Trans. Mob. Comput. 2022,21, 4263–4278. [CrossRef]
23.
Yılmaz, S.S.; Özbek, B. Multi-Helper NOMA for Cooperative Mobile Edge Computing. IEEE Trans. Intell. Transp. Syst.
2022
,23,
9819–9828. [CrossRef]
24.
Zeng, M.; Nguyen, N.-P.; Dobre, O.A.; Poor, H.V. Delay Minimization for NOMA-Assisted MEC Under Power and Energy
Constraints. IEEE Wirel. Commun. Lett. 2019,8, 1657–1661. [CrossRef]
25.
Du, J.; Sun, Y.; Zhang, N.; Xiong, Z.; Sun, A.; Ding, Z. Cost-Effective Task Offloading in NOMA-Enabled Vehicular Mobile Edge
Computing. IEEE Wirel. Commun. Lett. 2022,17, 928–939. [CrossRef]
26.
Ding, Z.; Xu, D.; Schober, R.; Poor, H.V. Hybrid NOMA Offloading in Multi-User MEC Networks. IEEE Trans. Wirel. Commun.
2022,21, 5377–5391. [CrossRef]
27.
Mao, S.; Leng, S.; Zhang, Y. Joint Communication and Computation Resource Optimization for NOMA-Assisted Mobile Edge
Computing. In Proceedings of the IEEE International Conference on Communications (ICC), Shanghai, China, 20–24 May 2019;
pp. 1–6.
28.
Standard 3GPP TR 38.811 (V15.4.0); Study on New Radio (NR) to Support Non-Terrestrial Networks (Release 15). 2020. Available
online: https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=3234 (accessed on 20
May 2023).
29.
Michael Grant and Stephen Boyd, (March 2014) CVX: Matlab Software for Disciplined Convex Programming, Version 2.1 [Online].
Available online: http://cvxr.com/cvx (accessed on 20 May 2023).
30.
Cai, Y.; Cui, F.; Shi, Q.; Zhao, M.; Li, G.Y. Dual-UAV-Enabled Secure Communications: Joint Trajectory Design and User Scheduling.
IEEE J. Sel. Areas Commun. 2018,36, 1972–1985. [CrossRef]
31. Lanckriet, G.; Sriperumbudur, B.K. On the Convergence of the Concave-Convex Procedure. Nips 2009,22, 1759–1767.
32.
Dai, Y.; Xu, D.; Maharjan, S.; Zhang, Y. Joint computation offloading and user association in multi-task mobile edge computing.
IEEE Trans. Veh. Technol. 2018,67, 12313–12325. [CrossRef]
33.
Cao, X.; Yang, B.; Shen, Y.; Yuen, C.; Zhang, Y.; Han, Z.; Vincent Poor, H.; Hanzo, L. Edge-Assisted Multi-Layer Offloading
Optimization of LEO Satellite-Terrestrial Integrated Networks. IEEE J. Sel. Areas Commun. 2023,41, 381–398. [CrossRef]
34.
Karabulut Kurt, G.; Khoshkholgh, M.G.; Alfattani, S.; Ibrahim, A.; Darwish, T.S.J.; Alam, M.S.; Yanikomeroglu, H.; Yongacoglu, A.
A Vision and Framework for the High Altitude Platform Station (HAPS) Networks of the Future. IEEE Commun. Surv. Tutor.
2021
,
23, 729–779. [CrossRef]
35.
Liu, B.; Liu, C.; Peng, M. Resource Allocation for Energy-Efficient MEC in NOMA-Enabled Massive IoT Networks. IEEE J. Sel.
Areas Commun. 2021,39, 1015–1027. [CrossRef]
36.
Tang, Q.; Fei, Z.; Li, B.; Han, Z. Computation Offloading in LEO Satellite Networks With Hybrid Cloud and Edge Computing.
IEEE Internet Things J. 2021,8, 9164–9176. [CrossRef]
37.
Zhu, X.; Jiang, C. Delay Optimization for Cooperative Multi-Tier Computing in Integrated Satellite-Terrestrial Networks. IEEE J.
Sel. Areas Commun. 2023,41, 366–380. [CrossRef]
38.
Ren, Q.; Abbasi, O.; Kurt, G.K.; Yanikomeroglu, H.; Chen, J. High Altitude Platform Station (HAPS) Assisted Computing for
Intelligent Transportation Systems. In Proceedings of the IEEE Global Communications Conference (GLOBECOM), Madrid,
Spain, 7–11 December 2021; pp. 1–6.
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