Computation Rate Maximization in UAV-EnabledWireless Powered Mobile-Edge Computing Systems

Fuhui Zhou, Member, IEEE, Yongpeng Wu, Senior Member, IEEE,Rose Qingyang Hu, Senior Member, IEEE, and Yi Qian, Senior Member, IEEE

Abstract—Mobile edge computing (MEC) and wireless powertransfer (WPT) are two promising techniques to enhance thecomputation capability and to prolong the operational timeof low-power wireless devices that are ubiquitous in Internetof Things. However, the computation performance and theharvested energy are significantly impacted by the severe prop-agation loss. In order to address this issue, an unmanned aerialvehicle (UAV)-enabled MEC wireless powered system is studiedin this paper. The computation rate maximization problems ina UAV-enabled MEC wireless powered system are investigatedunder both partial and binary computation offloading modes,subject to the energy harvesting causal constraint and the UAV’sspeed constraint. These problems are non-convex and challengingto solve. A two-stage algorithm and a three-stage alternativealgorithm are respectively proposed for solving the formulatedproblems. The closed-form expressions for the optimal centralprocessing unit frequencies, user offloading time, and usertransmit power are derived. The optimal selection scheme onwhether users choose to locally compute or offload computationtasks is proposed for the binary computation offloading mode.Simulation results show that our proposed resource allocationschemes outperforms other benchmark schemes. The results alsodemonstrate that the proposed schemes converge fast and havelow computational complexity.

Index Terms—Mobile-edge computing, wireless power transfer,unmanned aerial vehicle-enabled, resource allocation, binary

Manuscript received January 4, 2018; revised May 1, 2018 and acceptedJune 4, 2018. Date of publication ****; date of current version ****. Theresearch of F. Zhou was supported in part by the Natural Science Foundationof China under Grant 61701214, in part by the Young Natural ScienceFoundation of Jiangxi Province under Grant 20171BAB212002, in part byThe Open Foundation of The State Key Laboratory of Integrated ServicesNetworks under Grant ISN19-08, and in part by The Postdoctoral ScienceFoundation of Jiangxi Province under Grant 2017M610400, Grant 2017KY04and Grant 2017RC17. The research of Y. Wu was supported by the NaturalScience Foundation of China under Grant 61701301 and in part by Young EliteScientist Sponsorship Program by CAST. The research of Prof. R. Q. Hu wassupported in part by the National Science Foundation under Grants EECS-1308006, NeTS-1423348, EARS-1547312 and the Natural Science Foundationof China under Grant 61728104. The research of Prof. Y. Qian was supportedby the National Science Foundation under Grants EECS-1307580, NeTS-1423408 and EARS-1547330. The corresponding author is Yongpeng Wu.

F. Zhou is with the Department of Electrical and Computer Engineeringas a Research Fellow at Utah State University, U.S.A. F. Zhou is also withthe School of Information Engineering, Nanchang University, P. R. China,330031. He is also with State Key Laboratory of Integrated Services Networks,Xidian University, Xian, 710071, P. R. China (e-mail: zhoufuhui@ieee.org).

Y. Wu is with Shanghai Key Laboratory of Navigation and LocationBased Services, Shanghai Jiao Tong University, Minhang, 200240, China(Email:yongpeng.wu2016@gmail.com).

R. Q. Hu is with the Department of Electrical and Computer Engineering,Utah State University, USA. (e-mail: rose.hu@usu.edu).

Y. Qian is with the Department of Electrical and Computer Engineer-ing, University of Nebraska-Lincoln, Omaha, NE 68182, USA. (E-mail:yqian2@unl.edu).

computation offloading, partial computation offloading.

I. INTRODUCTION

THE Internet of Things (IoT) has been widely developedwith the unprecedented proliferation of mobile devices,

such as smart phones, cloud-based mobile sensors, tabletcomputers and wearable devices, which facilitates the real-ization of smart environment (e.g. smart city, smart home,smart transportation, etc.) [1]. IoT enables mobile users toexperience intelligent applications (e.g., automatic navigation,face recognition, unmanned driving, etc.) and to enjoy diverseservices with high quality of service (QoS) such as mobileonline gaming, augmented reality, etc. These services normallyrequire a massive number of size-constrained and low-powermobile devices to perform computation-intensive and latency-sensitive tasks [2]. However, it is challenging for mobiledevices to perform these services due to their low computingcapability and finite battery lifetime.

Mobile edge computing (MEC) and wireless power transfer(WPT) have been deemed two promising technologies totackle the above mentioned challenges [2]-[4]. Recently, MEChas received an ever-increasing level of attention from industryand academia since it can significantly improve the compu-tation capability of mobile devices in a cost-effective andenergy-saving manner [2]. It enables mobile devices to offloadpartial or all of their computation-intensive tasks to MECservers that locate at the edge of the wireless network, such ascellular base stations (BSs) and access points (APs). Differentfrom the conventional cloud computing, MEC servers aredeployed in a close proximity to end users. Thus, MEC hasthe potential to provide low-latency services, to save energyfor mobile users, and to achieve high security [2]. Up to now,there are a number of leading companies (e.g., IBM, Intel, andHuawei) that have identified MEC as a promising techniquefor the future wireless communication networks. In general,MEC has two operation modes, namely, partial and binarycomputation offloading. In the first mode, the computationtask can be partitioned into two parts, and one part is locallyexecuted while the other part is offloaded to the MEC serversfor computing [5]-[9]. For the second mode, computation taskscannot be partitioned. Thus they can be either executed locallyor completely offloaded [10].

On the other hand, WPT can provide low-power mobiledevices with sustainable and cost-effective energy supply byusing radio-frequency (RF) signals [3]. It facilitates a perpetual

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operation and enables users to have high QoE, especially inthe case that mobile devices do not have sufficient batteryenergy for offloading task or taking the services when thebattery energy is exhausted. Compared to the conventionalenergy harvesting techniques, such as solar or wind charging,WPT is more attractive since it can provide a controllable andstable power supply [4]. It is envisioned that the computationperformance can be significantly improved by integratingWPT into MEC networks [11]-[16]. However, the harvestedpower level can be significantly degraded by the severe prop-agation loss. Recently, an unmanned aerial vehicle (UAV)-enabled WPT architecture has been proposed to improve theenergy transfer efficiency [17]-[20]. It utilizes an unmannedaerial vehicle (UAV) as an energy transmitter for poweringthe ground mobile users. It was shown that the harvestedpower level can be greatly improved due to the fact thatthere is a high possibility that short-distance line-of-sight(LoS) energy transmit links exist [17]-[20]. Moreover, thecomputation performance can also be improved by using theUAV-assisted MEC architecture [21]-[25]. Furthermore, UAV-assisted architectures can provide flexible deployment and lowoperational costs, and are particularly helpful in the situationsthat the conventional communication systems are destroyed bynatural disasters [26]-[32].

Motivated by the above mentioned reasons, a UAV-enabledand wireless powered MEC network is studied in this paper.In order to maximize the achievable computation rate, thecommunication and computation resources and the trajectoryof the UAV are jointly optimized under both partial and binarycomputation offloading modes. To the authors’ best knowl-edge, this is the first work that considers the UAV-enabledwireless powered MEC network and studies the computationrate maximization problems in this type of network.

A. Related Work and Motivation

In wireless powered MEC systems, it is of great importanceto design resource allocation schemes so as to efficientlyexploit energy, communication, and computation resources andimprove the computation performance. Resource allocationproblems have been extensively investigated in the conven-tional MEC networks [5]-[10] and also in MEC networks rely-ing on energy harvesting [11]-[16]. Recently, efforts have alsobeen dedicated to designing resource allocation and trajectoryschemes in UAV-enabled wireless powered communicationsnetwork [17]-[20] and UAV-assisted MEC networks [21]-[25].These contributions are summarized as follows.

In MEC networks, the communication and computationresources and the selection of the offloading mode were jointlyoptimized to achieve the objective of the system design,e.g., the users’ consumption energy minimization [5], [6], therevenue maximization [7], the maximum cost minimization[8], etc. Specifically, in [5], the total energy of all users in amulti-cell MEC network was minimized by jointly optimizingthe user transmit precoding matrices and the central processingunit (CPU) frequencies of the MEC server allocated to eachuser. It was shown that the performance achieved by jointly

optimizing the communication and computation resources issuperior to that obtained by optimizing these resources sep-arately. The authors in [6] extended the energy minimizationproblem into the multi-user MEC systems with time-divisionmultiple access (TDMA) and orthogonal frequency-divisionmultiple access (OFDMA), respectively. It was proved thatthe optimal offloading policy has a threshold-based structure,which is related to the channel state information (CSI) [6].Particularly, mobile users offload their computation tasks whenthe channel condition is strong; otherwise, they can locallyexecute the computation tasks. In [7], the revenue of thewireless cellular networks with MEC was maximized byjointly designing the computation offloading decision, resourceallocation, and content caching strategy. The works in [5]-[7] focused on optimizing a single objective, which over-emphasizes the importance of one metric and may not achievea good tradeoff among multiple metrics. Recently, the authorsin [8] and [9] studied the fairness and multi-objective opti-mization problem in MEC networks. It was shown that thereexist multiple tradeoffs in MEC systems, such as the tradeoffbetween the total computation rate and the fairness amongusers. Different from the works in [5]-[9], MEC systemswith the binary computation offloading mode were consideredand the optimal resource allocation strategy was designed tominimize the consumption energy in [10].

Energy harvesting was not considered in the MEC systems[5]-[10]. Recently, the authors in [11]-[16] have studied theresource allocation problem in various MEC systems relyingon energy harvesting. In [11] and [12], The reinforcementlearning and Lyapunov optimization theory were used todesign resource allocation schemes in MEC systems relyingon the conventional energy harvesting techniques. Differentfrom [11] and [12], the resource allocation problems werestudied in wireless powered MEC systems [13]-[16]. Specif-ically, the authors in [13] proposed an energy-efficient com-puting framework in which the energy consumed for localcomputing and task offloading is from the harvested energy.The consumed energy was minimized by jointly optimizingthe CPU frequency and the mode selection. In [14], theenergy minimization problem was extended into a multi-inputsingle-out wireless powered MEC system, and the offloadingtime, the offloading bits, the CPU frequency and the energybeamforming were jointly optimized. Unlike [14], energyefficiency was defined and maximized in a full-duplex wirelesspowered MEC system by jointly optimizing the transmissionpower, offloaded bits, computation energy consumption, timeslots for computation offloading and energy transfer [15]. Incontrast to the work in [13]-[15], the computation bits weremaximized in a wireless powered MEC system under thebinary computation offloading mode [16]. Two sub-optimalalgorithms based on the alternating direction method wereproposed to solve the combinatorial programming problem.The proposed algorithms actually did not provide the optimalselection scheme for the user operation mode.

Although WPT has been exploited to improve the com-putation performance of MEC systems [13]-[16], the energy

harvested by using WPT can be significantly degraded bythe severe propagation loss. The energy conversion efficiencyis low when the distance between the energy transmitterand the harvesting users is large. In order to tackle thischallenge, the authors in [17]-[20] proposed a UAV-enabledwireless powered architecture where a UAV transmits energyto the harvesting users. Due to the high possibility of havingline-of-sight (LoS) air-to-ground energy harvesting links, theharvesting energy can be significantly improved by using thisarchitecture. Moreover, it was shown that the harvesting energycan be further improved by optimizing the trajectory of theUAV [18]-[20]. Thus, it is envisioned that the application of theUAV-enabled architecture into wireless powered MEC systemsis promising and valuable to be studied [26]. However, to theauthors’ best knowledge, few investigations have focused onthis area.

Recently, the UAV-enabled MEC systems have been studiedand their resource allocation schemes have been proposed[21]-[25]. In [21], the UAV-enabled MEC architecture wasfirst proposed and the computation performance was improvedby using UAV. The authors in [22] proposed a new cachingUAV framework to help small cells to offload traffic. It wasshown that the throughput can be greatly improved while theoverload of wireless backhaul can be significantly reduced.In order to further improve the computation performance,the authors in [23] and [24] designed a resource allocationscheme that jointly optimizes the CPU frequency and thetrajectory of the UAV. In [25], a theoretical game method wasapplied to design a resource allocation scheme for the UAV-enabled MEC system and the existence of Nash Equilibriumwas demonstrated.

Although resource allocation problems have been well stud-ied in MEC systems [5]-[10], MEC systems relying on energyharvesting [11]-[16] and UAV-enabled MEC systems [21]-[25], few investigations have been conducted for designingresource allocation schemes in the UAV-enabled wireless pow-ered MEC systems. Moreover, resource allocation schemesproposed in the above-mentioned works are inappropriate toUAV-enabled MEC wireless powered systems since the com-putation performance not only depends on the optimizationof energy, communication and computation resources, butalso relies on the design of the UAV trajectory. Furthermore,the application of UAV into wireless powered MEC systemshas the potential to enhance the user computation capabilitysince it can improve the energy conversion efficiency and taskoffloading efficiency [33], [34]. Thus, in order to improve thecomputation performance and provide mobile users with highQoE, it is of great importance and worthiness to study resourceallocation problems in UAV-enabled wireless powered MECsystems. However, these problems are indeed challenging totackle. The reasons are from two aspects. On one hand, thereexists dependence among different variables (e.g., the CPUfrequency, the task offloading time and the variables relatedto the trajectory of the UAV), which makes the problemsnon-convex. On the other hand, when the binary computationoffloading mode is applied, the resource allocation problems

in UAV-enabled wireless powered MEC systems have binaryvariables related to the selection of either local computationor offloading tasks. It makes the problem a mixed integer non-convex optimization problem.

B. Contributions and Organization

In contrast to [5]-[16], this paper studies the resourceallocation problem in UAV-enabled wireless powered MECsystems, where a UAV transmits energy signals to chargemultiple mobile users and provides computation servicesfor them. Although the computation performance is limitedby the flight time of the UAV, it is worth studying UAV-enabled wireless powered MEC systems since these systemsare promising in environments such as mountains and desertareas, where no terrestrial wireless infrastructures exist, andin environments where the terrestrial wireless infrastructuresare destroyed due to the natural disasters [33], [34]. Thus, inthis paper, the weighted sum computation bits of all usersare maximized under both partial and binary computationoffloading modes. The main contributions of this work aresummarized as follows:

1) It is the first time that the resource allocation frameworkis formulated in UAV-enabled MEC wireless poweredsystems under both partial and binary computation of-floading modes. The weighted sum computation bits aremaximized by jointly optimizing the CPU frequencies,the offloading times and the transmit powers of users aswell as the UAV trajectory. Under the partial computa-tion offloading mode, a two-stage alternative algorithmis proposed to solve the non-convex and challengingcomputation bits maximization problem. The closed-form expressions for the optimal CPU frequencies, theoffloading times and the transmit powers of users arederived for any given trajectories.

2) Under the binary computation offloading mode, theweighted sum computation bits maximization problemis a mixed integer non-convex optimization problem, forwhich a three-stage alternative algorithm is proposed.The optimal selection scheme on whether users chooseto locally compute or offload tasks is derived in a closed-form expression for a given trajectory. The structure forthe optimal selection scheme shows that whether userschoose to locally compute or offload their tasks to theUAV for computing depends on the tradeoff betweenthe achievable computation rate and the operation cost.Moreover, the trajectory of the UAV is optimized by us-ing the successive convex approximation (SCA) methodunder both partial and binary computation offloadingmodes.

3) The simulation results show that the computation per-formance obtained by using the proposed resource allo-cation scheme is better than these achieved by using thedisjoint optimization schemes. Moreover, it only takesseveral iterations for the proposed alternative algorithmsto converge. Furthermore, simulation results verify thatthe priority and fairness of users can be improved by

User1

User2

UseM

Usem

Energy

harvesting

Local

computing

Wireless powered link

Computation offloading link

Usem

x

y

z

Fig. 1: The system model.

using the weight vector. Additionally, it is shown thatthe total computation bits increase with the number ofusers.

The remainder of this paper is organized as follows. SectionII gives the system model. The resource allocation problemis formulated under the partial computation offloading modein Section III. Section IV formulates the resource allocationproblem under the binary computation offloading mode. Sim-ulation results are presented in Section V. Finally, our paperis concluded in Section VI.

II. SYSTEM MODEL

A UAV-enabled wireless powered MEC system is consid-ered in Fig. 1, where an RF energy transmitter and an MECserver are implemented in UAV. The UAV transmits energy toM users and provides MEC services for these users. Each userhas an energy harvesting circuit and can store energy for itsoperation. The UAV has an on-board communication circuitand an on-board computing processor. So does each user.The computing processor of each user is an on-chip micro-processor that has low computing capability and can locallyexecute simple tasks. The UAV has a powerful processor thatcan perform computation-intensive tasks [21]-[25]. Similarto [13]-[16], each user can simultaneously perform energyharvesting, local computing and computation offloading whilethe UAV can simultaneously transmit energy and performcomputation. In this paper, all devices are equipped with asingle antenna.

Without loss of generality, a three-dimensional (3D) Eu-clidean coordinate is adopted. Each user’s location is fixed onthe ground. The location of the mth ground user is denoted byqm, where qm = [xm, ym], m ∈M andM = {1, 2, · · · ,M}.Boldface lower case letters represent vectors and boldfaceupper case letters represent matrices. xm and ym are the hori-zontal plane coordinates of the mth ground user. It is assumedthat user positions are known to the UAV for designing the

trajectory [18]-[20]. A finite time horizon with duration T isconsidered. During T , the UAV flies at the same altitude leveldenoted by H (H > 0). In practice, the fixed altitude is theminimum altitude that is appropriate to the work terrain andcan avoid building without the requirement of frequent aircraftdescending and ascending. A block fading channel model isapplied, i.e., during each T , the channel remains static.

For the ease of exposition, the finite time T is discretizedinto N equal time slots, denoted by n = 1, 2, · · · , N . At thenth slot, it is assumed that the horizontal plane coordinate ofthe UAV is qu [n] = [xu[n], yu[n]]. Similar to [27]-[32], itis assumed that the wireless channel between the UAV andeach user is dominated by LOS. Thus, the channel power gainbetween the UAV and the mth user, denoted by hm [n], canbe given as

hm [n] = β0d−2m,n =

β0

H2 + ‖qu [n]− qm‖2,m ∈M, n ∈ N ,

(1)

where β0 is the channel power gain at a reference distanced0 = 1 m; dm,n is the horizontal plane distance betweenthe UAV and the mth user at the nth slot, n ∈ N , N ={1, 2, · · · , N}; ‖·‖ denotes its Euclidean norm. The details forthe UAV-enabled wireless powered MEC system are presentedunder partial and binary computation offloading modes in thefollowing, respectively.

A. Partial Computation Offloading Mode

Under the partial computation offloading mode, the com-putation task of each user can be partitioned into two parts,one for local computing and one for offloading to the UAV.The energy consumed for local computing and task offloadingcomes from the harvested energy. In this paper, in order toshed meaningful insights into the design of a UAV-enabledwireless powered MEC system, similar to [4], [13]-[16], thelinear energy harvesting model is applied. Thus, the harvestedenergy Em [n] at the mth user during n time slots is given as

Em [n] =

n∑i=1

Tη0hm [i]P0

N,m ∈M, n ∈ N , (2)

where η0 denotes the energy conservation efficiency, 0 < η0 ≤1 and P0 is the transmit power of the UAV. In this paper,the UAV employs a constant power transmission [18]-[20].The details for the operation of each user under the partialcomputation offloading mode are presented as follows.

1) Local Computation: Similar to [14]-[16], the energyharvesting circuit, the communication circuit, and the compu-tation unit are all separate. Thus, each user can simultaneouslyperform energy harvesting, local computing, and computationoffloading. Let C denote the number of CPU cycles requiredfor computing one bit of raw data at each user. In orderto efficiently use the harvested energy, each user adopts adynamic voltage and frequency scaling technique and then canadaptively control the energy consumed for performing localcomputation by adjusting the CPU frequency during each timeslot [14]-[16]. The CPU frequency of the mth user during

T

The first slot The second slot . . . The th slotn

UAVUserM

Offloading. . . User1UAV

Download

UAV

1 1t 0 0 1Mt

Offloading

User1 UAV

. . . The th slotN

Download

UserM. . . . . .

. . .

T

N

Fig. 2: The TDMA protocol for multiuser computation offload-ing.

the nth slot is denoted by fm [n] with a unit of cycles persecond. Thus, the total computation bits executed at the mthuser during n slots and the total consumed energy at the mth

user during n slots are respectively given asn∑k=1

Tfm[k]NC and

n∑k=1

γcf3m [k] [14]-[16], where γc is the effective capacitance

coefficient of the processor’s chip at the mth user, n ∈ N ,m ∈M. Note that γc is dependent of the chip architecture ofthe mth user.

2) Computation Offloading: In order to avoid interferenceamong users during the offloading process, a TDMA protocolshown in Fig. 2 is applied. Specifically, each time slot consistsof three stages, namely, the offloading stage, the computationstage, and the downloading stage. In the offloading stage, Musers offload their respective computation task one by oneduring each slot. Let tm [n] × T/N (0 ≤ tm [n] ≤ 1) denotethe duration in which the mth user offloads its computationtask to the UAV at the nth slot, n ∈ N , m ∈ M. Similarto [16], the computation task of the mth user to be offloadis composed of raw data and communication overhead, suchas the encryption and packer header. Let νmRm [n] denotethe total number of bits that the mth user offloads to the UAVduring the nth slot, where Rm [n] is the number of raw data tobe computed at the UAV and νm indicates the communicationoverhead included in the offloading task. Thus, one has

Rm [n] ≤ BTtm [n]

νmNlog2

(1 +

hm [n]Pm [n]

σ20

),

n ∈ N ,m ∈M, (3)

where B is the communication bandwidth; Pm [n] is thetransmit power of the mth user at the nth slot and σ2

0 denotesthe noise power at the mth user.

After all users offload their computation tasks at the nthslot, the UAV performs computing task and sends the com-puting results back to all the users. Similar to [14]-[16], thecomputation time and the downloading time of the UAV areneglected since the UAV has a much stronger computationcapability than the users and the number of the bits related tothe computation result is very small. Since the total offloadingtime of all users does not exceed the duration of one time slot,

one hasM∑m=1

tm [n] ≤ 1, n ∈ N . (4)

Since the energy consumed for local computing and taskoffloading comes from the harvested energy, the followingenergy harvesting causal constraint should be satisfied.

T

N

n∑k=1

[γcf

3m [k] + tm [k]Pm [k]

]≤ η0T

N

n∑k=1

hm [k]P0,

n ∈ N ,m ∈M.(5)

Under the partial computation offloading mode, the totalcomputation bits Rm of the mth user is given as

Rm =

N∑n=1

Tfm [n]

NC+BTtm [n]

νmNlog2

(1 +

hm [n]Pm [n]

σ20

),

m ∈M. (6)

B. Binary Computation Offloading Mode

Under the binary computation offloading mode, the compu-tation task cannot be partitioned. All the users need to chooseto either locally compute the task completely or offload theentire task. This case can be widely experienced in practice.For example, in order to improve the estimation accuracy,the raw data samples that are correlated need to be jointlycomputed altogether [10], [16]. LetM0 andM1 denote the setof users that choose to perform local computation and the setof users that choose to perform task offloading, respectively.Thus,M =M0∪M1 andM0∩M1 = Θ, where Θ denotesthe null set.

1) Users Choosing to Perform Local Computing: In thiscase, a user inM0 exploits all the harvested energy to performlocal computing. Thus, the total computation rate of the ithuser denoted by RLi can be given as

RLi =

N∑n=1

Tfi [n]

NC, i ∈M0. (7)

And the energy harvesting causal constraint for a user in M0

can be given as

T

N

n∑k=1

γcf3i [k] ≤ η0T

N

n∑k=1

hi [k]P0, n ∈ N , i ∈Mi. (8)

2) Users Choosing to Perform Task Offloading: Each userin M1 exploits all the harvested energy to perform task of-floading. The TDMA protocol is applied to avoid interferenceamong these users during the offloading process. Since thetotal offloading time of all users in M1 at the nth slot cannotexceed the duration of a time slot, one has∑

j∈M1

tj [n] ≤ 1, n ∈ N . (9)

Let ROj denote the total computation rate of the jth user inthe set M1. Then, one has

ROj =

N∑n=1

BTtj [n]

νjNlog2

(1 +

hj [n]Pj [n]

σ20

), j ∈M1.

(10)

The energy harvesting causal constraint for a user in M1 canbe given as

T

N

n∑k=1

tj [k]Pj [k] ≤ η0T

N

n∑k=1

hj [k]P0, n ∈ N , j ∈M1.

(11)

Sections III and IV will respectively formulate the compu-tation rate maximization problem for the partial and binarycomputation offloading modes.

III. RESOURCE ALLOCATION UNDER THE PARTIALCOMPUTATION OFFLOADING MODE

In this section, the resource allocation problem is studiedunder the partial computation offloading mode. The weightedsum computation bits are maximized by jointly optimizing theCPU frequencies, the offloading times and the transmit powersof users as well as the trajectory of the UAV. In order to tacklethis non-convex problem, a two-stage alternative algorithm isproposed.

A. Resource Allocation Problem Formulation

Under the partial computation offloading mode, theweighted sum computation bits maximization problem in theUAV-enabled wireless powered MEC system is formulated asP1,

P1 : maxfm[n],Pm[n],qu[n],tm[n]

M∑m=1

wm×[N∑n=1

Tfm [n]

NC+BTtm [n]

νmNlog2

(1 +

hm [n]Pm [n]

σ20

)](12a)

s.t. C1 : fm [n] ≥ 0, Pm [n] ≥ 0,m ∈M, n ∈ N , (12b)

C2 :T

N

n∑k=1

[γcf

3m [k] + tm [k]Pm [k]

]≤ η0T

N

n∑k=1

hm [k]P0

m ∈M, n ∈ N , (12c)

C3 :

M∑m=1

tm [n] ≤ 1, n ∈ N , (12d)

C4 : ‖qu [n+ 1]− qu [n]‖2 ≤ VmaxT

N, n ∈ N , (12e)

C5 : qu [1] = q0,qu [N + 1] = qF , (12f)

where Vmax denotes the maximum speed of the UAV in theunit of meter per second; q0 and qF are the initial and finalhorizontal locations of the UAV, respectively. In (12), wmdenotes the weight of the mth user, which takes the priorityand the fairness among users into consideration. C1 is the CPUfrequency constraint and the computation offloading power

constraint imposed on each user; C2 represents the energyharvesting causal constraint; C3 is the time constraint that thetotal time of all users offloading the computation bits cannotexceed the duration of each time slot; C4 and C5 are thespeed constraint and the initial and final horizontal locationconstraint of the UAV, respectively. P1 is non-convex sincethere exist non-linear couplings among the variables, fm [n],Pm [n],qu [n], tm [n] and the objective function is non-concavewith respect to the trajectory of the UAV. In order to solve it, atwo-stage alternative optimization algorithm is proposed. Thedetails for the algorithm are presented as follows.

B. Two-Stage Alternative Optimization Algorithm

Let zm [n] = tm [n]Pm [n] , n ∈ N . For a given trajectory,P1 can be transformed into P2.

P2 : maxfm[n],zm[n],tm[n]

M∑m=1

wm

×

[N∑n=1

Tfm [n]

NC+BTtm [n]

νmNlog2

(1 +

hm [n] zm [n]

tm [n]σ20

)](13a)

s.t. C1, C3, (13b)

C5 :T

N

n∑k=1

[γcf

3m [k] + zm [k]

]≤ η0T

N

n∑k=1

hm [k]P0,

m ∈M, n ∈ N . (13c)

It is easy to prove that P2 is convex and can be solved by usingthe Lagrange duality method [35], based on which the optimalsolutions for the CPU frequency and the transmit power canbe derived. Let foptm [n] and P optm [n] denote the optimal CPUfrequency and transmit power of the mth user at the nth timeslot, respectively, where m ∈M and n ∈ N . By solving P2,Theorem 1 can be stated as follows.

Theorem 1: For a given trajectory qu [n], the optimal CPUfrequency and transmit power of users can be respectivelyexpressed as

foptm [n] =

√√√√√ wm

3CγcN∑k=n

λm,k

, (14a)

P optm [n] =

0, if tm [n] = 0, wmB

νm ln 2N∑

k=n

λm,k

− σ20

hm[n]

+

, otherwise,

(14b)

where λm,n ≥ 0 is the dual variable associated with theconstraint C2; [a]

+= max (a, 0) and max (a, 0) denotes the

bigger value of a and 0.Proof: See Appendix A.

Remark 1: It can be seen from Theorem 1 that users chooseto offload their computation tasks only when the channel stateinformation between users and the UAV is stronger than a

threshold, namely, hm [n] ≥(σ20νm ln 2

N∑k=n

λm,k

)/ (wmB).

This indicates that the user chooses to perform local com-putation when the horizontal distance between the user andthe UAV is larger than β0wmB

σ20νm ln 2

N∑k=n

λm,k

− H2. Moreover,

it can be seen that the larger the weight is, the higher thechance for the user to chooses to offload its computation task.Furthermore, users prefers to offload their computation taskwhen the local computation frequency is very large, namely,foptm [n] ≥

√σ20νm ln 2

3CγcBhm[n] .Theorem 2: If there exists a time slot that foptm [n] = 0, the

equation foptm [k] = 0 must hold, 0 ≤ k ≤ n.Proof: Since λm,n is the dual variable and λm,n ≥ 0,

from Theorem 1 foptm [n] increases with n. Thus, if there existsa time slot n so that foptm [n] = 0, one must have foptm [k] = 0,for 0 ≤ k ≤ n. Theorem 2 is proved.

Remark 2: Theorem 2 indicates that the user CPU frequencyincreases with the time slot index. This means that the numberof computation bits obtained by local computing increaseswith the time slot index. Moreover, the user CPU frequencyincreases with the weight assigned to that user since moreresources are allocated to the user with a higher weight.

Theorem 3: For a given trajectory qu [n], the optimal useroffloading time can be obtained by solving the followingequation.

log2

(1 +

hm [n] zm [n]

σ20tm [n]

)− hm [n] zm [n]

ln 2 {σ20tm [n] + hm [n] zm [n]}

− νmNαnBT

= 0. (15)

Remark 3: Theorem 3 can be readily proved based on theproof for Theorem 1. Thus this proof is omitted for the sakeof saving space. Moreover, (15) can be solved by using thebisection method [35].

The values of the dual variables are needed in order to obtainthe optimal CPU frequency, the optimal transmit power and theoptimal offloading time for all users. The subgradient methodin Lemma 1 can be used to tackle this problem [36].

Lemma 1: The subgradient method for obtaining the dualvariables is given as

λm,n (l + 1) = [λm,n (l)− θ (l) ∆λm,n (l)]+,m ∈M, n ∈ N

(16a)

αn (l + 1) = [αn (l)− ϑ (l) ∆αn (l)]+, n ∈ N , (16b)

where l denotes the iteration index; θ (l) and ϑ (l) representthe iterative steps at the lth iteration. In (16), ∆λm,n (l) and∆αn (l) are the corresponding subgradients, given as

∆λm,n (l) =η0T

N

n∑k=1

hm [k]P0

− T

N

n∑k=1

[γc(f l,optm [k]

)3+ zm

l,opt [k]], (17a)

∆αn (l) = 1−M∑m=1

tl,optm [n], n ∈ N , (17b)

where f l,optm [n], zml,opt [n], and tl,optm [n] denote the optimalsolutions at the lth iterations. According to [35], the subgra-dient guarantees to converge to the optimal value with a verysmall error range.

C. Trajectory Optimization

For any given CPU frequency, transmit power, and offload-ing time of users, the trajectory optimization problem can beformulated as P3.

P3 : maxqu[n]

M∑m=1

wm

×

N∑n=1

BTtm [n]

νmNlog2

1 +β0Pm [n]

σ20

(H2 + ‖qu [n]− qm‖2

)

(18a)

s.t. C2 :T

N

n∑k=1

[γcf

3m [k] + tm [k]Pm [k]

]≤ η0T

N

n∑k=1

β0P0

H2 + ‖qu [k]− qm‖2,m ∈M, n ∈ N (18b)

C4 and C5. (18c)

Since C2 is non-convex and the objective function is non-concave with respect to qu [n], P3 is non-convex and we usethe SCA technique to solve the optimization problem. Theobtained solutions can be guaranteed to satisfy the Karush-Kuhn-Tucker (KKT) conditions of P3 [27]. By using the SCAtechnique, Theorem 4 is given as follows.

Theorem 4: For any local trajectory qu, [n] , n ∈ N at theth iteration, one has

n∑i=1

P0β0

H2 + ‖qu [i]− qm‖2≥ P0β0hm [n] , (19a)

hm [n] =

n∑i=1

H2 + 2‖qu, [i]− qm‖2 − ‖qu [i]− qm‖2(

H2 + ‖qu, [i]− qm‖2)2

(19b)

where the equality holds when qu [n] = qu, [n].Proof: Let f (z) = a

b+z , where a and b are positiveconstants, and z ≥ 0. Since f (z) is convex with respect to z,the following inequality can be obtained:

a

b+ z≥ a

b+ z0− a

(b+ z0)2 (z − z0) , (20)

where z0 is a given local point. By using (20), Theorem 4 isproved.

In order to tackle the objective function of P3, Lemma 2 isgiven as follows.

Lemma 2: [27] Using the SCA method, the followinginequality can be obtained,

log2

1 +β0Pm [n]

σ20

(H2 + ‖qu [n]− qm‖2

) ≥ ym, ({qu [n]}) ,

(21a)

ym, ({qu [n]}) = log2

1 +β0Pm [n]

σ20

(H2 + ‖qu, [n]− qm‖2

)

− β0Pm [n] log2e(σ20H

2 + β0Pm [n] + σ20‖qu, [n]‖2

)(H2 + ‖qu, [n]‖2

)×(‖qu [n]‖2 − ‖qu, [n]‖2

), (21b)

where the equality holds when qu [n] = qu, [n].

TABLE I: Two-stage alternative optimization algorithm

Algorithm 1: The two-stage alternative optimization algorithm

1: Setting:P0, T , N , Vmax, q0, qF , and the tolerance errors ξ, ξ1;

2: Initialization:The iterative number i = 1, λim,n, αi

n and qiu [n];

3: Repeat 1:calculate fopt,im [n] and P opt,i

m [n] using Theorem 1for given qi

u [n];use the bisection method to solve (20) and obtain ti,optm [n];update λim,n and αi

n using the subgradient algorithm;initialize the iterative number j = 1;Repeat 2:

solve P4 by using CVX for the given fopt,im [n], P opt,im [n]

and ti,optm [n];update j = j + 1, and qj

u [n];

ifN∑

n=1

∥∥∥qju [n]− qj−1

u [n]∥∥∥ ≤ ξ

qiu [n] = qj

u [n] ;break;

endend Repeat 2

update the iterative number i = i+ 1;if∣∣Ri −Ri−1

∣∣ ≤ ξ1break;

endend Repeat 1

4: Obtain solutions:foptm [n], P opt

m [n] and toptm [n] and qoptu [n].

Using Theorem 4 and Lemma 2, P3 can be solved byiteratively solving the approximate problem P4, given as

P4 : maxqu[n]

M∑m=1

wm

[N∑n=1

BTtm [n] ym, ({qu [n]})νmN

](22a)

s.t. C4 and C5, (22b)n∑k=1

[γcf

3m [k] + tm [k]Pm [k]

]≤ η0P0β0hm [n],

m ∈M, n ∈ N . (22c)

It can be seen that P4 is convex and can be readily solved byusing CVX [4]. By solving P2 and P4, a two-stage alternative

optimization algorithm denoted by Algorithm 1 is furtherdeveloped to solve P1. The details for Algorithm 1 can befound in Table I. In Table I, Ri denotes the value of theobjective function of P1 at the ith iteration.

IV. RESOURCE ALLOCATION IN BINARY COMPUTATIONOFFLOADING MODE

In this section, the weighted sum computation bits max-imization problem is studied in the UAV-enabled wirelesspowered MEC system under the binary computation offloadingmode. The CPU frequencies of the users that choose toperform local computation, the offloading times, the transmitpowers of users that choose to perform task offloading, thetrajectory of the UAV, and the mode selection are jointlyoptimized to maximize the weighted sum computation bitsof all users. The formulated problem is a mixed integernon-convex optimization problem, for which a three-stagealternative optimization problem is proposed.

A. Resource Allocation Problem Formulation

Under the binary computation offloading mode, theweighted sum computation bit maximization problem subjectto the energy harvesting causal constraints, the UAV speed andposition constraints is formulated as P5,

P5 : maxfi[n],Pj [n],q[n],tj [n],M0,M1

∑i∈M0

N∑n=1

wifi [n]T

CN

+∑j∈M1

wjBT

νjN

N∑n=1

tj [n] log2

(1 +

hj [n]Pj [n]

σ20

)(23a)

s.t.T

N

n∑k=1

γcf3i [k] ≤ η0T

N

n∑k=1

hi [k]P0, n ∈ N , i ∈M0,

(23b)

T

N

n∑k=1

tj [k]Pj [k] ≤ η0T

N

n∑k=1

hj [k]P0, n ∈ N , j ∈M1,

(23c)∑j∈M1

tj [n] ≤ 1, n ∈ N , (23d)

M =M0 ∪M1,M0 ∩M1 = Θ, (23e)fi [n] ≥ 0, Pj [n] ≥ 0, i ∈M0, j ∈M1, (23f)C4 and C5. (23g)

(23b) and (23c) are the energy harvesting causal constraintsimposed on these users who choose to perform local computa-tion and on these users who choose to perform task offloading,respectively; (23d) is the offloading time constraint duringeach slot and (23e) is the user operation selection constraint.In P5 there exist close couplings among different optimiza-tion variables. Furthermore, the binary user operation modeselection makes P5 a mixed integer programming problem.The exhaustive search method leads to a prohibitively highcomputational complexity, especially when there exist a largenumber of users. Motivated by how we solve P1, P5 has asimilar structure as P1 when the operation modes of users

are determined. Thus, the optimal CPU frequency, transmitpower, and offloading time of users can be obtained by usingthe same method as the one used for P1 and the trajectoryoptimization for the UAV can also be achieved by using theSCA method. As such, a three-stage alternative optimizationalgorithm is proposed based on the two-stage Algorithm 1.The details for the algorithm are presented as follows.

B. Three-Stage Alternative Optimization Algorithm

In order to efficiently solve P5, a binary variable denotedby ρm is introduced, where ρm ∈ {0, 1} and m ∈ M.ρm = 0 indicates that the mth user performs local computationmode while ρm = 1 means that the mth user performs taskoffloading. Moreover, the user operation selection indicatorvariable ρm is relaxed as a sharing factor ρm ∈ [0, 1]. Thus,P5 can be rewritten as

P6 : maxfm[n],Pn[n],q[n],tm[n],ρm

M∑m=1

N∑n=1

wm

{(1− ρm)

fm [n]T

CN

+BTtm [n] ρm

νmNlog2

(1 +

hm [n]Pm [n]

σ20

)}(24a)

s.t. (1− ρm)T

N

n∑k=1

γcf3m [k] + ρm

T

N

n∑k=1

tm [k]Pm [k]

≤ η0T

N

n∑k=1

hm [k]P0,m ∈M, (24b)

M∑m=1

ρmtm [n] ≤ 1, n ∈ N , (24c)

fm [n] ≥ 0, Pm [n] ≥ 0, n ∈ N ,m ∈M, (24d)C4 and C5. (24e)

Even by relaxing the binary variable ρm, P6 is still difficultto solve as there exist couplings among different variables.For any given ρm and the trajectory of the UAV, P6 hasa similar structure as P1. Thus, using the same techniquesapplied to P1, the optimal CPU frequency, transmit powerand offloading time of users for a given ρm and the UAVtrajectory can be obtained. It is easy to verify that the optimalCPU frequency, transmit power and offloading time of usersfor a given trajectory have the same forms given by Theorem1 and Theorem 3.

Theorem 5: For any given fm [n], Pm [n], tm [n] and qu [n],the user operation selection scheme can be obtained by

ρoptm =

{0 if G1 ≥ G2,1 otherwise; (25a)

G1 =

N∑n=1

{wmfm [n]

C− υm,n

n∑k=1

γcf3m [k]

}, (25b)

G2 =

N∑n=1

{Btm [n]

νmlog2

(1 +

hm [n]Pm [n]

σ20

)

−υm,nn∑k=1

tm [k]Pm [k]− N

Tεntm [n]

}, (25c)

where υm,n ≥ 0 and εn ≥ 0 are the dual variables associatedwith the constraints given by (24b) and (24c), respectively.

Proof: See Appendix B.Remark 4: Theorem 5 indicates that the user operation

selection scheme depends on the tradeoff between the achiev-able computation rate and the operation cost. If the tradeoffof the user achieved by local computing is better than thatobtained by task offloading, the user chooses to performlocal computing; otherwise, the user chooses to offload itscomputation tasks to the UAV for computing.

Finally, the trajectory optimization for any given ρm, fm [n],Pm [n] and tm [n] can be obtained by solving P7, given as

P7 : maxqu[n]

M∑m=1

wmρm

[N∑n=1

BTtm [n] ym, ({qu [n]})νmN

](26a)

s.t. C4 and C5, (26b)

(1− ρm)

n∑k=1

γcf3m [k] + ρm

n∑k=1

tm [k]Pm [k]

≤ η0P0β0hm [n],m ∈M, n ∈ N , (26c)

where hm [n] and yj ({qu [n]}) are given by (19b) and (21b),respectively. P7 is convex and can be efficiently solved byusing CVX [4]. Based on Theorem 1, Theorem 5 and the so-lutions of P7, a three-stage alternative optimization algorithmdenoted by Algorithm 2 is proposed to solve P5. The detailsfor Algorithm 2 are presented in Table 2. In Table 2, Rl andRi denote the value of the objective function of P5 at the lthand i iteration, respectively.

C. Complexity Analysis

The complexity of Algorithm 1 comes from four aspects.The first aspect is from the computation of the CPU frequencyand the offloading power. The second aspect is from thebisection method for obtaining the offloading time. The thirdaspect is from the subgradient method for computing thedual variables. The fourth aspect comes from the applicationof CVX for solving P4. Let L1 and L2 denote the num-ber of iterations required for the outer loop and the innerloop of Algorithm 1, respectively. Let `1 and `2 denote thetolerance error for the bisection method and the subgradi-ent method, respectively. Thus, according to the works in[35], [38] and [39], the total complexity of Algorithm 1 isO[L1

(2MN +M log2 (`1/T ) + 1/`22 + L2N

3)]

and O (·)is the big-O notation [35].

The complexity of Algorithm 2 comes from five aspects.Four aspects are the same as these of Algorithm 1. The fifthaspect is from the computation of the operation selectionindicator variable ρm. Let L1, L2 and L3 denote the numberof iterations required for the first, second and third loop ofAlgorithm 2, respectively. Similar to the complexity analysisfor Algorithm 1, the total complexity of Algorithm 2 isO[L1L2

(2MN +M +M log2 (`1/T ) + 1/`22 + L3N

3)]

.

TABLE II: Three-stage alternative optimization algorithm

Algorithm 2: The three-stage alternative optimization algorithm

1: Setting:P0, T , N , Vmax, q0, qF , and the tolerance errors ξ, ξ1 and ξ2;

2: Initialization:The iterative number i = 1, υim,n and εin, and qi

u [n];3: Repeat 1:

initialize the iterative number l = 1 and ρlm;Repeat 2:calculate fopt,im [n] and P opt,i

m [n] using Theorem 1for given qi

u [n] and ρopt,lm ;use the bisection method to solve (20) and obtain ti,optm [n];update υim,n and εin using the subgradient algorithm;calculate ρopt,lm using Theorem 5 and update l = l + 1;if∣∣Rl −Rl−1

∣∣ ≤ ξbreak;

endinitialize the iterative number j = 1;

Repeat 3:solve P7 by using CVX for the given fopt,im [n], P opt,i

m [n],ti,optm [n] and ρopt,lm ;update j = j + 1, and qj

u [n];

ifN∑

n=1

∥∥∥qju [n]− qj−1

u [n]∥∥∥ ≤ ξ

qiu [n] = qj

u [n] ;break;

endend Repeat 3

update the iterative number i = i+ 1;if∣∣Ri −Ri−1

∣∣ ≤ ξ1break;

endend Repeat 2

end Repeat 14: Obtain solutions:

foptm [n], P optm [n] and toptm [n], ρoptm and qopt

u [n].

V. SIMULATION RESULTS

In this section, simulation results are presented to comparethe performance of our proposed designs with that of otherbenchmark schemes. The convergence performance of theproposed algorithms is also evaluated. The simulation settingsare based on the works in [7], [14], [16] and [23]. Thepositions of users are set as: q1 = [0, 0], q2 = [0, 10],q3 = [10, 10], q4 = [10, 0]. The detailed settings are givenin Table III. The weight vector of each user [w1 w2 w3 w4]is set as [0.1 0.4 0.3 0.2].

Fig. 3 shows the UAV trajectory under different schemeswith T = 2 seconds. The UAV transmit power is set asP0 = 0.1 W. In the constant speed scenario, the UAV fliesstraight with a constant speed from the initial position to thefinal position. In the semi-circle scenario, the UAV flies alongthe trajectory that is a semi-circle with its diameter being‖qF − q0‖. The trajectory of the offloading mode is obtainedby using Algorithm 1 for the partial computation offloadingmode and the trajectory of the binary mode is obtained byusing Algorithm 2 for the binary computation offloading mode.It can be seen from the trajectories of our proposed schemesthe UAV is always close to user 2 and user 3, irrespective of

TABLE III: Simulation ParametersParameters Notation Typical Values

Numbers of Users M 4The height of the UAV H 10 mThe time length of the UAV flying T 2 secNumbers of CPU cycles C 103 cycles/bitEnergy conversation efficiency η0 0.8Communication bandwidth B 40 MHzThe receiver noise power σ2

0 10−9 WThe number of time slots N 50The effective switched capacitance γc 10−28

The channel power gain β0 −50 dBThe tolerance error ξ, ξ1 10−4

The initial position of the UAV q0 [0, 0]The final position of the UAV qF [10, 0]The maximum speed of the UAV Vmax 20 m/s

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

x (m)

y(m

)

The offloading mode

A constant speed

A semi−circle

User 2 (0,10)

User 4 (10,0)User 1 (0,0)

User 3 (10,10)

The binary mode

Fig. 3: The trajectory of the UAV under different schemes withT = 2 seconds.

the operation modes. The reason is that the weights of user 2and user 3 are larger than these of user 1 and user 4. Thus,the UAV needs to fly close to user 2 and user 3 so as toprovide more energy to them. This indicates that the priorityand the fairness among users can be obtained by using theweight vector.

Fig. 4 shows the weighted sum computation bits of all usersversus the transmit power of the UAV under different schemes.The optimal local computing is the mode that all usersonly perform local computing while the optimal offloadingmode is that all users only perform task offloading. And thetrajectory of the UAV is jointly optimized under these twobenchmark schemes. The results under the binary mode andthe partial offloading mode are obtained by using Algorithm2 and Algorithm 1, respectively. In Fig. 4 the weighted sumcomputation bits achieved under the partial offloading mode isthe largest among these obtained by other schemes. The reasonis that all the users can dynamically select the operation modebased on the quality of the channel state information under thepartial computation offloading mode. Moreover, the optimaloffloading mode outperforms the optimal local computing.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

1.5

2

2.5

3

3.5

4

4.5x 10

7

The transmit power of the UAV (W)

Th

e w

eig

hte

d s

um

co

mp

uta

tio

n b

its

of

all u

sers

(b

its)

Optimal local computing

Optimal offloading

The binary mode

The partial offloading mode

Fig. 4: The weighted sum computation bits of all users versusthe transmit power of the UAV under different schemes.

This result is consistent with the results obtained in [13].Furthermore, the weighted sum computation bits of all usersincrease with the UAV transmit power. It can be explained bythe fact that the harvesting energy increases with the transmitpower of the UAV. Thus, users have more energy to performlocal commutating or task offloading.

Fig. 5 shows the weighted sum computation bits of all theusers versus the transmit power of the UAV under differenttrajectories with the partial computation offloading mode andthe binary computation offloading mode. As shown in Fig. 5,the weighted sum computation bits of all the users achievedby using our proposed schemes are larger than that obtainedby using the trajectory with a constant speed and than thatobtained by using the semi-circle trajectory, irrespective of theoperation modes. This indicates that the optimization of thetrajectory of the UAV can improve the weighted sum computa-tion bits. It also verifies that our proposed resource allocationscheme outperforms the disjoint optimization schemes.

Fig. 6 shows the total computation bits of each user underdifferent operation modes. The transmit power of the UAV isset as P0 = 0.1 W. The total computation bits of user 2 anduser 3 are higher than those of user 1 and user 4. The reasonis that the weights of user 2 and user 3 are larger than thoseof user 1 and user 4. Thus, the resource allocation schemeshould consider the priority of user 2 and user 3. This furtherverifies that the application of the weight vector can improvethe priority and also the fairness of users.

Fig. 7 is given to verify the efficiency of our proposedAlgorithm 1 and Algorithm 2. The transmit power of theUAV is given as 0.1 W or 0.2 W. The results show thatAlgorithm 1 and Algorithm 2 only need several iterations toconverge. This indicates that the proposed Algorithm 1 andAlgorithm 2 are computationally effective and have a fastconvergence rate. It can also be seen that the weighted sumcomputation bits of all the users achieved under the partial

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

1.5

2

2.5

3

3.5

4

4.5x 10

7

The transmit power of the UAV (W)

Th

e w

eig

hte

d s

um

co

mp

uta

tio

n b

its

of

all

us

ers

(b

its

)

The partial offloading mode

The partial offloading mode with the semi−circle trajectory

The partial offloading mode with a constant speed

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

1.5

2

2.5

3

3.5

4

4.5x 10

7

The transmit power of the UAV (W)

Th

e w

eig

hte

d s

um

co

mp

uta

tio

n b

its

of

all

us

ers

(b

its

)

The binary mode with joint optimization

The binary mode with the semi−circle trajectory

The binary mode with a constant speed

(a) (b)

Fig. 5: (a) The weighted sum computation bits of all usersversus the transmit power of the UAV under different trajec-tories with the partial computation offloading mode; (b) Theweighted sum computation bits of all users versus the transmitpower of the UAV under different trajectories with the binarycomputation offloading mode.

computation offloading mode are larger than those obtainedunder the binary computation offloading mode. The reason isthat users can simultaneously perform local computing andtask offloading when the channel state information is strongunder the partial computation offloading mode. However, userscan only perform either local computing or task offloading inthe binary offloading mode even when the channel state infor-mation is strong. The computation performance is improvedby the flexible selection of the operation mode based on thechannel state information.

User 1 User 2 User 3 User 40

1

2

3

4

5

6

7x 10

6

Users

Th

e to

tal c

om

pu

atio

n b

its

of

each

use

r (B

its)

The binary mode

The partial offloading mode

Fig. 6: The total computation bits of each user under differentoperation modes with P0 = 0.1 W.

2 4 6 8 10 12 14 16 18 201.4

1.6

1.8

2

2.2

2.4

2.6

2.8x 10

7

The number of iterations

Th

e w

eig

hte

d s

um

co

mp

uta

tio

n b

its

of

all u

sers

(b

its)

P0=0.2 W, Algorithm 1

P0=0.2 W, Algorithm 2

P0=0.1 W, Algorithm 1

P0=0.1 W, Algorithm 2

Fig. 7: The weighted sum computation bits of all users versusthe number of iterations required by using Algorithms 1 and2 under different transmit powers of the UAV and differentoperation modes.

Fig. 8 shows the weighted sum computation bits of all usersversus the number of users under different operation modes.The transmit power of the UAV is set as P0 = 0.2 W orP0 = 0.4 W. In Fig. 8 the weighted sum computation bits ofall users increase with the number of users. The reason is thatmore users can exploit the harvesting energy to perform localcomputing and computation offloading. It is also observed thatthe growth rate decreases with the increase of the number ofusers. The reason is that the offloading time allocated for eachuser decreases with the increase of the number of users sincethe total offloading time is limited by T .

Table IV is given to evaluate the run times of Algorithm 1and Algorithm 2 shown in the top of the next page. The runtimes are obtained by using a computer with 64-bit Intel(R)

2 3 4 5 6 7 8 9 10 11 121

1.5

2

2.5

3

3.5

4x 10

7

The number of users

Th

e w

eig

hte

d s

um

co

mp

uta

tio

n b

its

of

all u

sers

(b

its)

The partial offloading mode, P0=0.4 W

The binary mode, P0=0.4 W

The partial offloading mode, P0=0.2 W

The binary mode, P0=0.2 W

Fig. 8: The weighted sum computation bits of all users versusthe number of users under different transmit powers of theUAV and different operation modes.

Core(TM) i7-4790 CPU, 8 GB RAM. From Table IV wecan see that the required run time of Algorithm 1 is smallerthan that of Algorithm 2. This indicates that the complexityof Algorithm 1 is lower than that of Algorithm 2. It can beverified by the complexity analysis presented in Subsection Cof Section IV. Moreover, the effect of the number of time slotson the run time is larger than that of the number of users. Thereason is that the complexity of these two algorithms mainlydepends on the number of time slots. This can also be verifiedby the complexity analysis.

VI. CONCLUSIONS

The resource allocation problems were studied for UAV-enabled wireless powered MEC systems under both the par-tial and binary computation offloading modes. The weightedsum computation rates of users were maximized by jointlyoptimizing the CPU frequencies, the user offloading times,the user transmit powers, and the UAV trajectory Two alter-native algorithms were proposed to solve these challengingproblems. The closed-form expressions for the optimal CPUfrequencies, user offloading times, and user transmit powerwere derived. Moreover, the optimal selection scheme whetherusers choose to locally compute or offload tasks was proposedfor the binary computation offloading mode. It was shownthat the performance achieved by using our proposed resourceallocation scheme is superior to these obtained by using thedisjoint optimization schemes. Simulation results also verifiedthe efficiency of our proposed alternative algorithms and ourtheoretical analysis.

The exploitation of UAV to improve the energy conversationefficiency and the computation performance was studied in thispaper. However, the computation performance is also limitedby the flight time of the UAV. It is interesting to exploitmultiple antennas techniques to tackle this challenge. This willbe investigated in our future work.

TABLE IV: Comparison of the required run time of Algorithm 1 with that of Algorithm 2 (s)`````````Algorithms(N,M)

(50, 2) (50, 4) (50, 8) (60, 2) (60, 4) (60, 8) (70, 2) (70, 4) (70, 8)

Algorithm 1 43.72 104.54 186.38 154.74 198.65 235.85 224.74 291.53 352.72Algorithm 2 89.35 167.17 265.46 223.19 275.42 321.87 308.56 388.92 468.39

APPENDIX APROOF OF THEOREM 1

Let λm,n and αn denote the dual variables associated withthe constraint C2 and C3, respectively, where λm,n ≥ 0 andαn ≥ 0. Then, the Lagrangian of P2 can be given by (27) atthe tope of this page, where Ξ denotes a collection of all the

primal and dual variables related to P2. Let µm,n =N∑k=n

λm,k

and gm [k] = η0hm [k]P0 − γcf3m [k] − zm [k]. Then, the

Lagrangian function L (Ξ) can be rewritten by (28) at thetope of this page. And the Lagrangian dual function of P2

can be presented as

g (λm,n, αn) = max0≤fm[n]

L (Ξ). (29)

Based on (29), the optimal solutions of P2 can be obtainedby solving its dual problem, given as

minλm,n,αn

g (λm,n, αn) . (30)

It can be seen from (30) that the dual problem can bedecoupled into M independent optimization problems, givenby (31) at the tope of the next page. Thus, let the derivationof (31b) with respect to fm [n] andzm [n] be zero, one has

TwmNC

− 3Tγcf2m [k]

N

N∑k=n

λm,k = 0, (32a)

wmBTtm [n]

νmN ln 2

hm [n]

σ20tm [n] + hm [n] zm [n]

− T

N

N∑k=n

λm,k=0.

(32b)

Note that zm [k] = tm [k]Pm [k] and Pm [k] ≥ 0. Moreover,the case that tm [n] = 0 can be identified as Pm [n] = 0. Thus,based on (32), Theorem 1 is proved. The proof for Theorem1 is complete.

APPENDIX BPROOF OF THEOREM 5

Let υm,n and εn denote the dual variables with respect tothe constraints given by (24b) and (24c), respectively, whereυm,n ≥ 0 and εn ≥ 0. Then, for any given fm [n], Pm [n],tm [n] and qu [n], the Lagrangian of P6 can be expressedby (33) at the tope of the next page, where Ξ1 denotes acollection of all the primal and dual variables related to P6.Ξ2 denotes a collection of υm,n, αn, fm [n] , zm [n], tm [n] andρm. Using the same techniques that are used for the proof ofTheorem 1, for any given fm [n], zm [n], tm [n] and qu [n],P6 can be solved by solving M independent optimizationproblems, given by (34) at the tope of the next page, where`m [n] = η0hm [n]P0 − (1− ρm) γcf

3m [n] − ρmzm [n] and

$m,n =N∑k=n

υm,k. Thus, according to [37], the optimal ρm

denoted by ρoptm can be obtained by (35) at the tope of the nextpage. Based on (35), since zm [n] = tm [n]Pm [n], Theorem5 is proved.

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L (Ξ) =

M∑m=1

wm

[N∑n=1

fm [n]

C

T

N+BTtm [n]

νmNlog2

(1 +

hm [n] zm [n]

σ20tm [n]

)]

+

M∑m=1

N∑n=1

λm,n

{η0T

N

n∑k=1

hm [k]P0 −T

N

n∑k=1

[γcf

3m [k] + zm [k]

]}+

N∑n=1

αn

{1−

M∑m=1

tm [n]

}, (27)

L (Ξ) =

M∑m=1

N∑n=1

wm

{T

N

fm [n]

C+BTtm [n]

νmNlog2

(1 +

hm [n] zm [n]

σ20tm [n]

)}+µm,ngm [k] +

αnM− αntm [n]. (28)

maxλm,n,αn,fm[n]≥0

Lm (λm,n, αn, fm [n] , zm [n] , tm [n]) (31a)

Lm (λm,n, αn, fm [n] , zm [n] , tm [n]) (31b)

=

N∑n=1

{wm

{T

N

fm [n]

C+BTtm [n]

νmNlog2

(1 +

hm [n] zm [n]

σ20tm [n]

)}+µm,ngm [n] +

αnM− αntm [n]

}. (31c)

L1 (Ξ1) =

M∑m=1

wm

[(1− ρm)

N∑n=1

fm [n]

C

T

N+BTρmtm [n]

νmNlog2

(1 +

hm [n] zm [n]

tm [n]σ20

)]

+

M∑m=1

N∑n=1

υm,n

{η0T

N

n∑k=1

hm [k]P0 −T

N

n∑k=1

[(1− ρm) γcf

3m [k] + ρmzm [k]

]}

+

N∑n=1

εn

{1−

M∑m=1

ρmtm [n]

}, (33)

maxυm,n,εn,fm[n]≥0

L1m (Ξ2) (34a)

L1m (Ξ2) =

N∑n=1

wm

{T (1− ρm) fm [n]

NC+BTρmtm [n]

νmNlog2

(1 +

hm [n] zm [n]

tm [n]σ20

)}

+N∑n=1

$m,n`m [n] +εnM− εntm [n], (34b)

∂L1m (Ξ2)

∂ρoptm

< 0, ρoptm = 0,= 0, 0 < ρoptm < 1,> 0, ρoptm = 1;

m ∈M (35a)

∂L1m (Ξ2)

∂ρoptm

=

{N∑n=1

−wmfm [n]

C

T

N+BTtm [n]

νmNlog2

(1 +

hm [n] zm [n]

tm [n]σ20

)}

+

N∑n=1

υm,n

{− TN

n∑k=1

[−γcf3m [k] + zm [k]

]}−

N∑n=1

εntm [n]. (35b)

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Fuhui Zhou received the Ph. D. degree from XidianUniversity, Xian, China, in 2016. He is an associateProfessor with School of Information Engineering,Nanchang University. He is now a Research Fellowat Utah State University. He has worked as aninternational visiting Ph. D student of the Universityof British Columbia from 2015 to 2016. His researchinterests focus on cognitive radio, green communi-cations, edge computing, machine learning, NOMA,physical layer security, and resource allocation. Hehas published more than 40 papers, including IEEE

Journal of Selected Areas in Communications, IEEE Transactions on WirelessCommunications, IEEE Wireless Communications, IEEE Network, IEEEGLOBECOM, etc. He has served as Technical Program Committee (TPC)member for many International conferences, such as IEEE GLOBECOM,IEEE ICC, etc. He serves as an Associate Editor of IEEE Access.

Yongpeng Wu (S’08–M’13–SM’17) received theB.S. degree in telecommunication engineering fromWuhan University, Wuhan, China, in July 2007,the Ph.D. degree in communication and signal pro-cessing with the National Mobile CommunicationsResearch Laboratory, Southeast University, Nanjing,China, in November 2013.

Dr. Wu is currently a Tenure-Track AssociateProfessor with the Department of Electronic Engi-neering, Shanghai Jiao Tong University, China. Pre-viously, he was senior research fellow with Institute

for Communications Engineering, Technical University of Munich, Germanyand the Humboldt research fellow and the senior research fellow with Institutefor Digital Communications, University Erlangen-Nurnberg, Germany. Duringhis doctoral studies, he conducted cooperative research at the Departmentof Electrical Engineering, Missouri University of Science and Technology,USA. His research interests include massive MIMO/MIMO systems, physicallayer security, signal processing for wireless communications, and multivariatestatistical theory.

Dr. Wu was awarded the IEEE Student Travel Grants for IEEE Inter-national Conference on Communications (ICC) 2010, the Alexander vonHumboldt Fellowship in 2014, the Travel Grants for IEEE CommunicationTheory Workshop 2016, and the Excellent Doctoral Thesis Awards of ChinaCommunications Society 2016. He was an Exemplary Reviewer of the IEEETransactions on Communications in 2015, 2016. He is the lead guest editorfor the upcoming special issue “Physical Layer Security for 5G WirelessNetworks” of the IEEE Journal on Selected Areas in Communications. He iscurrently an editor of the IEEE Access and IEEE Communications Letters. Hehas been a TPC member of various conferences, including Globecom, ICC,VTC, and PIMRC, etc.

Rose Qingyang Hu is a Professor of Electri-cal and Computer Engineering Department at UtahState University. She received her B.S. degree fromUniversity of Science and Technology of China,her M.S. degree from New York University, andher Ph.D. degree from the University of Kansas.She has more than 10 years of R&D experiencewith Nortel, Blackberry and Intel as a technicalmanager, a senior wireless system architect, anda senior research scientist, actively participating inindustrial 3G/4G technology development, standard-

ization, system level simulation and performance evaluation. Her currentresearch interests include next-generation wireless communications, wirelesssystem design and optimization, green radios, Internet of Things, Cloudcomputing/fog computing, multimedia QoS/QoE, wireless system modelingand performance analysis. She has published over 180 papers in top IEEEjournals and conferences and holds numerous patents in her research areas.Prof. Hu is an IEEE Communications Society Distinguished Lecturer Class2015-2018 and the recipient of Best Paper Awards from IEEE Globecom2012, IEEE ICC 2015, IEEE VTC Spring 2016, and IEEE ICC 2016.

Yi Qian received a Ph.D. degree in electrical engi-neering from Clemson University. He is a professorin the Department of Electrical and Computer En-gineering, University of Nebraska-Lincoln (UNL).Prior to joining UNL, he worked in the telecommu-nications industry, academia, and the government.Some of his previous professional positions includeserving as a senior member of scientific staff and atechnical advisor at Nortel Networks, a senior sys-tems engineer and a technical advisor at several start-up companies, an assistant professor at University

of Puerto Rico at Mayaguez, and a senior researcher at National Institute ofStandards and Technology. His research interests include information assur-ance and network security, network design, network modeling, simulation andperformance analysis for next generation wireless networks, wireless ad-hocand sensor networks, vehicular networks, smart grid communication networks,broadband satellite networks, optical networks, high-speed networks and theInternet. Prof. Yi Qian is a member of ACM and a senior member of IEEE.He was the Chair of IEEE Communications Society Technical Committee forCommunications and Information Security from January 1, 2014 to December31, 2015. He is a Distinguished Lecturer for IEEE Vehicular TechnologySociety and IEEE Communications Society. He is serving on the editorialboards for several international journals and magazines, including serving asthe Associate Editor-in-Chief for IEEE Wireless Communications Magazine.He is the Technical Program Chair for IEEE International Conference onCommunications (ICC) 2018.