THE Internet of Things (IoT) has been widely developed

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1 Coputation Rate Maxiization in UAV-Enabled Wireless Powered Mobile-Edge Coputing Systes Fuhui Zhou, Meber, IEEE, Yongpeng Wu, Senior Meber, IEEE, Rose Qingyang Hu, Senior Meber, IEEE, and Yi Qian, Senior Meber, IEEE arxiv: v [eess.sp] 17 Jul 018 Abstract Mobile edge coputing MEC) and wireless power transfer WP) are two proising techniques to enhance the coputation capability and to prolong the operational tie of low-power wireless devices that are ubiquitous in Internet of hings. However, the coputation perforance and the harvested energy are significantly ipacted by the severe propagation loss. In order to address this issue, an unanned aerial vehicle UAV)-enabled MEC wireless powered syste is studied in this paper. he coputation rate axiization probles in a UAV-enabled MEC wireless powered syste are investigated under both partial and binary coputation offloading odes, subject to the energy harvesting causal constraint and the UAV s speed constraint. hese probles are non-convex and challenging to solve. A two-stage algorith and a three-stage alternative algorith are respectively proposed for solving the forulated probles. he closed-for expressions for the optial central processing unit frequencies, user offloading tie, and user transit power are derived. he optial selection schee on whether users choose to locally copute or offload coputation tasks is proposed for the binary coputation offloading ode. Siulation results show that our proposed resource allocation schees outperfors other benchark schees. he results also deonstrate that the proposed schees converge fast and have low coputational coplexity. Index ers Mobile-edge coputing, wireless power transfer, unanned aerial vehicle-enabled, resource allocation, binary Manuscript received January 4, 018; revised May 1, 018 and accepted June 4, 018. Date of publication ****; date of current version ****. he research of F. Zhou was supported in part by the atural Science Foundation of China under Grant , in part by the Young atural Science Foundation of Jiangxi Province under Grant 0171BAB100, in part by he Open Foundation of he State Key Laboratory of Integrated Services etworks under Grant IS19-08, and in part by he Postdoctoral Science Foundation of Jiangxi Province under Grant 017M610400, Grant 017KY04 and Grant 017RC17. he research of Y. Wu was supported by the atural Science Foundation of China under Grant and in part by Young Elite Scientist Sponsorship Progra by CAS. he research of Prof. R. Q. Hu was supported in part by the ational Science Foundation under Grants EECS , es , EARS and the atural Science Foundation of China under Grant he research of Prof. Y. Qian was supported by the ational Science Foundation under Grants EECS , es and EARS he corresponding author is Yongpeng Wu. F. Zhou is with the Departent of Electrical and Coputer Engineering as a Research Fellow at Utah State University, U.S.A. F. Zhou is also with the School of Inforation Engineering, anchang University, P. R. China, He is also with State Key Laboratory of Integrated Services etworks, Xidian University, Xian, , P. R. China e-ail: zhoufuhui@ieee.org). Y. Wu is with Shanghai Key Laboratory of avigation and Location Based Services, Shanghai Jiao ong University, Minhang, 0040, China Eail:yongpeng.wu016@gail.co). R. Q. Hu is with the Departent of Electrical and Coputer Engineering, Utah State University, USA. e-ail: rose.hu@usu.edu). Y. Qian is with the Departent of Electrical and Coputer Engineering, University of ebraska-lincoln, Oaha, E 6818, USA. E-ail: yqian@unl.edu). coputation offloading, partial coputation offloading. I. IRODUCIO HE Internet of hings Io) has been widely developed with the unprecedented proliferation of obile devices, such as sart phones, cloud-based obile sensors, tablet coputers and wearable devices, which facilitates the realization of sart environent e.g. sart city, sart hoe, sart transportation, etc.) [1]. Io enables obile users to experience intelligent applications e.g., autoatic navigation, face recognition, unanned driving, etc.) and to enjoy diverse services with high quality of service QoS) such as obile online gaing, augented reality, etc. hese services norally require a assive nuber of size-constrained and low-power obile devices to perfor coputation-intensive and latencysensitive tasks []. However, it is challenging for obile devices to perfor these services due to their low coputing capability and finite battery lifetie. Mobile edge coputing MEC) and wireless power transfer WP) have been deeed two proising technologies to tackle the above entioned challenges []-[4]. Recently, MEC has received an ever-increasing level of attention fro industry and acadeia since it can significantly iprove the coputation capability of obile devices in a cost-effective and energy-saving anner []. It enables obile devices to offload partial or all of their coputation-intensive tasks to MEC servers that locate at the edge of the wireless network, such as cellular base stations BSs) and access points APs). Different fro the conventional cloud coputing, MEC servers are deployed in a close proxiity to end users. hus, MEC has the potential to provide low-latency services, to save energy for obile users, and to achieve high security []. Up to now, there are a nuber of leading copanies e.g., IBM, Intel, and Huawei) that have identified MEC as a proising technique for the future wireless counication networks. In general, MEC has two operation odes, naely, partial and binary coputation offloading. In the first ode, the coputation task can be partitioned into two parts, and one part is locally executed while the other part is offloaded to the MEC servers for coputing [5]-[9]. For the second ode, coputation tasks cannot be partitioned. hus they can be either executed locally or copletely offloaded [10]. On the other hand, WP can provide low-power obile devices with sustainable and cost-effective energy supply by using radio-frequency RF) signals [3]. It facilitates a perpetual

2 operation and enables users to have high QoE, especially in the case that obile devices do not have sufficient battery energy for offloading task or taking the services when the battery energy is exhausted. Copared to the conventional energy harvesting techniques, such as solar or wind charging, WP is ore attractive since it can provide a controllable and stable power supply [4]. It is envisioned that the coputation perforance can be significantly iproved by integrating WP into MEC networks [11]-[16]. However, the harvested power level can be significantly degraded by the severe propagation loss. Recently, an unanned aerial vehicle UAV)- enabled WP architecture has been proposed to iprove the energy transfer efficiency [17]-[0]. It utilizes an unanned aerial vehicle UAV) as an energy transitter for powering the ground obile users. It was shown that the harvested power level can be greatly iproved due to the fact that there is a high possibility that short-distance line-of-sight LoS) energy transit links exist [17]-[0]. Moreover, the coputation perforance can also be iproved by using the UAV-assisted MEC architecture [1]-[5]. Furtherore, UAVassisted architectures can provide flexible deployent and low operational costs, and are particularly helpful in the situations that the conventional counication systes are destroyed by natural disasters [6]-[3]. Motivated by the above entioned reasons, a UAV-enabled and wireless powered MEC network is studied in this paper. In order to axiize the achievable coputation rate, the counication and coputation resources and the trajectory of the UAV are jointly optiized under both partial and binary coputation offloading odes. o the authors best knowledge, this is the first work that considers the UAV-enabled wireless powered MEC network and studies the coputation rate axiization probles in this type of network. A. Related Work and Motivation In wireless powered MEC systes, it is of great iportance to design resource allocation schees so as to efficiently exploit energy, counication, and coputation resources and iprove the coputation perforance. Resource allocation probles have been extensively investigated in the conventional MEC networks [5]-[10] and also in MEC networks relying on energy harvesting [11]-[16]. Recently, efforts have also been dedicated to designing resource allocation and trajectory schees in UAV-enabled wireless powered counications network [17]-[0] and UAV-assisted MEC networks [1]-[5]. hese contributions are suarized as follows. In MEC networks, the counication and coputation resources and the selection of the offloading ode were jointly optiized to achieve the objective of the syste design, e.g., the users consuption energy iniization [5], [6], the revenue axiization [7], the axiu cost iniization [8], etc. Specifically, in [5], the total energy of all users in a ulti-cell MEC network was iniized by jointly optiizing the user transit precoding atrices and the central processing unit CPU) frequencies of the MEC server allocated to each user. It was shown that the perforance achieved by jointly optiizing the counication and coputation resources is superior to that obtained by optiizing these resources separately. he authors in [6] extended the energy iniization proble into the ulti-user MEC systes with tie-division ultiple access DMA) and orthogonal frequency-division ultiple access OFDMA), respectively. It was proved that the optial offloading policy has a threshold-based structure, which is related to the channel state inforation CSI) [6]. Particularly, obile users offload their coputation tasks when the channel condition is strong; otherwise, they can locally execute the coputation tasks. In [7], the revenue of the wireless cellular networks with MEC was axiized by jointly designing the coputation offloading decision, resource allocation, and content caching strategy. he works in [5]- [7] focused on optiizing a single objective, which overephasizes the iportance of one etric and ay not achieve a good tradeoff aong ultiple etrics. Recently, the authors in [8] and [9] studied the fairness and ulti-objective optiization proble in MEC networks. It was shown that there exist ultiple tradeoffs in MEC systes, such as the tradeoff between the total coputation rate and the fairness aong users. Different fro the works in [5]-[9], MEC systes with the binary coputation offloading ode were considered and the optial resource allocation strategy was designed to iniize the consuption energy in [10]. Energy harvesting was not considered in the MEC systes [5]-[10]. Recently, the authors in [11]-[16] have studied the resource allocation proble in various MEC systes relying on energy harvesting. In [11] and [1], he reinforceent learning and Lyapunov optiization theory were used to design resource allocation schees in MEC systes relying on the conventional energy harvesting techniques. Different fro [11] and [1], the resource allocation probles were studied in wireless powered MEC systes [13]-[16]. Specifically, the authors in [13] proposed an energy-efficient coputing fraework in which the energy consued for local coputing and task offloading is fro the harvested energy. he consued energy was iniized by jointly optiizing the CPU frequency and the ode selection. In [14], the energy iniization proble was extended into a ulti-input single-out wireless powered MEC syste, and the offloading tie, the offloading bits, the CPU frequency and the energy beaforing were jointly optiized. Unlike [14], energy efficiency was defined and axiized in a full-duplex wireless powered MEC syste by jointly optiizing the transission power, offloaded bits, coputation energy consuption, tie slots for coputation offloading and energy transfer [15]. In contrast to the work in [13]-[15], the coputation bits were axiized in a wireless powered MEC syste under the binary coputation offloading ode [16]. wo sub-optial algoriths based on the alternating direction ethod were proposed to solve the cobinatorial prograing proble. he proposed algoriths actually did not provide the optial selection schee for the user operation ode. Although WP has been exploited to iprove the coputation perforance of MEC systes [13]-[16], the energy

3 harvested by using WP can be significantly degraded by the severe propagation loss. he energy conversion efficiency is low when the distance between the energy transitter and the harvesting users is large. In order to tackle this challenge, the authors in [17]-[0] proposed a UAV-enabled wireless powered architecture where a UAV transits energy to the harvesting users. Due to the high possibility of having line-of-sight LoS) air-to-ground energy harvesting links, the harvesting energy can be significantly iproved by using this architecture. Moreover, it was shown that the harvesting energy can be further iproved by optiizing the trajectory of the UAV [18]-[0]. hus, it is envisioned that the application of the UAV-enabled architecture into wireless powered MEC systes is proising and valuable to be studied [6]. However, to the authors best knowledge, few investigations have focused on this area. Recently, the UAV-enabled MEC systes have been studied and their resource allocation schees have been proposed [1]-[5]. In [1], the UAV-enabled MEC architecture was first proposed and the coputation perforance was iproved by using UAV. he authors in [] proposed a new caching UAV fraework to help sall cells to offload traffic. It was shown that the throughput can be greatly iproved while the overload of wireless backhaul can be significantly reduced. In order to further iprove the coputation perforance, the authors in [3] and [4] designed a resource allocation schee that jointly optiizes the CPU frequency and the trajectory of the UAV. In [5], a theoretical gae ethod was applied to design a resource allocation schee for the UAVenabled MEC syste and the existence of ash Equilibriu was deonstrated. Although resource allocation probles have been well studied in MEC systes [5]-[10], MEC systes relying on energy harvesting [11]-[16] and UAV-enabled MEC systes [1]- [5], few investigations have been conducted for designing resource allocation schees in the UAV-enabled wireless powered MEC systes. Moreover, resource allocation schees proposed in the above-entioned works are inappropriate to UAV-enabled MEC wireless powered systes since the coputation perforance not only depends on the optiization of energy, counication and coputation resources, but also relies on the design of the UAV trajectory. Furtherore, the application of UAV into wireless powered MEC systes has the potential to enhance the user coputation capability since it can iprove the energy conversion efficiency and task offloading efficiency [33], [34]. hus, in order to iprove the coputation perforance and provide obile users with high QoE, it is of great iportance and worthiness to study resource allocation probles in UAV-enabled wireless powered MEC systes. However, these probles are indeed challenging to tackle. he reasons are fro two aspects. On one hand, there exists dependence aong different variables e.g., the CPU frequency, the task offloading tie and the variables related to the trajectory of the UAV), which akes the probles non-convex. On the other hand, when the binary coputation offloading ode is applied, the resource allocation probles in UAV-enabled wireless powered MEC systes have binary variables related to the selection of either local coputation or offloading tasks. It akes the proble a ixed integer nonconvex optiization proble. B. Contributions and Organization In contrast to [5]-[16], this paper studies the resource allocation proble in UAV-enabled wireless powered MEC systes, where a UAV transits energy signals to charge ultiple obile users and provides coputation services for the. Although the coputation perforance is liited by the flight tie of the UAV, it is worth studying UAVenabled wireless powered MEC systes since these systes are proising in environents such as ountains and desert areas, where no terrestrial wireless infrastructures exist, and in environents where the terrestrial wireless infrastructures are destroyed due to the natural disasters [33], [34]. hus, in this paper, the weighted su coputation bits of all users are axiized under both partial and binary coputation offloading odes. he ain contributions of this work are suarized as follows: 1) It is the first tie that the resource allocation fraework is forulated in UAV-enabled MEC wireless powered systes under both partial and binary coputation offloading odes. he weighted su coputation bits are axiized by jointly optiizing the CPU frequencies, the offloading ties and the transit powers of users as well as the UAV trajectory. Under the partial coputation offloading ode, a two-stage alternative algorith is proposed to solve the non-convex and challenging coputation bits axiization proble. he closedfor expressions for the optial CPU frequencies, the offloading ties and the transit powers of users are derived for any given trajectories. ) Under the binary coputation offloading ode, the weighted su coputation bits axiization proble is a ixed integer non-convex optiization proble, for which a three-stage alternative algorith is proposed. he optial selection schee on whether users choose to locally copute or offload tasks is derived in a closedfor expression for a given trajectory. he structure for the optial selection schee shows that whether users choose to locally copute or offload their tasks to the UAV for coputing depends on the tradeoff between the achievable coputation rate and the operation cost. Moreover, the trajectory of the UAV is optiized by using the successive convex approxiation SCA) ethod under both partial and binary coputation offloading odes. 3) he siulation results show that the coputation perforance obtained by using the proposed resource allocation schee is better than these achieved by using the disjoint optiization schees. Moreover, it only takes several iterations for the proposed alternative algoriths to converge. Furtherore, siulation results verify that the priority and fairness of users can be iproved by

4 x z User 1 y User Use Use M Wireless powered link Coputation offloading link Fig. 1: he syste odel. Energy harvesting Local coputing Use using the weight vector. Additionally, it is shown that the total coputation bits increase with the nuber of users. he reainder of this paper is organized as follows. Section II gives the syste odel. he resource allocation proble is forulated under the partial coputation offloading ode in Section III. Section IV forulates the resource allocation proble under the binary coputation offloading ode. Siulation results are presented in Section V. Finally, our paper is concluded in Section VI. II. SYSEM MODEL A UAV-enabled wireless powered MEC syste is considered in Fig. 1, where an RF energy transitter and an MEC server are ipleented in UAV. he UAV transits energy to M users and provides MEC services for these users. Each user has an energy harvesting circuit and can store energy for its operation. he UAV has an on-board counication circuit and an on-board coputing processor. So does each user. he coputing processor of each user is an on-chip icroprocessor that has low coputing capability and can locally execute siple tasks. he UAV has a powerful processor that can perfor coputation-intensive tasks [1]-[5]. Siilar to [13]-[16], each user can siultaneously perfor energy harvesting, local coputing and coputation offloading while the UAV can siultaneously transit energy and perfor coputation. In this paper, all devices are equipped with a single antenna. Without loss of generality, a three-diensional 3D) Euclidean coordinate is adopted. Each user s location is fixed on the ground. he location of the th ground user is denoted by q, where q = [x, y ], M and M = {1,,, M}. Boldface lower case letters represent vectors and boldface upper case letters represent atrices. x and y are the horizontal plane coordinates of the th ground user. It is assued that user positions are known to the UAV for designing the trajectory [18]-[0]. A finite tie horizon with duration is considered. During, the UAV flies at the sae altitude level denoted by H H > 0). In practice, the fixed altitude is the iniu altitude that is appropriate to the work terrain and can avoid building without the requireent of frequent aircraft descending and ascending. A block fading channel odel is applied, i.e., during each, the channel reains static. For the ease of exposition, the finite tie is discretized into equal tie slots, denoted by n = 1,,,. At the nth slot, it is assued that the horizontal plane coordinate of the UAV is q u [n] = [x u [n], y u [n]]. Siilar to [7]-[3], it is assued that the wireless channel between the UAV and each user is doinated by LOS. hus, the channel power gain between the UAV and the th user, denoted by h [n], can be given as h [n] = β 0 d β 0,n = H + q u [n] q, M, n, where β 0 is the channel power gain at a reference distance d 0 = 1 ; d,n is the horizontal plane distance between the UAV and the th user at the nth slot, n, = {1,,, }; denotes its Euclidean nor. he details for the UAV-enabled wireless powered MEC syste are presented under partial and binary coputation offloading odes in the following, respectively. A. Partial Coputation Offloading Mode Under the partial coputation offloading ode, the coputation task of each user can be partitioned into two parts, one for local coputing and one for offloading to the UAV. he energy consued for local coputing and task offloading coes fro the harvested energy. In this paper, in order to shed eaningful insights into the design of a UAV-enabled wireless powered MEC syste, siilar to [4], [13]-[16], the linear energy harvesting odel is applied. hus, the harvested energy E [n] at the th user during n tie slots is given as η 0 h [i] P 0 E [n] =, M, n, ) i=1 where η 0 denotes the energy conservation efficiency, 0 < η 0 1 and P 0 is the transit power of the UAV. In this paper, the UAV eploys a constant power transission [18]-[0]. he details for the operation of each user under the partial coputation offloading ode are presented as follows. 1) Local Coputation: Siilar to [14]-[16], the energy harvesting circuit, the counication circuit, and the coputation unit are all separate. hus, each user can siultaneously perfor energy harvesting, local coputing, and coputation offloading. Let C denote the nuber of CPU cycles required for coputing one bit of raw data at each user. In order to efficiently use the harvested energy, each user adopts a dynaic voltage and frequency scaling technique and then can adaptively control the energy consued for perforing local coputation by adjusting the CPU frequency during each tie slot [14]-[16]. he CPU frequency of the th user during 1)

5 he first slot he second slot... he n th slot User1 UAV Offloading UserM UAV... UAV User1... UAV UserM Offloading Download Download... t M 1 t he th slot Fig. : he DMA protocol for ultiuser coputation offloading. the nth slot is denoted by f [n] with a unit of cycles per second. hus, the total coputation bits executed at the th user during n slots and the total consued energy at the th f user during n slots are respectively given as [k] C and γ c f 3 [k] [14]-[16], where γ c is the effective capacitance coefficient of the processor s chip at the th user, n, M. ote that γ c is dependent of the chip architecture of the th user. ) Coputation Offloading: In order to avoid interference aong users during the offloading process, a DMA protocol shown in Fig. is applied. Specifically, each tie slot consists of three stages, naely, the offloading stage, the coputation stage, and the downloading stage. In the offloading stage, M users offload their respective coputation task one by one during each slot. Let t [n] / 0 t [n] 1) denote the duration in which the th user offloads its coputation task to the UAV at the nth slot, n, M. Siilar to [16], the coputation task of the th user to be offload is coposed of raw data and counication overhead, such as the encryption and packer header. Let ν R [n] denote the total nuber of bits that the th user offloads to the UAV during the nth slot, where R [n] is the nuber of raw data to be coputed at the UAV and ν indicates the counication overhead included in the offloading task. hus, one has R [n] B t [n] ν log 1 + h ) [n] P [n] σ0, n, M, 3) where B is the counication bandwidth; P [n] is the transit power of the th user at the nth slot and σ 0 denotes the noise power at the th user. After all users offload their coputation tasks at the nth slot, the UAV perfors coputing task and sends the coputing results back to all the users. Siilar to [14]-[16], the coputation tie and the downloading tie of the UAV are neglected since the UAV has a uch stronger coputation capability than the users and the nuber of the bits related to the coputation result is very sall. Since the total offloading tie of all users does not exceed the duration of one tie slot, one has t [n] 1, n. 4) =1 Since the energy consued for local coputing and task offloading coes fro the harvested energy, the following energy harvesting causal constraint should be satisfied. [ γc f 3 [k] + t [k] P [k] ] η 0 h [k] P 0, n, M. 5) Under the partial coputation offloading ode, the total coputation bits R of the th user is given as R = f [n] C B. Binary Coputation Offloading Mode + B t [n] ν log 1 + h ) [n] P [n] σ0, M. 6) Under the binary coputation offloading ode, the coputation task cannot be partitioned. All the users need to choose to either locally copute the task copletely or offload the entire task. his case can be widely experienced in practice. For exaple, in order to iprove the estiation accuracy, the raw data saples that are correlated need to be jointly coputed altogether [10], [16]. Let M 0 and M 1 denote the set of users that choose to perfor local coputation and the set of users that choose to perfor task offloading, respectively. hus, M = M 0 M 1 and M 0 M 1 = Θ, where Θ denotes the null set. 1) Users Choosing to Perfor Local Coputing: In this case, a user in M 0 exploits all the harvested energy to perfor local coputing. hus, the total coputation rate of the ith user denoted by Ri L can be given as R L i = f i [n] C, i M 0. 7) And the energy harvesting causal constraint for a user in M 0 can be given as γ c f 3 i [k] η 0 h i [k] P 0, n, i M i. 8) ) Users Choosing to Perfor ask Offloading: Each user in M 1 exploits all the harvested energy to perfor task offloading. he DMA protocol is applied to avoid interference aong these users during the offloading process. Since the total offloading tie of all users in M 1 at the nth slot cannot exceed the duration of a tie slot, one has j M 1 t j [n] 1, n. 9)

6 Let Rj O denote the total coputation rate of the jth user in the set M 1. hen, one has Rj O B t j [n] = ν j log 1 + h ) j [n] P j [n] σ0, j M 1. 10) he energy harvesting causal constraint for a user in M 1 can be given as t j [k] P j [k] η 0 h j [k] P 0, n, j M 1. 11) Sections III and IV will respectively forulate the coputation rate axiization proble for the partial and binary coputation offloading odes. III. RESOURCE ALLOCAIO UDER HE PARIAL COMPUAIO OFFLOADIG MODE In this section, the resource allocation proble is studied under the partial coputation offloading ode. he weighted su coputation bits are axiized by jointly optiizing the CPU frequencies, the offloading ties and the transit powers of users as well as the trajectory of the UAV. In order to tackle this non-convex proble, a two-stage alternative algorith is proposed. A. Resource Allocation Proble Forulation Under the partial coputation offloading ode, the weighted su coputation bits axiization proble in the UAV-enabled wireless powered MEC syste is forulated as P 1, P 1 : [ ax f [n],p [n],q u[n],t [n] f [n] C w =1 + B t [n] ν log 1 + h ) ] [n] P [n] σ0 1a) s.t. C1 : f [n] 0, P [n] 0, M, n, 1b) C : [ γc f 3 [k] + t [k] P [k] ] η 0 h [k] P 0 C3 : t [n] 1, n, =1 M, n, C4 : q u [n + 1] q u [n] V ax, n, C5 : q u [1] = q 0, q u [ + 1] = q F, 1c) 1d) 1e) 1f) where V ax denotes the axiu speed of the UAV in the unit of eter per second; q 0 and q F are the initial and final horizontal locations of the UAV, respectively. In 1), w denotes the weight of the th user, which takes the priority and the fairness aong users into consideration. C1 is the CPU frequency constraint and the coputation offloading power constraint iposed on each user; C represents the energy harvesting causal constraint; C3 is the tie constraint that the total tie of all users offloading the coputation bits cannot exceed the duration of each tie slot; C4 and C5 are the speed constraint and the initial and final horizontal location constraint of the UAV, respectively. P 1 is non-convex since there exist non-linear couplings aong the variables, f [n], P [n],q u [n], t [n] and the objective function is non-concave with respect to the trajectory of the UAV. In order to solve it, a two-stage alternative optiization algorith is proposed. he details for the algorith are presented as follows. B. wo-stage Alternative Optiization Algorith Let z [n] = t [n] P [n], n. For a given trajectory, P 1 can be transfored into P. P : ax f [n],z [n],t [n] [ s.t. C1, C3, C5 : f [n] C =1 w + B t [n] ν log [ γc f 3 [k] + z [k] ] η h ) ] [n] z [n] t [n] σ0 13a) 13b) h [k] P 0, M, n. 13c) It is easy to prove that P is convex and can be solved by using the Lagrange duality ethod [35], based on which the optial solutions for the CPU frequency and the transit power can [n] denote the optial CPU frequency and transit power of the th user at the nth tie slot, respectively, where M and n. By solving P, heore 1 can be stated as follows. heore 1: For a given trajectory q u [n], the optial CPU frequency and transit power of users can be respectively expressed as be derived. Let f opt f opt [n] = [n] = P opt [n] and P opt w, 3Cγ c λ,k k=n 0, if t [n] = 0, w B ν ln k=n σ 0 h [n] λ,k +, otherwise, 14a) 14b) where λ,n 0 is the dual variable associated with the constraint C; [a] + = ax a, 0) and ax a, 0) denotes the bigger value of a and 0. Proof: See Appendix A. Reark 1: It can be seen fro heore 1 that users choose to offload their coputation tasks only when the channel state inforation between users and the UAV is stronger ) than a threshold, naely, h [n] σ0ν ln λ,k / w B). k=n

7 his indicates that the user chooses to perfor local coputation when the horizontal distance between the user and the UAV is larger than H. Moreover, β 0w B σ 0 ν ln λ,k k=n it can be seen that the larger the weight is, the higher the chance for the user to chooses to offload its coputation task. Furtherore, users prefers to offload their coputation task when the local coputation frequency is very large, naely, f opt σ 0 ν ln 3Cγ cbh [n]. [n] heore : If there exists a tie slot that f opt equation f opt [k] = 0 ust hold, 0 k n. [n] = 0, the Proof: Since λ,n is the dual variable and λ,n 0, fro heore 1 f opt [n] increases with n. hus, if there exists a tie slot n so that f opt [n] = 0, one ust have f opt [k] = 0, for 0 k n. heore is proved. Reark : heore indicates that the user CPU frequency increases with the tie slot index. his eans that the nuber of coputation bits obtained by local coputing increases with the tie slot index. Moreover, the user CPU frequency increases with the weight assigned to that user since ore resources are allocated to the user with a higher weight. heore 3: For a given trajectory q u [n], the optial user offloading tie can be obtained by solving the following equation. log 1 + h ) [n] z [n] σ0 t [n] ν α n B h [n] z [n] ln {σ 0 t [n] + h [n] z [n]} = 0. 15) Reark 3: heore 3 can be readily proved based on the proof for heore 1. hus this proof is oitted for the sake of saving space. Moreover, 15) can be solved by using the bisection ethod [35]. he values of the dual variables are needed in order to obtain the optial CPU frequency, the optial transit power and the optial offloading tie for all users. he subgradient ethod in Lea 1 can be used to tackle this proble [36]. Lea 1: he subgradient ethod for obtaining the dual variables is given as λ,n l + 1) = [λ,n l) θ l) λ,n l)] +, M, n 16a) α n l + 1) = [α n l) ϑ l) α n l)] +, n, 16b) where l denotes the iteration index; θ l) and ϑ l) represent the iterative steps at the lth iteration. In 16), λ,n l) and α n l) are the corresponding subgradients, given as λ,n l) = η 0 α n l) = 1 h [k] P 0 [ =1 γ c f l,opt [k] ) ] 3 + l,opt z [k], 17a) t l,opt [n], n, 17b) where f l,opt [n], z l,opt [n], and t l,opt [n] denote the optial solutions at the lth iterations. According to [35], the subgradient guarantees to converge to the optial value with a very sall error range. C. rajectory Optiization For any given CPU frequency, transit power, and offloading tie of users, the trajectory optiization proble can be forulated as P 3. P 3 : ax w q u[n] =1 B t [n] ν log 1 + s.t. C : η 0 C4 and C5. σ 0 [ γc f 3 [k] + t [k] P [k] ] β 0 P [n] H + q u [n] q ) 18a) β 0 P 0 H, M, n 18b) + q u [k] q 18c) Since C is non-convex and the objective function is nonconcave with respect to q u [n], P 3 is non-convex and we use the SCA technique to solve the optiization proble. he obtained solutions can be guaranteed to satisfy the Karush- Kuhn-ucker KK) conditions of P 3 [7]. By using the SCA technique, heore 4 is given as follows. heore 4: For any local trajectory q u,j [n], n at the jth iteration, one has P 0 β 0 i=1 H + q u [i] q P 0β 0 h [n], 19a) H + q u,j [i] q q u [i] q h [n] = H + q u,j [i] q ) i=1 19b) where the equality holds when q u [n] = q u,j [n]. Proof: Let f z) = a b+z, where a and b are positive constants, and z 0. Since f z) is convex with respect to z, the following inequality can be obtained: a b + z a b + z 0 a b + z 0 ) z z 0), 0) where z 0 is a given local point. By using 0), heore 4 is proved. In order to tackle the objective function of P 3, Lea is given as follows.

8 Lea : [7] Using the SCA ethod, the following inequality can be obtained, β 0 P [n] log 1 + H + q u [n] q ) y,j {q u [n]}), σ 0 y,j {q u [n]}) = log 1 + σ 0 1a) β 0 P [n] H + q u,j [n] q ) β 0 P [n] log e σ 0 H + β 0 P [n] + σ 0 q u,j [n] ) H + q u,j [n] ) q u [n] q u,j [n] ), where the equality holds when q u [n] = q u,j [n]. ABLE I: wo-stage alternative optiization algorith Algorith 1: he two-stage alternative optiization algorith 1: Setting: P 0,,, V ax, q 0, q F, and the tolerance errors ξ, ξ 1 ; : Initialization: he iterative nuber i = 1, λ i,n, αi n and qi u [n]; 3: Repeat 1: calculate f opt,i for given q i u [n]; [n] and P opt,i [n] using heore 1 use the bisection ethod to solve 0) and obtain t i,opt update λ i,n and αi n using the subgradient algorith; initialize the iterative nuber j = 1; Repeat : [n]; solve P 4 by using CVX for the given f opt,i [n], P opt,i [n] and t i,opt [n]; update j = j + 1, and q j u [n]; if q j u [n] q j 1 u [n] ξ q i u [n] = qj u [n] ; break; end end Repeat update the iterative nuber i = i + 1; if R i R i 1 ξ1 break; end end Repeat 1 4: Obtain solutions: f opt [n], P opt [n] and t opt [n] and q opt u [n]. 1b) Using heore 4 and Lea, P 3 can be solved by iteratively solving the approxiate proble P 4, given as [ ] B t [n] y,j {q u [n]}) P 4 : ax w a) q u[n] ν =1 s.t. C4 and C5, b) [ γc f 3 [k] + t [k] P [k] ] η 0 P 0 β 0 h [n], M, n. c) It can be seen that P 4 is convex and can be readily solved by using CVX [4]. By solving P and P 4, a two-stage alternative optiization algorith denoted by Algorith 1 is further developed to solve P 1. he details for Algorith 1 can be found in able I. In able I, R i denotes the value of the objective function of P 1 at the ith iteration. IV. RESOURCE ALLOCAIO I BIARY COMPUAIO OFFLOADIG MODE In this section, the weighted su coputation bits axiization proble is studied in the UAV-enabled wireless powered MEC syste under the binary coputation offloading ode. he CPU frequencies of the users that choose to perfor local coputation, the offloading ties, the transit powers of users that choose to perfor task offloading, the trajectory of the UAV, and the ode selection are jointly optiized to axiize the weighted su coputation bits of all users. he forulated proble is a ixed integer non-convex optiization proble, for which a three-stage alternative optiization proble is proposed. A. Resource Allocation Proble Forulation Under the binary coputation offloading ode, the weighted su coputation bit axiization proble subject to the energy harvesting causal constraints, the UAV speed and position constraints is forulated as P 5, P 5 : ax f i[n],p j[n],q[n], t j[n],m 0,M 1 + w j B ν j j M 1 s.t. i M 0 γ c f 3 i [k] η 0 t j [k] P j [k] η 0 w i f i [n] C t j [n] log 1 + h ) j [n] P j [n] σ0 3a) h i [k] P 0, n, i M 0, 3b) h j [k] P 0, n, j M 1, t j [n] 1, n, j M 1 M = M 0 M 1, M 0 M 1 = Θ, f i [n] 0, P j [n] 0, i M 0, j M 1, C4 and C5. 3c) 3d) 3e) 3f) 3g) 3b) and 3c) are the energy harvesting causal constraints iposed on these users who choose to perfor local coputation and on these users who choose to perfor task offloading, respectively; 3d) is the offloading tie constraint during each slot and 3e) is the user operation selection constraint. In P 5 there exist close couplings aong different optiization variables. Furtherore, the binary user operation ode selection akes P 5 a ixed integer prograing proble. he exhaustive search ethod leads to a prohibitively high coputational coplexity, especially when there exist a large nuber of users. Motivated by how we solve P 1, P 5 has a siilar structure as P 1 when the operation odes of users

9 are deterined. hus, the optial CPU frequency, transit power, and offloading tie of users can be obtained by using the sae ethod as the one used for P 1 and the trajectory optiization for the UAV can also be achieved by using the SCA ethod. As such, a three-stage alternative optiization algorith is proposed based on the two-stage Algorith 1. he details for the algorith are presented as follows. B. hree-stage Alternative Optiization Algorith In order to efficiently solve P 5, a binary variable denoted by ρ is introduced, where ρ {0, 1} and M. ρ = 0 indicates that the th user perfors local coputation ode while ρ = 1 eans that the th user perfors task offloading. Moreover, the user operation selection indicator variable ρ is relaxed as a sharing factor ρ [0, 1]. hus, P 5 can be rewritten as P 6 : ax f [n],p n[n],q[n], t [n],ρ + B t [n] ρ ν s.t. 1 ρ ) η 0 =1 w { 1 ρ ) f [n] C log 1 + h [n] P [n] σ 0 γ c f 3 [k] + ρ h [k] P 0, M, ρ t [n] 1, n, =1 f [n] 0, P [n] 0, n, M, C4 and C5. )} 4a) t [k] P [k] 4b) 4c) 4d) 4e) Even by relaxing the binary variable ρ, P 6 is still difficult to solve as there exist couplings aong different variables. For any given ρ and the trajectory of the UAV, P 6 has a siilar structure as P 1. hus, using the sae techniques applied to P 1, the optial CPU frequency, transit power and offloading tie of users for a given ρ and the UAV trajectory can be obtained. It is easy to verify that the optial CPU frequency, transit power and offloading tie of users for a given trajectory have the sae fors given by heore 1 and heore 3. heore 5: For any given f [n], P [n], t [n] and q u [n], the user operation selection schee can be obtained by { 0 if G1 G, ρ opt = G 1 = G = υ,n 1 otherwise; { w f [n] υ,n C { Bt [n] log ν n n γ c f 3 [k] } 1 + h [n] P [n] σ 0 t [k] P [k] ε nt [n] } 5a), 5b) ), 5c) where υ,n 0 and ε n 0 are the dual variables associated with the constraints given by 4b) and 4c), respectively. Proof: See Appendix B. Reark 4: heore 5 indicates that the user operation selection schee depends on the tradeoff between the achievable coputation rate and the operation cost. If the tradeoff of the user achieved by local coputing is better than that obtained by task offloading, the user chooses to perfor local coputing; otherwise, the user chooses to offload its coputation tasks to the UAV for coputing. Finally, the trajectory optiization for any given ρ, f [n], P [n] and t [n] can be obtained by solving P 7, given as P 7 : ax q u[n] [ w ρ =1 ] B t [n] y,j {q u [n]}) ν 6a) s.t. C4 and C5, 6b) n 1 ρ ) γ c f 3 [k] + ρ t [k] P [k] η 0 P 0 β 0 h [n], M, n, 6c) where h [n] and y j {q u [n]}) are given by 19b) and 1b), respectively. P 7 is convex and can be efficiently solved by using CVX [4]. Based on heore 1, heore 5 and the solutions of P 7, a three-stage alternative optiization algorith denoted by Algorith is proposed to solve P 5. he details for Algorith are presented in able. In able, R l and R i denote the value of the objective function of P 5 at the lth and i iteration, respectively. C. Coplexity Analysis he coplexity of Algorith 1 coes fro four aspects. he first aspect is fro the coputation of the CPU frequency and the offloading power. he second aspect is fro the bisection ethod for obtaining the offloading tie. he third aspect is fro the subgradient ethod for coputing the dual variables. he fourth aspect coes fro the application of CVX for solving P 4. Let L 1 and L denote the nuber of iterations required for the outer loop and the inner loop of Algorith 1, respectively. Let l 1 and l denote the tolerance error for the bisection ethod and the subgradient ethod, respectively. hus, according to the works in [35], [38] and [39], the total coplexity of Algorith 1 is O [ L 1 M + M log l 1 / ) + 1/l + L 3)] and O ) is the big-o notation [35]. he coplexity of Algorith coes fro five aspects. Four aspects are the sae as these of Algorith 1. he fifth aspect is fro the coputation of the operation selection indicator variable ρ. Let L 1, L and L 3 denote the nuber of iterations required for the first, second and third loop of Algorith, respectively. Siilar to the coplexity analysis for Algorith 1, the total coplexity of Algorith is O [ L 1 L M + M + M log l 1 / ) + 1/l + L 3 3)].

10 ABLE II: hree-stage alternative optiization algorith Algorith : he three-stage alternative optiization algorith 1: Setting: P 0,,, V ax, q 0, q F, and the tolerance errors ξ, ξ 1 and ξ ; : Initialization: he iterative nuber i = 1, υ,n i and εi n, and qi u [n]; 3: Repeat 1: initialize the iterative nuber l = 1 and ρ l ; Repeat : calculate f opt,i [n] and P opt,i [n] using heore 1 for given q i u [n] and ρopt,l ; use the bisection ethod to solve 0) and obtain t i,opt [n]; update υ,n i and εi n using the subgradient algorith; calculate ρ opt,l using heore 5 and update l = l + 1; if R l R l 1 ξ break; end initialize the iterative nuber j = 1; Repeat 3: solve P 7 by using CVX for the given f opt,i t i,opt [n] and ρ opt,l ; update j = j + 1, and q j u [n]; if q j u [n] q j 1 u [n] ξ q i u [n] = qj u [n] ; break; end end Repeat 3 update the iterative nuber i = i + 1; if R i R i 1 ξ 1 break; end end Repeat end Repeat 1 4: Obtain solutions: f opt [n], P opt [n] and t opt [n], ρ opt and q opt u [n]. V. SIMULAIO RESULS [n], P opt,i [n], In this section, siulation results are presented to copare the perforance of our proposed designs with that of other benchark schees. he convergence perforance of the proposed algoriths is also evaluated. he siulation settings are based on the works in [7], [14], [16] and [3]. he positions of users are set as: q 1 = [0, 0], q = [0, 10], q 3 = [10, 10], q 4 = [10, 0]. he detailed settings are given in able III. he weight vector of each user [w 1 w w 3 w 4 ] is set as [ ]. Fig. 3 shows the UAV trajectory under different schees with = seconds. he UAV transit power is set as P 0 = 0.1 W. In the constant speed scenario, the UAV flies straight with a constant speed fro the initial position to the final position. In the sei-circle scenario, the UAV flies along the trajectory that is a sei-circle with its diaeter being q F q 0. he trajectory of the offloading ode is obtained by using Algorith 1 for the partial coputation offloading ode and the trajectory of the binary ode is obtained by using Algorith for the binary coputation offloading ode. It can be seen fro the trajectories of our proposed schees the UAV is always close to user and user 3, irrespective of ABLE III: Siulation Paraeters Paraeters otation ypical Values ubers of Users M 4 he height of the UAV H 10 he tie length of the UAV flying sec ubers of CPU cycles C 10 3 cycles/bit Energy conversation efficiency η Counication bandwidth B 40 MHz he receiver noise power σ W he nuber of tie slots 50 he effective switched capacitance γ c 10 8 he channel power gain β 0 50 db he tolerance error ξ, ξ he initial position of the UAV q 0 [0, 0] he final position of the UAV q F [10, 0] he axiu speed of the UAV V ax 0 /s y) User 0,10) A sei circle he binary ode User 1 0,0) A constant speed he offloading ode User 4 10,0) User 3 10,10) x ) Fig. 3: he trajectory of the UAV under different schees with = seconds. the operation odes. he reason is that the weights of user and user 3 are larger than these of user 1 and user 4. hus, the UAV needs to fly close to user and user 3 so as to provide ore energy to the. his indicates that the priority and the fairness aong users can be obtained by using the weight vector. Fig. 4 shows the weighted su coputation bits of all users versus the transit power of the UAV under different schees. he optial local coputing is the ode that all users only perfor local coputing while the optial offloading ode is that all users only perfor task offloading. And the trajectory of the UAV is jointly optiized under these two benchark schees. he results under the binary ode and the partial offloading ode are obtained by using Algorith and Algorith 1, respectively. In Fig. 4 the weighted su coputation bits achieved under the partial offloading ode is the largest aong these obtained by other schees. he reason is that all the users can dynaically select the operation ode based on the quality of the channel state inforation under the partial coputation offloading ode. Moreover, the optial offloading ode outperfors the optial local coputing.

11 he weighted su coputation bits of all users bits) 4.5 x Optial local coputing Optial offloading he binary ode he partial offloading ode he transit power of the UAV W) Fig. 4: he weighted su coputation bits of all users versus the transit power of the UAV under different schees. his result is consistent with the results obtained in [13]. Furtherore, the weighted su coputation bits of all users increase with the UAV transit power. It can be explained by the fact that the harvesting energy increases with the transit power of the UAV. hus, users have ore energy to perfor local coutating or task offloading. Fig. 5 shows the weighted su coputation bits of all the users versus the transit power of the UAV under different trajectories with the partial coputation offloading ode and the binary coputation offloading ode. As shown in Fig. 5, the weighted su coputation bits of all the users achieved by using our proposed schees are larger than that obtained by using the trajectory with a constant speed and than that obtained by using the sei-circle trajectory, irrespective of the operation odes. his indicates that the optiization of the trajectory of the UAV can iprove the weighted su coputation bits. It also verifies that our proposed resource allocation a) schee outperfors the disjoint optiization schees. Fig. 6 shows the total coputation bits of each user under different operation odes. he transit power of the UAV is set as P 0 = 0.1 W. he total coputation bits of user and user 3 are higher than those of user 1 and user 4. he reason is that the weights of user and user 3 are larger than those of user 1 and user 4. hus, the resource allocation schee should consider the priority of user and user 3. his further verifies that the application of the weight vector can iprove the priority and also the fairness of users. Fig. 7 is given to verify the efficiency of our proposed Algorith 1 and Algorith. he transit power of the UAV is given as 0.1 W or 0. W. he results show that Algorith 1 and Algorith only need several iterations to converge. his indicates that the proposed Algorith 1 and Algorith are coputationally effective and have a fast convergence rate. It can also be seen that the weighted su coputation bits of all the users achieved under the partial he weighted su coputation bits of all users bits) he weighted su coputation bits of all users bits) 4.5 x he partial offloading ode he partial offloading ode with the sei circle trajectory he partial offloading ode with a constant speed he transit power of the UAV W) 4.5 x he binary ode with joint optiization he binary ode with the sei circle trajectory he binary ode with a constant speed he transit power of the UAV W) Fig. 5: a) he weighted su coputation bits of all users versus the transit power of the UAV under different trajectories with the partial coputation offloading ode; b) he weighted su coputation bits of all users versus the transit power of the UAV under different trajectories with the binary coputation offloading ode. coputation offloading ode are larger than those obtained under the binary coputation offloading ode. he reason is that users can siultaneously perfor local coputing and task offloading when the channel state inforation is strong under the partial coputation offloading ode. However, users can only perfor either local coputing or task offloading in the binary offloading ode even when the channel state inforation is strong. he coputation perforance is iproved by the flexible selection of the operation ode based on the channel state inforation. b)

12 7 x x 107 he total copuation bits of each user Bits) he binary ode he partial offloading ode he weighted su coputation bits of all users bits) he partial offloading ode, P 0 =0.4 W he binary ode, P 0 =0.4 W he partial offloading ode, P 0 =0. W he binary ode, P 0 =0. W 0 User 1 User User 3 User 4 Users Fig. 6: he total coputation bits of each user under different operation odes with P 0 = 0.1 W. he weighted su coputation bits of all users bits).8 x P 0 =0. W, Algorith 1 P 0 =0. W, Algorith P 0 =0.1 W, Algorith 1 P 0 =0.1 W, Algorith he nuber of iterations Fig. 7: he weighted su coputation bits of all users versus the nuber of iterations required by using Algoriths 1 and under different transit powers of the UAV and different operation odes. Fig. 8 shows the weighted su coputation bits of all users versus the nuber of users under different operation odes. he transit power of the UAV is set as P 0 = 0. W or P 0 = 0.4 W. In Fig. 8 the weighted su coputation bits of all users increase with the nuber of users. he reason is that ore users can exploit the harvesting energy to perfor local coputing and coputation offloading. It is also observed that the growth rate decreases with the increase of the nuber of users. he reason is that the offloading tie allocated for each user decreases with the increase of the nuber of users since the total offloading tie is liited by. able IV is given to evaluate the run ties of Algorith 1 and Algorith shown in the top of the next page. he run ties are obtained by using a coputer with 64-bit IntelR) he nuber of users Fig. 8: he weighted su coputation bits of all users versus the nuber of users under different transit powers of the UAV and different operation odes. CoreM) i CPU, 8 GB RAM. Fro able IV we can see that the required run tie of Algorith 1 is saller than that of Algorith. his indicates that the coplexity of Algorith 1 is lower than that of Algorith. It can be verified by the coplexity analysis presented in Subsection C of Section IV. Moreover, the effect of the nuber of tie slots on the run tie is larger than that of the nuber of users. he reason is that the coplexity of these two algoriths ainly depends on the nuber of tie slots. his can also be verified by the coplexity analysis. VI. COCLUSIOS he resource allocation probles were studied for UAVenabled wireless powered MEC systes under both the partial and binary coputation offloading odes. he weighted su coputation rates of users were axiized by jointly optiizing the CPU frequencies, the user offloading ties, the user transit powers, and the UAV trajectory wo alternative algoriths were proposed to solve these challenging probles. he closed-for expressions for the optial CPU frequencies, user offloading ties, and user transit power were derived. Moreover, the optial selection schee whether users choose to locally copute or offload tasks was proposed for the binary coputation offloading ode. It was shown that the perforance achieved by using our proposed resource allocation schee is superior to these obtained by using the disjoint optiization schees. Siulation results also verified the efficiency of our proposed alternative algoriths and our theoretical analysis. he exploitation of UAV to iprove the energy conversation efficiency and the coputation perforance was studied in this paper. However, the coputation perforance is also liited by the flight tie of the UAV. It is interesting to exploit ultiple antennas techniques to tackle this challenge. his will be investigated in our future work.

13 ABLE IV: Coparison of the required run tie of Algorith 1 with that of Algorith s), M) 50, ) 50, 4) 50, 8) 60, ) 60, 4) 60, 8) 70, ) 70, 4) 70, 8) Algoriths Algorith Algorith APPEDIX A PROOF OF HEOREM 1 Let λ,n and α n denote the dual variables associated with the constraint C and C3, respectively, where λ,n 0 and α n 0. hen, the Lagrangian of P can be given by 7) at the tope of this page, where Ξ denotes a collection of all the prial and dual variables related to P. Let µ,n = λ,k k=n and g [k] = η 0 h [k] P 0 γ c f 3 [k] z [k]. hen, the Lagrangian function L Ξ) can be rewritten by 8) at the tope of this page. And the Lagrangian dual function of P can be presented as g λ,n, α n ) = ax 0 f [n] L Ξ). 9) Based on 9), the optial solutions of P can be obtained by solving its dual proble, given as in g λ,n, α n ). 30) λ,n,α n It can be seen fro 30) that the dual proble can be decoupled into M independent optiization probles, given by 31) at the tope of the next page. hus, let the derivation of 31b) with respect to f [n] andz [n] be zero, one has w C 3 γ cf [k] w B t [n] ν ln λ,k = 0, k=n h [n] σ0 t [n] + h [n] z [n] 3a) λ,k =0. k=n 3b) ote that z [k] = t [k] P [k] and P [k] 0. Moreover, the case that t [n] = 0 can be identified as P [n] = 0. hus, based on 3), heore 1 is proved. he proof for heore 1 is coplete. APPEDIX B PROOF OF HEOREM 5 Let υ,n and ε n denote the dual variables with respect to the constraints given by 4b) and 4c), respectively, where υ,n 0 and ε n 0. hen, for any given f [n], P [n], t [n] and q u [n], the Lagrangian of P 6 can be expressed by 33) at the tope of the next page, where Ξ 1 denotes a collection of all the prial and dual variables related to P 6. Ξ denotes a collection of υ,n, α n, f [n], z [n], t [n] and ρ. Using the sae techniques that are used for the proof of heore 1, for any given f [n], z [n], t [n] and q u [n], P 6 can be solved by solving M independent optiization probles, given by 34) at the tope of the next page, where l [n] = η 0 h [n] P 0 1 ρ ) γ c f 3 [n] ρ z [n] and ϖ,n = k=n υ,k. hus, according to [37], the optial ρ denoted by ρ opt can be obtained by 35) at the tope of the next page. Based on 35), since z [n] = t [n] P [n], heore 5 is proved. REFERECES [1] F. Zhou, Y. Wu, R. Q. Hu, Y. Wang, and K. K. 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14 [ L Ξ) = w =1 + =1 f [n] C λ,n { η 0 + B t [n] ν log h [k] P h ) ] [n] z [n] σ0 t [n] [ γc f 3 [k] + z [k] ]} + α n {1 } t [n], 7) =1 L Ξ) = =1 { w f [n] C + B t [n] ν log 1 + h )} [n] z [n] σ0 t +µ,n g [k] + α n [n] M α nt [n]. 8) ax L λ,n, α n, f [n], z [n], t [n]) λ,n,α n,f [n] 0 31a) L λ,n, α n, f [n], z [n], t [n]) = { { f [n] w C + B t [n] ν log 31b) 1 + h )} [n] z [n] σ0 t +µ,n g [n] + α } n [n] M α nt [n]. 31c) L 1 Ξ 1 ) = w [1 ρ ) =1 + + =1 ε n {1 υ,n { η 0 f [n] C + B ρ t [n] ν log 1 + h ) ] [n] z [n] t [n] σ0 h [k] P 0 [ 1 ρ ) γ c f 3 [k] + ρ z [k] ]} } ρ t [n], 33) =1 ax υ L1 Ξ ),n,ε n,f [n] 0 L 1 Ξ ) = + w { 1 ρ ) f [n] C ϖ,n l [n] + ε n M ε nt [n], + B ρ t [n] log ν 1 + h )} [n] z [n] t [n] σ0 34a) 34b) L 1 Ξ ) ρ opt L 1 Ξ ) ρ opt < 0, ρ opt = 0, = 0, 0 < ρ opt < 1, M > 0, ρ opt = 1; { = w f [n] C + B t [n] ν log { + υ,n [ γc f 3 [k] + z [k] ]} 1 + h ) } [n] z [n] t [n] σ0 ε n t [n]. 35a) 35b)

15 [17] H. Wang, J. Wang, G. Ding, L. Wang,. A. siftsis, P. K. Shara, Resource allocation for energy harvesting-powered DD counication underlaying UAV-assisted networks, IEEE rans. Cogn. etw., vol., no. 1, pp. 14-4, Jan [18] S. Yin, J. an, and L. Li, UAV-assisted cooperative counications with wireless inforation and power transfer, subitted to IEEE rans. Wireless Coun., [19] J. Xu, Y. Zeng, and R. Zhang, UAV-enabled wireless power transfer: rajectory design and energy region charaterization, in Proc. IEEE Global Coun. Conf. Singapore, 017, [0] J. Xu, Y. Zeng, and R. Zhang, UAV-enabled wireless power transfer: rajectory design and energy optiization, IEEE rans. Wireless Coun., to be published, 018. [1]. H. Motlagh, M. Bagaa, and. aleb, UAV-based Io platfor: A crowd surveillance use case, IEEE Coun. Mag., vol. 55, no., pp , Feb []. Zhao, F. Cheng, F. R. Yu, J. ang, Y. Chen, G. Gui, and H. 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Surveys uts., vol. 18, no., pp , nd Quart., 016. [33]. Cheng, W. Xu, W. Shi, Y. Zhou,. Lu, H. Zhou, and X. Shen, Aire-ground integrated obile edge networks: Architecture, challenges and opportunities, IEEE Coun. Mag., to be published, 018. [34] M. Mozaffari, W. Saad, M. Bennis, Y. H. a, and M. Debbah, A tutorial on UAVs for wireless networks: Applications, challenges, and open probles, IEEE Coun. Surveys uts., subitted, [35] S. P. Boyd and L. Vandenberghe, Convex Optiization. Cabridge, U.K.: Cabridge Univ. Press, 004. [36] F. Zhou,. C. Beaulieu, Z. Li, J. Si, and P. Qi, Energy-efficient optial power allocation for fading cognitive radio channels: Ergodic capacity, outage capacity and iniu-rate capacity, IEEE rans. Wireless Coun., vol. 15, no. 4, pp , Apr [37] F. Zhou, Z. Li, J. Cheng, Q. Li, and J. Si, Robust ax-in fairness resource allocation in sensing-based wideband cognitive radio with SWIP: Iperfect channel sensing, IEEE Syst. J., to be published, 017. [38] S. Bubeck, Convex optiization: Algoriths and coplexity, In Foundations and rends in Machine Learning, vol. 8, no. 3, pp , [39] C. Gutierrez, F. Gutierrez, M.C. Rivara, Coplexity on the bisection ethod, heoretical Coputer Science, vol. 38, pp , 007. Fuhui Zhou received the Ph. D. degree fro Xidian University, Xian, China, in 016. He is an associate Professor with School of Inforation Engineering, anchang University. He is now a Research Fellow at Utah State University. He has worked as an international visiting Ph. D student of the University of British Colubia fro 015 to 016. His research interests focus on cognitive radio, green counications, edge coputing, achine learning, OMA, physical layer security, and resource allocation. He has published ore than 40 papers, including IEEE Journal of Selected Areas in Counications, IEEE ransactions on Wireless Counications, IEEE Wireless Counications, IEEE etwork, IEEE GLOBECOM, etc. He has served as echnical Progra Coittee PC) eber for any 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 the B.S. degree in telecounication engineering fro Wuhan University, Wuhan, China, in July 007, the Ph.D. degree in counication and signal processing with the ational Mobile Counications Research Laboratory, Southeast University, anjing, China, in oveber 013. Dr. Wu is currently a enure-rack Associate Professor with the Departent of Electronic Engineering, Shanghai Jiao ong University, China. Previously, he was senior research fellow with Institute for Counications Engineering, echnical University of Munich, Gerany and the Huboldt research fellow and the senior research fellow with Institute for Digital Counications, University Erlangen-u rnberg, Gerany. During his doctoral studies, he conducted cooperative research at the Departent of Electrical Engineering, Missouri University of Science and echnology, USA. His research interests include assive MIMO/MIMO systes, physical layer security, signal processing for wireless counications, and ultivariate statistical theory. Dr. Wu was awarded the IEEE Student ravel Grants for IEEE International Conference on Counications ICC) 010, the Alexander von Huboldt Fellowship in 014, the ravel Grants for IEEE Counication heory Workshop 016, and the Excellent Doctoral hesis Awards of China Counications Society 016. He was an Exeplary Reviewer of the IEEE ransactions on Counications in 015, 016. He is the lead guest editor for the upcoing special issue Physical Layer Security for 5G Wireless etworks of the IEEE Journal on Selected Areas in Counications. He is currently an editor of the IEEE Access and IEEE Counications Letters. He has been a PC eber of various conferences, including Globeco, ICC, VC, and PIMRC, etc. Rose Qingyang Hu is a Professor of Electrical and Coputer Engineering Departent at Utah State University. She received her B.S. degree fro University of Science and echnology of China, her M.S. degree fro ew York University, and her Ph.D. degree fro the University of Kansas. She has ore than 10 years of R&D experience with ortel, Blackberry and Intel as a technical anager, a senior wireless syste architect, and a senior research scientist, actively participating in industrial 3G/4G technology developent, standardization, syste level siulation and perforance evaluation. Her current research interests include next-generation wireless counications, wireless syste design and optiization, green radios, Internet of hings, Cloud coputing/fog coputing, ultiedia QoS/QoE, wireless syste odeling and perforance analysis. She has published over 180 papers in top IEEE journals and conferences and holds nuerous patents in her research areas. Prof. Hu is an IEEE Counications Society Distinguished Lecturer Class and the recipient of Best Paper Awards fro IEEE Globeco 01, IEEE ICC 015, IEEE VC Spring 016, and IEEE ICC 016.

16 Yi Qian received a Ph.D. degree in electrical engineering fro Cleson University. He is a professor in the Departent of Electrical and Coputer Engineering, University of ebraska-lincoln UL). Prior to joining UL, he worked in the telecounications industry, acadeia, and the governent. Soe of his previous professional positions include serving as a senior eber of scientific staff and a technical advisor at ortel etworks, a senior systes engineer and a technical advisor at several startup copanies, an assistant professor at University of Puerto Rico at Mayaguez, and a senior researcher at ational Institute of Standards and echnology. His research interests include inforation assurance and network security, network design, network odeling, siulation and perforance analysis for next generation wireless networks, wireless ad-hoc and sensor networks, vehicular networks, sart grid counication networks, broadband satellite networks, optical networks, high-speed networks and the Internet. Prof. Yi Qian is a eber of ACM and a senior eber of IEEE. He was the Chair of IEEE Counications Society echnical Coittee for Counications and Inforation Security fro January 1, 014 to Deceber 31, 015. He is a Distinguished Lecturer for IEEE Vehicular echnology Society and IEEE Counications Society. He is serving on the editorial boards for several international journals and agazines, including serving as the Associate Editor-in-Chief for IEEE Wireless Counications Magazine. He is the echnical Progra Chair for IEEE International Conference on Counications ICC) 018.