Joint Power-Trajectory-Scheduling Optimization in A Mobile UAV-Enabled Network via Alternating Iteration

Xiaohan Qi;Minxin Yuan;Qinyu Zhang,2;Zhihua Yang,2,*

1 Communications Engineering Research Center,Harbin Institute of Technology,Shen zhen 518055,China

2 Peng Cheng Laboratory,Shenzhen 518052,China

Abstract: This work focuses on an unmanned aerial vehicle(UAV)-enabled mobile edge computing(MEC)system based on device-to-device(D2D)communication.In this system,the UAV exhibits caching,computing and relaying capabilities to periodically provide specific service to cellular users and D2D receiver nodes in the appointed time slot.Besides, the D2D transmitter can provide additional caching services to D2D receiver to reduce the pressure of the UAV.Note that communication between multi-type nodes is mutually restricted and different links share spectrum resources.To achieve an improved balance between different types of node, we aim to maximize the overall energy efficiency while satisfying the quality-of-service requirements of the cellular nodes.To address this problem, we propose an alternating iteration algorithm to jointly optimize the scheduling strategies of the user, transmitting power of the UAV and D2D-TX nodes, and UAV trajectory.The successive convex approximation, penalty function, and Dinkelbach method are employed to transform the original problem into a group of solvable subproblems and the convergence of the method is proved.Simulation results show that the proposed scheme performs better than other benchmark algorithms, particularly in terms of balancing the tradeoff between minimizing UAV energy consumption and maximizing throughput.

Keywords:UAV MEC network;D2D;joint optimization;energy efficiency

I.INTRODUCTION

With the rapid development of the internet and mobile communication technologies, several advances have been made in Internet of Things(IoT)technology for many applications[1]such as emergency communication[2],autonomous control,and environmental monitoring, etc.In IoT systems, many end devices and sensor devices are deployed to ensure functional integrity.A latency-sensitive system is essential to deal with real-time required data.However,intensive computation and communication impose pressure on the base station.

To tackle the issue mentioned above, unmanned aerial vehicle (UAV)-enabled network based on mobile edge computing (MEC) [3] provides an effective way to overcome the computation and communication limitations during the peak period.In the MEC system, owing to the limited local processing capabilities of ground users, a UAV is employed as a mobile edge server to provide edge computing or relay services to the users.Using the MEC scheme,the overall efficiency of the system can be increased by sharing or computing data through idle devices.Moreover,the communication services and coverage of a cellular network are limited because of the fixed characteristics of the ground infrastructure in the network [4].By employing UAV-enabled network,ubiquitous coverage and steady communication can be achieved in events when the existing fixed infrastructure is damaged or in the event of a disaster.In contrast to the traditional static relay,many other parameters such as the position and trajectory of the UAV are controllable.Note that the UAV-enabled network can add much value to the lives of people and can remove many limitations of the traditional ground communication.To meet the throughput and energy efficiency requirements, many important studies explored various aspects and attempted to make use of the potentials of UAV-enabled MEC networks via UAV position optimization[4-7],communication slot partitioning[4,6],and bandwidth scheduling[7].

Recently, the device-to-device (D2D) communication technology has evolved as a promising approach for supporting fifth-generation cellular communication, which is expected to match the actual cellular network and improve spectrum efficiency [8].The relevant studies on improving the spectrum effectiveness have been conducted.A millimeter-wave band based UAV communication network is studied in[2],which can provide more abundant frequency resources than the microwave band and much higher achievable rate.Moreover, a further research [9] aiming at enhancing the achievable rate based on the application of nonorthogonal multiple access in millimeter-Wave communications (mmWAVE-NOMA) solves the power allocation problem, which provides a reference for future UAV network optimization in 5G environment.

By reusing the same spectrum bands,the D2D communication and UAV-enabled network jointly provide an effective approach for further improving the MEC network performance.Some studies on the collaborative use of D2D and UAV-enabled technology have been reported.In order to solve the spectrum efficiency issue,UAVs equippied with the optical receiver and transmitter have been conducted in real communication scenarios and the research [10] is with significance for solving the optical communication based on UAV-enabled network optimization issue.An incentive mechanism was proposed to evaluate the contribution of D2D transmitters in a cache-enabled D2D underlying cellular network modeled using random geometry [11].The Stackelberg game approach was adopted to solve the conflict between operators and D2D transmitters.Further, the power control optimization of a D2D-based UAV-enabled system was explored, wherein the UAV served multiple UAV users and the D2D user multiplexed the UAV user channel [12].A low-complexity power control algorithm was designed using the Hessian matrix to maximize throughput.In another study,the UAV functioned as a mobile full-work relay to serve separate ground nodes and other nodes communicates using the D2D technology to share the spectrum [13].The total maximum throughput was optimized by jointly designing the UAV trajectory and transmitting power.

The durability of the UAV-enabled network is always limited by excess energy consumption.Therefore, energy efficiency is a significant parameter for evaluating network performance.Unlike previous research in which only the communication energy consumption was considered [14-16], in this work, the highest proportion of the UAV propulsion energy as the system energy consumption is considered according to practical conditions because the energy consumption of communication is several orders of magnitude lower than that of UAV propulsion.Herein,we investigate the cache-enabled UAV relay network based on D2D communication.In contrast to the fixed relay network[16],the high mobility and cache function of UAV are considered in this work.In particular, the UAV caches contents from the base station and provides content downloading services to both the D2D receiver (RX) and cellular user.Without the loss of generality, we consider that the UAV and the D2D transmitting(TX)user share the same frequency band for communicating with the D2D-TX and cellular users, respectively.The main goal of this work is to maximize the average throughput among different types of link by jointly optimizing the UAV transmitting power, UAV trajectory, and user scheduling and association under the relevant constraints.Considering the effect of mobility-dependent constraints, such as velocity and accelerated velocity,designing an optimized trajectory is essential.Moreover, adjusting the UAV transmitting power is an effective way to solve the problem.In particular, the solution always involves attempting to attain a balance between good channel conditions and lower interference.The contributions of this work can be summarized as follows:

• This work proposes a mobile D2D-based UAV MEC network in which the system energy efficiency is maximized by balancing the energy consumption and communication.We formulate this issue as an optimization problem by jointly considering the UAV transmitting power,UAV trajectory, and user scheduling/association under UAV mobility constraints.

• The proposed problem is a combinatorial optimization involving binary variables and other coupling items.Such a problem is extremely difficult to solve.Thus, an alternating iteration algorithm is proposed in this work by decomposing the original nonconvex problem into three subproblems.First, a penalty-function-based relaxed optimization method is proposed by relaxing binary variables into continuous ones.Second, a successive convex approximation (SCA)-based method is proposed to approximate the nonconvex problem into a solvable one.Third, the Dinkelbach method[17]is adopted to decompose the mixed integer fraction problem.Moreover,the convergence of the joint problem is established.

• This work compares the numerical results of the proposed method with the results of other benchmark schemes.The proposed method exhibits higher energy efficiency than the other schemes.In particular,the total energy efficiency of the system first monotonically increases and then monotonically decreases with respect to the flight period.

The remainder of this paper is organized as follows.The system model and problem formulation are presented in Section II.The main analysis, derivation,and iteration algorithm are described in Section III.The numerical results that verify the performance of the proposed algorithm are provided in Section IV.Finally, the conclusions of this work are presented in Section V.

II.PROBLEM FORMULATION

2.1 System Model

Considering the wide-range communication and obstacles in a real environment, a scenario involving a weak or negligible link between two nonadjacent nodes is employed.Thus, the UAV in this UAVenabled network plays a critical role as a dynamic relay in maintaining steady communication between any two nodes.As illustrated in Figure 1, the system comprises one fixed-wing UAV and three types of ground users,namely,M1cellular users(CUs)(indexed with{1,...M1}),M2D2D receiver (D2D-RX)users (indexed with{1,...M2}), andM3D2D transmitter(D2D-TX)users(indexed with{1,...M3}).

Figure 1. Illustration of the system.

In practice, a downloading or data forwarding request induces a surge in traffic at a specific period,which imposes pressure on the the base station operation.To handle this pressure, the micro base station(MBS)feedbacks the current status to the operator and the UAV is employed as a mobile server device, providing relay, a caching, and MEC service to ground users.Specifically, the UAV acts as a relay or MEC decive to serve cellular users,or provides caching service to D2D-RX users.In addition, D2D-TX users cache data that are in great demand in advance during the off-peak period to serve D2D-RX nodes to reduce the pressure of UAV.Thus, the optimization of the system secheduling,power control,UAV trajectory is necessary.The problem formulation and optimization process are presented in the following sections.

2.2 Communication Model

For convenience, the total mission completion periodTis divided intoNsubtime slots.Each subslot has a time interval ofand the total time slot set is denoted asN={1,2,...,N}.In addition,we assume that the time slot duration is sufficiently small to consider the scenario as quasistatic.As illustrated in this work,considering the D2D-TX shares the same spectrum with UAV, therefore, the channel interference is involved is the system model.Hence,the time-division multiple access(TDMA)protocol is employed in this UAV-Enabled system in order not to introduce additional interference,as illustrated in Figure 2.

Figure 2.The system scheduling under TDMA mode.

Without the loss of generality,the three-dimensional(3D) Cartesian coordinate system is employed in this work.The horizontal position of the MBS is denoted bywb= [xb,yb]T, and the CUs, D2D-RX users, and D2D-TX users are denoted aswm1=[xm1,ym1]m1∈M1,wm2= [xm2,ym2]m2∈M2, andwm3= [xm3,ym3]m3∈M3, respectively.For ease of exposition, we assume the UAVs fly at a fixed height H that is considerably higher than the height of the ground users.Owing to the fixed height of the UAV,the horizontal coordinate of the UAV at then-th time slot can be expressed as

For easy caching content updating, we assume that the UAV will return to the initial positionwb(0);then,the trajectory should satisfy the following relation:

According to the literature[18], the linear relationship between the position, speed and acceleration of the UAV can be expressed as follows:

wherev[n]anda[n]represent the velocity and acceleration of the UAV,respectively,in then-th time slot.

Considering the real environment,wireless communication between the UAV and ground users are assumed to be dominated by the line-of-sight channel.Hence, the free-space model is adopted.The channel gains from the UAV to them1-th CU[n]andm2-th D2D-RX[n]in then-th time slot are expressed as

whereρ0denotes the channel gain at a reference distance of 1 m.In then-th time slot,letpu[n]andpm3[n]denote the transmitting power by the UAV andm3-th D2D-TX for communication, respectively.Subsequently, the achievable rates (bps/Hz) from the UAV to them1-th CU andm2-th D2D-RX are respectively expressed as follows:

whereσ2is the noise power.Furthermore,the channel gains from the D2D-TX to them1-th CU]andm2-th D2D-RX[n] are, respectively, expressed as follows:

2.3 Scheduling Model

To describe the binary status of UAV to CU links,UAV to D2D-TX links, and D2D-TX to D2D-RX links, a series of binary variables αm1[n],2[n],βm3,m2[n] are introduced.The value of these variables are binary, value of 0 indicates the link is nonconnected.Otherwise, the link exists.For example,n]demonstrates the status between the UAV and D2D-RX.Here,[n] = 1 indicates that the UAV provides service to m2-th D2D-RX at n-th time slot;otherwise[n]=0).Therefore,the following constraints must be satisfied,expressed as

Moreover, the time-division multiple access(TDMA) protocol is employed in the system and the UAV shares the spectrum with D2D-TX.Hence, the assumptions that the UAV can only serve one CU node or one D2D-TX node and the D2D-TX node can only serve one D2D-TX node are made in this work.Accordingly, the following constraint for scheduling variables should be satisfied,expressed as

in which (9a) indicates that the UAV can only serve one node(CU or D2D-RX)at each time slot,(9b)indicates that any D2D-RX can connected to one server(D2D-TX or UAV) at most, (9c) indicates that any D2D-TX can serve one D2D-RX at most.Accordingly, the total throughput of the UAV and D2D-TX in period T is expressed as follows:

2.4 Problem Formulation

Considering that the flight energy consumption of the UAV is considerably greater than that of the UAV communication,only the flight energy consumption of the fixed-wing UAVs is considered.According to the literature[18], the total propulsion energy consumption of UAV over the whole timeTis expressed as follows:

To enhance the energy efficiency during data downloading and transmission while ensuring the quality of service for CU nodes in the network,we formulate the detailed process into a logical optimization problem.In terms of different variables and their significant effect on optimization,we jointly optimize user scheduling,UAV and D2D-TX’s transmitting power as well as UAV trajectory to achieve improved performance.

The following related variables sets are adopted:A1={αm1[n],∀n,m1},A2={2[n],∀n,m2},A3={βm3,m2[n],∀n,m2,m3},Q={q[n],v[n],a[n],∀n},P1={pu[n],∀n},P2={pm3[n],∀n,m3}.Additionly, by considering the issues introduced in the previous subsections, the optimization problem can be simplified as follows:

where(2)-(3)denotes the UAV trajectory constraints,(9a) - (9c) represent user scheduling variables constraints, (12b) ensures the user quality-of-service requirements andRminis the minimum QoS requirement, (12d)and(12e)guarantees that the energy consumption of the D2D-TX users and UAV cannot exceed the energy stored in the battery.The problem is challenging because of the complex objective function and nonconvex constraints (8), (12b), in which the achievable ratesγm1[n],γm2[n]andγm2,m3[n]are nonconvex.

III.ALGORITHM DESCRIPTION

In this section, an iterative algorithm is introduced to solve the energy efficiency optimization problem by decomposing the original problem into three subproblems, namely, user scheduling and association optimization,UAV and D2D transmitting power optimization,and UAV trajectory optimization.

3.1 User Scheduling and Association Optimization

In this section, we first optimize user scheduling and associationAwith given transmitting powerPand UAV trajectoryQ.The original problem can be expressed as follows:

For the discrete binary variable optimization problem, a series of auxiliary variables and equality constraints are introduced to relax problem (P2) into a solvable problem.

First, we introduce a set of new continuous variablesR|∀m1,m2,m3}and relax the user scheduling and association variableAto a continuous range [0,1].Subsequently, a series of equality constraints are employed to rewrite the original binary variable constraints.Accordingly,and the new constraints are expressed as follows:

The optimal solution to the original problem is restricted to a binary value using the introduced conversion process.However, (P2) is still intractable owing to the nonconvex constraints.To decrease the influence of the constraints, a penalty-function-based method is adopted to reflect the effect of relaxation constraint on the optimal solution.As described in(P2.1),τrepresents the penalty factor,and the penalty function part consists of the product ofτand equality constraints.Note that after performing a series of operations, the obtained problem becomes equivalent to the original problem, which can be simplified as follows:

To handle problem (P2.1), an iterative-based algorithm is proposed to achieve a convergence solution.During the computation process, penalty factorτis updated in every iteration until the algorithm converges.The convergence status will be satisfied under the condition shown in the equation(16),in whichRandRoldare respectively respresent the objection function value at current and last iteration, andωrespresents the iteration threshold corresponding to iteration precision.This equation signifies that the value of the penalty part is lower than the threshold or the number of iterations reaches the maximum:

Algorithm 1. Penalty-Based iterative algorithm for user scheduling sub-Problem.1: Initialize: Fixed transmitting power P and UAV trajectory Q;2: Set: Outer iteration index i = 0, inner iteration index j=0,penalty factor τ =1,incresing factor k=2,maximum iteration step I1=20,the threshold ω=10-3 3: for i=1,2,...,I1 do 4: Initialize: A(0)and Rold =10-7;5: for j =1,2,...,I1 do 6: Obtain the optimal ˜A(j) by (17a), (17b)and(17c)with fixed A(j-1);7: Solve problem(P2.1)and obtain the optimal A(j)and objective function value R;8: if(R-Rold)/Rold ≤ω or j >I1 then 9: Break;10: else 11: Rold =R;12: end if 13: Calculate: κ represents the sum of the penalty terms;14: end for 15: if κ ≤ω or i>I1 then 16: break;17: else 18: η =κη;19: end if 20: end for

3.2 UAV Transmitting Power Optimization

For any given user scheduling and association,as well as UAV trajectory, the transmitting power of UAV and D2D-TX nodes optimization can be formulated by solving the following problem:

Note that constraints (18a) and (18b) are nonconvex with respect to transmitting powersP1andP2,respectively, corresponding to UAV and D2D-TX user.Hence,problem(P3)is still intractable.To tackle this nonconvexity,the SCA technique is used to transform the optimization problem (P3) into a convex problem so that the approximate solution can be achieved.Constraint(18a)consists of three types of communication links,namely,the UAV to CUs,the UAV to D2D-RX users,and D2D-TX users to D2D-RX users.

According to the above discussion, we introduce Lemma 1, Lemma 2, and Lemma 3 to deal with the nonconvexity of constraints(18a)and (18b).

Lemma 1.With given transmitting power[n]],the first part γm1[n]of constraint(18a)can be approximated as a concave function.In particular,the converted inequality and the included items are specifically expressed as follows:

where

where

Proof.Refer to the proof of Lemma 1.

Lemma 3.With given transmitting power n][n], the third part γm3m2[n]of constraint(18a)can be approximated as a concave function.In particular, the convert inequality and the included items are specifically expressed as follows:

where

Proof.Refer to the proof of Lemma 1.

After the derivation process, the upper bounds of (19), (22),and (24) can be obtained.By combining the analysis and derivation processes,the problem(P3) can be approximated as a solvable problem, as expressed in(31).

Note that bothP1andP2are joint convex with respect to constraints (18a)and(18b)because bothand] are convex with respect toP1andP2.Moreover, note that (18c) and (18d) are linear constraints.Therefore,the optimized problem(P3.1)can be efficiently solved using standard convex optimization solvers such as CVX[19].

3.3 Trajectory Optimization

In this section,another subproblem aimed at optimizing the UAV trajectory is considered with the given scheduling and association as well as transmitting power.The subproblem is simplified as(P4).Note that the objective function in original problem(P1)is nonconvex;hence,the original problem is difficult.Therefore, we leverage the SCA technique and Dinkelbach method to approximate the subproblem into a solvable problem.

Inparticular,the nonconvexity of the problem arises because of two reasons: (1)the UAV trajectory is not concave with respect to constraints (27a) and (27c);and (2) the acceleration and velocity in the objective function are coupled.Therefore, the SCA method is employed to handle the intractable issue.In particular,problem (P4.1) can be equivalently expressed as the following problem by introducing an auxiliary variableφ[n]:

Next, the equivalence between (P4.1) and (P4) is proven.We assume that||v[n]||2> φ[n]2is satisfied in the case of the optimal solution of(P4.1).Under the circumstances,clearly,the increase in theφ[n]value will generate a strictly larger value of the objective function,which is contradictory to our hypothesis.Thus, the equivalence of the two is proved by the contradiction.Constraint(28d)is still nonconvex.However, function||v[n]||2is convex corresponding tov[n]; then, we obtain the following inequality by applying the first-order Taylor expansion at the given pointvj[n]:

Algorithm 2. Dinkelbach method for solving(P4.2).1: Initialize: maximum tolerance ε, ζ = 0, maximum iteration I2 =20 and iterative times k 2: repeat 3: Solve problem (P4.3) for given ζk,and obtain the optimal UAV trajectory Qk;4: if||η3k-ζkEk||≤ε then 5: ζ∗= η3∗E∗,Q∗=Qk;6: break;7: else 8: ζk+1 = η3k Ek,k =k+1;9: end if 10: until k ≤I2

Then,constraint(28d)can be rewritten as

Moreover, note that the rewritten constraint (30) is convex becauseγlb[n]is linear with respect tov[n].

Subsequently,the SCA method is employed again to handle the nonconvexity of constraint (28a).In addition,the three composed parts ofRtotare nonconvex.To overcome the convexity issue,we approximate the involved function into an operational one.In particular,several conclusions were obtained and derived,as summarized in Lemma 4,Lemma 5,and Lemma 6.

Lemma 4.For the given UAV trajectory,the first part of constraint(28a)can be approximated as a convex function which is expressed as follows:

The detailed items are expressed as follows:

Proof.Note that the functionγm1[n]can be rewritten asin which[n]is constant andn]can be represented as follows:

For the function‖q[n]-zm1‖2is convex with respect to[n],its lower bound can be achieved after thej-th iteration under thej-th given trajectory,written as

Lemma 5.For the given UAV trajectoryqj[n], the function γm2[n], which is the second part of constraint(28a),can be approximated as a concave function,which is expressed as

where

Proof.Refer to the proof of Lemma 4.

Lemma 6.For the given UAV trajectoryqj[n], function γm3,m2[n], which is the third part of constraint(28a),can be approximated as a concave function,which is expressed as follows:

where

For convenience, variableSm2[n] and the corresponding constraint are employed to equivalently transform function[n], the rewritten function of[n],and the new constraint as follows:

To handle the nonconvex constraint (40), we take the first-order Taylor expansion of the following inequality at the given pointat thej-th iteration,which is expressed as follows:

Eventually, the nonconvex constraint (28a) can be transformed into a convex constraint.Similarly, constraint (28c) is also transformed from a nonconvex constraint to a convex constraint according to Lemma 4.

Subsequently,with the given transmitting powerP,user scheduling and associationA1,A2, andA3, as well as the lower bounds with respect to (31), (35),and(37),the original optimization problem can be approximated as(P4.2)by introducing a set of auxiliary variables Θ={Q,η3,Sm2[n],φ[n]}.Specifically,the approximated problem is expressed as(P4.2).

Note that the objective function of problem(P4.2)is composed of two parts,namely,the convex denominator and concave numerator.Therefore,the Dinkelbach method is used to solve the problem.An indicatorζis employed to represent the energy efficiency according to the literature[17]:

Algorithm 3. Alternating iterative algorithm for solving(P1).1: Initialize: A0, P0,and Q0, the maximum tolerance ε = 10-3, set iterative index r = 0, maximum iteration I3 =20;2: repeat 3: Given {Qr,Pr}, solve problem (P2.1) and obtain the optimal solutions Ar+1;4: Given{Ar+1,Pr,Qr},solve problem(P3.1)and obtain the optimal solutions Pr+1;5: Given {Ar+1,Pr+1,Qr}, solve problem (P4.3)and obtain the optimal solutions Qr+1;6: Update r =r+1;7: until the fractional increase of the objective value is below a threshold ε,ie. υr+1-υr υr ≤ε or r ≥I3,

Assumingζ∗is the optimal energy efficiency, the relevant sufficient and necessary condition is defined in Theorem 1.

Theorem 1.The optimal energy efficiency of problem(P4.2)is satisfied if and only if

Proof.Refer to the literature[17].

Subsequently, problem (P4.2) can be rewritten as follows:

Consequently, a Dinkelbach base iteration scheme is proposed for solving problem (P4.3).This process is summarized in Algorithm 2.Therefore,the optimal solution of(P4)can be obtained.

3.4 Algorithm Convergence

By combining the three-step algorithms corresponding to subproblems(P2),(P3),and(P4),an overall iterative algorithm that jointly optimizes the UAV trajectory, transmitting power, and user scheduling and association is derived.Details are provided in Algorithm 3.In addition, Figure 3 presents an example of the updating process during every two adjacent iteration.In this section, the proof of the convergence of the proposed algorithm is provided.

Figure 3. The overall algorithm iteration update process.

Remark 1.It is noted that the variables are randomly initialized to those that satisfy the relevant constraints,represented as A0, P0and Q0.Then, the Step-1(User Scheduling and Association Optimization)of algorithm 3 is executed with fixed initial P0and Q0.The obtained solution A1becomes the fixed input of Step-2(UAV Transmitting Power Optimization).The solution of Step-2 is also set as the input of Step-3(Trajectory Optimization).The alternating iteration process is repeated until the stop condition achieves.

In this section, the proof of the convergence of the proposed algorithm is provided.First, the values of the objective function obtained in thej-th iteration are written asR1(Aj,Pj,Qj),R2(Aj,Pj,Qj), andEE(Aj,Pj,Qj), which correspond to the values of objective subproblems (P2), (P3), and (P4), respectively.Thus,the following inequalities(46a)and(46b)are obtained in the(j+1)-th iteration,wherea,b,andcin(46a)indicate the optimal solutions for subproblems(P2),(P3),and(P4),respectively.Moreover,inequality (46a) indicates that Algorithm 3 is nondecreasing in each iteration.Therefore, the upper bound of the objective function corresponding to problem (P1) is finite, thereby guaranteeing the convergence of Algorithm 3.

3.5 Computational Complexity Analysis

In this section, this work analyzes the computational complexity of the overall algorithm.

Therefore, the total computational complexity is aboutOtotal=I3O(O1+O2+O3), whereI3represents the iteration numbers of the Algorithm 3.

IV.SIMULATION RESULTS

In this section, the numerical results are presented to demonstrate the effectiveness of the proposed scheme using the joint optimization of user scheduling and association, transmitting power, and UAV trajectory.Furthermore,three benchmark schemes are introduced for performance comparison,and the details are listed as following:

• Fixed trajectory energy efficiency maximization scheme (FTEE): for this scheme, the UAV flies along a circular trajectory(initial trajectory).The system energy efficiency is obtained by jointly optimizing UAV scheduling and association and transmitting power[21].

• Energy minimization scheme (EMS): for this scheme, we first optimize the UAV trajectory by minimizing the UAV flight energy consumption.After obtaining the trajectory,the maximum throughput of the system is obtained by jointly optimizing the UAV scheduling and association and transmitting power.

• Fixed power energy efficiency maximization scheme(FPEE):for this scheme,we fix the transmitting power to an average value, and then jointly optimize the UAV scheduling and association and the UAV trajectory achieves the system energy efficiency.

Before comparing the performances, we first show the convergence of proposed Algorithm 3 withT=120 s (Figure 4).The energy efficiency of our proposed algorithm increases rapidly as the number of iterations increases, and the algorithm reaches convergence after about approximately seven iterations.

Figure 4. Convergence of the alternating-optimizationbased approach for solving the problem with T=120 s.

The optimized UAV trajectory is obtained using Algorithm 3.Figure 5 shows that there is a certain difference between the optimized trajectory and initial trajectory.Compared with the initial trajectory, the optimized trajectory is smoother, and the flight energy consumption is smaller,as observed in a previous work [18].Furthermore, the UAV will be as close to the ground users as possible to obtain a better channel condition, and at the same time, it will be away from the D2D-TX users to reduce interference.When the UAV is closer to the D2D-RX user, the UAV will provide services to the D2D-RX user.This is because the instantaneous maximum transmitting power of the UAV is considerably greater than that of the D2D-TX user,which can provide greater transmitting power.

Figure 5. Relationship between the optimized flight trajectory and the initial trajectory with T=120 s.

Figure 6 and Figure 7 respectively represent the scheduling of the UAV for the cellular user and the D2D-RX user.The UAV will select the appropriate service user according to the current channel state and transmitting power.When there is a better channel state between the UAV and the cellular user, the caching content downloading service will be provided for the cellular user, and vice versa, which demonstrates the effectiveness of the scheduling algorithm.

Figure 6. Convergence of the alternating-optimizationbased approach for solving the problem with T=120 s.

Figure 7. Relationship between the optimized flight trajectory and the initial trajectory with T=120 s.

Figure 8 shows the relationship between different flight cyclesTand throughput.The longer the flight cycle, the greater is the throughput.Moreover, the achieved throughput by employing our proposed scheme is higher than that achieved by the other three benchmark schemes,proving that trajectory and power optimizations can result in improved performance gains.Thus,the effectiveness of our algorithm is verified.

Figure 8. Relationship between different flight cycles and the system throughput.

Figure 9. Relationship between different flight cycles and system energy consumption.

Figure 10. Relationship between different flight cycles and system energy efficiency.

Next,we perform a new simulation.Figure 9 shows that the FTEE scheme consumes the most energy because this scheme does not optimize the trajectory.Hence, considerable energy is consumed by propulsion.Moreover,the gap between the proposed scheme and EMS scheme is very small,indicating that the proposed scheme achieves an optimal balance between minimizing the UAV energy consumption and maximizing the throughput.For the FPEE scheme,the trajectory is optimized and the energy consumption is almost the same as that in the proposed scheme.

As shown in Figure 10,the energy efficiency of the proposed algorithm is significantly higher than that of the other three benchmark algorithms.For the three benchmark schemes, the energy efficiency value first monotonously increases with the flight cycle because whenTis small,the throughput growth rate is higher than the energy consumption growth rate.After reaching an optimal flight period, asTincreases, the energy consumption growth rate becomes considerably higher than the throughput growth rate and the energy efficiency begins to decline.Although this decline is also observed in the case of the proposed algorithm,the rate of decline is lower than that in the other three benchmark schemes.Initially, the energy efficiency of the FPEE scheme is slightly lower than that of the FTEE solution.As the flight period becomes longer,the energy efficiency of the FPEE solution becomes higher than that of the FTEE scheme, implying that over a long period, the benefits of FTEE scheme are higher than those of FPEE scheme.

V.CONCLUSION

This work investigates the D2D-based UAV-enabled MEC system, where the UAV functions differernt roles to provide different services to CUs and D2D-RX users.In the D2D communication phase,the D2D-TX users can serve as local cache device to serve D2DRX users.The optimization problem involves maximizing the energy efficiency of the system while satisfying the involved constraints.To handle the nonconvex mixed integer fraction optimization problem,an effective iterative algorithm is proposed by jointing optimizing the user scheduling stratgies,the transmitting power and the UAV trajectory.Specifically,combining the penalty function, Dinkelbach method,and SCA technique.The simulation results show that the proposed scheme performs better than the other benchmark schemes.

ACKNOWLEDGEMENT

The authors would like to express their high appreciations to the supports from the National Natural Science Foundation of China (61571156) and Basic Research Project of Shenzhen (JCYJ20170413110004682 and JCYJ20150403161923521).