Energy-Efficient Full-Duplex UAV Relaying with Trajectory Optimization and Power Control in Maritime Communication Environments

Lili Guo ,Xiaodong Ji ,Shibing Zhang

1 School of Information Science and Technology,Nantong University,Nantong 226019,China

2 Nantong University Xinglin College,Nantong 226236,China

Abstract: This paper solves an energy-efficient optimization problem of a fixed-wing unmanned aerial vehicle (UAV) assisted full-duplex mobile relaying in maritime communication environments.Taking the speed and the acceleration of the UAV and the information-causality constraints into consideration,the energy-efficiency of the system under investigation is maximized by jointly optimizing the UAV’s trajectory and the individual transmit power levels of the source and the UAV relay nodes.The optimization problem is non-convex and thus cannot be solved directly.Therefore,it is decoupled into two subproblems.One sub-problem is for the transmit power control at the source and the UAV relay nodes,and the other aims at optimizing the UAV’s flight trajectory.By using the Lagrangian dual and Dinkelbach methods,the two sub-problems are solved,leading to an iterative algorithm for the joint design of transmit power control and trajectory optimization.Computer simulations demonstrated that by conducting the proposed algorithm,the flight trajectory of the UAV and the individual transmit power levels of the nodes can be flexibly adjusted according to the system conditions,and the proposed algorithm can achieve significantly higher energy efficiency as compared with the other benchmark schemes.

Keywords: UAV communication;full-duplex relaying (FDR);energy-efficiency;maritime communication

I.INTRODUCTION

Relay techniques have been widely applied in wireless communications because it can significantly enhance the communication performance and coverage[1—5].In recent years,due to the significant decrease in manufacturing costs,unmanned aerial vehicles (UAVs) have been widely used.In the field of wireless communications,utilizing UAV relay has the advantages of high mobility and are more likely to provide line-of-sight (LoS) links with ground terminals so that it can serve as a good supplement to ground relays [6].In addition,on-demand UAV systems can be swiftly deployed,making them suitable for unexpected or limited-duration missions.However,due to the limited payload capacity of the UAV,it is impossible to payload a large amount of energy after carrying necessary communication equipment.Therefore,how to complete as many communication tasks as possible with as little energy consumption as possible is an urgent problem to be solved for UAV assisted communication systems[7—12].

The energy efficient optimization for UAV assisted communication systems has attracted increasing interest recently.In general,UAVs can be classified into two categories: rotary-wing and fixed-wing UAVs.In[13] and[14],rotary-wing UAVs are utilized to communicate with multiple pairs of ground nodes,and the UAV’s trajectory and communication time are optimized with the purpose of minimizing the total energy consumption of the system.Compared with rotarywing UAVs,fixed-wing UAVs are more energy efficient and thus can fly longer distances.In [15],an energy efficient trajectory design is proposed for the communications between a fixed-wing UAV and a ground node.According to the aerodynamic parameters,as well as the UAV’s mass,flying speed and acceleration,a theoretical model on energy consumption of fixed-wing UAVs is first derived in [15].In addition,an energy efficient trajectory design is developed for the communications between the fixed-wing UAV and the ground nodes.In [16],an optimal trajectory design of a fixed-wing UAV is presented so as to achieve the tradeoff between the throughput and the energy consumption.However,power control of UAV and ground nodes is not investigated in[16].The authors of [17] consider a multi-antenna fixed-wing UAV-enabled relaying system,and investigate a joint design of power control,flight speed and circular radius for energy efficiency.However,it is assumed that the UAV always follows a circular trajectory.In[18],a UAV swarm assisted multi-hop relaying system is studied with the aim of enhancing the system energy efficiency.It is worth-noting that all of the studies mentioned earlier focused only on the network settings of terrestrial communications.For maritime environments,UAV-assisted communications can also play an important role for increasing communication coverage and performance,and thus deserves a thorough study.

It should be pointed out that due to the differences between terrestrial and maritime communication environments,especially the discrepancy of the channel,the algorithms for improving system performance of terrestrial communications cannot be applied to maritime communications.Therefore,it is necessary to design novel algorithms suitable for maritime communications.Currently,there are some works in literature that exploit UAVs to assist maritime communications [19—24].In order to extend the communication coverage,the authors of [19] present a UAV system for maritime machine-type communications.In [20],a UAV is dispatched in a maritime data collection system to collect data from buoys.By optimizing the UAV’s flight trajectory and the communication time of the buoys,the UAV’s energy consumption is minimized.The authors of [21] and [22]explore a satellite-terrestrial maritime communication system,where UAVs are deployed to enhance coverage.With the purpose of maximizing the minimum achievable rate of the system,the trajectory and the transmit power level of the UAV are jointly optimized.In [23],a non-orthogonal multiple accessbased maritime UAV communication system is developed to serve more ships.By jointly optimizing the power and the transmission duration of the UAV,the minimum ship throughput is maximized.In [24],the UAV’s trajectory is optimized for maritime radar wide area persistent surveillance.It should be noted that the minimum rate or throughput is maximized without considering the UAV’s energy consumption in [21—23].However,in maritime communications,UAVs are usually powered by batteries,and thus cannot land on the sea surface to replenish energy,therefore the energy consumption of UAVs is quite important.How to design the flight trajectories of UAVs to achieve high throughput with low energy consumption,namely to improve the energy efficiency,is a significant issue in UAV maritime communications,which is not yet considered in[19—24].

In this paper,we study an energy efficient fullduplex mobile relaying system in maritime communication environments,where a fixed-wing UAV is employed to communicate with the source and destination nodes located on ships.The transmit power and the flight trajectory of the UAV are jointly optimized for energy efficiency of the system,where the initial and final velocity and position of the UAV,and the maximum acceleration and velocity of the UAV as well as the information-causality constraint are considered together.It is worth-mentioning that joint UAV trajectory and/or transmit power allocation of UAV relay assisted communication networks has been studied in[15]and[25].However,the proposed methods in [15] and [25] cannot be applied to solve the problem of our paper.The reason is twofold.On one hand,the user equipments in[25]and the ground terminal in[15]are on the ground,whereas the terminals(nodes S and D) in our paper are on the sea surface,meaning that the communication environments and the channel models are different.In our paper,we assume that the channel from S to R is LoS link and the channel from R to D follows the 2-ray path loss model,which is different from the Rician faded channel assumption in [25] and the all LoS links assumption in[15].On the other hand,the objective of[25]is to improve the system throughput,whereas our goal is to enhance the energy efficiency of the system.In addition,although [15] has the same objective with our paper,transmit power optimization of the UAV is not considered in[15].Therefore,the optimization problems of [15] and our paper are different.Therefore,the proposed methods in[15]and[25]are not suitable for solving the problem of our paper.The main contributions of the paper are summarized as follows:

1) We propose a model for a UAV-assisted maritime communication system and formulate an optimization problem to maximize the energy efficiency of the UAV-assisted relaying system.To the best of our knowledge,there is no similar work that optimizes the transmit power and the flight trajectory of the UAV for energy efficiency maximization in maritime communication environments,where the link from the UAV to the destination is modelled as 2-ray path model.

2) We then study the transmit power control and the UAV’s flight trajectory for solving the formulated optimization problem.In order to deal with the non-convexity issue,the original optimization problem is decoupled into two sub-problems which are solved utilizing the Lagrangian dual and Dinkelbach methods.On this basis,we develop an iterative algorithm for the joint design of transmit power control and trajectory optimization.

3) Lastly,we analyze the convergence and the complexity of the iteration algorithm,and provide simulation results to validate the performance of the joint design.From the simulation results,we show that the energy efficiency of the joint design is better than that of the trajectory optimization only scheme and the transmit power control only scheme.

The rest of this paper is organized as follows.First,the system model under investigation and the corresponding optimization problem are described in Section II.In Section III,the optimization problem is solved by using the Lagrangian dual and Dinkelbach methods,leading to an iterative algorithm that jointly optimizes the transmit power levels of the nodes and the relay trajectory for energy efficiency.The simulation results and comparisons are presented in SectionIV.Finally,Section V concludes the paper.In addition,the key notations are listed in Table 1 to facilitate the readers.

Table 1.Key notations used in this paper.

II.SYSTEM MODEL AND PROBLEM FORMULATION

2.1 System Model

We consider a full-duplex mobile relaying system in maritime communication environments,where a fixed-wing UAV denoted by R is employed as a mobile relay to receive data from the source node S and forward data to the destination node D.Considering the limited energy of S and D,suppose that the two nodes stay stationary during the communication.The distance between S and D isLm.Assume that S and D cannot communicate directly,and thus all the data need to be forwarded through the UAV relay R.The UAV relay R operates in a full-duplex relaying(FDR)mode and adopts the decode-and-forward(DF) protocol.In order to store the received data,it is assumed that the data buffer of the UAV relay R is large enough during the communication process.It is noted that for a fixed-wing UAV,frequent lifting and descending during flight will bring additional energy consumption.Therefore,it is assumed that the UAV relay R flies at a fixed altitude ofHmeters.

In the paper,a three-dimensional coordinate system is established as shown in Figure 1.The nodes S and D are located atS=(0,0,0)andD=(L,0,0),respectively.The UAV relay R starts from the initial position(x0,y0,H) at the initial speedv0and stops at the terminal position (xF,yF,H) at the final speedvF.This paper focuses on the UAV’s flight stage,and ignores its take-off and landing phases.Suppose that the communication time of the UAV-assisted relaying system isTseconds.Here,Tis divided intoNtime-slots,and the time of each time-slot is denoted byδ,i.e.

Figure 1.The UAV-assisted relaying system under investigation.

For the case thatδis small enough,the position of the UAV in one time-slot can be considered to remain unchanged.Therefore,the system throughput at the beginning of each time-slot is regarded as the data rate of the whole time-slot in this paper.Denote byqS=[0,0] andqD=[L,0] the horizontal coordinates of S and D,respectively.In addition,q(n)=[x(n),y(n)]is used to represent the horizontal coordinate of the UAV relay R in time-slotn.Assume that R is at the initial position whenn=1 and at the terminal position whenn=N+1,meaning thatq(1)=[x0,y0] andq(N+1)=[xF,yF].Therefore,in then-th time-slot,the distance between R and S and that between R and D can be respectively expressed as

wheren=1,2,...,N.

2.2 Signal and Channel Model

In maritime communication environments,the channel fading is actually composed of large-scale and small-scale fading.However,it is usually challenging to acquire the small-scale fading due to its dynamic property.Therefore,only large-scale fading is considered,which varies relatively slowly and is location dependent.According to [26],the path loss of ground-to-air communication systems generally follows the free-space curve when the distance between the ground and air nodes is less than 10 km,and the two-ray effect is apparent only at the larger values of distance(>10 km).Here,the distance between S and R is less than 10 km,therefore the two-ray effect is not apparent and the channel from S to R in Figure 1 is dominated by LoS link,following the free-space path loss model [27].For the channel from R to D which corresponds to an air-to-ground communication,there is a reflected ray from the sea surface besides the LoS path,therefore it follows the 2-ray path loss model,which is widely adopted in the literature,e.g.[19]and[28].Furthermore,Doppler effect caused by the UAV mobility is assumed to be perfectly compensated[29].Thus,in then-th time slot,the channel gains from S to R and from R to D can be respectively expressed as

whereβdenotes the channel power at the reference distanced=1m,αis the large-scale fading factor,λdenotes the wavelength,htis the height of the transmitter which is equal to the flight altitude of the UAV,andhris the height of the receiver at D.Here,we give a brief explanation of the acquisition of (5).From [28] we can know that,in then-th time-slot,the 2-ray propagation loss of the channel from R to D isL2?ray=then (5)can be obtained by usingTherefore,in then-th time slot,the signals received by the UAV and by the destination node D can be respectively written as

wherexS(n)andxR(n)denote the transmit signals of S and R,respectively,zR(n)andzD(n)are the noises at R and D,PS(n)andPR(n)are the transmit power of S and R,kandhRRrepresent the self-interference elimination factor and the self-interference channel gain of the UAV relay R,respectively.Suppose that the communication links from S to R and from R to D have the same channel bandwidthB,and the noise power at R and D is the same.Then,the instantaneous channel capacity of the links from S to R and from R to D can be written as[30]

wheren=1,2,...,N,gRR=k|hRR(n)|2denotes the residual self-interference (RSI) at the UAV relay side,andσ2is the noise power.Assume that the UAV relay R cannot forward the received data immediately,and at least one additional time-slot is needed for R to process the data.Therefore,no data can be sent by R to D in the first time-slot and S should not transmit data to R in the last time-slot.It means thatRRD(1)=0 andRSR(N)=0 hold.Furthermore,R can only forward data that has already been received from S,and thus the following information-causality constraint(10)must be satisfied.

2.3 UAV Energy Consumption Model

Generally,the total energy consumption of a UAVassisted relaying system consists of three parts,i.e.,the UAV flight and the communication related energy consumptions in addition to the static energy consumption of circuit.However,the latter two parts are usually much smaller than the UAV flight energy,and thus can be ignored.According to [15],for a fixed-wing UAV with level flight,its flight related energy consumption can be expressed as(11)

wherev(n) anda(n) represent the flight speed and the acceleration of the UAV in then-th time-slot,v0andvFdenote the initial and final velocity of the UAV,respectively,mis the UAV’s mass,gstands for the gravitational acceleration,c1andc2are two parameters related to the air density,aircraft’s weight,wing area,etc[15].

It should be noted that for the UAV relay R,the values ofq(n),v(n) anda(n) in then-th time-slot will determine its velocity and position in the next timeslot,which can be expressed as

2.4 Energy Efficiency

According to the discussions in section 2.2 and section 2.3,and with the aim of maximizing the energy efficiency of the UAV-assisted relaying system,the optimization problem corresponding to the joint design of transmit power control and flight trajectory optimization can be formulated as follows

whereBis the bandwidth of the system,Eis the UAV flight related energy consumption given by (11),(14b) denotes the information-causality constraint,(14c),(14d) and (14e) refer to the maximum and average transmit power constraints of S and R,(14f) represents the UAV’s initial velocity and location,(14g)denotes the UAV’s final velocity and location,and(14j)is the velocity and acceleration limits of the UAV.

III.JOINT DESIGN OF TRANSMIT POWER CONTROL AND TRAJECTORY OPTIMIZATION

It can be observed that the objective function of problem (14) as well as the constraint (14b) are nonconvex,meaning that problem(14)cannot be directly solved with standard convex optimization techniques.Thus,two sub-problems are investigated,namely,1)transmit power control of S and R with fixed relay trajectory;2) UAV’s trajectory optimization with fixed transmit power.By solving the two sub-problems,an iterative algorithm is developed to achieve a suboptimal solution of problem (14),leading to a joint design of transmit power control and UAV trajectory optimization.

3.1 Optimal Power Control with Fixed Relay Trajectory

Since the UAV relay’s trajectory is assumed to be fixed,the values ofa(n),v(n) andq(n) are known.In addition,it can be observed from (4),(5) and (11)that the channel gainshSR(n)andhRD(n),and the system energy consumptionEare fixed in this situation.According to (9),PR(n) can be written as a function with respect toRRD(n),i.e.

Likewise,according to(8),PS(n)can be written as

Then,according to the above discussions,the optimization problem of power control with fixed relay trajectory can be written as

It can be observed that problem (18) is a convex optimization problem with respect to{RSR(n),RRD(n)},which can be numerically solved by standard convex optimization techniques.However,instead of relying on a generic solver,here,we apply the Lagrange dual method to obtain the optimal solution to problem(18).To this end,we first introduce the Lagrangian dual variables{λn,μ1,μ2}.Then the Lagrangian function of problem(18)can be expressed as

Furthermore,using the constraints (18c) and (18d)leads to

Here,θrepresents the step size of the gradient algorithm.The algorithm for solving problem(18)is summarized in Algorithm 1.

Algorithm 1.The iterative process for solving problem(18).

3.2 Trajectory Optimization with Fixed Power

Here,the UAV relay’s trajectory optimization with fixed transmit power levels of S and R is investigated.As a first step,the channel capacity from R to D is analyzed.By substituting (3) and (5) into (9),RRD(n)can be rewritten as

In(27),the sine function has the oscillation characteristic,and thus it is difficult to deal with.To this end,an approximation of (27) is adopted,as described in the following.

Suppose thatv0=vF,therefore the second term of(11)is 0.Then,the trajectory optimization problem with fixed power can be formulated as

whereE′is equal to the first term of(11).

Obviously,problem (29) is not a convex problem.In order to solve it,slack variablesRr(n) andτ(n)are introduced so that the following constraints should be satisfied.

On this basis,problem(29)can be reformulated as

It can be observed from (33) that when the optimal solution is obtained,Rr(n)=RRD(n) andτ(n)=∥v(n)∥must hold,otherwise,a better target value can be obtained by increasing the values ofRr(n) andτ(n).Therefore,problem (33) is equivalent to problem (29),and the optimal flight trajectory of the UAV can be obtained by solving problem (33).After the introduction of the slack variables,the constraints(30),(31)and(33b)are still nonconvex.Therefore,the continuous convex approximation method is used.

It can be observed from (28) thatRRD(n) is nonconcave with respect top(n),but it is convex with respect to∥p(n)∥2.According to the fact that the first-order Taylor expansion of a convex function is its global under-estimator,for the(j+1)-th iteration,we can find a lower bound ofby using its firstorder Taylor expansion at∥pj(n)∥2as follows

Thus,(33b) and (31) can be respectively transformed into

and

Therefore,for the(j+1)-th iteration,problem(33)can be transformed into

Problem(40)is a fractional maximization problem,which can be efficiently solved via fractional programming methods.Here,we employ the Dinkelbach method to solve problem (40).The Dinkelbach method is an iterative algorithm.For thel-th iteration(Here,ldenotes the number of iterations so as to distinguish it from the symboljabove),let

and for the(l+1)-th iteration,let

With a given parameterωl,problem (43) is a standard convex optimization problem with convex objective function and constraints,which can be solved by the interior-point method.By updating parametersωl,problem(40)can be solved iteratively.The detailed iteration process is summarized in Algorithm 2.Based on the solution of problem (40),problem (33) can be solved iteratively through sequential convex approximation,as detailed in Algorithm 3.

3.3 Joint Power and Trajectory Optimization

According to Algorithms 1 and 3 proposed in sections(3.1)and (3.2),an iterative algorithm is proposed for the joint design of power control and trajectory optimization,which finally solves problem(14).The iterative algorithm is summarized in Algorithm 4.

Algorithm 2.The iterative process of problem(40).

Algorithm 3.The iterative process of problem(33).

3.4 Algorithm Convergence and Complexity Analysis

The convergence of Algorithm 4 is proved as follows.we denote byEE(aj,Pj)the acceleration of the UAV,the transmit power of S and the UAV,the objective function of problem (14) in thej-th iteration,respectively.First,in step 3 of Algorithm 4,since the optimal solutionPj+1of problem(18)is obtained through Algorithm 1 for givenaj,we have the following inequality

Then,in step 4 of Algorithm 4,after running Algorithm 3,we further have

Algorithm 4.Joint design of power control and trajectory optimization.

Based on(44)and(45),we obtain

which indicates that the objective value of problem (14) is non-decreasing after each iteration of Algorithm 4.Moreover,the maximum objective value of problem (14) is upper-bounded by a finite value through a finite of iterations.Therefore,Algorithm 4 is guaranteed to converge.

IV.NUMERICAL RESULTS

In this section,computer simulation results are provided to validate the proposed design.The distanceLbetween S and D is 2000m.The flying altitude of the UAV is fixed atH=200m,and the UAV flies from the initial position (700,200,200) to the final position(1300,200,200).The maximum and minimum UAV’s speed are set tovmax=50m/s andvmin=5m/s,respectively,and the maximum UAV’s acceleration is set toamax=5m/s2[15].The communication bandwidth isB=1MHZ with the frequency at 5GHz,and the noise power spectrum density at the UAV and the node D is assumed to beN0=-120dBm/Hz[15].The height of the receiver at D ishr=20m.Furthermore,c1=0.000926 andc2=2250 are assumed[15].

The flight path of the UAV varies with the flight timeT.The average transmit power levels of S and D are set toFigure 2 gives the flight trajectories of the UAV in maritime communication environments with flight timeT=40s,T=60s,T=80s,T=100s andT=120s by using the joint design of transmit power control and trajectory optimization.For comparisons,the UAV trajectories in the case of terrestrial communications where the links from S to R and from R to D are both LoS are also provided in Figure 2.In Figure 2 (a),when the flight timeTis short,the UAV flies in closely“U”-shape path,which is because the fixed wing UAV needs radian to change direction and cannot change its flight direction instantaneously.With the increase of time,the UAV first moves to S to receive more data,then flies towards D to forward the received data to D,and finally returns to the final position.In summary,since the channels from S to R and R to D in terrestrial communications are both LoS links,the flight trajectories of the UAV are approximately symmetric.In Figure 2 (b) Since the channel between S and R has LOS link,its condition is better than that between R and D.In order to forward the received data to D,the UAV flies in the direction of D.WhenTis short,the UAV will return to the final position before it flies over D.When the flight time increases,the UAV first flies to D,then flies around D for some time,and finally returns to its final position.It can be seen that the UAV is able to adjust its flight path according to the flight time,thus improving the system energy efficiency.

Figure 2.Trajectories of the UAV for different flight time.

Figure 3.Transmit power of S under three different schemes.

Figure 4.Transmit power of the UAV under three different schemes.

As compared to the terrestrial communications,the R-D link is worse than the S-R link in maritime environments,and thus the UAV flies as closely as possible to D so as to achieve more data rates from S to D.

Figure 3 and Figure 4 give the transmit power levels of S and R versus the UAV’s flight time.Here,three different schemes are included,namely,1) trajectory optimization only,2)transmit power control only,and 3)joint design of transmit power control and trajectory optimization.For the scheme of trajectory optimization only,the transmit power levels of S and R remain constant,and are equal to their average transmit powers.For the scheme of transmit power control only,the UAV flies straight and uniformly from the initial position to the final position at the initial speed.As deduced earlier,with the increase of flight time,the UAV flights far away from S and closer to D.Therefore,in order to obtain more throughput,the transmit power of S decreases monotonically,while the transmit power of R increases gradually.For the joint design scheme,in order to reduce the energy consumption of the system,the transmit power of S also decreases gradually.For the UAV,at beginning,it is far away from D and thus the channel condition between R and D is poor.In this situation,the transmit power of S is small.When R and D get close,the channel condition becomes better.Then,the transmit power of R becomes larger so that more data can be transferred to D.At the final phase,R flies towards the final position.Then,the distance between R and D increases again,and thus R sends with small transmit power.

Figure 5.Trajectories of the UAV under different schemes.

Figure 5 plots the flight trajectories of the UAV under the aforementioned three different schemes as well as the rate maximization and energy minimization schemes.It is observed from Figure 5 that,for the scheme of transmit power control only,since the flight trajectory of the UAV is not took into account,the UAV flies straight and uniformly from the initial position to the final position at the initial speed.For the trajectory optimization only and joint design schemes,the UAV first flies toward D,then flies around D in an approximate ellipse for a period of time,and lastly flies back to the final position.Compared to the scheme of trajectory optimization only,however,the UAV’s flying range around node D of the joint design scheme is smaller and the distance between R and D is closer,thus achieving higher energy efficiency of the system.For the rate maximization scheme,the UAV hovers around the node D so as to achieve the maximum possible duration to improve the throughput performance,which is actually more power consuming.For the energy minimization scheme,the UAV follows a path with large turning radius which is less power consuming,however,the throughput performance is worse due to the resulting large distance between R and D.Therefore,the rate maximization and energy minimization schemes are inefficient.The joint design scheme is able to obtain relatively good throughput performance without excessive power consumption,which is more energy efficient.

Figure 6.Energy efficiency versus flight time T.

In Figure 6,the energy efficiency achieved by the three schemes in maritime environments and a benchmark scheme is plotted versus the flight timeT.The benchmark scheme refers to that the UAV flies straight from the initial position to the final position with average power where the S-R and R-D channels are LoS links.It can be observed from Figure 6 (a) that the energy efficiency of the benchmark scheme decreases gradually with increasing the flight time.This is because of the fact that the system energy consumption increases gradually with the increase of time.In addition,Figure 6 demonstrates that the benchmark scheme outperforms the three schemes given in Figure 6 (b) in view of energy efficiency.The reason is that the R-D link of the benchmark scheme has LoS and is much better than that in the maritime environments.It is observed from Figure 6 (b) that for the scheme of transmit power control only,the energy efficiency of the system decreases slightly with the increase of flight time of R.This is because the energy consumption of the UAV also increases with the increment of flight time.For the scheme of transmit power control only,the achieved improvement of the throughput of the UAV is very limited,as a result,the energy efficiency decreases.Compared with the scheme of transmit power control only,the scheme of trajectory optimization only improves the energy efficiency of the system to a large extent,however,it is still not the optimal solution.On the other hand,the joint design scheme proposed in this paper can greatly enhance the energy efficiency of the system.With the increase of flight time,the energy efficiency of the joint design scheme is the highest,due to the fact that the UAV has more time to adjust its trajectory,and thus greatly improves the throughput and reduces the energy consumption.

V.CONCLUSION

This paper studied the energy efficiency of a fullduplex UAV relaying system in maritime communication environments.The energy efficiency of the system is maximized through a joint design of transmit power control of the nodes and the UAV’s trajectory optimization.For the non-convex original problem that cannot be solved directly,the progressive optimization method is adopted to first optimize the transmit power and the trajectory,separately.On this basis,an iterative algorithm is proposed for the joint optimization of transmit power and trajectory.Simulation results showed that the energy efficiency of the system of the proposed scheme is better than that of the compared schemes.The longer the flight time,the more time can be used by the UAV to adjust its flight path flexibly and achieves greater energy efficiency.

ACKNOWLEDGEMENT

This work was supported by National Natural Science Foundation of China (No.61871241) and Nantong Science and Technology Project (JC2019114,JC2021129).

NOTES1The approximation adopted here is valid.The reason is twofold.On one hand,by adopting this approximation,the optimization problem can be solved and the resulting joint design scheme outperforms the benchmark schemes,confirming that the approximation is effective.On the other hand,the approximation only affects the information causality constraint of the optimization problem,which can be always satisfied through simulation verification.