Zhen Wang,Fuhui Zhou,Yuhao Wang,Qihui Wu

1 School of Artificial Intelligence,Beijing University of Posts and Telecommunications,Beijing 100876,China

2 School of Information Engineering,Nanchang University,Nanchang 330031,China

3 Nanjing University of Aeronautics and Astronautics,Nanjing,211106,China

4 Shaanxi Key Laboratory of Information Communication Network and Security,Xi’an University of Posts and Telecommunication,Xi’an,710061,China

Abstract:In this paper,we consider a new spectrum sharing scenario for a cognitive relay network,where a secondary unmanned aerial vehicle(UAV)relay receives information from the ground secondary base station(SBS)and transmits information to the ground secondary user(SU),coexisting with the primary users(PUs)at the same wireless frequency band.We investigate the optimization of the UAV relay’s three-dimensional(3D)trajectory to improve the communication throughput performance of the secondary network subject to the interference constraints of the PUs.The information throughput maximization problem is studied by jointly optimizing the UAV relay’s 3D trajectory and the transmit power of the SBS and the UAV,subject to the constraints on the velocity and elevation of the UAV relay,the maximum and average transmit power,and the information causality,as well as a set of interference temperature(IT)constraints.An efficient algorithm is proposed to solve the admittedly challenging non-convex problem by using the path discretization technique,the successive convex approximation technique and the alternating optimization method.Finally,simulation results are provided to show that our proposed design outperforms other benchmark schemes in terms of the throughput.

Keywords:cognitive radio;UAV communication;3D trajectory design;mobile relaying;power allocation

I.INTRODUCTION

Unmanned aerial vehicles(UAVs)have been widely applied to various fields,ranging from civil to military,due to their flexibility and fast mobility.With the progress of unmanned aerial vehicle(UAV)manufacturing technology and the reduction of their manufacturing cost,more and more people are aware of their application values[1].Up to now,UAVs have been applied to many fields of civil and commerce,such as cruise detection,photography,wireless communication,which have brought great application values and commercial benefits[2].Recently,UAVs have been being used in the field of wireless communication networks to help information transmission.The hotspot research on UAV-assisted wireless communication has attracted more and more attention of scholars and experts from all over the world.Due to the operation at a high elevation,a UAV as an air information transmitter[3],a relay or an access point[4]can cover the entire community in a communication network.The UAV was combined with edge computing(MEC)technology to minimize the power consumption[5]or maximize the computation rate[6]in the communication network.The UAV-assisted communication network can provide more reliable communication links by establishing line-of-sight(LoS)connection with terrestrial users or base stations.The UAV can enhance the communication performance of a wireless network due to its high probability of providing LoS transmission links.Moreover,it can further improve communication performance by dynamically adjusting its position in 3D space[7].Thus,a UAV-assisted wireless communication network not only can effectively reduce the deployment cost of communication facilities,but also can improve the service quality of a communication system.

1.1 Related Work and Motivation

Under the circumstances of communication infrastructure failure or non-wireless coverage areas,a UAV can play the role of a relay that provides data transmission service to restore communication.A UAV relay-assisted wireless communication has the potential to improve communication performance and expand communication coverage.In the wireless communication system,the roles of UAV relays are mainly classified as static relays[8–12]and mobile relays[13–18].The research purpose of static UAV relays is to search the best hover point to maximize the performance of the wireless network system[8–12].The authors of[8]proposed a fine-grained LoS algorithm to acquire the optimum hover point of the UAV for the system throughput maximization.In[9],the authors considered a static UAV as the relay and studied its optimal location for the reliability maximization of the system.A UAV acting as a relay served many communication pairs in[10],where an effective approach was proposed to maximize the total throughput through the UAV position optimization and resource allocation.In[11],the system signal-to-noise ratio(SNR)was maximized by optimizing multiple relay UAVs’ locations based on the channel models and the relaying protocols.The location optimization of a UAV in a relaying network was studied in[12],where the total data rate of relaying network was maximized under the SNR and the transmit power constraints.

The study and application of UAV-enabled mobile relaying have attracted great attention recently[13–18].A mobile UAV relay was used to assist communication of isolated communities after disasters in[13],where the worst-case performance among communities was maximized via optimizing UAV’s carried data volume and its flight path.In a mobile UAV relay network,the authors researched the maximization problem of the system throughput subject to the mobility constraint and the information-causality constraint in[14].A mobile UAV relay network in[15]was considered and a spectrum-efficiency maximization problem was proposed.A UAV relay network based on the movability of the UAV,the amplifying and forwarding techniques[16]and the multi-hop links[17]were studied to maximize the system throughput.The authors in[18]aimed to research the outage probability minimization for a relay system through power allocation and trajectory optimization of a mobile UAV relay.Compared with the relaying approaches of statistic UAVs,the dynamic trajectory of UAVs as mobile relays which are able to offer more reliable connectivity links and more cost-effective schemes can improve the communication performance of wireless networks.

In order to improve spectrum utilization in wireless communication networks,there are many investigations focusing on cognitive UAVs[19–27].The authors in[19]and[20]optimized the power and path of the UAV in order to maximize the average rate of information transmission for the secondary user(SU)in a UAV-assisted cognitive system,where the communication of the primary users(PUs)is protected by setting interference thresholds.There are research on the secrecy rate maximization of the UAV in the cognitive secondary network[21,22].Thereinto,the authors in[21]exploited the S-Procedure algorithm to maximize the secrecy rate for the cognitive UAV in the regulatory application of urban environment.The authors in[22]studied a UAV with interference noise to maximize the system security rate for a secondary transmitter,while the inference threshold for the primary receiver was satisfied.In[23],the authors proposed a resource allocation algorithm of the location and bandwidth based on the swarm intelligence to manage spectrum and energy effectively in cognitive UAV wireless communication.

According to[24],the launch power of the UAV,the perception time and the perception threshold based on location information were jointly optimized in a cognitive network to solve a trade-off problem among them.In[25]and[26],the authors analyzed the information rate of a UAV relay and proposed a special linear precoding scheme in the cognitive MIMO system.In[27],the authors aimed to maximize the information rate of the satellite users based on the UAV trajectory optimization and the power optimization of the BS and the UAV,subject to the interference and the UAV location constraints for a satellite network.It is noted that the works in[19–24]and[27]studied the UAV application in a cognitive network,but did not investigate UAV-assisted cognitive relay networks.In[25]and[26],although they investigated the linear precoding scheme for a UAV relay-assisted cognitive radio MIMO system,they did not study the optimization problem of joint the UAV trajectory and its power.

It is worth noting that the location placement or the trajectory optimization of a UAV in 3D space has been studied to improve the system communication performance[20],[28–35].For example,the work[20]studied the UAV’s 3D location deployment to maximize information transmit rate in order to enhance cognitive system performance.In[28],the transmit power and 3D location of the UAV were optimized to maximize the transmit rate of all mobile users in a relay network.In[29],a UAV harvested solar energy and served multiple terrestrial users to maximize the system throughput through the UAV’s 3D trajectory and its power optimization.The work[30]focused on the UAV-assisted wireless networks and investigated 3D deployment and trajectory optimization of UAVs due to their mobility,maneuverability and flexibility.The work[31]proposed two effective online 3D placement algorithms for obtaining the optimal location of a UAV.In[32]and[33],a UAV was used to collect information from the sensor nodes in wireless sensor network and optimized its 3D trajectory to maximize information collection rate.A UAV secretive communication system was considered in[34],where the maximization problem of the average secrecy rate was studied based on the UAV 3D trajectory optimization.In the relay network of multiple UAVs collaboration,the system data flows were maximized via the 3D trajectories optimization of multiple UAVs[35].The above literatures[28–35]have not studied the UAV’s 3D trajectory optimization and designed in a cognitive radio system except for the work in[20].However,the authors in[20]have not considered the UAV relay in a cognitive network system.

Additionally,resource allocation schemes have been proposed for single-UAV and multiple-UAVs communication systems.For example,the resource allocation strategy and trajectory of multiple UAVs were jointly optimized to maximize the average minimum secrecy rate[36]and the energy efficiency[37]in the secure UAV communication systems.The sum power minimization problems were proposed based on power,UAV location and bandwidth resource allocation in a single UAV-enabled[38]and multiple UAVs-enabled[39]wireless communication system.

Although wireless communication technologies make great progress,there still exist the non-wireless covered areas and the spectrum resource scarcity problem[40].A UAV acting as a relay is introduced to wireless communication networks for expanding communication areas in emergency communication areas.A UAV which is applied to a cognitive wireless system can solve the spectrum shortage problem effectively and improve spectrum efficiency.Therefore,there is great research value for a UAV relay-assisted cognitive radio networks.In this paper,the secondary UAV relay’s 3D trajectory and the transmit power of the secondary base station(SBS)and the UAV are jointly optimized to maximize the information throughput of the SU in a cognitive wireless network,subject to the constraints of the initial and final location of the UAV relay,the constraints of the maximum speed and altitude range of the UAV relay,the maximum and average power constraints,the information causality constraint,as well as a set of IT constraints.According to the relevant investigation and comparison,our work is a novel work,which takes into account the joint power allocation and 3D trajectory optimization of a UAV in a UAV relay-assisted cognitive radio system.

1.2 Contributions and Organization

In this paper,we consider a UAV relay-assisted cognitive radio system,in which the UAV plays the role of a relay in the secondary network,receiving information from the SBS in the uplink and transmitting information to the SU in the downlink,while protecting the PUs’communication.In regard to main contributions of our work,it is summarized as follows.

1)A novel cognitive UAV relay network is studied.The UAV relay can help the secondary network to transmit information from the SBS to the SU,coexisting with PUs at the same wireless frequency band.The UAV should control the caused interference to the ground PU and cannot affect communication among the PUs in the primary network.We formulate the information throughput maximization problem for the SU,and jointly optimize the UAV relay’s 3D flight path and its transmit power,as well as the SBS’s transmit power,subject to IT constraints,the information causality constraint,the UAV relay’s maximum velocity and elevation range constraints,and the peak transmit powers constraints.

2)It is difficult to find a direct method to solve original problem,because it is non-convex.To address this non-convex problem,first,we convert the original problem into the discretization problem based on the path discretization method.Then,we adopt the techniques of successive convex approximation(SCA)and alternating optimization method to transform nonconvex discretization problem into a convex problem,in order to solve the original problem.

3)By the relevant comparison and analysis of simulations,it is shown that the performance of our proposed designs is superior to other benchmark design with respect to the flexible deployment and the throughput.

In this paper,the organization of the remainder content is as follows.In Section II,we put forward a novel system model and formulate the throughput maximization problem of the SU in the continuous time domain.In Section III,the algorithm based on path discretization and alternating optimization is proposed to address the original problem.By the relevant comparison and analysis of simulations,the effectiveness of our proposed solution is verified in Section IV.In Section V,we conclude our work of this paper.

II.SYSTEM MODEL

As shown in Figure 1,we consider a UAV relayassisted cognitive radio network,where a UAV relay is deployed in the sky to establish communication between the SBS and the SU,both of which are located on the ground.Since the SBS is far away from the SU and they cannot communicate with each other in the existence of a primary network between them,a secondary UAV relay is applied to assist communication in the secondary network.The full-duplex mode is considered in our work.The UAV first receives information from the SBS and then forwards it to the SU,while controlling the caused interference to the ground PUklocated at(xPU,k,yPU,k,0),k∈K,K={1,···,K}within a tolerable level.Note that the italic letter of this paper represents scalar.In this system model,the SBS and the SU are supposed at stationary positions(x0,y0,0)and(x1,y1,0)respectively in a 3D Cartesian coordinate system,wherewSS=(x0,y0)andwSU=(x1,y1)are defined as the horizontal coordinates of the SBS and the SU,respectively.In the primary network,the horizontal coordinate PUkis written aswPU,k=(xPU,k,yPU,k),k∈K.Suppose that the specific locations of the SBS,the SU and the PUs are informed to the UAV relay in advance,so as to optimize transmission resource allocation and design UAV’s fight trajectory.In the total fight timeTt,the relay UAV is supposed to fly with the maximum horizontal speed ˙Vmax.Let(x(t),y(t),H(t)),t∈[0,Tt],represent the UAV’s 3D position.The altitudeH(t)is between the maximum flight altitudeHmaxand the minimum flight altitudeHmin.Let q(t)=(x(t),y(t))∈R2×1,0≤t ≤Ttrepresent the UAV relay’s horizontal position,where the boldface letter andrepresent vector and the space of 2-dimensional real-valued vector,respectively.The straight-line distance between the UAV relay and the SBS can be expressed as

Figure 1.The system model.

Figure 2.The UAV relay’s horizontal trajectory.

Figure 3.The UAV relay’s altitudinal trajectory.

where‖.‖represents vector’s Euclidean norm.In our considered scenario,the SBS,SU and PUs are all located in a spacious area.In this case,the wireless channel between the UAV and the ground users is dominated by the LoS link[36,37].By applying the free-space path loss model[14]into the communication channel between the SBS and the UAV relay,we can attain the channel power gain of the communication link between them as

whereλ0is on behalf the power gain of the reference channel based on one meter communication distance.Although the trajectory of the UAV changes as timet,the straight-line distance between the UAV relay and the ground SU at any timetcan be calculated as

Likewise,a free-space path loss model is considered in the communication channel between the UAV relay and the terrestrial SU.Thus,the channel power gain between them is written as

In this paper,suppose that the UAV relay with an adequate data buffer follows a time-division multiple access(TDMA)transmission mechanism for information collected from the SBS and transmitted to the SU.In the cognitive system,the UAV relay communicates with the terrestrial SBS and the ground SU,in the presence of PUs operating over the same wireless frequency band.It is assumed that the Doppler effect is ideally offset[41]and is not considered in this model.In the secondary network,the ground SBS transmits information to the UAV relay with the transmission powerPB(t).Assume that the interferences at the SU and the UAV from the PUs are circularly symmetric complex Gaussian.This interference model is the worst case model which has been widely used in[42].Thus,in the uplink of the cognitive secondary network,the data transmission rate of the terrestrial SBS at timetin Bit/s/Hz is expressed as whereσ2denotes the total power of receiver noise and the primary network interference at the UAV and the SU[20],[42],Brepresents the channel bandwidth in the cognitive network,andis defined as the reference signal to interference plus noise ratio(SINR).Analogously,the UAV relay transmits the collected information to the SU,and its transmission rate is expressed as

wherePU(t)is on behalf of the UAV relay’s transmit power for forwarding information to the SU.Hence,in the communication time periodTt,the aggregated information throughput of the ground SU is written as

The UAV relay can collect the information from the terrestrial SBS.Meanwhile,the UAV relay can transmit it to the ground SU.In order to ensure the balance of total data bits,the cumulative amount of the transmitted information of the UAV relay cannot exceed the cumulative amount of the received information of it over a period.The information-causality constraint for the secondary network at any timetis given as

Whether the SBS transmits information or the UAV relay forwards data in this cognitive communication network,it causes interference to all PUs in the primary network.In the cognitive radio,we adopt the IT technique[43]to protect the communication among PUs,thus,the power interference for every terrestrial PU is no more than the tolerant IT threshold.The distances from the PUkto the UAV relay and the SBS are written asanddBP,k=‖wSS ?wPU,k‖,respectively.When the interferences of the PUs are caused by the transmit power of the SBS,the tolerant IT threshold for each PU is set as ΓB.When the interference is within ΓB,the communication among the PUs cannot be affected.Since the SBS and the PUs are all fixed on ground,the channel model between the SBS and the PUs is assumed to follow independent Rayleigh fading with channel power gainwhereθandζdenote the path loss exponent and an exponentially distributed random variable with mean one,respectively[22,44].According to Rayleigh fading model,the IT constraint which avoids the average interference from the SBS for each PU is expressed as

In the cognitive system,we optimize the UAV relay’s horizontal trajectory q(t),UAV heightH(t),the transmission powerPB(t)of the ground SBS and the UAV relay’s transmission powerPU(t),so as to maximize the system throughput for the secondary network.To simplify the expression of notations,we defineandAccording to the above content,this problem is formulated as

From problem(P1),it is observed that the optimized variables q(t),H(t),PB(t)andPU(t)are all continuous functions in time domain.Because of the continuous variables,the non-convex constraints(8)and(10),and the non-convex objective function,it is difficult to directly address(P1)to obtain optimal values.Thus,the problem(P1)needs to be converted by disposing of continuous variables.In Section III,we adopt path discretization technique to convert the continuous variables into the discrete variables,and transform the problem(P1)into a discrete equivalence problem.Based on SCA technique,an efficient algorithm of alternating optimization is put forward to solve the discrete equivalence problem.

III.PATH DISCRETIZATION AND PROPOSED SOLUTION TO PROBLEM

By using path discretization technique to dispose of continues time variablesPB(t),PU(t),q(t)andH(t),the throughput maximization problem is reformulated in this section.According to the discretization idea,the UAV relay’s path is divided intoMsmall segments and its flight timeTtis divided intoMequal time slots.We define time instantwhere the time incrementδtis supposed to be enough small so that the distance change value of the UAV relay is constant.Thus,the UAV relay’s horizontal trajectory q(t)and its altitudeH(t)over flight timeTtare discretized asrespectively.By definingthe constraint conditions of the UAV relay’s trajectory change are expressed asandwhereis defined as.

Based on discretization method,the data transmit rateRUU[m]between the UAV relay and the SU in the downlink is written as

Thus,the total amount of transmission information of the UAV relay from the SBS to the SU in(7)overMtime slots is discretely expressed as

Suppose that the data disposing time of the UAV relay needs one time slot before forwarding information,and the transmission mode is simplex communication in the cognitive secondary network.As a consequence,the UAV relay collects information from the SBS at one time slot,in the meantime,transmits the previous information to the SU.Due to the data disposal requirement of one time slot,the UAV relay does not transmit information to the SU at the first time slot,i.e.,RUU[1]=0,and does not receive information from the SBS at last time slotM,i.e.,RBU[M]=0.At time slotm,the information-causality constraint is written as

In this paper,the total information throughput of the secondary network is required to be maximized by optimizing both the SBS and the UAV relay power allocationsand the UAV relay’s 3D trajectoryIn the discrete solution,these symbolsP,QandHneed to be rewritten as{q[m],?m}andrespectively.Based on the discretization method disposal for(P1),we can obtain the discrete optimization problem(P2),which is formulated as

where(16c)and(16d)represent the average and maximum power constraints of the SBS and the UAV relay,(16e)is the UAV relay’s horizontal speed constraint,(16f)denotes the UAV relay’s initial point and final point constraints.(16g)and(16h)indicate that the constraints on UAV’s maximum ascending speed and maximum descending speed,and its range of flight altitude,respectively.(16i)and(16j)denote the PUs’IT constraints.The left hand side(LHS)of(16i)is obtained by dealing withSince the channel model between the SBS and the PUs is assumed to follow independent Rayleigh fading[22],[44],we can obtainwhereis constant term with a value of one.So,we can also obtainWe notice that the constraints(16c)-(16h)and(16i)are all convex in(P2).Nevertheless,(P2)still is non-convex problem on account of non-convex objective function,non-convex information-causality constraint(16b),as well as non-convex PUs’IT constraints(16j).Therefore,we cannot directly use standard convex optimization techniques to solve(P2).For the sake of attaining an optimal solution of(P2),we put forward an effective algorithm based on the alternating optimization technique.

In the next section,(P2)is separated into two sub problems which are a sub-problem of power optimization with fixed the UAV relay’s 3D trajectory and a sub-problem of the UAV relay’s 3D trajectory optimization under the given power,respectively.We optimize the two sub-problems alternately based on SCA technique to attain optimal solution for problem(P2)until converge.

3.1 Transmit Power Optimization with Fixed 3D Trajectory

In the first sub problem,the transmit powerPB[m]andPU[m]are optimized with given the UAV relay’s horizontal trajectory q[m]and its altitudeH[m].Based on the alternating optimization method,we can formulate the sub problem(P2.1),which is written as

In problem(P2.2),note that the newly introduced objective function(18a)and inequality constraint(18b)are obtained by replacing the objective function(17a)and inequation(17b),and meanwhile a new constraint condition(18c)is added.In constraint(18c),if there exists one optimal solution satisfying inequality strictly,it is always able to make both sides of the constraint(18c)equal by reducing transmit powerPU[m][14].This implies that(P2.2)is an approximate problem of(P2.1)under the fixed UAV’s 3D trajectory.We can observe that all constraints of(P2.2)are convex.Thus,(P2.2)is a convex problem.In order to attain the optimal solution for(P2.2),we adopt the interior point method[45]to solve(P2.2).The interior point method is an optimization algorithm for solving linear programming or nonlinear convex optimization problems based on the penalty function[45].

3.2 3D Trajectory Optimization with Fixed Transmit Power Allocation

In the second sub-problem,the UAV relay’s 3D trajectory,which includes its horizontal trajectory q[m]and altitudeH[m],is optimized with the given transmit powerPB[m]andPU[m].Likewise,based on the idea of alternating optimization variables,we can formulate the sub problem(P2.1),which is written as

where a slack variable?[m]is introduced for convex disposal of the objective function and the constraints.It’s worth noting for(P2.3)that the newly introduced objective function(19a)and the inequality constraint(19b)are obtained from(16a)and(16b),and a new constraint condition(19c)is added.Because the new objective function(19a)and the constraints(19e)are linear with one variable,they are all convex constraint conditions or function.However,problem(P2.3)is still a non-convex because of nonconvex constraints(19b)-(19d).Hence,these nonconvex constraints(19b)-(19d)need to be converted into convex constraints to acquire optimal solution of(P2.3)by using the Taylor expansion method and the SCA technique.

In the inequality constraint(19b),although the LHS function of(19b)is a convex,the function of its right hand side(RHS)is a non-concave by jointly considering variables q[m]andH[m].Based on the Taylor expansion method of bivariate vector functions,we can obtain the lower bound function for the RHS of(19b)as follows.

We can notice that the LHS of(19c)is not concave in regard to variables q[m]andH[m].Likewise,the first order Taylor expansion for the LHS of(19c)is written as

Then,the constraint(19d)is rewritten as

We notice that the constraint(22)is non-convex because the RHS of inequality(22)is non-concave in regard to the UAV horizontal path q[m]and altitudeH[m].At given iterative valuethe first-order Taylor expansion of bivariate vector functions is applied for the RHS of(22),and the lower bound of the inequality is written as

Therefore,the constraint(22)is rewritten as

According to above processing,(P2.3)is reformulated as

The new optimization problem(P2.4)is a convex problem,which is obtained via disposing of non convex constraints(19b)-(19d)of problem(P2.3).Based on the toolbox CVX[46],the convex problem(P2.4)is solved to attain its optimal values of global lower bound,which are also able to satisfy problem(P2.3).Therefore,(P2.4)is equivalent to(P2.3)for given transmit power allocation.

Algorithm 1.The alternating optimization for(P1).1:Initialization:Set the initial path of the UAV relay asq(0)[m],H(0)[m],and set IT threshold ΓB and ΓU,and f=0.2:Repeat:3:With givenq(f)[m]andH(f)[m],attain the optimal power allocation images/BZ_204_859_1046_890_1092.png P(f+1)B[m]o and images/BZ_204_290_1133_321_1178.png P(f+1)U[m]o by solving(P2.2).4:For given images/BZ_204_492_1219_522_1265.png P(f+1)B[m]o and images/BZ_204_851_1219_882_1265.png P(f+1)U[m]o,update the UAV 3D trajectoryq(f+1)[m]andH(f+1)[m]by solving(P2.4).5:Update the iterative number f=f +1.6:Until the objective value of(P2.4)converges within a given accuracy ε.7:Obtain solutions:Popt B[m],PoptU[m],qopt[m]and Hopt[m].

We propose an efficient algorithm and summarize as Algorithm 1 based on the alternating optimization technique.In sub problem(P2.2),the upper bound value of the transmit powerPB[m]andPU[m]is obtained by constraint conditions(18d),(18e)and(18f).Based on the upper bound value of the transmit powerPB[m]andPU[m],there exists always an optimal value of objective functionφ[m]to satisfy the inequality(18b)and(18c),i.e.we can obtain the feasible solution of sub problem(P2.2).In sub problem(P2.4),the lower bound value of the slack variableμ[m]is obtained by constraint(26d).When the constraints(26f)are met and the constraint(26e)is strictly equal,the lower bound value of the formula‖q[m]?wPU,k‖2+H[m]2is obtained.Based on the lower bound value of the formula‖q[m]?wPU,k‖2+H[m]2,there exists always an optimal value of objective function?[m]to satisfy the inequality(26b)and(26c),i.e.we can obtain the feasible solution of sub problem(P2.4).Since the solutions of problem P2.2 and P2.4 are the suboptimal solutions of the original problem.Thus,the feasible solution of P2.2 and P2.4 are the feasible solution of the original problem.In Algorithm 1,the optimal values are all updated at each iteration until convergence to attain global optimal solution for problem(P2.2)and(P2.4).On the basis of the analysis method of algorithm complexity in[47]and[48],the total complexity of Algorithm 1 is calculated aswhereM1represents the iteration number of the SCA method,andεdenotes given accuracy threshold.Since the SCA technique is used to tackle the challenging non-convex original problem,our algorithm can obtain the sub-optimal solution.

IV.SIMULATION RESULT

In this section,numerical results are presented to evaluate the performance of our proposed algorithm for jointly optimizing the UAV relay’s 3D trajectory and transmit power in a cognitive UAV relay network.In the following simulations,we set the UAV relay’s maximum horizontal speed asVmax=60 m/s[14],the UAV’s maximum ascending speed asVA=5 m/s,and the UAV’s maximum descending speed asVB=5 m/s.In this simulation,the range of flight height for the UAV relay is set to be not lower than the lowest altitudeHmin=50 m and be not higher than the highest altitudeHmax=100 m.We set the power gain of the reference channel asλ0=?30 dB and the interference power aswhich leads to SINR asFurthermore,the terrestrial SBS is fixed at horizontal position(500m,1000m),and the terrestrial SU is fixed at horizontal position(2500m,1000m).In the simulation,the UAV relay takes off from the its set initial point(0m,500m),and eventually flies to its set final destination location(3000m,500m).The UAV’s initial altitude is set as 50m.We set the average transmit power of the SBS and the UAV relay asdBm anddBm,respectively.The SBS’s transmit power can not exceed set maximum power valuedBm.Likewise,the UAV’s transmit power cannot exceed set maximum power valuedBm.In the cognitive network,we consider three PUs,i.e.K=3,and adopt blue triangles to mark their positions in the simulation diagram.For the interference constraint(16i),the path loss exponent is set asθ=3[49].The interference of the PUs all comes from the SBS or the UAV relay at any timeslot.Since the stored energy of the UAV is limited during its flight,we set the flight time of the UAV asT=65 s.In addition,we set the initial trajectory of the UAV relay which is a straight line segment between initial point and final point.

Figure 2 and Figure 3 show the horizontal optimization trajectory and altitudinal optimization trajectory of the UAV relay based on four groups of IT thresholds ΓBand ΓU,respectively.From the observation of Figure 2,the UAV relay takes off from the initial point and flies to the nearby SBS for collecting information,then flies to the SU and transmits information to the SU while keeping away from the PUs,and finally flies to the final point after completing the mission.In Figure 3,It is shown that first the UAV relay gradually flies to the highest point from the original height of 50 meters,then comes back to the original height during the period from the SBS to the SU.From the observation of Figure 3,the closer the UAV flies to the PUs,the higher the UAV will fly in the altitude direction.In Figure 2,when the tolerant IT thresholds are set as ΓB=?103 dBm and ΓU=?62 dBm,the UAV relay is closest to PUs horizontally from the SBS to the SU;when the tolerant IT thresholds are given as ΓB=?119 dBm and ΓU=?70 dBm,the UAV relay is farthest to the PUs in the horizontal direction.This is because as the IT thresholds ΓBand ΓUdecrease,the PUs are more sensitive to the interference from the SBS and the UAV relay.As a result,when the UAV relay passes the PUs,it is not only far away from the PUs at the horizontal direction,but also flies higher from the height in order to avoid interfering with the PUs.As shown in Figure 2,when the ΓBthresholds are set to equal values and the ΓUthresholds are set to different values in two groups of IT thresholds,the two flight trajectories of the UAV from the SBS to the SU are far apart from each other.When the ΓBthresholds are set to different values and the ΓUthresholds are set to equal value in other two groups of IT thresholds,we can observe that two path curves of the UAV relay flying from the SBS to the SU are close to each other.This indicates that the PUs are more sensitive to the interference caused by UAV relay than produced by the SBS.

Figure 4.The change of throughput for the SU versus duration T with different trajectories of the UAV relay.

Figure 4 shows the change of communication throughput of the SU versus flight durationTwith different trajectories of the UAV relay.In Figure 4,the simulation results of the four designs are all based on a group of IT thresholds,i.e.,ΓB=?103 dBm and ΓU=?62 dBm,which are arbitrarily selected in four groups of the IT thresholds.Note that as transmission timeTincreases,the information throughput received by the SU all increases for four different trajectory schemes.It is worth noting that when the flight durationTis less than 35 s,the cumulative information throughput of the SU increases slowly;when the flight durationTis greater than 35 s,the cumulative information throughput of the SU increases rapidly.This is because the UAV relay mainly collects data from the SBS before the 35th second,and the UAV relay principally transmits information to the SU after the 35th second to enable the information throughput of the SU to accumulate quickly.From the observation of Figure 4,when the transmit power of the SBS and the UAV relay are optimized for four different trajectory designs,the information throughput of the SU based on the UAV relay’s 3D trajectory optimization is larger than that based on the optimization scheme of the UAV relay’s 2D trajectory and design scheme of the UAV relay’s straight flight trajectory in general.Although the information throughput of the SU based on the UAV relay’s 3D trajectory optimization is slightly larger than that based on the optimization scheme of the UAV relay’s 2D trajectory with fixed heightH=50 m,the former with flexible height adjustment can obtain better communication channel than the latter with fixed height.This indicates that the proposed design of joint 3D trajectory optimization of the UAV relay and power optimization of the UAV relay and the SBS is the optimal scheme among four designs in terms of the throughput and flexible deployment.Meanwhile,this also shows the significance of 3D trajectory optimization which is able to improve transmission throughput in the cognitive relay network.

Figure 5.Information transmission scheduling of the UAV relay.

For the four groups of IT thresholds,the scheduling strategies of information transmission of the UAV relay are almost the same according to simulation results.Therefore,we arbitrarily choose one group of IT thresholds and display the scheduling scheme of information transmission for the UAV relay.Figure 5 shows scheduling scheme of information transmission about the UAV relay when the values of tolerant IT thresholds are ΓB=?103 dBm and ΓU=?70 dBm.In Figure 5,we can observe that the front part time slots of the entire time slots are all scheduled for the UAV relay collecting information from the SBS,the middle time slots are allocated for the UAV relay both collecting information and transmitting information,the back time slots are all allocated to transmit information from the UAV relay to the SU.Through the above analysis of simulation result of Figure 5,we can clearly know the scheduling mechanism of information transmission for the secondary network of cognitive system.

Figure 6.The change of optimization power of the SBS and the UAV relay versus time T.

Figure 6 shows the change of optimization power of the SBS and the UAV relay versus time T with the IT thresholds ΓB=?103 dBm and ΓU=?70 dBm.We can observe from the blue curve that the value of the SBS transmit powerPBrapidly goes up to the peak and then slowly goes down to zero.This is because when the UAV relay moves near the SBS,the SBS increases the transmit power so as to quickly transmit information to the UAV relay.When it moves far away from the SBS,the SBS reducesPBvalue due to the average power limit.Figure 6 shows that the power valuePUfor the UAV relay slowly enlarges from zero to the maximum value and then quickly descends to certain power value.It is shown that during the UAV relay flying to the SU,the UAV relay slowly enlarges its transmit power to not only increase the transmission of information for the SU,but also avoid large interference to the PUs.

Figure 7.The causality of total collecting and transmitting information of the UAV relay versus time T.

The causality of total collecting and transmitting information of the UAV relay versus time T based on the tolerant IT thresholds ΓB=?103 dBm and ΓU=?70 dBm is shown in Figure 7.From Figure 7,the UAV relay continuously receives information from the SBS before the 42th second,and constantly transmits information to the SU from the 20th second until the last moment.It is obviously observed from Figure 7 that the two curves of collecting and transmitting information for the UAV relay finally intersect at the same point.That is due to the information causality according to(16b),that is to say,the sum transmitting information of the UAV relay is equal to or less than the sum collecting information of the UAV relay.

Figure 8.The convergence of Algorithm 1 with different tolerant IT thresholds.

Figure 9.The number of iterations for solving problem 2.2 and problem 2.4.

Figure 8 shows the convergence of Algorithm 1 with four groups of tolerant IT thresholds.From Figure 8,we can observe that four curves go up very rapidly and reach stable values by a few iterations.Figure 9 shows the number of iterations for solving problem 2.2 and problem 2.4 under the IT thresholds ΓB=?103 dBm and ΓU=?62 dBm.In Figure 9,we can observe that the required number of iterations for solving problem 2.2 and problem 2.4 are few.It indicates that our proposed algorithm is able to converge efficiently.It also verifies the efficiency of our algorithm based on 3D trajectory optimization and power allocation design in the cognitive network.

V.CONCLUSION

In this paper,a new spectrum sharing scenario was considered for a cognitive relay network,where the secondary UAV relay received information from the ground SBS and transmitted information to the ground SU.The problem of joint the transmit power and the UAV relay’s 3D trajectory optimization was studied in the cognitive UAV-assisted relay network.The total information throughput of the SU was maximized via the 3D trajectory optimization of the secondary UAV relay,the power allocation of the SBS and the UAV relay subject to the UAV relay’s velocity and altitude constraints,the maximum and average power constraints,the information causality constraint,as well as a set of IT constraints.We exploited path discretization,SCA and alternating optimization method and presented an efficient algorithm to solve the challenging non-convex problem.By comparing the simulation of our proposed design with it of other benchmark schemes,this indicated that our proposed scheme outperforms the benchmark schemes in terms of the throughput of the SU.

ACKNOWLEDGEMENT

This work was supported by the National Key Research and Development Project under Grant 2020YFB1807602,Natural Science Foundation of China under Grant 62071223,62031012,61701214 and 61661028,by the National Key Scientific Instrument and Equipment Development Project under Grant No.61827801,the Open Project of the Shaanxi Key Laboratory of Information Communication Network and Security under Grant ICNS201701,the Excellent Youth Foundation of Jiangxi Province under Grant 2018ACB21012 and in part by the Young Elite Scientist Sponsorship Program by CAST.