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1906IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING, VOL. 5, NO. 4, DECEMBER 2021Energy-Efficient Resource Allocation in Multi-UAVNetworks With NOMASaif Najmeddin , Graduate Student Member, IEEE, Sonia Aïssa , Fellow, IEEE,and Sofiène Tahar , Senior Member, IEEEAbstract—This paper investigates the energy efficiency (EE)optimization in a wireless communication network wheremultiple UAVs serve different types of devices, namely,information receivers (IRs) and energy receivers (ERs). The UAVstransmit power signals towards the ERs, and then enable datatransmission to IRs on the downlink and from ERs on the uplinkwith non-orthogonal multiple access (NOMA). The optimizationproblem to maximize the overall EE is formulated and solvedusing Lagrangian optimization and gradient-descent methods.The optimization is decomposed into two sub-problems. Firstly,by connecting the path loss of the devices’ channels with theirrate demands, the UAVs’ optimal positions are obtained. Then,based on the obtained UAVs’ optimal positions and a closed-formexpression for the EE, a resource allocation aiming to maximizeEE is developed. For the simulations, two main scenarios forsingle and multiple UAVs are considered. Numerical results andcomparisons are provided. In particular, for the single-UAV scenario, the results show an enhancement in EE for the operationwith NOMA compared with OMA. For the multiple-UAV scenario, several cases depending on different combinations of thedevices’ rate requirements are considered. The results show thesuperiority of NOMA over OMA in all use cases. The results alsoreveal the effect of considering the devices’ rate requirements onthe EE, where the case with equal rate requirements has the bestperformance.Index Terms—UAV, wireless power transfer, WIPT, NOMA,resource allocation, energy efficiency.I. I NTRODUCTIONNMANNED aerial vehicles (UAVs) are becoming morereachable and available to be used in numerous applications. With their cost-effectiveness, flexibility, and 3D mobility, UAVs are considered to be an appealing and efficientsolution for many challenges. One of UAVs’ crucial applications is in the area of wireless communications, wherereliable and cost-effective services can be provided througha network of single or multiple UAVs [1]. For example, UAVsUManuscript received February 15, 2021; revised May 20, 2021 and July 19,2021; accepted July 20, 2021. Date of publication July 30, 2021; date of current version November 22, 2021. This article was presented in part at the 2020IEEE Global Communication Conference, Taipei, Taiwan. (Correspondingauthor: Saif Najmeddin.)Saif Najmeddin is with the ECE Department, Concordia University,Montreal, QC H3G 1M8, Canada, and also with the Institut Nationalde la Recherche Scientifique, Montreal, QC H5A 1K6, Canada (e-mail:s najmed@ece.concordia.ca).Sonia Aïssa is with the Institut National de la Recherche Scientifique,Montreal, QC H5A 1K6, Canada (e-mail: sonia.aissa@inrs.ca).Sofiène Tahar is with the ECE Department, Concordia University, Montreal,QC H3G 1M8, Canada (e-mail: tahar@ece.concordia.ca).Digital Object Identifier 10.1109/TGCN.2021.3101200can be deployed to enable power and information transfer inInternet of things (IoT) networks, in which the devices areenergy-constrained and their limited battery capacity may notallow communication over long ranges [2], [3]. Depending onthe application, an UAV can enable service to/from differenttypes of devices, namely, devices transmitting and/or receivingdata, termed information receivers (IR) hereafter, and devicescapable of harvesting energy and transmitting data, referredto as energy receivers (ER) hereafter. In fact, UAVs can beefficiently used to charge ERs via downlink wireless powertransfer (WPT) to enable their data communication on theuplink, and also transmit data to IRs according to their servicerequirements.In many B5G use cases, its expected that UAVs will becalled to concurrently serve ERs and IRs to provide efficient WPT along with reliable data services. The use ofsuch a concept needs to meet the radio resource sharing ofB5G, where non-orthogonal multiple access (NOMA) willvery likely be replacing the conventional orthogonal multipleaccess (OMA) approach [4]. In fact, NOMA has recentlyreceived significant attention for its promising performance.However, this comes with additional complexity, where successive interference cancellation (SIC) has to be performed forreliable services [5], [6].Although the use of UAV to serve multiple IRs and ERsbased on the NOMA scheme is interesting and promising, thiscomes with many challenges, including the limited power budget of the UAV, the constraints on its positioning, the devices’quality of service (QoS) requirements, etc. Intuitively, additional complexities appear when the network involves multipleUAVs, which is becoming essential in many use cases toenhance the coverage of the network. For example, a collision avoidance scheme should be in place. Moreover, unlikesingle-UAV networks, where all devices are linked to the sameUAV, the device association problem in deployment cases withmultiple UAVs has to be tackled efficiently.A. Related WorkIn the related literature, some works focused on the resourceallocation to enhance the performance of UAV-enabled WPTor wireless information transfer. For instance, the work in [7]addressed maximization of the system throughput by exploiting trajectory design of the UAV jointly with the resourceallocation optimization, where a single UAV transfers power tomultiple ERs by changing its position periodically. The authorsc 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.2473-2400 See l for more information.

NAJMEDDIN et al.: ENERGY-EFFICIENT RESOURCE ALLOCATION IN MULTI-UAV NETWORKS WITH NOMAin [8] investigated the energy efficiency optimization in a WPTnetwork, where ERs are wirelessly powered from a single UAVto enable their uplink information transmission, by optimizingthe transmit power towards each ER after getting the optimalplacement of the UAV. In [9], a placement algorithm wasproposed to optimize the UAV transmit power and maximizethe coverage of the ground nodes (GNs). Also, the authorsof [10] considered the perfect user location information (ULI)to maximize the system throughput by optimizing the UAVplacement. In [11], on the other hand, partial ULI was usedto develop an adaptive UAV deployment scheme, where theposition of the UAV is optimized based on limited informationabout the GNs.Few other works considered networks where several IRsand ERs are served by a single UAV. The work in [12] studied the problem of maximizing the end-to-end cooperativethroughput for a network of UAV-enabled simultaneous wireless information and power transfer (SWIPT), by optimizingthe UAV’s decision profile, power profile, and trajectory, fordifferent protocols. Also, [13] considered a SWIPT networkthat consists of a single UAV and IoT devices, and appliedconcave-convex procedure to maximize the devices’ minimumrates. In [14], the authors considered a network of IoT devicesenabled by a single UAV, and tackled maximization of theminimum harvested energy among the IoT devices by optimizing the power allocation and the trajectory design of theUAV. Leveraging the benefits of NOMA over OMA, the workin [15] proposed a cooperative NOMA scheme to maximizethe weighted sum-rate of the UAV and GNs by optimizing the power allocations and the UAV’s rate. Furthermore,minimization of the energy consumption of GNs with acceptable QoS was tackled in [16], where offloading was enabledby uplink and downlink communications between the GNs andthe UAV via NOMA or OMA protocols.In addition to the above, few studies investigated theperformance of multiple-UAV communication systems. Forinstance, the authors of [17] investigated the download coverage probability in a network of multiple UAVs which weremodeled as a uniform binomial point process at the same altitude. The work in [18] investigated stochastic modelling ofUAV base stations, where different coverage models were suggested. Also, [19] studied the maximization of the minimumdata rate of GNs by jointly optimizing the 3D locations, userassociation, and power allocation in multiple-UAV networks.The aforementioned works have presented promising resultsin this area, but there is considerable potential for furthergains. For example, many works considered single-antennaUAV in the models, which basically degrades the UAV’s ability to meet the service requirements of the GNs. Also, only afew works considered scenarios with multiple UAVs, whichare crucial to provide efficient coverage in most practicalcases. Furthermore, some systems were based on the OMAscheme, with no consideration of NOMA. Moreover, mostworks ignored the most critical aspect in this particular setup,namely, energy efficiency (EE), which is extremely importantas we are dealing with limited on-board energy resources. Dueto its significant impact on performance, EE of UAV-aidedcommunication systems requires careful consideration.1907B. ContributionsIn this work, we address the optimization of the EE of awireless network, where several multiple-antenna UAVs serveas simultaneous power and information transmitters towardsERs and IRs, respectively, and where energy harvested by theERs is used for their uplink communications towards theirassociated UAV, based on NOMA scheme. Considering partial ULI about the ERs and IRs, we present a user distributionand association model for each device cluster in the network.We propose collision avoidance constraints to avoid UAVs’collisions as they move to enhance the links for the ERs andIRs. Moreover, a time allocation scheme is enabled to specify the optimal switching between the energy and informationtransmissions. We also consider several constraints on the mainsystem parameters, including the required QoS of the devices,and the thresholds to enable SIC. Considering the aforementioned constraints, we propose two algorithms to maximize theEE by first optimizing the UAVs’ positions and then optimizing the power pertaining to the IR and ER devices in eachcluster.Specifically, the main contributions of this paper can besummarized as follows: (i) We present a system model ofmultiple-UAV enabled WIPT with NOMA. We formulate andsolve a highly coupled non-convex optimization problem,where the goal is to maximize the system’s EE while satisfyingconstraints related to user association, power budget, collisionavoidance, acceptable QoS, and SIC thresholds. (ii) We propose two algorithms to solve the EE maximization problembased on the Lagrangian multipliers and gradient-descentmethod. Firstly, we optimize the UAVs’ locations to providebetter transmission links for the ERs and IRs; this is doneby introducing a demand requirement variable and connecting it to the path loss of each device. Secondly, we optimizethe power for each ER and IR to maximize the EE. (iii) Weconduct extensive simulations to assess the effectiveness of theproposed algorithms in two scenarios. For the single-UAV scenario, we detail the superiority of the NOMA-based schemeover the OMA scheme. For the multiple-UAV scenario, wepresent different cases based on different combinations of thedevices’ QoS requirements, and provide a comparison betweenall cases for the NOMA and OMA schemes.Next, Section II details the network model. Formulation ofthe EE is described in Section III-A. The optimization problemis formulated and solved in Section III. Numerical resultsare presented and discussed in Section IV. Finally, Section Vconcludes the paper.1II. S YSTEM AND C HANNEL M ODELSA. Multiple-UAV Based WIPTA network of multiple devices that are enabled by multipleUAVs is considered. There are two types of devices; IRsand ERs. We consider M multi-antenna UAVs serving several single-antenna devices that are distributed in a region ofinterest (ROI) (Fig. 1). We assume that the ROI can be divided1 Notation: Symbol E{.} is used for the expectation operator, (.)† denotesthe conjugate transpose, . denotes the modulus, . is the Euclidian norm,and [.] refers to max(0, .).

1908Fig. 1.IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING, VOL. 5, NO. 4, DECEMBER 2021Multiple-UAV wireless information and power transfer network.into a number of clusters that can be determined to providethe required coverage for the ROI, such that each cluster ofdevices will be served by a single UAV. A UAV does nothave perfect ULI of the devices in its cluster. The total number of antennas at the UAV is N NE NI , with NE usedfor the ERs, and NI dedicated to the IRs; this is the samefor all UAVs. The time slot T is divided into two phases. Inthe first phase, αm T (0 αm 1), each UAV transmitsenergy signals to the scheduled ERs in its cluster. In the second phase, (1 αm )T , the ERs make use of the harvestedenergy to transmit their always-available data to their associated UAV, while the UAV transmits information to the IRs,simultaneously. The data transmissions on the uplink (U) anddownlink (D) are performed according to the NOMA protocol.Without loss of generality, the time slot duration T is set tounity. The position of UAVm , m 1, . . . , M , is denoted by(xm , ym , hm ).B. Distribution of DevicesWe consider the partial ULI approach [20]. Initially, a UAVwill not have perfect information about the locations of theGNs. Each UAV will be sent to a specific cluster in the ROI.A cluster is defined as a circular coverage area of radius rm .The partial information that is known by a given UAV is thedistribution of the GNs within its cluster [21]. Specifically, weconsider that a cluster is subdivided into rings and segmentsas shown in Fig. 2. Denote the number of rings as Φ and thenumber of segments as Ψ. The rings are co-centered aroundthe origin and are such that the radius of the outer circle of ringφ is rm φ/Φ, and the angle between any two adjacent segmentsis 2π/Ψ. At the beginning, each UAV will be hovering at theminimum allowable height over the center of its correspondingcluster, then the devices that need to be served will send sideinformation to the UAV with the best link to each of them,which usually has the shortest distance to each of them. Thisinformation is related to their identities, e.g., ID of the GNlocated on the intersection between segment ψ and circle φis (ψ, φ) (cf. Fig. 2), along with their rate demands. Basedon the received information and the predetermined numberof scheduled GNs, the UAV chooses the devices that will beFig. 2.Distribution of devices in cluster m.served within its cluster, and positions itself accordingly tostart sending power and sending/receiving data.For simplicity of exposition, we replace the notation GNψ,φdepending on the device type. The notation becomes ERm,jfor ER devices, IRm,k for the IR nodes. In each cluster,there are J ERs and K IRs. The location of ERm,j isdenoted (xERj , yERj , hERj), and the one of IRm,k is denoted(xIRk , yIRk , hIRk). A quantized level of the uplink rate requirement is sent from each ER to its associated UAV to indicateits WPT demand. Based on this side information, and knowledge of the rate requirements of the IRs, each UAV determinesDthe relative demand of each ER and IR, denoted ΥUj and Υk , UDrespectively, such thatj ,k Υj Υk 1. Here, a largervalue of Υ means a higher rate demand. A binary variableof ER association with a specific UAVm is denoted χm,j ,and the one for IR is denoted χm,k . If ERm,j is served byUAVm , then χm,j 1, otherwise it is zero. Note that UAVmcan serve multiple ERs and IRs; but each device can only beserved by one UAV. These can be formulated as follows:M m 1M m 1χm,j 1, j .(1)χm,k 1, k .(2)χm,j {0, 1},χm,k {0, 1}, m, j .(3) m, k .(4)C. Channel ModelsThere are three types of channels in the network: 1) airto-ground (A2G) from the UAVs to IRs and ERs; 2) groundto-air (G2A) from the ERs to the UAVs; and 3) ground-toground (G2G) between the ERs and IRs. Consider UAVm ,m 1, . . . , M . The complex channel vector of the A2Glink UAVm -ERm,j is denoted gm,j C1 NE , for j 1, . . . , J . For the A2G link UAVm -IRm,k , k 1, . . . , K ,the complex channel vector of the A2G link is denoted C1 NI . First, we have NI . First, we have gm,j hm,k Dgm,j / LDERm,j , where LERm,j is the average path-loss, and

NAJMEDDIN et al.: ENERGY-EFFICIENT RESOURCE ALLOCATION IN MULTI-UAV NETWORKS WITH NOMA gm,j [gm,j, gm,j, . . . , gm,j] is the normalized channel12NE fading vector. With Rician fading, gm,jcan be written as [8]: K1 11 NE g̃ , (5)gm,jK 1K 1 m,jwhere K is the Rice factor, 11 NE is a unity row vector, andthe non-line-of-sight (NLoS) fading component g̃m,j is a rowvector the elements of which are i.i.d. complex Gaussian random variables with zero mean and unit variance, i.e., CN(0, 1).The average A2G free-space distance-dependent path loss ofERm,j , LDERm,j in dB, is given by: LD pL 1 pLoSm,j LoSm,jLoSm,j LNLoSm,j , (6)ERm,jwhere the LoS and NLoS path losses are expressed as 4πfdm,j ξLoSm,j ,LLoSm,j 20 log10c 4πfdm,j ξNLoSm,j ,LNLoSm,j 20 log10c11 a exp b 180π θm,j a(8),(9)where a and b are constant values related to the environment, and θm,j arccos(hUAVm /dm,j ) is the elevation anglein radian between UAVm and ERm,j , where dm,j is theEuclidean distance:dm,j xm xERm,j 2 ym yERm,j 2 hm hERm,j 2.(10)Using (6)-(10), we obtain:LDERm,j ξLoSm,j ξNLoSm,j1 a exp b 180π θm,j a 4πfdm,j ξNLoSm,j . 20 logcD. Energy TransmissionFor cluster m, UAVm transmits energy signal xm,1 CNE 1 , which consists of J energy beams, one for each ER,i.e.,xm,1 βm PmJ j 1ERwm,j sm,j,(12)ER CN(0, 1)where Pm is the transmit power of UAVm , sm,jdenotes the energy-carrying signal, and wm,j CNE 1 is thecorresponding energy beamforming vector. Here, βm indicatesthe percentage of power destined to the ERs in the m th cluster,and (1 βm ) indicates the percentage of power destined to theIRs. Hence, a larger value for βm means that higher prioritywill be given to the WPT. For the j th ER served by the UAVmin the m th cluster, its received signal is given by:(7)in which f is the carrier frequency, c is the speed of light, andξLoSm,j and ξNLoSm,j are the average environment-dependentexcessive path losses in dB [22]. In (6), pLoSm,j denotes theprobability that UAVm has LoS with ERm,j [22], given by:pLoSm,j 1909ERym,j gm,j βm PmJ ERwm,i sm,ii 1 M gl,jβl Pll 1,l mJ ERERwl,i sl,i nm,j,(13)i 1ER CN(0, σ 2 ) is the AWGN, and assumed withwhere nm,jσ 2 1 for all ERs. The second term in (13) represents theeffect on ERm,j from the simultaneous WPT from other UAVsto the ERs in their clusters. It is assumed that the harvestedenergy results from the energy signals in the cluster wherethe device is located, and that noise does not take part in it.2Assuming the availability of perfect channel state information† is gm,j/ gm,j . Hence,(CSI), the optimal weight vector wm,jthe harvested energy by ERm,j during the first phase isgiven by 2J gm,j 2 DDPm,i ζj α mPm,Em,j ζj αm gm,j wm,jDLm,ji 1(14)(11)The A2G channel model described above w.r.t. ERs (g)applies to the IRs (h) by replacing k with j and IR withER in (5)-(11). For the G2A link ERm,j -UAVm , the complex channel vector is denoted zm,j CNE 1 , and wealso considera Rician model as for gm,j , with zm,j Uzm,j / LERm,j , and LUERm,j being the average G2A distancedependent path-loss. As for the G2G channels, the complexchannel of link ERm,j -IRm,k is denoted em,j ,k , m 1, . . . , M , j 1, . . . , J , and k 1, . . . , K , which includesthe Rayleigh fading between ERm,j and IRm,k as well as thepath loss. Considering no LoS component as adopted in [23], em,j ,k em,j ,k / LNLoSm,j ,k , where em,j,k is the normalized channel fading, and LNLoSm,j ,k is the average path-losssimilar to (8) with the distance being between ERm,j andIRm,k .where 0 ζj 1 is the energy-harvesting circuit effiD ciency [24],the same for all ERs, and Pm JassumedDβm Pm j 1 Pm,j is the sum-power dedicated by UAVmto its J ERs.E. Information TransmissionIn the second phase, ERs use the harvested energy for theiruplink communication with the their associated UAV, simultaneously with the downlink transmission from the UAV to itsIRs.1) Uplink Information Transmission: The transmit powerU from the j th ER in cluster m served by UAVm is Pm,jEm,j1 αm .The UAV receives the superposed message signal of JERs, and applies SIC to decode each device’s message. The2 Since the energy signals that come from other clusters will be smallercompared to the signals that are beamed to the ERs in a specific cluster, weassume that their effects can be neglected.

1910IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING, VOL. 5, NO. 4, DECEMBER 2021IR CN(0, σ 2 ) is the AWGN, and assumed withwhere nm,k2σ 1 for all IRs. In the right-hand-side of (17), the secondterm represents the interferences on IRm,k from the uplinksignals of ERs in all clusters, and the third term representsthe interferences on IRm,k from the downlink signals to IRsin other clusters. For any IRm,k , since the interferences fromthe ERs and IRs in other clusters are small compared to theinterferences from ERs and other IRs in its cluster, their effectscan be neglected. Assuming the availability of perfect CSI, is h†m,k / hm,k . Hence, thethe optimal weight vector vm,ksignal-to-interference-plus-noise ratio (SINR) at IRm,k isreceived signal at UAVm , is expressed asym J j 1ERU zPm,jm,j sm,jK HSIm (1 βm )Pmk 1IRvm,k sm,k nm ,(15)ER CN(0, 1) is the normalized data symbolwhere sm,jof ERm,j towards UAVm , vm,k CNI 1 is the correIRsponding beamforming vector, sm,k CN(0, 1) denotesthe information-bearing signal of the k th IR, and nm isthe AWGN vector with zero mean and covariance matrixE{nm n†m } σ 2 INE , where INE is the identity matrix.Further, HSIm CNE NI is the self-interference (SI) channeldue to the simultaneous uplink and downlink processes [25],2 ) where σ 2with independent entries drawn from CN(0, σSISIaccount for the residual SI power after suppression [26], andit is assumed to be unity. We assume that powerful SI cancellation is in place [25], but since some SI will remain [27], weconsider the effect of the residual SI.2) Downlink Information Transmission: The data signalxm,2 CNI 1 sent by UAVm to its IRs consists of Kinformation beams, one for each IR:xm,2 (1 βm )PmK k 1IRvm,k sm,k. ,γm,k 2 2K J U D QD 1Qmi 1 hm,k vm,i j 1 Pm,j em,j ,km,ki k(18)D is the transmit power used for the data transferwhere Qm,kD (1 β )P is the powerfrom UAVm to IRm,k , and Qmm mdedicated to the IRs.III. E NERGY E FFICIENCY M AXIMIZATIONA. Energy Efficiency FormulationTo formulate the EE of the system under consideration,we have to construct the throughputs of the downlink anduplink stages for all clusters. For the downlink informationNOMA setup, where the channel gains of IRs are increasingwhen closer to the associated UAV (channel gain of IRm,1is larger than IRm,2 , and so on until IRm,K ) [28], thenbased on (14) and (18), the rate related to a given IR can beexpressed in the unit of bps as shown in (19), at the bottomof the page, where W is the bandwidth, assumed the samefor all GNs. According to the principles of power-domainNOMA, for a given IR, the strong interfering signals aremainly due to the transmissions towards devices with lowchannel gains. The weakest-channel device, IRm,K , whichreceives low interferences due to the relatively low powers ofdevices’ messages with high channel gains, cannot cancel anyinterference. However, the device with highest channel gain,IRm,1 , which receives strong interference due to the relativelyhigh powers of the transmissions to weak devices, can cancelall interfering signals [4].(16)In each cluster, each IR encounters interference from theuplink signals of ERs towards the UAV, as well as interferencefrom the UAVs’ downlink beams to other IRs. Hence, thereceived signal at IRm,k is given byIR hm,k (1 βm )Pmym,k M J m 1 j 1 M K IRvm,i sm,ii 1ERU ePm,jm,j ,k sm,jhl,k (1 βl )Pll 1,l mK IRIRvl,i sl,i nm,k, (17)i 1 2 D h Qm,k m,k DRm,k (1 αm )W log2 1 2 D Qm,k hm,k vm,k LDIR D(1 βm )Pm Qm,km,k 2 (1 αm ) hm,k K i 1,i k LD(1 αm )IRm,i 2 2 2 D g ζPm,j m,j z m,j em,j,k αmJ 1j 1 LULDLNLoSj ,k (1 αm )ERERm,jm,j 2 2 D g ζPm,j m,j z m,j αm URm,j (1 αm ) W log2 1 Dβm Pm Pm,jDLUERj ,m LERm,j (1 αm ) 2 2ζ gm,l zm,l αmJl j 1 LUERLD(1 αm )m,l ERm,l (1 βm )Pm (19) 2K k 1 HSIm vm,k 1 (20)

NAJMEDDIN et al.: ENERGY-EFFICIENT RESOURCE ALLOCATION IN MULTI-UAV NETWORKS WITH NOMAOn the other hand, for the uplink NOMA throughput, knowing that the channel gains are stronger when ERs are closerto their UAV (channel gain of ERm,1 is larger than ERm,2 ,and so on until ERm,J ) [28], then based on (14) and (15),the rate related to a given ER in a given cluster can beexpressed as shown in (20), at the bottom of the previouspage. The signal of the device with the highest channel gain,i.e., ERm,1 , is decoded first at the UAV. As a result, ERm,1experiences interference from all other ERs. Then, the signalfor the second-highest channel gain device is decoded, and soon until the last device, ERm,J , [4].asFor a specific UAVm , let us define the uplink throughputU JUthe sum-rate of all ERs in the cluster, i.e., Rmj 1 Rm,j ,and the downlink throughput as the sum-rate of all IRs, i.e.,KD DRmk 1 Rm,k . The EE of the system is expressed as M(Total Throughput)mη M m 1m 1 (Total Consumed Energy)m MUDm 1 Rm Rm,(21) MDDm 1 PDCm Pm Qm (1 αm )where PDCm is the constant power consumption of UAVm , JD β PDDand where Pmm m j 1 Pm,j and Qm (1 KDβm )Pm k 1 Qm,k are the powers dedicated to the ERsD QD.and the IRs, respectively, i.e., Pm PmmB. Problem FormulationThe optimization problem which aims to maximize EE isformulated as follows:(OP)maxD ,Q D ,dPm,jm,k m,j ,θm,jηs.t.: Pm Pm,max ,UPm,j m,UPm,j,max , j , m,αm 1, m,0 βm 1, m,hm,min dm,j cos θm,j , j , m,hm,min dm,k cos θm,k , k , m,dm,max rm rUAVm , m,M χm,j 1,m 1χm,j {0, 1},M χm,k 1,m 1χm,k {0, 1},U Pm,thr j , m k k , mUURm,j Rm,j,min , j , m,DDRm,k Rm,k ,min , k , m,J UUPm,jzm,j Pl,jzl,j , j , m,l j 1 DQm,thr j Q D m,kK i 1,i k D hm,K , k , m,(22)Qm,i1911DUand Pm,jwhere Pm,max,max are the maximum transmit powersof UAVm and ERm,j , respectively, hm,min is the minimumallowed height for UAVm , dm,max is the maximum allowabledistance that UAVm can travel during T, rm is the cluster radius,rUAVm is the UAV radius, and where is the UAV radius, andUDwhere Rm,j,min and Rm,k ,min denote the minimum requiredUrates of ERm,j and IRm,k , respectively. Finally, Pm,thrandDQm,thr are the SIC detection thresholds of the uplink anddownlink, zm,j ( z m,l 2 /LUERm,j ) is the channel gain betweenERm,k and UAVm , and hm,K ( h m,K 2 /LDIRm,K ) is thechannel gain between UAVm and IRm,K .The optimization problem is a non-convex problemwith highly coupled variables; therefore, it is hard to besolved directly by existing convex optimization methods.Accordingly, we decompose the optimization problem into twosub-problems. In the first one (OP1 ), we aim to find the UAVs’optimum positions, i.e., the optimal distances and elevationangles w.r.t. the ERs and IRs according to their demands andtheir associations to the UAVs. After getting the UAVs’ optimum positions, in the second problem (OP2 ), we determinethe optimal powers towards each GN in each cluster.C. The UAV Positioning and Device AssociationIn OP1 , we care about (θm,j , dm,j ) and (θm,k , dm,k ) whichare contained in (11), for all scheduled ERs and IRs that areassociated with any specific UAV in each cluster at the sametime. This can be achieved by connecting the path losses forA2G channels related to each GN by the parameters pertainingto the nodes’ demands. So, OP1 will be as follows: DDminΥUΥD(OP1 )j LERm,j k LIRm,kdm,j ,dm,k ,θm,j ,θm,kjks.t.: hm,min dm,j cos θm,j , j , m,hm,min dm,k cos θm,k , k , m,dm,max rm rUAVm , m,M χm,j 1,m 1χm,j {0, 1}M m 1χm,k 1,χm,k {0, 1} j j , m k k , m.(23)As mentioned, at the beginning of the process, each UAVwill be hovering at the minimum allowable height over thecenter of its cluster, and each device (ERs or IRs) to be servedwill send its ID to the UAV of its cluster. Accordingly, χm,jof each ER and χm,k of each IR that ask to be served in eachcluster can be determined. This optimization problem can besolved by introducing the Lagrangian multipliers ΩIRm 0and ΩERm 0, where ΩIRm [ΩIRm,1 , ΩIRm,2 , . . . , ΩIRm,K ]and ΩERm [ΩERm,1 , ΩERm,2 , . . . , ΩERm,J ]. The objectivefunction then becomesL1 ΩERm , ΩIRm , dm ,j , dm ,k , θm ,j , θm ,k

1912IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING, VOL. 5, NO. 4, DECEMBER 2021 J j 1 DΥUj LERm,jJ j 1 K k 1 K k 1Algorithm 1 3D UAV Location OptimizationDΥDk LIRm,kΩERm,j hm,min dm,j cos θm,jΩIRm,k hm,min dm,k cos θm,k .(24)Exploiting the Karush-Kuhn-Tucker (KKT) conditions, onecan obtain the optimal position of the UAV by solving thefirst derivatives of L1 w.r.t. dm,j , dm,k , θm,j and θm,k ,respectively, as follows:DInput: ΥUj , Υk , ξLoS , ξNLoS a, b, hm,min , f, rm , rUAVm ,and GNs’ ID, j , k , m.Output: (xm , ym , hm ) , m.Initialization: (xm , ym , hm )0 , ΩERm,j 0, ΩIRm,k 0, j , k , m.1: Determine χm,j , as per (1) and (3), j , m.2: Determine χm,k , as per (2) and (4), k , m.3: Update ΩERm,j and ΩIRm,k according to (29) and (30).4: Solve (25) for dm,j , j , m.5: Solve (26) for dm,k , k , m.6: Solve (27) for θm,j , j , m.7: Solve (28) for θm,k , k , m.8: Compute the optimal (xm , ym ,

Energy-Efﬁcient Resource Allocation in Multi-UAV Networks With NOMA Saif Najmeddin , Graduate Student Member, IEEE, Sonia Aïssa , Fellow, . transmission to IRs on the downlink and from ERs on the uplink with non-orthogonal multiple access (NOMA). The optimization . allow communication over long ranges [2], [3]. Depending on

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