uav-leo integrated backbone: a ubiquitous data collection

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 39, NO. 11, NOVEMBER 2021 3491

UAV-LEO Integrated Backbone: A Ubiquitous DataCollection Approach for B5G Internet of

Remote Things NetworksTing Ma , Member, IEEE, Haibo Zhou , Senior Member, IEEE, Bo Qian , Student Member, IEEE,

Nan Cheng , Member, IEEE, Xuemin Shen , Fellow, IEEE, Xiang Chen, and Bo Bai , Senior Member, IEEE

Abstract— With the advance of unmanned aerial vehicles(UAVs) and low earth orbit (LEO) satellites, the integration ofspace, air and ground networks has become a potential solutionto the beyond fifth generation (B5G) Internet of remote things(IoRT) networks. However, due to the network heterogeneity andthe high mobility of UAVs and LEOs, how to design an efficientUAV-LEO integrated data collection scheme without infrastruc-ture support is very challenging. In this paper, we investigatethe resource allocation problem for a two-hop uplink UAV-LEOintegrated data collection for the B5G IoRT networks, wherenumerous UAVs gather data from IoT devices and transmit theIoT data to LEO satellites. In order to maximize the data gather-ing efficiency in the IoT-UAV data gathering process, we study thebandwidth allocation of IoT devices and the 3-dimensional (3D)trajectory design of UAVs. In the UAV-LEO data transmissionprocess, we jointly optimize the transmit powers of UAVs and theselections of LEO satellites for the total uploaded data amountand the energy consumption of UAVs. Considering the relayrole and the cache capacity limitations of UAVs, we merge theoptimizations of IoT-UAV data gathering and UAV-LEO datatransmission into an integrated optimization problem, which issolved with the aid of the successive convex approximation (SCA)and the block coordinate descent (BCD) techniques. Simulationresults demonstrate that the proposed scheme achieves betterperformance than the benchmark algorithms in terms of bothenergy consumption and total upload data amount.

Index Terms— B5G IoRT, UAV-LEO integrated data collection,resource allocation, 3D trajectory design.

Manuscript received October 16, 2020; revised February 22, 2021; acceptedApril 12, 2021. Date of publication June 14, 2021; date of current versionOctober 18, 2021. This work was supported in part by the National KeyResearch and Development Program of China under Grant 2020YFB1806104,in part by the Natural Science Foundation Jiangsu Province Youth Projectunder Grant BK20180329, in part by the Innovation and Entrepreneurship ofJiangsu Province High-Level Talent Program, in part by the Summit of the SixTop Talents Program Jiangsu Province, and in part by the Natural Sciences andEngineering Research Council of Canada (NSERC). (Corresponding author:Haibo Zhou.)

Ting Ma, Haibo Zhou, and Bo Qian are with the School of ElectronicScience and Engineering, Nanjing University, Nanjing 210023, China (e-mail:[email protected]; [email protected]; [email protected]).

Nan Cheng is with the School of Telecommunication Engineering and theState Key Laboratory of ISN, Xidian University, Xi’an 710071, China (e-mail:[email protected]).

Xuemin Shen is with the Department of Electrical and Computer Engi-neering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail:[email protected]).

Xiang Chen and Bo Bai are with the Theory Lab, 2012 Labs, HuaweiTechnologies Co., Ltd., Hong Kong (e-mail: [email protected];[email protected]).

Color versions of one or more figures in this article are available athttps://doi.org/10.1109/JSAC.2021.3088626.

Digital Object Identifier 10.1109/JSAC.2021.3088626

I. INTRODUCTION

W ITH the increasing demands of seamless and ubiq-uitous network access in the beyond fifth genera-

tion (B5G), the integration of space, air, and ground (SAG)networks has attracted rising attention, which significantlybenefits the B5G Internet of remote things (IoRT) [1]–[4]. TheIoRT network has been widely adopted in various applications,for instance, the remote surveillance systems for monitoringwild animals, natural disasters and climate change [5]–[7].However, in remote areas, the ground base station (GBS) isusually difficult to deploy due to geographical limitation orhigh cost, which leads to that the data cached in distributedIoT devices have to be forwarded to a far data center for furtheranalysis. Hence, reliable and efficient data collection and datatransmission in IoRT networks are of great significance.

The satellite communication system can offer seamlesswireless access to wide geographical areas, and provide anefficient solution to the IoRT where GBSs are usually notavailable [5], [8]. Comparing to traditional satellite systemsof medium earth orbit (MEO) and geostationary earth orbit(GEO), the low earth orbit (LEO) satellite has the advantagesof small propagation loss, low propagation delay and globalcoverage [9]. However, there are also many challenges inthe LEO satellites assisted IoRT networks. Considering thehuge number of IoT devices in the ground and the longtransmission delay for the data transmission, it is usually notfeasible to directly access numerous IoT devices to the satelliteconstellation [10]. Meanwhile, the IoT device is difficult toachieve long-distance transmission due to its transmit powerand energy consumption limitations.

Recently, the significant development of unmanned aer-ial vehicles (UAVs) has been witnessed. According to thereport [11], the global market for UAV estimated at $24.3 bil-lion in 2020 is expected to reach $77.5 billion by 2027,growing at a compound annual growth rate of 18% overthe analysis period 2020-2027. Moreover, the UAV-basednetworks have attracted much interest and investigations invarious applications [12]–[15]. Considering the benefits ofhigh mobility, economic and flexible deployment, and line-of-sight (LoS) transmission [16], [17], the UAV swarm can beefficiently applied to the B5G IoRT networks as a relay fordata transmission. The UAV swarm can assist LEO satellitesto improve the SAG channel capacity, achieve seamless cov-

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https://orcid.org/0000-0002-6964-220X

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3492 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 39, NO. 11, NOVEMBER 2021

erage, and dynamically move to IoT devices and transmit thecollected data to LEO satellites. However, when introducingthe UAV as a relay in the B5G IoRT networks, the uplink datacollection becomes more challenging because of the differentchannel characteristics of UAV-ground and UAV-satellite links,high mobility of UAVs and LEO satellites, cache capacitylimitations of UAVs, etc.

In this paper, for the hierarchical UAV-LEO integrated datacollection in the B5G IoRT networks assisted with UAV swarmrelays, we divide the two-hop uplink communication taskinto two layers, i.e., IoT-UAV data gathering as layer 1, andUAV-LEO data transmission as layer 2. For layer 1, we firstdivide the IoT devices into different areas based on theirgeographic locations due to the wide range of surveillance,and one UAV gathers data from IoT devices in each area.To achieve the high transmission rate of each IoT deviceduring the mission time period in each area, we maximizethe average achievable rate of each IoT device by optimizingthe uplink bandwidth allocation of IoT devices and the 3Dtrajectory of the UAV. For layer 2, in order to maximizethe uploaded data amount from UAVs to LEO satellite con-stellation and minimize the energy consumption of UAVs,we optimize the transmit powers of UAVs and the selectionsof LEO satellites. Meanwhile, considering the limited cachecapacity of UAV relays, we merge optimizations of layer 1 andlayer 2 into an integrated optimization problem and propose ablock coordinate descent (BCD) based framework to solve it.

The main contributions of the paper are summarized asfollows:

• Hierarchical SAG-IoRT network design: We propose aUAV swarm and LEO satellite constellation assisteddata collection for the B5G IoRT networks. The taskconsists of the IoT-UAV data gathering and UAV-LEOdata transmission, which can achieve reliable and efficientIoRT data collection without infrastructure support.

• IoT bandwidth allocation and UAV 3D trajectory design:To optimize the data gathering efficiency of UAVs,we propose the bandwidth allocation of IoT devicesand the 3D trajectory of UAVs by leveraging successiveconvex approximation (SCA) and BCD techniques.

• UAV power allocation and LEO satellite selection: Tooptimize the data transmission process from UAVs toLEO satellites, we optimize the transmit powers of UAVsand the selections of LEO satellite constellation by usingthe Lagrangian dual decomposition method.

• Joint optimization and computational complexity analy-sis: We propose a BCD-based approach to solve the abovetwo layer optimizations alternately. Meanwhile, we ana-lyze the computational complexity and its convergencetowards at least a locally optimal solution for the BCDbased approach.

The remainder of the paper is organized as follows.Section II reviews the related works. The system model andproblem formulation are described in Section III. Section IVprovides the problem solution. Section V presents the simula-tion results, and Section VI concludes the paper.

II. RELATED WORKS

In the literature, several works have been appeared forthe UAV-assisted ground devices data collection. In [18],Wang et al. proposed a UAV-assisted IoT network, where theUAV is deployed as an anchor node and aerial data collector,and assists the base station (BS) for device positioning anddata collecting. In [19], Sun et al. studied the optimal 3Dtrajectory design and resource allocation for maximizationof the system sum throughput over a given time period inthe UAV communication systems. In [20], Mozaffari et al.analyzed the deployment of UAVs as BSs for the grounduser (GU) communication, while the trade-off between delayand coverage is also argued. In [21], Zhang et al. considereda UAV-enabled radio access network where the UAV servesas the aerial platform to communicate with GUs, and pro-posed iterative algorithms to perform joint UAV trajectory andcommunication resource allocation optimization such that theUAV periodic flight duration is minimized. In [22], Wu et al.investigated a multi-UAV enabled wireless communicationsystem with multiple UAVs employed as aerial BSs to serveGUs. To achieve fair performance over all GUs, the minimumthroughput in the downlink communication is maximized viajoint trajectory and communication design. In [23], taking theenergy consumption of UAVs into account, Cai et al. studiedthe trajectory and resource allocation design for downlinkenergy-efficient secure UAV communication systems. How-ever, due to the communication distance and power energylimitations of UAVs, the UAV-assisted communication is dif-ficult to ensure that data in IoRT networks are transmitted tothe far data center in a timely manner.

To address these issues, satellites are considered in the B5GIoRT networks. In [24], Li et al. introduced the coordinationof UAVs with hybrid GEO satellite-terrestrial networks toenhance the maritime coverage. Under some limitations suchas backhaul and energy capacity and UAV kinematics, theyjointly optimized the UAV trajectory and transmit power.In [25], Wang et al. applied the Lagrangian dual decomposi-tion method to solve a two-stage joint hovering altitude designand power control for the SAG IoT networks. Jia et al. [9]minimized the total energy consumption of UAVs for theLEO satellite assisted UAV data collection in the IoRT whilesatisfying the IoRT demands. In [26], Wang et al. considereda SAG-IoRT framework, and proposed an iterative algorithmto optimize the system capacity via jointly designing powercontrol, smart devices connection scheduling and UAV’s tra-jectory. Most of the existing works are concentrated on a singleLEO satellite scenario, where the focus is on the optimizationof IoT devices to UAVs. However, in practice, a surveillancearea is often covered by multiple LEO satellites due to thewide coverage of satellites. Therefore, in this paper, we willconsider the optimization on not only the bandwidth allocationof IoT devices and the 3D trajectory design of UAVs, butalso the power control of UAVs and access selections to LEOsatellites. To the best of our knowledge, this is the first workto consider these performance indicators simultaneously forthe SAG-IoRT networks.

Notations: The scalars and matrices are written as italicletters and bold-face lower-case letters, respectively. Let R

n


MA et al.: UAV-LEO INTEGRATED BACKBONE: UBIQUITOUS DATA COLLECTION APPROACH FOR B5G IoRT NETWORKS 3493

Fig. 1. The UAV-LEO integrated data collection scenario in the B5G IoRTnetworks.

be the space of n-dimensional real vectors, and I representthe identity matrix with proper dimension. For a matrixX ∈ R

n×m, define its Frobenius norm as �X� (the Euclideannorm of a vector is its special case). Denote log2(·) as thelogarithm with base 2. Denote q̇(n) as the first-order derivativeof a time-varying function q(n) with respect to time slot n.For a continuously differentiable function f(x), let ∇f(x) and∇2 f(x) be the first and second order derivatives of f(x),respectively.

III. SYSTEM MODELING

As shown in Fig. 1, we investigate the UAV-LEO integrateddata collection scheme in the B5G IoRT networks, wheremassive IoT devices get data and then transmit these datato a far ground data center through uplinks by leveragingon UAV swarms and LEO satellites. Assume that there areoverall M IoT devices distributed in K disjoint areas with

Area k having Nk IoT devices, i.e.,K�

k=1

Nk = M . Denote

Ik = {I1,k, . . . , INk,k} as the set of IoT devices in Area k,k = 1, . . . , K . In our setup, one UAV is designated to gatherdata of IoT devices within each area. Hence, K UAVs aredeployed in the air. Let U = {U1, . . . , UK} be the set of UAVswith UAV Uk soaring in Area k, k = 1, . . . , K . In our setup,we consider the ultra-dense LEO satellite constellation (tensof thousands of LEO satellites), and there are always multipleLEO satellites serving these K UAVs during a short time. EachUAV chooses the proper LEO satellite to handover its data, andthese LEO satellites can temporally store their received dataand transmit them to the data center on the ground eventually.In this paper, we only consider data collection through uplinks.

During an appointed mission period of T , we aim todesign an optimal UAV and LEO satellite assisted schedulingmechanism for data collection from the B5G IoRT networks,which maximizes the total received data amount of LEOsatellites from IoT devices and minimizes the total energyconsumption of UAVs without data backlogs at UAVs. Forthe convenience of follow-up analyses, we divide the missiontime period T equally into N time slots with a slot lengthδ, i.e., T = Nδ. Denote N = {1, 2, . . . , N} to represent thetime slot set. At time slot n, we assume that there are Ln LEO

TABLE I

MAIN NOTATIONS

satellites serving these K UAVs in the region, and the servingrelationship between LEO satellites and UAVs are unchanged.

Important notations are listed in Table I.

A. IoT-UAV Data Gathering

These K areas are supposed to be far away from each other.That is to say, there is no interference among different areas,and data gathering of each area is independent. Hence, we takeArea k as an example to analyze the data gathering of UAVUk from IoT devices Ik.

Since IoT devices may be deployed in mountain regions,we assume the coordinate of IoT device Ii,k is si,k ∈ R

3 andthe time-varying coordinate of UAV Uk is qk,n ∈ R

3 at timeslot n. The uplinks from IoT devices to UAV Uk are dominatedby LoS. Hence, the channel gain h̃i,k,n between IoT deviceIi,k and UAV Uk at time slot n is

h̃i,k,n = ρ0d−2i,k,n =

ρ0

�qk,n − si,k�2,

where ρ0 is the channel power gain at the reference distance ofd0 = 1 m and di,k,n is the distance between Ii,k and Uk at timeslot n. Remarkably, UAVs cannot fly too close to IoT devicesdue to collision avoidance. Hence, we modify the channel gainof IoT device Ii,k as follows:

hi,k,n =ρ0

max(�qk,n − si,k�2, d2min)

, (1)



where dmin is the minimum safe distance between UAV andIoT devices for collision avoidance.

Suppose that the UAV adopts frequency division multipleaccess (FDMA) with dynamic bandwidth allocation among allIoT devices, that is, the UAV can receive data from multipleIoT devices at one time slot. Denote ai,k,n as the bandwidthfraction that is allocated for Ii,k at time slot n. Then, variableai,k,n should satisfy:

Nk�i=1

ai,k,n � 1, ∀ k, n,

ai,k,n � 0, ∀ i, k, n.

This scheme includes time division multiple access (TDMA)with dynamic time scheduling (ai,k,n is a binary variable) andFDMA with fixed bandwidth allocation (ai,k,n = ai,k, ∀n) asspecial cases.

Denote the total available bandwidth of each UAV by B,and assume that IoT device Ii,k uploads its sensing data with aprescribed transmit power pi,k, i = 1, . . . , Nk. Subsequently,when IoT device Ii,k transmits data to the UAV (i.e., ai,k,n >0), the instantaneous achievable rate in bits/second (bits/s) forIoT device Ii,k is presented as

ri,k,n = ai,k,nB log2

�1 +

pi,khi,k,n

ai,k,nBN0

�= ai,k,nB

× log2

�1 +

pi,kρ0

max(�qk(n) − ski�2, d2min)ai,k,nBN0

�, (2)

where pi,k stands for the transmit power of Ii,k, B is the totalavailable bandwidth of Area k, and N0 represents the additivewhite Gaussian noise (AWGN) power spectral density.

Then, the average achievable rate of IoT device Ii,k duringall time slots is formulated as

1N

�n∈N

ri,k,n.

In each area, via optimizing the UAV’s trajectory and band-width allocation, we can maximize the minimum averageachievable rate over all IoT devices in this area.

B. UAV-LEO Data Transmission

For data uplink transmission between UAVs and LEOsatellites, let bk,l,n be the 0-1 binary indicator variable oftime-varying uplink between UAV k and LEO satellite l attime slot n, k ∈ K = {1, . . . , K}, l ∈ Ln = {1, . . . , Ln},n ∈ N . When there exists an uplink transmission from UAVk to LEO satellite l at n, we let bk,l,n = 1, and otherwisebk,l,n = 0. We assume that one UAV transmits data to at mostone LEO satellite at one time slot. Hence, it holds�

l∈Ln

bk,l,n � 1, ∀k, n,

bk,l,n = {0, 1}, ∀k, l, n.

Similar to [27], to avoid data upload overlapping, we dividethe frequency bandwidth for UAV satellite uplinks into agroup of orthogonal subchannels by exploiting the Orthogonal

Frequency Division Multiplexing (OFDM) technology. Thenwe assume that different UAVs utilize different orthogonalsubchannels to connect to the same LEO at the same timeslot. That is to say, there is no interference at the LEOsatellites. As in [27], we present the relationship betweentransmission rate and power allocation of an uplink referringto the concave rate-power curve. According to [27], for givenchannel condition c, transmit power p and bandwidth W ,the classic Shannon’s Theorem based rate-power functiong(p, c) in bits/s is obtained as

g(p, c) = W log2(1 + ν(c) · p), (3)

where ν(c) represents the fading coefficient under c. We alsouse the three-state condition model [28], where ν(c) equals1.0, 3.46 and 5.03, which corresponds to the bad, mediumand good conditions based on weather conditions. Obviously,g(p, c) is a concave function of p.

Define ck,l,n as the time-varying channel state of uplinkbetween UAV k and LEO satellite l at n. We can getck,l,n from either direct measurement by some communicationsystems [29] or prediction based on existing channel statesby a linear prediction equation [28]. Then, ck,l,n can beassumed to be known by the system controller all the timein our framework. Additionally, we denote variable Pk,l,n asthe power allocated to the uplink between UAV k and LEOsatellite l at n. Then the total uploaded data amount of UAVk to LEO satellites during N time slots is

Dtuk =

�n∈N

�l∈Ln

bk,l,n · g(Pk,l,n, ck,l,n) · δ. (4)

To avoid data backlogs in UAVs at arbitrary time slot,the uplink transmission data amount of UAV k should besmaller than its received data amount from IoT devices ina prescribed threshold. Specifically, till arbitrary time slotN � ∈ N , the overall uploaded data amount of UAV k canbe calculated as

Duk (N �) =

�n�N �

�l∈Ln

bk,l,n · g(Pk,l,n, ck,l,n) · δ. (5)

According to arguments in Subsection III-A, the overallreceived data amount of UAV k from IoT devices till N � isformulated as

Drk(N �) =

�n�N �

Nk�i=1

ri,k,n · δ. (6)

As a consequence, denoting the cache capacity of UAV kas Ck, the following relationship should hold true:

Drk(N �) − Du

k (N �) � Ck, ∀k, ∀N �. (7)

Meanwhile, the power supply of UAVs is the bottleneckresource. Hence, when a UAV uploads data to LEO satellites,we should minimize its energy consumption. The total energyconsumption of UAV k spent on data-uploading during timeperiod T can be calculated as

Ek =�n∈N

�l∈Ln

bk,l,n · Pk,l,n · δ. (8)



To optimize the total uploaded data amount to LEO satellitesand the energy consumption simultaneously, we introduce apenalty function which positively associates with the totaluploaded data amount Dtu

k in Eq. (4) and reversely associateswith the energy consumption Ek in Eq. (8). Then, the penaltyfunction can be denoted by

Fk := Dtuk − βEk, (9)

where β is the weight of energy consumption.By maximizing the penalty function Fk with respect to bk,l,n

and Pk,l,n, we can get the optimal data transmitting mecha-nism from UAVs to LEO satellites. Remarkably, the involvedterm Dr

k in (7) is relevant to the instantaneous achievablerate ri,k,n in Eq. (2), which depends on the trajectory andbandwidth allocation of UAV k. Hence, the optimization oftransmission from UAVs to LEO satellites is related to thetransmission from IoT devices to UAVs.

C. Integrated Optimization on Uplink Data Collection

Based on the arguments in Subsections III-A and III-B,we can present the integrated optimization problem (IOP) asthat LEO satellites collect data from IoT devices with UAVrelaying. Denote Qk = {qk,n} as the trajectory of UAV k,Ak = {ai,k,n} represents the bandwidth allocation among IoTdevices in Area k, and let B = {bk,l,n} and P = {Pk,l,n} bethe indicator variable set and the power allocation of UAVs,respectively. Then, IOP can be expressed as

IOP : maxηk,Ak,Qk,

B,P

�k∈K

ηk + Fk

s.t.1N

�n∈N

ri,k,n � ηk, ∀i, k, (c1)

qk,0 = qk,N , ∀k, (c2)

�q̇k,n� � Vmax, ∀k, n, (c3)Nk�i=1

ai,k,n � 1, ∀k, n, (c4)

ai,k,n � 0, ∀i, k, n, (c5)

Pk,l,n � 0, ∀k, l, n, (c6)

Pk,l,n � Pmax, ∀k, l, n, (c7)

Drk(N �) � Du

k (N �), ∀k, N � ∈ N , (c8)

Drk(N �) − Du

k (N �) � Ck, ∀k, n, (c9)�k∈K

bk,l,ng(Pk,l,n, ck,l,n) � Rmax, ∀l, n,

(c10)�l∈Ln

bk,l,n � 1, ∀k, n, (c11)

bk,l,n ∈ {0, 1}, ∀k, l, n. (c12)

Constraint (c1) together with the term “max ηk” in theobjective function means maximizing the minimum averageachievable rate among all IoT devices in each area. Constraint(c2) gives the constraint on UAVs’ initial and final locations,which is meaningful in practical scenarios such as periodicaldata collections [21], and constraint (c3) is the velocity limit of

UAVs. Constraints (c4) and (c5) are limitations of bandwidthallocation. Constraints (c6) and (c7) are the minimum and themaximum transmit power constraints on UAVs, respectively.Constraint (c8) is a natural constraint that the overall uploaddata amount of each UAV should not exceed its receiveddata amount from IoT devices, while constraint (c9) avoidsdata backlogs in UAVs. Constraint (c10) implies the totaldata uploading rate of each LEO satellite cannot exceed themaximum data receiving rate Rmax, and constraints (c11)and (c12) are limitations on the choice of LEO satellites.By solving IOP, during the allocated mission time periodT , we can maximize the minimum average achievable rateamong all IoT devices as well as the data amount that IoTdevices transmit to LEO satellites, and minimize the energyconsumption of UAVs without data backlogs in UAVs.

For the proposed IOP, variables {Ak,Qk,B,P} are all orpartly coupled in the objective function as well as constraints(c1), (c8)-(c10), which leads to their non-convexities. More-over, the 0-1 constraint (c12) is also non-convex. Therefore,IOP is difficult to handle. To obtain the solution to thisproblem, a widely used method is the well-known BCDtechnique [21], [30]–[33]. That is, dividing IOP into two sub-problems, and then repeatedly and alternatively solve thesetwo subproblems until the objective function value changeswithin a prescribed threshold. Specifically, we divide IOP intobandwidth allocation and trajectory (Ak,Qk) optimizationwith fixed (B,P) in IoT-UAV data gathering, and powerallocation and uplink selection (B,P) optimization with fixed(Ak,Qk) in UAV-LEO data transmission.

IV. PROBLEM SOLUTION

In this section, IOP is divided into two sub-problems:bandwidth allocation and trajectory optimization, and powerallocation and uplink selection optimization. We argue how tosolve the two sub-problems separately, and then use the BCDtechnique to get the solution to IOP.

A. Sub-Problem 1: Bandwidth Allocation and TrajectoryOptimization With Fixed Power Allocation and UplinkSelection

For fixed power allocation and uplink selection (B,P),we design the optimal trajectory for each UAV by solvingIOP. Considering that each UAV’s trajectory is independent ofothers’, we design the optimal trajectory of the UAV in Areak as an example, and we omit the index k for notation brevity.For this area, removing irrelevant terms with A = {ai,n} andQ = {qn}, IOP is transformed to

(SP1) maxη,A,Q

η

s.t.1N

�n∈N

ri,n � η, ∀i, (10a)

q0 = qN , (10b)

�qn+1 − qn�2 � δ2V 2max, ∀n, (10c)

Nk�i=1

ai,n � 1, ∀ n, (10d)



ai,n � 0, ∀ i, n, (10e)

Dr(N �) � Du(N �), ∀N � ∈ N , (10f)

Dr(N �) � Du(N �) + C, ∀N � ∈ N , (10g)

where constraint (10c) is an equivalence of constraint (c3) inIOP, while expressions of ri,n and Dr(N �) are

ri,n = ai,nB log2

�1 +

piρ0

max(�qn − si�2, d2min)ai,nBN0

�

and

Dr(N �) =�

n�N �

Nk�i=1

ri,n · δ,

respectively. For fixed (B,P), Du(N �) is a known constantfor arbitrary N �. Since variables A and Q are coupled in ri,n,similar to [21], [30], we again use the BCD approach to solveproblem (SP1).

1) Bandwidth Allocation Optimization With Fixed Trajec-tory: Supposing that the trajectory Q = {qn} is fixed, thenproblem (SP1) is evolved to

(SP1-1) maxη,A

η

s.t.1N

�n∈N

ri,n � η, ∀i, (11a)

Nk�i=1

ai,n � 1, ∀ n, (11b)

ai,n � 0, ∀ i, n, (11c)

�n�N �

Nk�i=1

ri,nδ � Du(N �), ∀N �, (11d)

�n�N �

Nk�i=1

ri,nδ � Du(N �) + C, ∀N �. (11e)

Denoting Δ1 = piρ0max(�qn−si�2,d2

min)BN0for notation brevity,

let ri,n = r1(ai,n) = ai,nB log2

�1 + Δ1

ai,n

�. Due to

∇2r1(a) =BΔ1

(a + Δ1) ln 2

�1

a + Δ1− 1

a

�< 0,

we conclude that r1(ai,n) is a concave function of ai,n. Hence,except for constraint (11e), all other constraints are convex.To cope with the non-convexity of (11e), we use the SCAtechnique to relax it.

For the clarity and integrity, before relaxing constraint (11e),we first present the following well-known result.

Lemma 1: (Proposition B.3 in [34]) For a convex functionf(x), it can be lower bounded by

f(x) ≥ f(x0) + ∇f(x0)(x − x0),

where x0 is a given point in the domain of f . Moreover,f(x) = f(x0) if and only if x = x0.

Since r1(ai,n) is concave with respect to ai,n, according toLemma 1, we can relax ri,n = r1(ai,n) by its upper bound

r̂(ai,n) = r1(ati,n) + ∇r1(at

i,n)(ai,n − ati,n)

=BΔ1(at

i,n − ai,n)(at

i,n + Δ1) ln 2+ ai,nB log2

�1 +

Δ1

ati,n

,

where ati,n is given. Obviously, we have r(ai,n) � r̂(ai,n) and

r̂(ai,n) is convex with respect to ai,n. Consequently, we relaxproblem (SP1-1) to

(SP1-2) maxη,A

η

s.t. (11a), (11b), (11c), (11d)�n�N �

Nk�i=1

r̂(ai,n)δ � Du(N �)+C, ∀N �, (12)

where we replace constraint (11e) in problem (SP1-1) by theconvex constraint (12). Therefore, problem (SP1-2) is a convexprogramming that can be solved efficiently by CVX [35].

Constraint (12) is more conservative than the original con-straint (11e). Hence, the optimal solution of problem (SP1-2)is a lower bound of that of problem (SP1-1). To improve thequality of the solution, we iteratively solve problem (SP1-2)multiple times. According to [36], with a feasible initial point,the iterative procedure is convergent to a saddle point or a localminimum. As a consequence, with fixed trajectory, we can getthe optimal bandwidth allocation.

2) Trajectory Optimization With Fixed Bandwidth Alloca-tion: For fixed bandwidth allocation, by removing irrelevantterms with A, we reduce problem (SP1) to

(SP1-3) maxη,Q

η

s.t.1N

�n∈N

ri,n � η, ∀i, (13a)

q0 = qN , (13b)

�qn+1 − qn�2 � δ2V 2max, ∀n, (13c)

Dr(N �) � Du(N �), ∀N � ∈ N , (13d)

Dr(N �) � Du(N �) + C, ∀N � ∈ N , (13e)

Note that, ri,n is a neither convex nor concave functionof qn, which causes the non-convexity of constraints (13a),(13d) and (13e). Hence, problem (SP1-3) is non-convex, whichis generally difficult to cope with. Nevertheless, we can usethe SCA technique to transform non-convex constraints (13a),(13b), (13d) and (13e) to convex ones as follows.

For constraints (13a) and (13d), thanks to the specialexpression of ri,n, we first relax ri,n by a concave lower-boundfunction. Based on Lemma 1, the following result holds true.

Lemma 2: For a given Qt � {qtn}, ri,n can be lower

bounded by r̃i,n with

r̃i,n � ai,nB log2

�1 +

Δ2

ai,nzti,n

− φt

i,n(zi,n − zti,n), (14)

where Δ2 = piρ0BN0

, zi,n = max(�qn − si�2, d2min), zt

i,n =max(�qt

n − si�2, d2min), and φt

i,n = ai,nBΔ2

zti,n(ai,nzt

i,n+Δ2) ln 2.

According to Lemma 3 in [37], we conclude r̃i,n is concavedue to the convexity of zi,n with respect to qn and φt

i,n > 0.Via replacing ri,n by r̃i,n in constraints (13a) and (13d), thesetwo constraints become convex.



As for the non-convex constraint (13e), we are going toreplace ri,n by its convex upper approximation. Because ofmax(�qn − si�2, d2

min) � �qn − si�2, we first obtain theupper bound r̆i,n of ri,n with

r̆i,n = ai,nB log2

�1 +

Δ2

ai,n�qn − si�2

�. (15)

Since r̆i,n is non-convex with respect to qn, we will find theconvex upper bound of r̆i,n. We first show the related Hessianmatrix.

Lemma 3: Denote r2(q) = log2

�1 + c

�q−s�2

�: R

3 → R,

where c is a known positive constant and s ∈ R3 is a known

vector. Then for the Hessian matrix ∇2 r2(q), it holds

∇2r2(q) � 6c�q− s�2 + 2c2

�q− s�2(�q− s�2 + c)2 ln 2I.

Proof: Define f1(z) = log2

1 + c

z

�and f2(q) = �q −

s�2. Then it follows r2(q) = f1(f2(q)). According to thechain rule [38], we can obtain

∇2r2(q) = ∇2f1(f2(q)) · ∇f2(q) · ∇f2(q)T

+∇f1(f2(q)) · ∇2 f2(q).

By taking the first and second order derivations of f1(z)and f2(q) respectively, one has

∇f1(z) = − c

z(z + c) ln 2, ∇2f1(z) =

c(2z + c)z2(z + c)2 ln 2

,

and

∇f2(q) = 2(q − s), ∇2f2(q) = 2I.

Substituting above equations to ∇2r2(q), it yields

∇2r2(q) =4c(2z + c)(q − s)(q − s)T

z2(z + c)2 ln 2− 2c

z(z + c) ln 2I,

with z = �q− s�2.Matrix Λ = (q − s)(q − s)T ∈ R

3 has only onenonzero eigenvalue, while other two eigenvalues are both zero.Moreover, for arbitrary two dimension compatible matrices Aand B, AB and BA admit the same nonzero eigenvalues.Thus, the eigenvalue vector of matrix Λ is (�q − s�2, 0, 0)T .Furthermore, the identity matrix I can be simultaneously diag-onalized with arbitrary matrices, which implies the eigenvaluesof ∇2r2(q) are�

6cz + 2c2

z(z + c)2 ln 2,− 2c

z(z + c) ln 2,− 2c

z(z + c) ln 2

�.

The proof is completed.Now we present the following theorem to show the convex

upper bound of ri,n.Theorem 1: For a given trajectory qt

n, ri,n can be upperbounded by r̄i,n with

r̄i,n = ai,nB log2

�+

Δ2

ai,nzti,n

− 2ai,nBΔ2(qtn − si)T (qn − qt

n)zt

i,n(ai,nzti,n + Δ2) ln 2

+ai,nBΔ2(3ai,nzt

i,n + Δ2)�qn − qtn�2

zti,n(ai,nzt

i,n + Δ2)2 ln 2, (16)

where Δ2 = piρ0BN0

and zti,n = �qt

n − si�2. Moreover, r̄i,n isconvex with respect to qn.

Proof: As aforementioned, max(�qn − si�2, d2min) �

�qn − si�2 leads to ri,n � r̆i,n with r̆i,n defined in (15).In the sequel, we will show r̆i,n � r̄i,n.

For a function f(x), its second-order Taylor expansion atthe given point x0 is expressed as

f(x) = f(x0) + ∇f(x0)T (x − x0)

+(x − x0)T∇2 f(x0)(x − x0)

2+ o(�x− x0�2).

If the Hessian matrix ∇2f(x0) is smaller than matrix A,then we obtain

f(x)�f(x0)+∇f(x0)T (x − x0)+(x − x0)T A(x − x0)

2.

(17)

Regarding r̆i,n as a function of qn with f(qn) =ai,nB log2

�1 + Δ2

ai,n�qn−si�2

�and combining with Lemma 3,

then it immediately follows from Eq. (17) that r̆i,n � r̄i,n withr̄i,n defined in (16). In addition, r̄i,n is obviously convex withrespect to qn.

Based on the convexity of r̄i,n in (16), replacing ri,n by r̄i,n

can transform the non-convex constraint (13e) to a convex one.According to the above arguments, we turn to solve the

approximate convex problem of problem (SP1-3) as follows:

(SP1-4) maxη,Q

η

s.t.1N

�n∈N

r̃i,n � η, ∀i, (18a)

q0 = qN , (18b)

�qn+1 − qn�2 � δ2V 2max, ∀n, (18c)

�n�N �

Nk�i=1

r̃i,nδ � Du(N �), ∀N �, (18d)

�n�N �

Nk�i=1

r̄i,nδ � Du(N �) + C, ∀N �, (18e)

where r̃i,n and r̄i,n are defined in (14) and (16), respectively.We can utilize the CVX toolbox to solve problem (SP1-4)

efficiently. Furthermore, due to ri,n � r̃i,n and ri,n � r̄i,n, theoptimal solution of problem (SP1-4) is a lower bound of thatof problem (SP1-3). We iteratively solve problem (SP1-4) mul-tiple times to improve the quality of the solution. Followinga similar analysis to Subsection IV-A, the iterations convergeto a local minimum or a saddle point with a feasible startingpoint. Consequently, we can obtain the optimal trajectory withfixed bandwidth allocation.

In summary, for Area k, the bandwidth allocation andtrajectory optimization is shown in Algorithm 1. Notably,when implementing Algorithm 1, giving the initial trajectoryQ(0) and bandwidth allocation A(0) is necessary. We generateQ(0) by the traveling salesman problem (TSP) based initial



Algorithm 1: IoT Bandwidth Allocation and UAV 3DTrajectory Design Algorithm

Input: Initial trajectory Q(0) and bandwidth allocationA(0), prescribed threshold �1, initial differenceϕ(0) = �1 + 1, iteration index s = 0.

Output: Optimal bandwidth allocation and trajectory(A∗,Q∗).

1: while ϕ(s) � �1 do2: Solve problem (SP1-2) to obtain (η(s+1,1),A(s+1));3: Solve problem (SP1-4) to obtain (η(s+1),Q(s+1));4: Compute the difference ϕ(s+1) = η(s+1)−η(s)

η(s) ;5: s = s + 1.6: end while

trajectory design, which is detailedly presented in [21], [37]and thereby is omitted. For the initial bandwidth allocationA(0), we can select A(0) as a matrix with each element in [0, 1]and the sum of each column being one. If the constraint (11e)is not satisfied, we can simultaneously shrink each elementof A(0) until it is met. Moreover, since the objective functionvalue is not decreasing and upper bounded, Algorithm 1 can beconvergent to the local optimal solution of problem (SP1) [21].

B. Sub-Problem 2: Power Allocation and Uplink SelectionOptimization With Fixed Bandwidth Allocation andTrajectory

When the bandwidth allocation Ak and trajectory Qk arefixed, by removing irrelevant terms with (B,P), IOP becomes

(SP2) maxB,P

�k∈K

Fk

s.t. Pk,l,n � 0, ∀k, l, n, (19a)

bk,l,nPk,l,n � Pmax, ∀k, l, n, (19b)

Duk (N �) � Dr

k(N �), ∀k, N � ∈ N , (19c)

Duk (N �) � Dr

k(N �)−Ck, ∀k, N � ∈ N , (19d)�k∈K

bk,l,ng(Pk,l,n, ck,l,n) � Rmax, ∀l, n,

(19e)�l∈Ln

bk,l,n �1, ∀k, n, (19f)

bk,l,n ∈ {0, 1}, ∀k, l, n. (19g)

Constraint (19b) is equivalent to (c7), and Drk(N �) is a

known constant for any N � when (Ak,Qk) is fixed. Due to thecoupled expression of (B,P) in the objective function as wellas (19c)-(19e), together with the binary constraint in (19g),problem (SP2) is obviously not convex with respect to (B,P).

In order to cope with the non-convexity, we first introducean auxiliary variable ωk,l,n = g(Pk,l,n, ck,l,n). Then based onthe definition of g(p, c) in (3), we can express Pk,l,n as afunction of ωk,l,n as follows:

Pk,l,n = f(ωk,l,n) =2

ωk,l,nW − 1

ν(ck,l,n), (20)

which is clearly a convex function of ωk,l,n. Clearly, Pk,l,n �0 is equivalent to ωk,l,n � 0. Furthermore, let ρk,l,n =bk,l,nωk,l,n and relax the inter programming constraint (19g)to a convex constraint bk,l,n ∈ [0, 1]. Then according to thedefinition of Du

k (N �) in Eq. (5) and definition of Fk in Eq. (9),with ρ = {ρk,l,n}, we can approximate problem (SP2) by

(SP2-1) maxB,ρ

�k∈K

�n∈N

�l∈Ln

δ

�ρk,l,n − βbk,l,nf

�ρk,l,n

bk,l,n

�

s.t. ρk,l,n � 0, ∀k, l, n, (21a)

bk,l,nf

�ρk,l,n

bk,l,n

�� Pmax, ∀k, l, n, (21b)�

n�N �

�l∈Ln

ρk,l,nδ � Drk(N �), ∀k, N �, (21c)

�n�N �

�l∈Ln

ρk,l,nδ � Drk(N �) − Ck, ∀k, N �,

(21d)�k∈K

ρk,l,n � Rmax, ∀l, n, (21e)

�l∈Ln

bk,l,n � 1, ∀k, n, (21f)

bk,l,n ∈ [0, 1], ∀k, l, n. (21g)

To begin with, we claim the convexity of problem (SP2-1).Proposition 1: Problem (SP2-1) is convex.

Proof: For b > 0, we denote function Υ(b, ρ) = bf(ρb )

with f(·) given by (20) and ρ � 0. By taking the second orderderivative of Υ(b, ρ) with respect to (b, ρ), we obtain

∇2Υ(b, ρ) =∇2 f(ρ

b )b3

�b2 −bρ

−bρ ρ2

�.

Since f(·) is a convex function, it holds ∇2 f(ρb ) � 0. Then,

it yields ∇2Υ(b, ρ) � 0, which means that bk,l,nf�

ρk,l,n

bk,l,n

�is

convex with respect to (B, ρ). Therefore, the objective functionin problem (SP2-1) is concave while all constraints are convex,which leads to the convexity of problem (SP2-1).

Inspired by [25], we adopt the Lagrangian dual decompo-sition method to get the optimal solution of problem (SP2-1).

1) Lagrangian Dual Decomposition Method: By introduc-ing nonnegative Lagrangian multipliers λ = {λk,l,n}, γ ={γk,N �}, μ = {μk,N �}, ξ = {ξl,n}, θ = {θk,n} associatedwith corresponding constraints (21b)-(21f), respectively, weformulate the Lagrangian function by

L (B, ρ, λ, μ, γ, ξ, θ)

=�k∈K

�n∈N

�l∈Ln

δ

�ρk,l,n − βbk,l,nf

�ρk,l,n

bk,l,n

�

+�k∈K

�n∈N

�l∈Ln

λk,l,n

�Pmax − bk,l,nf

�ρk,l,n

bk,l,n

�

+�

N �∈N

�k∈K

γk,N ��Dr

k(N �) −�

n�N �

�l∈Ln

ρk,l,nδ�

+�

N �∈N

�k∈K

μk,N ��

n�N �

�l∈Ln

ρk,l,nδ − Drk(N �) + Ck

�

+�n∈N

�l∈Ln

ξl,n(Rmax −�k∈K

ρk,l,n)



+�k∈K

�n∈N

θk,n(1 −�l∈Ln

bk,l,n).

Notice that, constraints (21a) and (21g) are not involved inthe Lagrangian function.

The dual function is

G(λ, γ, μ, ξ, θ) = max(21a),(21g)

L(B, ρ, λ, γ, μ, ξ, θ). (22)

Then the Lagrangian dual problem is given by

minλ,γ,μ,ξ,θ

G(λ, γ, μ, ξ, θ)

s.t. λ, γ, μ, ξ, θ � 0.

We first deduce how to determine the optimal (ρ∗k,l,n, b∗k,l,n)with given Lagrangian multipliers (λ, γ, μ, ξ, θ), ∀k, l, n.

Since problem (SP2-1) is convex with respect to (B, ρ),taking the constraint ρk,l,n � 0 in (21a) into account, theoptimal solution ρ∗k,l,n should satisfy the condition⎧⎪⎪⎨⎪⎪⎩

ρ∗k,l,n = 0, if∂L

∂ρk,l,n|ρk,l,n=0 < 0,

∂L

∂ρk,l,n|ρk,l,n=ρ∗

k,l,n= 0, otherwise,

(23)

where ∂L∂ρk,l,n

is the partial derivative of L with respect toρk,l,n. It is not difficult to compute

∂L

∂ρk,l,n= δ − (δβ + λk,l,n)(ln 2)2

ρk,l,nW bk,l,n

Wν(ck,l,n)

+ δ�

N ��n

(μk,N � − γk,N �) − ξl,n.

Then by the optimal condition Eq. (23), we can obtain

ρ∗k,l,n = max�

0, bk,l,nW log2

Wν(ck,l,n)Δ(δβ + λk,l,n) ln 2

�(24)

with Δ = δ − ξl,n + δ�

N ��n

(μk,N � − γk,N �). Recalling the

transformation ρk,l,n = bk,l,nωk,l,n, it immediately holds

ω∗k,l,n = max

�0, W log2

Wν(ck,l,n)Δ(δβ + λk,l,n) ln 2

�. (25)

According to expression Pk,l,n = f(ωk,l,n) in Eq. (20), wefurther get the optimal solution P ∗

k,l,n for problem (SP2) as

P ∗k,l,n =

2ω∗

k,l,nW − 1

ν(ck,l,n). (26)

Using a similar argument and considering the constraintbk,l,n ∈ [0, 1] in (21g), the optimal solution b∗k,l,n is givenby ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

b∗k,l,n = 0, if∂L

∂bk,l,n|bk,l,n=0 < 0,

b∗k,l,n ∈ (0, 1), if∂L

∂bk,l,n|b∗

k,l,n= 0,

b∗k,l,n = 1, if∂L

∂bk,l,n|bk,l,n=1 > 0,

(27)

where ∂L∂bk,l,n

is the partial derivative of L with respect tobk,l,n. We can easily derive

∂L

∂bk,l,n=

(δβ+λk,l,n)((ωk,l,n ln 2−W )2ωk,l,n

W + W )Wν(ck,l,n)

−θk,n.

As can be seen from the above expression, when ω∗k,l,n in

Eq. (25) is determined, ∂L∂bk,l,n

is a constant with uncertain

sign. When ∂L∂bk,l,n

< 0 does not hold for all l, there exist atleast one index l such that bk,l,n > 0. In this case, due tobk,l,n ∈ {0, 1} in problem (SP2) and

�l∈Ln

bk,l,n � 1, i.e., one

UAV is supposed to transmit data to at most one LEO satelliteat one time slot, we obtain the optimal solution b∗k,l,n forproblem (SP2) as

bk,l∗,n = 1 with l∗ = argmaxl

∂L

∂bk,l,n. (28)

2) Update of Lagrangian Multipliers: Because theLagrangian dual function in (22) may be non-differentiable,the subgradient method is used to update the Lagrangianmultipliers (λ, μ, γ, ξ, θ) [39]. It is not difficult to deduce thesubgradient of L with respect to (λ, μ, ξ, θ) are respectively

∂L

∂λk,l,n= Pmax − bk,l,nf

�ρk,l,n

bk,l,n

�,

∂L

∂γk,N �= Dr

k(N �) −�

n�N �

�l∈Ln

ρk,l,nδ,

∂L

∂μk,N �=�

n�N �

�l∈Ln

ρk,l,nδ − Drk(N �) + Ck,

∂L

∂ξl,n= Rmax −

�k∈K

ρk,l,n,

∂L

∂θk,n= 1 −

�l∈Ln

bk,l,n.

Then, we update the Lagrangian multipliers as follows

λ(s+1)k,l,n

=�λ

(s)k,l,n − τ

(s)1

�Pmax − bk,l,nf

�ρk,l,n

bk,l,n

�� +, (29)

γ(s+1)k,N �

=�γ

(s)k,N � − τ

(s)2

�Dr

k(N �) −�

n�N �

�l∈Ln

ρk,l,nδ� +

, (30)

μ(s+1)k,N �

=�μ

(s)k,N �−τ

(s)3

� �n�N �

�l∈Ln

ρk,l,nδ−Drk(N

�)+Ck

� +, (31)

ξ(s+1)l,n =

�ξ(s)l,n − τ

(s)4 (Rmax −

�k∈K

ρk,l,n) +

, (32)

θ(s+1)k,n =

�θ(s)k,n − τ

(s)5 (1 −

�l∈Ln

bk,l,n) +

, (33)

where s is the iteration index, τ = {τ1, . . . , τ5} represents thestep size, and the notation [·]+ means max{0, ·}. Therefore,



Algorithm 2: UAV Power Allocation and LEO SatelliteSelection Algorithm

Input: Initial Lagrangian multipliers λ(0), γ(0), μ(0), ξ(0),θ(0), prescribed threshold �2, initial differenceφ(0) = �2 + 1, step size {τ}, iteration index s = 0.

Output: Optimal power allocation and uplink selectionpolicy (B∗,P∗).

1: while φ(s) � �2 do2: Use (25) and (26) to obtain the optimal power

allocation Ps+1;3: Use (27) and (28) to obtain the optimal uplink

selection Bs+1;4: Use (29), (30), (31), (32), (33) to update multipliers

λ(s+1), γ(s+1), μ(s+1), ξ(s+1), θ(s+1);5: Compute the difference

φ(s+1) = �λ(s+1)−λ(s)��λ(s)� + �γ(s+1)−γ(s)�

�γ(s)� +�μ(s+1)−μ(s)�

�μ(s)� + �ξ(s+1)−ξ(s)��ξ(s)� + �θ(s+1)−θ(s)�

�θ(s)� ;

6: s = s + 1.7: end while

the power allocation and uplink selection optimization isshown in Algorithm 2.

Since the subgradients are bounded, if {τ (s)} is generatedby a diminishing step-size rule, i.e.,

∞�s=1

τ (s) = ∞, lims→∞ τ (s) = 0,

the multiplier sequence {(λ(s), γ(s), μ(s), ξ(s), θ(s))} gener-ated by Algorithm 2 is convergent to the optimal value [40].In addition, the primal variables (Bs,Ps) are updated inan analytical form, and thereby the convergence rate mainlyrelies on the optimization of the dual variables. Since theoptimization of dual variables is based on the subgradientmethod, we can speed up the convergence by adopting theadaptive step size

τi(s) =

1√s, i = 1, . . . , 5.

Consequently, based on the above analyses, we can obtainthe optimal power allocation and uplink selection.

C. BCD Based Approach for IOP and ComputationalComplexity

In Subsections IV-A and IV-B, we propose Algorithms 1and 2 to solve sub-problems (SP1) and (SP2), respectively.To jointly optimize the bandwidth allocation, trajectory, powerallocation and uplink selection, on basis of obtained solutionsof sub-problems (SP1) and (SP2), we implement the BCDprocess as follows. With fixed power allocation and uplinkselection (B,P), we apply Algorithm 1 to optimize (Ak,Qk),k = 1, . . . , K . Then with obtained (Ak,Qk), we adoptAlgorithm 2 to solve (Ak,Qk). Algorithms 1 and 2 arealternatively executed until the objective function value of IOPchanges in a prescribed threshold. The BCD based approach

can converge to at least a locally optimal solution of IOPfollowing the analysis similar to [21].

The computational complexity of the BCD based approachfor IOP mainly depends on those of Algorithms 1 and 2.For Algorithm 1, it involves solving convex problems(SP1-2) and (SP1-4), where their variable numbers areMN + K and 3M + K , respectively. By employing aprimal-dual interior point method to solve problems (SP1-2)and (SP1-4), the computation complexities are respectivelyO((MN + K)3 log(�−1)) and O((3M + K)3 log(�−1))with � being the accepted duality gap. Supposing thatthe number of iterations in Algorithm 1 is S1, then thetotal computation complexity for Algorithm 1 can becalculated as O

S1((MN + K)3 + (3M + K)3) log(�−1)

�.

For Algorithm 2, since an analytical iteration is performedin each step, assuming that the total iterative numberis S2, then computation complexity for Algorithm 2is O (S2KLN). Therefore, given the total iterationnumber S of the BCD based approach for IOP,its total computational complexity is formulated asOSS1((MN + K)3 + (3M + K)3) log(�−1) + SS2KLN

�.

V. NUMERICAL SIMULATIONS

In this section, numerous simulations are carried out tovalidate the effectiveness of the proposed BCD based approachfor IOP.

Assume that a mountain region under surveillance with50 km × 50 km is divided into K = 10 areas which are farapart from each other. In each area, a single UAV gathers datafrom Nk = 10 IoT devices, k = 1, . . . , 10. In addition, theseIoT devices within each area are randomly and dependentlydistributed in a polyhedron area with height 100 m, whilethe lengths in Areas 1-2, 3-5, 6-8, 9-10 are respectively2000 m, 3000 m, 4000 m and 5000 m. Meanwhile, there areLn = L = 5 LEO satellites in the air that can simultaneouslyreceive data from UAVs of these K areas, n = 1, . . . , N .The maximum receiving rate of LEO satellite Rmax is setto 10 Mbits/s. The weight coefficient β is selected as 0.5.When optimizing the objective function Fk = Dtu

k − βEk inproblem (SP2), we modify Fk = Dtu

k − 106βEk by takingthe magnitudes of Dtu

k and Ek into account. We assume thatthe appointed mission period T is T = 100 s. As mentionedbehind Eq. (3), during the mission period T , the fadingcoefficient ν(ck,l,n) is randomly generated from 5.03, 3.46,and 1.0, k = 1, . . . , 10, l = 1, . . . , 5. Other main parametersof our numerical simulations are set in Table II.

With the above setup, we first display the trajectory andLEO satellite selection of UAVs in Areas 1-10 in Fig. 2(a),where the selection situation corresponds to the first time slot.As shown in Fig. 2(a), at the first time slot, UAVs U2, U7,and U8 transmit data to LEO 1, UAV U5 has the uplink withLEO 2, UAVs U1 and U9 transmit data to LEO 3, UAVsU3, U4 and U10 transmit data to LEO 4, while UAV U6 hasthe uplink with LEO 5. In order to show the trajectory moreclearly, we plot Area 1 as an example in Fig. 2(b). With theTSP based initial trajectory, we can obtain the optimal 3Dtrajectory. Since the appointed time is shorter than its TSP



Fig. 2. Optimal trajectory of UAVs: (a) Trajectory of all areas and LEO satellite selection; (b) Trajectory of area 1.

Fig. 3. Performance comparison of three methods: (a) Efficiency of energy consumption (W/bit); (b) IoT transmission data amount (Mbits); (c) Total uploadeddata amount of UAVs (Mbits).

TABLE II

MAIN SIMULATION PARAMETERS

time, the UAV cannot arrive at each IoT device in this area.Work [37] has shown that the obtained 3D trajectory admitsbetter performance than the 2D trajectory.

To the best of our knowledge, there was no algorithmfor solving IOP. In order to evaluate the performance ofthe proposed algorithm, we compare it with two benchmarkmethods: determined method and random method. For thedetermined method, the total bandwidth of the UAV is equallyallocated to all IoT devices in each area, the trajectory ofthe UAV is set to be the TSP based initial trajectory, eachUAV select the LEO satellite which admits the best channel

condition, and the transmission rate of each UAV is the samewhile the total received rate of each LEO satellite is just equalto Rmax. For the determined method, when the constraints (c8)and (c9) in IOP are not satisfied, the bandwidth allocated toeach IoT device and the transmission rate of each UAV willshrink until the two constraints hold. For the random method,we randomly generate the bandwidth allocation, randomlyselect the LEO satellites and randomly give the transmit powerof each UAV until the constraints (c8) and (c9) are met, andthe trajectory of the UAV still adopts the TSP based initialtrajectory. When characterizing the algorithm performance,we use the efficiency of energy consumption of UAVs, the IoTtransmission data amount, and total uploaded data amount byUAVs as metrics. Here the efficiency of energy consumptionof UAV k is defined by the ratio of its energy consumption onuploading data to LEO satellites and its uploaded data amountas Ek/Dtu

k , where Ek and Dtuk are the energy consumption

given by (8) and the uploaded data amount given by (4),respectively. Without UAV backlogs, the lower the efficiencyof energy consumption and the larger the IoT transmission dataamount and total uploaded data amount, the better performancethe method admits.

Then we depict the efficiency of energy consumption, IoTtransmission data amount, and total uploaded data amountwith respect to time slots for the proposed method, determinedmethod and random method in Fig. 3. It is easy to see, theefficiencies of energy consumption of the proposed method



Fig. 4. Performance comparison of 10 areas: (a) Efficiency of energy consumption (W/bit); (b) IoT transmission data amount (Mbits); (c) Total uploadeddata amount of UAVs (Mbits).

differ small during all the time slots, which implies theyare balanced in each time slot. With the increase of timeslots, both the IoT transmission data amount and the totaluploaded data amount of UAVs are increasing nearly in alinear trend. Obviously, the proposed method is superior tothe other two methods in all the three aspects. As can beseen from Fig. 3, our method has a much lower efficiency ofenergy consumption and much larger uploaded data amount.Therefore, our method admits better performance.

Moreover, since the IoT device densities in Area 1-Area 10are not all the same, we compare efficiency of energy con-sumption, IoT transmission data amount, and total uploadeddata amount of UAVs in Areas 1-10. Recalling that thelengths in Areas 1-2, 3-5, 6-8, 9-10 are respectively 2000 m,3000 m, 4000 m and 5000 m, the IoT device densities inAreas 1-2, 3-5, 6-8, 9-10 are decreasing. From Figs. 4(a)and 4(c), the efficiency of energy consumption and the totaluploaded data amount have no obvious trend for these threemethods, whereas the IoT transmission data amount of thethree methods have a decreasing trend for Areas 1-2, 3-5, 6-8,9-10 in Fig. 4(b). Because the smaller IoT device density leadsto larger distances among 10 IoT devices, the data amountgathered by UAV will decrease in a same time period. On theother hand, since the 10 UAVs in each area transmit data toLEO satellites collaboratively, the total uploaded data amountas well as the efficiency of energy consumption does not differgreatly in areas.

In the following, we will show how the maximum receiv-ing rate Rmax and the number of LEO satellites L affectthe proposed method. We consider the scenario that thelength of each area is equal to 5000 m, and the timeslot length is set to 5 s. Other simulation parameters keepunchanged.

1) Comparison of Different Maximum Receiving Rate Rmax:In order to illustrate the effect of the maximum receiv-ing rate Rmax of LEO satellites, we compare eight caseswith Rmax = {1, 3, 5, 7, 9, 11, 13, 15} Mbits/s, respectively.As shown in Figs. 5 and 6, for all these eight cases, the pro-posed method performs better than the determined method andthe random method in terms of both the efficiency of energyconsumption and the total uploaded data amount, while thedetermined method and the random method have no clearsuperiority to each other. Moreover, when Rmax becomes

Fig. 5. Efficiency of energy consumption with different Rmax.

Fig. 6. Total uploaded data amount with different Rmax.

larger, the LEO satellites can receive more data at eachtime slot, which leads to larger total uploaded data amount.However, the efficiency of energy consumption becomes worsewith larger Rmax. In addition, when Rmax exceeds a certainthreshold (about 11 Mbits/s for this example), the gain inuploaded data amount almost disappears. Actually, by onlyadding Rmax to a certain value, the IoT transmission datawill not change any longer, which further causes that theuploaded data amount nearly keeps unchanged. Therefore,we can use different LEO satellites with proper maximumreceiving rate Rmax rather than a large one in practicalapplications.

2) Comparison of Different Numbers of LEO SatellitesL: When the number of LEO satellites L varies in L ={1, 2, 3, 4, 5}, we show the efficiency of energy consumption



Fig. 7. Efficiency of energy consumption with different L.

Fig. 8. Total uploaded data amount with different L.

and total uploaded data amount in Figs. 7 and 8, respectively.It is easy to see, the proposed method outperforms the othertwo methods. Meanwhile, the total uploaded data amountis increasing with respect to L, as shown in Fig. 8. WhenL becomes larger, UAVs have more chances to select theLEO satellite with better channel state. Meanwhile, withthe increase of L, the LEO satellite constellation possessesmore data receiving capacity. However, the efficiency ofenergy consumption becomes slightly worse with respect toL. In practical applications, we can adjust the number of LEOsatellites to satisfy different preference on energy consumptionor uploaded data amount.

VI. CONCLUSION AND FUTURE WORK

In this paper, we have investigated a UAV-LEO inte-grated data collection in the B5G IoRT networks. Specifically,to maximize the total uploaded data amount to LEO satellitesand minimize the energy consumption of UAVs simultane-ously, we have proposed a BCD-based method to jointlyoptimize the IoT bandwidth allocation, UAV 3D trajectorydesign, UAV power allocation and LEO satellite selection.Numerical results have shown the superiority and effective-ness of the proposed method. The work could provide use-ful guidelines for deployment and data collection algorithmdesign in B5G IoRT networks. For the future work, we willconsider the dynamic interconnection and transmission opti-mization among satellites for massive LEO satellite network-ing to provide better data collection sevices in B5G IoRTnetworks.

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Ting Ma (Member, IEEE) received the B.S., M.S.,and Ph.D. degrees in statistics from Sichuan Uni-versity, Chengdu, China, in 2013, 2016, and 2020,respectively. She is currently a Post-Doctoral Fellowwith the School of Electronic Science and Engineer-ing, Nanjing University, Nanjing, China. Her maincurrent research interests include robust hypothesistesting, space-air-ground integrated networks, con-vex optimization theory, and game theory.

Haibo Zhou (Senior Member, IEEE) received thePh.D. degree in information and communicationengineering from Shanghai Jiao Tong University,Shanghai, China, in 2014. From 2014 to 2017,he was a Post-Doctoral Fellow with the BroadbandCommunications Research Group, Department ofElectrical and Computer Engineering, University ofWaterloo. He is currently an Associate Professorwith the School of Electronic Science and Engi-neering, Nanjing University, Nanjing, China. Hisresearch interests include resource management and

protocol design in vehicular ad hoc networks, 5G/B5G wireless networks,and space-air-ground integrated networks. He won the 2020 Norbert WienerReview Award of IEEE/CAA JOURNAL OF AUTOMATICA SINICA. He wasnamed as the 2020 highly cited researcher in cross-field. He was a recipientof the 2019 IEEE ComSoc Asia–Pacific Outstanding Young ResearcherAward. He has served as the Invited Track Co-Chair for ICCC 2019 andVTC-Fall 2020 and a TPC Member for many IEEE conferences, includingGLOBECOM, ICC, and VTC. He has served as an Associate Editor forthe IEEE Comsoc Technically Co-Sponsored the Journal of Communicationsand Information Networks (JCIN) from April 2017 to March 2019, and aGuest Editor for the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY

in 2021, the IEEE INTERNET OF THINGS JOURNAL in 2021, IEEE Communi-cations Magazine in 2016, the International Journal of Distributed Sensor Net-works (Hindawi) in 2017, and IET Communications in 2017. He is currentlyan Associate Editor of the IEEE INTERNET OF THINGS JOURNAL, IEEENetwork Magazine, the IEEE WIRELESS COMMUNICATIONS LETTERS, andJCIN.

Bo Qian (Student Member, IEEE) received the B.S.and M.S. degrees in statistics from Sichuan Univer-sity, Chengdu, China, in 2015 and 2018, respectively.He is currently pursuing the Ph.D. degree withthe School of Electronic Science and Engineering,Nanjing University, China. His current researchinterests include intelligent transportation systemsand vehicular networks, wireless resource manage-ment, blockchain, convex optimization theory, andgame theory. He was a recipient of the IEEEVTC-Fall Best Paper Award in 2020.

Nan Cheng (Member, IEEE) received the B.E.and M.S. degrees from the Department of Electron-ics and Information Engineering, Tongji University,Shanghai, China, in 2009 and 2012, respectively, andthe Ph.D. degree from the Department of Electricaland Computer Engineering, University of Waterloo,in 2016. He has worked as a Post-Doctoral Fellowwith the Department of Electrical and ComputerEngineering, University of Toronto, from 2017 to2019. He is currently a Professor with the StateKey Laboratory of ISN and the School of Telecom-

munication Engineering, Xidian University, Shaanxi, China. His currentresearch interests include B5G/6G, space-air-ground integrated networks, bigdata in vehicular networks, and self-driving systems. His research interestsalso include performance analysis, MAC, opportunistic communication, andapplication of AI for vehicular networks.


http://dx.doi.org/10.1109/JSYST.2020.3019463


Xuemin (Sherman) Shen (Fellow, IEEE) receivedthe Ph.D. degree in electrical engineering from Rut-gers University, New Brunswick, NJ, USA, in 1990.

He is currently a University Professor with theDepartment of Electrical and Computer Engineering,University of Waterloo, Waterloo, ON, Canada. Hiscurrent research interests include network resourcemanagement, wireless network security, the Internetof Things, 5G and beyond, and vehicular ad-hoc andsensor networks.

Dr. Shen is a registered Professional Engineer inthe State of Ontario, Canada, a fellow of the Engineering Institute of Canada,the Canadian Academy of Engineering, and the Royal Society of Canada,a Chinese Academy of Engineering Foreign Member, and a DistinguishedLecturer of the IEEE Vehicular Technology Society and CommunicationsSociety. He was a recipient of the Joseph LoCicero Award in 2015 and theEducation Award in 2017 from the IEEE Communications Society, the JamesEvans Avant Garde Award from the IEEE Vehicular Technology Societyin 2018, the R. A. Fessenden Award in 2019 from IEEE, Canada, the Award ofMerit from the Federation of Chinese Canadian Professionals (ON) in 2019,and the Technical Recognition Award from the Wireless CommunicationsTechnical Committee in 2019 and AHSN Technical Committee in 2013.He was also a recipient of the Premiers Research Excellence Award from theProvince of Ontario, Canada, in 2003, and the Excellent Graduate SupervisionAward from the University of Waterloo in 2006. He was the TechnicalProgram Committee Chair/Co-Chair of IEEE Global TelecommunicationsConference in 2007, IEEE Vehicular Technology Conference in 2010, IEEEInternational Conference on Computer Communications in 2014, and IEEEGlobal Communications Conference in 2016, and the Chair for the IEEE Com-munications Society Technical Committee on Wireless Communications. He isthe elected IEEE Communications Society Vice-President for Technical andEducational Activities, the Vice-President for Publications, Member-at-Largeon the Board of Governors, the Chair of the Distinguished Lecturer SelectionCommittee, and a member of IEEE ComSoc Fellow Selection Committee.He was/is the Editor-in-Chief of the IEEE INTERNET OF THINGS JOURNAL,IEEE NETWORK, IET Communications, and Peer-to-Peer Networking andApplications.

Xiang Chen received the B.E. degree in electronicsand information engineering from the HuazhongUniversity of Science and Technology (HUST)in 2008 and the Ph.D. degree from the Department ofElectronic and Computer Engineering, Hong KongUniversity of Science and Technology (HKUST),in 2013. After graduation, he was a Senior Engineerwith the Hong Kong Applied Science and Tech-nology Research Institute (ASTRI) from 2013 to2019. He is currently with the Theory Laboratory,Huawei Hong Kong Research Institute, as a Principal

Engineer. His broad research interests include system and algorithm designfor emerging wireless technologies and theory, including massive MIMO,interfering networks, and B5G/6G cell-free architecture.

Bo Bai (Senior Member, IEEE) received the B.S.degree (Hons.) in communication engineering fromXidian University, Xi’an, China, in 2004, andthe Ph.D. degree in electronic engineering fromTsinghua University, Beijing, China, in 2010.

From 2009 to 2012, he was a Research Assistant(from April 2009 to September 2010) and a ResearchAssociate (from October 2010 to April 2012) withthe Department of Electronic and Computer Engi-neering, The Hong Kong University of Science andTechnology (HKUST). From July 2012 to Janu-

ary 2017, he was an Assistant Professor with the Department of ElectronicEngineering, Tsinghua University. He has also obtained the support from theBackbone Talents Supporting Project of Tsinghua University. He is currentlya Senior Researcher with the Future Network Theory Laboratory, 2012 Lab-oratories, Huawei Technologies Company Ltd., Hong Kong. He has authoredmore than 70 articles in major IEEE journals and flagship conferences, twobook chapters, and one textbook. His research interests include hot topics inwireless networking, network information theory, network control, fog/edgecomputing, and massive network analysis. He has also served on the WirelessCommunications Technical Committee (WTC) and the Signal Processing andCommunications Electronics (SPCE) Technical Committee. He has servedas a TPC Member for several IEEE ComSoc conferences, such as ICC,GLOBECOM, WCNC, VTC, ICCC, and ICCVE. He received the Honorof Outstanding Graduates of Shaanxi Province and the Honor of YoungAcademic Talent of Electronic Engineering, Tsinghua University. He was arecipient of the Student Travel Grant at IEEE GLOBECOM 2009. He wasinvited as a Young Scientist Speaker at IEEE TTM 2011. He was a recipientof the Best Paper Award in IEEE ICC 2016. He has also served as a reviewerfor a number of major IEEE journals and conferences.


uav-leo integrated backbone: a ubiquitous data collection

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