energy efficiency and traffic offloading optimization in...

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2020.2964236, IEEETransactions on Wireless Communications

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Energy Efficiency and Traffic OffloadingOptimization in Integrated Satellite/Terrestrial Radio

Access NetworksJian Li, Kaiping Xue, Senior Member, IEEE, David S.L. Wei, Senior Member, IEEE, Jianqing

Liu, Yongdong Zhang, Senior Member, IEEE

Abstract—In order to cope with the explosive growth of mobiletraffic, many traffic offloading schemes such as heterogenousnetworks have been developed to enhance network capacity ofthe Radio Access Network (RAN). Among them, networkingof Low-Earth Orbit (LEO) satellites promises to significantlyimprove the RAN performance due to its economical prospectand advantages in high bandwidth and low latency. In this paper,by introducing the cache-enabled LEO satellite network as a partof RAN, we propose an integrated satellite/terrestrial cooperativetransmission scheme to enable an energy-efficient RAN byoffloading traffic from base stations through satellite’s broadcasttransmission. Considering energy-constraints of satellites, wethen formulate a nonlinear fractional programming problemaiming at optimizing transmission energy efficiency of the system.In order to effectively solve this problem, we transform itinto an equivalent one, and then adopt iteration and sub-problem decomposition to obtain the optimal solution for eachoptimization variable, i.e., block placement, power allocation, andcache sharing variable. Numerical results show that comparedwith traditional terrestrial scheme, our cooperative transmissionscheme achieves significant performance improvement in termsof traffic offloading and energy efficiency, especially in anenvironment of high request consistency degree.

Index Terms—Radio access network, integrated satel-lite/terrestrial cooperative transmission, energy efficiency, trafficoffloading

I. INTRODUCTION

With the rapid increase of wireless devices and mobiletraffic, the conventional cellular network is facing severechallenges in terms of wireless/backhaul capacity, energyefficiency and so on [1]–[3]. To better handle these challenges,one straightforward solution is to deploy dense small cells tooffload Base Station (BS)’s traffic by exploiting cooperationin heterogeneous networks such as different tiers of BSsand low-power Access Points (APs) [4]–[7]. However, thetraditional offloading schemes in heterogenous networks canonly provide limited improvement. On the one hand, thedense-deployed BSs and APs will bring in more notoriouscompetition and interference given limited spectrum resourcesin the current Radio Access Network (RAN). On the other

J. Li, K. Xue and Y. Zhang are with the department of ElectronicEngineering and Information Science, University of Science and Technologyof China, Hefei 230027, China.

D. Wei is with the Computer and Information Science Department, FordhamUniversity, NY 10458, USA.

J. Liu is with the Department of Electrical and Computer Engineering,University of Alabama in Huntsville, Huntsville, AL 35899, USA.

Corresponding Author: K.Xue (e-mail: [email protected]).

hand, due to the upper bound of energy efficiency and capacityimprovement, there also exists densification limits for theconventional cellular network [4], [6]. In this case, somenovel technologies, such as satellite communication, are alsoconsidered in heterogenous networks to bring in simple butefficient access approach and further enhance the performanceof cellular network.

In the next generation cellular network, satellite commu-nication has been considered as a promising complementapproach, and satellite access technology should also be sup-ported to assist terrestrial RAN [8], [9]. In the past, becauseof satellite’s high cost, only a few researches consideredto utilize satellite’s advantages to assist terrestrial networks.Thanks to the rapid development of small satellite launchand maintenance technologies, Low-Earth Orbit (LEO) smallsatellites and networking, which can achieve low latency andhigh bandwidth [10], have become economic-friendly for in-dustrial implementation. Many companies such as SpaceX andOneWeb, are planning to construct large-scale LEO satellitenetworks to provide worldwide Internet access service [11]–[14]. Thus, one can foresee that, considering its efficientbroadcast transmission, satellite communication will becomeubiquitous in the next few decades. In this case, more andmore researches have been taking satellite into considerationin the design and implementation of a high performance andenergy-efficient RAN.

While the benefit of satellite assistance has been proven inRAN [7], [8], [15], [16], introducing satellite also puts extrapressure on BSs and the performance of satellite access islimited by satellite backhaul link. To diminish the burden ofBSs and break through the restriction of backhaul link, oneeffective solution is to take full advantage of each node’scapability of storage, computation, and communication. Forexample, in the conventional cellular network, the combinationof caching, centralized/distributed management, and novelaccess technologies, e.g., millimeter-wave communication andNon-Orthogonal Multiple Access (NOMA), have become acommon idea in existing works [4]–[6], [17]–[19]. With thedevelopment of satellite and Information and CommunicationsTechnology (ICT), onboard caching in satellite becomes apromising approach in practice. Many works consider howto leverage cache capacity to help optimize delivery, e.g.,building Information Centric Networking (ICN)-based satellitenetworks [20]–[26]. For integrated satellite/terrestrial RAN,the combination of satellite and caching can both serve mul-



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tiple small cells through broadcast transmission and provideefficient traffic offloading without introducing extra load onBSs nor getting pressure from the restriction of backhaul link.Moreover, with the help of some fine-grained caching schemessuch as coded caching [5], [27], [28], satellite can achievecooperative caching and transmission with terrestrial cellularnetwork to further enhance the cache efficiency. Unfortunately,none of the existing works consider to adopt cooperativecaching and transmission scheme to assist terrestrial RAN.

In order to enhance the capacity of conventional cellularnetwork and overcome the limitations of traditional heteroge-neous networks, in this paper, we consider a satellite networkthat consists of LEO satellites equipped with certain comput-ing and storage resources to take full advantage of satellite’sbroadcast characteristic. By exploiting storage capabilities ofsatellite and dense-deployed APs, the proposed system can of-fload cellular traffic from BS in a cooperative manner with thehelp of coded caching technology. Considering the heavy loadon backhaul and energy-saving concern, a joint optimizationproblem, which considers both traffic offloading and energyefficiency in integrated satellite/terrestrial RAN, is formulated.Furthermore, we also propose an effective algorithm that cansignificantly improve network performance in traffic offloadingand energy efficiency compared with terrestrial scheme. Forthe convenience of the study of performance evaluation and tohightlight the advantage of employing the broadcast functionof a satellite system, we define request consistency degree asthe percentage of the cells that have the same request occur-rences. Numerical results show that the proposed schemes canoutperform terrestrial schemes in all environments of differentrequest consistency degree.

The contributions of this paper can be summarized asfollows:• By introducing the cache-enabled LEO satellite net-

work as a part of RAN, we propose an integratedsatellite/terrestrial cooperative caching and transmissionscheme, which leverages the broadcast characteristic insatellites to efficiently provide traffic offloading for ter-restrial networks. Considering satellite’s limited storagecapability, a cache sharing scheme, which enables ter-restrial AP to share its cached content to the satellite,is also proposed to better exploit satellite’s broadcasttransmission.

• Considering the energy-constraint of satellites, we for-mulate the offloading problem aiming at maximizing theenergy efficiency of RAN in terms of block (i.e., a partof the original content) placement, power allocation, andcache sharing decisions. For this formulated nonlinearfractional programming problem, we exploit a parametricmethod to transform it into an equivalent one, which isfurther divided into three solvable sub-problems. Eachsub-problem is associated with one variable to be op-timized. Furthermore, we thoroughly analyze all thesesub-problems, and propose corresponding optimizationalgorithms to solve them.

• We conduct evaluations to verify the superiority of ourscheme in terms of energy efficiency and traffic of-floading. Numerical results demonstrate that, compared

with traditional terrestrial schemes, our proposed schemecan achieve several times of improvement in energyefficiency for the similar traffic offloading performance,and furthermore such advantages are more remarkable inthe environment of high request consistency degree.

The rest of this paper is organized as follows. At first, therelated works about terrestrial traffic offloading schemes andintegrated satellite/terrestrial schemes are discussed in SectionII. Then, the system model is given in Section III. To improveenergy efficiency in our cooperative transmission scheme, afractional optimization problem is formulated in Section IV,and the problem analysis and designed algorithms are givenin Section V. At last, the performance evaluation is conductedin Section VI, and conclusions are drawn in Section VII.

II. RELATED WORKS

Considering the aggressive objectives in the next generationcellular network in terms of 1000-fold higher capacity, 100-fold higher energy efficiency, and 10-fold lower latency [6],[29], a lot of existing works try to enhance the system perfor-mance by exploiting novel access technologies (e.g., Multiple-Input Multiple-Output (MIMO) and NOMA). In terrestrialRAN, the densification of small cells and cooperation inheterogeneous networks have been considered as promisingsolutions. Xu et al. [30] proposed a cooperative NOMAtransmission that combined Macro Base Station (MBS) andpico-BS, and formulated a resource allocation problem toimprove the system capacity. Inspired by this, a cooperativeaccess scheme that organizes multiple APs in ultra-densenetwork is investigated by Liu et al. [6]. However, simulationresults show that the system capacity improvement will reacha bottleneck with the increasing density of APs. Since NOMAsystem exploits the power-domain for user multiplexing, thepower allocation in NOMA system becomes an importantissue, and most of the related works adopt centralized allo-cation scheme. To achieve distributed power control, Di et al.[31] proposed a novel NOMA-based scheme which combinescentralized scheduling at the BS and distributed power controlat the vehicles, and the results show that this scheme cansignificantly improve data rates compared with OMA scheme.Considering the phenomenon of multiple requests for popularcontents in content distributions, in 2012, Golrezaei et al. [32]first proposed to deploy helpers with weak backhaul links butlarge storage capacity to assist the MBS offloading traffic ofpopular files that have been cached. In order to further improvecache efficiency and provide fine-granularity caching opera-tions, Bioglio et al. [28] proposed a MDS-encoded cachingscheme in heterogeneous network. Based on that, Xu et al.[5] further proposed a NOMA-based coded caching schemeamong APs in small-cell networks, which means that each usercan receive coded packets from multiple APs simultaneously.However, considering the spectrum resource competition andlimited coverage of low power AP, the improvement of systemcapacity is indeed limited. At the same time, the explosivegrowth of mobile traffic has also triggered a dramatic increasein the energy consumption of RAN. Since energy consumptionis a key concern for the operator as it is always the main part



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of the entire operational expenses [33], Prasad et al. [34] andYunas et al. [35] investigated the influence of massive MIMOtechnique and the cooperation among dense deployed BSs inenergy efficiency, respectively. Unfortunately, these existingworks only consider terrestrial access approaches, none ofthem consider to leverage satellite’s broadcast transmission toprovide energy-efficient transmission for conventional cellularnetwork.

Compared to the terrestrial dense-deployed APs, satel-lite has advantages in providing energy-efficient transmissionthrough broadcast transmission. Some existing works haveconsidered integrated satellite/terrestrial network and cache-enabled satellite to provide content access service. In thecellular network, Zhu et al. [7] first considered the thecombination of satellite and terrestrial RAN, and proposedan integrated satellite/terrestrial architecture to cooperativelyprovide downlink transmission based on NOMA. Then, bydistinguishing users’ content requests and dividing users intodifferent group, Zhu et al. [8] also proposed a downlinkmulticast transmission scheme to offload content traffic fromBS. Considering the emerging C-RAN, a cloud based integrat-ed satellite/terrestrial architecture was considered in [15]. Bydoing so, the operator can utilize centralized signal processingto achieve energy-efficient resource management at cloud andfurther achieve seamless coverage. Driven by the ongoingLEO constellation projects of SpaceX and OneWeb, Di etal. [36] proposed a terrestrial-satellite network architectureto achieve efficient data offloading. By utilizing ultra-denseLEO constellation, each terrestrial terminal can be servedby multiple LEO satellites simultaneously, and further sim-ulation results show that the integrated network significantlyoutperforms the non-integrated ones in terms of the sumdata rate. Due to the long propagation delay (typical delayis 14ms [37]) of satellite communication, bent-pipe satellitesuffers even longer transmission delay (over 50ms) since itneeds to retrieve user’s requested data from ground station.In order to alleviate the transmission delay and communi-cation overhead between satellite and ground, researchersconsider to combine satellite’s wide-area coverage and in-network caching. Salvatore et al. [23] proposed a profile-awaresatellite caching strategy. After that, Wu et al. [24] proposeda two-layer caching model for content distribution servicesand formulated a nonlinear integer programming problem.By considering both global and local content popularity, thecaching strategy based on the genetics can significantly reduceboth the downlink and uplink of bandwidth consumption.To further offload traffic from terrestrial network backhaul,Kalantari et al. [38] proposed an offline caching approachwhich considers both global content popularity with mono-beam satellite and local content popularity with multi-beamsatellite in a hybrid satellite/terrestrial architecture. To alleviatethe spectrum shortage and meet the requirements of improvedspectral efficiency, An et al. [39] incorporated wireless contentcaching into satellite/terrestrial network. By storing frequentlyrequired contents and serving users’ requests conveniently,the intrinsic issues of satellite/terrestrial network includingbandwidth inefficiency and excessive propagation delay couldbe largely reduced. However, none of these existing works

consider to adopt cache-enabled satellite as a part of RAN tocooperatively offload wireless traffic of APs from BSs.

III. SYSTEM MODEL

A. Network ModelAs illustrated in Fig. 1, we consider a downlink cooperative

traffic offloading scheme in an integrated satellite/terrestrialcache-enabled RAN, where a number of APs and a LEOsatellite network serve users in a cooperative manner. In eachsmall cell, there are a MBS and multiple APs. APs and usersare assumed to be spatially distributed on a plane according totwo independent homogeneous poisson point processes withdensities λa and λu, respectively. MBS is connected to thecore network gateway via the reliable optical fiber backhaullink, while APs and each LEO satellite are with unreliablebackhaul links and are connected to MBS through wirelesslinks to update their cached contents. Note that we considereach satellite serves non-overlapping terrestrial area in thispaper, that is to say, each user can only be served by onesatellite anytime. Without loss of generality, we focus on theanalysis of one satellite and multiple cells in its coverage area,and J and U are used to denote the cell set and the user setin the coverage, respectively.

Due to the rapid movement of LEO satellite, each LEOsatellite can provide access service to terrestrial cells for acertain duration. The handover process and communicationresource allocation shall be managed by Network ControlCenter (NCC) [40], [41]. According to satellite’s predictabletrajectory, each LEO satellite can provide access service for thesame area periodically under the control of NCC. In Fig. 1, ifwe assume the start time of LEO2’s coverage for Area2 is t1and the coverage duration is T , then LEO2 will serve Area2during [t1, t1 + T ) and serve Area3 during [t1 + T, t1 + 2T ).Actually, in dense deployed LEO networks such as Starlinkproject, thousands of satellites are deployed and the samelocation can be covered by multiple satellites simultaneously[13], [36]. Thus, seamless coverage of terrestrial RAN canbe guaranteed. In this paper, we consider the single satellitescenario that each LEO satellite serves the terrestrial usersduring its service period.

In our integrated satellite/terrestrial RAN, each user isserved by unicast transmissions of APs and/or broadcasttransmissions of the satellite with their cached contents. Orthe user could be served by MBS only when his/her demandscan not be satisfied by APs or/and the satellite. In order toimprove spectrum efficiency, NOMA-based transmission isadopted among APs. Thus, multiple APs will simultaneouslyserve the same user with their cached contents over thesame spectrum resource. In order to avoid severe interferencebetween satellite’s broadcast and terrestrial transmission, weassume that LEO satellite operates over exclusive frequencybands such as S band (direct access service) and Ka band(indirect access service) [37], [42], [43]. Concerning the issueof what contribute to most traffic in content-based applications[1], we only concentrate on content distribution and retrievalapplications in this paper.

To make our scheme easier to understand, we depict Fig. 2to describe the basic procedure of our traffic offloading



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2019/5/9 SystemModel_Modify_v2.svg

file:///D:/论文数据备份/INFOCOM改投/素材/SystemModel_Modify_v2.svg 1/1

Internet

...

Core network gateway

AP

...

Cache Sharing

Cache Sharing

AP APAP

AP

AP

AP

AP

MBS

AP

Cache Cache SharingTransmit Cached BlocksGatewayUser

2.Broadcast Coded Blocks retrieved

from APs

1.Broadcast Cached Coded Blocks in

Satellite

LEO Satellite Network

LEO2LEO1LEO3

Area1

...

......

Area3

MBS

Move to Area2

Small cell

MBS

Move to Area3

Area2Terrestrial RAN

Fig. 1. The proposed system model of integrated satellite/terrestrial RAN.

scheme. The basic idea behind our scheme is to utilize cache-enabled LEO satellite and terrestrial APs to offload trafficfrom base station and its backhaul link. In this case, afterreceiving user’s request, LEO satellite and APs will first servethe user with their cached blocks (a part of user’s requestedcontent file) in a cooperative manner. If user’s request can notbe satisfied by the satellite and APs, e.g., content recoveryfailure or transmission failure, the user will be served byMBS for content retrieval through backhaul link. The specificcooperative transmission approach in Phase 1 will be describedin more detail in Section III-D.

2019/5/15 Procedure.svg

file:///D:/论文数据备份/INFOCOM改投/素材/Procedure.svg 1/1

AP3

AP2

AP1

Broadcast

Phase 1 Phase 2

MBS

MBS Transmits C2 and a part of C4 retrieved from backhaul link

u1

u2

u3

u4

u5u1

u2

u3

u4

u5

APs Transmit Cached Blocks Satellite Broadcasts Cached Blocks MBS service

Unsatisfied UserCache-enabled LEO Satellite

f2

Cached Blocks in APs and on the satellite:f1 f3 f4 f5

Request f1u1

Request f2u2

Request f3u3

Request f4u4

Request f5u5

Fig. 2. The overall traffic offloading procedure for LEO satellite and APswhen users request cached contents.

B. Coded Caching Model

In order to improve caching efficiency, a coded cachingscheme similar to that of [5] is adopted in our work. Weconsider a content library consisting of N files, denoted byF . All files are assumed to have the same size and each oneis split into c equal-sized original blocks, where each one iswith size L. Then c original blocks of each file are encodedinto an arbitrarily large number of coded blocks to be cachedby terrestrial APs and the satellite.

With coded caching, when a user receives an arbitrarynumber of blocks, n (n ≥ c), from APs and the satellite,he/she can recover the original file from the received blocks.By carefully selecting coding coefficients, each access node(i.e., AP or satellite) can provide linearly independent blocks

to the user with high probability. In practice, it can be achievedthrough, for example, MDS (Maximum-Distance Separable)[28] and RLNC (Random Linear Network Coding) codes [5].The local cache of each AP and satellite can store up to MLand MSatL bits, respectively. We assume that all APs in thesame cell j have the same cached blocks of i-th file in blockplacement phase, i.e., mi,j . Thus, each user can access thesame service from any AP in the same cell.

C. Channel Model

In the downlink channel of terrestrial APs, we considerboth large-scale fading and small-scale fading. The large-scalefading is modeled by a standard distance-dependent power lawpath loss attenuation, while the Rayleigh fading is consideredas small-scale fading. The transmission power of each AP foruser u in cell j is the same, i.e., Pj,u. Thus, the received signalpower at user u in cell j can be written as |h|2(1+rα)−1Pj,u,where h ∼ CN (0, 1) represents fading coefficient, r denotesthe distance between u and AP, and α is the path loss exponent.

Different from the terrestrial case, the satellite channelgenerally experiences less fluctuation considering the line-of-sight link between the satellite and terrestrial users. Thus, thechannel model of the satellite can be considered as an AdditiveWhite Gaussian Noise (AWGN) channel [8]. According to thelarge-scale fading model in literatures [44], the received signalof a terrestrial user for i-th file can be computed by

y(x) =λ′G

√P Sati

4πrSatxi + n0, (1)

where xi denotes the symbol transmitted from the satellite fori-th file, λ′ denotes the wave length, rSat denotes the distancebetween terrestrial users and the satellite, G is antenna gainand n0 ∼ CN (0, N0) is the complex AWGN of power N0. Inorder to successfully transmit cached blocks of i-th file fromthe satellite to terrestrial users, the minimum transmission ratemSati L/t should be satisfied (i.e., C ≥ Cmin = mSat

i L/t),where mSat

i is cached blocks of i-th file on the satellite and tis the time slot in RAN. According to the Shannon equation,C = W Satlog(1+SNR), on-board transmission power of thesatellite for i-th file can be computed by

P Sati = N0(

4πrSat

λ′G)2 · (2

mSati L

WSatt − 1), (2)

where W Sat is the subcarrier bandwidth in satellite system.

D. File Request and Delivery Model

For user u, there are two different phases during thetransmission, i.e., file request and file delivery. User u firstsends a request for i-th file to MBS during the request phase.Then, during the file delivery phase, MBS coordinates with thenearest APs and the satellite to transmit their cached blocksof i-th file to u. Note that APs and the satellite can serve thesame user for the i-th file simultaneously over non-overlappingfrequency band. If i-th file can be recovered from receivedblocks at u, the request is satisfied; Otherwise, the rest of theblocks will be served by MBS.



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The file popularity is modeled as the Zipf distribution withshape parameter θ. Then the popularity of the i-th ranked filein cell j is

pi,j =1/iθ∑Nn=1 1/nθ

. (3)

We assume that in file request phase, each user in the same cellrequests for i-th file with the same probability of popularitydistribution, i.e., pi,j = pi,j,u, which denotes the requestprobability of each user for i-th file in cell j.

In file delivery phase, a user’s request can be satisfiedby three ways, i.e., only NOMA-based transmission fromAPs, only broadcast transmission from the satellite, or thecombination of these two transmissions. Since we only con-sider AWGN channel with large-scale fading during broadcasttransmission from the satellite, satellite’s signal can be surelydecoded when Eq. (2) is satisfied. Fig. 3 shows an exam-ple of cooperative transmission with both NOMA-based andbroadcast transmission for u1. Since MBS is in charge of thecoordination of APs and the satellite, the number of controlsignal transmitted from MBS to APs and the satellite can berespectively calculated by Oj =

∑i∈F

∑u∈Uj pi,j ·sgn(mi,j)

and OSat =∑i∈F sgn(mSat

i ), where function sgn(·) equals1 when mi,j > 0, otherwise, equals 0.2019/4/15 OffloadingScheme.svg

file:///D:/%E8%AE%BA%E6%96%87%E6%95%B0%E6%8D%AE%E5%A4%87%E4%BB%BD/INFOCOM%E6%94%B9%E6%8A%95/%E7%B4… 1/1

u1: request f1u2: request f2

MBS

Decodery

-Decoder

y=h0x0+h1x1+n0 x0

x1

A1 : h0x0 / h1x1+n0≥τ, h1x1 / n0≥τ

h1x1+n0

h0x0

f2f1

MBS

SIC Decoding Process at u1:

Cache SharingTransmit Cached Blocks User’s Request

2.Retrieve blocks of f2 from terrestrial AP and broadcast

u3: request f2

Control link

A2 : h0x0 / h1x1+n0≥τ, h1x1 / n0<τ

A3 : h0x0 / h1x1+n0<τ, h1x1 / n0<τ

Possible Decoding Situa�ons:

Block Placementin the cell:

f1

f1f2f1

Block Placementon the satellite:

f1 f2f1

Block Placementin the cell:f1

x2

+

x2

Recover original file

1.AP group for serving u1

h1x1AP0

AP1

h0x0AP

Fig. 3. The proposed cooperative transmission and cache sharing scheme(split original blocks of each file c = 4 and cache size M = MSat = 3).

For APs, we consider a NOMA-based transmission schemesimilar to [5], [6]. If the i-th file, requested by user u, iscached by APs in the cell, these APs can simultaneouslytransmit cached blocks of the requested file to u over thesame frequency band. User u adopts successive interferencecancellation receiver to decode the signals successively inthe descending order of the average received signal strength.Assume that each AP adopts the same power Pj,u to transmitsignals to user u in cell j, so the Signal-to-Interference andNoise Ratio (SINR) at user u for decoding the signal fromk-th AP can be computed by

γu,k =|hk|2(1 + rk

α)−1Pj,u∑k′∈Ku,k′>k

|hk′ |2(1 + rk′α)−1Pj,u +N0, (4)

where Ku represents the number of APs in AP group forserving user u and N0 is the AWGN power.

Considering the complexity of SIC receiver is related to thenumber of decoding layer in practice [45], we assume that

at most 2 nearest APs can share the same frequency band toserve the same user, i.e., |Ku| ≤ 2.

In this case of 2 served APs for user u, there are threepossible situations during the transmission: 1) Both trans-missions are successful, i.e., A1 : γu,0, γu,1 ≥ τ ; 2) Onlythe transmission of the nearest AP is successful, i.e., A2 :γu,0 ≥ τ, γu,1 < τ ; 3) Both transmissions are failed, i.e.,A3 : γu,0, γu,1 < τ . A decoding example is also shown inFig. 3. Obviously, we have Pr{A1}+Pr{A2}+Pr{A3} = 1.Therefore, the average traffic of user u served by APs for i-thfile in cell j, qi,j,u, can be represented as

qi,j,u =

{mi,j(2Pr{A1}+ Pr{A2}), mi,j ∈ L1,

cPr{A1}+mi,jPr{A2}, mi,j ∈ L2,(5)

where mi,j represents cached blocks of i-th file in every APof cell j, L1 = [0, c/2], L2 = (c/2, c], and τ denotes thedecoding threshold.

In order to take full advantage of satellite’s broadcast capac-ity, we also consider a cache sharing scheme in the integratedsatellite/terrestrial RAN considering the limited storage ofLEO satellites. By sharing cached blocks of terrestrial AP tothe satellite, some popular files can be cached by APs and thesatellite can retrieve blocks from terrestrial AP on demand.An example is shown in Fig. 3. Once the cache sharing fori-th file is enabled, multiple users who request i-th file willonly be served by the satellite.

IV. PROBLEM FORMULATION

In this section, we first analyze the expected traffic of-floading and energy consumption in our scheme, respectively.After that, energy efficiency optimization in our scheme, whichjointly considers block placement, power allocation and cachesharing, is formulated as a nonlinear fractional programmingproblem.

A. Traffic Offloading

The total traffic served by APs can be computed by

BT =∑i∈F

∑j∈J

∑u∈Uj

(1− atoSi ) · pi,jqi,j,u, (6)

where atoSi denotes cache sharing variable. When atoSi = 1,AP will forward its cached i-th file to the satellite with thehelp of MBS, and users who request i-th file will be served bythe satellite through broadcasting; otherwise, each user will beserved by APs. In order to obtain the closed-form expressionof qi,j,u in Eq. (6), we have the following proposition.

Proposition 1. For user u, there are three possible situationsat u by decoding signals from two nearest APs with SICreceiver, and the probability of at least one successful decodingsituations, i.e., A1 and A2, can be computed by{

Pr{γu,0 ≥ τ, γu,1 ≥ τ} = ϕexp(−λω),

P r{γu,0 ≥ τ, γu,1 < τ} = ϕ[exp(−λd0)− exp(−λω)],(7)

where ϕ = d1τd0+d1

, λ = τN0

2σ2Pj,u, ω = d0(τ + 1) + d1, d0 =

(1 + rα0 ), d1 = (1 + rα1 ) and τ denotes decoding threshold.



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Proof. According to the conditional probability formula andEq. (4), when both transmissions are successful, we have

Pr(γu,0 ≥ τ, γu,1 ≥ τ) = Pr(γu,1 ≥ τ)Pr(γu,0 ≥ τ |γu,1 ≥ τ)= Pr(|h1|2 ≥ ξ) · Pr(|h0|2 ≥

τ(|h1|2(1 + rα1 )−1Pij +N0)

(1 + rα0 )−1Pj,u

|γu,1 ≥ τ)

(a)=

∫ ∞ξ

Pr(x)Pr(|h0|2 ≥τ(x(1 + rα1 )

−1Pj,u +N0)

(1 + rα0 )−1Pj,u

|x)dx

(b)=

1

2σ2

∫ ∞ξ

exp(− x

2σ2)exp(−τ(x(1 + rα1 )

−1Pj,u +N0)

(1 + rα0 )−12σ2Pj,u

)dx

=1

2σ2

∫ ∞ξ

exp(−x[τ d0

d1+ 1]Pj,u + τN0d0

2σ2Pj,u)dx

=Pj,u

τPj,u(τ1+rα01+rα1

+ 1)exp(−τN0[τd0 + d1] + τN0d0

2σ2Pj,u)

= ϕexp(−τN0(τd0 + d1) + τN0d02σ2Pj,u

). (8)

Meanwhile, for the situation of successful transmission onlyfrom the nearest AP, we have

Pr(γu,0 ≥ τ, γu,1 < τ)

= Pr(γu,1 < τ)Pr(γu,0 ≥ τ |γu,1 < τ)

(a)=

∫ ξ

0

Pr(x)Pr(|h0|2 ≥τ(x(1 + rα1 )−1Pij +N0)

(1 + rα0 )−1Pij|x)dx

= ϕ[exp(−τN0d02σ2Pj,u

)− exp(−τN0(τd0 + d1) + τN0d02σ2Pj,u

)],

(9)

where ξ = τN0

(1+rα1 )−1Pij. Here, we let x = |h1|2 in (a)

and utilize the following conclusion in (b): For the squareof Reyleigh fading variable y, the PDF can be computed byfY (y) = 1

2σ2 exp(− y2σ2 ), and the CDF can be computed by

FY (y) = Pr(Y ≤ y) = 1− exp( y2

2σ2 ).

According to Proposition 1, by substituting Eq. (7) into Eq.(5), we have

qi,j,u =

mi,jϕ(exp(−λd0) + exp(−λω)), mi,j ∈ L1,

ϕ(mi,jexp(−λd0) + (c−mi,j)

· exp(−λω)), mi,j ∈ L2.

Now we can compute the total traffic served by APs.For the satellite, broadcast transmission is used to serve

users in its coverage region. Since the satellite can broadcastcached blocks and also cached blocks in terrestrial APsthrough cache sharing, the traffic offloaded from satellitethrough broadcast can be computed by

BSat =∑i∈F

(mSati +m∗i a

toSi )ρSati Ui, (10)

where ρSati denotes the probability of terrestrial users forsuccessfully decoding the signal from the satellite, Ui =∑j∈J

∑u∈Uj pi,j represents the average users that request i-

th file in satellite coverage region and m∗i = maxj∈J {mi,j}represents the maximum number of cached blocks of i-th file

in APs. In order to avoid duplicate caching for the same filein APs and the satellite, we also have a constraint as

mSati ≤ 1−Ki,um∗i , ∀i ∈ F , ∀u ∈ U , (11)

where Ki,u denotes the number of APs serving user u for i-th

file and Ki,u =

{1,mi,j = c

2, 0 < mi,j < cshould be satisfied.

B. Energy Consumption

For energy efficiency concerns in integrated satel-lite/terrestrial RAN, we compute the energy consumed by bothAPs and the satellite. Since APs can provide multiple accessto each user and cache sharing to the satellite, the energyconsumption of terrestrial transmission can be computed by

PT =∑i∈F

∑j∈J

∑u∈Uj

Ki,uPj,upi,j(1− atoSi ) +∑i∈F

P toSi (m∗i )a

toSi ,

(12)

where P toSi (m∗i ) denotes the power consumption for forward-

ing m∗i cached blocks of i-th file from AP to the satellitethrough MBS.

For the satellite, energy consumption is an important con-cern since it has the direct impact on the system designand satellite lifespan. In order to offload traffic from cellularnetwork, it is inevitable that the satellite’s energy consumptionwill increase for more content data transmission over highspeed channel. The energy consumption of satellite is com-posed of two parts, i.e., broadcast cached blocks in the satelliteand blocks retrieved from APs. Thus, the energy consumptionof satellite can be computed by

P Sat =∑i∈F

Pr(Ui ≥ 1)[P Sati (mSat

i ) + P Sati (m∗i )a

toSi ], (13)

where Pr(Ui ≥ 1) = (1 − Πj∈J (1 − pij)|Uj |) denotes the

probability that at least one user requests i-th file, and P Sati is

the power consumption for broadcast mSati blocks of i-th file

and it can be computed by Eq. (2).

C. Objective

After we obtain the formulation of traffic offloading andenergy consumption from APs and satellite, the total trafficserved by APs and satellite can be computed by

Btotal = BT +BSat, (14)

and the total energy consumption can be computed by

Ptotal = PT + P Sat. (15)

In order to maximize the energy efficiency, our objective canbe formulated as

Problem 1 : maxa,m,P

Btotal(a,m,P)

Ptotal(a,m,P), (16)



7

s.t.∑

i∈Fpi,j = 1, ∀j ∈ J , (C1)∑

i∈Fmi,j ≤M, ∀j ∈ J , (C2)∑

i∈FmSati ≤MSat, (C3)

mSati ≤ 1−Ki,um∗i , ∀i ∈ F , u ∈ U , (C4)∑i∈F

(P Sati (mSat

i ) + atoSi P Sati (m∗i )) ≤ P Sat

total, (C5)

Pj,u ≤ Pmax, PSati ≤ P Sat

max, (C6)

atoSi ∈ {0, 1},mSati ,mi,j ∈ N+, (C7)

where a = {atoSi },m = {mi,j ,mSati } and P = {Pj,u}

(i ∈ F , j ∈ J , u ∈ U) represent cache sharing vector, blockplacement vector and power allocation vector, respectively.P Sattotal denotes the power constraint of each LEO satellite, andPmax and P Sat

max represent the maximum transmission powerfor AP and the satellite, respectively.

V. PROBLEM ANALYSIS AND ALGORITHM DESIGN

A. Problem Analysis

Problem 1 is a nonlinear fractional programming problemconsisting of integer variables and also continuous variables,which is difficult to derive a global optimal solution. Consider-ing that a number of cells and APs are involved in an integratedsatellite/terrestrial RAN, in order to solve the problem in poly-nomial time, we introduce a parametric method to transformthe original nonlinear fractional objective function [46], [47]in Problem 1 and respectively consider three solvable sub-problems. At first, a problem equivalence theorem is given asfollows. For notation convenience, G is defined as the set offeasible solutions of Problem 1 and g = (a,m,P) ∈ G.

Theorem 1. (Problem Equivalence): η∗ is achieved if andonly if

maxg∗Btotal(g)−η∗Ptotal(g) = Btotal(g∗)−η∗Ptotal(g

∗) = 0,

(17)where g∗ is the optimal solution of Problem 1 and η∗ =Btotal(g∗)/Ptotal(g

∗).

Proof. By referring to [47], [48], we give the following proofprocess.

At first, we prove the sufficient condition of Theorem1. Since η∗ = Btotal(g∗)/Ptotal(g

∗) represents the maximalenergy efficiency performance, it is obvious that η∗ holds, i.e.,

η∗ =Btotal(g∗)Ptotal(g∗)

>Btotal(g)

Ptotal(g), (18)

where g ∈ G is the feasible solution for solving Problem1, and Ptotal(g′) > 0 (total power consumption can not benegative). Then, according to (18), we can derive the followingformulas {

Btotal(g)− ηPtotal(g) ≤ 0,

Btotal(g∗)− η∗Ptotal(g∗) = 0.

(19)

Consequently, we can conclude that maxg∗ Btotal(g) −η∗Ptotal(g) = 0 can be achieved by the optimal solution g∗.The sufficient condition is proved.

Secondly, we prove the necessary condition of Theorem1. Let g be the optimal solution of the transformed objectivefunction, we can have Btotal(g) − η∗Ptotal(g) = 0. For anyfeasible solution g, they can be expressed as

Btotal(g)− η∗Ptotal(g) ≤ Btotal(g)− η∗Ptotal(g) = 0. (20)

The above inequality can be derived as

Btotal(g)

Ptotal(g)≤ η∗ and

Btotal(g)

Ptotal(g)= η∗. (21)

Therefore, the optimal solution g for the transformed objectivefunction is also the optimal solution for the original objectivefunction. The necessary condition of Theorem 1 is proved.

Based on the optimal condition stated in Theorem 1, theoriginal problem can be transformed to Problem 2 if we canfind the optimal value η∗.

Problem 2 : maxa,m,P

Btotal(g)− η∗Ptotal(g), (22)

s.t. Conditions C1, C2, C3, C4, C5, C6, C7 are satisfied.

Then an iteration algorithm is proposed to update η in Algo-rithm 1 and ε is a constant which can make the algorithmconverge to η∗ with a superlinear convergence rate [47].Inspired by Block Coordinate Descent (BCD) [49], [50], wedivide problem 2 into three sub-problems according to therelationship of each variable. To optimize a multi-variableobjective in BCD method, the coordinates of variables are firstpartitioned into blocks 1. Through another iterative process(i.e., line 4-8 in Algorithm 1), we optimize the objective interms of one of the coordinate blocks while the other coor-dinates are fixed at each iteration. Moreover, three algorithmsare proposed to solve three sub-problems of block placement,power allocation and cache sharing, respectively. Then we canapply them to Algorithm 1 to obtain a global sub-optimalsolution in an iterative manner.

B. Block Placement Algorithm

In order to obtain the optimal block placement vector m∗

in the integrated satellite/terrestrial RAN, we consider a two-step solving process as described in Algorithm 2. The basicidea is that, we first find the optimal block placement vectorfor terrestrial APs in each cell. Then, we try to find theoptimal block placement vector on the satellite. Since theterrestrial block placement mi,j and satellite block placementmSati are coupled, we also consider the influence between mi,j

and mSati . In the following, we will specifically analyze the

property of block placement sub-problem and explain why ouralgorithm can obtain the optimal placement vector m∗.

1) Terrestrial Block Placement: At first, we only considerthe optimal block placement mi,j for APs, and the objectivefunction related to mi,j in Eq. (22) can be written as

1Note that the block here is different from content block we mentioned inSection III-B (Coded Caching Model).



8

Q1i,j(mi,j , ηt) =

∑u∈Uj

(1− atoSi )(qi,j,u

− ηtKi,uPj,u)pi,j − ηtP toSi (m∗i )a

toSi . (23)

Algorithm 1: Iteration Algorithm for Problem 2Input: The maximum number of iteration T1, T2 and

convergence factor δ, δ′;Output: Optimal solution g∗ for each sub-problem;

1 Initialize: Take η0 and set t = t′ = 0;2 while Btotal − ηtPtotal > δ and t < T1 do3 Set t′ = 0;4 while Et′ − Et′−1 < δ′ and t′ < T2 do5 Apply sub-algorithm to obtain solution of

at′+1,mt′+1 and Pt′+1 for each sub-problemwhile fixing (mt′ ,Pt′), (at′+1,Pt′) and(at′+1,mt′+1) respectively;

6 gt′+1 = (at′+1,mt′+1,Pt′+1);7 Et′+1 = Btotal(gt′+1)− ηtPtotal(gt′+1),

t′ = t′ + 1;8 end9 Let gt = (at′ ,mt′ ,Pt′), take ηt+1 = Btotal(gt)

Ptotal(gt)+ ε,

t = t+ 1;10 end

Terrestrial block placement can be classified as a multiple-choice knapsack problem. By utilizing the monotonicity ofQ1i,j , a specific process of finding the optimal terrestrial block

placement is given in line 2-18 of Algorithm 2. For each loopin line 3-17, the algorithm first calculates the gain of cachingone more block for each file in line 5, and finds the mostvaluable caching block with maximum gain by implementingline 7-16. Note that only one block will be selected to beadded to cache for each loop in line 3-17, and I representsthe set of files that could not be cached anymore. The analysisof the property of Q1

i,j is described as follows.

Proposition 2. qi,j,u is a monotonic increasing and piece-wisefunction of variable mi,j with fixed SINR threshold τ .

Proof. At first, we relax mi,j as continuous variableand let f(mi,j) represent qi,j,u. When mi,j ∈ L1 =

[0, c/2], the derivative df(mi,j)dmi,j

= d1τd0+d1

[exp(− τN0

2σ2Pj,ud0) +

exp(− τN0

2σ2Pj,u(d0(τ + 1) + d1))] > 0; When mi,j ∈

L1 = (c/2, c], df(mi,j)dmi,j

= d1τd0+d1

[exp(− τN0

2σ2Pj,ud0) −

exp(− τN0

2σ2Pj,u(d0(τ + 1) + d1))], due to d0 < d0(τ + 1) + d1,

we have − τN0

2σ2Pj,ud0 > − τN0

2σ2Pj,u(d0(τ + 1) + d1). Thus,

exp(− τN0

2σ2Pj,ud0) > exp(− τN0

2σ2Pj,u(d0(τ + 1) + d1)), and

the derivative df(mi,j)dmi,j

> 0 can be obtained. Meanwhile, weassume δ is an arbitrary small value, then we have f(c/2 +δ) − f(c/2) = δexp(− τN0

2σ2Pj,ud0) − δexp(− τN0

2σ2Pj,u(d0(τ +

1) + d1)) > 0. In this case, Proposition 2 is proved.

Corollary 1. Q1i,j is a monotonic increasing and piece-wise

function of variable mi,j with fixed SINR threshold τ .

Proposition 3. The optimal placement vector for maximizingQ1i,j satisfies that, m1,j > m2,j for any given file popularity

p1,j > p2,j when atoS1 = atoS2 = 0.

Proof. We prove this proposition by contradiction. Let a < band a, b ∈ N+. Assume that there are two files f1, f2 ∈ F andp1,j > p2,j in cell j. We further suppose that m∗ = {m1,j =a,m2,j = b} is an optimal caching strategy. Accordingly, wehave another caching strategy m′ = {m1,j = b,m2,j = a},which is obviously not the optimal caching strategy. Based onthe above supposition, we have

Q1j (m

∗) =∑

u∈Uj[p1,jqi,j,u(a) + p2,jqi,j,u(b)− ηK′a,bPj,u].

Then we exchange the placement for file f1, f2, and we have

Q1j (m

′) =∑

u∈Uj[p1,jqi,j,u(b) + p2,jqi,j,u(a)− ηK′b,aPj,u],

where K′a,b = K1,u(a) + K2,u(b) and K′b,a = K1,u(b) +K2,u(a). Then, we have K′a,b = K′b,a. At last, we make thecomparison between Q1

j (m∗) and Q1

j (m′):

Q1j (m

∗)−Q1j (m

′)

= p1,jqi,j,u(a) + p2,jqi,j,u(b)− [p1,jqi,j,u(b) + p2,jqi,j,u(a)],

= p1,j [qi,j,u(a)− qi,j,u(b)]− p2,j [qi,j,u(a)− qi,j,u(b)],

=∑

u∈Uj(p1,j − p2,j)[qi,j,u(a)− qi,j,u(b)]. (24)

From the assumption and Proposition 2, we know thatp1,j > p2,j and qi,j,u(a) < qi,j,u(b). Then we can furtherget Q1

j (m∗) < Q1

j (m′), so m′ represents a better block

placement strategy, which leads to a contradiction to ourprevious assumption that the optimal block placement m∗

should have m1,j < m2,j when p1,j > p2,j . Thus, the optimalplacement should satisfy m1,j > m2,j for any given filepopularity p1,j > p2,j when atoS1 = atoS2 = 0. Proposition3 is thus proved.

2) Satellite Block Placement: Considering the broadcasttransmission of satellite, satellite block placement will influ-ence the terrestrial block placement and constraint (C4) shouldbe satisfied. Similar to Eq. (23), the objective related to thesatellite can be written as

Q2i (m

Sati , ηt)

= (mSati +m∗i a

toSi )Ui − ηt(P Sat

i (mSati ) + P Sat

i (m∗i )atoSi ).(25)

Proposition 4. Q2i is a concave function of variable mSat

i .

Proof. P Sati , related to variable mSat

i in Q2i , can be obtained

by Eq. (2). By computing second order derivative of P Sati , we

can obtain that d2P Sati /d(mSat

i )2 > 0 and −ηP Sati must be

a concave function. Considering that the mSati Ui is a linear

function, Q2i is a concave function can be proven according

to convexity preserving property [51].

Proposition 5. The optimal placement vector for maximizingQ2i,j satisfies that, mSat

1 > mSat2 for any given file popularity

U1 > U2 when atoS1 = atoS2 = 0.



9

Algorithm 2: Global Block Placement Algorithm

Input: Cache Size M and MSat, number of originalblocks c and ηt at t-th iteration;

Output: The optimal block placement vector m∗;1 Initialize:

Set I = �, mi,j = 0 and mSati = 0, ∀i ∈ F , j ∈ J ;

Sort the file popularity of each cell;2 for j ∈ J do3 while

∑i∈F mi,j ≤M and |I| < |F| do

4 for i ∈ F do5 Compute

δi = Q1i,j(mi,j + 1, ηt)−Q1

i,j(mi,j , ηt);6 end7 while true do8 Let i′ = argmaxi∈{F−I}δi;9 if mi′,j < c then

10 Set mi′,j = mi′,j + 1;11 break;12 end13 else14 Set I = I

⋃{i′};

15 end16 end17 end18 end

Proof. Similar to the proof of Proposition 3.

Considering the property of Q2i (m

Sati , ηt) and the coupling

of terrestrial and satellite block placement, Algorithm 2 co-operatively considers terrestrial and satellite block placementto obtain the optimal solution after obtaining terrestrial blockplacement in line 2-18. Let J ∗ represent terrestrial cells whichcache m∗i blocks of i-th file. According to the average requestnumber of i-th file, i.e., Ui, Algorithm 2 adds blocks oneby one and computes the corresponding caching gain basedon the ordered sequence of F ′ in line 19. In line 22-25, thealgorithm first computes the derivative of Q2

i (mSati , ηt). If

the derivative is not positive, it means that there is no gainto cache i-th file on the satellite. Thus, the algorithm wouldterminate the rest of the procedure and continue another loopin line 20-43. In line 26, c−Ki,um∗i represents the number ofunique blocks that can be directly cached on the satellite. IfmSati + 1 ≤ c−Ki,um∗i , i-th file could be directly cached on

the satellite once, and constraints (C4) and (C5) are satisfied.Otherwise, the algorithm compares the gain of caching i-th fileon the satellite and the gain of caching i-th file in terrestrialAPs. According to the comparison result of the gain of cachingi-th file in terrestrial APs and on the satellite (i.e., ∆1 and ∆2),when ∆2 > ∆1 and constraints (C4) and (C5) are satisfied,i-th file will be cached on the satellite ( i.e., mSat

i = mSati +1)

as shown in line 30-34. Accordingly, when ∆2 ≤ ∆1 orconstraints (C4) and (C5) are not satisfied, i-th file would notbe cached on the satellite and the algorithm continues anotherloop in line 20-43. In this way, the algorithm can find theoptimal block placement vector m∗ in a greedy manner.

19 Sort the file set F ′ according to the value of Ui;20 for i ∈ F ′ do21 while

∑i∈F m

Sati ≤MSat do

22 Compute the derivative of Q2i (m

Sati , ηt) at

mSati = 0;

23 if f ′(mSati ) ≤ 0 then

24 Continue loop in line 20;25 end26 if mSat

i + 1 > c−Ki,um∗i then27 Compute the differences ∆1 =∑

j∈J ∗ [Q1i,j(m

∗i , ηt)−Q1

i,j(m∗i −Ki,u, ηt)],

and ∆2 = Q2i (m

Sati + 1, ηt)−Q2

i (mSati , ηt);

28 Find the optimal placement ∆mi′,j for APsto replace Ki,u cached blocks of i-th file inj ∈ J ∗ cell with Ki,u blocks of i′-th file inj ∈ J ∗ cell;

29 Compute the increasing gain∆1 = ∆1 +

∑j∈J ∗ [Q

1i′,j(mi′,j +

∆mi′,j , ηt)−Q1i′,j(mi′,j , ηt)];

30 if ∆2 > ∆1 then31 if mSat

i + 1 satisfies constraint (C4) and(C5) then

32 Set mSati = mSat

i + 1;33 Set mi′,j = mi′,j + ∆mi′,j and

mi,j = mi,j −Ki,u for j ∈ J ∗;34 end35 end36 end37 else38 if mSat

i + 1 satisfies constraint (C4) and (C5)then

39 Set mSati = mSat

i + 1;40 end41 end42 end43 end

3) Computational Complexity: The complexity of the op-timal exhaustive search for m∗ is O(2(M ·|J |+M

Sat)·N ) andthe complexity of our block placement algorithm is O((M +MSat) · (NlogN) · |J |).

C. Power Allocation Algorithm

Since satellite channel model is considered as AWGNchannel with large-scale fading, the transmission power ofthe satellite can be computed by Eq. (2). In this case, weonly consider the power allocation of APs. Here, we have thefollowing theorem about power allocation sub-problem.

Theorem 2. Objective function (22) is a concave func-tion when power allocation variable satisfying Pj,u ≥τN0ωu/2,∀j, u; Objective function (22) is a convex func-tion when power allocation variable satisfying Pj,u ≤τN0d0/2,∀j, u, where ωu = du,0(τ + 1) + du,1.



10

Proof. Let f(Pj,u) represents the objective in Eq. (22), thenby computing the second order derivative of f(Pj,u), we have

d2f(Pj,u)

dP 2j,u

= a1exp(−λ1/Pj,u)(τN0d0 − 2Pj,u)+

a2exp(−λ2/Pj,u)(τN0ωu − 2Pj,u),

where a1 =τN0d0(2σ

2)2mi,jϕu(2σ2Pj,u)4

, a2 =τN0ωj,umi,jϕu

(2σ2Pj,u)4or

τN0ωj,u(N−mi,j)ϕu(2σ2Pj,u)4

, λ1 = τN0du,0/2σ2, λ2 = τN0ωu/2σ

2 >

λ1 and ωu = du,0(τ + 1) + du,1. Since τN0ωu >τN0du,0,∀u ∈ U is satisfied, when Pj,u ≥ τN0ωu/2, we haved2f(Pj,u)

dP 2j,u

≥ 0; When Pj,u ≤ τN0d0/2, we have d2f(Pj,u)

dP 2j,u

≤ 0.Thus, Theorem 2 is proven.

As described in Theorem 2, power allocation sub-problemsatisfies concavity or convexity when Pj,u ∈ P =[Pmax, τN0ωu/2]∪[τN0du,0/2, 0]. In order to efficiently solvepower allocation sub-problem, we assume that the optimalpower allocation could be found in partial solution spaceP with a great probability. If we assume the gap betweenτN0ωu/2 and τN0du,0/2 as β, β = τN0ωu/2−τN0du,0/2 =τN0(τdu,0 + du,1)/2. Typically, N0 ≈ 3.981 ∗ 10−14 (pow-er spectral density of noise = −174dBm/Hz ≈ 3.981 ∗10−21W/Hz, and subcarrier bandwidth = 10MHz) and τ =0.414 (file size = 50kb, time slot = 10ms and subcarrierbandwidth = 10MHz). Considering du,0, du,1 ≤ 1 in smallcell (1km ∗ 1km cell size is considered in our evaluation),the gap β will be smaller than 1 ∗ 10−13. In this case,our assumption is reasonable. Hence, the objective functionbecomes a combination of a concave and convex function.By setting variable value range, interior-point method can beapplied to the problem and obtain the optimal power allocationefficiently.

According to our numerical results, when request consis-tency degree becomes low, the performance of the proposedalgorithm in terms of traffic offloading will decrease andbecome worse than the baseline2. We further consider that theperformance of traffic offloading is also important for practicalapplication. In this case, we set the minimum threshold oftransmission power to improve the performance of energyefficiency without any sacrifice of traffic offloading comparedwith the baseline. By doing this, regardless of the degreeof request consistency, our numerical results show that theproposed algorithm with threshold can outperform the baselineboth in terms of energy efficiency and traffic offloading.

D. Cache Sharing Algorithm

In order to determine cache sharing decision, the relatedobjective function can be written as

Q3i (ai, ηt) = atoSi [m∗iUi − ηt(P Sat

i + P toSi (m∗i ))]

+∑

j∈J

∑u∈Uj

(1− atoSi )[pi,jqi,j,u −Ki,uPj,upi,j ].(26)

2For the purpose of conducting performance comparison, the performanceof traditional terrestrial schemes (i.e., Pure Terrestrial in the evaluation) isconsidered as the baseline.

Algorithm 3: Cache Sharing AlgorithmInput: ηt at t-th iteration and block placement vector

m∗;Output: Cache sharing vector a∗;

1 for i ∈ F do2 m∗i = maxj∈J {mi,j};3 if m∗i == 0 then4 Ei = 0;5 else6 Compute the gain

Ei = Q3i (a

toSi + 1, ηt)−

∑j∈J Q

1i,j(mi,j , ηt);

7 end8 end9 end

10 Sort the file set F ′ according to the value of Ei;11 for i ∈ F ′ do12 if Ei > 0 and atoSi + 1 satisfies power constraint (C5)

then13 atoSi = atoSi + 1;14 end15 end

Considering the constraint in (C7), the cache sharing sub-problem can be treated as 0-1 knapsack problem with powerconstraint. Although there are some general algorithms toobtain the optimal solution [52], these algorithms can onlyprovide non-polynomial complexity such as O(2N · |J |) forbranch and search algorithm. In order to accelerate Algorithm1 in each iteration, we propose Algorithm 3 to efficientlyobtain a sub-optimal solution through a greedy approach. Thealgorithm first finds maximum cached number of blocks foreach file, i.e., m∗i = maxj∈J {mi,j} in line 2. To obtain thegain by enabling cache sharing for i-th file in line 3-8, theoriginal gain by caching i-th file in terrestrial APs can bededucted. After that, according to the sorting result in line 10,the algorithm further tries to find the best choice for cachesharing with maximum gain. If the benefit of enabling cachesharing of i-th file is positive (i.e., Ei > 0) and atoSi + 1also satisfies constraint (C5), i-th file will be selected forcache sharing. Otherwise, the algorithm continues the loop inline 11-15 to find other files for possible cache sharing. Thecomplexity of cache sharing algorithm isO((N ·(logN+|J |)).Meanwhile, we also provide performance comparison betweenthe proposed scheme and the scheme without cache sharing inthe evaluation. Results show that our proposed Algorithm 3can also achieve significant improvement compared with thescheme without cache sharing.

VI. NUMERICAL EVALUATION

In this section, we evaluate the performance of the proposedalgorithm compared with traditional terrestrial scheme. Weconsider a LEO satellite covering an urban area with anumber of cells, the square area of each cell is 1km× 1km.The distribution of users and APs in each cell follows twoindependent homogeneous Poisson point processes. Table I



11

summarizes the key evaluation parameters, and the comparisonschemes are given as follows.• Random Caching: Instead of performing Algorithm 2,

APs and the satellite randomly choose files to cache.• Pure Terrestrial: Using our proposed algorithm in the

environment with only APs.• Non-Cooperative Scheme: Only local popularity is con-

sidered in each cell and the satellite without consideringconstraint (C5), and cache sharing between APs and thesatellite is also disabled.

Note that we first conduct the experiments that the users’requests in each cell j satisfy pi,j = pi for the resultsin Fig. 5 and Fig. 6. After that, we investigate the systemperformance versus request inconsistency in Fig. 7, Fig. 8 andFig. 9. The cache size in the evaluation represents storagecapacity of the percentage of content library. Without specialnotification in the figures, our parameters are set as: shapeparameter in Zipf distribution θ=1, cache size=2%, numberof cells=50, and user density=40 users/cell. Different fromterrestrial communication, the power spectral density of noisefor satellite communication is set as -171dBm/Hz [53], [54].

TABLE ITHE SIMULATION PARAMETERS

Parameter ValueThe APs density λa 20APs/km2

The users density λu 10-80users/km2

Path loss exponent 2Files in the content library 100Original blocks 8Satellite attitude 780kmTime slot 10msCarrier center frequency/Subcarrier bandwidthof satellite system 3GHz/10MHz

Carrier center frequency/Subcarrier bandwidthof terrestrial APs 2GHz/1MHz

The maximum transmission power P Satmax of satellite 46dBm

The maximum transmission power Pmax of AP 24dBmPower spectral density of noise -174dBm/Hz

A. Energy Efficiency vs Satellite Coverage

We make a preliminary comparison between our cooperativescheme and the pure terrestrial scheme. As shown in Fig. 4,the proposed scheme can achieve 3.3-7.7 times improvementwith different user density in 80 km2 coverage, and acquireapproximately linear increase of energy efficiency along withthe increase of satellite’s coverage compared with the pureterrestrial scheme. However, the proposed scheme is worsethan terrestrial scheme when users in the satellite coverageare less than 200. The reason is that the transmission powerof satellite is greater than AP, then the energy efficiency of thesatellite transmission is greater than the pure terrestrial schemeonly if there are certain number of users served by satellite’sbroadcast.

B. Energy Efficiency & Traffic Offloading vs User Density

We make a performance comparison among differen-t schemes in terms of energy efficiency as well as traffic

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Fig. 4. Energy efficiency comparison between the proposed cooperativescheme and the pure terrestrial scheme (request consistency degree=0%).

offloading as shown in Fig. 5(a) and Fig. 5(b). Comparedto the pure terrestrial scheme, our cooperative scheme canachieve 15.9 times improvement of energy efficiency and14.6% improvement of traffic offloading with 80 users ineach cell. For non-cooperative scheme, the performance ismuch worse than our cooperative scheme, which proves theeffectiveness of our global block placement algorithm.

In Fig. 5(b), we also find out that the performance of non-cooperative scheme in terms of traffic offloading is worsethan the pure terrestrial scheme, which can be explained asfollows. Due to the low energy efficiency of AP’s unicasttransmission, our proposed algorithm tends to satisfy users’srequests through the satellite and avoid terrestrial transmission.Meanwhile, non-cooperative scheme disables cache sharing,which makes the satellite only broadcast the blocks cachedby its own to users. Thus, extra satellite can barely bring anygains in terms of overall traffic offloading to terrestrial users.

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Fig. 5. Performance comparison vs user density (cache size=2%, number ofcells=50, request consistency degree=100%).

Since the performance of traffic offloading is also importantin practical application, we also set a minimum transmissionpower threshold of AP in our power allocation algorithm toachieve further traffic offloading improvement and make acomparison. In Fig. 5(a) and Fig. 5(b), we set it as 15dBmand 17dBm, respectively. Compared with the pure terrestrialscheme, results show that they can respectively achieve 20.5%and 21.4% improvements of traffic offloading and 2.8 and 5.1times increasing of energy efficiency with 80 users in eachcell.



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C. Energy Efficiency & Traffic Offloading vs Cache Size

To investigate the influence of cache size at APs and thesatellite, we make a performance comparison as shown inFig. 6, and “Proposed Algorithm (M = 1%)” representsthe cache size of APs in our proposed algorithm is fixedand only the cache size of satellite is changing. As shownin Fig. 6(a), energy efficiency of the pure terrestrial schemeslowly increases with the increase of AP’s cache size, How-ever, energy efficiency of our cooperative scheme will declinewith the increase of the satellite’s cache size. The reason isthat the request possibility of files is exponentially decreasingaccording to Zipf distribution, and considering satellite servesterrestrial users through broadcast transmission, satellite’s unitcache gain is also decreasing with the increasing size of cachesize. In this case, from the perspective of traffic offloading andenergy efficiency, simply increasing satellite’s cache size is notan efficient way to improve the system performance accordingto the results in Fig. 6(a) and Fig. 6(b).

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Fig. 6. Performance comparison vs cache size (number of cells=50, userdensity=40 users/cell, request consistency degree=100%).

D. Energy Efficiency & Traffic Offloading vs Request Consis-tency Degree

During our evaluation process, we also found out an inter-esting phenomenon that the performance of our cooperativetransmission scheme can be significantly influenced by requestconsistency degree. Here, we give an explanation. For allusers in satellite coverage, if users’ request preference in eachcell is the same, then we consider these users’ requests havehighest request consistency degree; otherwise, these users’requests have lowest request consistency degree. The degreeof request consistency in Fig. 7 represents the percentage ofcells follows the same request preference. To be specific, wehave pi,j = pi,j′ ,∀j, j′ ∈ J when request consistency degree= 100% and pi,j 6= pi,j′ ,∀j, j′ ∈ J when request consistencydegree = 0%.

According to our explanation, it is clear that higher requestconsistency degree can make popular files in all cells concen-trate on less files and satellite’s broadcast transmission can bebenefited. Results in Fig. 7 also verify this fact. In Fig. 7,all schemes consisting of the satellite will be influenced bythe request consistency degree in various degrees. For ourproposed cooperative scheme, which takes full advantage ofsatellite’s broadcast transmission, it is significantly influencedby request consistency degree and has 22.2% and 19.1%performance difference in terms of energy efficiency and traffic

offloading between the highest and lowest request consistencydegree, respectively. When request consistency degree is lowerthan 70%, it can observed that the performance of our pro-posed algorithm in terms of traffic offloading becomes worsethan the pure terrestrial scheme in Fig. 7(b). In this case,by setting minimum transmission power threshold of APs,regardless of the degree of request consistency, our proposedalgorithm with threshold can guarantee the improvement onboth energy efficiency and traffic offloading compared withthe pure terrestrial scheme.

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Fig. 7. Performance comparison vs request consistency degree (cachesize=2%, number of cells=50 and user density=40 users/cell).

In order to show performance comparisons in request in-consistency, we also make performance comparison amongdifferent schemes in the lowest request consistency degreeenvironment as shown in Fig. 8 and Fig. 9. In this case,without minimum transmission power threshold of AP, al-though our proposed algorithm can provide maximum 10.9times improvement of energy efficiency compared with thepure terrestrial scheme, it also has maximum 13.3% decreasingof traffic offloading. Thus, in a low request consistency degreeenvironment, if we want to make a tradeoff between energy ef-ficiency and traffic offloading, we have to enforce the proposedalgorithm to use low energy-efficient terrestrial transmissions.By setting minimum transmission power threshold as 15dBm,our proposed algorithm can provide 3.6 times improvement inenergy efficiency and also 4.4% increase of traffic offloadingwith 80 users in each cell compared with the pure terrestrialscheme in Fig. 8.

Different from the highest request consistency degree en-vironment in Fig. 6, in the lowest request consistency degreeenvironment as shown in 9(a) and 9(b), our proposed algorithmhas 27.4%-16.3% decreasing of traffic offloading comparedwith the pure terrestrial scheme. It can also provide 9.9-2.1times improvement of energy efficiency, and the improvementis decreasing with the increasing of cache size. By settingminimum transmission power threshold of AP as 15dBm, ourproposed algorithm can provide less improvement of energyefficiency but more increasing of traffic offloading. The specif-ic number becomes 3.8%-1.7% increasing of traffic offloadingand 3.2-1.4 times improvement of energy efficiency withdifferent cache size. Furthermore, comparing the performanceof 15dBm with 17dBm, it can be also seen that the highertransmission power threshold of terrestrial AP will lead to lessenergy efficiency and more traffic offloading for the proposedcooperative transmission scheme.



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Fig. 8. Performance comparison vs user density (cache size=2%, number ofcells=50, request consistency degree=0%).

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Fig. 9. Performance comparison vs cache size (number of cells=50, userdensity=40 users/cell, request consistency degree=0%).

The reason of such phenomenon in the lowest requestconsistency degree environment can be explained as follows.Since the difference of the most popular files in each terrestrialcell become larger in lower request consistency degree envi-ronment, the total offloading traffic through broadcast trans-mission is declining and the advantage of satellite’s broadcasttransmission also becomes weaker. In this situation, NOMA-based transmission of terrestrial APs becomes a more effectiveapproach to offload traffic in each cell. Although it willdegrade the performance of energy efficiency, it can satisfymore users’ requests in each terrestrial cell and significantlyimprove performance of traffic offloading. Meanwhile, thanksto the assistance of satellite’s broadcast, the performanceof our cooperative transmission scheme in terms of energyefficiency is always better than pure terrestrial scheme with orwithout minimum terrestrial transmission power threshold.

E. Performance of Traffic Offloading in MBS

Since the objective of the proposed scheme is to offloadtraffic from MBS, we also evaluate the traffic served byMBS in different scenarios. Note that “MBS Traffic 1” and“MBS Traffic 2” represent the traffic served by MBS for pureterrestrial scheme and the proposed scheme respectively. Theperformance comparison is depicted in Fig. 10. In Fig. 10(a),with the increasing of user density in each cell, the percentageof offloading traffic from MBS remains stable, changes from32.6% to 32.5% for pure terrestrial scheme and 34% to 34.9%for the proposed scheme. In Fig. 10(b), both pure terrestrialscheme and the proposed scheme will offload more traffic fromMBS with stronger cache ability, the offloaded traffic changesfrom 20.7% to 50.1% and 22.4% to 53.6%, respectively. InFig. 10(c), the performance of pure terrestrial scheme is notinfluenced by request consistency degree in which offloaded

traffic remains 32.6%. For the proposed scheme, the offloadedtraffic changes from 34% to 39.5%.

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Fig. 10. Traffic served by MBS, APs, and the satellite (number of cells=50,user density=40 users/cell, request consistency degree=0%).

In conclusion, the numerical results show that our proposedalgorithm can efficiently solve the problem in Eq. (16) tomaximize the energy efficiency in integrated satellite/terrestrailRAN, and the proposed algorithm can also provide significantimprovement in both traffic offloading and energy efficiencycompared with pure terrestrial scheme. However, in order toensure better performance in terms of traffic offloading inthe environment with low request consistency degree, settingminimum transmission power threshold of terrestrial APs inthe algorithm is also required.

VII. CONCLUSION

In this paper, we introduced a LEO satellite network tocooperatively serve users with terrestrial APs in cache-enabledRAN. We first formulated a nonlinear fractional programmingproblem to maximize the energy efficiency in the integratedsatellite/terrestrial RAN. We further adopted a parametricmethod to obtain an equivalent problem and divided it intothree sub-problems, and we also designed efficient algorithmsto obtain the optimal solution for each sub-problem. Thenumerical results show that our scheme can provide significantimprovement of energy efficiency with similar traffic offload-ing performance compared with traditional terrestrial schemein a cooperative manner. For the next generation cellularsystem, an integrated satellite/terrestrial RAN can also be aneffective solution to alleviate the competition of terrestrialMBS and APs and provide high energy efficiency service forterrestrial users.

ACKNOWLEDGMENT

The authors sincerely thank the editor, Dr. Dimitrie C.Popescu, and the anonymous referees for their invaluable



14

suggestions that have led to the present improved version fromthe original manuscript. This work is supported in part by theNational Key Research and Development Program of Chinaunder Grant No. 2016YFB0800301, the National Natural Sci-ence Foundation of China under Grant No. 91538203 and No.No. 61972371, and Youth Innovation Promotion Associationof the Chinese Academy of Sciences (CAS) under Grant No.2016394.

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Jian Li received his bachelor’s degree from theDepartment of Electronics and Information Engi-neering, Anhui University, Hefei, China, in 2015. Heis currently working toward the Ph.D degree in theDepartment of Electronic Engineering and Informa-tion Science, University of Science and Technologyof China. His research interests include satellite net-works, cooperative transmission in integrated satel-lite/terrestrial networks and cache-enabled wirelessheterogeneous networks.

Kaiping Xue (M’09-SM’15) received his bachelor’sdegree from the Department of Information Security,University of Science and Technology of China(USTC), in 2003 and received his Ph.D. degreefrom the Department of Electronic Engineering andInformation Science (EEIS), USTC, in 2007. FromMay 2012 to May 2013, he was a postdoctoralresearcher with the Department of Electrical andComputer Engineering, University of Florida. Cur-rently, he is an Associate Professor in the School ofCyber Security and the Department of EEIS, USTC.

His research interests include next-generation Internet, distributed networksand network security. He serves on the Editorial Board of several journals,including the IEEE Transactions on Wireless Communications (TWC), theIEEE Transactions on Network and Service Management (TNSM), Ad HocNetworks, IEEE Access and China Communications. He has also served as aguest editor of IEEE Journal on Selected Areas in Communications (JSAC)and a lead guest editor of IEEE Communications Magazine. He is an IETFellow and an IEEE Senior Member.

David S.L. Wei (SM’07) received his Ph.D. degreein Computer and Information Science from the U-niversity of Pennsylvania in 1991. From May 1993to August 1997 he was on the Faculty of ComputerScience and Engineering at the University of Aizu,Japan (as an Associate Professor and then a Pro-fessor). He has authored and co-authored more than100 technical papers in various archival journals andconference proceedings. He is currently a Professorof Computer and Information Science Department atFordham University. His research interests include

cloud computing, big data, IoT, and cognitive radio networks. He was aguest editor or a lead guest editor for several special issues in the IEEEJournal on Selected Areas in Communications, the IEEE Transactions onCloud Computing and the IEEE Transactions on Big Data. He also servedas an Associate Editor of IEEE Transactions on Cloud Computing, 2014-2018, and an Associate Editor of Journal of Circuits, Systems and Computers,2013-2018.

Jianqing Liu (M’18) received his B.Eng. degreefrom the University of Electronic Science and Tech-nology of China, Chengdu, China, in 2013 andreceived his Ph.D. degree with the Department ofElectrical and Computer Engineering, University ofFlorida, Gainesville, FL, USA, in 2018. Currently,He is an assistant professor in the Department ofElectrical and Computer Engineering at the Univer-sity of Alabama in Huntsville. His research interestsinclude wireless networking and network security incyber-physical systems.

Yongdong Zhang (A’09-SM’13) received the Ph.D.degree in electronic engineering from Tianjin Uni-versity, Tianjin, China, in 2002. He is currently aProfessor in the Department of Electronic Engineer-ing and Information Science (EEIS), University ofScience and Technology of China (USTC). He hasauthored over 100 refereed journal and conferencepapers. His current research interests are in the fieldsof multimedia content analysis and understanding,multimedia content security, video encoding, andstreaming media technology. He was a recipient of

the Best Paper Awards in PCM 2013, ICIMCS 2013, and ICME 2010, and theBest Paper Candidate at ICME 2011. He is a member of the Editorial Boardof the IEEE Transactions on Multimedia and Multimedia Systems journal.

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