IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 1, JANUARY Jin-Bae Park, Student Member, IEEE, and Kwang Soon Kim

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 1, JANUARY Loa-Balaning Sheme With Small-Cell Cooperation for Clustere Heterogeneous Cellular Networks Jin-Bae Park, Stuent Member, IEEE, an Kwang Soon Kim, Senior Member, IEEE Abstrat In this paper, a joint user assoiation UA) sheme with JP-CoMP using a hybri self-organizing network SON) is propose for a pratial lustere heterogeneous ellular network HCN) to maximize the network-wie proportional fairness among users. The ell range expansion an the enhane interell interferene oorination have been onsiere as key items in the long-term evolution-avane to offloa maroell users to smallell base stations sbss). However, in a HCN where sbss are not istribute at ranom but are lustere instea, the overage of inner sbss in a small-ell luster woul be harly expane an an inrease bias may result in muh poor link quality as well as muh higher loa in outer sbss. Thus, the loa-balaning apability beomes muh lower than expete in a HCN. In orer to ope with suh a problem, a network arhiteture an protool for the HCN is suggeste, an a feasible suboptimal iterative algorithm for etermining the joint UA solution of the propose hybri SON is provie. It is shown that the propose hybri SON sheme with the propose joint UA solution is very effetive in hanling the loa balaning in a pratial HCN not only improving the performane of the inner sbs users by reuing the interell interferene, espeially for intratier offloae users, but also enabling more aggressive intertier offloaing by effetively improving the link quality of luster ege users without ausing an unneessary resoure waste. Inex Terms Clustere HCN, CoMP, loa balaning. I. INTRODUCTION IN CURRENT ellular networks, onventional maro ells are being overlai with low-powere small ells as a way to enhane the spetral effiieny per area [1]. Espeially in realisti senarios suh as those base on real measurement ata [2], [3] an those in the tehnial report by 3GPP [4], more than Manusript reeive September 19, 2016; revise Marh 29, 2017 an August 6, 2017; aepte August 22, Date of publiation September 4, 2017; ate of urrent version January 15, This work was supporte by the Institute for Information an ommuniations Tehnology Promotion grant fune by the Korea government , Next Generation WLAN System with High Effiient Performane an , High Aurate Positioning Enable MIMO Transmission an Network Tehnologies for Next 5G-V2X vehile-toeverything) Servies) an Basi Siene Researh Program through the National Researh Founation of Korea NRF) fune by the Ministry of Euation, Siene an Tehnology NRF-2014R1A2A2A ). The review of this paper was oorinate by Prof. Y.-B. Lin. Corresponing author: Kwang Soon Kim.) The authors are with the Department of Eletrial an Eletroni Engineering, Yonsei University, Seoul 03722, South Korea spaey2k@ l.yonsei.a.kr; ks.kim@yonsei.a.kr). Color versions of one or more of the figures in this paper are available online at Digital Objet Ientifier /TVT one small-ell BSs sbss) might be installe in hotspot areas [5], [6], whih an be moele as a lustere HCN HCN) where sbss an users are lustere in hotspot areas [7], [8]. In an HCN or a HCN whih an be onsiere as an HCN with ense small ells in some loations, one of the most important hallenges for ahieving the full potential of a small-ell eployment is how to balane the loas among ells [9] [11]. There have been many efforts on eveloping effetive loa balaning shemes in an HCN an they an be ategorize into istribute loa balaning shemes [5], [12] [18] an joint loa balaning shemes [19] [26]. Among istribute loa balaning shemes, a ell range expansion CRE) sheme using a fixe bias [12] [15] ombine with an enhane inter-ell interferene oorination eicic) sheme using almost blank subframes ABS) [5], [16] [18] has been aopte in the 3GPP long term evolution-avane LTE-A) as a user assoiation UA) sheme with resoure partitioning RP) to effiiently offloa more traffi from maro ells to small ells. When sbss are uniformly istribute, the above istribute UA with an RP sheme allows small ells to be expane while maintaining overall link-quality of the small-ell users ompare to the maximum signal-to-noise power ratio SNR) approah where eah user is assoiate to the ell with the strongest SNR [27], [28]. However, the performane might not be optimal for a given user an BS geometry ue to the istribute nature an the use of the ommon bias an ABS ratio values. On the other han, the joint loa balaning shemes have been propose to further improve a network-wie utility suh as the network-wie proportional fairness [19] [24], the network apaity [25] or the minimum throughput [26]. Sine suh a joint UA with RP sheme as in [22] [24] an jointly etermine the UA an the ABS ratio of eah maro ell for a given user an BS geometry, lightly-loae sbss an be expane more aggressively so that more maroell users as well as small-ell users in heavily-loae sbss an be off-loae without eteriorating the overall link-quality, whih results in better network utility [22]. However, in a HCN where sbss are not istribute at ranom but are lustere instea, the overage of inner sbss in a small-ell luster woul be harly expane by the istribute approah an an inrease bias for offloaing as many maroell users to the small-ell layer as in an HCN results in muh poor link quality as well as muh higher loa in outer sbss. Thus, the loa balaning apability of a istribute sheme beomes muh lower than expete in a HCN. Although the IEEE. Personal use is permitte, but republiation/reistribution requires IEEE permission. See stanars/publiations/rights/inex.html for more information.

2 634 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 1, JANUARY 2018 former is harly mitigate, the latter an be alleviate to some extent by using a joint approah. In this approah, some portion of the loa of outer sbss an be offloae to lightly-loae inner sbss. However, the impat is limite ue to the poor link quality of suh offloae users. In orer to improve the poor link quality of offloae users, using a joint proessing oorinate multi-ell proessing JP- CoMP) suh as multi-ell zero-foring beamforming ZFBF) [29] or maximum ratio transmission MRT) [30] within a smallell luster is very promising. This is beause a ell ooperation using JP-CoMP may improve the link quality by mitigating inter-ell interferene among small ells or inrease the effetive signal power from a small-ell luster by applying the ZFBF an MRT shemes seletively for eah user. Here, the aaptive CoMP seletion an be realize by the joint loa balaning sheme suh as in [19], [22] in onjuntion with an RP sheme suh as the e-icic. However, although mbss an be onfigure uniformly, sbss in a HCN an be quite ifferently onfigure in ifferent lusters in terms of the number of antennas, the transmission sheme, the resoure partitioning an sheuling strategy, an the bakhaul quality whether it allows a ell ooperation or not, et. Thus, it is not suitable for a pratial system suh as the LTE-A to ollet suh information on eah sbs at a entralize network ontroller an introuing a JP-CoMP into a joint loa balaning sheme in a HCN is not straightforwar an is atually very hallenging. Note that the LTE-A ellular network may inlue a small-ell layer luster mobility management entity C-MME) an luster gateway C-GW) to ontrol sbss in a small-ell luster so that JP-CoMP an be favore but the ore network onsiers eah small-ell luster as an mbs [31]. Therefore, suh a ore network arhiteture shoul be taken into aount an a novel joint assoiation sheme suitable for a pratial HCN is require. In this paper, a joint UA sheme with JP-CoMP using a hybri self-organizing network SON) is propose for a pratial HCN to maximize the network-wie proportional fairness among users. In this sheme, a entral SON algorithm manages a marosopi user assoiation an a istribute loal SON algorithm in eah luster manages a joint UA with an RP sheme by onsiering aaptive CoMP moe seletion for given user loations. A network arhiteture an protool for the HCN is suggeste an a feasible suboptimal iterative algorithm for etermining the joint UA solution of the propose hybri SON is provie. It is shown that the propose hybri SON sheme with the propose joint UA solution is very effetive in hanling the loa balaning in a pratial HCN. This omes from the fat that the propose sheme not only improves the performane of the inner sbs users by reuing the inter-ell interferene, espeially for intra-tier offloae users, but also enables more aggressive inter-tier offloaing by effetively improving the link quality of luster ege users without ausing an unneessary resoure waste. The novelty an main ontribution of this paper an be summarize as follows. i) When onsiering an effiient loa balaning sheme for a HCN, JP-CoMP nees to be onsiere among small ells, espeially with a non-stati BS grouping to alleviate the problems of group-ege users as previously esribe. However, Fig. 1. The HCN moel. suh a joint UA problem with a ynami BS grouping is intratable. In this paper, suh a iffiulty is solve by suggesting a joint UA problem with a semi-ynami BS grouping an resoure partitioning an proposing its suboptimal solution at a polynomial-time omplexity, an ii) When onsiering the implementation feasibility, existing shemes are not appropriate beause a entralize sheme suh as in [22] suffers from impratial signalling overhea an omputational loa at the entral entity. Although it may be implemente in a istribute way as in [19], it involves iterations between BSs an users using wireless resoure in a synhronize manner, whih is not suitable for a pratial system, either. In this paper, a hybri approah is propose where iterations are performe among ore network entities only, whih is more suitable for a pratial implementation. Also, the implementation feasibility of the propose sheme is heke for a typial senario. The remaining of this paper is organize as follows. In Setion II, the system moel is presente. In Setion III, the propose hybri arhiteture an protool are illustrate. In Setion IV, the propose joint loa balaning sheme is presente. In Setion V, simulation results an orresponing isussions are provie an onluing remark is given in Setion VI. II. THE CHCN MODEL Consier a ownlink two-tier HCN in whih maro ells are overlai with lustere) small ells using a lower transmit power as shown in Fig. 1. Aoring to realisti senarios where there oul be some hotspots with ifferent user ensities [32] an an operator eploys both maro-ell BSs mbss) an sbss to provie overage flexibly an promptly [4], more than one sbss an be installe in hotspot areas [5], [6]. Eah luster, enote as ξ), is moele as a lose region entere at an the set of luster enter loations is enote as C = { 1, 2,...} whih is assume to follow a point proess Φ with ensity of λ. Also, enote the set of user loations as U = {u 1, u 2,...} an it is assume to be a mixture point proess Φ u C Φu, where Φ u is a point proess with ensity of λ u an Φ u is a point proess over ξ) with ensity of λ h. Note that we fous on an operator-installe small-ell eployment senario with an open aess strategy an truste bakhauls.

3 PARK AND KIM: LOAD-BALANCING SCHEME WITH SMALL-CELL COOPERATION FOR HCNs 635 Fig. 2. Network arhiteture for a two-tier HCN. a) Hybri SON for a two-tier HCN. b) sbs lustering phase for a two-tier HCN. As shown in Fig. 1, it is assume that an operator eploys maro-ell BSs mbss) network-wiely an sbss in eah luster. Denote the set of mbs loations an the set of sbs loations in luster as B m = {b m 1, bm 2,...} an Bs = {b s,1, bs,2,...}, respetively. Here, B m is assume to follow a point proess Φ m with ensity of λ m an B s is assume to follow a point proess Φ s over ξ) with ensity of λ s ). The ore network arhiteture is assume as shown in Fig. 2a). Here, sbss are assume to be lustere an the sbss for eah luster are onnete via wire bakhaul lines to the C-MME an the C-GW as in [33], whih may be assume to be o-loate an onnete via X2 with the nearest mbs. Also, eah mbs, C-MME, an C-GW are onnete to the enhane paket ore EPC) ompose of the MME, the serving gateway S-GW), an the paket ata network gateway P-GW). Note that in [31], a home enoe B HeNB) gateway is efine in the 3GPP speifiation an it an play a role as a C-MME with an S1 interfae between C-MMEs an an EPC-MME. Then, HeNBs onnete to the same HeNB gateway naturally form a smallell luster. Thus, suh a HCN moel an the orresponing network arhiteture an moel a pratial LTE-A heterogeneous network. For the abstrate air-interfae, it is assume that one frame is omprise of N S subframes an eah subframe onsists of N RB multiple resoure bloks RBs), where the user assoiation an BS grouping an be upate for eah frame if neessary ue to user mobility. Consiering the ase where previously installe small ells or user-installe open aess small ells exist together in suh hotspots, the sbs lustering phase shown in Fig. 2b) is performe by EPC-MME. Here, base on the reporte user measurement information {γ u }, EPC-MME an transform γ u into approximate relative istane between the user an the orresponing sbs an fin the relative loation of eah sbs by utilizing a least-square soure loation estimation, suh as the total least square algorithm [34]. Then, the sbss are lustere by using a wiely-use lustering algorithm, suh as the k-means algorithm [35] with the elbow metho [36]. The SON moel for a joint user assoiation is also shown in Fig. 2. Here, eah user u reports its measurement γ u to the EPC-MME via its urrently assoiate BS. In an LTE system, the user measurement report γ u is elivere as the neighbor ell measurement report if a preefine event trigger riterion is met, in whih suh a riterion an be set aoring to the servie provier s strategy, the ell loations, et. Also, the C-MME in luster informs the EPC-MME of its luster uplink information Γ. The EPC-MME also informs the C-MME in luster of its luster ownlink information Ψ. Base on {γ u u U} an {Γ C}, the EPC-MME performs its SON funtion an elivers the upate user assoiation information vetor I b to eah BS b an its upate assoiation information J u of eah user u via eah urrently assoiate BS. Note that the above SON moel an inlue a fully entralize SON sheme suh as in [22], a entralize SON sheme implemente by using a istribute omputation suh as in [19], an a istribute SON sheme suh as the CRE an e-icic sheme with the networkwiely selete optimal bias an ABS ratio values. In a entralize SON sheme suh as in [22], γ u is a measure average SNR value set from its neighboring BSs an Γ is the full information require for evaluating the expete throughput of eah user if assoiate to eah ell in luster aoring to the number of antennas, the transmission sheme, the resoure partitioning an sheuling strategy, the bakhaul quality, et. Base on them, the EPC-MME jointly etermines I b an J u for all b B m C Bs an u U an elivers them to eah BS an C-MME via Ψ. Finally, eah BS elivers the assoiation information to its assoiate users. The entralize SON sheme an ahieve the maximum performane of the joint user assoiation but the luster uplink information {Γ C} an the omputational loa at the EPC-MME beome so high that it is inappropriate to be applie in pratie. Although suh a entralize SON may be implemente by using a istribute omputation, suh as in [19], in whih γ u is the assoiation request from user u an J u is the set of BS-speifi information suh as the prie information or the alloate ABS ratio of the neighboring BSs require for user u to etermine its assoiation. Also, Γ an Ψ enote the information from luster to the EPC-MME aoring to the user requests in luster an the information for the luster to upate its BS-speifi information by onsiering others, respetively. Then, an iterative SON proeure is performe among all the entities so that eah user an etermine its assoiate BS in a istribute manner. However, although its omputational omplexity an bakhaul overhea o not ause any problem, all the involve entities shoul be

4 636 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 1, JANUARY 2018 synhronize an wireless resoures nee to be waste uring the istribute iteration among the BSs an users, whih is also not suitable in pratie. On the other han, a istribute SON an be easily implemente in pratie by performing UA loally an exhanging some measure statistis an the network-wie bias an ABS ratio values as the luster uplink an ownlink informations, respetively. However, the loa balaning apability is expete to be low, espeially in a HCN. III. HYBRID SON ARCHITECTURE AND PROTOCOL In this paper, a 2-level hybri SON sheme is onsiere. In this sheme, the EPC-MME performs the marosopi UA base on the user reporte information {γ u u U} an the luster uplink information {Γ C} from the C-MME in eah luster an elivers the luster ownlink information {Ψ C}. On the other han, the C-MME in eah luster etermines the joint UA for its loal luster base on its loal information an upates the luster uplink information, whih are performe in an iterative manner. For the propose hybri SON, eah user u measures the average SNR values γ u,b of its neighboring BSs b B u B m C Bs to form γ u = {γ u,b b B u } an reports it to the EPC-MME via its urrently assoiate BS. Base on {γ u u U}, the EPC-MME eies the marosopi user assoiation {U, X,ς B m C}, where U U, X = {x u, u U }, an x u,,ς [0, 1] enote the user assoiation variable of user u an the ABS ratio of an mbs or luster, respetively, an elivers U, X, an ς to eah mbs B m ) or to eah C-MME C) by setting Ψ = [U,ς ] for B m an Ψ =[U, X,ϕ ] for C, where ϕ enotes the ABS ratio information of an mbs aroun C, whih will be efine later. Here, the EPC-MME partitions the lusters aoring to eah mbs as {C B m } ρc), where ρa) enotes the olletion of all partitions of a set A, so that a ommon ABS ratio is use among eah mbs an sbss in its assoiate lusters, i.e., ς = ς for C. In this paper, JP-CoMP with a semi-ynami BS grouping an resoure partitioning is onsiere to alleviate the problem of group-ege users an improve the loa balaning apability for a HCN. In the luster of interest, the sbss in B s are partitione to form isjoint BS groups 1 an eah user in U is alloate to one of the subframe types, whih involves alloating eah user to one of the BS groups for eah resoure in the selete subframe type. Also, eah BS group is assume to be able to serve its users by using transmission sheme χ X = {Z, M}, where χ = Z an χ = M enote the ZFBF [29] an MRT [30] shemes, respetively. Denote B t = {B t,1, Bt,2,...} ρbs ) as the BS group set an A t = {A t,1, At,2,...} as the orresponing user assoiation set for resoure t, respetively, where A t,j =[At,χ,j ] χ X an A t,χ,j U. Here, B t,j an A t,χ,j enote the jth BS group element of B t an the jth user assoiation set of A t using transmission sheme χ X, respetively. Then, B = [B, 1 B, 2..., B T ] an A =[A 1, A 2,..., A T ] esribe the joint UA with a BS grouping for luster etermine by its 1 In ase of not using a CoMP, eah BS group ontains only one BS. C-MME, where T enotes the number of ifferent resoures. 2 Note that suh a resoure partitioning into T resoures is luster-wise, i.e., all sbss an users in a luster share the same RP synhronously. On the other han, eah BS group an hoose its urrent transmission sheme among X inepenently. Let I b =[I b,1, I b,2,..., I b,t ] an J u =[J u,1, J u,2,..., J u,t ] enote the user assoiation vetor for BS b an the assoiate BS group vetor for user u, respetively, where I b,t = [I χ b,t ] χ X an J u,t =[J χ u,t] χ X enote the users assoiate toabsgroupwhihbsb belongs to an serve by using transmission sheme χ X at resoure t an the set of BSs that form the BS group whih serves user u by using the transmission sheme χ X at resoure t, respetively. Then, the C-MME elivers I b to eah b B s an J u to eah u U by setting I χ b,t = At,χ,π b t) an Jχ u,t = B t,κ χ u t), where π b t) =arg j {1,2,..., B t }{1 {b B t,j } = 1} an κ χ ut) = arg j {1,2,..., B t }{1 {u A t,χ,j } = 1}. Also, the C-MME elivers its luster uplink information to the EPC-MME by setting Γ = {Q,, Δ }, where Q,, an Δ enote the parameter set for the pre-etermine approximate user rate evaluation, the parameter set for the linear approximation of the resiual metri error, an the orresponing trust regions, respetively. In eah mbs b B m, the ABS pattern for eah frame is etermine aoring to ς b an shares it to the sbss of the lusters in C b via the orresponing C-MMEs. Eah mbs b selets a user among U b by using a sheuling algorithm suh as the proportional fair sheuling PFS) [37] uring its normal subframe NS) while it keeps silent uring its ABS. On the other han, for eah resoure t in eah luster, eah BS group B B t or its hief BS) an hoose the ZFBF sheme or the MRT sheme at eah RB. For user sheuling, a set of users equal to its group size B for the ZFBF sheme an a single user for the MRT sheme are assume to be selete by using a sheuling algorithm suh as the PFS metho for the multiuser ase [37], respetively. In Table I, the notations use in this paper are summarize. Also, Fig. 3 shows a toy example of the joint UA sheme with JP-CoMP in a luster, usingt = 2resoures. Here, 4 sbss, B s = {b s,1, bs,2, bs,3, bs,4 } are partitione into B 1 = {{b s,1, bs,2 }, {bs,3, bs,4 }} for t = 1 an B 2 = {{b s,1, bs,4 }, {bs,2, bs,3 }} for t = 2 as esribe. Also, eah of the 9 luster users, U = {u 1, u 2,..., u 9 }, is assoiate to one of the BS groups in eah resoure as A 1 = {[{u 3, u 4, u 5 }, {u 1, u 2 }], [{u 6, u 9 }, {u 7, u 8 }]} for t = 1 an A 2 = {[{u 5, u 6, u 7, u 8 }, {u 3 }], [{u 1, u 4, u 9 }, {u 2 }]} for t = 2 as esribe in Fig. 3. Note that I b s an J u1 are given as, 1 I b s, 1 J u1 =[[{u 3, u 4, u 5 }, {u 1, u 2 }], [{u 5, u 6, u 7, u 8 }, {u 3 }]] an =[[, {b s,1, bs,2 }], [{bs,2, bs,3 }, ]], respetively. IV. PROPOSED LOAD-BALANCING SCHEMEINACHCN A. Network-Wie Fairness Metri in a HCN The proportional fairness sheuling, originally propose in [38], has been wiely onsiere not only in literature but also 2 The typial e-icic an be onsiere as the T = 2 ase the NS for t = 1 an the ABS for t = 2).

5 PARK AND KIM: LOAD-BALANCING SCHEME WITH SMALL-CELL COOPERATION FOR HCNs 637 TABLE I SUMMARY OF THE NOTATIONS Symbol Desription C, U, B m, B s Sets of lusters, users, mbss, an sbss in luster γ u, Γ, Ψ, I b, J u B u C B, A B t = { B t,j}, A t = { A t,j [ ] B t,j, At,j = A t,χ,j χ X A t,χ,j } measurement for user u, luster uplink information for luster, luster ownlink information for luster, UA information for BS b, an the assoiation information for user u Sets of neighboring BSs for user u Set of lusters partitione to mbs etermine at the EPC-MME BS group information an UA information etermine at the C-MME in luster BS group olletion an UA vetor olletion for resoure t in luster the jth BS group an the j th UA set vetor for resoure t in luster the jth UA set for resoure t using transmission sheme χ in luster [ I b = I b,t ]t [T, J ] u =[J u,t ] t [T ] UA vetor for BS b, assoiate BS group vetor [ for user u ] [ ] I b,t = I χ b,t, J u,t = J χ χ X u,t UA vetor for BS b, χ X assoiate BS group vetor for user u for resoure t I χ b,t, Jχ u,t U, X, ς Γ = {Q,, Δ } users for BS b an assoiate BS group for user u using transmission sheme χ for resoure t Sets of assoiate users an assoiation variables for an mbs or a luster an ABS ratio for mbs B m etermine at the EPC-MME the luster uplink information for C-MME in luster for real implementations of wireless ellular networks [39], [40] ue to not only its ability to sheule users in their peak hannel states while proviing balane throughput among users but also its implementation feasibility. Thus, in this paper, the Fig. 3. A toy example of the joint UA sheme with JP-CoMP. network-wie proportional fairness among users is onsiere as the network utility for the loa balaning in a HCN, similarly as in [19] [24], whih an be written as Υ= u U U R u ), 1) where R u enotes the average rate of user u an U r) enotes the general α-fairness utility funtion for a rate r. Here, U r) = logr) for α = 1, an U r) =r 1 α / 1 α) for α 1,α>0. First, we fous only on the ase where α = 1, i.e., the proportional fairness [41] is onsiere. In orer to perform a joint UA to improve the network utility, R u nees to be antiipate from the reporte information an may be approximate as 2) an 3) as shown at the bottom of this page, where I u, enotes therateofuserufrom mbs if sheule, φ u) enotes the probability that user u is sheule by mbs, η t enotes the portion that resoure t takes, ν t,χ,j enotes the portion that BS group j takes for transmission sheme χ at resoure t, φ t,χ,j u) enotes the probability that user u is sheule by BS group j using transmission sheme χ at resoure t, an I t,χ u, Bt,j ) enotes the rate of user u from BS group j using transmission sheme χ at resoure t if sheule. For the maro-ell users, the rate of user u from mbs if sheule, I u,, an be approximate as I u, = ) q log S u ) + W u ) T u )+V u ) V S u )+W u )) 2 u ) W u 2 ) ) log 2 e ), S u ) W u ) γ th, 0, o.w., 4) Δ where q = min N A, U ) enotes the number of users that an be sheule simultaneously by mbs, S u ) = Δ k θ, W u ) = Δ b B u {} γ u,b, T u) = Δ k θ 2, an V u ) = Δ b B u {} γ2 u,b enote the average signal power, the R u = 1 ς ) φ u) I u,, u U, B m, 2) ) B t,j, u U, C, 3) T B t t=1 j=1 χ X ηt νt,χ,j φt,χ,j u)it,χ u, ) I t,χ ) q t,χ u, B t,j log S u χ B t,j) T u + χ B t,j)+vu t B t,j) V t,j = W u t B t,j) S u χ B t,j)+wu t B t,j)) 2 ) ) u B t,j) log W u t B t,j)) 2 2 e, 0, o.w. S χ u B t,j) W t u B t,j) γ th, 5)

6 638 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 1, JANUARY 2018 average interferene power, the variane of the signal power, an the variane of the interferene power, respetively. Here, { Δ 1 N A k F A 1 ) p μ );N A, 1 <N A < U, = N A q 6) + 1, o.w., enotes the shape parameter for the signal power when it is moele as a Gamma ranom variable as in [42], where N A enotes the number of antennas at the maro-ell BS, F A x; N A )=1 1 x)n A 1 enotes the umulative istribution funtion CDF) of square absolute inner prout between the normalize hannel vetor of size N A an the orresponing zero foring preoing vetor of size N A for a ranomly selete user, p μ )=μ /μ +1) enotes a perentile value orresponing to the largest value among μ values in a CDF, an { Δ l ) U ; N A μ =, 1 < U < 2, N A 7) U, o.w., enotes the effetive number of users onsiering multiuser MIMO ZFBF). Here, l ) ) ) x; N A = 2 1/N A x N A + 1 enotes a linear transformation, by whih N A <x<2n A is mappe to 1 <l ) x; N A < 2N A. Note that the shape parameter gain for the signal power ue to the use of multiple antennas is reflete similarly as in [43]. In aition, Δ θ = m γ u, /N A 8) enotes the sale parameter for the signal power when it is moele as a Gamma ranom variable, where Δ m = 2 )1 {N A > 1 } F 1 p μ );N A, N A ) 1 ) )1 { U >N A } 9) reflets the multiuser iversity gain ue to PFS similarly as in [44] an F x; k, θ)=γk, x θ )/Γk), γk, x θ )= x/θ 0 t k 1 e t t. Note that in 6) an 9), two onstants 1 an 2 are introue to reflet the orrelation effet between the shape parameter gain for the signal power ue to the use of multiple antennas an the multiuser iversity gain obtaine from the instantaneous hannel gain of the selete signal of the ZFBF ue to PFS. Here, the values are etermine as follows. Let A n 1) an Bn 1) enote the largest value among A 1,A 2..., A n generate from a ranom variable A an among B 1,B 2..., B n generate from a ranom variable B, respetively, an A n 1 an Bn 1 enote the orresponing values of A an B for the largest one among A 1 B 1,A 2 B 2,..., A n B n. Then, the values of 1 an 2 are etermine as 1 =E[An 1 ]/E[An 1) ] an 2 =E[Bn 1 ]/E[Bn 1) ] for a ranom variable A with the CDF of F A x; N A ) an a Gamma ranom variable B ΓN A, N A ) 1 ) enoting the normalize hannel gain, similarly as in [42]. Note that 4) aopts the Gamma istribution approximation as in [42] an is further moifie by onsiering PFS, in whih the total interferene power an be approximate as the sum of the average powers from interfering BSs so that the first term represents the rate expete from the average ombine signal power an the average interferene power an the remaining term enotes the rate ue to the variations on the signal an interferene powers, whih omes from the approximate expression on the igamma funtion [42]. Here, the signal power is approximate as a Gamma ranom variable as in [42] with the moifie shape an sale parameter onsiering the multiuser iversity ue to PFS. For the small-ell luster users, 3) onsiers ifferent ombinations of RP an CoMP. By aopting the Gamma istribution approximation again, I t,χ u, Bt,j ) an be similarly approximate as in 5). Here, q t,χ Δ,j = min B t,j 1 {χ = Z }, A t,χ,j ) enotes the number of users that an be sheule simultaneously, Su χ B t,j )Δ =k t,χ,j θt,χ,j, W ub t t,j ) = Δ b B t,j γ u, u,b, Tu χ B t,j )Δ =k t,χ,j θt,χ,j )2, an Vu t B t,j ) = Δ b B t,j γu,b 2 enote u, the average signal power, the average interferene power, the variane of the signal power, an the variane of the interferene power, respetively. Here, θ t,χ,j Δ ) = m,χ B t,j b B t,j γ u,b / B t,j 10) enotes the sale parameter for the signal power when it is moele as a Gamma ranom variable, where ) m,χ B t Δ= ) 4 1 ) )) 2F 1 3 1,j,j p μ t,χ,j ; ε t,χ,j, ε,j) t,χ, 11) with 1 =1 {χ=z }, 2 =1 { B t,j >1}, an 3 =1 { A t,χ,j > B t,j 1 } reflets the multiuser iversity gain ue to PFS by introuing a onstant 4,j at the effetive numbers of users an BSs onsiering CoMP, given by ) A t,χ l μ t,χ Δ,j, B t,j, if 1 4 = 1,,j = 12) o.w., A t,χ,j with 4 = 1 { A t,χ,j <2 B t,j ε t,χ,j Δ = A t,χ,j 1 u A t,χ,j respetively. In aition, k t,χ,j Δ = 3,j B t,j } an b B t,j ) γ u,b / max γ u,b, 13) b B t,j ) ) 1 F A p μ t,χ,j ; B t,j, if = 1, q t,χ,j + 1, o.w., 14) B t,j enotes the shape parameter for the signal power when it is moele as a Gamma ranom variable, where the shape parameter gain is reflete similarly as in 6). 15) as shown at the bottom of the next page. Here, B t,j Δ u, = B u {b )} B t,j ) for t T A, B t,j Δ u, = B u B t,j for t T N, T N T A ) enotes the set of resoures using an NS or an ABS), an b ) enotes the mbs to whih luster is assoiate. Similarly as in 4), the first term in 5) represents the rate expete from the average ombine signal power an the average interferene power ue to the ooperation an the remaining term enotes the rate ue to the variations

7 PARK AND KIM: LOAD-BALANCING SCHEME WITH SMALL-CELL COOPERATION FOR HCNs 639 on the signal an interferene powers. In ase of MRT with PFS, sine a signal is transmitte towars its hannel iretion, the shape parameter is given as the number of antennas or the number of ooperating sbss, similarly as in [42], while the sale parameter nees to be moifie to reflet the multiuser iversity gain. One reasonable way is to magnify the original sale parameter in [42] by the amount of the multiuser iversity gain obtaine from the use of PFS as in 10), assuming that μ t,χ,j users are ompeting with their normalize hannel gains. On the other han, in ase of ZFBF with PFS, the multiuser gain ue to PFS may be introue as follows. Let A be a ranom variable with the f of F A x; B t,j ) enoting the square absolute inner prout between the normalize hannel vetor an the orresponing zero foring preoing vetor using CoMP among BSs in B t,j for a ranomly selete luster user an B Γ B t,j, Bt,j 1 ) be a ranom variable enoting the normalize hannel gain assuming that the effetive number of BSs is B t,j. Then, the values of 3,j an 4,j are etermine as 3,j =E[An 1 ]/E[An 1) ] an 4,j =E[Bn 1 ]/E[Bn 1)], respetively, for refleting the orrelation effet between the shape parameter gain for the signal power ue to the use of multiple BSs an the multiuser iversity gain obtaine from the instantaneous hannel gain of the selete signal of the ZFBF or MRT) CoMP ue to PFS in the shape an sale parameters similarly as in the maro-ell ase. B. EPC-MME Operation If the EPC-MME an obtain the full information on the transmission sheme an the resoure partitioning with sheuling strategy for eah possible BS grouping set on eah resoure of eah luster C, 2) an 3) an be evaluate from {γ u } so that the EPC-MME an etermine {U B m C Bs } ρu) an {ς B m } as well as the resoure partitioning an BS grouping in eah luster to maximize the network-wie proportional fairness among users. However, although the joint UA an ahieve an optimal solution, the EPC-MME suffers from formiable signaling overhea an omputational omplexity. On the other han, the propose sheme oes not require the full information an only the marosopi UA is performe at the EPC-MME as esribe in Setion III. For this, it is assume that another approximate user rate ˆR u,, instea of R u in 3), is use. Although any goo ˆR u, an be applie, ˆR u, Q ) = max χ X ξ,χ,a I t A,χ u, ωu S,χ )) + ξ,χ,n I t N,χ u, ωu S,χ ))), 16) for the luster uplink information from luster, enote as Q = { S,χ,k,χ,m,χ,ξ,χ,A,ξ,χ,N χ X }, is assume, where the values for S,χ, k,χ m,χ, ξ,χ,a, an ξ,χ,n ome from the result of the previous iteration at eah C- MME, ω u S) ={b B u B s rankγ u,b, {γ u,b b B u B s }) S}, an ranka, A) for a A enotes the rank in a esening orer) of a in A. Although suh parameters for ˆR u, are selete to fit R u well in eah C-MME an elivere to the EPC-MME, there remains a resiual error in evaluating the network-wie fairness metri an a linear approximation on the resiual metri error is aitionally taken into aount, in whih the orresponing parameter sets are also etermine an elivere from C-MMEs uring the previous iteration. At the nth iteration, the EPC-MME performs the marosopi UA by onsiering eah small-ell luster as an mbs with approximate user rates for eah small-ell luster users. The resiual error in the network-wie fairness metri ause by using suh approximate user rates is further ompensate by using the luster uplink information. Denoting x u, as a marosopi UA variable for user u to the maro-ell BS or luster, the marosopi UA problem at the nth iteration an be written as in 15) with the following onstraints: B m C x u, = 1,x u, [0, 1], u U, B m C, 17) x u, x n 1) u, δ n 1), u U n 1), C, 18) { } ς ς n 1) min ε n 1) C,ς [0,1], B m, 19) where X n) 0.5}, U n) = { u U ={xn) u, max χ X,t T A u Un) }, Ũn) [ ])) Su χ S n 1) ω u,χ [ S W u t n 1) ω u,χ { u U S u ) W u ) γ th an φ u) an be given by = {u U n) xn) u, ])) γ th }, for C, }, for B m, 20) φ u) =r n) u, / x u,r n) u,, 21) u U { X n),ςn) } = arg max x u, U φ u) {X,ς } u U B m + ς ς n 1) ) μ n 1) + B m C C Ũn 1) R ) u + x u, U φ u) C u U n 1) σ n 1) u, Ũn 1) ˆR u, Q n 1) )) ) x u, x n 1) u, ). 15)

8 640 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 1, JANUARY 2018 where r n) u, = Ũ n 1) R ) 1 α α u, for B m, ˆR )) u, Q n 1) 1 α α, for C, 22) Ũ n 1) similarly as in [41]. Here, the first part of 15) is the approximate metri using ˆR u, an the remaining part ompensates the resiual error by using a linear approximation. Also, the onstraint 17) is for a relaxe single-bs assoiation as in [19], the onstraints 18) an 19) are for limiting the marosopi user assoiation variables {x u, } an the ABS ratio variables {ς } within their trust regions 3 for this iteration etermine by C- MMEs, respetively, an X n) an Ũ n) enote the set of the marosopi user assoiation variables an the set of effetive users for B m C at the nth iteration, respetively. In aition, Q n) = {S,χ,k n),χ,m n) n),χ,ξ n),χ,a,ξn),χ,n χ X}, n) =[{σ u, u n) U n) },δ n) ], an Δ n) =[α n),β n) ] enote the luster uplink information from luster uring the nth iteration, where S n),χ, k,χ, n) m n),χ, ξ n),χ,a, an ξn),χ,n enote enote the graients of the resiual metri error ue to the hanges in the user assoiation variable x u, an in the orresponing ABS ratio variable the typial rank set, the shape parameter, the multiuser iversity gain of the sale parameter, the sheuling probability at an ABS, an the sheuling probability at an NS using transmission sheme χ, respetively, σ u, n) an δ n) ς, respetively, an α n) an β n) enote the suggestions on the half length of the ege of the ubi trust region aoring to the user assoiation variable an the ABS ratio, respetively. Note that the above problem is not onvex but it has a speial struture that lets it beome onvex in {x u, u U, B m C} for a given {ς B m } an vie versa similarly as in [19]. Thus, {x u, u U, B m C} an {ς B m } an be foun by fixing eah other an using a onvex programming tool suh as CVX [45] iteratively. Finally, the luster ownlink information Ψ n) [U n) where, X n) ϕ n),ϕ n) = {ς n),nn), = ] is upate an elivere to eah luster, ) = mu) for u Un) or = b suh that C b }, N n), = r n) u Ũ n ) U n ) u,, mu) = arg max B m B u γ u,. 3 The trust region onept is aopte from [48]. an C. C-MME Operation 1: Joint UA an Resoure Partitioning Base on the luster ownlink information, the C-MME nees to etermine the joint UA an resoure partitioning for T resoures, i.e., A, η = {η} t t [T ], ν = {ν t,χ,j } t [T ],j [ B t ],χ X for a pre-etermine B. Also, the luster uplink information Γ n) nees to be upate. As esribe in Setion II, JP-CoMP with a semi-ynami BS grouping an resoure partitioning is aopte for the joint UA in eah C-MME to improve the loa balaning apability in a HCN. Let z u, {0, 1} enote the ABS subframe assoiation iniator in luster for user u, w u, {0, 1} enote the maroell assoiation iniator in luster for user u, u,,j {0, 1} enote the user assoiation iniator of user u for BS group j using transmission sheme χ at resoure t in luster, Z = {z u, u U n) } enote the set of the ABS subframe assoiation iniators in luster, W = {w u, u U n) } enote the set of the maro-ell assoiation iniators in luster, an Y = { u,,j u Un), χ X, t [T ], j [ B ]} t enote the set of the user assoiation iniators in luster. Here, φ t,χ,j u) in 3) an be given by φ t,χ,j u) =rt,χ u,,j / u U n ) u,,j rt,χ u,,j, 24) where r t,χ u,,j = ην t t,χ )) 1 α,j It,χ u, B t α,j, 25) similarly as in [41]. Then, a ynami optimization problem at the nth iteration in the C-MME of luster an be written as in 23), as shown at the bottom of the page, with the following onstraints: u,,j,z u,,w u, {0, 1},z u, +w u, 1, u U n), χ X, t [T ],j [ B t ], 26) u,,j z u,, u U n),t T A, 27) j [ B t ] χ X j [ B t ] χ X χ X u,,j 1 w u, z u,, u U n),t T N, ν t,χ,j = 1,νt,χ,j [0, 1],t [T ],χ X, j [ B t ], η t = ς n) b), t T A t T N 28) 29) η t = 1 ς n) b),ηt [0, 1],t [T ], 30) { Y n), Z n) argmax, W n) {Y,Z,W,η,ν },η n) u U n ) },ν n) = U t [T ] j [ B t ] χ X u,,j φt,χ,j u) ηt ν t,χ ) ),j It,χ u, B t,j + wu, φ m u)1 ς n) mu) I u,mu). 23)

9 PARK AND KIM: LOAD-BALANCING SCHEME WITH SMALL-CELL COOPERATION FOR HCNs 641 where φ m φ m where u) =r n) u) an be given by u,mu) / N n) mu), + u U n ),mu )=mu) w u,r n) u,mu ), 31) ) ) r n) u,mu) = 1 ς n) 1 α α mu) I u,mu), 32) similarly as in [41]. Here, the first part of 23) is the expete rate from the small-ell luster an the seon part is the expete rate from the neighboring mbss. Also, 33)-39) are shown at the bottom of this page, the onstraint 26) is for the single-bs assoiation so that z u, + w u, shoul be less than or equal to 1, the onstraint 27) is for the ABS subframe assoiation suh of user u at eah resoure t T A shoul be onsistent to z u, less than z u, if not assoiate to the resoure or equal to z u, if assoiate to the resoure), the onstraint 28) is for the NS subframe assoiation in a similar way, the onstraint 29) is for setting the sum of the portions aoring to all possible transmission shemes to 1 for eah BS group, an the onstraint 30) is for setting the sum of the resoure portions aoring to ABS an NS to ς n) that the sum of the assoiation iniators u,,j b) an 1 ς n) b), respetively. Note that the above problem in 23) is a non-onvex mixe-integer nonlinear programming problem an is NP-har as state in [46]. Thus, fining its optimal solution is intratable. In orer to effiiently fin a eent suboptimal solution, a semi-ynami approah is taken, in whih it is assume that eah ABS NS) user is assoiate to all the ABS NS) resoures. Then, equality is instea use in 27) or 28), similarly as in [47], an only an aequate portion for eah resoure nees to be etermine. By relaxing the onstraints u,,j,z u,,w u, {0, 1} in 26) with u,,j,z u,,w u, [0, 1] an applying a series of lower bouns utilizing the Jensens inequality an the inequality of arithmeti an geometri means, a lower boun for 23) is obtaine, whih has a multi-onvex struture as in 15) an the original problem is similarly separate into the iterations between two subproblems. The propose optimization problem at the nth iteration in the C-MME of luster is written as in 33) 39). Note that P1) an P2) are the subproblems of the original one in the ith iteration for given latest solutions from P2) an P1) in the i 1)th iteration, respetively. 4 Here, P1) has a speial struture that lets it beome onvex in {Y, Z, W } or ν by fixing the other an vie versa an P2) is onvex in η. Thus, a suboptimal solution an be obtaine by solving P1) an P2) iteratively by using a onvex programming tool [45] with a rouning proeure, whih is summarize in Fig. 4. Then, eah sbs in luster partitions the resoure aoring to η synhronously an A t,χ,j an be etermine as At,χ,j = {u Û n) u,,j = 1}. In eah resoure t, eah BS group j uses transmission sheme χ with the portion ν t,χ,j an uring the portion, users in A t,χ,j are sheule aoring to the PFS strategy an serve by the transmission sheme χ. D. C-MME Operation 2: Cluster Uplink Information Upate In orer to upate the luster uplink information Γ n) the C-MME first etermines the parameter set Q n) {S n),χ,k n),χ,m n),χ,ξ n),χ,a,ξn),χ,n 4 Here, the original PF metri for U n ), = χ X} for the approximate is use in P2). P1) { Y n,i) u U n ), Z n,i), W n,i) t [T ] j [ B t ] χ X j [ B t ] χ X },ν n,i) = argmax {Y,Z,W,ν } u,,j U φ t,χ,j u) ηt ν t,χ )),j It,χ u, B t,j + wu, U φ m ) ) u) 1 ς n) mu) I u,mu), 33) s.t.z u, + w u, 1, u,,j,z u,,w u, [0, 1], u U n),χ X, t [T ],j [ B t ], 34) u,,j = z u, max {t T A η t > 0}, 1), u Un),t T A, 35) j [ B t ] χ X χ X u,,j = P2) η n,i) 1 w u, z u, max {t T N η t > 0}, 1), u Un),t T N, 36) ν t,χ,j = 1,νt,χ,j [0, 1],t [T ],χ X, j [ B t ]. 37) = argmax η s.t. η t = ς n) b), t T A t T N u U n ) U t [T ] j [ B t ] χ X u,,j φt,χ,j u) ηt ν t,χ,j It,χ u, ) B t,j, 38) η t = 1 ς n) b),ηt [0, 1],t [T ]. 39)

10 642 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 1, JANUARY 2018 Fig. 4. Optimization proeure at eah C-MME. user rate as { } S,χ,k n),χ,m n) n),χ,ξ n),χ,a,ξn),χ,n = argmin {S,χ,k,χ,m,χ,ξ,χ,A,ξ,χ,N } 2 u Û n ) ξ,χ,a I t A,χ u, R )) u ω u S,χ +ξ,χ,n I t N,χ u, )) 1. ω u S,χ 40) Sine fining the best solution to the above problem might not be ritial for the overall optimization, a suboptimal solution an be aopte in this paper, whih is summarize in Fig. 5. First, the effetive number of users for the transmission sheme χ in luster, enote as μ n),χ, an the effetive number of BSs for the multiuser iversity, enote as ε n), whih are neessary to evaluate the shape parameter an the multiuser iversity gain for ˆR u, Q n) ) in the EPC-MME, are assume to be given as the largest number of the assoiate users among the BS groups in luster an the mean of the effetive number of BSs for the multiuser iversity gain over all users in luster, respetively, as shown in step 1. In step 2, several variables are set, in whih 3,χ an 4,χ are etermine for a ranom variable A with the CDF of F A x; S,χ ) n) an a ranom variable B Γ S,χ, n) S,χ n) 1 ), similarly as in IV-A, χ,1 χ,2 ) enotes the mean value of the alloate resoure portion for ABS NS) an χ,3 χ,4 ) enotes the mean value of the number of the assoiate users for eah group in ABS NS). Then, by assuming that BSs for eah user are given as the rank set S,χ, n) the shape parameter k,χ n) an the multiuser iversity gain m n),χ are etermine as in step 3, similarly as in 14) an 12). Also, the effetive sheuling portion ξ n),χ,a ξn),χ,n ) for ABS NS) for eah transmission sheme χ is set to the mean value of the alloate resoure portion ivie by the mean value of the number Fig. 5. Proeure for etermining Q n ). of the assoiate users for eah group in ABS NS). Finally, the rank set S,χ n) is selete to fit R u. Also, efine the resiual error at the nth iteration as ) ) ϕ n) = U φ u) g X n) x n) Ru u, u U n ) U φ u) Ũn) ˆR )), u, Q n) 41) u, 0.5) ) 1 for some on- where gx n) )= 1 + e u U n ) x n ) stant >0isasmooth funtion of x n) u, approximating the number of assoiate users an φ u) an be given by 1 α)/α φ u) = R u / R 1 α)/α u xn) u,, 42) u U n ) similarly as in [41]. In a typial trust region algorithm solving a very omplex problem suh as in [48], an approximate moel suh as a linear approximation or a quarati approximation) is use to obtain the trust region trial step an the ratio between the atual reution inrement) in the original funtion an the preite reution inrement) in the approximate moel within a trust region with an aeptable trial step nees to be greater than a given trust region threshol value say X n) 0.75). Note that 41) is just for the urrently given U n) an an the whole funtion for the resiual error is not available at eah C-MME. In orer to ompute a proper trust region for EPC-MME, the trust region onept [48], whih provies how to ompute the trust region trial step an eie whether a trial step is aeptable or not, is applie. In this paper, it is

11 PARK AND KIM: LOAD-BALANCING SCHEME WITH SMALL-CELL COOPERATION FOR HCNs 643 Fig. 6. Equations for etermining n ) an Δ n ). assume that a linear approximation moel is use to obtain the trust region trial step an the original funtion is approximate by a quarati approximation using the Taylor series of 41). As a result, an approximate ratio between the reutions inrements) of the quarati an linear approximations using the Taylor series of 41) is instea use. For pre-etermine trust region threshols e 1) th,e2) th from σ n) u, an σ n) erivatives of ψ n) u, δ n) > 0, the approximate ratio is obtaine n) an δ ), whih are the first an seon in 41) with respet to x n) u, ς n) b) ), respe- u, u U n) },δ n) ] an Δ n) =[α n),β n) ] tively, an n) =[{σ n) are upate as summarize in Fig. 6. E. Complexity Analysis an Implementation Feasibility for the Propose Hybri SON Sheme On the one han, onsier the asymptoti time omplexity require to solve the optimization problems in 15) for an EPC- MME an in 33) 39) for a C-MME aoring to the number of users. The optimization problem in 15) for the EPC-MME is not onvex but it has a speial struture that it beomes onvex in {x u, u U, B m C} for a given {ς B m } an vie versa. Thus, {x u, u U, B m C} an {ς B m } an be foun by fixing eah other iteratively. To solve eah onvex subproblem for {x u, u U, B m C} or {ς B m }, the interior point metho [49] utilizing an iterative Newton step an be use, in whih for a onvex problem with size of n, a matrix inversion with omplexity of On 2.3 ) floating-point operations is require to ompute a new Newton step for eah iteration [50] an O n logn)) iterations are require [49]. Sine a finite number of iterations are require between the two subproblems, the time omplexity require for the optimization problem in the EPC-MME is given as O U 2.8 log U ). Similarly, the optimization problem P1) in 33) 37) for the C-MME is not onvex but it has a speial struture that it beomes onvex in {Y, Z, W } or ν by fixing the other. Thus, eah subproblem for {Y, Z, W } or ν an be solve similarly as in the EPC-MME ase. In aition, P2) in 38) an 39) is onvex an a finite number of iterations are performe between P1) an P2), whih leas to the time omplexity of O U n) 2.8 log U n) ). On the other han, onsier the implementation feasibility of the propose sheme. In a typial LTE system, there are hunres to thousans of maro ells onnete to an EPC-MME [51] an there are about 200 simultaneously raio resoure ontrol RRC)-onnete users per eah maro ell [52]. Also, a typial hotspot area an be haraterize by its user ensity about 10 times higher than that in a normal maro-ell area an its area of about 10 4 m 2 [32]. If we assume one mbs per 1 km 2 an several sbss in eah hotspot area, the number of simultaneously RRC-onnete users hanle by eah C-MME is about a few tens. Suppose that the propose sheme is use for the etermination an upate of the target enoe B for the user plane of eah RRC-onnete user. Then, the allowe ontrol plane lateny in the EPC-MME for an RRC-onnetion request is about 15 ms [53]. Then, it seems impratial to hanle up to hunres of thousans of users in an EPC-MME. However, only users in a small portion of maro ells neighboring hotspots nee to partiipate in the propose sheme. Also, among suh users, users with a ominant referene signal reeive power RSRP) from a ell an be pre-etermine. Finally, the EPC-MME an ivie the whole problem into geographially-ivie inepenent subproblems omprise of neighboring mbss an hotspot lusters. For an example of a typial urban ity [54], 10% of measurement points are lassifie as hotspot points so that the number of maro ells overlai with hotspots in an EPC-MME is at most a few hunres. If these maro ells are ivie into several tens of isjoint groups, about a thousan RRC-onnete users nee to be jointly onsiere in the propose UA sheme for eah group in the EPC-MME. Sine only a part of users are loate in ege area, users with a ominant RSRP from a ell an be automatially assoiate an the effetive number of users for the propose sheme an be muh smaller. Note that a general onvex problem an be solve iteratively by approximating an original problem to a quarati program QP) problem an an open soure suh as CVXGEN [55] an generate {{X,ς Bm }, {X, Y, Z,η,ν C}} = arg max {{X,ς B m },{X,Y,Z,η,ν C}} U x u, φ u)1 ς ) I u, + u U B m C t [T ] j [ B t ] χ X u,,j φt,χ,j u) ηt ν t,χ,j It,χ u, ) B t,j. 43)

12 644 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 1, JANUARY 2018 a fast ustom oe for QP-representable onvex optimization. Thus, by assuming a eiate proessor for the omputation in eah EPC-MME or C-MME, the propose sheme an be easily implemente in a pratial ellular system, whih will be onfirme by a numerial example in Setion V. 43) as shown at the bottom of the previous page. V. SIMULATION RESULTS In orer to evaluate the avantages of the propose joint UA sheme with JP-CoMP using hybri SON, enote as H-SON, a two-tier network is onsiere, where Φ for eah luster ξ) is assume to follow a Matérn har-ore proess of type 3 with ensity of λ = generate from a homogeneous Poisson point proess HPPP) an ξ) is assume to be a irle entere at with the raius of R = 65 m) to set about 10% overage of the total area as hotspot areas to reflet a typial hotspot area reporte in [32][56]. Also, for user loations, it is assume that Φ u is an HPPP with ensity of λ u = users/m 2 ) an Φ u is an HPPP over ξ) with ensity of λ h = 10λ u to reflet a typial user ensity ratio reporte in [32]. In orer to serve users in the above HCN environment, it is assume that a servie provier eploys maro-ell BSs equippe with N A {1, 2, 4}, Bm, antennas with ensity of λ m = an single-antenna sbss, 10 in average, for eah small-ell luster, i.e., πr 2 λ s ) =10. The minimum istane between a maro-ell BS an a luster enter an that between neighboring luster enters are set to 1.5R an 3R, respetively, for a pratial HCN senario, whih follows the 3GPP reommenations an its evaluation methoology parameters for small-ell luster eployment senario [57]. In orer to valiate the performane of the propose sheme, the lustering phase is first performe. Here, base on the reporte user measurement information {γ u }, EPC-MME an transform γ u into approximate relative istane between the user an the orresponing sbs as follows: u,b =N 0 /P s γ u,b ) 1/θ, 44) where P s, N 0, an θ enote the transmit power of sbss, the noise power, an the pathloss exponent, respetively. Then, using the above istane values between users an sbss, the istane between sbss might be approximate as follows: 1 b,b = u,b +, 45) U b,b U b,b u U b, b u U b, b u,b where U b,b = {u U b = arg max b B u γ u,b, b B u }. Then, by utilizing the total least square algorithm [34] among ranomly selete sbss repeately, the relative loation of eah sbs an be estimate an the k-means algorithm [35] follows to luster the sbss, in whih the effetive number of lusters is etermine by using the elbow metho [36]. Here, it is assume that the role for C-MME for eah assigne luster is supporte by its nearby mbs an the sbss in the assoiate lusters are onnete to the orresponing C-MME. The performane results of the propose sheme in Figs are obtaine with Fig. 7. The onvergene performane of the propose H-SON. the automatially lustere sbss. The transmit powers of the mbss an sbss are set to 46 Bm an 30 Bm, respetively, the noise power spetral ensity is set to 174 Bm/Hz, an the system banwith is assume to be 10 MHz. By refleting the fat that a maro ell has a relatively larger overage than a small ell, the require average SINR level of the system is set to 9 B for maro-ell users an 6 B for small-ell luster users by onsiering QPSK with oe rate 193/1024, whih orrespons to the LTE hannel quality information CQI) 3 with maximum 3 re-transmissions for maro-ell users an 1 re-transmission for small-ell luster users [58], [59]. Also, it is assume that eah frame onsists of N S = 10 subframes an eah subframe of 1ms interval onsists of N RB = 100 multiple RBs as in the LTE an the hannel for eah RB between eah antenna of eah BS an eah user is assume to be an inepenent flat Rayleigh faing hannel with log 10 R) B for maro-ell pathloss moel an log 10 R) B for small-ell pathloss moel, in whih R enotes the istane between a BS an a user in [km]. For omparison, a entralize joint UA sheme employing the same semi-ynami approah for small-ell lusters, enote as C-SON, is onsiere to provie an upper-boun on the performane of the propose H-SON sheme for eah given realization. Note that all information is assume to be available at the EPC-MME so that the expete user rate an be iretly alulate at the EPC-MME. However, it is har to be implemente in pratial senarios ue to its high signalling overhea an omputational loa at the EPC-MME. Suh an optimization problem for C-SON an be written as in 43) with the following onstraints: x u, = 1,x u, [0, 1], u U, 46) B m C j [ B t ] u,,j = χ X z u, {t T A η t > 0},t T A, u U, C, 47)

13 PARK AND KIM: LOAD-BALANCING SCHEME WITH SMALL-CELL COOPERATION FOR HCNs 645 j [ B t ] u,,j = χ X η t = ς n) b), t T A χ X t T N x u, z u, {t T N η t > 0},t T N, u U, C, 48) η t = 1 ς n) b),t [T ], C, 49) ν t,χ,j = 1,νt,χ,j [0,1],χ X, t [T ],j [ B t ], C. 50) Here, a suboptimal solution is obtaine by transforming the above problem similarly as in 23) an solving the transforme problem with a onvex programming tool [45] iteratively an the same rouning proeure use in Setion IV-B is applie for eah luster. Note that the C-SON an be onsiere as a relaxe version of the original ombinatorial problem so that it provies an upper-boun on the performane of the propose H-SON sheme for eah given realization sine the same relaxation an rouning metho are applie exept that a suboptimal istribute metho is use for the propose H-SON. In aition to the joint UA sheme, three onventional single-ell base assoiation shemes, the entralize joint UA without onsiering CoMP [19], the CRE an e-icic sheme [5], an the maximum SNR sheme [27], [28], are ompare, whih are enote as SC-SON, SD-SON, an S-MAX, respetively. Also, SD-SON is optimize by seleting the ommon bias an ABS ratio values foun by an exhaustive searh to maximize the PF metri. Note that, although UA is ifferently performe in eah of the above five shemes, the same MU-MIMO or CoMP shemes are utilize with the same sheuling poliy in every sheme in orer to ompare the performane aoring to the loa balaning strategy. In Fig. 7, the onvergene performane of the propose sheme for a typial HCN realization is shown. In orer to give the performane boun of the propose sheme, the performane of C-SON is plotte by using a otte line with no mark. From the results, it is shown that the performane of the propose sheme approahes that of the C-SON, i.e., the upper boun, only within several exhanges of Γ an Ψ between EPC-MME an C-MMEs, whih implies that the propose iterative algorithm works very well. 5 It is also shown that the onvergene performane is affete by the seletion of the luster uplink information so that it nees to be selete arefully. Here, H-SON, ba S, H-SON, 0.3e th, H-SON, ifferent hat R, 10e th, an H-SON, user pre-lassifiation enote the H-SON sheme with a ba seletion of the rank set S,χ, that with e 1) th = 0.9 an e2) th = 0.06, that using ˆR u, Q )= max χ X 0.01ξ,χ,A I t A,χ u, β u S,χ )) + ξ,χ,n I t N,χ u, β u S,χ ))) instea of 16) with e 1) th = 30 an e2) th = 2, an that with pre-lassifie effetive users, respetively. Comparing them with the propose H-SON using the luster uplink information 5 In ase of an upate where only a part of users move or are replae, only a few exhanges of Γ an Ψ between EPC-MME an C-MMEs are require for eah upate of the joint assoiation. in Fig. 5 shows that the onvergene spee is signifiantly egrae if the rank set is not properly selete. This omes from the fat that the resiual error beomes larger an eviate from the linear approximation so that not only muh more iterations are require but also the point of onvergene itself is eviate from the optimal point. In aition, the trust region threshols nee to be properly selete for a goo onvergene performane. In this simulation, the trust region threshol values of e 1) th = 3 an e2) th = 0.2 are selete by a trial an error beause the performane is not muh sensitive to the values if the propose ˆR u, Q ) is use. However, if we use e 1) th = 0.9 an e 2) th = 0.06 instea, i.e., use a too small trust region, the onvergene spee may beome signifiantly egrae even if a properly approximate ˆR u, Q ) is use. On the other han, we may want to inrease the onvergene spee by enlarging the trust region. However, as shown in the urve enote as H-SON, ifferent hat R, 10e th, if the mismath is ause by seleting not so goo ˆR u,, the onvergene spee may be inrease but the point of onvergene an be eviate from the optimal point. Also, users with a ominant RSRP an be pre-etermine as isusse earlier to reue the omplexity. As shown in Fig. 7, it is shown that similar performane an be ahieve when users with a ominant RSRP 6 B threshol an 7 B bias for sbss) are pre-etermine. In this simulation, about 80% of users were pre-etermine an only 20% of users partiipate in the propose sheme. Lastly, in orer to show the effet of user mobility an asynhronous measurement reports, a isrete event simulation is performe, in whih it is assume that previous user loations are obtaine from the urrent user loations by a ranom isplaement following a 2-imensional Gaussian istribution with the mean of 0 an the stanar eviation of 20 m) an that the measurement report of eah user follows a Poisson ranom proess with the mean arrival rate of 0.1 per seon. It is also assume that eah iteration takes 4ms. As shown from the urve enote as H-SON, isrete event with axes at the top an the right sie in Fig. 7, the performane gets better as more measurement information is ollete an the propose sheme works well in the ase of user mobility an asynhronous measurement reports. In Figs. 8 an 9, the assoiation results for the users near a small-ell luster in a typial HCN realization are shown with the orresponing CDFs on the system-wise SINR an the user-wise average rate. By omparing the user assoiation results in S-MAX Fig. 8a)) with SD-SON Fig. 8b)), SC-SON Fig. 8)), an the propose H-SON Fig. 8)), it is learly shown that i) the loa balaning apability of SD-SON is poor in a HCN so that inner sbss are harly expane an outer sbss suffer from higher loa an poor link quality, ii) although the loa balaning apability an be improve by aopting a joint approah SC-SON) so that some portion of the loa of outer sbss are offloae to inner sbss, the impat is quite limite beause CoMP is not onsiere at the assoiation stage, iii) the propose H-SON allows not only more aggressive intertier offloaing but also more flexible intra-tier offloaing for better loa balaning as expete so that the loa balaning

14 646 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 1, JANUARY 2018 Fig. 10. The average performane gain of the propose H-SON over SD-SON for various maximum group sizes an number of resoures. a) # of maximum group size. b) # of resoures. Fig. 8. Assoiation results of S-MAX, SD-SON, SC-SON, an the propose H-SON for a typial HCN realization. a) S-MAX. b) SD-SON. ) SC-SON. ) The propose H-SON. Fig. 9. Loa-balaning apability evaluation an omparison. a) Atual an expete link quality istribution. b) Average user rate istribution. apability an be greatly improve. To onfirm that the link quality is manage while aggressive inter-tier an intra-tier offloaings are allowe in the propose H-SON, the atual system-wise SINR CDF an that expete at the assoiation stage when employing the propose H-SON are ompare to those employing S-MAX, SD-SON an SC-SON, respetively, in Fig. 9a). From the results, it is shown that the atual link quality of S-MAX, SD-SON or SC-SON is quite ifferent to that expete at the assoiation stage beause the onventional shemes o not take the effet of using CoMP in small-ell lusters into aount so that the loa balaning apability beomes quite limite. However, the propose H-SON an manage the link quality quite aurately while muh more aggressive offloaing is allowe so that the loa balaning apability an be greatly improve. The loa balaning apability of eah sheme is evaluate in terms of the average user rate istribution when the maro-ell BS employs 4 antennas an the maximum BS group size an the number of resoures for the small-ell layer CoMP are 4 an 2, respetively, an is shown in Fig. 9b), whih onfirms the superiority of the propose H-SON over onventional shemes. In Fig. 10, the average performane gain of the propose H-SON over SD-SON in terms of the ratio of the bottom 5% average user rate of the propose H-SON over that of the SD-SON is evaluate for various onfigurations of the maximum BS group size an the number of ifferent resoures. From the results, it is shown that although larger gain is ahieve as the BS group size an/or the number of resoures inrease, the growth rate reues quikly. This result exhibits that the propose H-SON works well in a wie range of luster onfigurations an BS groups with a few to several BSs an more than one resoure for eah NS an ABS are enough. Thus, it is onfigure that the propose H-SON is quite suitable for pratial senarios. In Fig. 11, in orer to evaluate the average performane gain of the propose H-SON over SD-SON in pratial HCN senarios, the ratios of the bottom 5%, 10%, an 15% average user rates are evaluate an ompare from 100 realizations on 5000 m 5000 m area. Here, S1 S4), S2, an S3 enote a basi eployment senario as state in the beginning of this setion, the other senario with 50% more sbss per luster, an another senario with 50% more lusters, respetively, an eah small-ell luster an be ifferently onfigure so that the maximum BS group size for eah luster is ranomly pike among {2, 3, 4} for senarios S1, S2, S3 an among {1, 5} for senario S4. Compare with the average performane gain of the

15 PARK AND KIM: LOAD-BALANCING SCHEME WITH SMALL-CELL COOPERATION FOR HCNs 647 Fig. 11. The average performane gain of the propose H-SON over SD-SON in pratial HCN senarios. Fig. 12. The average performane gain of the propose H-SON extene for α-fairness over SD-SON. propose sheme in the baseline senario S1, that in S2, S3, or S4 beomes higher, i.e., as there is more room for loa balaning more lusters or more sbss per luster) or more ranomness in onfiguring small-ell lusters, the superiority of the propose sheme inreases, whih implies that the propose sheme is expete to work well if applie to a pratial ellular network, suh as the LTE-A. In orer to exten the propose sheme to a general α-fairness ase α 1), we may use U r) =r 1 α / 1 α) instea of U r) = logr) in 15), 33), or 38) an those in Figs. 4 an 6 an upate the user sheuling probability variables with the other optimization variables alternately by relaxing them as inepenent variables. In Fig. 12, the bottom 5%, 10%, an 15% average performane gains of the propose H-SON sheme over SD-SON are evaluate an plotte for α = 0.5, 1, 1.5, an 2 by using the above extension when the maximum group size is set to 4 an T = 2, whih onfirms that although the gain may vary aoring to a speifi sheuling strategy, the propose sheme an be well extene to the ase of using a general α-fairness sheuling. Finally, in orer to onfirm the implementation feasibility of the propose sheme, a numerial example on the omputing time for the propose UA sheme in a typial LTE senario is onsiere, where eah subproblem in the EPC-MME onsists of 4 mbss an 4 hotspots eah with 10 sbss for eah mbs. Then, there are about 25 π /10 6 ) RRC-onnete users aroun eah luster onsiering that there are about 200 simultaneously RRC-onnete users per eah maro ell an the higher user ensity an the area of a typial hotspot, whih results in about 1200 = ) RRC-onnete users for the above senario. As shown in Fig. 7, it is suffiient to inlue only part of users say, 20%) so that about 240 = ) users for eah subproblem in the EPC-MME an about 25 users for eah C-MME nee to be jointly hanle. By using CVX matlab) with an Intel Core i ores an 5.18 GFLOPS/ore) an assuming parallel proessing for inepenent omputation of the ABS ratio optimization for eah mbs or matrix inversion suh as in [60], the omputing times for {X B m C} an {ς B m C} are about 0.4 s an 4 s, respetively, an those for the iteration between P1) an P2) in eah C-MME are about 2.4 s. Note that a realtime optimization omputing using CVXGEN is well known to be 500, 2000, or times faster than that using CVX for a large-size, meium-size, or small-size problem, respetively [55]. Thus, by assuming a state-of-the-art proessor suh as Intel Xeon E v3 12 ores an 33.6 GFLOPS/ore) [61], whih has its omputing apaity about 18 = 3 6) times greater than that of the Intel Core i5-4670, the omputing times for one iteration in 18 subproblems in the EPC-MME an one iteration in eah C-MME woul be about 0.9 ms an 0.2 ms, respetively. Then, by assuming 4 iterations among the EPC-MME an eah C-MME an 1ms lateny for eah luster information, the EPC- MME ontrol plane lateny of about 15 ms an be ahieve. Also, assuming a pipeline proessing among subproblems in the EPC-MME, it an be implemente by employing a eiate proessor in the EPC-MME with urrent state-of-the-art tehnologies. VI. CONCLUSION In this paper, a joint UA sheme with JP-CoMP using a hybri SON was propose for a pratial HCN to maximize the network-wie proportional fairness among users, in whih a entral SON algorithm manages a marosopi user assoiation an a istribute loal SON algorithm in eah luster manages a joint UA with an RP sheme by onsiering aaptive CoMP moe seletion for given user loations. The network arhiteture an protool for the hybri SON in a HCN was suggeste, whih oinies with the ore network arhiteture of the LTE-A an an be easily aopte in pratie, an then a feasible suboptimal iterative algorithm for etermining the joint UA solution of the propose hybri SON was provie with the time omplexity analysis for implementation feasibility. It is shown that the propose hybri SON sheme is very effetive in hanling the loa balaning in a pratial HCN not only improving the performane of the inner sbs users by reuing the inter-ell interferene, espeially for intra-tier offloae users, but also enabling more aggressive inter-tier offloaing by effetively improving the link quality of luster ege users without ausing an unneessary resoure waste. Thus, it woul be

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17 PARK AND KIM: LOAD-BALANCING SCHEME WITH SMALL-CELL COOPERATION FOR HCNs 649 [49] S. Boy an L. Vanenberghe, Convex Optimization. Cambrige, U.K.: Cambrige Univ. Press, [50] D. Coppersmith an S. Winogra, Matrix multipliation via arithmeti progressions, J. Symboli Comput., vol. 9, pp , [51] NOKIA, LTE raio transport seurity, White paper, pp. 1 27, Jun. 2015, [Online]. Available: [52] H. Holma, A. Toskala, an J. Reunanen, LTE Small Cell Optimization: 3GPP Evolution to Release 13. New York, NY, USA: Wiley, Nov [53] Universal Mobile Teleommuniations System UMTS); LTE; Feasibility Stuy for Evolve Universal Terrestrial Raio Aess UTRA) an Universal Terrestrial Raio Aess Network UTRAN), 3GPP TR V9.0.0, Ot [54] A. Farsha, M. K. Marina, an F. Garia, Urban WiFi haraterization via mobile rowsensing, in Pro. IEEE Netw. Oper. Manag. Symp., May 2014, pp [55] J. Mattingley an S. Boy, CVXGEN: A oe generator for embee onvex optimization, Optim. Eng., vol. 13, no. 1, pp. 127, [56] M. Tolstrup, Inoor Raio Planning: A Pratial Guie for 2G, 3G an 4G. New York, NY, USA: Wiley, May [57] Evaluation Assumptions for Small Cell Enhanements-Physial Layer, Huawei, HiSilion, 3GPP R , Feb [58] J. Colom Ikuno, M. Wrulih, an M. Rupp, Performane an moeling of LTE H-ARQ, in Pro. ITG Int. Workshop Smart Antennas, Feb. 2009, pp [59] J. Colom Ikuno, M. Wrulih, an M. Rupp, System level simulation of LTE networks, in Pro. IEEE Veh. Tehnol. Conf., May 2010, pp [60] P. Ezzatti, E. Quintana-Orti, an A. Remon, High performane matrix inversion on a multi-ore platform with several GPUs, in Pro. 19th Euromiro Int. Conf. Parallel, Distrib. Netw.-Base Proess., Feb. 2011, pp [61] Evolve Paket Core EPC) for Communiations Servie Proviers, Solutions Referene Arhiteture revision 1.2, Intel Corporation, Mountain View, CA, USA, May 2016, pp Kwang Soon Kim S 95 M 99 SM 04) was born in Seoul, South Korea, in He reeive the B.S. summa um laue), M.S.E., an Ph.D. egrees in eletrial engineering from Korea Avane Institute of Siene an Tehnology, Daejeon, South Korea, in 1994, 1996, an 1999, respetively. From 1999 to 2000, he was with the Department of Eletrial an Computer Engineering, University of California at San Diego, La Jolla, CA, USA, as a Postotoral Researher. From 2000 to 2004, he was a senior member of the researh staff with the Mobile Teleommuniation Researh Laboratory, Eletronis an Teleommuniation Researh Institute, Daejeon. Sine 2004, he has been a Professor with the Department of Eletrial an Eletroni Engineering, Yonsei University, Seoul. His researh interests inlue signal proessing, ommuniation theory, information theory, an stohasti geometry applie to wireless heterogeneous ellular networks, wireless loal area networks, wireless evie-to-evie networks an wireless a o networks, an new raio aess tehnologies for 5G. Dr. Kim reeive the Postotoral Fellowship from the Korea Siene an Engineering Founation in 1999, the Outstaning Researher Awar from the Eletronis an Teleommuniation Researh Institute in 2002, the Jak Neubauer Memorial Awar Best System Paper Awar, the IEEE TRANSAC- TIONS ON VEHICULAR TECHNOLOGY) from the IEEE Vehiular Tehnology Soiety in 2008, an the LG Researh an Development Awar: Inustry- Aaemi Cooperation Prize, LG Eletronis, in He serve as an Eitor of the Korean Institute of Communiations an Information Sienes KICS) from 2006 to 2012, an the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS from 2009 to He has been an Eitor of the Journal of Communiations an Networks sine He has been the Eitor-in-Chief of the KICS sine Jin-Bae Park was born in Inheon, South Korea, on June 22, He reeive the B.S. an M.S.E. egrees in eletrial an eletroni engineering in 2006 an 2008, respetively, from Yonsei University, Seoul, South Korea, where he is urrently working towar the Ph.D. egree with the Department of Eletrial an Eletroni Engineering. His researh interests inlue heterogeneous ellular network, oorinate multiell proessing, an raio resoure management.