A Practical Tessellation-Based Approach for Optimizing ...downloads.hindawi.com/journals/mpe/2017/4764103.pdfA Practical Tessellation-Based Approach for Optimizing Cell-Specific Bias

Research ArticleA Practical Tessellation-Based Approach forOptimizing Cell-Specific Bias Values in LTE-AHeterogeneous Cellular Networks

Jin-Bae Park and Kwang Soon Kim

Department of Electrical and Electronic Engineering Yonsei University 50 Yonsei-ro Seodaemun-guSeoul 03722 Republic of Korea

Correspondence should be addressed to Kwang Soon Kim kskimyonseiackr

Received 26 December 2016 Accepted 22 May 2017 Published 28 June 2017

Academic Editor Alessandro Tasora

Copyright copy 2017 Jin-Bae Park and Kwang Soon Kim This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In order to implement an optimized solution for cell range expansion (CRE) and enhanced intercell interference coordination(eICIC) schemes in long-term evolution-advanced (LTE-A) heterogeneous cellular networks (HCNs) and to realize good load-balancing performance in existing LTE-A systems a practical tessellation-based algorithm is proposed In this algorithm aglobalized cell-specific bias optimization and a localized almost blank subframe (ABS) ratio update are proposed The proposedscheme does not require major changes to existing protocols Thus it can be implemented in existing LTE-A systems with anylegacy user equipment (UE) with only a partial update to the BSs and core networks From simulation results it is shown thatthe tessellation formed by the proposed approach is quite consistent with the optimal one for various realistic scenarios Thus theproposed scheme can provide a much better load-balancing capability compared with the conventional common bias schemeOwing to the improved load-balancing capability the user rate distribution of the proposed scheme is much better than thatobtained from the conventional scheme and is even indistinguishable from that of the ideal joint user association scheme

1 Introduction

In current cellular networks low-powered small cells arebeing installed with conventional macrocells to form hetero-geneous networks (HCNs) as a way to meet users increasingdemand for mobile broadband traffic [1] Considering acochannel deployment in which macrocells and small cellsuse the same carrier frequencies and conventional cell asso-ciation this may mislead most users by selecting macrocellsas the best-serving cells owing to the large difference indownlink transmit powers Thus to achieve the potential ofsuch an HCN appropriate load balancing is essential andis expected to play an important role in offloading loadsfrom macrocells to small cells [2ndash4] For this cell rangeexpansion (CRE) and enhanced intercell interference coor-dination (eICIC) using almost blank subframes (ABS) havealready been adopted in 3GPP long-term evolution-advanced(LTE-A) 3GPP LTE-A allows for offloading even to legacy

UEs and protects such offloaded small-cell users by providinga certain muted portion of subframes so that more users canbe offloaded from macrocells to small cells with a significantperformance gain [5ndash7]

There have been many load-balancing schemes in litera-ture to determine the bias values for CRE and the ABS ratiofor the eICIC which can be categorized as follows (i) a jointoptimization of user association and ABS ratios such as in[8 9] (ii) a global optimization of CRE bias values and ABSratios such as in [10 11] and (iii) a local optimization ofABS ratios for a given common bias value such as in [12ndash14]As an ideal approach for CRE and eICIC optimization jointoptimization methods for user association and ABS ratioshave been studied [8 9] In [8] a centralized optimizationproblem for user association considering the ABS ratio isformulated and solved to maximize a network-wide utilityand shows a large gain in network performance In [9] ajoint problem for user association the ABS ratio and radio

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 4764103 11 pageshttpsdoiorg10115520174764103

2 Mathematical Problems in Engineering

resource scheduling is studied and a distributed algorithmis developedThe algorithm shows improvement in network-wide resource utilization However in order to implementsuch a joint approach in an existing network architectureexisting network elements should be updated and legacy UEsneed to bemodified or even replaced to support this new userassociation process In the current LTE-A user associationcan adopt the CRE method by using a bias value [15] wherea positive bias is assigned to each cell and each user isassociated with the cell of the maximum biased referencesignal received power (RSRP) In order to determine a properbias value and ABS ratio a global optimization methodusing cell-specific bias values [10] or a common bias value[11] for small-cell CRE has been studied In this method acentralized approach is considered where the CRE bias valuesand ABS ratios are determined at a central entity [eg theenhanced packet core- (EPC-) mobility management entity(MME)] to provide good performance Although they maybe compatible with legacy UEs a large amount of overhead iscaused by frequent signal exchanges for updating each userrsquosSNR or each BS information These events are necessary toestimate user rates and an overall update to the BSs and thecore network is also required As an efficient implementationin an existing network a local optimization of ABS ratiosbased on a given common CRE bias value has been alsostudied [12ndash14] In this optimization simple centralized ordistributed algorithms for determining eICIC ABS ratiosbased on a given common CRE bias value are proposedby comparing local load situations in each macrocell andneighboring small cells Although this approach can beapplied to legacy UEs and requires only a partial update tothe BSs and the core network its performance is limitedmainly owing to the use of a common CRE bias value evenwithout any optimization Thus in order to achieve moresuccessful load balancing in existing LTE-A networks a moreefficient method for determining cell-specific bias valuesand ABS ratios needs to be developed This method shouldbe implemented without major changes to existing cellularnetworks

In this paper a practical tessellation-based approachis proposed to maximize the network-wide proportionalfairness (PF) among users in LTE-A HCNs In these HCNscell-specific bias values are determined to form a suboptimaltessellation similar to an optimal tessellation that may beobtained from a joint optimization for the CRE bias valuesand ABS ratios The proposed scheme does not require anymajor modifications to existing protocols and thus can beeasily applicable to practical LTE-A systems The proposedalgorithm consists of the following two steps (i) based onthe long-term accumulated user measurement informationcell-specific bias values are optimized and updated globallyby the EPC-MME in a long-term manner and are deliveredinfrequently to small cells and (ii) the ABS ratio andABSNS resource scheduling are optimized locally amongeach mBS and its associated sBSs only It is shown that theproposed scheme can be easily realized in practical LTE-A systems without modifying any existing protocols whileachieving a good load-balancing performance comparedwithconventional methods The rest of this paper is organized

as follows In Section 2 an abstract system model for anLTE-AHCN is provided and the proposed tessellation-basedapproach for efficient load balancing in an existing LTE-AHCN is described in Section 3 In Section 4 simulation resultsfor various realistic scenarios and corresponding discussionsare provided and concluding remarks are given in Section 5

2 The System Model

Consider a downlink two-tier HCN in which macrocells areoverlaid with small cells using a lower transmit power Thetransmit powers of an mBS and an sBS are denoted as 119875119898and 119875119904 respectively In addition the set of user locationsthe set of mBS locations and the set of sBS locations aredenoted as U = u1 u2 B119898 = b1198981 b1198982 andB119904 = b1199041 b1199042 respectively Here each sBS location canbe configured for different small-cell service scenarios Forexample in rural environments sBSs can be deployed in ruralcommunities and remote industries [16] For urban (denseurban) environments sBSs can be deployed to support cityhot zones or transportation hubs (eg airports or railwaystations) [17]

The LTE-A core network architecture is abstracted asshown in Figure 1 The sBSs are connected via X2 to thenearest mBS Here the nearest mBS for sBS b isin B119904 is denotedas 120596(b) In addition each mBS or sBS is connected via S1 toan EPC composed of theMME the serving gateway (S-GW)and the packet data network gateway (P-GW) In additionthe LTE-A air interface is abstracted so that each subframe of1ms intervals consists of 119873RB multiple resource blocks (RBs)that are divided into ABSs and normal subframes (NSs) Foran ABS interference from the nearest mBS is almost mutedso that the signal quality of small-cell users in the range-expanded regions can be greatly improved

Globally the EPC-MME determines a set of bias valuesfor sBSs denoted as 120581 = 120581b | b isin B119904 These values arebased on long-term accumulated SNR measurement reportsfromusers where 120581b denotes the bias value for sBS b which isupdated infrequently and delivered to each mBS or sBS Eachuser obtains bias information for neighbor sBSs via a systeminformation (SI) block mapped on the radio resource control(RRC) SI message over the downlink shared channel (DL-SCH) After receiving the bias values of its neighbor sBSseach user chooses its serving BS based on the biased RSRPinformation as

blowastu = argmaxbisinBu

10 log10120574ub + 120581b (1)

where 120574ub denotes the averaged received signal-to-noisepower ratio (SNR) between BS b and user u and reports itsmeasurement 120574u = 120574ub | b isin Bu and Bu sub B119898 cup B119904 denotesa neighbor BS list for user u to the selected BS Note that (1)becomes conventional cell selection with a maximum RSRPwhen 120581b = 0 forb isin B119898cupB119904 Here denote the set of associatedusers as b isin B119898 cup B119904 as Ub = u isin U | blowastu = b Based onthe current user association results the ABS ratio 120589d of eachmBS d isin B119898 is optimized locally among each mBS d and itslocal sBSs in B119904d = b1015840 isin B119904 | 120596(b1015840) = d For each mBSd isin B119898 to determine the ABS ratio 120589d each mBS d collects

Mathematical Problems in Engineering 3

Globalized CRE bias update

MME

S-GWS11

P-GWS5S8 Packetdata

network

EPC

SGi

S1S1S1

Localized ABS

mBSmBS

S1ratio update

mBS

sBS sBS sBS

휅b훾uΞb

휍bX2 backhaul

Figure 1 Abstract LTE-A HCNmodel

all SNR measurement information via the sBSrsquos message Ξbfrom its local sBSs in B119904d = b1015840 isin B119904 | 120596(b1015840) = d Then themBS optimizes the ABS ratio as well as the ABSNS resourcescheduling for each sBS which is broadcast to each sBS Foruser scheduling eachmBSb isin B119898 can select any users amongthe associated user set Ub only in the NS period while eachsBS b isin B119904 needs to select users among the associated user setUNS

b (or UABSb ) only in the NS period (or the ABS period)

3 Proposed Tessellation-Based Approach forCRE and eICIC Scheme

In this section a practical tessellation-based approach isproposed For this approach the optimal tessellation of agiven system deployment is estimated over a long period andthe cell-specific bias values are determined infrequently toform cell coverage that is as similar to the optimal tessellationas possible in an LTE-A HCN The proposed approachutilizes existing protocols for data collection and bias valuedelivery so that it can be easily adopted in a practical LTE-AsystemThe proposed algorithm consists of the following twosteps (i) based on long-term accumulated user measurementinformation cell-specific bias values are updated by using theproposed tessellation-based approach in the EPC-MME overa long period and are delivered infrequently to small cellsand (ii) the ABS ratio and ABSNS resource scheduling areoptimized locally among each mBS and its associated sBSsonly

31 Optimal Tessellation Each BS can deliver its aperiodicSNR measurement reports from its associated users to theEPC-MME via the S1AP management messages [18] so that

the EPC-MME can observe and store the reported averagedSNR information for many realizations of user locationsThesample SNR realization at time instance 119894 denoted as Γ(119894) =u 120574u | u isin U is collected within each given time periodNote that the location information is already available inmost smartphone devices and it is assumed that each BS canattach the location information of associated users to its SNRmeasurement report

For a given deployment B = B119898 cup B119904 each cell coveragecan be regarded as a tessellation for a given system coverageR which can be written as T = Tb | b isin B isin 120588(R)where Tb denotes the cell coverage for BS b isin B and 120588(R)denotes the collection of all partitions of R Here user u isassumed to be associatedwith BSb ifu isin TbThen for a givendeploymentB and system coverageR the optimal tessellationmay be formulated as

Tlowast (B) = argmaxTisin120588(R)

119864[ sumuisinU(119899)

log119877u (T) | B] (2)

where 119877u(T) denotes the expected user rate of user u fora given tessellation T The expectation is taken over allpossible user realizations and channel realizations Howeverthis expectation is difficult to compute for every candidatetessellation in 120588(R) Thus instead of solving direct opti-mization using (2) Tlowast(B) is estimated from the collectedsamples of the joint user association results as summarizedin Algorithm 1 In this algorithm jointly optimized userassociation results for every SNR realization available at theEPC-MME are obtained and stored For SNR realization Γ(119899)at time instance 119899 the expected user rate in the ABS and NS


(1) Step 0 Initialize N(2) Step 1 For each 119899 isin N solve the following joint UA problem by using Γ(119899)X(119899) 120589b(119899) | b isin B119898

= argmaxX120589b |bisinB119898

sumuisinU(119899)

( sumbisinB119904

sum120591isinABSNS

119909120591ub log 120578120591b119868120591ub(119899)sumu1015840isinU(119899) 119909120591u1015840 b + sumbisinB119898

119909ub log(1 minus 120589b) 119868NS

ub (119899)sumu1015840isinU(119899) 119909u1015840 b

)

st sumuisinU(119899)

( sumbisinB119904

sum120591isinABSNS

119909120591ub + sumbisinB119898

119909ub) = 1119909ub isin [0 1] u isin U(119899) b isin B119898 119909ABS

ub 119909NSub isin [0 1] u isin U(119899) b isin B119904120589b isin [0 1] b isin B119898

where X(119899) = 119909120591ub(119899) | 120591 isin ABSNS u isin U(119899) b isin B119904cup119909ub(119899) | u isin U(119899) b isin B119898(3) Step 2 For each b isin B set

Ub (119899) = u isin U (119899) | 119909ub (119899) ge 119909ub1015840 (119899) for forallb1015840 isin Bwhere 119909ub(119899) = max

120591isinABSNS119909120591ub(119899)

(4) Step 3 Estimate the optimal tessellation asTlowast (B) = Tb = t isin R | 119908 (t b) ge 119908 (t b1015840) for forallb1015840 isin B | b isin B

where 119908(t b) = sumuisinUb(119899)119899isinN 119891(t minus u) for a kernel function 119891(119909) = (1radic2120587120590)119890minus119909221205902 Algorithm 1 Proposed estimation method for optimal tessellation

of user u if associated with BS b 119868120591ub(119899) for 120591 = ABSNS isapproximated as

119868120591ub (119899) = log2 (1 + 119864119878 (b)119864120591119868 (b))

+ ( 1198642119878 (b) + 119881120591119868 (b)(119864119878 (b) + 119864120591119868 (b))2 minus119881120591119868 (b)(119864120591119868 (b))2) log2119890

(3)

where 120578ABSb = 120589120596(b) 120578NSb = 1 minus 120589120596(b) for b isin B119904 119864119878(b) ≜120574ub 119864120591119868(b) ≜ sumb1015840isinBuminusb 120574ub1015840 minus 1120591=ABS120574u120596(b) and 119881120591119868 (b) ≜

sumb1015840isinBuminusb 1205742ub1015840 minus 1120591=ABS1205742u120596(b) Here (3) adopts the Gammadistribution approximation as in [19] with the assumptionthat the total interference power can be approximated as thesum of the average power from interfering BSs Note thatthe optimization problem in Step 1 is not convex but has aspecial structure that lets the problem become convex in Xfor a given 120589b | b isin B119898 and vice versa Thus X and120589b | b isin B119898 can be found by fixing each other and using aconvex programming tool such as CVX [20] iteratively Fromthe relaxed association result X(119899) the set of sample pointsUb(119899) | b isin B for estimating the optimal tessellation isobtained Then from the obtained sample point sets overa long period N the optimal tessellation is estimated as inStep 3 by using a kernel function 119891(119909) Here a Gaussiankernel functionwithmean of 0 and variance of 1205902 = 4 is usedbut other kernel functions can also be applied

32 Suboptimal Tessellation Formed by Using Cell-Specific BiasValues In this subsection based on the estimated optimaltessellation from the previous subsection the cell-specificbias values denoted as 120581 = 120581b | b isin B119904 are determined toform cell coverage that is as similar to the estimated optimaltessellation as possible Here 120581b = 0 for b isin B119898 is assumedDenote the tessellation formed by applying CRE with bias

values in 120581 for a given deployment B as T(120581B) which canbe written as

T (120581B) = Tb (120581B) = t isin R | 10 log10120574tb + 120581bge 10 log10120574tb1015840 + 120581b1015840 for forallb1015840 isin B | b isin B (4)

where 120574tb denotes the SNR information of BSb isin Bmeasuredat t isin RThen the cell-specific bias valuesmay be determinedas

120581lowast = argmax120581

sumbisinB

1003816100381610038161003816Tlowastb (B) cap Tb (120581B)1003816100381610038161003816 (5)

Since the optimal bias value set in (5) is difficult to computedirectly a suboptimal algorithm using the hill-climbingmethod with a random walk [21] is applied which is sum-marized in Algorithm 2 Here the consistency value 120585b(120581119895)defined as the cardinality (area) of the intersection betweenthe cell coverage of BS b in the optimal tessellation and thatformed by applying CRE with bias values in 120581 is utilizedIn each iteration the BS with the lowest consistency valueis selected in Step 2 and the cell-specific bias value of theselected BS is updated in a greedy manner In Step 5 a newbias value set is accepted if it is better than the currently bestbias value set A random neighbor for the next iteration isgenerated in Step 6 After a sufficient number of iterationsthe cell-specific bias values for the suboptimal tessellation aredetermined and then are delivered to the corresponding cells

33 Localized ABS Ratio and Resource Scheduling Optimiza-tion After receiving 120581b each sBS b updates its bias value andbroadcasts it via the SI block mapped on the RRC SI messageover DL-SCH [22] Then each user chooses a serving BS asin (1) by using the biased RSRP information of its neighborsBSs Based on the user association results the ABS ratio 120589dof each mBS d isin B119898 is optimized by each mBS d locally To


(1) Step 0 Initialize 120581119895 = 120581119895b = 0 | b isin B119904 for 119895 = 1 |B119904| 119897 = 0 119897max ge 30 120585best = 0 Δ bias(= 05)(2) Step 1 Set 119895 = 0 and L1 = B119904(3) Step 2 Increase 119895 by 1 and select the sBS with the minimum value by calculating the degree

of consistency for each b isin L119895 120585b(120581119895) = |Tlowastb(B) cap T119895b(120581119895B)| asb = argmin

bisinL119895120585b(120581119895)

(4) Step 3 For b repeat the following process until 120585(120581119895) = sumbisinB 120585b(120581119895) cannot be further maximizedIf an increase in 120581119895

bresults in a better consistency value such that 120585(120581119895

b+) gt 120585(120581119895) set 120581119895 = 120581119895

b+

Otherwise if a decrease in 120581119895bresults in a better consistency value such that 120585(120581119895

bminus) gt 120585(120581119895) set 120581119895

= 120581119895bminus Here 120581119895

b+= 120581119895bbisinB119904b cup 120581119895

b+ Δ bias and 120581119895

bminus= 120581119895bbisinB119904b cup 120581119895

bminus Δ bias

(5) Step 4 If L119895 = 0 set L119895+1 = L119895 minus b and 120581119895+1 = 120581119895 and go back to Step 2(6) Step 5 If 120585(120581|B119904 |) gt 120585best set 120581lowast = 120581|B119904 | and 120585best = 120585(120581|B119904 |)(7) Step 6 If 119897 lt 119897max go back to Step 1 by setting 1205811 = 120576(120581lowast) and increasing 119897 by 1 Otherwise terminate

the algorithm Here 120576(120581) generates a random neighbor around 120581Algorithm 2 Proposed algorithm for determining cell-specific bias values

do that each mBS d isin B119898 collects the SNR measurementinformation Ξb = 120574u | u isin Ub from its neighboring sBSs B119904d

via X2 interfacesThen based on Ξb | b isin B119904d the followingoptimization problem is solved periodically at mBS d

Xlowastd 120589lowastd = argmaxXd120589d

sumbisinB119904d

sumuisinUb

sum120591isinABSNS

119909120591ublog 120589d119868120591ubsumu1015840isinUb119909120591u1015840 b + sum

uisinUd

log(1 minus 120589d) 119868NS

ud1003816100381610038161003816Ud1003816100381610038161003816

st 119909NSub + 119909ABS

ub = 1119909ABSub 119909NS

ub isin [0 1] u isin Ubb isin B119904d120589d isin [0 1]

(6)

where Xd = 119909120591ub | 120591 isin ABSNS u isin Ub b isin B119904d Notethat the above optimization problem is not convex but it hasa special structure that lets the problem become convex inXdfor a given 120589d and vice versa so that Xd and 120589d can be foundby fixing each other and using a convex programming toolsuch as CVX [20] iteratively From the relaxed associationresult Xd UNS

b and UABSb are obtained as UNS

b = u isin Ub |119909NSub ge 119909ABS

ub and UABSb = Ub minus UNS

b respectively Then thedetermined ABS ratio value and user association results aredelivered to the corresponding sBS

For user scheduling each mBS b isin B119898 can select anyusers among the associated user setUb only in the NS periodwhile each sBS b isin B119904 needs to select users among theassociated user set UNS

b (or UABSb ) only in the NS period (or

the ABS period)

4 Simulation Results

For realistic LTE-A HCN deployment scenarios the rural[16] urban [17] and dense (or ultradense) urban [23]

scenarios are assumed In the rural scenario mBSs aredeployed regularly to cover a wide area with a long intersitedistance (ISD) [eg 1732 (m)] [24] and 5ndash30 sBSs permBS are sparsely deployed across the entire macrocell area(excluding locations very close to the macrocells) [25] Forthe urban scenario dense mBSs are deployed irregularlywith a minimum distance from other BSs [eg at least 2 lowast(cell radius) from sBSs] [26] and a single sBS or a few sBSsare deployed to primarily serve as hotspots such as indoorshopping malls or transportation hubs For the dense urbanscenario denser small-cell deployment (eg 10 or more sBSs[27]) for each given localized hotspot region is consideredto support wireless traffic demand more aggressively in suchhotspots

In order to obtain deployment realizations and variousSNR realizations per a given deployment for each scenarioappropriate point process models [28] are used to modelthe locations of mBSs sBSs and users on a given 4000-m times4000-m area according to the statistical characteristics ofeach scenario For the rural scenario since the rural mBS


minus500 0 500minus500

minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS

(a) Optimal tessellation


minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS

(b) Tessellation using cell-specific bias values


minus400

minus300

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0

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200

300

400

500

mBSsBS

(c) Tessellation using common bias


minus400

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minus100

0

100

200

300

400

500

mBSsBS

(d) Tessellation using no bias

Figure 2 Tessellation examples for urban scenario

deployment is quite regular and the sBSs are typically sparseand isolated mBS locations are modeled as typical hexagonalcells Meanwhile sBS locations are modeled by a Maternhardcore process of type 3 with a density of 120582119904 generatedfrom a homogeneous Poisson point process (HPPP) For theurban or dense urban scenario since mBSs are deployedirregularly and sBSs are deployed to serve local hotspots aclustered HCN is considered as in [29] in which a set ofcluster center points C = c1 c2 is modeled by a Maternhardcore process of type 3 with a density of 120582119888 generatedfrom an HPPP with the constraint that each cluster center isnot located within a predetermined distance from any other

cluster center or any mBS In addition sBSs for each clusterc denoted as B119904c are generated from an HPPP with a densityof 120582119904(c) over a circular region of radius 119877119888 centered at cwhich results in B119904 = ⋃cisinC B

119904c The mBS location set B119898 is

also generated by a Matern hardcore process of type 3 with adensity of 120582119898 generated from an HPPP with the constraintthat a macrocell BS is not located within a predetermineddistance from any cluster center To evaluate the performanceof the proposed approach for the rural scenario the ISD forthe hexagonal cell model is set to 1732 (m) and 5 sBSs permBS in average are generated For the urban and the denseurban scenarios 120582119898 = 4 times 10minus6 (mminus2) 120582119888 = 8 times 10minus6 (mminus2)


076078

08082084086

066068

07072074

The c

onsis

tenc

y ra

tio

Proposed schemeCommon bias scheme

Rural Urban Dense urban

Figure 3 Average consistency ratio

Consistent cell

More aggressive intertier offloading

Not consistent cellrange expansion

range expansion

minus150 minus100 minus50 0 50 100 150 200 250 300 350minus550

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mBSsBS

UserUA

mBSsBS

UserUA

mBSsBS

UserUA


minus500

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minus500

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minus50

(a) Joint UA scheme (b) Proposed scheme

(c) Common bias scheme

Figure 4 Typical UA association examples for rural scenario


Consistent cell



range expansion

0 50 100 150 200 250 300 350100

150

200

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300

350

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450

0 50 100 150 200 250 300 350100

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0 50 100 150 200 250 300 350100

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450

sBSUserUA

sBSUserUA

sBSUserUA



Figure 5 Typical UA association examples for urban scenario

119877119888 = 65 (m) the minimum distance between a macrocellBS and a cluster center and that between neighboring clustercenters are set to 15119877119888 and 2119877119888 and 3 and 10 sBSs on averagefor each small-cell cluster are deployed that is 1205871198771198882120582119904(c) =3 and 1205871198771198882120582119904(c) = 10 respectively For user locations inthe rural and urban scenarios the set of user locations isgenerated fromanHPPPwith density of 77times10minus5 (usersm2)and 4 times 10minus4 (usersm2) respectively while in the denseurban scenario the set of user locations is generated from amixture point process Φ119906 cup ⋃cisinC Φ119906c where Φ119906 is an HPPPwith a density of 120582119906 = 4times10minus4 (mminus2) andΦ119906c is anHPPP overthe circular region centered at c with a density of 120582ℎ = 10120582119906In [30] it is shown that a typical hotspot area size follows aWeibull distribution with parameters 120582 = 814 and 119896 = 089for hotspots having more than five times the mean traffic of a

normal area by which a typical mean value of 10 for the userdensity ratio and 119877119888 = 65 (m) corresponding to the upper20 of the area sizes are picked for the simulation setupThe transmit powers of the mBSs and sBSs are set to 46 dBmand 23 dBm respectively the noise power spectral density isset to minus174 dBmHz and the system bandwidth is assumedto be 10MHz In addition 119873RB = 100 and the channel foreach RB between each BS and each user is assumed to bean independent flat Rayleigh fading channel with a path-lossexponent of 120572 = 4 For comparison the centralized jointscheme for UA and ABS ratios [8] denoted as ldquoJointrdquo isconsidered to provide an upper bound on the performance inwhich all information is assumed to be available at the EPC-MME and the joint optimization is performed by consideringthe user locations jointly In addition to the ldquoJointrdquo scheme


Consistent cell range

More flexibleintertier offloading

Higher load in outer sBSs

minus600 minus550 minus500 minus450 minus400 minus350 minus300 minus250minus950

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sBSUserUA



Figure 6 Typical UA association examples for dense urban scenario

a scheme using a common bias value and the maximumRSRP scheme with no bias are also compared They aredenoted as ldquoCommonrdquo and ldquoMAXrdquo respectively Here forthe common bias scheme the common bias value is set toa typical value of 6 dB [31] and the same localized ABSand resource scheduling optimization are applied as in theproposed scheme

In Figure 2 some typical tessellation examples for theurban scenario are illustrated These examples exhibit animproved similarity to the optimal tessellation of the pro-posed scheme over the common and no-bias schemesTo quantify such an improvement achieved by using theproposed scheme the normalized sum consistency value ofsBSs (by the total sBS area in the optimal tessellation) of the

proposed scheme is compared with that of the common biasscheme in the three realistic scenarios as shown in Figure 3From the results it is confirmed that the proposed schemecan provide cell-specific bias values that form a tessellationhighly consistent with the optimal one while conventionalschemes are not sufficiently consistent

In Figures 4ndash6 some typical UA association examplesof the joint UA scheme the proposed scheme and thecommon bias scheme are illustrated for the three scenariosrespectively A comparison among the user association resultscan be summarized as follows (i) compared with the jointUA scheme a similar UA association can be achieved byusing the proposed scheme without considering the userlocations jointly while the UA association obtained by using


015010050Average user rate

0

01

02

03

04

05

06

07

08

09

1

CDF

JointProposedCommonMAX


mBSs

sBSs

Figure 7 User rate distribution according to load-balancing capa-bilities in urban scenario

the common bias scheme deviates significantly especially forsBSs near an mBS as consistently seen in Figures 4ndash6 (ii)although it seems that lightly loaded sBSs not close to anmBS can expand aggressively even by using the common biasscheme in the rural scenario as seen in Figure 4 such lightlyloaded sBSs not close to anmBS begin to fail when expandingtheir ranges successfully in the urban scenario as seen inFigure 5 and (iii) they are barely expanded in the dense urbanscenario as seen in Figure 6 Especially in the dense urbanscenario it is shown that the proposed scheme can providea flexible intratier offloading (between sBSs in a hotspot)as well as an aggressive intertier offloading (from mBSs tosBSs) similar to those achieved in the joint UA scheme whilethe common bias scheme suffers from almost no offloadingbetween sBSs and limited intertier offloading

In Figure 7 the load-balancing capability of the proposedscheme is evaluated and compared with the joint UA andcommon bias schemes for the urban scenario in terms of thecumulative distribution function (CDF) of the user averagerate From the results it is confirmed that the improvedconsistency in the tessellation significantly enhances the userrate distribution Note that the user rate distribution achievedby the load-balancing capability of the proposed scheme issignificantly better than that obtained from the commonbias scheme and is even indistinguishable from that of theoptimal joint UA scheme considering the user locationsjointly

In Figure 8 the average performance gain of the proposedscheme over the common bias scheme in terms of the ratio ofthe bottom 5 10 and 15 average user rates is evaluatedand compared for the three realistic HCN scenarios Thisanalysis shows a significant improvement in network-wideutilization especially as the traffic demand and the corre-sponding deployment become denser

107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()

5 user rate10 user rate15 user rate

Figure 8 Average performance gain of proposed scheme overcommon bias scheme in various HCN scenarios

5 Concluding Remark

In this paper a practical tessellation-based approach foroptimizing cell-specific biases is proposed to improve theperformance of existing LTE-A HCNs In this approach (i)based on long-term accumulated user measurement infor-mation cell-specific bias values are optimized and updatedglobally by the EPC-MME to form a suboptimal tessellationin a long-term manner and are infrequently delivered tosBSs and (ii) the ABS ratio and ABSNS resource schedulingof each mBS and its associated sBSs are determined locallyand independently The proposed scheme does not requiremajor changes to existing protocol and can adopt legacyUEs Thus the scheme is well suited for implementationin existing LTE-A systems From the simulation results inrealistic scenarios it is shown that the proposed scheme isvery efficient in forming cell coverage that is as similar aspossible to the optimal tessellation so that the performancein terms of the user rate distribution is almost identical tothat achievable from an ideal one Thus it is beneficial toemploy the proposed solution in existing LTE-A HCNs forbetter network performance during system updates at lowcost

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education Scienceand Technology (NRF-2014R1A2A2A01007254 and NRF-2015K2A3A1000189) in part and Institute for Informationamp Communications Technology Promotion (IITP) grantfunded by the Korea Government (MSIP) (2014-0-00552


Next Generation WLAN System with High Efficient Perfor-mance) in part

References

[1] R Q Hu Y Qian S Kota and G Giambene ldquoHetnetsmdasha newparadigm for increasing cellular capacity and coveragerdquo IEEEWireless Communications vol 18 no 3 pp 8-9 2011

[2] J G Andrews S Singh Q Ye X Lin and H S Dhillon ldquoAnoverview of load balancing in HetNets old myths and openproblemsrdquo IEEEWireless Communications vol 21 no 2 pp 18ndash25 2014

[3] S Corroy L Falconetti and R Mathar ldquoCell association insmall heterogeneous networks downlink sum rate andmin ratemaximizationrdquo in Proceedings of the IEEE Wireless Communi-cations and Networking Conference WCNC 2012 pp 888ndash892Shanghai China April 2012

[4] H Kim G De Veciana X Yang and M VenkatachalamldquoDistributed-optimal user association and cell load balancingin wireless networksrdquo IEEEACM Transactions on Networkingvol 20 no 1 pp 177ndash190 2012

[5] Y Wang and K I Pedersen ldquoPerformance analysis of enhancedinter-cell interference coordination in LTE-advanced hetero-geneous networksrdquo in Proceedings of the IEEE 75th VehicularTechnology Conference VTC Spring 2012 June 2012

[6] K I Pedersen Y Wang B Soret and F Frederiksen ldquoeICICfunctionality and performance for LTE HetNet co-channeldeploymentsrdquo in Proceedings of the 76th IEEE Vehicular Tech-nology Conference (VTC Fall rsquo12) pp 1ndash5 IEEE Quebec CityCanada September 2012

[7] M Shirakabe A Morimoto and N Miki ldquoPerformanceevaluation of inter-cell interference coordination and cellrange expansion in heterogeneous networks for LTE-Advanceddownlinkrdquo in Proceedings of the 2011 8th International Sympo-sium onWireless Communication Systems ISWCS 2011 pp 844ndash848 Aachen Germany November 2011

[8] Q YeMAl-Shalashy C Caramanis and J GAndrews ldquoOnoffmacrocells and load balancing in heterogeneous cellular net-worksrdquo in Proceedings of the IEEE Global CommunicationsConference GLOBECOM 2013 pp 3814ndash3819 IEEE AtlantaGa USA December 2013

[9] WTang R Zhang Y Liu and S Feng ldquoJoint resource allocationfor eICIC in heterogeneous networksrdquo in Proceedings of the 2014IEEE Global Communications Conference GLOBECOM 2014pp 2011ndash2016 December 2014

[10] S Deb P Monogioudis J Miernik and J P SeymourldquoAlgorithms for enhanced inter-cell interference coordination(eICIC) in LTE HetNetsrdquo IEEEACM Transactions on Network-ing vol 22 no 1 pp 137ndash150 2014

[11] Q Zhang T Yang Y Zhang and Z Feng ldquoFairness guaranteednovel eICIC technology for capacity enhancement in multi-tierheterogeneous cellular networksrdquo EURASIP Journal onWirelessCommunications and Networking vol 2015 no 1 2015

[12] B Soret and K I Pedersen ldquoCentralized and distributedsolutions for fastmuting adaptation in LTE-AdvancedHetNetsrdquoIEEE Transactions on Vehicular Technology vol 64 no 1 pp147ndash158 2015

[13] H Zhang Y Li and Y Li ldquoTraffic-based adaptive resourcemanagement for eICIC and CRE in heterogeneous networksrdquoin Proceedings of the 2013 IEEE 24th International Symposiumon Personal Indoor andMobile Radio Communications PIMRCWorkshops 2013 pp 117ndash121 London UK September 2013

[14] A Tall Z Altman and E Altman ldquoSelf organizing strategiesfor enhanced ICIC (eICIC)rdquo in Proceedings of the 2014 12thInternational Symposium on Modeling and Optimization inMobile Ad Hoc and Wireless Networks WiOpt 2014 pp 318ndash325 Hammamet Tunisia May 2014

[15] 3GPP ldquoEvolved universal terrestrial radio access (e-UTRA) andevolved universal terrestrial radio access network (e-UTRAN)overall description stage 2rdquo TS 36300 version 10110 Release 10September 2013

[16] Small cell forum ldquoSmall cell services in rural and remote envi-ronmentsrdquo version 1570701 pp 1-8 March 2015 httpwwwsmallcellforumorg

[17] Small cell forum ldquoSmall cell services in the urban environmentrdquoversion 0900701 pp 1-7 February 2014 httpwwwsmallcell-forumorg

[18] R Kreher and K Gaenger LTE Signaling Troubleshooting andOptimization Wiley 2010 ISBN 978-0-470-97767-5

[19] R W Heath Jr T Wu Y H Kwon and A C SoongldquoMultiuser MIMO in distributed antenna systems with out-of-cell interferencerdquo IEEE Transactions on Signal Processing vol59 no 10 pp 4885ndash4899 2011

[20] CVX Research Inc httpcvxrcom 2012[21] F Xie H Nakhost andM Muller ldquoPlanning via random walk-

driven local searchrdquo in Proceedings of the 22nd InternationalConference on Automated Planning and Scheduling ICAPS 2012pp 315ndash322 June 2012

[22] 3GPP ldquo3rd generation partnership project technical specifi-cation group GSMEDGE radio access network mobile radiointerface layer 3 specification radio resource control (RRC)protocolrdquo TS 44018 version 8100 Release 8 March 2010

[23] Ultra dense network (UDN) ldquoUltra dense network (UDN)rdquoWhite Paper pp 1ndash26 2016 httpresourcesalcatel-lucentcomasset200295

[24] 3GPP ldquoLTE evolved universal terrestrial radio access (E-UTRA) radio frequency (RF) system scenariosrdquo TR 36942version 1020 Release 10 2011

[25] Real Wireless An Assessment of the Value of Small Cell Servicesto Operators Virgin Media Version 31 2012

[26] J G Andrews F Baccelli and R K Ganti ldquoA tractable approachto coverage and rate in cellular networksrdquo IEEE Transactions onCommunications vol 59 no 11 pp 3122ndash3134 2011

[27] V Fernandez-Lopez K I Pedersen and B Soret ldquoEffects ofinterference mitigation and scheduling on dense small cellnetworksrdquo in Proceedings of the 80th IEEE Vehicular TechnologyConference VTC 2014-Fall can September 2014

[28] S N Chiu D Stoyan W S Kendall and J Mecke StochasticGeometry And Its Applications Wiley Series in Probability andStatistics JohnWiley amp Sons Ltd Chichester 3rd edition 2013ISBN 978-0-470-66481-0

[29] T Nakamura S Nagata A Benjebbour et al ldquoTrends in smallcell enhancements in LTE advancedrdquo IEEE CommunicationsMagazine vol 51 no 2 pp 98ndash105 2013

[30] H Klessig V Suryaprakash O Blume A Fehske and GFettweis ldquoA framework enabling spatial analysis of mobiletraffic hot spotsrdquo IEEE Wireless Communications Letters vol 3no 5 pp 537ndash540 2014

[31] 3GPP ldquo3rd generation partnership project Technical specifica-tion group radio access network Evolved universal terrestrialradio access (e-UTRA) Mobility enhancements in heteroge-neous networksrdquo TR 36839 version 1100 Release 11 September2012

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Journal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


resource scheduling is studied and a distributed algorithmis developedThe algorithm shows improvement in network-wide resource utilization However in order to implementsuch a joint approach in an existing network architectureexisting network elements should be updated and legacy UEsneed to bemodified or even replaced to support this new userassociation process In the current LTE-A user associationcan adopt the CRE method by using a bias value [15] wherea positive bias is assigned to each cell and each user isassociated with the cell of the maximum biased referencesignal received power (RSRP) In order to determine a properbias value and ABS ratio a global optimization methodusing cell-specific bias values [10] or a common bias value[11] for small-cell CRE has been studied In this method acentralized approach is considered where the CRE bias valuesand ABS ratios are determined at a central entity [eg theenhanced packet core- (EPC-) mobility management entity(MME)] to provide good performance Although they maybe compatible with legacy UEs a large amount of overhead iscaused by frequent signal exchanges for updating each userrsquosSNR or each BS information These events are necessary toestimate user rates and an overall update to the BSs and thecore network is also required As an efficient implementationin an existing network a local optimization of ABS ratiosbased on a given common CRE bias value has been alsostudied [12ndash14] In this optimization simple centralized ordistributed algorithms for determining eICIC ABS ratiosbased on a given common CRE bias value are proposedby comparing local load situations in each macrocell andneighboring small cells Although this approach can beapplied to legacy UEs and requires only a partial update tothe BSs and the core network its performance is limitedmainly owing to the use of a common CRE bias value evenwithout any optimization Thus in order to achieve moresuccessful load balancing in existing LTE-A networks a moreefficient method for determining cell-specific bias valuesand ABS ratios needs to be developed This method shouldbe implemented without major changes to existing cellularnetworks

In this paper a practical tessellation-based approachis proposed to maximize the network-wide proportionalfairness (PF) among users in LTE-A HCNs In these HCNscell-specific bias values are determined to form a suboptimaltessellation similar to an optimal tessellation that may beobtained from a joint optimization for the CRE bias valuesand ABS ratios The proposed scheme does not require anymajor modifications to existing protocols and thus can beeasily applicable to practical LTE-A systems The proposedalgorithm consists of the following two steps (i) based onthe long-term accumulated user measurement informationcell-specific bias values are optimized and updated globallyby the EPC-MME in a long-term manner and are deliveredinfrequently to small cells and (ii) the ABS ratio andABSNS resource scheduling are optimized locally amongeach mBS and its associated sBSs only It is shown that theproposed scheme can be easily realized in practical LTE-A systems without modifying any existing protocols whileachieving a good load-balancing performance comparedwithconventional methods The rest of this paper is organized

as follows In Section 2 an abstract system model for anLTE-AHCN is provided and the proposed tessellation-basedapproach for efficient load balancing in an existing LTE-AHCN is described in Section 3 In Section 4 simulation resultsfor various realistic scenarios and corresponding discussionsare provided and concluding remarks are given in Section 5

2 The System Model

Consider a downlink two-tier HCN in which macrocells areoverlaid with small cells using a lower transmit power Thetransmit powers of an mBS and an sBS are denoted as 119875119898and 119875119904 respectively In addition the set of user locationsthe set of mBS locations and the set of sBS locations aredenoted as U = u1 u2 B119898 = b1198981 b1198982 andB119904 = b1199041 b1199042 respectively Here each sBS location canbe configured for different small-cell service scenarios Forexample in rural environments sBSs can be deployed in ruralcommunities and remote industries [16] For urban (denseurban) environments sBSs can be deployed to support cityhot zones or transportation hubs (eg airports or railwaystations) [17]

The LTE-A core network architecture is abstracted asshown in Figure 1 The sBSs are connected via X2 to thenearest mBS Here the nearest mBS for sBS b isin B119904 is denotedas 120596(b) In addition each mBS or sBS is connected via S1 toan EPC composed of theMME the serving gateway (S-GW)and the packet data network gateway (P-GW) In additionthe LTE-A air interface is abstracted so that each subframe of1ms intervals consists of 119873RB multiple resource blocks (RBs)that are divided into ABSs and normal subframes (NSs) Foran ABS interference from the nearest mBS is almost mutedso that the signal quality of small-cell users in the range-expanded regions can be greatly improved

Globally the EPC-MME determines a set of bias valuesfor sBSs denoted as 120581 = 120581b | b isin B119904 These values arebased on long-term accumulated SNR measurement reportsfromusers where 120581b denotes the bias value for sBS b which isupdated infrequently and delivered to each mBS or sBS Eachuser obtains bias information for neighbor sBSs via a systeminformation (SI) block mapped on the radio resource control(RRC) SI message over the downlink shared channel (DL-SCH) After receiving the bias values of its neighbor sBSseach user chooses its serving BS based on the biased RSRPinformation as

blowastu = argmaxbisinBu

10 log10120574ub + 120581b (1)

where 120574ub denotes the averaged received signal-to-noisepower ratio (SNR) between BS b and user u and reports itsmeasurement 120574u = 120574ub | b isin Bu and Bu sub B119898 cup B119904 denotesa neighbor BS list for user u to the selected BS Note that (1)becomes conventional cell selection with a maximum RSRPwhen 120581b = 0 forb isin B119898cupB119904 Here denote the set of associatedusers as b isin B119898 cup B119904 as Ub = u isin U | blowastu = b Based onthe current user association results the ABS ratio 120589d of eachmBS d isin B119898 is optimized locally among each mBS d and itslocal sBSs in B119904d = b1015840 isin B119904 | 120596(b1015840) = d For each mBSd isin B119898 to determine the ABS ratio 120589d each mBS d collects



MME

S-GWS11

P-GWS5S8 Packetdata

network

EPC

SGi

S1S1S1

Localized ABS

mBSmBS

S1ratio update

mBS

sBS sBS sBS

휅b훾uΞb

휍bX2 backhaul










119864[ sumuisinU(119899)

log119877u (T) | B] (2)





sumuisinU(119899)

( sumbisinB119904

sum120591isinABSNS


119909ub log(1 minus 120589b) 119868NS

ub (119899)sumu1015840isinU(119899) 119909u1015840 b

)


( sumbisinB119904

sum120591isinABSNS

119909120591ub + sumbisinB119898





120591isinABSNS119909120591ub(119899)




119868120591ub (119899) = log2 (1 + 119864119878 (b)119864120591119868 (b))

+ ( 1198642119878 (b) + 119881120591119868 (b)(119864119878 (b) + 119864120591119868 (b))2 minus119881120591119868 (b)(119864120591119868 (b))2) log2119890

(3)








sumbisinB







bisinL119895120585b(120581119895)



b+) gt 120585(120581119895) set 120581119895 = 120581119895

b+


bminus) gt 120585(120581119895) set 120581119895

= 120581119895bminus Here 120581119895

b+= 120581119895bbisinB119904b cup 120581119895

b+ Δ bias and 120581119895


bminus Δ bias






sumbisinB119904d

sumuisinUb

sum120591isinABSNS


uisinUd

log(1 minus 120589d) 119868NS

ud1003816100381610038161003816Ud1003816100381610038161003816

st 119909NSub + 119909ABS

ub = 1119909ABSub 119909NS


(6)








the ABS period)







minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS








076078

08082084086

066068

07072074

The c

onsis

tenc

y ra

tio




Consistent cell



range expansion


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

mBSsBS

UserUA

mBSsBS

UserUA

mBSsBS

UserUA


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50





Consistent cell



range expansion

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

sBSUserUA

sBSUserUA

sBSUserUA











minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600

sBSUserUA

sBSUserUA

sBSUserUA










0

01

02

03

04

05

06

07

08

09

1

CDF



mBSs

sBSs





107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()



5 Concluding Remark




Acknowledgments




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






MME

S-GWS11

P-GWS5S8 Packetdata

network

EPC

SGi

S1S1S1

Localized ABS

mBSmBS

S1ratio update

mBS

sBS sBS sBS

휅b훾uΞb

휍bX2 backhaul










119864[ sumuisinU(119899)

log119877u (T) | B] (2)





sumuisinU(119899)

( sumbisinB119904

sum120591isinABSNS


119909ub log(1 minus 120589b) 119868NS

ub (119899)sumu1015840isinU(119899) 119909u1015840 b

)


( sumbisinB119904

sum120591isinABSNS

119909120591ub + sumbisinB119898





120591isinABSNS119909120591ub(119899)




119868120591ub (119899) = log2 (1 + 119864119878 (b)119864120591119868 (b))

+ ( 1198642119878 (b) + 119881120591119868 (b)(119864119878 (b) + 119864120591119868 (b))2 minus119881120591119868 (b)(119864120591119868 (b))2) log2119890

(3)








sumbisinB







bisinL119895120585b(120581119895)



b+) gt 120585(120581119895) set 120581119895 = 120581119895

b+


bminus) gt 120585(120581119895) set 120581119895

= 120581119895bminus Here 120581119895

b+= 120581119895bbisinB119904b cup 120581119895

b+ Δ bias and 120581119895


bminus Δ bias






sumbisinB119904d

sumuisinUb

sum120591isinABSNS


uisinUd

log(1 minus 120589d) 119868NS

ud1003816100381610038161003816Ud1003816100381610038161003816

st 119909NSub + 119909ABS

ub = 1119909ABSub 119909NS


(6)








the ABS period)







minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS








076078

08082084086

066068

07072074

The c

onsis

tenc

y ra

tio




Consistent cell



range expansion


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

mBSsBS

UserUA

mBSsBS

UserUA

mBSsBS

UserUA


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50





Consistent cell



range expansion

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

sBSUserUA

sBSUserUA

sBSUserUA











minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600

sBSUserUA

sBSUserUA

sBSUserUA










0

01

02

03

04

05

06

07

08

09

1

CDF



mBSs

sBSs





107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()



5 Concluding Remark




Acknowledgments




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







sumuisinU(119899)

( sumbisinB119904

sum120591isinABSNS


119909ub log(1 minus 120589b) 119868NS

ub (119899)sumu1015840isinU(119899) 119909u1015840 b

)


( sumbisinB119904

sum120591isinABSNS

119909120591ub + sumbisinB119898





120591isinABSNS119909120591ub(119899)




119868120591ub (119899) = log2 (1 + 119864119878 (b)119864120591119868 (b))

+ ( 1198642119878 (b) + 119881120591119868 (b)(119864119878 (b) + 119864120591119868 (b))2 minus119881120591119868 (b)(119864120591119868 (b))2) log2119890

(3)








sumbisinB







bisinL119895120585b(120581119895)



b+) gt 120585(120581119895) set 120581119895 = 120581119895

b+


bminus) gt 120585(120581119895) set 120581119895

= 120581119895bminus Here 120581119895

b+= 120581119895bbisinB119904b cup 120581119895

b+ Δ bias and 120581119895


bminus Δ bias






sumbisinB119904d

sumuisinUb

sum120591isinABSNS


uisinUd

log(1 minus 120589d) 119868NS

ud1003816100381610038161003816Ud1003816100381610038161003816

st 119909NSub + 119909ABS

ub = 1119909ABSub 119909NS


(6)








the ABS period)







minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS








076078

08082084086

066068

07072074

The c

onsis

tenc

y ra

tio




Consistent cell



range expansion


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

mBSsBS

UserUA

mBSsBS

UserUA

mBSsBS

UserUA


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50





Consistent cell



range expansion

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

sBSUserUA

sBSUserUA

sBSUserUA











minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600

sBSUserUA

sBSUserUA

sBSUserUA










0

01

02

03

04

05

06

07

08

09

1

CDF



mBSs

sBSs





107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()



5 Concluding Remark




Acknowledgments




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







bisinL119895120585b(120581119895)



b+) gt 120585(120581119895) set 120581119895 = 120581119895

b+


bminus) gt 120585(120581119895) set 120581119895

= 120581119895bminus Here 120581119895

b+= 120581119895bbisinB119904b cup 120581119895

b+ Δ bias and 120581119895


bminus Δ bias






sumbisinB119904d

sumuisinUb

sum120591isinABSNS


uisinUd

log(1 minus 120589d) 119868NS

ud1003816100381610038161003816Ud1003816100381610038161003816

st 119909NSub + 119909ABS

ub = 1119909ABSub 119909NS


(6)








the ABS period)







minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS








076078

08082084086

066068

07072074

The c

onsis

tenc

y ra

tio




Consistent cell



range expansion


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

mBSsBS

UserUA

mBSsBS

UserUA

mBSsBS

UserUA


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50





Consistent cell



range expansion

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

sBSUserUA

sBSUserUA

sBSUserUA











minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600

sBSUserUA

sBSUserUA

sBSUserUA










0

01

02

03

04

05

06

07

08

09

1

CDF



mBSs

sBSs





107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()



5 Concluding Remark




Acknowledgments




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS



minus400

minus300

minus200

minus100

0

100

200

300

400

500

mBSsBS








076078

08082084086

066068

07072074

The c

onsis

tenc

y ra

tio




Consistent cell



range expansion


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

mBSsBS

UserUA

mBSsBS

UserUA

mBSsBS

UserUA


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50





Consistent cell



range expansion

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

sBSUserUA

sBSUserUA

sBSUserUA











minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600

sBSUserUA

sBSUserUA

sBSUserUA










0

01

02

03

04

05

06

07

08

09

1

CDF



mBSs

sBSs





107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()



5 Concluding Remark




Acknowledgments




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





076078

08082084086

066068

07072074

The c

onsis

tenc

y ra

tio




Consistent cell



range expansion


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

mBSsBS

UserUA

mBSsBS

UserUA

mBSsBS

UserUA


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50


minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50





Consistent cell



range expansion

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

sBSUserUA

sBSUserUA

sBSUserUA











minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600

sBSUserUA

sBSUserUA

sBSUserUA










0

01

02

03

04

05

06

07

08

09

1

CDF



mBSs

sBSs





107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()



5 Concluding Remark




Acknowledgments




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Consistent cell



range expansion

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350100

150

200

250

300

350

400

450

sBSUserUA

sBSUserUA

sBSUserUA











minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600

sBSUserUA

sBSUserUA

sBSUserUA










0

01

02

03

04

05

06

07

08

09

1

CDF



mBSs

sBSs





107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()



5 Concluding Remark




Acknowledgments




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of









minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600


minus900

minus850

minus800

minus750

minus700

minus650

minus600

sBSUserUA

sBSUserUA

sBSUserUA










0

01

02

03

04

05

06

07

08

09

1

CDF



mBSs

sBSs





107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()



5 Concluding Remark




Acknowledgments




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






0

01

02

03

04

05

06

07

08

09

1

CDF



mBSs

sBSs





107

108

109

110

111

104

105

106


Aver

age p

erfo

rman

ce g

ain

()



5 Concluding Remark




Acknowledgments




References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Documents

A Practical Tessellation-Based Approach for Optimizing ...downloads.hindawi.com/journals/mpe/2017/4764103.pdfA Practical Tessellation-Based Approach for Optimizing Cell-Specific Bias