Interference Minimization in 5G Heterogeneous Networks

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by  Tao Han

Noname manuscript No.
(will be inserted by the editor)
Interference Minimization in 5G Heterogeneous Networks
Tao Han · Guoqiang Mao · Qiang Li · Lijun Wang · Jing Zhang
7
1
0 Accepted by Mobile Networks and Applications. The final publication is available at Springer via
2 http://dx.doi.org/10.1007/s11036-014-0564-1.

n
a Abstract In this paper, we focus on one of the repre- ation scheme is able to significantly reduce the down-
J
sentative 5G network scenarios, namely multi-tier het- link interference comparedwith existing schemes while
1
erogeneous cellular networks.User associationis inves- maintaining a reasonably good QoS.

] tigated in order to reduce the down-link co-channelin-
T Keywords Heterogeneous cellular networks · user
terference. Firstly, in order to analyze the multi-tier
I association · performance analysis model · interference
. heterogeneouscellularnetworkswherethebasestations
s management
c in different tiers usually adopt different transmission
[ powers, we propose a Transmission Power Normaliza-

tion Model (TPNM), which is able to convert a multi-
1 1 Introduction
v tier cellular network into a single-tier network, such
2 that all base stations have the same normalized trans-
A heterogeneous cellular network (HCN) usually con-
0
mission power. Then using TPNM, the signal and in-
2 sists of multiple tiers including a macrocell tier and
terference received at any point in the complex multi-
0 probablysomesmallcelltiers,e.g.,picocelltier,femto-
0 tier environment can be analyzed by considering the
cell tier and so on [1]. In general, there are three chan-
. same point in the equivalent single-tier cellular net-
1 nel allocation strategies among tiers, namely orthogo-
0 work model, thus significantly simplifying the analy-
nal deployment, co-channel deployment, and partially
7 sis. On this basis, we propose a new user association
shareddeployment[3].Inordertoimprovethespectral
1
scheme in heterogeneous cellular networks, where the
: efficiency to match the ever growing demand for high
v base station that leads to the smallest interference to
data rate nowadaysand future, co-channeldeployment
i
X other co-channel mobile stations is chosen from a set amongtiersandspatialfrequencyreuse arewidely em-
of candidate base stations that satisfy the quality-of-
r ployed in HCNs. In the small cell tier, since base sta-
a service(QoS)constraintforanintendedmobilestation.
tions(BSs)areoftendeployedinanunplannedmanner,
Numerical results show that the proposed user associ-
itcausesmoreseriousco-channelinterferenceinhetero-
geneous networks than that in conventional single-tier
TaoHan·QiangLi(Corresponding author) ·JingZhang
cellular networks. In view of the severe co-channel in-
SchoolofElectronicInformationandCommunications,Huazhong
UniversityofScienceandTechnology, China terferenceunderbothintra-tierandinter-tiersituations
E-mail:{hantao, qli_patrick,zhangjing}@hust.edu.cn [12], interference management is very important in a
GuoqiangMao HCN [7].
School of Computing and Communications, University of Tech- User association, also called cell association or BS
nologySydney, Australia
association,is one of the important approaches to per-
NationalICTAustralia(NICTA),Australia
forming interference managementas wellas to improv-
E-mail:[email protected]
ing the spectral efficiency and energy efficiency [13].
LijunWang
Fooladivandaet al.proposedaunifiedstaticframework
DepartmentofInformationScienceandTechnology,WenhuaCol-
lege,China to study the interplaybetween user associationandre-
E-mail:[email protected] sourceallocationinHCNs[3].Ghimireetal.formulated
2 TaoHanetal.
aflow-basedframeworkforthejointoptimizationofre- user association scheme to minimize the down-link co-
source allocation, transmission coordination, and user channel interference in section 4. Section 5 shows the
association in a heterogeneous network comprising of numerical results for the performance of the proposed
a macro BS and a number of pico BSs and/or relay user association scheme. In section 6, we conclude the
nodes [5], where the performance of different combina- paper.
tions of resource allocation schemes and transmission
coordination mechanisms was characterized. Jin et al.
proposed a marginal utility based user association al-
gorithm to transform the combinatorial optimization 2 System model
problemintoanetwork-wideutilitymaximizationprob-
lem [8]. Jo et al. developed a tractable framework for Weconsideraheterogeneouscellularmulti-tiernetwork
signal-to-interference-plus-noise ratio (SINR) analysis thatiscomposedofK-tiernetworkswhereK ∈Nwith
indownlinkHCNswithflexible cellassociationpolicies only a single BS located winthin eachcell of the multi-
[6].Madanetal.describednewparadigmsforthedesign tier networks. The transmission powers at the BSs of
and operation of HCNs, where cell splitting, cell range the k-th tier network are assumed to be equal and de-
expansion, semi-static resource negotiation on third- noted as Pk. We assume that the distribution of the
party backhaulconnections, and fast dynamic interfer- BSs in the k-th tier network follows a homogeneous
ence managementfor quality-of-service(QoS)viaover- Poisson point process ΦBS with intensity λBS. Assum-
k k
the-air signaling were investigated [10]. ing that the multiple cells of different tiers are over-
In HCNs, an active mobile station (MS) needs to laid in the same area geographically, then the distri-
associate itself with a particular cell, which belongs to bution of the BSs in multi-tier HCNs is governed by a
one of the tiers in a multi-tier network. Convention- Poisson point process ΦBS = Kk=1ΦBkS with intensity
ally, a MS is associated with the nearest BS or the BS λBS = K λBS.
k=1 k S
thatprovidesthehighestreceivedSINR.However,these Furthermore, we assume that the distribution of
P
MSassociationschemesdonotconsiderthepossibleco- active MSs which are associated with the BSs in the
channel interference caused to other active MSs. Moti- k-th tier network follows a homogeneous Poisson pro-
vated by this, in this paper using stochastic geometry cess ΦMS of intensity λMS. Thus the distribution of all
k k
methods [2], we propose a MS association scheme in MSs in multi-tier HCNs is also governed by a Poisson
multi-tier networks that is able to significantly reduce point process ΦMS = K ΦMS with intensity λMS =
k=1 k
the down-link co-channel interference while guarantee- K λMS.
k=1 k S
ing a predefined QoS of mobile users in HCNs with
This paper focuses on the down-links in multi-tier
P
open-access small cell. Consider the interference in up-
HCNs, where all BSs reuse the same frequency that is
link is not alwaysminimized when we minimize the in-
dividedintoorthogonalchannels.ABSallocatesdiffer-
terferenceindown-linkbyauserassociationscheme,we
entorthogonalchannelstotheMSsinacell.Undersuch
will not investigate the issue on interference in up-link
circumstances, there is no intra-cell interference. How-
in this paper. The contributions of this paper are:
ever,due to the frequency reuse acrosscells,there may
exist severe inter-cell co-channel interference in multi-
1. ATransmissionPowerNormalizationModel(TPNM)
tier HCNs if the same sub-channel is occupied in dif-
foranalyzingtheperformanceofmulti-tierHCNsis
ferentcells[11].Forexample,giventhattheBSsassign
proposed, which significantly simplifies the analysis
the channels randomly and independently, at a partic-
of the performance of multi-tier HCNs.
ular time instant, only a fraction of the BSs, denoted
2. Based on TPNM, a new user association scheme is
byPoissonpointprocessΦN_BS ofintensityλN_BS,are
proposed to minimize the down-link co-channel in-
using a specific channel C simultaneously to transmit
terference, which can be used in both conventional n
to the corresponding MSs, denoted by Poisson point
single-tier cellular networks and multi-tier HCNs.
processΦN_MS ofintensityλN_MS =λN_BS,wherethe
3. Extensivesimulationsareconducted,theresultsdemon-
BSs in ΦN_BS and the MSs in ΦN_MS are communica-
stratethattheproposedschemecansignificantlyre-
tion pairs.
ducethedown-linkinterferenceundertheconstraint
AssumingBSsassigndown-linkchannelstotheMSs
that predefined QoS requirements are satisfied.
associatedwiththemrandomly,thentheMSsusingthe
The rest of the paper is organized as follows. Section same channel C , i.e. ΦN_MS, can be consideredto fol-
n
2 describes the system model. Section 3 introduces the lowahomogeneousPoissonpointprocess[15],whichis
proposedTPNM for performance analysis in multi-tier thinnedfrompointprocessΦMS.ThenwedefineΦN_MS
HCNs. Based on TPNM, we proceed to propose a new asaninterferingset,inwhichMSsareinterferedbythe
Interference Minimizationin5GHeterogeneous Networks 3
BSs that are transmitting to other MSs in the set be-
cause they use the same channel C .
n
For ease of exposition, only path loss effect is con- BS x21 BS x2'1 BS x3'1
sidered in the wireless channel models. Without loss of BS x
31
generality, we consider a given BS x and a desired MS
y. Then the desired signal power Pxy received at y is BS x11MS yBS x BS x1'1 BMSS x y'
expressed as 22 22
P =P l(x−y), (1)
xy x
(cid:37)(cid:54)(cid:3)(cid:76)(cid:81)(cid:3)(cid:55)(cid:76)(cid:72)(cid:85)(cid:3)(cid:20) (cid:37)(cid:54)(cid:3)(cid:76)(cid:81)(cid:3)(cid:55)(cid:76)(cid:72)(cid:85)(cid:3)(cid:22)
whereP denotesthetransmissionpoweroftheBSand
x (cid:37)(cid:54)(cid:3)(cid:76)(cid:81)(cid:3)(cid:55)(cid:76)(cid:72)(cid:85)(cid:3)(cid:21) (cid:48)(cid:54)
l(·)=k·k−α denotes the path loss in wireless channels
Fig. 1 ByTPNM,eachtier isscaledbyusingthelocation ofa
where α is the path loss exponent.
specificMSy asthescalingcenter.
In this paper, we focus on the interference-limited
scenario. When a MS y is associated with a BS x, the
signal-to-interference ratio (SIR) at y is given as In order to analyze the multi-tier HCN, we pro-
pose a TPNM in this paper, which is able to convert a
Pxy Pxl(x−y) multi-tier HCN to a virtual single-tier cellular network
SIR(x,y)= = , (2)
I P l(x −y) by first scaling each tier according to its correspond-
y xi∈ΦN_BS\{x} xi i
ing transmission power and path-loss effect, and then
P
whereIy denotestheinterferencereceivedfromtheBSs combining the different tiers into a single-tier cellular
in ΦN_BS except xi. network, such that all BSs have the same normalized
In view of the severe co-channel interference, we transmission power and the signal power and interfer-
consider a user association scheme where the MS y ∈ ence received at a specific MS from the BSs in the vir-
ΦN_MS chooses a BS x ∈ ΦBS to associate with, and tualsingle-tiercellularnetworkareexactlythe sameas
at the same time the interference from x to other MSs those received from the BSs in the original multi-tier
ΦN_MS\{y} is minimized. cellular network.
In order to minimize the interference caused by the Asanexample,considera3-tierHCNshowninFig.
chosen BS x to other co-channel MSs, for ease of anal- 1.ThereareBSsinvarioustiersincludingBSx intier
11
ysis, we consider a MS z ∈ ΦN_MS\{y} that receives 1, BS x and x in tier 2, and BS x in tier 3, with
21 22 31
the most severe interference Ixz from BS x [9]. Then differenttransmissionpowers.MSyreceivesthedesired
the minimization ofthe interference seenat z probably signalfromtheassociatedBSandinterferencefromthe
implies a minimization of the co-channel interference. other BSs. For ease of analysis, we set the location of
Ontheotherhand,tosatisfyareasonableQoScon- the MS y as the origin and scale each tier by using
straint,itisassumedthatthedistancebetweenthespe- differentfactorssuchthatvirtualBSsx′ ,x′ ,x′ and
11 21 22
cific MS y and the corresponding BS x ∈ ΦBS should x′ with the same normalized power 1 are obtained,
31
be no more than the distance between y and any BS and the received signal/interference powers at y from
∀xi ∈ΦN_BStransmittinginthesamechannel.Inother thesevirtualBSsareexactlythesameasthosereceived
words,weintendtochooseasuitableBSforysuchthat fromthe originalBSs, e.g., the powerreceivedat MS y
theco-channelinterferencecausedtootherMSsismin- from BS x before scaling is exactly the same as that
11
imized,undertheconstrainttheQoSoftheMSyissat- from virtual BS x′ after scaling.
11
isfied. If in ΦBS there is no BS satisfies this constraint, InaK-tierHCN,theBSsintierk, k ∈{1,2,...,K},
then MS y will try to search another channel. have transmissionpower P and follow a Poissonpoint
k
process ΦBS of intensity λBS. Without loss of general-
k k
ity, we consider a MS y located at origin o, then the
3 TPNM of HCN receivedsignalpowerP at MS y from a BS x∈Φ is
xy k
given as
3.1 Definition of TPNM
−1 −α
P = P l(x−o)=P l(x)=1· P α kxk
xy k k k
Differentfromsingle-tierhomogeneouscellularnetworks
wherealltheBSstransmitsignalusingthesamepower, = 1· P−α1 ·x −α =1·l P−(cid:16)α1 ·x , (cid:17) (3)
k k
in multi-tier HCNs, the BSs of different tiers have dif-
(cid:13) (cid:13) (cid:16) (cid:17)
ferent transmission powers and follow different distri- where1is(cid:13)thenorm(cid:13)alizedtransmissionpowerandl(x−
(cid:13) (cid:13)
butions geographically. o) is the path loss function from x to y.
4 TaoHanetal.
From Eq. (3), it is observed that the signal power ThenthesignalpowerreceivedatMSy,i.e.,P =
xky
received at y from x is equal to that received from a P R−α, has the following PDF
k k
virtualBSx′ =P−α1 ·x withtransmissionpower1and
k 1 ′
plorcoacteesds aΦtBkSPk−caα1n·bxe. sFcoallleodwitnogathpiso,inttheprPooceissssonΦkBpSo′in=t fPxky(pxky) =fRk(rk)·(cid:12)(cid:12) (cid:18)pPxkky(cid:19)α!(cid:12)(cid:12)
2 (cid:12) (cid:12)
iPnk−wα1hi·cΦhBkaSllotfhientveinrtsuitaylBλBkSSs′h=av(cid:18)epthk−1eα1s(cid:19)amλeBktSra=nsPmkα2isλsBkioSn, = 2απpλxBkkyS (cid:18)P(cid:12)(cid:12)(cid:12)Pxkky(cid:19)α2 e−πλBkS(cid:16)(cid:12)(cid:12)(cid:12)pxPkky(cid:17)α2. (8)
(poorwienrte1rfearnedncperpodowuceer)tahtetshaemMeSreyceaisvethdesoigrnigailnaploBwSesr Defining Dxky , Px−kαy1 = Pk−α1Rk, we obtain the
PDF of D as follow:
in ΦBS. xky
k
Fromtheaboveanalysis,wescalethe Poissonpoint f (d )=f (P )· d−α ′
processesinall K tiersto normalizethe BSs’transmis- Dxky xky Pxky xky xky
Psiooinsspoonwpeorisnttop1r,ocaensds then combine them into a single =2πλBkSPkα2dxky(cid:12)(cid:12)(cid:12)(cid:0)·e−πλ(cid:1)BkS(cid:12)(cid:12)(cid:12)Pkα2d2xky, (9)
andthecorrespondingcumulativedistributionfunction
K
ΦBS′ = P−α1 ·ΦBS, (4) (CDF) is derived as
k k
k[=1 dxky
F (d )= f (d ) dd
which is of intensity λBS′ = K Pα2λBS. Dxky xky ˆ−∞ Dxky xky xky
k=1 k k
2
P =1−e−πλBkSPkαd2xky. (10)
3.2 Received signal power based on TPNM The BS that MS y is associated with should have
thelargestP ,soitshouldhavethe smallestD as
In this section, we give an example to demonstrate the xky xky
well.Denote the smallestD by D , andthe largest
advantage of using TPNM by considering analysis of xky xy
P by P , we obtain
cell association where a MS always associate with the xky xy
BS delivering the highest received signal strength. We Pxy =k∈{1m,2a,.x..,K}Pxky, (11)
first analyze the case without TPNM, then we present
the analysis by using TPNM. and
D = min D . (12)
3.2.1 The received signal power without TPNM xy k∈{1,2,...,K} xky
Since random variables D , k ∈ {1,2,...,K} are
ConsideraspecificreceivingMS y,withoutlossofgen- xky
erality, we place it at the origin o ∈ R2. Then the BS mutually independent, then the CDF of Dxy can be
derived as
x=argxmi∈aΦxBSPxikxik−α, (5) FDxy(dxy)=1− K 1− 1−e−πλBkSPkα2d2xky
whichcanproduce the highestreceivedsignalpowerat k=1(cid:18) (cid:18) (cid:19)(cid:19)
Y
y, isAssesluemctiendgttohearsesoacrieaKte wtieitrhsiyn.thenetworkwithcor- =1−e−πd2xkyPKk=1λBkSPkα2, (13)
responding transmission power Pk,k ∈ {1,2,...,K}, and the PDF of Dxy can be derived as
we find the nearestBS x from each tier ΦBS to y, i.e.,
k k
K 2
xk =argxkmj∈iΦnBkSkxkjk. (6) fDxy(dxy)=(2π)d2xyk=1λBkSPkα2 ·e−πd2xkyPKk=1λBkSPkα.
X
According to Slivnyak theorem [14], ΦBS∪{o} has the (14)
k
same properties as the Poisson point process ΦBS, so
k −1
the distance R , kx −yk = kx −ok = kx k be- Because Dxy =Pxyα, we have
k k k k
tween BS xk and MS y satisfies the following probabil- −1
ity density function (PDF) FPxy(Pxy)=FDxy Pxyα
(cid:16) −2(cid:17) 2
fRk(rk)=2πλBkSrk·e−λBkSπrk2. (7) =1−e−πPxyα PKk=1λBkSPkα. (15)
Interference Minimizationin5GHeterogeneous Networks 5
3.2.2 The received signal power with TPNM
−1 fRxkzk (rxkzk)=2πλN_MSrxkzk ·e−πλN_MSrx2kzk. (22)
By using TPNM, we scale each tier with factor Pk α, Accordingto (18), we considerthe probabilitythat the
and then combine them to a virtual Poissonpoint pro- BS x, which is serving MS y, belongs to the k-th tier
cess ΦBS′ of intensity λBS′ = K Pα2λBS. Denote the also as N¯ . Then the expectation of the interference
k=1 k k k
distancebetweenMSy andthe nearestBSx∈ΦBS′ by received at MS z from BS x can be derived as
P
R, which has the following CDF K ∞
E(I )= N¯ f (r )·P l(r ) dr
FR(r)=1−e−λBS′πr2 =1−e−PKk=1Pkα2λBkSπr2. (16) xz kX=1 kˆ0 Rxkzk xkzk k xkzk xkzk
BecausePxy =1·R−α a2ndthus−R1 =2 Px−yα1, wehave = PKk=Kk=11λλBkBkSPSPkα2kα2+1 ·ˆ0∞l(rxkzk)fRxkzk (rxkzk) drxkzk.
F (p )=1−e− Kk=1PkαλBkSπ(cid:18)pxyα(cid:19) P (23)
Pxy xy P
−2 2
=1−e−πpxyα Kk=1λBkSPkα. (17) 4.2 Interference minimized user association scheme
P
Since Eq. (17) is of the same form as Eq. (15),
Intheproposeduserassociationscheme,consideraspe-
TPNM can be used to analyze the received signal and
cificMS,theBSx thatgeneratesthelargestreceived
interference powers at an arbitrary MS with path loss opt
SIR at this MS is selected under the constraint on the
effect, which significantly simplifies the derivations.
predefined QoS.
Consider an arbitrary MS y, we first transform the
4 Interference minimized user association multi-tier HCN to a virtual single-tier cellular network
scheme ΦBS′ = K P−α1·ΦBSofintensityλBS′ = K Pα2λBS
k=1 k k k=1 k k
byTPNM.Thenwehavetheinterferingsetthattrans-
S P
4.1 Interference modeling of HCNs mit simultaneously in channel C as ΦN_BS′ ⊂ΦBS′ of
n
intensity λN_BS′, which is transformed from ΦN_BS by
In a multi-tier HCN with different transmission pow- TPNM as well.
ers across tiers, each active MS chooses the BS that To satisfy the QoS constraint, not all BSs in ΦBS′
produces the highest received SINR to associate with. canbechosentocommunicatewiththeMSy,wedenote
Consider an arbitrary MS y, by using TPNM, the thesubsetofBSsthatareallowedtocommunicatewith
multi-tier HCN can be transformed to a virtual single- y by T ⊂ΦBS′. Then the distance between y and each
y
tier cellular network ΦBS′ = Kk=1Pk−α1 ·ΦBkS of inten- BS in Ty is no more than the distance between y and
sity λBS′ = K Pα2λBS. Then the averagefractionof any other transmitting-in-the-same-channelBS, i.e.,
k=1 k k S
users that are served by tier k in open access is given
P
as T = x′ :kx′ −yk≤ x′ −y
y i i j
N¯ = λBkS′ = λBkSPkα2 . (18) (cid:8) ,x′i ∈ΦBS′,∀(cid:13)(cid:13)x′j ∈ΦN(cid:13)(cid:13)_BS′ . (24)
k λBS′ K λBSPα2 WedenotethenumberofBSsin(cid:9)subsetTy byaran-
k=1 k k
dom variable N . N is the number of points from
Then in tiePr k, the nearest BS xk is selected asso- ΦBS′ in the voiTdyballTyV = b y,RN_BS′ of ΦN_BS′,
ciate with MS y. To evaluate the interference caused where RN_BS′ is the void distance of ΦN_BS′, whose
byx to otherco-channelMSs,we considerthe nearest (cid:0) (cid:1)
k PDF is [14]
MS to x other than y, i.e.,
k
z =arg min kx −z k, (19) fRN_BS′ rN_BS′ =2πλN_BS′rN_BS′·e−πλN_BS′(rN_BS′)2.
k k i
zi∈ΦN_MS\{y} (cid:0) (cid:1) (25)
then the received interference at zk from xk is given as Then an estimated value N¯Ty of NTy is given as
Ixkzk =Pkl(Rxkzk)=Pkkxk−zkk−α, (20) N¯Ty ,E NTy =λBS′·A(V)
∞
wzkheforlelotwhes tdhisetafonlcloewRinxgkzCkD=Fkxaknd−PzDkkFbreetswpeeecntivxeklya:nd =λB(cid:0)S′ˆ0(cid:1) π rN_BS′ 2·fRN_BS′ rN_BS′ drN_BS′
λBS′ (cid:0) (cid:1) (cid:0) (cid:1)
FRxkzk (rxkzk)=1−e−λN_MSπrx2kzk, (21) = λN_BS′, (26)
6 TaoHanetal.
where A(V) denotes the area of V. Proposed scheme vs. conventional scheme in multi−tier cellular networks
0.9
We assume that the proportion of the transmitting conventional, α=2.5
0.8 conventional, α=3
BSs in each tier is the same. Then according to (26), conventional, α=4
we obtain 0.7 pprrooppoosseedd,, αα==23.5
N¯Ty = λNλ_BSB′S′ = λN_λBSBS·′λλBBSS′ = λNλ_BSBS. (27) malized interference000...456 proposed, α=4
Nor0.3
Accordingto(18),theaveragefractionofusersserved 0.2
by tier k in open access can thus be derived as 0.1
0
0 0.02 0.04 0.06 0.08 0.1
λBSPα2 Normalized intensity of receiving mobile stations
N¯ = k k . (28)
k Kk=1λBkSPkα2 F{1i0g,.1,20.I1n}t,erλfBkerSen=ce{0i.n01a,03.1-t,i1e}r acneldluλlaBrS/nλeNtw_oBrSk=w3h.ere Pk =
P
Then the BS that satisfies Proposed scheme in multi−tier cellular networks with various N
Ty
0.35
proposed, N =1
Ty
xopt =argxm′i∈iTnyzj′∈ΦNm_aMxS′\{y}1· x′i−zj′ −α (29) 0.3 ppprrrooopppooossseeeddd,,, NNNTTyy===235
(cid:13) (cid:13) 0.25 Ty
itwsheasethlareevcceteeidvetsothaessloacrigaetsetwinittehrfyer.eFn(cid:13)ocreftrhoemc(cid:13)ox-ocpht,ain.en.e,lzoMptS, malized interference0.01.52
Nor 0.1
z =arg min kx −z′k. (30)
opt z′∈ΦN_MS′\{y} opt i 0.05
i
0
0 0.02 0.04 0.06 0.08 0.1
Denotethedistancebetweenx andz byR = Normalized intensity of receiving mobile stations
opt opt opt
kxopt−zoptk, then the CDF and PDF of Ropt are de- Fig. 3 Interference in a 3-tier cellular network where Pk =
rived as {10,1,0.1},λBkS={0.01,0.1.1}andα=4.
FRopt(ropt)= 1−e−λN_MSπro2pt N¯Ty , (31) 5 Numerical results
(cid:16) (cid:17)
In this section, we present the analytical results of the
proposed BS association scheme and compare it to the
fRopt(ropt)=2πN¯TyλN_MSropt·e−λN_MSπro2pt conventionalschemethatissubjecttosevereco-channel
· 1−e−λN_MSπro2pt N¯Ty−1, (32) itniotnerfle(r·e)nicne.(2T3o)aavnodid(3t3h)e,swineguuslaerlit(yr)o=f p(a1th+lroαss)−fu1n[c4-]
(cid:16) (cid:17) insteadofl(r)=r−α inderivingthe analyticalresults.
respectively. InFig.2,theinterferenceina3-tiercellularnetwork
And then the expectation of the interference re- is demonstrated and compared between the proposed
ceivedatMSz fromBSx canbesimilarlyderived schemeandtheconventionalscheme.TheBStransmis-
opt opt
as sion powers in tier 1, 2 and 3 are 10, 1 and 0.1 respec-
tively, and the intensities of BSs in tier 1, 2 and 3 are
∞ K 0.01, 0.1 and 1 respectively. The result indicates that
E Ixzopt =ˆ fRopt(ropt)· N¯kPk· l(ropt) dropt the proposed scheme is effective to reduce the interfer-
0 k=1 ence in multi-tier cellular networks. Fig. 2 also shows
(cid:0) (cid:1) X
K λ Pα2+1 ∞ that for both the proposedinterference minimized user
= Pk=Kk=11λkkPkkα2 ·ˆ0 fRopt(ropt)· l(ropt) dropt. amsosorecisaetvioenrespchaethmelosasndefftehcet,ctohneveinntteiorfnearelnsccehecmaues,ewdittho
(33)
other co-channel MSs is reduced.
P
Interference Minimizationin5GHeterogeneous Networks 7
In Fig. 3, we show how interference is affected by larsystem.IEEETransactionsonCommunications
various values of N . A greater N means that there 60(5):1443 – 1450
Ty Ty
are more candidate BSs to chose from such that it is 5. Ghimire J, Rosenberg C (2013) Resource allo-
more probably to select a BS which leads to less in- cation, transmission coordination and user asso-
terference to other co-channel receiving MSs. Whereas ciation in heterogeneous networks: A flow-based
whenN →1,theproposedschemedegeneratestothe unified approach. IEEE Transactions on Wireless
Ty
conventionalscheme. Communications 12(3):1340–1351
6. Han-Shin J, Young Jin S, Ping X, Andrews JG
(2012) Heterogeneous cellular networks with flexi-
6 Conclusions blecellassociation:Acomprehensivedownlinksinr
analysis. IEEE Transactions on Wireless Commu-
Inthispaper,wefirstproposeatransmissionpowernor- nications 11(10):3484–3495
malizationanalysismodel,whichsignificantlysimplifies 7. Heath RW, Kountouris M, Tianyang B (2013)
theanalysisofthereceivedsignalandinterference,thus Modelingheterogeneousnetworkinterferenceusing
SIR, in multi-tier HCNs. Then we propose an interfer- poissonpointprocesses.IEEETransactionsonSig-
ence minimized user association scheme, which can be nal Processing 61(16):4114–4126
applied in both single-tier and multi-tier HCNs. Using 8. JinY,QiuL(2013)Jointuserassociationandinter-
the proposed TPNM, we proceed to analyze the inter- ference coordination in heterogeneous cellular net-
ference in multi-tier HCNs. Results demonstrate that works.IEEECommunicationsLetters17(12):2296–
theproposedschemesignificantlyreducesthedown-link 2299
interference in multi-tier HCNs, meanwhile the con- 9. Kyuho S, Lee S, Yung Y, Song C (2011) Re-
straint on the QoS of users is satisfied. fim: A practical interference management in het-
erogeneouswireless access networks.IEEE Journal
on Selected Areas in Communications 29(6):1260–
Acknowledgements The authors would like to acknowledge
the support from the International Science & Technology Co- 1272
operation Program of China (Grant No. 2014DFA11640, 0903 10. MadanR,BorranJ,SampathA,BhushanN,Khan-
and 2012DFG12250), the National Natural Science Foundation dekarA,TingfangJ(2010)Cellassociationandin-
ofChina(NSFC)(GrantNo.61471180,61271224and61301128),
terference coordination in heterogeneous lte-a cel-
NSFC Major International Joint Research Project (Grant No.
61210002),theHubeiProvincialScienceandTechnologyDepart- lular networks. IEEE Journal on Selected Areas in
ment (Grant No. 2013CFB188 and 2013BHE005), the Funda- Communications 28(9):1479–1489
mental Research Funds for the Central Universities (Grant No. 11. PalanisamyP,NirmalaS(2013)Downlinkinterfer-
2013ZZGH009,2013QN136,2014TS100and2014QN155),theSpe-
ence management in femtocell networks - a com-
cial Research Fund for the Doctoral Program of Higher Educa-
tion(GrantNo.20130142120044),andEUFP7-PEOPLE-IRSES prehensive study and survey. In: 2013 Interna-
(Contract/Grant No.247083,318992and610524).Thisresearch tional Conference on Information Communication
isalsosupportedbyAustralianResearchCouncilDiscoveryprojects and Embedded Systems (ICICES), pp 747–754
DP110100538 andDP120102030.
12. Saquib N, Hossain E, Long Bao L, Dong In K
(2012) Interference management in ofdma femto-
cell networks: issues and approaches. IEEE Wire-
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