On the Performance of Practical Ultra-Dense Networks: The Major and Minor Factors

2.2 MB·

by  Ming Ding

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On the Performance of Practical Ultra-Dense
Networks: The Major and Minor Factors
Ming Ding‡, Member, IEEE, David L´opez-P´erez†, Member, IEEE
Abstract—In this paper, we conduct performance evaluation fold from 1950 to 2000, in which an astounding 2700× gain
for Ultra-DenseNetworks(UDNs), andidentifywhichmodelling was achieved through network densification using smaller
factors play major roles and minor roles. From our study, we
cells[2].Inthefirstdecadeof2000,networkdensificationcon-
draw the following conclusions. First, there are 3 factors/models
tinuedto serve the 3rdGenerationPartnershipProject(3GPP)
thathaveamajorimpactontheperformanceofUDNs,andthey
should be considered when performing theoretical analyses: i) a 4th-generation (4G) Long Term Evolution (LTE) networks,
multi-piecepathlossmodelwithline-of-sight(LoS)andnon-line- and is expected to remain as one of the main forces to drive
of-sight (NLoS) transmissions; ii) a non-zero antennaheightdif- the 5th-generation (5G) networks onward [2], [3].
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ference between base stations (BSs) and user equipments(UEs);
1 Indeed,in thefirstdeploymentphaseof5G, theorthogonal
iii)afiniteBS/UEdensity.Second,thereare4factors/modelsthat
0 deployment of ultra-dense (UD) small cell networks (SCNs),
haveaminorimpactontheperformanceofUDNs,i.e.,changing
2 the results quantitatively but not qualitatively, and thus their or simply ultra-dense networks (UDNs), within the existing

r incorporationintotheoreticalanalysesislessurgent:i)ageneral macrocell network at sub-6GHz frequencies, is envisaged as
p multi-pathfadingmodel based on Rician fading;ii) acorrelated one of the workhorses for capacity enhancement in 5G, due
A shadow fading model; iii) a BS density dependent transmission
to its large spatial reuse of spectrum and its easy manage-
3 fpaocwtoerrs;/mivo)daelsdefoterrfmuitnuirsetisctuBdSy/:usi)eradBeSnvsietryt.icFailnaanlltye,ntnhaerpeatatreern5; ment. The latter one arises from its low interaction with the
ii) multi-antenna and/or multi-BS joint transmissions; iii) a macrocell tier, e.g., no inter-tier interference [2].
] proportional fair BS scheduler; iv) a non-uniform distribution Here, the orthogonal deployment means that small cells
I
N of BSs; v) a dynamic time division duplex (TDD) or full duplex andmacrocellsareoperatingondifferentfrequencyspectrum,
(FD) network. Our conclusions can guide researchers to down-
. i.e., 3GPP Small Cell Scenario #2a [3]. In contrast, another
s select the assumptions in their theoretical analyses, so as to
c avoid unnecessarilycomplicated results, whilestillcapturingthe wayofdeployingsmallcellsandmacrocellsistheco-channel
[ fundamentals of UDNs in a meaningful way. deployment, where they are operating on the same frequency

spectrum, i.e., 3GPP Small Cell Scenario #1 [3].
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v
I. INTRODUCTION
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B. The Performance Analysis of Ultra-Dense Networks
6 Recent market forecasts predict that the mobile data traffic
9 volume density will keep growing towards 2030 and beyond TheperformanceanalysisofUDNs,however,ischallenging
7 the so-called 1000× wireless capacity demand [1]. This in- because UDNs are fundamentally different from the current
0 crease is expected to be fuelled by the growth of mobile 4G sparse/dense networks, and thus it is difficult to iden-
.
1 broadbandservices,wherehigh-qualityvideos,e.g.,ultra-high tify the essential factors that have a key impact on UDN
0 definition and 4K resolution videos, are becoming an integral performance. To elaborate on this, Table I provides a list
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part of today’s media contents. Moreover, new emerging of key factors/models/parameters related to the performance
1
: services such as machine type communications (MTC) and analysis of SCNs, along with their assumptions adopted in
v internet of things (IoT) will contribute to the increase of the 3GPP. This list is far from exhaustive, but it includes
i
X massive data. Thisposesan ultimate challengeto the wireless those assumptions that are essential in any SCN performance
r industry, which must offer an exponentially increasing traffic evaluation campaign in the 3GPP [4], [5]. For clarity, the
a in a profitable and energy efficient manner. To make things assumptions in Table I are classified into two categories, i.e.,
even more complex, the current economic situation around network scenario (NS) and wireless system (WS).
the globe aggravates the pressure for mobile operators and More specifically,
vendors to stay competitive, rendering the decision on how • TheassumptionsontheNScharacterisethedeployments
to increase network capacity in a cost-effective manner even of base stations (BSs) and user equipments (UEs).
more critical. • The assumptions on the WS characterise the channel
models and the transmit/receive capabilities.
A. The Role of Ultra-Dense Networks in 5G Considering the 12 factors listed in Table I, a straightfor-
Previous practice in the wireless industry shows that the ward methodology to understand the fundamental differences
wireless network capacity has increased around one million between UDNs and sparse/dense networks would be to in-
vestigate the performance impact of those factors and their
‡Ming Ding is with Data61, CSIRO, Australia (e-mail: combinations one by one, thus drawing useful conclusions
[email protected]).
†DavidL´opez-P´ereziswithNokiaBellLabs,Ireland(email: david.lopez- on which factors should define the fundamental behaviours
[email protected]). of UDNs. Since the 3GPP assumptions on those factors were
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TableI
ALISTOFFACTORSFORTHEPERFORMANCEANALYSISOFUDNS.
Factor Factor Assumption in our SG analysis Assumption in
Factor and its assumption in the 3GPP [4], [5]
category index (Sections II and III) our simulation
NS 1 Finite BS and UE densities X X
Network NS 2 Deterministic BS and UE densities Random BS and UE numbers X [Focus of this paper]
Scenario (Poisson-distributed)
(NS) Non-uniform distribution of BSswith some Unconstrained uniform Unconstrained uniform
NS 3
constraints on the minimum BS-to-BS distance distribution of BSs distribution of BSs
NS 4 Downlink, uplink, dynamic TDD (dynamic link) Downlink only Downlink only
WS 1 Multi-piece path loss with LoS/NLoS transmissions X X
3D BS-to-UE distance for path loss calculation
WS 2 X X
considering BS/UE antenna heights
Wireless WS 3 Generalized Rician fading Rayleigh fading X [Focus of this paper]
System WS 4 Correlated shadow fading None X [Focus of this paper]
(WS) WS 5 BS density dependent BS transmission power Constant BS transmission power X [Focus of this paper]
WS 6 BS vertical antenna pattern None None
WS 7 Multi-antenna and/or multi-BS joint transmissions None None
WS 8 PF scheduler RR scheduler RR scheduler
agreed upon by major companies in the wireless industry all It is veryimportantto note thatwe have already excluded
overthe world,themoreoftheseassumptionsananalysiscan two popular NS assumptions from Table I, i.e., millimetre
consider, the more practical the analysis will be. wave communications and heterogeneous network scenar-
The theoretical community has already started to explore ios. Our reasons are as follows,
this approach, and some of those assumptions in Table I • UDNsdonotnecessarilyhavetoworkwiththemillimetre
have already been considered in various works to derive the wave spectrum, as such topic stands on its own and
performanceofUDNs,e.g.,throughstochasticgeometry(SG) requires a completely new analysis [15], [16]. Hence, in
analyses. In more detail, in SG analyses, BS positions are this paper, we focus on the spatial reuse gain of UDNs
typically modelled as a Homogeneous Poisson Point Process at sub-6GHz frequencies, and we do not consider the
(HPPP)ontheplane,andclosed-formexpressionsofcoverage new features of millimetre wave communications, such
probability can be found for some scenarios in single-tier as short-range coverage, very low inter-cell interference,
cellular networks [6] and multi-tier cellular networks [7]. the blockage effect, a very high Doppler shift [16].
Using a simple modelling, the major conclusion in [6], [7] • AsbrieflydiscussedinSubsectionI-A,therearetwoways
is that neitherthe numberof cells northe numberof cell tiers of deploying UDNs within the existing macrocell net-
changesthe coverageprobabilityin interference-limitedfully- works: the orthogonaland the co-channel deployments.
loaded wireless networks.
– In the former case, UDNs and the macrocell net-
Recently,afewnoteworthystudieshavebeencarriedoutto
workscanbestudiedseparately,makingthenetwork
revisitthenetworkperformanceanalysisofUDNsundermore
scenario for UDNs a homogeneousone.
practical assumptions[8]–[14]. These new studies include the
– In the latter case, the strong inter-tier interfer-
following assumptions in Table I: i) a multi-piece path loss
ence [17] from the macrocell networks to UDNs
model with line-of-sight (LoS) and non-line-of-sight (NLoS)
should be mitigated by some time domain inter-
transmissions(WS1),ii) a non-zeroantennaheightdifference
cell interference coordination techniques, e.g., the
between BSs and UEs (WS2), and iii) a finite BS/UE den-
almost blank subframe (ABS) mechanism [2]. Dif-
sity (NS1). The inclusion of these assumptions significantly
ferent from a normal subframe, in an ABS, no
changed the previous conclusion, indicating that the coverage
controlor data signals butonlyreferencesignalsare
probability performance of UDNs is neither a convex nor a
transmitted in the macrocell tier, thus significantly
concave function with respect to the BS density.
reducing the inter-tier interference since reference
signalsonlyoccupyaverylimitedportionofatime-
frequency resource block. However, when the small
C. Our Contributions and Paper Structure
cellnetworkgoesultra-dense,themacrocellnetwork
In lightofsuch drastic changeof conclusions,onemay ask needs to convert all subframes to ABSs, so as to
the followingintriguingquestion:What if we furtherconsider decreaseitsinterferencetothelargenumberofsmall
moreassumptionsinSGanalyses?Willitqualitativelychange cells in its vicinity. In other words, the macrocell
the recently obtained conclusions in [8]–[14]? In this paper, network would basically mute itself to clear the
we willaddress thisfundamentalquestionby investigating way for UDNs, and thus again making the network
theperformanceimpactofthe3GPPassumptionsofWS3, scenario for UDNs a homogeneousone.
WS4, WS5 and NS2 in Table I. Therefore, we come to the conclusion that there is no
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strong motivation to study UDNs in a heterogeneous where L is in the order of several meters for the current 4G
network scenario, which is thus absent in Table I. networks. For example, according to the 3GPP assumptions
The rest of this paper is structured as follows: for small cell networks, L equals to 8.5m, as the BS antenna
heightandtheUE antennaheightareassumedto be10mand
• SectionIIdescribesthenetworkscenarioandthewireless
1.5m, respectively [19].
system model used in our SG analysis, mostly recom-
Followingthe3GPPrecommendations[4],[5],weconsider
mended by the 3GPP.
• Section III presents our previous theoretical results in practical line-of-sight (LoS) and non-line-of-sight (NLoS)
transmissions, and treat them as probabilistic events. Specifi-
terms of the coverage probability, and discusses our
cally, we adopt a very general path loss model, in which the
main results on the performance impact of the 3GPP
assumptions of WS1, WS2 and NS1 in Table I. path loss ζ(w) is segmented into N pieces, i.e.,
• Section IV describes in more detail the newly consid- ζ1(w), when 0≤w≤d1
ered assumptions addressed in this paper, i.e., the 3GPP
assumptions of WS3, WS4, WS5 and NS2. ζ2(w), when d1 <w≤d2
• Section V discloses our simulation results on the perfor- ζ(w)=... ... , (2)
mance impact of these newly considered assumptions.
ζN(w), when w >dN−1
• SpaeccttioofnthVeIrpermoaviindiensgd3iGscPuPssaiosnsuomnpttihoenspoerffWormSa6n,cWeSim7-, where each piece ζn(w),n∈{1,2,...,N} is modelled as
WS8, NS3 and NS4, whichare leftas ourfuturework.
• The conclusions are drawn in Section VII. ζn(w)=(ζζnnLNL(w(w))==AALnNnwL−wα−Ln,αNnL, LNoLSoSPrPorbo:bP:r1Ln−(wP)rLn(w),
(3)
II. NETWORK SCENARIO AND WIRELESS SYSTEMMODEL where
In this section, we present the network scenario and the
wirelesssystemmodelconsideredinthispaper.Notethatmost • ζnL(w)andζnNL(w),n∈{1,2,...,N}arethen-thpiece
path loss functions for the LoS transmission and the
of our assumptions on cellular networks are in line with the
NLoS transmission, respectively,
recommendations by the 3GPP [4], [5].
• ALn and ANnL are the path losses at a reference distance
r =1 for the LoS and the NLoS cases, respectively,
A. Network Scenario • αLn and αNnL are the path loss exponentsfor the LoS and
the NLoS cases, respectively.
We consider a cellular network with BSs deployed on a
plane according to a homogeneous Poisson point process • In practice, ALn, ANnL, αLn and αNnL are constants obtain-
2 able from field tests [4], [5].
(HPPP) Φ with a density of λBSs/km . Active UEs are also
Poisson distributed in the considered network with a density • PrLn(w) is the n-th piece LoS probability function that
2 a transmitter and a receiver separated by a distance w
of ρUEs/km . We only consider active UEs in the network
has a LoS path, which is assumed to be a monotonically
because non-active UEs do not trigger data transmission, and
decreasing function with regard to w. Such assumption
thus they are ignored in our analysis. Note that the total UE
has been confirmed by [4], [5].
number in cellular networks should be much higher than the
number of the active UEs, but at a certain time slot and on For convenience, ζL(w) and ζNL(w) are further
n n
a certain frequency band, the active UEs with data traffic stacked into piece-wise functions written as
demandsmaynotbetoomany.A typicaldensityofthe active (cid:8) (cid:9) (cid:8) (cid:9)
UEs in 5G should be around 300UEs/km2 [2]. ζ1Path(w), when 0≤w ≤d1
In practice, a BS should mute its transmission if there Path ζ2Path(w), when d1 <w ≤d2
icselnlointUerEfecreonncneecatneddetnoeritg,ywchoincshumrepdtuiocnes[1u4n]n.eScienscsearUyEisntaerre- ζ (w)=... ... , (4)
randomly and uniformly distributed in the network, it can be ζNPath(w), when w >dN−1
aΦ˜ss[u1m8]e,dththeadtethnesitayctoivfewBhSicshalissodfeonlolotewdabnyHλ˜PBPSPsd/kismtr2i.buNtiootne w“NhLer”efothrethsetrLinogSvaanrdiabthlee NPLatohS tcaakseess,trheespveacltuiveeloyf. B“Le”sidaensd,
that 0≤λ˜ ≤λ, and a larger ρ leads to a larger λ˜. Details on PrL(w) is also stacked into a piece-wise function as
n
the computation of λ˜ can be found in [14].
(cid:8) (cid:9) PrL1(w), when 0≤w ≤d1
B.WWeirdeelensosteSbysytermthMeotwdeol-dimensional(2D)distancebetween PrL(w)=P... rL2(w), w... hen d1 <w ≤d2 . (5)
a BS and an a UE, and by L the absolute antenna height dif- PrLN(w), when w>dN−1
ferencebetweenaBSandaUE.Hence,thethree-dimensional Asaspecialcase,inthefollowingsubsections,weconsider
(3D) distance between a BS and a UE can be expressed as
a two-piece path loss function and a LoS probability function
w = r2+L2, (1) defined by the 3GPP [4]. Specifically, we use the following
p
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path loss function,
ALw−αL, LoS Prob: PrL(w)
ζ(w)= , (6)
( ANLw−αNL, NLoS Prob: 1−PrL(w)
together with the following LoS probability function,
PrL(w)= 1−5exp(−R1/w), 0<w ≤d1 , (7)
( 5exp(−w/R2), w >d1
where R1 = 156 m, R2 = 30 m, and d1 = lnR110 [4]. The
combination of the path loss function in (6) and the LoS
probabilityfunctionin (7) can be deemed as a special case of
the proposed path loss model in (2) with the following sub-
stitutions: N = 2, ζL(w) = ζL(w) = ALw−αL, ζNL(w) =
1 2 1
ζ2NL(w) = ANLw−αNL, PrL1(w) = 1−5exp(−R1/w), and
PrL2(w) = 5exp(−w/R2). For clarity, this model is referred Fig.1. Theoreticalperformancecomparisonofthecoverageprobabilitywhen
to as the 3GPP Path Loss Model hereafter. the SINR threshold γ = 0dB. Note that all the results are obtained using
the3GPPPathLossModelintroducedinSubsectionII-B.Moreover,theBS
Moreover, in this paper, we also assume a practical user
densityregionsforthe4Gand5Gnetworkshavebeenillustratedinthefigure,
association strategy (UAS), in which each UE is connected consideringthatthemaximumBSdensityofthe4GSCNsisintheorderof
to the BS with the smallest path loss (i.e., with the largest 102BSs/km2 [2],[3].
ζ(r)) to the UE [4], [5]. We also assume that each BS/UE
and gi is the multi-path fading channel gain associated with
is equipped with an isotropic antenna, and that the multi-path
bi. Note that when all BSs are assumed to be active, the set
fading between a BS and a UE is modelled as independently
of all BSs Φ should be used in the expression of I [8], [9],
identical distributed (i.i.d.) Rayleigh fading [8], [11]–[14]. agg
[11]–[13].However,inoursystemmodelwithidlemodeatthe
small cell BSs and a finite UE density (see Subsection II-A),
III. DISCUSSION ON THESTATE-OF-THE-ARTRESULTS only the active BSs in Φ˜ \bo inject effective interference into
ONTHE PERFORMANCE ANALYSIS OF UDNS thenetwork,whereΦ˜ denotesthesetoftheactiveBSs.Hence,
Using the theory of stochastic geometry (SG) and the theBSsinidlemodearenottakenintoaccountintheanalysis
presentedassumptionsinprevioussubsections,weinvestigated of I shown in (10), due to their muted transmissions.
agg
the coverageprobabilityperformanceofSCNs byconsidering
the performance of a typical UE located at the origin o. In
B. Summary of Previous Findings
such studies [12]–[14], we analysed in detail the performance
As a summary, to illustrate our findings in [12]–[14], we
impact of the 3GPP assumptions of WS1, WS2 and NS1 in
plot the SCN performance results in terms of the coverage
Table I. The concept of coverage probability and a summary
probability in Fig. 1.
of our results are presented in the following.
The results in Fig. 1 are analytical ones validated by
simulations in [12]–[14]. Note that in Fig. 1, L denotes the
A. The Coverage Probability
absolute antenna height difference between BSs and UEs. As
The coverage probability is defined as the probability that indicated in Subsection II-B, L = 8.5m in the current 3GPP
the signal-to-interference-plus-noiseratio (SINR) of the typi- assumption for small cell scenarios, while L = 0m is a
cal UE is above a designated threshold γ: futuristic assumption where BS antennas are installed at the
UE height. Besides, the other parameters used to obtain the
pcov(λ,γ)=Pr[SINR>γ], (8)
results in Fig. 1 are αL =2.09, αNL =3.75, AL =10−10.38,
where the SINR is computed by ANL =10−14.54, P =24 dBm, PN =−95 dBm [4].
From Fig. 1, we can draw the following observations:
Pζ(r)h
SINR= Iagg+PN, (9) • Performance impact of WS1: The curve with plus
markersrepresentstheresultsin [12], wherewe consider
where h is the channel gain, which is modelled as an ex- the 3GPP multi-piece path loss function with LoS/NLoS
ponentially distributed random variable (RV) with a mean of transmissions [4] and ignore the 3GPP assumptions of
one (due to our consideration on Rayleigh fading presented WS2 and NS2, i.e., setting L = 0m and deploying an
before), P is the transmission power at each BS, PN is the infinitenumberofUEs.Fromthoseresults,itcanbeseen
additive white Gaussian noise (AWGN) power at the typical thatwhentheBSdensityislargerthanathresholdaround
UE, and Iagg is the cumulative interference given by 102BSs/km2, the coverage probability will continuously
decrease as the SCN becomes denser. This is because
Iagg = Pβigi, (10) UDNs imply high probabilities of LoS transmissions
i:biX∈Φ˜\bo between BSs and UEs, which leads to a performance
where bo is the BS serving the typical UE, bi is the i-th degradationcausedbyafastergrowthoftheinterference
interfering BS, βi is the path loss from bi to the typical UE, power compared with the signal power [12]. This is due
5
to the transition of a large number of interference paths widely adopted [5]. Hence, we consider the practical multi-
fromNLoS(usuallywithalargepathlossexponentαNL) path Rician fading model defined in the 3GPP [5], where the
to LoS (usually with a small path loss exponent αL). K factorindBscale(theratiobetweenthepowerinthedirect
• Performance impact of WS2: The curve with square path and the power in the other scattered paths) is modelled
markersrepresentsthe resultsin [13], whereweconsider as K[dB]=13−0.03w, where w is defined in (1).
the 3GPP assumptions of multi-piece path loss function
with LoS/NLoS transmissions and L = 8.5m [4], while
B. A correlated shadow fading model (WS4 in Table I)
still keeping the assumption of an infinite number of
InSGanalyses,theshadowfadingisusuallynotconsidered
UEs. From those results, it can be seen thatthe coverage
or simply modelled as independently identical distributed
probability shows a concerning trajectory toward zero
when the BS density is larger than 103BSs/km2. This (i.i.d.) RVs. However, in the 3GPP, a more practical corre-
lated shadow fading is often used [4], [5], [20]. Hence, we
is because UDNs make the antenna height difference
considerthepracticalcorrelatedshadowfadingmodeldefined
between BSs and UEs non-negligible, which gives rise
to another performance degradation due to a cap on in 3GPP [4], where the shadow fading in dB is modelled as
zero-mean Gaussian a random variable, e.g., with a standard
the signal power, resulted from the bounded minimum
deviation of 10dB [4]. The correlation coefficient between
distance between a UE and its serving BS [13].
• Performance impact of NS1: The curves with circle the shadow fading values associated with two different BSs
and trianglemarkersrepresentsthe resultsin [14], where is denoted by τ, where τ =0.5 in [4].
we consider the 3GPP assumptions of multi-piece path
loss function with LoS/NLoS transmissions and a finite C. A BS density dependent BS transmission power (WS5 in
2
UE density of 300UEs/km (a typical UE density in Table I)
5G [2]).Moreover,boththe assumptionsofL=0m and
In SG analyses, the BS transmission power is usually
L=8.5m are investigatedin Fig. 1. As we can observe,
assumedtobeaconstant.However,inthe3GPP,itisgenerally
when the BS density surpasses the UE density, i.e.,
2 agreed that the BS transmission power should decrease as the
300BSs/km ,thuscreatingasurplusofBSs,thecoverage
SCN densifies because the per-cell coverage area shrinks [4].
probabilitywillcontinuouslyincrease.Suchperformance
Hence, we embrace the practical self-organisingBS transmis-
behaviourofthecoverageprobabilityincreasinginUDNs
sion power framework presented in [2], in which P varies
isreferredtoastheCoverageProbabilityTakeoff in[14].
withtheBSdensityλ.Specifically,thetransmitpowerofeach
The intuition behind the Coverage Probability Takeoff is
BS is configured such that it provides a signal-to-noise-ratio
thatUDNsprovideasurplusofBSs withrespecttoUEs,
(SNR) of η0 = 15 dB at the edge of the average coverage
which providea performanceimprovement, thanksto the
area for a UE with NLoS transmissions. The distance from
BS diversity gain and the BS idle mode operation. In
a cell-edge UE to its serving BS with an average coverage
more detail, as discussed in II-A, since the UE density
1
is finite in practical networks, a large number of BSs area is calculated by r0 = λπ, which is the radius of an
could switch off their transmission modules in a UDN, equivalent disk-shaped coverqage area with an area size of 1.
λ
thus enter idle modes, if there is no active UE within Therefore,theworst-casepathlossisgivenbyANLr−αNL and
0
their coverage areas. This helps to mitigate unnecessary therequiredtransmissionpowertoenableaη0 dBSNRinthis
inter-cell interference and reduce energy consumption. case can be computed as [2]
η0
1010PN
IV. DISCUSSION ON THEINCORPORATION OF MORE 3GPP P (λ) = . (11)
ASSUMPTIONS INTOTHEMODELING ANLr0−αNL
Toinvestigatewhetherthepreviousconclusionsstillholdin In Fig. 2, we plot the BS density dependent transmission
more practical network scenarios, additional assumptions [4], power in dBm to illustrate this realistic power configuration
[5]willalsobeconsideredinouranalysisthroughsimulations. when η0 =15 dB. Note that our modelling of P is practical,
The results will be discussed in Section V. Such additional covering the cases of macrocells and picocells recommended
practical assumptions are the 3GPP assumptions of WS3, in the LTE networks. More specifically, the typical BS densi-
WS4, WS5 and NS2 in Table I, which are presented in the ties of LTE macrocells and picocells are respectively several
2 2
sequel. Note thatthe authorsof [10] haverecently proposeda BSs/km and around 50 BSs/km [19], respectively. As a
newapproachofnetworkperformanceanalysisbasedonHPPP result, the typical P of macrocell BSs and picocells BSs are
intensity matching, which facilitates the theoretical study of respectively assumed to be 46 dBm and 24 dBm in the 3GPP
some of these additional 3GPP assumptions. standards [19], which match well with our modelling.
A. A generalmulti-pathfading modelbased on Rician fading D. A deterministic BS/UE density (NS2 in Table I)
(WS3 in Table I)
In SG analyses, the BS/UE number is usually modelled
In SG analyses, the multi-path fading is usually modelled as a Poisson distributed random variable (RV). However, in
as Rayleigh fading for simplicity. However, in the 3GPP, a the 3GPP, a deterministic BS/UE number is commonly used
more practical model based on generalised Rician fading is for a given BS/UE density [4]. Hence, we use deterministic
6
Fig. 2. The BS density dependent transmission power in dBm. (In the Fig.3. Simulated performance comparison ofthecoverage probability with
3GPP[19],46dBmand24dBmareassumedformacrocell andpicocells. more3GPPassumptions whentheSINRthresholdγ=0dB.
densities λBSs/km2 and ρUEs/km2 to characterize the BS the 2G/3G systems is indeed much larger than 24 dBm,
and UE deployments, respectively, instead of modelling their which is the case for Fig. 1. Nevertheless, such BS
numbers as Poisson distributed RVs. densitydependenttransmissionpowerhasaminorimpact
on UDNs, because BSs in UDNs usually work in a
interference-limitedregion,andthusthe BS transmission
V. MAIN RESULTSON THEPERFORMANCE IMPACT OF THE
power in the signal power and that in the aggregated
ADDITIONAL 3GPPASSUMPTIONS
interferencepowercancelouteachother.Thisis obvious
On top of the 3GPP assumptions discussed in Subsec- from the SINR expression in (9).
tion III-B, in this section, we consider the 4 additional
3GPP assumptions described in Section IV, and study their
VI. FUTURE WORK
performance impacts on UDNs. More specifically, using the
same parameter values for Fig. 1, we conduct simulations The performance impact of the remaining 5 assumptions
to investigate the coverage probability performance of SCNs in Table I, i.e., the 3GPP assumptions of WS6, WS7,
while also consideringthe 3GPP assumptionsof WS3, WS4, WS7, NS3 and NS4, are left to our future work, but briefly
WS5 and NS2 in Table I. The results are plotted in Fig. 3. discussed in the following subsections.
Comparing Fig. 1 with Fig. 3, we can draw the following
observations:
A. Discussion on The Remaining 5 Assumptions
• Those 4 additional 3GPP assumptions introduced in • A 3D antenna pattern (WS6 in Table I): In SG
SectionIVdonotchangethefundamentalbehaviours
analyses,theverticalantennapatternateachBSisusually
of UDNs shown in Fig. 1, i.e.,
ignored for simplicity. However, in the 3GPP perfor-
– the performancedegradationdueto the transitionof mance evaluations, it is of good practice to consider 3D
a large number of interfering links from NLoS to antenna patterns, where the main beam is mechanically
LoS, when λ∈ 102,103 BSs/km2, and/orelectricallytilteddownwardstoimprovethesignal
– the further performance degradation, due to the cap poweraswellastoreduceinter-cellinterference[4],[5].
(cid:2) (cid:3)
on the signal power caused by the non-zeroantenna • Multi-antenna and/or multi-BS joint transmissions
height difference between BSs and UEs, when L= (WS7inTableI):InSGanalyses,eachBS/UEisusually
8.5m and λ is larger than 103BSs/km2, and equipped with one omni-directional antenna for sim-
– the performance improvement when λ is larger than plicity. However, in the 3GPP performance evaluations,
ρ, thus creating a surplus of BSs and thus allowing it is usual to consider multi-antenna transmissions and
for idle mode operation to mitigate unnecessary receptions[21]–[23],evenwithanenhancementofmulti-
inter-cell interference. BS cooperation [24]–[26]. The consideration of multi-
• The performance behaviour of sparse networks (λ ∈ antenna technologies in small cell networks expands the
10−1,100 BSs/km2) is different in Fig. 3 compared realmofUDNs,whichopensupnewavenuesofresearch
with that in Fig. 1. This is mainly due to the larger BS topics for further study.
(cid:2) (cid:3)
transmissionpowerusedinFig.3forsparsenetworks,as • A proportional fair scheduler (WS8 in Table I): In
displayed in Fig. 2, which is helpfulto remove coverage SG analyses, usually a typical UE is randomly chosen
holesinthenoise-limitedregion.Basedonourknowledge for the performanceanalysis, which implies that a round
ofthesuccessfuloperationoftheexisting2G/3Gsystems, Robin(RR) scheduleris employedineach BS. However,
the results in Fig. 3 make more sense than those in in the 3GPP performanceevaluations,a proportionalfair
Fig. 1, since the macrocell BS transmission power in (PF) scheduler is often used as an appealing scheduling
7
Thus, dynamicTDD can providea tailored configuration
of DL/UL subframe resources for each cell or a cluster
of cells at the expense of allowing inter-cell inter-link
interference,e.g.,DLtransmissionsofacellmayinterfere
with UL ones of a neighboring cell, and vice versa.
The study of dynamic TDD is particularly important
for UDNs because dynamic TDD is the predecessor of
full duplex (FD) [40], [42] technology, which has been
identified as one of the candidate for 5G. In more detail,
– In an FD system, a BS can simultaneously transmit
to and receive from different UEs, thus enhancing
spectrum reuse, but creating both inter-cell inter-
link interference and intra-cell inter-link interfer-
ence, a.k.a., self-interference [42].
– The main difference between an FD system and a
Fig.4. Illustration oftheidealBSdeployment inahexagonalgridnetwork. dynamic TDD one is that self-interference does not
TheBSdensityisaround50BSs/km2,whichisatypical onein4G.
exist in dynamic TDD [40].
The inter-link interference is expected to have a non-
technique that can offer a better system throughput than
minorimpactontheperformanceofUDNsinthecontext
the RR scheduler, while maintaining the fairness among
of a dynamic TDD or FD network, because the DL gen-
UEs with diverse channel conditions [27]. Some prelim-
erally overpowersthe UL, which creates high imbalance
inary simulation results on the performanceof small cell
among interference links in UDNs.
networks considering the RR scheduler can be found in
[2], [28].
B. Qualitative Results vs. Quantitative Results
• A non-uniform distribution of BSs with some con-
straints on the minimum BS-to-BS distance (NS3 in Finally, it is very important to point out that even if an
Table I): In SG analyses, BSs are usually assumed to analysis can treat all the assumptions in Table I, a non-
be uniformly deployed in the interested network area. negligible gap may still exist between the analytical results
However,inthe3GPPperformanceevaluations,smallcell andtheperformanceresultsinreality,becauseofthefollowing
clusters are often considered,and it is forbiddento place non-tractable factors [4]:
anytwoBSstooclosetoeachother[4].Suchassumption • non-full-buffertraffic,
is in line with the realistic network planning to avoid • hybrid automatic repeat request (HARQ) processes,
strong inter-cell interference.It is interesting to note that • non-linear channel measurement errors,
several recent studies are looking at this aspect from • quantized channel state information (CSI),
difference angles [29]–[31]. In particular, a deterministic • UE misreading of control signalling,
hexagonalgridnetworkmodel[6]mightbeusefulforthe • discrete modulation and coding schemes,
analysis.Morespecifically,wecanconstructanidealistic • UE mobility and handover procedures,
BS deployment on a perfect hexagonal lattice, and then • imperfect backhaul links, and so on;
we can perform a network analysis on such BS deploy-
Hence, in the context of the performance analysis for
menttoextractanupper-boundoftheSINRperformance.
UDNs, a high priority should be given to identifying the
NotethattheBSdeploymentonahexagonallatticeleads
performance trends qualitatively, rather than improving
to an upper-bound performance because BSs are evenly
the numerical results quantitatively.
distributed in the network scenario, and thus very strong
interference due to close proximity is precluded in the
VII. CONCLUSION
analysis [6]. Illustration of such hexagonal grid network
In this paper, we have conducted a performance evaluation
is provided in Fig. 4.
ofUDNs,andidentifiedwhichmodellingfactorsreallymatter
• A dynamic time division duplex (TDD) or full duplex
intheoreticalanalyses.Fromourstudy,wehaveidentifiedthat
(FD) network (NS4 in Table I): In SG analyses, most
3 factors/modelshave a major impact on the performance
studies focus on the downlink (DL) network scenario as
of UDNs, and they should be considered when performing
in [8]–[14]. It is of great interest to see whether new
theoretical analyses:
conclusions can be drawn for the uplink (UL) network
scenario. Different from the DL, a fractional power • a multi-piece path loss model with LoS/NLoS transmis-
controlmechanismiscommonlyusedattheUEside[32], sions;
[33].Moreover,anewtechnology,referredtoasdynamic • a non-zero antenna height difference between BSs and
TDD, has been standardized in the 3GPP [34]–[41]. In UEs;
dynamicTDD,the DL/UL subframenumberin each cell • a finite BS/UE density.
or a cluster of cells can be dynamically changed on In contrast, we have found that the following 4 fac-
a per-frame basis, i.e., once every 10 milliseconds [4]. tors/models have a minor impact on the performance of
8
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