Evolution of 3D User Distribution Models in Real Network Simulator

UPTEC F10068

Examensarbete 30 hp December 2010

Evolution of 3D User Distribution Models in Real Network Simulator

Sara Bladlund

Teknisk- naturvetenskaplig fakultet UTH-enheten

Besöksadress:

Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

Postadress:

Box 536 751 21 Uppsala

Telefon:

018 – 471 30 03

Telefax:

018 – 471 30 00

Hemsida:

http://www.teknat.uu.se/student

Abstract

Evolution of 3D User Distribution Models in Real Network Simulator

Sara Bladlund

The report treats the development and evaluation of a three dimensional user distribution model for a real network simulator. The simulator is used to create realistic predictions of real networks with the use of high resolution maps including a building data base and network data and also an advanced radio model for LTE.

Previously all simulations have been performed with a two dimensional user

distribution, i.e. all users situated on the ground level. Since it is considered plausible that many LTE users will be indoors in buildings with multiple floors, several three dimensional user distribution models with users not only on the ground floor but also on the higher floors has been developed and implemented in the simulator. The models all account for the change in path loss and SINR to be expected and have been compared in computational time and credibility. The simulations show that by the use of such a three dimensional model there is a significant improvement at low loads but at high loads the interference becomes dominant and the results show a deterioration and approaches the results of the ordinary two dimensional model. The seventh and last model to be investigated shows a desirable computational speed that still does not compromise too much with the accuracy and detailing of the model and is therefore recommended for normal use.

Examinator: Tomas Nyberg

Ämnesgranskare: Mikael Sternad

Handledare: Lars Klockar

1 Introduction 4

1.1 Background . . . 4

1.2 Previouswork. . . 4

1.3 Projectdescription . . . 5

2 Theory 6 2.1 Propagationmechanisms. . . 6

2.1.1 FreeSpacePropagation . . . 6

2.1.2 Reection,RefractionandScattering. . . 7

2.1.3 Diraction . . . 9

2.1.3.1 IdealKnife EdgeDiraction . . . 9

2.1.4 Guiding . . . 11

2.1.5 Dispersion. . . 11

2.2 PropagationModels . . . 11

2.2.1 PiecewiseLinear(Multislope)Model . . . 12

2.2.2 Building Penetration Loss at LOS Conditions in COST 231 . . . 12

2.2.2.1 HeightGainin COST231. . . 13

2.2.3 Outdoor-to-IndoorPropagationinUrbanAreasat 1.8Ghz 14 2.2.4 Multi-FrequencyPathLossinanOutdoortoIndoorMacro- cellularScenario . . . 15

2.2.4.1 Excess PathLossInsteadofAbsoluteValues . . 17

2.2.5 EricssonUrban Model . . . 17

2.2.5.1 IndoorPropagation . . . 18

3 DescriptionofRealNetworkSimulatorand3DPathLossMod- els 20 3.1 ShortDescriptionoftheReal NetworkSimulatorAstrid . . . 20

3.1.1 SINRCalculations . . . 21

3.1.1.1 SINRCalculationsfor3DUserDistributions . . 22

3.2 3DModels . . . 22

3.2.1 ModelswhitoutLOS considerations . . . 22

3.2.1.1 DescriptionofFirstModel . . . 22

3.2.1.2 DescriptionofSecondModel . . . 23

3.2.2.1 DescriptionofThirdmodel . . . 23

3.2.2.2 DescriptionofFourthModel . . . 25

3.2.2.3 DescriptionofFifth model . . . 25

3.2.2.4 DescriptionofSixth model . . . 26

3.2.2.5 DescriptionofSeventhModel. . . 27

3.2.2.6 DescriptionofCrowded3DModelUsingModel Six . . . 29

4 Simulations and Results 30 4.1 Comparison ofcomputationaltimes . . . 30

4.2 InvestigationoftheG-Matrix . . . 31

4.3 Models. . . 35

4.3.1 WithoutLOS Considerations . . . 35

4.3.1.1 Resultsfrom theFirst Model . . . 35

4.3.1.2 Resultsfrom theSecondModel. . . 36

4.3.2 ModelsWithLOS Considerations . . . 39

4.3.2.1 Resultsfrom theThird Model . . . 39

4.3.2.2 Resultsfrom theFourthModel . . . 41

4.3.2.3 Resultsfrom theFifth Model . . . 43

4.3.2.4 Resultsfrom theSixth Model. . . 43

4.3.2.5 Resultsfrom theSeventhModel . . . 47

4.3.2.6 ResultsfromCrowded3DModelUsingModelSix 49 4.3.3 All modelsinthesameplots . . . 51

4.3.3.1 Pathloss . . . 51

4.3.3.2 SINR . . . 51

4.3.3.3 Mean BitratesandCapacity . . . 53

5 Discussionand Conclusions 56 5.1 Discussionand Conclusions . . . 56

5.2 Continuation . . . 60

A AllPlots 68 A.1 First Model . . . 68

A.1.1 MeanBitrates andCapacity. . . 68

A.1.2 SINR . . . 69

A.1.3 PathLoss . . . 69

A.2 SecondModel . . . 70

A.2.1 MeanBitrates andCapacity. . . 70

A.2.2 SINR . . . 70

A.2.3 PathLoss . . . 71

A.3 Third Model . . . 72

A.3.1 MeanBitrates andCapacity. . . 72

A.3.2 SINR . . . 72

A.3.3 PathLoss . . . 73

A.4 FourthModel . . . 74

A.4.2 SINR . . . 74

A.4.3 PathLoss . . . 75

A.5 Fifth Model . . . 76

A.5.1 MeanBitrates andCapacity. . . 76

A.5.2 SINR . . . 76

A.5.3 PathLoss . . . 77

A.6 Fifth ModelwithLowerWallLossConstants . . . 78

A.6.1 MeanBitrates andCapacity. . . 78

A.6.2 SINR . . . 78

A.6.3 PathLoss . . . 79

A.7 Sixth Model . . . 80

A.7.1 MeanBitrates andCapacity. . . 80

A.7.2 SINR . . . 80

A.7.3 PathLoss . . . 81

A.8 SeventhModel . . . 82

A.8.1 MeanBitrates andCapacity. . . 82

A.8.2 SINR . . . 82

A.8.3 PathLoss . . . 83

Introduction

1.1 Background

Realnetworksimulationswasstartedacoupleofyearsagotogetmorerealistic

resultsinsteadofhexagonsimulationswhoseresultsstartedtodivergetomuch

from measurements performed in real networks. The ongoing work on real

network simulations is a cooperation between Ericsson AB and some of the

world'sleadingmobilenetworkoperators. Itconsistsofhighaccuracypathloss

predictionsfromacommercialcellplanningtoolcontainingdetailedinformation

includingabuildingdatabase,basestationsitedataandantennapatternsanda

propagationmodelthatistunedwithdrivetestmeasurementsfromthestudied

area. In addition to the cell planningtoolit also includes an advanced radio

model for LTE, support for heterogeneous trac distributions and dierent

optionsfor distributingthe resourcesof the system. The propagation models

canbetunedto tthetypeofareaitisused for,forexampleifitisanurban

area ora rural. The real network simulator can be used to produce reliable

predictionsusedtoanalyzeandevaluatepossiblechangesmadetothenetwork

whitout having to implement them in the operating system. It is considered

plausiblethatmanyoftheLTEuserswillbeindoorsandconsequentlyonboth

higher oors and the ground oor. This motivates the present investigation

on how to best include propagation models for such users into the network

simulator.

1.2 Previous work

Themodelling of outdoorto indoorpropagation of radio waveshave been in-

vestigated and severaland sometimesquitedierent attemptsto model it has

beenproposed,forexample[6,12]to mentiontwo. Thetaskencounters many

obstaclesand risesmany questions. How detailed the model should be is an

importantbalancebetweenaccuracyandeaseofusage. Whenmodellingindoor

propagation,theheightofthebuildingalsocomesinasafactortobedealtwith.

Itisnaturaltoassumeacertaindependence onheightforthepropagationifit

is assumedthat the radio wavemeets less obstructing objects onits path the

higherthereceiveris situated. Thisis indeed the casewhenthe antennas are

placedon roof tops asis often thecase in macrocellular environments. That

also raisesthe question of apath lossdependencyon line of sight conditions.

For example [7] suggests a model with considerations taken for line of sight

circumstances.

1.3 Project description

All previouspredictions havebeenperformed onthe groundoor. Sinceit is

considered plausible that many of the LTE users will be indoors and conse-

quentlyonhigheroorsthanthegroundoor,thequestionariseshowthiswill

aect the system. It is known that the attenuationfrom the base station to

theuserequipmentisdependantoftheuserequipmentheight,i.e. theooron

which theuseris situated. It is thereforealsoreasonableto believethat users

in tallbuildingsmay experiencehigh interferencefrom neighboring cells. The

purposeofthisprojectistoinvestigatewhetherathreedimensionaldistribution

forindoorusers willimpact theresultof thesimulationsof theLTEnetworks

andhowsuchadistributionanditsimplicationscanbemodeled.

Theory

2.1 Propagation mechanisms

To describe the methods of radio wave propagation, Maxwell's equations are

usuallythestartingpoint. However,agoodpracticalapproachistoconsiderthe

waypower

P [W]

^{propagatesoutwardsfromasourceofenergy[1]. Anisotropic}

radiatorisasourcethatradiatesuniformlyinalldirectionsinasphericalfashion.

Thepowerdensity

p Wm ⁻² 

is dened as thetransmitted power dividedby

thesurfaceofthesphereanditenablesthecalculationofthegainofaradiator.

Anisotropicradiatordoesnotexistinreality,sinceitassumestheexistensofa

pointsourceofenergybutitisausefultoolwhentalkingaboutthedirectivity

of realradiators. The gain

G

^{of the radiatoris ameasure of howmuch more}

powerdensityarealradiatorisableto transmitin thepreferreddirection[1].

Inrealitytheradiowavepropagatesduetointeractionbetweenanelectrical

andamagneticeld. Whenthestrengthofasignalisdiscussed,itisthemag-

nitudeoftheelectriceldthatisintended. Thetwoelds areperpendicularto

eachotherandtotheirdirectionofpropagation,atleastinfreespaceconditions.

Becauseof thistherayis ausefulconceptwhentalking aboutradio waves. A

rayisanimaginaryline alongthedirectionoftravelofthewaveperpendicular

tothewavefront[2]. Whatfreespace conditionmeans andotherpropagation

phenomenawill bedescribed below. Ingeneral,awavewill experienceseveral

ofthephenomenasimultaneously.

2.1.1 Free Space Propagation

Ifatransmissionisperformedwellawayfromtheearth'ssurface,avoidingany

eectsfromit,thenitissaidtobeinfreespacepropagationconditions. Theray

ofthesignalisundertheseconditionsspreadaccordingtoaninversesquarelaw

[1]. FriisRadiationFormula(2.1)describesasignalbeingtransmittedbetween

twopointsspaced

d [m]

^apart,

P r = G r G t P t

 λ 4πd

 ²

[W]

^(2.1)

Inequation(2.1)

P t [W]

^isthetransmittedpower,

P r [W]

^{isthereceivedpower,}

G r

^{is the gain of the receiver and}

G t

^{is the gain of the} transmitter. If the logarithmof (2.1)istaken,itcanbewritten as:

10 log 10 P r = 10 log 10 G r + 10 log 10 G t + 10 log 10 P t + 20 log 10

λ

4πd

^(2.2)

Ifthepowerandthegainisrelatedto1mWandthegainofanisotropicsource

respectively,(2.2)canequivalentlybeexpressedas:

P r [dBm] = P t [dBm] + G r [dBi] + G t [dBi] − 20 log 10

4πd

λ [dB]

^(2.3)

Thelastterm in(2.3) iscalled thefreespacepath loss

L f sp

^{, expressedin dB.}

It represents the loss of a signal transmitted through free space without any

obstaclesorinterfering objects. If

λ

^isreplacedby

_f ^c

^where

f

^{isthe frequency}

inGHzand

c

^{isthespeedoflightmultipliedby}

10 ⁹

^{andthetermsareseparated}

andtheconstantiscalculated,thefollowingexpressionisobtainedforfreespace

propagationpathloss:

L f sp [dB] = 32, 4 + 20 log 10 (d) + 20 log 10 (f )

^(2.4)

Thisisanequationthat isverycommonlyusedin radiopropagationcontexts,

asit istheminimumlossthatwill occurwhiletransmitting. Equation(2.3)is

expressedinwordsas:

received power = transmitted power + antenna gains − losses

^(2.5)

Thisenablesequation(2.5)tobeconsideredasageneralexpressionfordescrib-

ingpropagation wherelosses notonlyaccountsfor freespacepropagation loss

butalllossesinvolvedinthetransmission. Thisincludesforexamplelossesdue

toreection,refraction,diractionandscattering.

2.1.2 Reection, Refraction and Scattering

Reection describes an incident wave being reected at an interface between

two media and refraction describes an incident wave being transmitted from

amedia into another. A wave most often suers both phenomena. Specular

reectionisreectionat asmoothsurfaceanddiusereection isreectionat

aroughsurface. Reection and refractionchangesnot onlythe direction and

powerofthewave,butalsothepolarizationwhich isanimportantpropertyof

awaveasitaectstheabilityto transferpower.

ThespecularcaseisecientlydescribedbySnell'slaws,thelawofreection

(2.6)and thelaw ofrefraction(2.7). Theindex of refraction

n

^ofamatrialis

aninterface.

Θ i,r,t

^{aretheangles betweenthenormalof theinterfaceand the}

dierentraysand

n 1,2

^aretherefractionalindexesofthedierentmaterials.

heavilydependentonthefrequencyoftheincidentwave.Theangles

Θ i

^,

Θ r

^and

Θ t

^{are theanglesbetweenthenormalofthesurfaceandtheincident,reected}

andrefracted/transmittedwaverespectively.

Θ i = Θ r

^(2.6)

n 1 cos Θ i = n 2 cos Θ t

^(2.7)

Diuse reection and refractionoccurs when asurface isnot ideallysmooth,

which is generallythe case. Wether a surfaceis considered smoothor rough,

the level of roughness and how much it aects an incident wave is of course

dependent on the material, but also on the wavelength

λ

^{of the wave. Also}

the anglewith which it imposes on the surfaceis important [1]. A surfaceis

generally thought of as smooth if its vertical height variation

h

^{satises the}

Rayleighcriterion;

h < λ 8 cos Θ i

(2.8)

where

Θ i

^{is theangle betweentheincident rayandthe normalofthe surface,}

seegure2.2. Equation(2.8)impliesthat mostmanufacturedsurfaces canbe

regarded as smooth and treated as such for wavelengths

λ

^{at the decimeter}

scale. However,when thewavestrikesaroughsurfaceorheterogeneitieswith

smalldimensionscomparedtothewavelengthsuchassoilortreesthereection

canno longer betreated as specular. From such surfaces,the outgoing wave

andthegrayraysarethelessenergeticscatteredrays.

is scattered, see gure 2.2. Scattering means that the energy of the wave is

distributedinseveraldirections[3]thusreducingthepowerintheidealreected

direction. However,scattering cansometimes bedesired asitprovidesagood

spreadingofthewave.

2.1.3 Diraction

Thewayelectromagneticwavesbehavewhentheyimpingeonobstaclesoraper-

tureswith dimensionslargerthanthewavelengthis describedbythepropaga-

tionphenomenonknownasdiraction. Tounderstandit,itiseasiesttoabandon

theraydescriptionandinsteadconsiderthewavefrontsofthewaves. According

toHuygens'sprincipleallpointsonawavefrontcanberegardedasanisotropic

radiator radiating spherically, see gure 2.3. This implicates that the future

behaviorcanbesynthesizedfromtheinterferenceoftheeldsfromtheseimag-

inary secondaryradiators [1]. Diraction enablesradiation to bend around

cornersatthe expensesof energylossin thewave. It arisesfrom manyoccur-

rences,forexamplethecurvatureoftheearth,hillyorirregularterrain,building

edgesorobstructionsblockingthelineofsight[LOS]pathbetweenthereceiver

andthetransmitter[4].

2.1.3.1 IdealKnife Edge Diraction

DiractioncanbeverydemandingtomodelandtherefortheapproximateFres-

nelknifeedgediractioniscommonlyused[4]. Theidealknife edgediraction

usetherayconcept. Thegeometryofthemodelwithonesingleknifeedgeand

obstructedLOSbetweenthetransmitterandthereceiverisshowningure2.4

wherethediractingobjectisassumedtobeasymptoticallythin andinnitely

Thegrayercirclessymbolizestheimaginarywavefrontsofthepointsources. The

wavefrontthus curvesaroundthecorner.

Figure2.4: Geometryofknife edgediraction.

wide. TherecanalsobeknifeedgeeectsfromobjectsnotobstructingtheLOS

aslongas theyaresucientlyclose totheLOS path. Besidestheapproxima-

tion of asymptotically thin and innite objects, the model does not consider

diractor parametersuch as polarization, conductivity and surfaceroughness.

TheelectriceldstrengthbetweenthetwoantennasisdependentontheFresnel

cosineandsineintegrals;

C (ν) = Z ^ν

0

cos πt ²

2 dt

^(2.9)

S (ν) = Z ν

0

sin πt ²

2 dt

^(2.10)

wherethedimensionlessFresnelparameter

ν

^isdenedas:

ν = h d + d ⁰ dd ⁰

s 2 λ

 1 d + 1

d ⁰



(2.11)

Thedistances

d [m]

^,

d ⁰ [m]

^and

h [m]

^{aredened ingure2.4and}

λ [m]

^{is the}

wavelength[3]. TheFresnelparameterexpressestheobstructionbytheobstacle

oftheLOS. ThedevelopmentoftheFresnelintegralsin seriesleadstoapprox-

imate relations for the attenuation relative free space due to the obstructing

object. Oneexampleofsuchanapproximationisequation(2.12)foundin[4].

L (ν) [dB] =



 

 

 

 

 

 

20 log 10 (0.5 − 0.62ν) −0.8 ≤ ν < 0 20 log 10 0.5e ^−0.95ν

0 ≤ ν < 1 20 log 10

 0.4 −

q

0.1184 − (0.38 − 0.1ν) ²



1 ≤ ν ≤ 2.4 20 log 10 (0.255/ν) ν > 2.4

(2.12)

There arealso models for multiple diracting edgesand even forrounded ob-

stacles[3].

2.1.4 Guiding

Some environmental features like street canyons, tunnels and other building

constructionsact like waveguides for radio waves. This is thecase especially

whenthewavelengthisverysmallcompared tothecrosssectionofthefeature

[3]. Awaveguideisintheelectromagnetictheorydenedasatubeofperfectly

conducting material with open ends and constant cross section[5]. The tube

can be of arbitrary shape but most often the square or the circular shape is

considered. A wave propagating inside a wave guide is restricted to certain

modesduetothefact thatthewavehastoterminateatthewallsoftheguide.

Thisimpliesthatthereisaminimumwavelengthforsignalspropagatinginside

aspecic waveguide[1]. Thecorrespondingfrequencyisknownasthecuto

frequency,that istosaythewaveguideactsasahigh passlter.

2.1.5 Dispersion

Dispersion denotes frequency dependent eects in wave propagation. In the

presenceof dispersion,wavevelocityis nolonger uniquelydened. This gives

risetothedistinctionbetweenphasevelocity,thevelocitywithwhichapointof

constantphasemovesandgroupvelocity,thevelocitywithwhich anymodula-

tionofthewavetravels[1]. Awellknown eectofphasevelocitydispersionis

thecolordependenceoflightrefractionthatcanbeobservedinprismsandrain-

bows. Dispersionmaybecaused by geometric boundariessuch aswaveguides

orbyinteractionbetweenwaves.

2.2 Propagation Models

Asaresultofthepropagationphenomenadescribedabove,numerouspropaga-

tionmodelshavebeendeveloped,oftenforaspecicscenarioandcircumstances.

Inthissectionsomeofthemodelsthathavebeenimportantpartsofthecreation

presented.

2.2.1 Piecewise Linear (Multislope) Model

The piecewise linear model, also called the multislope model, relatesdB loss

tolog distance. Itis anempiricalmethod formodeling pathlossusedin both

outdoor and indoor cases[4]. Thearea of interest is dividedinto

N

^dierent

regions. Theregions

s ¹ , . . . , s N

^{areseparatedby}breakpoints

(d ¹ , d ² , . . . , d N−1 )

andeachregionhasaspeciclinearslope. Thebreakpointsandtheslopeshas

tobedecidedinthemodeldesign. Equation(2.13)belowdescribesaspecialcase

of themultislopemodel, thedual slopemodel. Inthe dual slope model, only

twopath lossregions are considered. The rst region with slope

γ ¹

^stretches

fromareferencedistance

d ⁰ [m]

^{toacriticaldistance}

d c [m]

^{wherethepathloss}

exponentchangesto

γ ² .

P r (d) [dB] =







P t + K − 10γ ¹ log 10

 _d

d 0

 d ⁰ ≤ d ≤ d c

P t + K − 10γ 1 log 10

 d _c d 0



− 10γ 2 log 10

 d d _c

 d > d c

(2.13)

In equation (2.13)

P r [dB]

^{is the received power,}

P t [dB]

^{is the} transmitted powerand

K [dB]

^{is a constant path lossfactor. The path lossexponents}

K

and

d c

^{areusually foundtrough aregressiontto empiricaldata.}

2.2.2 BuildingPenetrationLossatLOSConditionsinCOST

231

Themodelproposedin[6]isanattempttodescribemanydierentpropagation

modelsproposedbytheCOST231participants. Themodelassumesfreespace

propagation path lossbetweenthe external antenna and the illuminated wall

andisnotbasedonanoutdoorreferencelevel.

L [dB] = 32.4+20 log 10 (f )+20 log 10 (S + d)+W e +W G e

 1 − D

S

 ²

+max (Γ 1 , Γ 2 )

(2.14)

( Γ 1 = W i · p

Γ ¹ = β · d

^(2.15)

Γ ² = α · (d − 2) ·

 1 − D

S

 ²

(2.16)

The model parameters, theangle

θ [deg]

^{and thedistances}

S [m]

^,

D [m]

^and

d [m]

^{aredenedingure2.5. Thefrequency}

f

^isin

GHz

^and

W e

^isthelossin

dB

in theexternallyilluminatedwallat perpendicularpenetration(

θ = 90 [deg]

^).

The only time when

θ = 90 [deg]

^{is when}

S

^and

D

^{are equal, that is when}

theexternalantennaislocatedatthesameheightastheoorheightandat a

perpendiculardistancefromthewall. TheadditionallossindBintheexternal

wallwhen

θ = 0 [deg]

^isrepresentedby

W G e

^,

W i [dB]

^{in(2.15)isthelossin the}

internalwallsand

p

^{isthenumberofindoorwalls. Incasethere isnointernal}

walls,thentheindoorlossisdecidedwithanindoorslopein

dB/m

^{. Inequation}

(2.15),therst expressionfor

Γ ¹

^{canbereplacedbythesecond,}

β · d

^where

β

is a slope in

dB/m

^{, if the average indoor wall loss and the average distance}

betweentheindoorwallsareknown. Finally

α

^{isaslopeconstantin}

dB/m

^.

2.2.2.1 HeightGainin COST231

Theoutside-to-insidepenetrationlossatdierentoorlevelsissometimesfound

todecrease withincreasingoorlevels,somethingthatis alsodiscussedin [6].

Thedependence iscalled oorheightgainand isgivenin

dB/m.

^{Gainin this}

contextispathgain,theinverseofthepathloss,andisnottobeconfusedwith

antenna gains as described in section 2.1 on page 6. The sum of the outside

referencepath loss value and theheight gainloss, can neverbe less than the

freespace propagation path loss, sincethat would be highly unrealistic. The

oorheightgainceasestobeapplicableatoorlevelsthatisconsiderablyabove

theaverageheightoftheneighboringbuildings. Themostnotableoorheight

gainisfoundinnonlineofsights[NLOS]conditions,whenthemainpartofthe

receivedsignalpoweroriginatesfromraysthatduetoreectionsanddiraction

havepropagateddownfromthesurroundingrooflevel. Thisisusuallythecase

in macro-cellular 1

environmentswith thebase station[BS] at aheightgreater

thantheaverageheightoftheneighboringbuildings.

1

Macrocellsaredenedbytheheightandtransmittingpoweroftheemployedantennas.

Heightsareabovetheaveragesurroundingbuildingheightsandthepowerisintherangeof

40to80

W

.

Figure2.6: Denitionofoutdoorpixels. Only

P k,2−6

^isoutdoor.

2.2.3 Outdoor-to-Indoor Propagation in Urban Areas at

1.8Ghz

In[7]amodeltreatingoutdoortoindoorpropagation isproposed. It ispartly

based on [6] and consists of two parts, one empirical and one semiempirical.

Bothpartsusetheheightgainmodeldescribedbelowinsomeform.

Theheightgainmodelinshortusesthepathlosspredictedatgroundoor

todecidepathlossathigheroors. Eachoorisconsideredtobe3

m

^highand

subtracts3

dB

^{from thepathloss,therebyrenderingtheresultingpathlossat}

higheroors lesser than at ground level. The model is considered to be valid

uptooornumber5ifthegroundooris setto0.

Theempiricalmodelcontainsthreedierentparts. Therstisthecalcula-

tionrulesdescribinghowtheindoorpathlossisderivedfromtheoutdoorpath

lossofallsurroundingpixels. Thesecondisanempiricalpenetrationlossfactor

describingthesignalstrengthdierenceinsideandoutsidethebuildingandthe

thirdistheempiricalheightgainmodeldescribedabove.

Firstthebinstobeconsideredhastobedecided. Theset

P in

^containsall

N

binsbelongingtothesamebuildingwithat leastoneneighboringoutdoorbin.

Then,foreverybin

P k

ⁱⁿ

P in

^theset

P out,k

^ofallneighboringoutdoorpixelsis determined,seegure2.6. Equation(2.17)calculates

L ¯ building,f loor [dB]

^which

isthemeanindoorpathlossforaparticularbuildingandoor. Itisdetermined

byaveragingthe

N

^{pathlossvaluesin}

L in,k [dB]

^.

L ¯ building,f loor [dB] =

P ^N

k=1 L in,k

N

^(2.17)

L in,k [dB] = min 

L f sp,k + L emp , ´ L in,k



(2.18)

L ´ in,k [dB] = min

∀i,P i P _out,k (L k,i ) + L pen

^(2.19)

L pen [dB] = L emp − G h

^(2.20)

Tocalculate

L in,k

^{thehelpvariable}

L ´ in,k

^{isused. Itisthesumoftheminimum}

outdoor path lossof all

P k,i  P out,k

^{and the} penetrationloss

L pen

^{. Thepene-}

trationloss

L pen

^{is theempirical loss factor}

L emp

^{reducedby the height gain}

G h

^{. Thepathloss}

L in,k

^{isthentakenastheminimumof}

L ´ in,k

^andthesumof

freespacepath loss

L f sp

^{, see equation(2.4)onpage 7,and}

L emp

^{. This limits}

L in,k

^{to realisticphysicalvalues. Thevariable}

L k,i

^{is thepath losscalculated}

bytheoutdoormodelat bin

P k,i

^{. Thevalueof}

L emp

^{is setto between19and}

22

dB

^{, valuesthatarededucedfrom} measurements.

The semiempirical model improveson the empirical model by introducing

somedeterministiccomponentsifLOSbetweentheBSandatleastsomeparts

ofthebuildingexist. ThemodelstartswithdistinguishingLOSandNLOSfor

eachbinoneveryoor. Thentwoseparatemethodsforpathlosscalculationin

caseofLOS orNLOSaredeployed. IfthebinshaveLOS thenthepathlossis

calculatedas

L in,LOS,k = 32, 4 + 20 log 10 (f ) + 20 log 10 (s + d0) + L perp + L par

 1 − D

S

 ²

(2.21)

whichisfreespacepropagationpathlosswithaddedlossforenteringthehouse.

Thedistances

d0

^,

S

^,and

D

^{all in}

m

^{aredened in gure 2.5onpage 13. The}

empiricalpenetrationfactor describingpenetrationlossforperpendicularinci-

denceofthewaveisrepresentedby

L perp

^and

L par

^{isanempirical}penetration factor describing an additional penetration loss factor for

θ → 0 [deg]

^{. The}

angle

θ

^{isdened ingure2.5.}

ThepathlossintheNLOScaseiscalculatedasintheempiricalmodelwith

thesmall dierence that when calculatingtheoorheight gainthemaximum

number of oors is limited to the number of oors which corresponds to the

mean building height along the path between the BS and the mobile station

[MS].

2.2.4 Multi-FrequencyPathLossin anOutdoor toIndoor

Macrocellular Scenario

The article[9] describes the connection between dierent frequenciesand the

excesspathlosstheygenerate. Theexcesspathloss

L E

^{is denedin equation}

(2.22)asthelossrelativetofreespacepropagationpathloss

L f sp

^(seeequation

(2.4)),

L E [dB] = L P − L f sp

^(2.22)

where

L P [dB]

^{isthepathlossasdenedinequation(2.23),}

L P [dB] = P t − P r + G t + G r

^(2.23)

The variables

P t [W]

^and

P r [W]

^{are the} transmitted and received power re- spectivelyand

G t

^and

G r

^{aretheantennagainsofthe}transmitterandreceiver respectively. An advantageof usingexcesslossinsteadof absolutelossis that

thefrequencydependantapertureofthereceiverantenna,whichdoesnotreect

anyenvironmental propagationproperties,isremoved.

0 5 10 15 20 20

25

30

35

40

45

50

Average Building Penetration Loss

Floor Llos = 24,5 dB Gfl=3dB

LOS floor: 7

Figure 2.7: Average building penetration loss, using

G F l = 3.0 dB

^,

n F lb = 7

^,

a = 4

^and

L LOS = 24.5 dB

^.

Thearticlealsodescribeslossdependencyonoorlevelsandproposesasim-

pleempiricalmodeltomodelthedependencyasanaveragebuildingpenetration

loss

L [dB]

^:

L [dB] = 10

a log 10

 10 ^{− nF lGF la 10} + 10 ^{− nF lbGF la 10} 

+ n F lb G F l + L LOS

^(2.24)

L LOS [dB] = L mes,in − L f sp,out

^(2.25)

Themodel isbasedon thebuildingpenetrationlossat LOS conditions,

L LOS

as dened in equation (2.25), and the corresponding gain with oor level in

NLOSconditions,

G F l [dB]

^{. Theoornumberis}representedby

n F l

^and

n F lb

^is

theoornumberforthelowest oorat which thereisLOS conditionstowards

the transmitter.

a

^{is a parameter adjusting the size of the model transition}

zone between the LOS and the NLOS conditions. The loss factor

L mes,in

^is

the measuredvalue inside thebuilding and

L f sp,out

^{is the} theoretical outside freespacepropagation pathlossreferencevalue. Themodelin equation(2.24)

hasbeenttedtomeasurementsmadeinside andoutsidebuildings[9]and the

resultingvaluesof

G F l

^{isbetween1and 4}

[dB/floor]

^{and of}

L LOS

^between20

and35

[dB]

^.

Thevalueof

L LOS

^{cannotalwaysbemeasuredsincesomebuildingsnever}

reach therequired height. In such casesit is suggestedthat

L LOS

^{istaken as}

L Dif f

^{whichis thedierencebetweenthemeasuredlossindoors andoutdoors}

atgroundlevel. Incaseswhenthisisnotapossibilityeither,

L LOS

^issuggested

tobesetasaparameterwithavaluein therangeofthevaluesmeasuredin[9]

whicharein therangeof20-30

dB

^.

In[10]twowaysofcalculatingpenetrationlossiscompared. Therstiswhen

penetrationlossisdeterminedusingthedierencebetweenthepathlossindB

from measurements in the building and reference measurements outside the

building. The second is to use the theoretical free space propagation path

loss as the outside reference loss instead of measured reference levels. The

articlesuggeststhelatteras themoreaccuratemodel. Fordetails onhow the

measurements were made, see [10]. Measured penetration losses are found to

varybetween5dBand30dB.Ifinsteadatheoreticalreferencevalueisused,two

major dierences appear. First that the penetration loss increases when the

theoreticalpathlossvalueisusedasreferencevalue,andthesecondisthat the

spreadof penetration lossvaluesdecreases to instead vary between23dB and

32dB. By using the theoretical values instead of the measured, abnormalities

canbeavoidedandthepenetrationvaluesbecomesmoresuitableformodelling.

Anotherresult presentedis that dierencein penetrationlossbetweendif-

ferentfrequencies,inthiscase900MHzand1700MHz,issignicantlydecreased

usingthetheoreticalvaluesasreferencevalue.

2.2.5 Ericsson Urban Model

TheEricssonUrbanModelisaconceptthatcombinestwodierentwaveprop-

agation algorithms, the half screen model and the recursive microcell model

[8].

Thehalf-screenmodelisusedforcalculatingthepropagationaboverooftops.

ObstaclessuchasbuildingsandtreesbetweentheBSandtheMSaremodelled

with anumber of screens with heights correlated to the heightsof the obsta-

cles. The path loss

L above [dB]

^{is then calculated using a multiple knife-edge}

approach, see part 2.1.3.1 on page 9. Two kinds of screens are employed to

describetheproleoftheenvironment,permanentscreensthatareplacedin a

statistical way, and temporary screens that are placedin adeterministic way.

Thepermanent screensare used to describe theenvironmentalong thecalcu-

lation prolein ageneral way and thetemporary screenswill describedetails

of the environment more accurately, near the mobile antenna. For example,

thescreensmodelling aforest wouldtypicallybeset in astatistical way,while

screensmodelingbuildingswouldbesetdeterministically.

The recursive microcell model is used for calculating the propagation be-

tweenbuildings,forexamplealongstreets. Fordeningthepropagationpaths,

theexactlocationsof buildings accordingto thebuildingdata base,are used.

Thepathloss

L below [dB]

^{iscalculatedby}determiningthesocalledillusorydis- tancebetweentheBS andthe MSin astreetsystem. Theillusorydistance is

determinedwitharecursivemethod,usinginputdatafromastreetsystemand

takesintoconsiderationthemultiplestreetcrossingsandturnsthatarepresent.

TheresultingpathlossarisingfromtheUrbanModel

L urban [dB]

^istheleast

ofthetwovaluesgeneratedbythetwomodels,

L urban [dB] = min (L above , L below )

^(2.26)

Closetothebasestationand inLOS cases,themicrocellmodeldominatesand

only the value of

L below

^{is used. Otherwise it is the half screen model that}

dominatesand onlythe valueof

L above

^{is used. In reality bothvaluesalways}

contributetothetotalpathlossbut theeectsofthisapproximationaresmall

enoughnottobesignicant.

Themodelisconsideredvalidforfrequenciesfrom450MHzupto2200MHz

andat distancesbothclosetoandfarfrom,atleast50

km

^{,theBSantenna. It}

isalsoconsideredvalidforhighMSheights.

2.2.5.1 Indoor Propagation

For indoor propagation in the Ericsson Urban Model, given it has access to

a detailed land use map containing the locations and heights of buildings, a

specialindoormodelwiththefollowingpropertiesisused. Anindoorpathloss

valuefor aparticular bin is calculatedby rstdeciding the four outdoorbins

closestoutsidethebuildingtothenorth,thesouth,theeastandthewestofthe

indoor bin,see gure2.8. Thepath lossvaluesofthese binshavebeenchosen

accordingtoequation(2.27).

L out [dB] = max (L urban , L f sp + W ge )

^(2.27)

Thepath loss

L urban

^{[dB] is avaluecalculated by theUrban Model, which is}

treatedaboveand

L f sp [dB]

^{is thefreespace} propagationto that outdoorbin fromthebasestationcalculatedaccordingtoequation(2.4). Theadditionalloss

W ge [dB]

^{is walllossthat accountsfor extralosses due to agrazingincidence}

angle. ThegrazeconstantonlyoccurswhenaLOSpathisassumed,sinceNLOS

pathsoftenarescatteredfrommultipledirections,leavingatleastonethat has

aperpendicularincidenceangle,whileLOSpathsonlyhaveoneincidenceangle

and it can't be assumed to be perpendicular to the building wall. From the

path lossvalues of these outsidebins, an external wall lossconstant

W e [dB]

issubtracted andthen alossper meter,asocalledslope,

α [dB/m]

^{isused to}

account forthe additionalpath lossof thenal indoordistance

s [m]

^{, leaving}

theindoorpathloss

L in [dB]

^{asinequation(2.28)}

L in [dB] = L out [dB] + W e + s · α

^(2.28)

Theindoorpathlossvalueiscalculatedforallfourstartingpositionsandthen

thebestindoorpathlossisused.

startingpositionsforindoorpropagation.

Description of Real Network

Simulator and 3D Path Loss

Models

Inthefollowingchapters,theconceptofpathlosswillbefrequentlydiscussed,

itisthereforeimportanttodenewhatisintendedwiththisconcept. Pathloss

isaccordingto ITU 1

dened aslosses dueonlytothephenomenadescribedin

section2.1onpage6andsimilarpropagationfactors. Inthefollowingchapters

alsoantennaandotherequipmentpropertiesareincludedinthecalculationsof

thetotalpathloss. ITUwouldclassifythatassystemloss.

3.1 Short Description of the Real Network Sim-

ulator Astrid

TEMSCellPlanner[TCP]

2

isacellplanningtoolthatcanbeusedforpathloss

predictionsofradio networks. Inthepredictionsperformedfor thisrapportit

usesthemodeldescribedinsection2.2.5onpage17. Thepathlosspredictions

consider terrain and building information depending on thelevelof details in

the map data employed. For example, in the predictions performed for this

report the positions and lobe patterns of the antenna and building locations

andheightsareknownwithaprecisionofsquareswiththesidesof5

m

^,called

bins.

The data is exported to the stationary MATLAB real network simulator

called Astrid. Astrid usesanadvanced radio modelspecic forLTE technolo-

gies. Itenablessimulationsoffairlylarge,inhomogeneousnetworkswithtrac

distributionswithaspeciedpercentageofindoorandoutdooruserequipment

1

ITUistheUNagencyforinformationandcommunicationtechnologies.

2

RecentlychangedtoMENTUMCellPlanerfornewreleasesoftheprogram.

[UE].Astrid also enablesdierent trac levels between cells. The simulation

considersarestrictedareaofalargecity. Inordertomodelrealisticinterference

situations at allsimulated cells,interference contributionsfrom outside of the

restrictedareahavetobeconsidered,seegure3.1.

Thepredictions in Astridcanbeperformed atdierentloads. Theloadis

theratio between used and total resources. If all theresources are allocated,

meaning that oneUE orBS per cellis transmitting with full bandwidth and

fullpowerallthetime, the loadis100%. Should theloadbelower,then the

transmission is only ongoing partof the time. In each instant, only one UE

orBSisactiveineverycell. Everysimulationconsistsofseveraltimeinstants.

Theresourcescanbeadministeredindierentwaysbutinthisreporttheyhave

beendistributedsothatallUEregardlessoftheirSINRwillgetequalaccessto

theresources. This meansthat UE with poorSINRwill transmitand receive

less data than a UE with good SINR. The capacity of the system is closely

entwinedwith theload. A systemcapableof deliveringacertain bitratefor a

specic timei.e. aspecicloadhasahighercapacitythanasystemcapableof

deliveringthesamebitrateforlesserperiodsoftime, i.e. atlowerloads.

3.1.1 SINR Calculations

TheSINRcalculationsdiersbetweentheuplink[UL]andthedownlink[DL].

TheinterferersintheDLareBSfromsurroundingcells. Theyarestationaryand

thereforetheirlocationandnumberareeasiertopredictthantheinterferersin

theUL.IntheULtheinterferersareUEintheneighboringcellsandtherefore

mobile which makesthe interference hard to predict. The DL interference is

basedonpathgainpredictionsfrominterferingcellstotheconsideredcell,and

informationaboutBSpowersfrominterferingcells. Astatedpowerlevelisused

forallloadsituations.

TheULinterferenceis modeled byintroducing aMonte Carlodistribution

ofUE tocreate interference. Thisdistribution ofUE isrepeatedseveraltimes

to create astatistically credible scenario. Equation (3.1) describesthe SINR

calculationofabin. Thevariable

P [W]

^isthepowertransmittedfromtheBS,

g

^{is the path gaini.e theinverse of path loss,calculated foreach cellto each}

binand

N [W]

^isthenoise.

SIN R bin = P best sell · g best cell

P

i6=best cell P i · g i + N

^(3.1)

TheSINRvaluesaretranslatedtobitratesaccordingtoalink tosystemmodel

relatingSINRto bitrates.

Theresultsof asimulationcanbepresentedastheresultineverybin,this

isreferredtoasbinprobing. Thealternativeistoonlypresentthebinsselected

bytheMonte Carloprocess. Thisisreferredtoasuserdistribution.

3.1.1.1 SINR Calculations for3D UserDistributions

TheSINRcalculationsare essentiallythesameasbeforewhenthebinsorUE

are distributed in a3D fashion. The dierenceis that as theheight of a bin

isincreased, therewill besomedecreasein pathlossand thisapplies forboth

theconnection between theUE and its serving BS aswellas theUE and in-

terfering BS or BS and interfering UE. This has been modeled by giving the

gaincalculatedbetweenthe UE and itsserving BSto not onlythat path loss

predictionbut alsotoalltheinterfererspathlosspredictions. Thismightbea

slightlypessimisticassumptionbut sincenomeasurementsaddressingtheissue

hasbeenmaderegardingthis,itisthebestapproximationavailable.

3.2 3D Models

Inthissectionthestructureandconceptofthe3Duserdistributionmodelsthat

hasbeencreatedaredescribed. Theyaredescribedin thechronologicalorder

thattheywerecreatedandtestedandthereforesimplynamedasmodeloneto

modelseven.

3.2.1 Models whitout LOS considerations

ThersttwomodelsdoesnottakeanyLOScalculationsinto consideration.

3.2.1.1 DescriptionofFirst Model

This model is based on the article [7], that describes outdoor and outdoor-

to-indoorpropagation. Inthe article, measurements were made in the towns

ofCologneand Leipzigand amodelwascreated,tested and comparedto the

measureddata. Theyfound the predictionsmade by theirmodel to befairly

accuratecomparedtotheirmeasurements. Notallof theirmodelisused here,

butsomeassumptionsconcerningbuildingandoorproperties.

The indoor bins are given a oornumber according to a uniform random

distribution from ground oor, oor 1, and up to a specic maximum oor

level. Thismaximumis givenbyaparametercalledmaxoor. Maxoorisset

to6inthesimulationsandeachooris consideredtobe3mhigh,bothvalues

inaccordancewith [7],see section2.2.3onpage14.

6oors. Inallothermodelstheheightof thebuildings variesaccordingto the

buildingdata.

ThepathlossiscalculatedinTCPatgroundlevel,whichinthiscasemeans

1.5

m

^{aboveground, for allbins, indoorand outdoor. Forthe indoor bins, 3}

dB

^{path gainisadded for each oorabovegroundoor. Themodeldoes not}

separateindoorbins at theedge of the housefrom indoorbinslocated in the

middleofthehouse,theyareallgiventhesameoorheightgainof3

dB/floor

^.

3.2.1.2 DescriptionofSecond Model

The second model is almost identical to the rst. The dierence lies in the

parametermaxo. Maxoisnotonexedvalueforallbuildingsin thismodel,

but the highest possible oor in every building. Since the number of oors

arenotknownfromthebuildingdatabase,but thebuilding heightsare,every

oor is assumed to be 3

m

^{high asin model one and in all modelsto follow.}

Floornumbersaredistributedrandomlyaccordingtoauniformdistributionfrom

groundoor,tothemaximumoorofthebuildingandallindoorbinsareagain

givenagainof3

dB/floor

^{foreveryoorabovegroundoor.}

3.2.2 Models With LOS Considerations

ThefollowingmodelstaketheexistensofaLOSbetweenbuildingandBSinto

consideration.

3.2.2.1 DescriptionofThird model

Thisthird model investigates wheatherabinhasaLOSto thebase stationit

uses, and ifit has, at what height that occurs. The LOS-informationis later

used to decide what kind of height gain a particular bin should have. The

oorsaredistributed asinthesecondmodel,uptothemaximumheightofthe

building,withanassumedoorheightof3

m

^{. Eachbin,nowgivenaoor,then}

getsaoorheightgainthatdependsonwhetherthatparticularoorhasaLOS

draw betweenthe BS and twoconsecutiveoors, thelowerwhitout LOS and

thehigherwithLOS.

or not. This idea comes from the samesource asbefore [7]. Theassumption

is that once aoorhas LOS, allhigher oors also haveLOS. The calculation

of LOS or NLOSare done between abin and its serving BS. Thebin is rst

assumedtobeatgroundlevel,1.5

m

^{aboveground. Animaginarystraightline}

isdrawnbetweentheBSandthebin. Ifanyintermediatebuildingobstructsthe

line,thenitsstatedthatthebindoesnothaveLOSconditions. Thisprocedure

isthenrepeatedat 3

m

^{intervals,i.e. attheoors,untileitheraLOS hasbeen}

conrmedorthebuildingrun outofoors. Only binsthat aresituated onthe

edgeofabuildingcanhaveLOS.

AbinwithoutLOSattheoorgiven,getstheusual3

dB/floor

^oorheight

gain. Thebinswith LOS atthegivenoorgetapathgainvalueinterpolated

frompredictionsin TCPinstead. Onepredictionismadeat groundlevel,one

ataheightthatcorrespondsto6oors,i.e. 15

m

^{,andoneismadeataheight}

of 40

m

^{and then the path lossvalues in betweenare} interpolated linearly in

dB

^{3. Whenchoosingtheheightfortheupperpredictionlevel,thevaluesfound}

in table 3.1 were considered. Thetable describes the distribution of building

heights in the considered area. The height chosen, 40

m

^{, is high enough to}

include almostallofthe indoorbins(only2.03%of thebinsbelong to higher

buildings),butnotsohighthattheanglebetweentheoorandthebasestation

becomestoolarge. Itis importantthat theupperheightisnottoohigh since

atoogreat an angle would cause the pattern of theantennalobeto increase

thepath lossin a manner that is nolonger probableto be linearin

dB

^{. The}

assumptionof40

m

^{beingagoodchoicewillbefurther}investigatedinsection4.2 onpage31.

3

Notethatthe LOScalculationsareperformed1.5

m

uponeveryoor,while15

m

isat thebottomofa oor. Thisiscompensated byusingan interpolatedvaluethat is1

m

up.

Thedecreasefrom1.5

m

to1

m

isconsideredreasonablegiventhatUEathigheroorsmight beataworkingdeskheight.

percentofallbins

[%](totalnumber

of bins263516)

percentofindoor

bins[%]

numberofbins

higherthanX

(totalnumberof

indoorbins

119647)

X [m]

0.0748 0.1647 197 90

0.0964 0.2123 254 80

0.1150 0.2532 303 70

0.2178 0.4797 574 60

0.3419 0.7530 901 50

0.9210 2.0285 2427 40

5.4653 12.0371 14402 30

23.8946 52.6265 62966 20

43.1146 94.9577 113614 10

45.3786 99.9440 119580 5

3.2.2.2 DescriptionofFourth Model

This model is basically the same asthe third model in that it separates the

indoor binswithLOS fromthose withNLOS.TheLOS binsarealsofound in

thesame manner and theoors are distributed to all bins asin model three.

ThedierenceisthattheNLOSbinsaregiventheirpathlossvalueinadierent

way. Given aparticular oorare associated with the LOS bins at that oor.

TheNLOSbinspathlossvaluesarethencalculatedaccordingto

L k [dB] = L k,los [dB] + d k · α

^(3.2)

L [dB] = min

k (L k )

^(3.3)

where

d k [m]

^{isthedistancefromtheNLOSbintoLOSbinnumber}

k

^onthat

oor with pathlossvalue

L k,los

^{.The valueof thelossfactor}

α

^{is 0.6}

dB/m

^as

suggested in [6]. The least of the calculated path losses

L

^{is then chosen as}

thepathlossvalue forthat NLOSbin. Thevaluefor

L k,los

^{istaken from the}

interpolated values as described in the previous section. This dierence be-

tweenmodelthreeandfourwasconstructedtomakesurethattheinnervalues,

supposedlydependantontheLOS tobinssituated attheedge ofthebuilding

actuallyhadanimpactonthechoiceofbinstostartfromwhencalculatingpath

lossforindoor bins.

All NLOSbinswithoutaLOS binon thesameoorisgiven aoorheight

gainof3

dB/floor

^{foreveryoorabovegroundoor.}

3.2.2.3 DescriptionofFifth model

In this model, the LOS calculations diers slightly from model three and 4.

Insteadofusingindoorbinssituatedontheedgeofthebuildings,animaginary

thenusedfortheLOScalculationsdescribedabove. Thischangeisdonetoavoid

theoutdoor-to-indoorcalculationsmadein TCP,see 2.2.5.1onpage 18andit

entails the need to introduce a new loss to account for building penetration

lossessincethosearenolonger contributedbythepathlossvaluesfromTCP.

Thereforeequation(3.3)usedinmodelfourisreplacedbyequation(3.4)inthis

model.

L [dB] = min

k (L k ) + W e + W ge

^(3.4)

Thevariable

W e [dB]

^{istheexternalwalllossfactorand}

W ge [dB]

^isthegrazing

anglelossfactor. Novectorinformationaboutthebuildingsareaccessible,dis-

ablingthecalculationofangleofarrivalfortheLOSraysreachingthebuilding.

Thereforeitis notpossibleto tunethegrazingangleslossandthe worstcase,

raysarrivingalmostparalleltothebuilding,isassumedforallbins. Intherst

setof simulations,

W e = 12 [dB]

^and

W ge = 20 [dB]

^{. Note that}

L k,los

^in(3.4)

is changedfrom being valuespredicted to theinside of thebuilding, to being

valuespredictedtojust outsidethebuilding.

The second set of simulations use a lowervalue for the grazing angle loss

factor. Insteadof 20

dB

^,

W ge = 12 [dB]

^{. Thiscould beconsidered asifit uses}

akindofaveragevalueinsteadoftheworstcasevalue.

3.2.2.4 DescriptionofSixth model

Section 2.2.4 on page 15 describes a simple model for outdoor to indoor loss

that is used asabase forthis sixth model. The average building penetration

loss

L [dB]

^{iscalculatedasinequation(2.24)onpage16. Thevalueof}

L

^isonly

specicfortheoor,notforeverybin,meaningthatallbinsontheoorgetthe

sameoorheightgain. However,sincethegainisadded toindoorpredictions

madebyTCPongroundoor,therewillstillbeagradientinsidewithmostloss

in themiddleofthebuilding. Theoorgainconstant

G F l

^{isset to}

3 dB

^asin

previousmodels,sinceitwasintherangeproposedinisin[9]andcoincideswith

thepreviouslyusedvalues,enablinganeasiercomparisonbetweenmodels. The

valueof

L LOS

^{isset to24.5}

dB

^{whichisin therangesuggestedin section2.2.4}

onpage15. If

L LOS

^{is thoughtofasa}replacementforwalllossconstantsand grazingangle losses asin 3.2.2.3 on thepreceding page, then the

L LOS

^value

is quite lower,maybeimplying that adecrease of the additionallosses might

be more suitable. The oor number

n F l

^{is assigned to the indoor bins as in}

all previous models except the rst. The variable

n F lb

^{describing the lowest}

oor at which abuilding hasLOS, is calculatedfor everybuilding. The LOS

calculationsare performed asin model four. It could also have been done as

in model vesincethe calculationsonly areused to set the variable

n F lb

^and

doesnotcontributeto the choice oroutdoorbinsused for indoorpredictions.

When a path loss value for an indoor bin is to be predicted, the value of

L

corresponding to that bin, or really, theoorthat bin is on, is calculated. It

isthenaddedtothetheoreticalpathlossincaseoffreespacepropagation,see

10 15 20 25 30 35 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

C.D.F.

Building penetration loss [dB]

0 1 2 3 4 5 6 7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

C.D.F.

floor heigt gain [dB]

Figure3.4: Cdfofbuildingpenetrationloss

L LOS

^{(totheleft) andoorheight}

gain

G F l

^.

(2.4)onpage7,ofthenearestoutdoorbingivingthetotalpathloss

L tot

^asin

equation(3.5). Thecalculationsarealsoperformedatgroundlevel,i.e. withall

thebinsat groundoor. This is toenablethe dierenceto becalculatedand

thenbeusedasoorheightgainaddedto thepredictionsmadebyTCP.

L tot = L + L f sp

^(3.5)

3.2.2.5 DescriptionofSeventh Model

Theseventhmodelisidenticaltomodelsixin everythingexceptintwothings.

Therstis that theparameters

L LOS

^and

G F l

^{arenot constant anymorebut}

distributedtoeverybinaccordingtoaGaussiandistributionwiththeirprevious

valuesastheirnewmeanvalue. Thestandarddeviationof

L LOS

^isthreeandof

G F l

^{itisone. Thesevaluesareselectedtokeeptheparameterswithintherange}

proposedin[9]. Thecdfcurvesof

L LOS

^and

G F l

^{canbeseeningure3.4. The}

seconddierenceisthatthereisanadditionallossaddedduetotheantennatilt

andverticallobepatternsoftheservingBS.Thelobepatternsaecttheresult

sincetheydirecttheeectoftheBSincertainanglesthatmightbefarofrom

theLOS between theBS anda binat acertain level. Thesamelobepattern

hasbeen used forall BS's antennas. This is anapproximationsince thelobe

patternsreally dier sightly, howeverthelobepatterns aresimilar enoughfor

theresulttobesignicantfortheuseofsuchalobepattern. Shouldtheeect

bemajor,itmightbeinterestingtousetheexactlobepatternforallantennas.

Theusedantennalobepatterncanbeseeningure3.5. Asisevidentthere,the

electricaltiltofthatantennais6degrees,thatiswhat75%ofalltheantennas

intherestrictedareahave,whichmotivatesthechoiceoftypicalantenna. The

lossdue to the lobe pattern is calculated in the following manner: Theangle

betweenthebinanditsservingBSiscalculated. IftheBSservingthebinhas

a mechanical tilt, that angle is added to the calculated angle. The resulting

angle is subtracted from 360 degrees, this is done to adopt the values to the

lobe pattern denition of angles that is, asseenin gure3.5, opposite to the

Theantennagainis16.0

dBi

^.

oor in building A, Band C will be counted8, 4and 6times respectively, to

create adata series forthe groundoorpredictionscomparable to the higher

levelpredictionsthat willbeperformedonce foreveryoorin abuilding.

convention. The result is theangle used to nd thecorresponding additional

loss

L lobe

^{dueto theangulardeviationfromthelobemaximum. Thislossneed}

toberelated tothe antennagain

G antenna

^{whichfor theantennausedis 16.0}

dBi

^{. Equation(3.6)describesthe}calculations. Note that

L

^{isreplaced by}

L G

sincetwoparametersusedtocalculateitisGaussian distributed.

L tot,lobe = L G + L f sp − G antenna + L lobe

^(3.6)

3.2.2.6 DescriptionofCrowded 3DModel UsingModel Six

Thismodelisslightlydierentfromallothermodels. ItisnotapartofAstrid

but completely separatewhich meansthat it onlycalculate pathlossbetween

the BS and the bins. No SINR calculations are performed and therefore, no

bitratescanbecalculated. Theintentionwiththismodelistodemonstratethe

pathlossimprovementsthatoccurwhenusersarehigherupin abuilding. The

pathlosscalculationsareperformedasinmodelsix. Thedierenceisthatonly

indoor bins areconsidered and the way the oors are distributed. Instead of

givingeverybinjustoneheightandperformingonesimulation,thismodelruns

asmanytimes asthe highestbuilding haveoors. Therst simulationplaces

allusersatgroundoorgivingaoorheightgainof 0

dB

^{. Nextsimulationis}

performed at thesecond oorand all buildings that are high enoughto have

asecond oorare considered. This continuesupto thehighestbuildingin the

area. All of these bins and their path loss values are then compared to the

correspondingvaluesatgroundoor,seegure3.6.

Simulations and Results

4.1 Comparison of computational times

The computational times of the calculations were measured using the tic tac

MATLABcommando. Thesimulationtimes arefor12separatecomplete sim-

ulationsinAstrid, 6withthe 3Dmodel activeand 6without. Italso includes

timeforplotting,butsincethat isthesameforallmodels, thattime doesnot

eect thecomparisons. Theresults areshown in table 4.1. Sincethe table is

based on one simulation of each model, the values can not be considered as

absolutelytruesincethereareotherfactorssuchasavailablememoryaecting

the simulation. However, the absolute value of the time consumption is less

important,therealinterestis inthecomparisonbetweenthe dierentmodels.

Thecomparisonshowsthattherstandsecondmodelsarethefastestbutthat

the sixth and seventh model are equalin speed. The forth and fth models

areconsiderablymuchmorecomputationallydemanding,andthatisobviousin

theirprocessingtimes. Thethirdmodelissomewherein between.

Therearealso somepreparationsneededtoperformbefore each model,for

exampletheLOScalculationsdescribedinchapter3. Modeloneandtwoneed

nopreparations. modelsixandsevenneedone(calculationofLOSandassoci-

atingbins to buildingswhich isperformedsimultaneously)while model three,

fourandveneedanothertwoquitetimeconsumingpreparationsconsistingof

pathlosspredictionsathigherlevelsperformedbyTCP.Allthesepreparations

areonlyneededtobeperformedonetime. Oncetheyaredone,themodelscan

beusedasmanytimesaswished.

Table 4.1: The computational times of the dierent models normalized with

respecttoDLinmodelone.

Model 1 2 3 4 5 6 7

TimeforDL 1 0.69 3.5 7.4 7.6 0.99 1.1

TimeforUL 1.7 1.3 5.2 11 8.4 1.8 1.6

Nameofgainmatrixofprediction g g0 g1 gref g2

heightofmobileantennasinprediction[m] 1.5 15 18 28 40

Table4.3: Gainmatrixdierence

Totalnumberofbins: 123045 g-g0 g-g1 g-gref g-g2

numberofbinswithapositivedierence 23627 23512 36074 953

g0-g1 g0-gref g0-g2

numberofbinswithapositivedierence 55766 65554 99784

g1-gref g1-g2

numberofbinswithapositivedierence 73359 99869

gref-g2

numberofbinswithapositivedierence 87217

4.2 Investigation of the G-Matrix

Thisinvestigationaimsatinvestigatingthepathlossinformation predictedby

TCP. The information is provided in the form of abig matrix containing the

path gain predictions between the bins in the considered area and a certain

numberof BSs withbest predicted path gainto the binsin question. In this

investigation, the prediction is masked so that the matrix only contains the

indoor bins in the restrictedarea, see gure 3.1 on page 21. This yields 123

045 bins to study. Predictions for mobile antennas at dierent heights have

beencomparedtoinvestigatewhethertheassumptionofalogarithmicincrease

in gain with mobile antenna height is correct. The names and heightsof the

dierentgainmatricesarefoundintable4.2. Thegainvaluescomparedarethe

valuesbetweenthebinsandtheirservingBS.

Thedierencesarecalculatedasthedierencebetweenalowerprojectand

ahigher. It is expected to be negativesince the pathgain is supposed to be

morenegativeonthelowerlevelsandslightlylessnegativeonthehigherlevels.

Apositivedierencemeanstherehasbeenalosswithheightinsteadofagain.

There are a signicant number of bins that does not follow the anticipated

behavior. Thebinswithpositivedierencesi.eanextralosswithheight,donot

completelycoincidebetweenthedierentprojects.

This problemmightarise fromthetilt oftheantennas,that is,thepredic-

tionsare correct but theassumption that the path lossshould decrease loga-

rithmically(indB)astheheightsofthemobileantennasincreaseisinadequate.

Toinvestigateifthisis reallythecasethepredictionat 1.5

m

^{called gand the}

predictionat15

m

^{calledg0wasusedfora}comparison. Theangleinthevertical planebetweentheMSand theirserving BSwascalculatedfor5dierent bins

thatgotpositivedierences. Theangleswerethenusedtocountbackwardsvia

theverticallobepatternsandcomparetheresultstothedierencefound. The

resultisfoundin4.4. ItisthesameservingBSin allbinsandatbothheights.

17.8

dBi

^.

Thelobepatternof theemployedantennacanbeseenin gure4.1.

ThereisalsotheissuethattheservingBSmighthavechangedbetweenthe

predictionson the dierent levels. In table 4.5 the numbers of bins changing

serving BS are shown. However, this is a process that would occurin reality

too,sonomeasuresweremadeto makethesameBSbeservingat allheights.

Modelthree,fourandveindierentwaysallusepathlossvaluespredicted

byTCPinbinsfoundtobeinLOSoftheBSbyAstrid. Therefore,acomparison

betweenthepathlossvaluethatwasfoundtobeinLOSoftheBSthroughthe

LOS calculationsperformed asin section 3.2.2.3 onpage 25 i.e. with outside

bins and a theoretical free space propagation path loss (2.4), can be seen in

table 4.6a. There is aalso a comparison to a freespace propagation with an

added approximate vertical lobe pattern loss. In table 4.6b it is investigated

how much the angle between the bin and it's serving BS aects the loss due

to the directional lobe pattern of the antennas. This is done to see if any

dierencein lossin table4.6acouldbeexplainedbytheverticallobepatterns,

therebyshowingthat thepathlosspredictionsin TCPcorrespondtothepath

lossassumptionsmadeonthem.