UPTEC F10068

Examensarbete 30 hpDecember 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 RealNetwork Simulator

Sara Bladlund

The report treats the development and evaluation of a three dimensional userdistribution model for a real network simulator. The simulator is used to createrealistic predictions of real networks with the use of high resolution maps including abuilding data base and network data and also an advanced radio model for LTE.Previously all simulations have been performed with a two dimensional userdistribution, i.e. all users situated on the ground level. Since it is considered plausiblethat many LTE users will be indoors in buildings with multiple floors, several threedimensional user distribution models with users not only on the ground floor but alsoon the higher floors has been developed and implemented in the simulator. Themodels all account for the change in path loss and SINR to be expected and havebeen compared in computational time and credibility. The simulations show that bythe use of such a three dimensional model there is a significant improvement at lowloads but at high loads the interference becomes dominant and the results show adeterioration and approaches the results of the ordinary two dimensional model. Theseventh and last model to be investigated shows a desirable computational speed thatstill does not compromise too much with the accuracy and detailing of the model andis therefore recommended for normal use.

Sponsor: Ericsson ABISSN: 1401-5757, UPTEC F10068Examinator: Tomas NybergÄmnesgranskare: Mikael SternadHandledare: Lars Klockar

Contents1 Introduction 41.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Project description . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Theory 62.1 Propagation mechanisms . . . . . . . . . . . . . . . . . . . . . . . 62.1.1 Free Space Propagation . . . . . . . . . . . . . . . . . . . 62.1.2 Re�ection, Refraction and Scattering . . . . . . . . . . . . 72.1.3 Di�raction . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.3.1 Ideal Knife Edge Di�raction . . . . . . . . . . . 92.1.4 Guiding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1.5 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Propagation Models . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.1 Piecewise Linear (Multislope) Model . . . . . . . . . . . . 122.2.2 Building Penetration Loss at LOS Conditions in COST231 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2.1 Height Gain in COST 231 . . . . . . . . . . . . . 132.2.3 Outdoor-to-Indoor Propagation in Urban Areas at 1.8Ghz 142.2.4 Multi-Frequency Path Loss in an Outdoor to IndoorMacro-cellular Scenario . . . . . . . . . . . . . . . . . . . . . . . 152.2.4.1 Excess Path Loss Instead of Absolute Values . . 172.2.5 Ericsson Urban Model . . . . . . . . . . . . . . . . . . . . 172.2.5.1 Indoor Propagation . . . . . . . . . . . . . . . . 183 Description of Real Network Simulator and 3D Path Loss Mod-els 203.1 Short Description of the Real Network Simulator Astrid . . . . . 203.1.1 SINR Calculations . . . . . . . . . . . . . . . . . . . . . . 213.1.1.1 SINR Calculations for 3D User Distributions . . 223.2 3D Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2.1 Models whitout LOS considerations . . . . . . . . . . . . 223.2.1.1 Description of First Model . . . . . . . . . . . . 223.2.1.2 Description of Second Model . . . . . . . . . . . 231

3.2.2 Models With LOS Considerations . . . . . . . . . . . . . 233.2.2.1 Description of Third model . . . . . . . . . . . . 233.2.2.2 Description of Fourth Model . . . . . . . . . . . 253.2.2.3 Description of Fifth model . . . . . . . . . . . . 253.2.2.4 Description of Sixth model . . . . . . . . . . . . 263.2.2.5 Description of Seventh Model . . . . . . . . . . . 273.2.2.6 Description of Crowded 3D Model Using ModelSix . . . . . . . . . . . . . . . . . . . . . . . . . 294 Simulations and Results 304.1 Comparison of computational times . . . . . . . . . . . . . . . . 304.2 Investigation of the G-Matrix . . . . . . . . . . . . . . . . . . . . 314.3 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3.1 Without LOS Considerations . . . . . . . . . . . . . . . . 354.3.1.1 Results from the First Model . . . . . . . . . . . 354.3.1.2 Results from the Second Model . . . . . . . . . . 364.3.2 Models With LOS Considerations . . . . . . . . . . . . . 394.3.2.1 Results from the Third Model . . . . . . . . . . 394.3.2.2 Results from the Fourth Model . . . . . . . . . . 414.3.2.3 Results from the Fifth Model . . . . . . . . . . . 434.3.2.4 Results from the Sixth Model . . . . . . . . . . . 434.3.2.5 Results from the Seventh Model . . . . . . . . . 474.3.2.6 Results from Crowded 3D Model Using Model Six 494.3.3 All models in the same plots . . . . . . . . . . . . . . . . 514.3.3.1 Path loss . . . . . . . . . . . . . . . . . . . . . . 514.3.3.2 SINR . . . . . . . . . . . . . . . . . . . . . . . . 514.3.3.3 Mean Bitrates and Capacity . . . . . . . . . . . 535 Discussion and Conclusions 565.1 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . 565.2 Continuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60A All Plots 68A.1 First Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68A.1.1 Mean Bitrates and Capacity . . . . . . . . . . . . . . . . . 68A.1.2 SINR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69A.1.3 Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 69A.2 Second Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70A.2.1 Mean Bitrates and Capacity . . . . . . . . . . . . . . . . . 70A.2.2 SINR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70A.2.3 Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 71A.3 Third Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72A.3.1 Mean Bitrates and Capacity . . . . . . . . . . . . . . . . . 72A.3.2 SINR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72A.3.3 Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 73A.4 Fourth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 742

A.4.1 Mean Bitrates and Capacity . . . . . . . . . . . . . . . . . 74A.4.2 SINR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74A.4.3 Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 75A.5 Fifth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76A.5.1 Mean Bitrates and Capacity . . . . . . . . . . . . . . . . . 76A.5.2 SINR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76A.5.3 Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 77A.6 Fifth Model with Lower Wall Loss Constants . . . . . . . . . . . 78A.6.1 Mean Bitrates and Capacity . . . . . . . . . . . . . . . . . 78A.6.2 SINR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78A.6.3 Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 79A.7 Sixth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80A.7.1 Mean Bitrates and Capacity . . . . . . . . . . . . . . . . . 80A.7.2 SINR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80A.7.3 Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 81A.8 Seventh Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82A.8.1 Mean Bitrates and Capacity . . . . . . . . . . . . . . . . . 82A.8.2 SINR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82A.8.3 Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3

Chapter 1Introduction1.1 BackgroundReal network simulations was started a couple of years ago to get more realisticresults instead of hexagon simulations whose results started to diverge to muchfrom measurements performed in real networks. The ongoing work on realnetwork simulations is a cooperation between Ericsson AB and some of theworld's leading mobile network operators. It consists of high accuracy path losspredictions from a commercial cell planning tool containing detailed informationincluding a building database, base station site data and antenna patterns and apropagation model that is tuned with drive test measurements from the studiedarea. In addition to the cell planning tool it also includes an advanced radiomodel for LTE, support for heterogeneous tra�c distributions and di�erentoptions for distributing the resources of the system. The propagation modelscan be tuned to �t the type of area it is used for, for example if it is an urbanarea or a rural. The real network simulator can be used to produce reliablepredictions used to analyze and evaluate possible changes made to the networkwhitout having to implement them in the operating system. It is consideredplausible that many of the LTE users will be indoors and consequently on bothhigher �oors and the ground �oor. This motivates the present investigationon how to best include propagation models for such users into the networksimulator.1.2 Previous workThe modelling of outdoor to indoor propagation of radio waves have been in-vestigated and several and sometimes quite di�erent attempts to model it hasbeen proposed, for example [6, 12] to mention two. The task encounters manyobstacles and rises many questions. How detailed the model should be is animportant balance between accuracy and ease of usage. When modelling indoorpropagation, the height of the building also comes in as a factor to be dealt with.4

Figure 1.1: Plausible scenarios?It is natural to assume a certain dependence on height for the propagation if itis assumed that the radio wave meets less obstructing objects on its path thehigher the receiver is situated. This is indeed the case when the antennas areplaced on roof tops as is often the case in macrocellular environments. Thatalso raises the question of a path loss dependency on line of sight conditions.For example [7] suggests a model with considerations taken for line of sightcircumstances.1.3 Project descriptionAll previous predictions have been performed on the ground �oor. Since it isconsidered plausible that many of the LTE users will be indoors and conse-quently on higher �oors than the ground �oor, the question arises how this willa�ect the system. It is known that the attenuation from the base station tothe user equipment is dependant of the user equipment height, i.e. the �oor onwhich the user is situated. It is therefore also reasonable to believe that usersin tall buildings may experience high interference from neighboring cells. Thepurpose of this project is to investigate whether a three dimensional distributionfor indoor users will impact the result of the simulations of the LTE networksand how such a distribution and its implications can be modeled.5

Chapter 2Theory2.1 Propagation mechanismsTo describe the methods of radio wave propagation, Maxwell's equations areusually the starting point. However, a good practical approach is to consider theway power P [W] propagates outwards from a source of energy [1]. An isotropicradiator is a source that radiates uniformly in all directions in a spherical fashion.The power density p [Wm−2] is de�ned as the transmitted power divided bythe surface of the sphere and it enables the calculation of the gain of a radiator.An isotropic radiator does not exist in reality, since it assumes the existens of apoint source of energy but it is a useful tool when talking about the directivityof real radiators. The gain G of the radiator is a measure of how much morepower density a real radiator is able to transmit in the preferred direction [1].In reality the radio wave propagates due to interaction between an electricaland a magnetic �eld. When the strength of a signal is discussed, it is the mag-nitude of the electric �eld that is intended. The two �elds are perpendicular toeach other and to their direction of propagation, at least in free space conditions.Because of this the ray is a useful concept when talking about radio waves. Aray is an imaginary line along the direction of travel of the wave perpendicularto the wave front [2]. What free space condition means and other propagationphenomena will be described below. In general, a wave will experience severalof the phenomena simultaneously.2.1.1 Free Space PropagationIf a transmission is performed well away from the earth's surface, avoiding anye�ects from it, then it is said to be in free space propagation conditions. The rayof the signal is under these conditions spread according to an inverse square law[1]. Friis Radiation Formula (2.1) describes a signal being transmitted between6

two points spaced d [m] apart,Pr = GrGtPt

(

λ

4πd

)2

[W] (2.1)In equation (2.1) Pt [W] is the transmitted power, Pr [W] is the received power,Gr is the gain of the receiver and Gt is the gain of the transmitter. If thelogarithm of (2.1) is taken, it can be written as:

10 log10

Pr = 10 log10 Gr + 10 log10 Gt + 10 log10 Pt + 20 log10λ

4πd(2.2)If the power and the gain is related to 1 mW and the gain of an isotropic sourcerespectively, (2.2) can equivalently be expressed as:

Pr [dBm] = Pt [dBm] +Gr [dBi] +Gt [dBi]− 20 log104πd

λ[dB] (2.3)The last term in (2.3) is called the free space path loss Lfsp, expressed in dB.It represents the loss of a signal transmitted through free space without anyobstacles or interfering objects. If λ is replaced by c

fwhere f is the frequencyin GHz and c is the speed of light multiplied by 109 and the terms are separatedand the constant is calculated, the following expression is obtained for free spacepropagation path loss:

Lfsp [dB] = 32, 4 + 20 log10 (d) + 20 log10 (f) (2.4)This is an equation that is very commonly used in radio propagation contexts,as it is the minimum loss that will occur while transmitting. Equation (2.3) isexpressed in words as:received power = transmitted power + antenna gains− losses (2.5)This enables equation (2.5) to be considered as a general expression for describ-ing propagation where losses not only accounts for free space propagation lossbut all losses involved in the transmission. This includes for example losses dueto re�ection, refraction, di�raction and scattering.2.1.2 Re�ection, Refraction and ScatteringRe�ection describes an incident wave being re�ected at an interface betweentwo media and refraction describes an incident wave being transmitted froma media into another. A wave most often su�ers both phenomena. Specularre�ection is re�ection at a smooth surface and di�use re�ection is re�ection ata rough surface. Re�ection and refraction changes not only the direction andpower of the wave, but also the polarization which is an important property ofa wave as it a�ects the ability to transfer power.The specular case is e�ciently described by Snell's laws, the law of re�ection(2.6) and the law of refraction (2.7). The index of refraction n of a matrial is7

Figure 2.1: The re�ected and transmitted component of a wave incident onan interface. Θi,r,t are the angles between the normal of the interface and thedi�erent rays and n1,2 are the refractional indexes of the di�erent materials.heavily dependent on the frequency of the incident wave. The angles Θi, Θr andΘt are the angles between the normal of the surface and the incident, re�ectedand refracted/transmitted wave respectively.

Θi = Θr (2.6)n1 cosΘi = n2 cosΘt (2.7)Di�use re�ection and refraction occurs when a surface is not ideally smooth,which is generally the case. Wether a surface is considered smooth or rough,the level of roughness and how much it a�ects an incident wave is of coursedependent on the material, but also on the wavelength λ of the wave. Alsothe angle with which it imposes on the surface is important [1]. A surface isgenerally thought of as smooth if its vertical height variation h satis�es theRayleigh criterion;

h <λ

8 cosΘi(2.8)where Θi is the angle between the incident ray and the normal of the surface,see �gure 2.2. Equation (2.8) implies that most manufactured surfaces can beregarded as smooth and treated as such for wavelengths λ at the decimeterscale. However, when the wave strikes a rough surface or heterogeneities withsmall dimensions compared to the wavelength such as soil or trees the re�ectioncan no longer be treated as specular. From such surfaces, the outgoing wave8

Figure 2.2: Scattering from a rough surface. The black ray is the incoming rayand the gray rays are the less energetic scattered rays.is scattered, see �gure 2.2. Scattering means that the energy of the wave isdistributed in several directions [3] thus reducing the power in the ideal re�ecteddirection. However, scattering can sometimes be desired as it provides a goodspreading of the wave.2.1.3 Di�ractionThe way electromagnetic waves behave when they impinge on obstacles or aper-tures with dimensions larger than the wavelength is described by the propaga-tion phenomenon known as di�raction. To understand it, it is easiest to abandonthe ray description and instead consider the wavefronts of the waves. Accordingto Huygens's principle all points on a wavefront can be regarded as an isotropicradiator radiating spherically, see �gure 2.3. This implicates that the futurebehavior can be synthesized from the interference of the �elds from these imag-inary secondary radiators [1]. Di�raction enables radiation to �bend� aroundcorners at the expenses of energy loss in the wave. It arises from many occur-rences, for example the curvature of the earth, hilly or irregular terrain, buildingedges or obstructions blocking the line of sight [LOS] path between the receiverand the transmitter [4].2.1.3.1 Ideal Knife Edge Di�ractionDi�raction can be very demanding to model and therefor the approximate Fres-nel knife edge di�raction is commonly used [4]. The ideal knife edge di�ractionuse the ray concept. The geometry of the model with one single knife edge andobstructed LOS between the transmitter and the receiver is shown in �gure 2.4where the di�racting object is assumed to be asymptotically thin and in�nitely9

Figure 2.3: Di�raction of energy from a wavefront as it impinges on an obstacle.The grayer circles symbolizes the imaginary wavefronts of the point sources. Thewavefront thus curves around the corner.Figure 2.4: Geometry of knife edge di�raction.wide. There can also be knife edge e�ects from objects not obstructing the LOSas long as they are su�ciently close to the LOS path. Besides the approxima-tion of asymptotically thin and in�nite objects, the model does not considerdi�ractor parameter such as polarization, conductivity and surface roughness.The electric �eld strength between the two antennas is dependent on the Fresnelcosine and sine integrals;

C (ν) =

∫ ν

0

cosπt2

2dt (2.9)

S (ν) =

∫ ν

0

sinπt2

2dt (2.10)where the dimensionless Fresnel parameter ν is de�ned as:

ν = hd+ d′

dd′

√

2

λ

(

1

d+

1

d′

) (2.11)10

The distances d [m], d′ [m] and h [m] are de�ned in �gure 2.4 and λ [m] is thewavelength [3]. The Fresnel parameter expresses the obstruction by the obstacleof the LOS. The development of the Fresnel integrals in series leads to approx-imate relations for the attenuation relative free space due to the obstructingobject. One example of such an approximation is equation (2.12) found in [4].L (ν) [dB] =

20 log10

(0.5− 0.62ν) −0.8 ≤ ν < 0

20 log10

(

0.5e−0.95ν)

0 ≤ ν < 1

20 log10

(

0.4−

√

0.1184− (0.38− 0.1ν)2

)

1 ≤ ν ≤ 2.4

20 log10

(0.255/ν) ν > 2.4 (2.12)There are also models for multiple di�racting edges and even for rounded ob-stacles [3].2.1.4 GuidingSome environmental features like street canyons, tunnels and other buildingconstructions act like wave guides for radio waves. This is the case especiallywhen the wavelength is very small compared to the cross section of the feature[3]. A wave guide is in the electromagnetic theory de�ned as a tube of perfectlyconducting material with open ends and constant cross section [5]. The tubecan be of arbitrary shape but most often the square or the circular shape isconsidered. A wave propagating inside a wave guide is restricted to certainmodes due to the fact that the wave has to terminate at the walls of the guide.This implies that there is a minimum wavelength for signals propagating insidea speci�c wave guide [1]. The corresponding frequency is known as the cut o�frequency, that is to say the wave guide acts as a high pass �lter.2.1.5 DispersionDispersion denotes frequency dependent e�ects in wave propagation. In thepresence of dispersion, wave velocity is no longer uniquely de�ned. This givesrise to the distinction between phase velocity, the velocity with which a point ofconstant phase moves and group velocity, the velocity with which any modula-tion of the wave travels [1]. A well known e�ect of phase velocity dispersion isthe color dependence of light refraction that can be observed in prisms and rain-bows. Dispersion may be caused by geometric boundaries such as waveguidesor by interaction between waves.2.2 Propagation ModelsAs a result of the propagation phenomena described above, numerous propaga-tion models have been developed, often for a speci�c scenario and circumstances.In this section some of the models that have been important parts of the creation11

of the three dimensional [3D] user distribution models treated in this report, arepresented.2.2.1 Piecewise Linear (Multislope) ModelThe piecewise linear model, also called the multislope model, relates dB lossto log distance. It is an empirical method for modeling path loss used in bothoutdoor and indoor cases [4]. The area of interest is divided into N di�erentregions. The regions s1, . . . , sN are separated by breakpoints (d1, d2, . . . , dN−1)and each region has a speci�c linear slope. The breakpoints and the slopes hasto be decided in the modeldesign. Equation (2.13) below describes a special caseof the multislope model, the dual slope model. In the dual slope model, onlytwo path loss regions are considered. The �rst region with slope γ1 stretchesfrom a reference distance d0 [m] to a critical distance dc [m] where the path lossexponent changes to γ2.Pr (d) [dB] =

Pt +K − 10γ1 log10

(

dd0

)

d0 ≤ d ≤ dc

Pt +K − 10γ1 log10

(

dcd0

)

− 10γ2 log10

(

ddc

)

d > dc (2.13)In equation (2.13) Pr [dB] is the received power, Pt [dB] is the transmittedpower and K [dB] is a constant path loss factor. The path loss exponents Kand dc are usually found trough a regression �t to empirical data.2.2.2 Building Penetration Loss at LOS Conditions in COST231The model proposed in [6] is an attempt to describe many di�erent propagationmodels proposed by the COST 231 participants. The model assumes free spacepropagation path loss between the external antenna and the illuminated walland is not based on an outdoor reference level.L [dB] = 32.4+20 log

10(f)+20 log

10(S + d)+We+WGe

(

1−D

S

)2

+max (Γ1,Γ2)(2.14){

Γ1 = Wi · p

Γ1 = β · d(2.15)

Γ2 = α · (d− 2) ·

(

1−D

S

)2 (2.16)The model parameters, the angle θ [deg] and the distances S [m], D [m] andd [m] are de�ned in �gure 2.5. The frequency f is inGHz andWe is the loss in dBin the externally illuminated wall at perpendicular penetration (θ = 90 [deg]).The only time when θ = 90 [deg] is when S and D are equal, that is when12

Figure 2.5: De�nition of angles and distances. The building is seen from above.the external antenna is located at the same height as the �oor height and at aperpendicular distance from the wall. The additional loss in dB in the externalwall when θ = 0 [deg]is represented by WGe,Wi [dB] in (2.15) is the loss in theinternal walls and p is the number of indoor walls. In case there is no internalwalls, then the indoor loss is decided with an indoor slope in dB/m. In equation(2.15), the �rst expression for Γ1 can be replaced by the second, β · d where βis a slope in dB/m, if the average indoor wall loss and the average distancebetween the indoor walls are known. Finally α is a slope constant in dB/m.2.2.2.1 Height Gain in COST 231The outside-to-inside penetration loss at di�erent �oor levels is sometimes foundto decrease with increasing �oor levels, something that is also discussed in [6].The dependence is called �oor height gain and is given in dB/m. Gain in thiscontext is path gain, the inverse of the path loss, and is not to be confused withantenna gains as described in section 2.1 on page 6. The sum of the outsidereference path loss value and the height gain loss, can never be less than thefree space propagation path loss, since that would be highly unrealistic. The�oor height gain ceases to be applicable at �oor levels that is considerably abovethe average height of the neighboring buildings. The most notable �oor heightgain is found in non line of sights [NLOS] conditions, when the main part of thereceived signal power originates from rays that due to re�ections and di�ractionhave propagated down from the surrounding roof level. This is usually the casein macro-cellular1 environments with the base station [BS] at a height greaterthan the average height of the neighboring buildings.1Macro cells are de�ned by the height and transmitting power of the employed antennas.Heights are above the average surrounding building heights and the power is in the range of40 to 80 W. 13

Figure 2.6: De�nition of outdoor pixels. Only Pk,2−6 is outdoor.2.2.3 Outdoor-to-Indoor Propagation in Urban Areas at1.8GhzIn [7] a model treating outdoor to indoor propagation is proposed. It is partlybased on [6] and consists of two parts, one empirical and one semiempirical.Both parts use the height gain model described below in some form.The height gain model in short uses the path loss predicted at ground �oorto decide path loss at higher �oors. Each �oor is considered to be 3 m high andsubtracts 3 dB from the path loss, thereby rendering the resulting path loss athigher �oors lesser than at ground level. The model is considered to be validup to �oor number 5 if the ground �oor is set to 0.The empirical model contains three di�erent parts. The �rst is the calcula-tion rules describing how the indoor path loss is derived from the outdoor pathloss of all surrounding pixels. The second is an empirical penetration loss factordescribing the signal strength di�erence inside and outside the building and thethird is the empirical height gain model described above.First the bins to be considered has to be decided. The set Pin contains all Nbins belonging to the same building with at least one neighboring outdoor bin.Then, for every bin Pk in Pin the set Pout,k of all neighboring outdoor pixels isdetermined, see �gure 2.6. Equation (2.17) calculates L̄building,floor [dB] whichis the mean indoor path loss for a particular building and �oor. It is determinedby averaging the N path loss values in Lin,k [dB].L̄building,floor [dB] =

∑N

k=1 Lin,kN

(2.17)Lin,k [dB] = min

(

Lfsp,k + Lemp, Ĺin,k

) (2.18)Ĺin,k [dB] = min

∀i,Pi�Pout,k(Lk,i) + Lpen (2.19)

Lpen [dB] = Lemp −Gh (2.20)To calculate Lin,k the help variable Ĺin,k is used. It is the sum of the minimumoutdoor path loss of all Pk,i � Pout,k and the penetration loss Lpen. The pene-tration loss Lpen is the empirical loss factor Lemp reduced by the height gain14

Gh. The path loss Lin,k is then taken as the minimum of Ĺin,k and the sum offree space path loss Lfsp, see equation (2.4) on page 7, and Lemp. This limitsLin,k to realistic physical values. The variable Lk,i is the path loss calculatedby the outdoor model at bin Pk,i. The value of Lemp is set to between 19 and22 dB, values that are deduced from measurements.The semiempirical model improves on the empirical model by introducingsome deterministic components if LOS between the BS and at least some partsof the building exist. The model starts with distinguishing LOS and NLOS foreach bin on every �oor. Then two separate methods for path loss calculation incase of LOS or NLOS are deployed. If the bins have LOS then the path loss iscalculated asLin,LOS,k = 32, 4 + 20 log10 (f) + 20 log10 (s+ d′) + Lperp + Lpar

(

1−D

S

)2(2.21)which is free space propagation path loss with added loss for entering the house.The distances d′, S, and D all in m are de�ned in �gure 2.5 on page 13. Theempirical penetration factor describing penetration loss for perpendicular inci-dence of the wave is represented by Lperp and Lpar is an empirical penetrationfactor describing an additional penetration loss factor for θ → 0 [deg]. Theangle θ is de�ned in �gure 2.5.The path loss in the NLOS case is calculated as in the empirical model withthe small di�erence that when calculating the �oor height gain the maximumnumber of �oors is limited to the number of �oors which corresponds to themean building height along the path between the BS and the mobile station[MS].2.2.4 Multi-Frequency Path Loss in an Outdoor to IndoorMacrocellular ScenarioThe article [9] describes the connection between di�erent frequencies and theexcess path loss they generate. The excess path loss LE is de�ned in equation(2.22) as the loss relative to free space propagation path loss Lfsp (see equation(2.4)),LE [dB] = LP − Lfsp (2.22)where LP [dB] is the path loss as de�ned in equation (2.23),

LP [dB] = Pt − Pr +Gt +Gr (2.23)The variables Pt [W] and Pr [W] are the transmitted and received power re-spectively and Gt and Gr are the antenna gains of the transmitter and receiverrespectively. An advantage of using excess loss instead of absolute loss is thatthe frequency dependant aperture of the receiver antenna, which does not re�ectany environmental propagation properties, is removed.15

0 5 10 15 20

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rage

Bui

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LOS floor: 7

Figure 2.7: Average building penetration loss, using GFl = 3.0 dB, nFlb = 7,a = 4 and LLOS = 24.5 dB.The article also describes loss dependency on �oor levels and proposes a sim-ple empirical model to model the dependency as an average building penetrationloss L [dB]:

L [dB] =10

alog

10

(

10−nFlGFla

10 + 10−nFlbGFla

10

)

+ nFlbGFl + LLOS (2.24)LLOS [dB] = Lmes,in − Lfsp,out (2.25)The model is based on the building penetration loss at LOS conditions, LLOSas de�ned in equation (2.25), and the corresponding gain with �oor level inNLOS conditions, GFl [dB]. The �oor number is represented by nFl and nFlb isthe �oor number for the lowest �oor at which there is LOS conditions towardsthe transmitter. a is a parameter adjusting the size of the model transitionzone between the LOS and the NLOS conditions. The loss factor Lmes,in isthe measured value inside the building and Lfsp,out is the theoretical outsidefree space propagation path loss reference value. The model in equation (2.24)has been �tted to measurements made inside and outside buildings [9] and theresulting values of GFl is between 1 and 4 [dB/floor] and of LLOS between 20and 35 [dB].The value of LLOS can not always be measured since some buildings neverreach the required height. In such cases it is suggested that LLOS is taken as

LDiff which is the di�erence between the measured loss indoors and outdoorsat ground level. In cases when this is not a possibility either, LLOS is suggestedto be set as a parameter with a value in the range of the values measured in [9]which are in the range of 20-30 dB. 16

2.2.4.1 Excess Path Loss Instead of Absolute ValuesIn [10] two ways of calculating penetration loss is compared. The �rst is whenpenetration loss is determined using the di�erence between the path loss in dBfrom measurements in the building and reference measurements outside thebuilding. The second is to use the theoretical free space propagation pathloss as the outside reference loss instead of measured reference levels. Thearticle suggests the latter as the more accurate model. For details on how themeasurements were made, see [10]. Measured penetration losses are found tovary between 5dB and 30dB. If instead a theoretical reference value is used, twomajor di�erences appear. First that the penetration loss increases when thetheoretical path loss value is used as reference value, and the second is that thespread of penetration loss values decreases to instead vary between 23dB and32dB. By using the theoretical values instead of the measured, abnormalitiescan be avoided and the penetration values becomes more suitable for modelling.Another result presented is that di�erence in penetration loss between dif-ferent frequencies, in this case 900MHz and 1700MHz, is signi�cantly decreasedusing the theoretical values as reference value.2.2.5 Ericsson Urban ModelThe Ericsson Urban Model is a concept that combines two di�erent wave prop-agation algorithms, the half screen model and the recursive microcell model[8]. The half-screen model is used for calculating the propagation above rooftops.Obstacles such as buildings and trees between the BS and the MS are modelledwith a number of screens with heights correlated to the heights of the obsta-cles. The path loss Labove [dB] is then calculated using a multiple knife-edgeapproach, see part 2.1.3.1 on page 9. Two kinds of screens are employed todescribe the pro�le of the environment, permanent screens that are placed in astatistical way, and temporary screens that are placed in a deterministic way.The permanent screens are used to describe the environment along the calcu-lation pro�le in a general way and the temporary screens will describe detailsof the environment more accurately, near the mobile antenna. For example,the screens modelling a forest would typically be set in a statistical way, whilescreens modeling buildings would be set deterministically.The recursive microcell model is used for calculating the propagation be-tween buildings, for example along streets. For de�ning the propagation paths,the exact locations of buildings according to the building data base, are used.The path loss Lbelow [dB] is calculated by determining the so called illusory dis-tance between the BS and the MS in a street system. The illusory distance isdetermined with a recursive method, using input data from a street system andtakes into consideration the multiple street crossings and turns that are present.The resulting path loss arising from the Urban Model Lurban [dB] is the leastof the two values generated by the two models,17

Lurban [dB] = min (Labove, Lbelow) (2.26)Close to the basestation and in LOS cases, the microcell model dominates andonly the value of Lbelow is used. Otherwise it is the half screen model thatdominates and only the value of Labove is used. In reality both values alwayscontribute to the total path loss but the e�ects of this approximation are smallenough not to be signi�cant.The model is considered valid for frequencies from 450 MHz up to 2200 MHzand at distances both close to and far from, at least 50 km, the BS antenna. Itis also considered valid for high MS heights.2.2.5.1 Indoor PropagationFor indoor propagation in the Ericsson Urban Model, given it has access toa detailed land use map containing the locations and heights of buildings, aspecial indoor model with the following properties is used. An indoor path lossvalue for a particular bin is calculated by �rst deciding the four outdoor binsclosest outside the building to the north, the south, the east and the west of theindoor bin, see �gure 2.8. The path loss values of these bins have been chosenaccording to equation (2.27).Lout [dB] = max (Lurban, Lfsp +Wge) (2.27)The path loss Lurban [dB] is a value calculated by the Urban Model, which istreated above and Lfsp [dB] is the free space propagation to that outdoor binfrom the basestation calculated according to equation (2.4). The additional loss

Wge [dB] is wall loss that accounts for extra losses due to a grazing incidenceangle. The graze constant only occurs when a LOS path is assumed, since NLOSpaths often are scattered from multiple directions, leaving at least one that hasa perpendicular incidence angle, while LOS paths only have one incidence angleand it can't be assumed to be perpendicular to the building wall. From thepath loss values of these outside bins, an external wall loss constant We [dB]is subtracted and then a loss per meter, a so called slope, α [dB/m] is used toaccount for the additional path loss of the �nal indoor distance s [m], leavingthe indoor path loss Lin [dB] as in equation (2.28)Lin [dB] = Lout [dB] +We + s · α (2.28)The indoor path loss value is calculated for all four starting positions and thenthe best indoor path loss is used.

18

Figure 2.8: Indoor bin and the four surrounding outdoor bins considered asstarting positions for indoor propagation.

19

Chapter 3Description of Real NetworkSimulator and 3D Path LossModelsIn the following chapters, the concept of path loss will be frequently discussed,it is therefore important to de�ne what is intended with this concept. Path lossis according to ITU1 de�ned as losses due only to the phenomena described insection 2.1 on page 6 and similar propagation factors. In the following chaptersalso antenna and other equipment properties are included in the calculations ofthe total path loss. ITU would classify that as system loss.3.1 Short Description of the Real Network Sim-ulator AstridTEMS CellPlanner [TCP]2 is a cell planning tool that can be used for path losspredictions of radio networks. In the predictions performed for this rapport ituses the model described in section 2.2.5 on page 17. The path loss predictionsconsider terrain and building information depending on the level of details inthe map data employed. For example, in the predictions performed for thisreport the positions and lobe patterns of the antenna and building locationsand heights are known with a precision of squares with the sides of 5 m, calledbins.The data is exported to the stationary MATLAB real network simulatorcalled Astrid. Astrid uses an advanced radio model speci�c for LTE technolo-gies. It enables simulations of fairly large, inhomogeneous networks with tra�cdistributions with a speci�ed percentage of indoor and outdoor user equipment1ITU is the UN agency for information and communication technologies.2Recently changed to MENTUM CellPlaner for new releases of the program.20

Figure 3.1: Analysis area[UE]. Astrid also enables di�erent tra�c levels between cells. The simulationconsiders a restricted area of a large city. In order to model realistic interferencesituations at all simulated cells, interference contributions from outside of therestricted area have to be considered, see �gure 3.1.The predictions in Astrid can be performed at di�erent loads. The load isthe ratio between used and total resources. If all the resources are allocated,meaning that one UE or BS per cell is transmitting with full bandwidth andfull power all the time, the load is 100 %. Should the load be lower, then thetransmission is only ongoing part of the time. In each instant, only one UEor BS is active in every cell. Every simulation consists of several time instants.The resources can be administered in di�erent ways but in this report they havebeen distributed so that all UE regardless of their SINR will get equal access tothe resources. This means that UE with poor SINR will transmit and receiveless data than a UE with good SINR. The capacity of the system is closelyentwined with the load. A system capable of delivering a certain bitrate for aspeci�c time i.e. a speci�c load has a higher capacity than a system capable ofdelivering the same bitrate for lesser periods of time, i.e. at lower loads.3.1.1 SINR CalculationsThe SINR calculations di�ers between the up link [UL] and the down link [DL].The interferers in the DL are BS from surrounding cells. They are stationary andtherefore their location and number are easier to predict than the interferers inthe UL. In the UL the interferers are UE in the neighboring cells and thereforemobile which makes the interference hard to predict. The DL interference isbased on path gain predictions from interfering cells to the considered cell, andinformation about BS powers from interfering cells. A stated power level is usedfor all load situations.The UL interference is modeled by introducing a Monte Carlo distributionof UE to create interference. This distribution of UE is repeated several timesto create a statistically credible scenario. Equation (3.1) describes the SINRcalculation of a bin. The variable P [W] is the power transmitted from the BS,g is the path gain i.e the inverse of path loss, calculated for each cell to eachbin and N [W] is the noise. 21

SINRbin =Pbest sell · gbest cell

∑

i6=best cell Pi · gi +N(3.1)The SINR values are translated to bitrates according to a link to system modelrelating SINR to bitrates.The results of a simulation can be presented as the result in every bin, thisis referred to as binprobing. The alternative is to only present the bins selectedby the Monte Carlo process. This is referred to as user distribution.3.1.1.1 SINR Calculations for 3D User DistributionsThe SINR calculations are essentially the same as before when the bins or UEare distributed in a 3D fashion. The di�erence is that as the height of a binis increased, there will be some decrease in path loss and this applies for boththe connection between the UE and its serving BS as well as the UE and in-terfering BS or BS and interfering UE. This has been modeled by giving thegain calculated between the UE and its serving BS to not only that path lossprediction but also to all the interferers path loss predictions. This might be aslightly pessimistic assumption but since no measurements addressing the issuehas been made regarding this, it is the best approximation available.3.2 3D ModelsIn this section the structure and concept of the 3D user distribution models thathas been created are described. They are described in the chronological orderthat they were created and tested and therefore simply named as model one tomodel seven.3.2.1 Models whitout LOS considerationsThe �rst two models does not take any LOS calculations into consideration.3.2.1.1 Description of First ModelThis model is based on the article [7], that describes outdoor and outdoor-to-indoor propagation. In the article, measurements were made in the townsof Cologne and Leipzig and a model was created, tested and compared to themeasured data. They found the predictions made by their model to be fairlyaccurate compared to their measurements. Not all of their model is used here,but some assumptions concerning building and �oor properties.The indoor bins are given a �oornumber according to a uniform randomdistribution from ground �oor, �oor 1, and up to a speci�c maximum �oorlevel. This maximum is given by a parameter called max�oor. Max�oor is setto 6 in the simulations and each �oor is considered to be 3m high, both valuesin accordance with [7], see section 2.2.3 on page 14.22

Figure 3.2: Floor distribution. In the �rst model the height of all buildings is6 �oors. In all other models the height of the buildings varies according to thebuilding data.The path loss is calculated in TCP at ground level, which in this case means1.5 m above ground, for all bins, indoor and outdoor. For the indoor bins, 3dB path gain is added for each �oor above ground �oor. The model does notseparate indoor bins at the edge of the house from indoor bins located in themiddle of the house, they are all given the same �oor height gain of 3 dB/floor.3.2.1.2 Description of Second ModelThe second model is almost identical to the �rst. The di�erence lies in theparameter max�o. Max�o is not one �xed value for all buildings in this model,but the highest possible �oor in every building. Since the number of �oorsare not known from the building data base, but the building heights are, every�oor is assumed to be 3 m high as in model one and in all models to follow.Floornumbers are distributed randomly according to a uniform distribution fromground �oor, to the maximum �oor of the building and all indoor bins are againgiven a gain of 3 dB/floor for every �oor above ground �oor.3.2.2 Models With LOS ConsiderationsThe following models take the existens of a LOS between building and BS intoconsideration.3.2.2.1 Description of Third modelThis third model investigates wheather a bin has a LOS to the base station ituses, and if it has, at what height that occurs. The LOS-information is laterused to decide what kind of height gain a particular bin should have. The�oors are distributed as in the second model, up to the maximum height of thebuilding, with an assumed �oor height of 3 m. Each bin, now given a �oor, thengets a �oor height gain that depends on whether that particular �oor has a LOS23

Figure 3.3: LOS calculations. The green and red lines are the imaginary linesdraw between the BS and two consecutive �oors, the lower whitout LOS andthe higher with LOS.or not. This idea comes from the same source as before [7]. The assumptionis that once a �oor has LOS, all higher �oors also have LOS. The calculationof LOS or NLOS are done between a bin and its serving BS. The bin is �rstassumed to be at ground level, 1.5 m above ground. An imaginary straight lineis drawn between the BS and the bin. If any intermediate building obstructs theline, then its stated that the bin does not have LOS conditions. This procedureis then repeated at 3 m intervals, i.e. at the �oors, until either a LOS has beencon�rmed or the building run out of �oors. Only bins that are situated on theedge of a building can have LOS.A bin without LOS at the �oor given, gets the usual 3 dB/floor �oor heightgain. The bins with LOS at the given �oor get a path gain value interpolatedfrom predictions in TCP instead. One prediction is made at ground level, oneat a height that corresponds to 6 �oors, i.e. 15 m, and one is made at a heightof 40 m and then the path loss values in between are interpolated linearly indB3. When choosing the height for the upper prediction level, the values foundin table 3.1 were considered. The table describes the distribution of buildingheights in the considered area. The height chosen, 40 m, is high enough toinclude almost all of the indoor bins (only 2.03 % of the bins belong to higherbuildings), but not so high that the angle between the �oor and the base stationbecomes too large. It is important that the upper height is not too high sincea too great an angle would cause the pattern of the antenna lobe to increasethe path loss in a manner that is no longer probable to be linear in dB. Theassumption of 40m being a good choice will be further investigated in section 4.2on page 31.3Note that the LOS calculations are performed 1.5 m up on every �oor, while 15 m is atthe bottom of a �oor. This is compensated by using an interpolated value that is 1 m up.The decrease from 1.5 m to 1 m is considered reasonable given that UE at higher �oors mightbe at a working desk height.

24

Table 3.1: Building height distributionspercent of all bins[%] (total numberof bins 263516) percent of indoorbins [%] number of binshigher than X(total number ofindoor bins119647) X [m]0.0748 0.1647 197 900.0964 0.2123 254 800.1150 0.2532 303 700.2178 0.4797 574 600.3419 0.7530 901 500.9210 2.0285 2427 405.4653 12.0371 14402 3023.8946 52.6265 62966 2043.1146 94.9577 113614 1045.3786 99.9440 119580 53.2.2.2 Description of Fourth ModelThis model is basically the same as the third model in that it separates theindoor bins with LOS from those with NLOS. The LOS bins are also found inthe same manner and the �oors are distributed to all bins as in model three.The di�erence is that the NLOS bins are given their path loss value in a di�erentway. Given a particular �oor are associated with the LOS bins at that �oor.The NLOS bins path loss values are then calculated according toLk [dB] = Lk,los [dB] + dk · α (3.2)

L [dB] = mink

(Lk) (3.3)where dk [m] is the distance from the NLOS bin to LOS bin number k on that�oor with path loss value Lk,los.The value of the loss factor α is 0.6 dB/m assuggested in [6]. The least of the calculated path losses L is then chosen asthe path loss value for that NLOS bin. The value for Lk,los is taken from theinterpolated values as described in the previous section. This di�erence be-tween model three and four was constructed to make sure that the inner values,supposedly dependant on the LOS to bins situated at the edge of the buildingactually had an impact on the choice of bins to start from when calculating pathloss for indoor bins.All NLOS bins without a LOS bin on the same �oor is given a �oor heightgain of 3 dB/floor for every �oor above ground �oor.3.2.2.3 Description of Fifth modelIn this model, the LOS calculations di�ers slightly from model three and 4.Instead of using indoor bins situated on the edge of the buildings, an imaginary25

shell of outdoor bins was created for each house. This shell of outdoor bins isthen used for the LOS calculations described above. This change is done to avoidthe outdoor-to-indoor calculations made in TCP, see 2.2.5.1 on page 18 and itentails the need to introduce a new loss to account for building penetrationlosses since those are no longer contributed by the path loss values from TCP.Therefore equation (3.3) used in model four is replaced by equation (3.4) in thismodel.L [dB] = min

k(Lk) +We +Wge (3.4)The variable We [dB] is the external wall loss factor and Wge [dB] is the grazingangle loss factor. No vector information about the buildings are accessible, dis-abling the calculation of angle of arrival for the LOS rays reaching the building.Therefore it is not possible to tune the grazing angles loss and the worst case,rays arriving almost parallel to the building, is assumed for all bins. In the �rstset of simulations, We = 12 [dB] and Wge = 20 [dB]. Note that Lk,los in (3.4)is changed from being values predicted to the inside of the building, to beingvalues predicted to just outside the building.The second set of simulations use a lower value for the grazing angle lossfactor. Instead of 20 dB, Wge = 12 [dB]. This could be considered as if it usesa kind of average value instead of the worst case value.3.2.2.4 Description of Sixth modelSection 2.2.4 on page 15 describes a simple model for outdoor to indoor lossthat is used as a base for this sixth model. The average building penetrationloss L [dB] is calculated as in equation (2.24) on page 16. The value of L is onlyspeci�c for the �oor, not for every bin, meaning that all bins on the �oor get thesame �oor height gain. However, since the gain is added to indoor predictionsmade by TCP on ground �oor, there will still be a gradient inside with most lossin the middle of the building. The �oor gain constant GFl is set to 3 dB as inprevious models, since it was in the range proposed in is in [9] and coincides withthe previously used values, enabling an easier comparison between models. Thevalue of LLOS is set to 24.5 dB which is in the range suggested in section 2.2.4on page 15. If LLOS is thought of as a replacement for wall loss constants andgrazing angle losses as in 3.2.2.3 on the preceding page, then the LLOS valueis quite lower, maybe implying that a decrease of the additional losses mightbe more suitable. The �oor number nFl is assigned to the indoor bins as inall previous models except the �rst. The variable nFlbdescribing the lowest�oor at which a building has LOS, is calculated for every building. The LOScalculations are performed as in model four. It could also have been done asin model �ve since the calculations only are used to set the variable nFlb anddoes not contribute to the choice or outdoor bins used for indoor predictions.When a path loss value for an indoor bin is to be predicted, the value of Lcorresponding to that bin, or really, the �oor that bin is on, is calculated. Itis then added to the theoretical path loss in case of free space propagation, see26

10 15 20 25 30 350

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.F.

Building penetration loss [dB]0 1 2 3 4 5 6 7

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.F.

floor heigt gain [dB]Figure 3.4: Cdf of building penetration loss LLOS(to the left) and �oor heightgainGFl.(2.4) on page 7, of the nearest outdoor bin giving the total path loss Ltot as inequation (3.5). The calculations are also performed at ground level, i.e. with allthe bins at ground �oor. This is to enable the di�erence to be calculated andthen be used as �oor height gain added to the predictions made by TCP.Ltot = L+ Lfsp (3.5)3.2.2.5 Description of Seventh ModelThe seventh model is identical to model six in everything except in two things.The �rst is that the parameters LLOS and GFl are not constant anymore butdistributed to every bin according to a Gaussian distribution with their previousvalues as their new mean value. The standard deviation of LLOS is three and of

GFl it is one. These values are selected to keep the parameters within the rangeproposed in [9]. The cdf curves of LLOS and GFl can be seen in �gure 3.4. Thesecond di�erence is that there is an additional loss added due to the antenna tiltand vertical lobe patterns of the serving BS. The lobe patterns a�ect the resultsince they direct the e�ect of the BS in certain angles that might be far o� fromthe LOS between the BS and a bin at a certain level. The same lobe patternhas been used for all BS's antennas. This is an approximation since the lobepatterns really di�er sightly, however the lobe patterns are similar enough forthe result to be signi�cant for the use of such a lobe pattern. Should the e�ectbe major, it might be interesting to use the exact lobe pattern for all antennas.The used antenna lobe pattern can be seen in �gure 3.5. As is evident there, theelectrical tilt of that antenna is 6 degrees, that is what 75 % of all the antennasin the restricted area have, which motivates the choice of typical antenna. Theloss due to the lobe pattern is calculated in the following manner: The anglebetween the bin and its serving BS is calculated. If the BS serving the bin hasa mechanical tilt, that angle is added to the calculated angle. The resultingangle is subtracted from 360 degrees, this is done to adopt the values to thelobe pattern de�nition of angles that is, as seen in �gure 3.5, opposite to the27

Figure 3.5: The vertical lobe pattern used to represent all BS in model seven.The antenna gain is 16.0 dBi.

28

Figure 3.6: Floor distribution in the crowded 3D model. The path loss at ground�oor in building A, B and C will be counted 8, 4 and 6 times respectively, tocreate a data series for the ground �oor predictions comparable to the higherlevel predictions that will be performed once for every �oor in a building.convention. The result is the angle used to �nd the corresponding additionalloss Llobe due to the angular deviation from the lobe maximum. This loss needto be related to the antenna gain Gantenna which for the antenna used is 16.0dBi. Equation (3.6) describes the calculations. Note that L is replaced by LGsince two parameters used to calculate it is Gaussian distributed.

Ltot,lobe = LG + Lfsp −Gantenna + Llobe (3.6)3.2.2.6 Description of Crowded 3D Model Using Model SixThis model is slightly di�erent from all other models. It is not a part of Astridbut completely separate which means that it only calculate path loss betweenthe BS and the bins. No SINR calculations are performed and therefore, nobitrates can be calculated. The intention with this model is to demonstrate thepath loss improvements that occur when users are higher up in a building. Thepath loss calculations are performed as in model six. The di�erence is that onlyindoor bins are considered and the way the �oors are distributed. Instead ofgiving every bin just one height and performing one simulation, this model runsas many times as the highest building have �oors. The �rst simulation placesall users at ground �oor giving a �oor height gain of 0 dB. Next simulation isperformed at the second �oor and all buildings that are high enough to havea second �oor are considered. This continues up to the highest building in thearea. All of these bins and their path loss values are then compared to thecorresponding values at ground �oor, see �gure 3.6.29

Chapter 4Simulations and Results4.1 Comparison of computational timesThe computational times of the calculations were measured using the tic tacMATLAB commando. The simulation times are for 12 separate complete sim-ulations in Astrid, 6 with the 3D model active and 6 without. It also includestime for plotting, but since that is the same for all models, that time does note�ect the comparisons. The results are shown in table 4.1. Since the table isbased on one simulation of each model, the values can not be considered asabsolutely true since there are other factors such as available memory a�ectingthe simulation. However, the absolute value of the time consumption is lessimportant, the real interest is in the comparison between the di�erent models.The comparison shows that the �rst and second models are the fastest but thatthe sixth and seventh model are equal in speed. The forth and �fth modelsare considerably much more computationally demanding, and that is obvious intheir processing times. The third model is somewhere in between.There are also some preparations needed to perform before each model, forexample the LOS calculations described in chapter 3. Model one and two needno preparations. model six and seven need one (calculation of LOS and associ-ating bins to buildings which is performed simultaneously) while model three,four and �ve need another two quite time consuming preparations consisting ofpath loss predictions at higher levels performed by TCP. All these preparationsare only needed to be performed one time. Once they are done, the models canbe used as many times as wished.Table 4.1: The computational times of the di�erent models normalized withrespect to DL in model one.Model 1 2 3 4 5 6 7Time for DL 1 0.69 3.5 7.4 7.6 0.99 1.1Time for UL 1.7 1.3 5.2 11 8.4 1.8 1.630

Table 4.2: Predictions at di�erent heights.Name of gain matrix of prediction g g0 g1 gref g2height of mobile antennas in prediction [m] 1.5 15 18 28 40Table 4.3: Gain matrix di�erenceTotal number of bins: 123045 g-g0 g-g1 g-gref g-g2number of bins with a positive di�erence 23 627 23 512 36 074 953g0-g1 g0-gref g0-g2number of bins with a positive di�erence 55 766 65 554 99 784g1-gref g1-g2number of bins with a positive di�erence 73 359 99 869gref-g2number of bins with a positive di�erence 87 2174.2 Investigation of the G-MatrixThis investigation aims at investigating the path loss information predicted byTCP. The information is provided in the form of a big matrix containing thepath gain predictions between the bins in the considered area and a certainnumber of BSs with best predicted path gain to the bins in question. In thisinvestigation, the prediction is masked so that the matrix only contains theindoor bins in the restricted area, see �gure 3.1 on page 21. This yields 123045 bins to study. Predictions for mobile antennas at di�erent heights havebeen compared to investigate whether the assumption of a logarithmic increasein gain with mobile antenna height is correct. The names and heights of thedi�erent gain matrices are found in table 4.2. The gain values compared are thevalues between the bins and their serving BS.The di�erences are calculated as the di�erence between a lower project anda higher. It is expected to be negative since the path gain is supposed to bemore negative on the lower levels and slightly less negative on the higher levels.A positive di�erence means there has been a loss with height instead of a gain.There are a signi�cant number of bins that does not follow the anticipatedbehavior. The bins with positive di�erences i.e an extra loss with height, do notcompletely coincide between the di�erent projects.This problem might arise from the tilt of the antennas, that is, the predic-tions are correct but the assumption that the path loss should decrease loga-rithmically (in dB) as the heights of the mobile antennas increase is inadequate.To investigate if this is really the case the prediction at 1.5 m called g and theprediction at 15m called g0 was used for a comparison. The angle in the verticalplane between the MS and their serving BS was calculated for 5 di�erent binsthat got positive di�erences. The angles were then used to count backwards viathe vertical lobe patterns and compare the results to the di�erence found. Theresult is found in 4.4. It is the same serving BS in all bins and at both heights.31

Figure 4.1: Vertical lobe pattern of serving BS antenna. The antenna gain is17.8 dBi.The lobe pattern of the employed antenna can be seen in �gure 4.1.There is also the issue that the serving BS might have changed between thepredictions on the di�erent levels. In table 4.5 the numbers of bins changingserving BS are shown. However, this is a process that would occur in realitytoo, so no measures were made to make the same BS be serving at all heights.Model three, four and �ve in di�erent ways all use path loss values predictedby TCP in bins found to be in LOS of the BS by Astrid. Therefore, a comparisonbetween the path loss value that was found to be in LOS of the BS through theLOS calculations performed as in section 3.2.2.3 on page 25 i.e. with outsidebins and a theoretical free space propagation path loss (2.4), can be seen intable 4.6a. There is a also a comparison to a free space propagation with anadded approximate vertical lobe pattern loss. In table 4.6b it is investigatedhow much the angle between the bin and it's serving BS a�ects the loss dueto the directional lobe pattern of the antennas. This is done to see if anydi�erence in loss in table 4.6a could be explained by the vertical lobe patterns,thereby showing that the path loss predictions in TCP correspond to the pathloss assumptions made on them.32

Table 4.4: Path loss due to vertical angles.height ofserving BS[m] height of MS[m] vertical anglebetween BS andMS [deg] angle in lobepattern aftercorrection formechanicaldowntilt additional lossdue to the lobepattern [dB]26 15 0.6727 358.6727 (0.5)-1.2515 0.2459 358.2458 (1.25)-2.0mechanicaldowntilt[deg] 15 1.1975 359.1975 (0.25)-0.52 15 0.8658 358.8658 0.5-(1.25)electricaldowntilt[deg] 1.5 1.4981 359.4981 0.25-(0.5)0 1.5 0.5478 358.5478 (0.5)-1.251.5 2.6656 0.6656 0.15-(0.3)1.5 1.9278 359.9278 0-(0.25)(a) Comparison of four di�erent bins with a positive di�erence g-g0. The two values in the last columncorresponds to the loss values at the two nearest half-degrees. The value within parenthesis is the lossvalue corresponding to the angle the furthest away from the calculated angle in the forth column.Di�erence in pathgain g0-g1 [dB](loss) Maximal di�erencein additional loss[dB] Minimal di�erencein additional loss[dB]0.3900 1 00.4000 1.75 00.3800 0.35 -0.050.3900 1.25 0.25(b) Comparison of the loss values rendered by the di�erences between the di�erentpredictions and losses due to vertical beam shapingTable 4.5: Gain matrix, serving BS di�erenceTotal # of bins 123 045 g vs g0 g vs g1 g vs gref g vs g2# that has changed serving BS 40 212 46 878 68 252 961g0 vs g1 g0 vs gref g0 vs g2# that has changed serving BS 18 134 55 480 39 707g1 vs gref g1 vs g2# that has changed serving BS 47 469 46 438gref vs g2# that has changed serving BS 67 99133

Table 4.6: Loss of LOS bins.(a) Comparison between predicted loss and theoretical free space propagation loss.Number ofbinsparticipatingincomparison:3589 loss fromTCP (loss1)[dB] losses fromfree spacecalculations(loss2) [dB] losses fromfree spacecalculations(loss3) +added lossfrom antennalobe (1dB)[dB]di�erence1between loss1and loss2(loss1-loss2)[dB] di�erence2between loss1and loss3(loss1-loss3)[dB]max 127.2190 113.3136 114.3136 47.1564 48.1564min 56.8890 53.6442 54.6442 0.0038 0.0141mean 92.3005 84.2029 85.2029 8.0976 7.0976median 89.6590 85.2711 86.2711 9.2829 8.2829(b) Angles between the LOS bins and their serving BSs and the loss that angles give rise to due to the verticallobe patterns of the antennas.angle betweenBS and bin[deg] angle ofdeviationfrommaximum oflobe patternof theantenna in�gure 4.1 onpage 32[deg]

correspondsto a lossminusantenna gaindue to thelobe patternof theantenna in�gure 4.1 onpage 32 [dB]angle ofdeviationfrommaximum oflobe patternof theantenna in�gure 3.5 onpage 28 [deg]

correspondsto a lossminusantenna gaindue to thelobe patternof theantenna in�gure 3.5 onpage 28 [dB]max 86.7509 273.2491 9.70 - (9.70) 267.2491 13.70 -(12.75)min -81.8152 81.8152 (21.05) -20.90 75.8152 (20.10) -20.20max(absolutevalue ofangles) 86.7509 273.2491 9.70 - (9.70) 267.2491 13.70 -(12.75)min (absolutevalue ofangles) 0.00 0.00 -17.80(antennagain) 0.2006 -16.00 -(-15.90)meandeviationfrommaximum ofantenna lobe 15.0301 344.9699 (3.25) - 2.20 338.9699 (8.70) - 10.10median 9.0401 350.9599 (8.95) - 4.40 344.9599 (8.40) - 8.1034

Table 4.7: Parameter settings used for simulations.General Basestation TerminalBandwidth 20 MHz Outputpower 40 W Max outputpower 21 dBmFrequencyband 2.6 GHz Noise �gure 2.2 dB (UL) Noise �gure 8 dB (DL)Down linkmodulation 64 QAM,MIMO Up linkmodulation 16 QAM,SIMO4.3 ModelsFrom every simulation a set of plots are outputted. The set includes plots of cdffor SINR, cdf for path loss distributions, cdf for bitrate distributions, averageand worst 10 percentile of mean bitrates in Mbps plotted against the capacityof the system, the average cell load in GB/h for di�erent loads. The averagecell load Caverage [GB/h] is calculated as shown in equation (4.1)Caverage [GB/h] =

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8 · 1000(4.1)where R [Mb/s] is the bitrates for all bins and l [%] is the fractional load. Theworst 10 % bitrates are calculated in the same way but with the worst 10-percentile of the bitrates instead of the mean of the bitrates. In all the plots itis the di�erence in bitrates arising from the 3D models with gain for higher binsrelative the two dimensional [2D] models where all the bins are on the ground�oor that is important. The absolute values that of course is highly dependanton the used radio access technique, in this case LTE, is less important, however,the parameters applied can be seen in table 4.7.The green 2D curves present in all plots are meant to be a reference, so theyare constant and does not vary between the di�erent models. The exception isin the results in 4.3.2.6 on page 49 where an additional 2D curve is present thatis not identical to the other models'.4.3.1 Without LOS Considerations4.3.1.1 Results from the First ModelThe employment of the 3 dB/floor �oor height gain model results in signi�cantimprovement of indoor path loss distribution, see �gure 4.2. The improvementsseem to be distributed evenly over all bins, i.e. the 3D path loss curve followsthe 2D curve on almost equal distance all the way. The SINR is also improved,both in DL and UL. In �gure 4.3 the SINR for a system with 30 % load isshown. Especially the bins with poorest SINR in the UL are improved. Thisimprovement renders higher bitrates, both average and the worst 10 %, see �gure4.4. The di�erence in absolute bitrate values decreases with increasing tra�c35

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Figure 4.3: SINR in DL (to the left) and UL in �rst model.load in the cell as expected, however the di�erence expressed as a percentage isstill signi�cant and the capacity, the average cell load is still increased.4.3.1.2 Results from the Second ModelThis model using 3 dB/floor height gain up to the highest �oor of the building,gives an even more optimistic result than the �rst model. This is evedent in�gure 4.5 showing path loss for indoor bins, �gure 4.6 showing the SINR inDL and UL and consequently also in �gure 4.7 showing the mean bitrates andcapacity. The general behavior of the improvements are the same as in the �rstmodel, which is expected considering how similar the models are. However, theaverage height of the buildings in the city considered is 22.12 m and the medianheight is 21.00 m which corresponds to 7.42 �oors and 7.00 �oors respectively.That means that more than half of the indoor bins are given �oors higherthan the max�oor in the �rst model, a max�oor that the �oor height gain of 3dB/floor is adapted to [7]. 36

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Figure 4.12: SINR in DL (to the left) and UL in fourth model.4.3.2.2 Results from the Fourth ModelThe simulations performed using the fourth model with indoor loss calculations,results in an indoor path loss curve that looks very di�erent from all threeprevious models. As seen in �gure 4.11, the 3D curve and the 2D curve intersectsand the highest path loss is increased in the 3D model. This means that somebins get a negative �oor height gain, a loss. The SINR in the DL seen in �gure4.12 is quite una�ected in that the 3D model still improves on the 2D model.The improvement is less than in other 3D models. The UL SINR at 30 % loadis a�ected in that the 3D curve now intersects the 2D curve in two places3meaning that the worst SINR is worse and the best SINR is also worse. Theaverage SINR is better.The bitrates shown in �gure 4.13 are signi�cantly di�erent from previousresults. The DL bitrates are indeed higher for lower loads, but at high loadsthe bitrates and the capacity, or average cell load, decrease to be lower thanthe values in the 2D model. The same can be found in the UL but only for the3They actually intersect at more places but there are two major trends.41

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Figure 4.14: Path loss predictions with �fth model in indoor bins.average bitrates. The worst 10 percentile are still improved in bitrates comparedto the 2D model for all loads. The capacity however decreases for the really highloads.4.3.2.3 Results from the Fifth ModelThe path loss curve resulting from the �fth model using outdoor bins for LOSconsiderations and indoor path loss calculations, intersects the curve from the2D model as seen in �gure 4.14 just like the path loss curve resulting frommodel four. However, the number of bins with a negative height gain, or lossis smaller in model �ve than in model four. The SINR curves when the systemis loaded to 30 % show, in �gure 4.15, the poorest values in the DL decreasingwith respect to the 2D model. The UL SINR is as always more complex butit also shows a decrease with respect to the 2D model in SINR for the poorestvalue. In addition also the best SINR values are decreased compared to the 2Dmodel but the average SINR values are increased. The bitrates in �gure 4.16show nice increases compared to the 2D models bitrates for both DL and UL.The capacity is not improving as much but it is never lower than that of the 2Dmodel. The higher the load, the smaller the increase in bitrates and capacity.Results from the Fifth Model with Lower Wall Loss Constants Theresults from this model which is basically the same as the �fth model but hasa lower wall loss constant added, see section 3.2.2.3 on page 25, are of coursequite similar to the results of the �fth model. The di�erences are better pathloss results, 4.17, better SINR curves 4.18 and higher bitrates and capacity 4.19.4.3.2.4 Results from the Sixth ModelThere results from the sixth model with building speci�c path loss curves showsa path loss curve that improves on the 2D model for all bins. The improvementis slightly larger for the higher path loss values as seen in �gure 4.20. The SINR43

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(b) Average (to the left) and the worst 10 percentile bitrates at di�erent loads in the UL of model �ve.Figure 4.16: Mean bitrates at 7 di�erent loads: 5 %, 10 %, 20 %, 30 %, 50 %,70 % and 99 %. The highest bitrate corresponds to the lowest load and viceversa. 44

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Figure 4.17: Path loss predictions with �fth model with lower wall loss constantsin indoor bins.

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Figure 4.18: SINR in DL (to the left) and UL in �fth model with lower wall lossconstants.45

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(a) Average (to the left) and the worst 10 percentile bitrates at di�erent loads in the DL of model �vewith lower wall loss constants.0 0.5 1 1.5 2 2.5 3 3.5

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(b) Average (to the left) and the worst 10 percentile bitrates at di�erent loads in the UL of model �vewith lower wall loss constants.Figure 4.19: Mean bitrates at 7 di�erent loads: 5 %, 10 %, 20 %, 30 %, 50 %,70 % and 99 %. The highest bitrate corresponds to the lowest load and viceversa.46

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Figure 4.20: Path loss predictions with sixth model in indoor bins.−20 −10 0 10 20 30 40 50 60 700

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Figure 4.21: SINR in DL (to the left) and UL in sixth model.also shows improvements towards the 2D model for all bins, at least in the DLat 30 % load. The UL SINR is poorer for the high SINR values but improves onthe low values, see �gure 4.21. This means that the DL bitrates and capacityshown in �gure 4.22 also are improvements compared to the 2D model. The ULaverage bitrates and capacity decreases to be lower than the 2D models values,when the load increases from 50 % to 70 %. The worst 10 percentile bitrates inthe UL improves on the 2D model for all loads and compared to the �fth model,the improvement is larger but the capacity decreases for higher loads.4.3.2.5 Results from the Seventh ModelThe results from the simulations performed with the seventh model are quitesimilar to the results of the sixth model since apart from the constant distribu-tions and vertical lobe patterns they are identical. The path loss curve foundin �gure 4.23 shows an decrease in path loss for all bins compared to the 2Dmodel even though the gain is not as large as in the sixth model. The SINRcurves from when the system is loaded to 30 % shown in �gure 4.24 also showthe same behavior as model six with improvements for all bins in the DL and47

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