baca master thesis outdoor indoor 23651

7/30/2019 BACA Master Thesis Outdoor Indoor 23651

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Kings College London

University of London

MSc in Telecommunications by Research

An Outdoor-Indoor Interface Model for

Radio Wave Propagationfor 2.4, 5.2 and 60 GHz.

Prepared by:

Michael Dhler

Supervised by:

Prof. A. H. Aghvami

A thesis submitted for the degree of MSc by Research.

1998-1999


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Dedication

ii

To the particles of any race and colour,

which have to obey their live long

Maxwells equations.


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Acknowledgements

iii

Acknowledgments

This first line is dedicated to my supervisor Monica DellAnna, who never tired of

supplying me with new work and a healthy portion of encouragement using her alluringItalian smile. My special gratitude is for Prof. Aghvami who showed me what is really

important in the abstruse world of Digital Communications.

I had the pleasure of working with Roger Cheung whose generous good-

naturedness and copiously interesting ideas helped me more than once out of a sheer

unsolvable situation. Without him this year would have been a tedious drudgery.

, .

. .

: , , , ,

, , , ,

.

Besonders lieblichen Dank meinem Bruder Eddie, welcher schlafend mein Leben

manchmal in einen strmischen Ozean verwandelt hat. Auch meiner lieben Schwester

Anita, die ich einfach ungemein gern habe. Lchelnder Dank meinen Freunden Steffen,

Andr, Ilia und Friedi in Deutschland, jeder welcher in seiner Art skuril, witzig und eigen

meinen Weg begleitet hat. Leiser Dank auch Anja. Stiller Dank meinem Vater.

Most gratitude to those who made London's gloomy days shiny. To my flat-mates

Yunis, Max, Ulrike, Yukako and Helena; to my lab-mates Victor, Vasileios, Patrick,

Giorgio, Nelly, Jean-Philippe and Julio; to the Chemist-mafia Eva, Marco, Piero, Alex

and Alberto; and not least to Victoria, Marta and Leo.

Muchsimas gracias a mis amigos castellanos y catalanes, cuya sangre

mediterrnea fue como una brisa fresca en mi vida.

Gemmuli, deixam emprar aquesta llengua secreta per dir-te com testimo! Tumhas alliberat i mhas fet florir.

London, 9.9.1999 Mischa


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Table of Contents

iv

Table of Contents

ACKNOWLEDGMENTS ..........................................................................................................................III

TABLE OF CONTENTS ...........................................................................................................................IV

ABSTRACT.................................................................................................................................................VI

INTRODUCTION ........................................................................................................................................1

1. AVAILABLE OUTDOOR-INDOOR MODELS...............................................................................8

1.1. INTRODUCTION ................................................................................................................................ 8

1.2. PATH-LOSS MODELS ....................................................................................................................... 8

1.2.1 Linear Path-Loss Model.......................................................................................................... 8

1.2.2 Angle dependent Path-Loss Model ......................................................................................... 9

1.2.3. COST 231 Keenan and Motley Model.................................................................................... 9

1.3. FIELD-STRENGTH PREDICTING METHODS ...................................................................................... 10

1.3.1. Ray tracing............................................................................................................................ 10

1.3.2. Method of Moments (MoM).................................................................................................10

1.4. PARAMETERDEPENDENCIES AND TENDENCIES ............................................................................. 11

1.4.1. Grazing Angle....................................................................................................................... 11

1.4.2. Penetration Loss Model Parameter ....................................................................................... 11

1.4.3. Frequency dependent Loss....................................................................................................11

1.4.4. Receiver Height inside a Building ........................................................................................ 12

1.4.5. Moisture Effects.................................................................................................................... 12

1.4.6. Penetration Loss Statistics .................................................................................................... 12

2. PROPAGATION ALLOTMENTS ...................................................................................................13

2.1. INTRODUCTION .............................................................................................................................. 13

2.2. TRANSMISSION COEFFICIENTS ....................................................................................................... 16

2.3. NON-SPECULARTRANSMISSION DUE INTERIORPERIODIC STRUCTURES ........................................19

2.4. SCATTERING DUE TO SURFACE ROUGHNESS..................................................................................23

2.5. SCATTERING DUE TO WALL INTERIORMETALLIC LATTICES AND MESHES....................................24

2.6. DIFFRACTION................................................................................................................................. 26

3. THE PROPAGATION MODEL....................................................................................................... 28

3.1. INTRODUCTION .............................................................................................................................. 28

3.2. DETERMINISTIC TRANSFORMATION...............................................................................................29

3.3. TRANSFORMATION OF THE PROBABILITY FUNCTIONS ...................................................................31

3.4. OUTDOORTRANSMITTER AND INDOORRECEIVER......................................................................... 36


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Table of Contents

v

4. APPLICATION .................................................................................................................................. 38

4.1. INTRODUCTION .............................................................................................................................. 38

4.2. THE GENERIC CELL ....................................................................................................................... 38

4.3. THE MODIFIED COST 231 MOTLEY MODEL ...............................................................................42

5. CONCLUSIONS ................................................................................................................................. 48

5.1. CONCLUSION ................................................................................................................................. 48

5.2. FURTHEROUTLOOK....................................................................................................................... 49

6. APPENDIX I (GRAPHICS)............................................................................................................... 50

6.1. INTRODUCTION .............................................................................................................................. 50





6.6. DIFFRACTION................................................................................................................................. 55

6.7. THE GENERIC CELL ....................................................................................................................... 57

7. APPENDIX II (FORMULAS) ...........................................................................................................59

7.1. INTRODUCTION .............................................................................................................................. 59





7.6. DIFFRACTION................................................................................................................................. 70

7.7. PROOF OF ABSENCE OF SIDE LOBES FOR THE CELL-PHILOSOPHY ....................................................85

8. APPENDIX III (MATLAB) ...............................................................................................................87

8.1. INTRODUCTION .............................................................................................................................. 87





8.6. DIFFRACTION................................................................................................................................. 91

TABLE OF FIGURES................................................................................................................................95

BIBLIOGRAPHY....................................................................................................................................... 97

INDEX ..................................................................................................................................................... MM


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Abstract

vi

Abstract

The study presented in this thesis has been undertaken as part of the Radio Environment

work area of the UKs Mobile VCE, whose Core Program of research involves seven UK

universities and more than twenty industrial organizations. The main objective of this

work is to provide a model for electromagnetic wave propagation through a windowed

wall, possibly with an internal periodic structure. The model operates as an interface

between outdoor and indoor propagation models at frequencies of 2.4GHz, 5.2GHz and

60GHz. An approximated deterministic approach has been chosen to be able to match

existing semi-empirical, deterministic and stochastic outdoor models to the appropriate

indoor models. The model embraces all participating propagation phenomena like

specular & non-specular transmission, scattering and diffraction. The extracted

approaches are then utilized to ease site-specific calculations. One approach considers a

generic wall as several sufficiently large cells embedding typical window-wall

constellations. The formulas elaborated in this thesis can be applied to such cells to give

tabled field and power distributions, where the cell shares should be added to give an

overall prediction. Another approach extends the COST 231 - Motley outdoor-indoor

model justified by strong influences of diffraction in primary penetrated rooms.

Furthermore, to make use of existing statistical indoor models, the given outdoor pdf's are

transformed into indoor pdf's using the well-known transformation of multi-dimensional

random variables. Thus the model developed allows one to predict the transformed

indoor field parameters from the known outdoor field-state, including their pdfs. This

method is a trade-off between calculation time, accuracy and the ability to transform

pdf's.


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Introduction

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Introduction

Suddenly it appears to be so obvious why the

evolution brought us out of the water to the land,

since its quite impossible to use a Mobile Phone,what for some among us seems to be the crme de la

crme of the evolutionary ladder, under water.

From its very beginnings humankind seems to have been ruled by the desire to

commune. Wasnt it this aspiration that made us speak? Wasnt it this craving that forced

our brains to develop, not to talk nonsense the whole day long? Humans started to talk, to

express themselves and not last, to communicate. First they merely used their vocal

chords. When the distances increased they started to utilize tools like drums to make

noise over vast wilds. But all these methods were disadvantageous. They were annoying,

unreliable and everybody could listen and intercept the ongoing conversation. For those

reasons the Mobile Phone was just a question of time. In fact the only thing humanity

always had plenty of. A couple of milleniums have had to pass before a bunch of

celebrities like Kirchhoff, Maxwell, Sommerfeld or Shannon were born to make this

dream come true. None of them initially had a clue about what kind of ball they set

rolling. With the aid of them and thousands of famous and fameless scientists, many of

them not even capable of holding a normal conversation, we juggle around with

acronyms like UMTS, WLAN or CDMA and actually do know what they are supposed to

mean.

Not all the work is done, though. The main path is hinted at, what remains is to

walk it. The edge to the second Millennium is characterized by the endeavour to merge

all telecommunication services into UPT (Universal Personal Telecommunications). It

should offer access to all kinds of services at a reasonable expense at any place and any


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Introduction

2

time. Certain steps have already been mastered as the elaboration of the 3rd

generation

mobile phones standardized in UMTS (Universal Mobile Telecommunications System)

via GSM (Global System for Mobile Communications), DECT (Digital European

Cordless Telecommunications), TETRA (Trans-European Trunked Radio) and ERMES

(European Radio Message System). UMTS gives way to the accelerating and rising

demand for ISDN (Integrated Services Digital Network) and B-ISDN (Broadband-

ISDN), emphasizing high-bit-rate services, like multimedia, as well as voice and low-bit-

rate services. Restrictions of the transmitted bit rate are due to the limits of physical

resources such as the electromagnetic spectrum or the available power. Therefore highly

sophisticated coding, modulation and transmission techniques have to be investigated and

applied. The engineers struggle to achieve dBm coding or modulation gain certainly

reaches its limits. Yet there is still some hope left to ameliorate existing technologies or

even to find new ones. For example, I believe, quantum electrodynamics could be

exploited for novel transmission techniques. The work undertaken in this Master attaches

more importance to the approach mentioned first. The aim of the following is to give a

profound and complete background of the theory applied, namely classical

electrodynamics, which is then being used to extract a new model for outdoor-indoor

wave propagation.

As mentioned above, both emerging and well-established Personal

Communications Services (PCS) require an accurate prediction of the wave propagation

mechanisms for development of new techniques as well as system deployment. The

limited bandwidth available and the tremendously increasing number of users does

compel cell-network operators to a highly terse frequency re-use pattern. The objective is


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Introduction

3

to minimize interference with maximum range depending on cell type and power control

mechanisms. Coverage and power control algorithms are less crucial for cells with base

stations located above rooftop level, i.e. Macro, Large, Small or Umbrella Cells, since

those cells cover more or less geometrically manageable areas. Problems arise lowering

the base station below rooftop level, as it is for Micro and Pico cells, where the path

between transmitter and receiver is usually more randomly obstructed. Frontiers of this

cell type are uppermost fractal and naturally follow externally imposed architectural

patterns, e.g. street alignments or a certain room distribution on a floor. Interferences

become more predominant since cell isolation is an arduous task to achieve. Until

recently Micro and Pico Cells were exclusively restricted to either outdoor or indoor

environment. Soon the question arose whether an outdoor base station was able to cover a

given indoor area and vice versa or whether the loss through building walls is high

enough to reliably separate indoor and outdoor cells. Therefore, Micro and Pico cells

demand a meticulous knowledge of the radio wave behaviour through a buildings wall.

Assuming the channel characteristics to be known in a certain area of interest,

accurate prognosis about Base Station and Mobile Station coverage-area, power-drop

probability, inter-cell and intra-cell interferences, etc. can be made. Various models exist

which predict both outdoor and indoor propagation parameters such as field strength,

polarization, (spatial) angle of arrival, time of arrival and their pdfs. All these models

assume that the mobile and base stations are located in a similar environment, i.e. either

outdoor or indoor. They can be classified into Models for Field Prediction and Radio

Channel Models [1] that is circumstantiated below.


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Introduction

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Models for Field Prediction give as one output the main transmission paths

including the losses along them. These models can be subclassified into Empirical,

Abstract-structure-based, Semi-empirical and Deterministic Models [2]. Empirical

Models are extracted from measurement data by means of regression methods. Typical

representatives are the legendary Okumura, Hata, COST-231-Hata and RACE dual-slope

Models. Abstract-structure-based Models, as the Walfish&Bertoni and Ikegami Models,

analytically provide propagation loss assuming a facile terrain structure. In the Semi-

empirical Models the given parameters of the Abstract-structure-based Models are

empirically corrected, as was done in the COST-231-Walfisch-Ikegami Model. All

models that use electrodynamic field integral equations or ray tracing/launching

techniques form the intricate, but not necessarily superior, class of Deterministic Models.

The more accurate output of these models is taken from a detailed terrain database.

Radio Channel Models provide a more comprehensive description of the

propagation phenomenon providing the full characterization of the CIR (channel impulse

response) in a mobile radio environment. It has been distinguished between Stored,

Deterministic and Stochastic Channel Models. The first retain gathered site specific

channel impulse responses, the second make use of field calculations, whereas the latter

gives its parameters as realizations of random processes.

The few existing outdoor-indoor studies and models [3-13] belong to the Models

for Field Prediction. In fact it makes little sense to extract a channel impulse response

exclusively for the interface. It is common to attach the outdoor-indoor model at least to

the indoor environment where predictions are required. The reason is that the large

number of different interface constellations would give raise to a enormous amount of


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Introduction

5

CIRs or a too broad spread for the statistical parameters. It is perspicuous that the wave

penetration loss through a building is a function of parameters such as construction

materials of the buildings, distribution and size of the windows, existence of frames, fire

escapes, air conditioners, internal wall-reinforcement, foliage, the nature of the

surrounding buildings, the structure of the rooms, and the position of transmitter and

receiver. Beside this the direction of arrival has a predominant leverage, which is

therefore the main input parameter for all available interface models. Due to this broad

gamut of partially non-comparable parameters it became customary to distinguish

between several parameter classes. The first differentiation is made with the sites of

concern, such as Urban (typical, bad or dense), Suburban (hilly or non-hilly) and Rural.

The distinction is necessary to use the appropriate models to predict the field-strength at

the exterior wall with a given outside base station. The second differentiation classifies

various building types. In literature [3] it became normal to distinguish between eight

classes given as (1) Residential houses in suburban areas; (2) Residential houses in urban

areas; (3) Office buildings in suburban areas; (4) Office buildings in urban areas; (5) Factory

buildings with heavy machinery; (6) Other factory buildings, sports halls, exhibition

centres; (7) Open environment, e.g. railway stations or airports; (8) Underground. The

building type supplies information about the choice of the interface model and the values

of the parameters to be inserted into these deterministic models. A third differentiation

sorts the availability of certain more specific building details, e.g. frames, coating,

reinforcement, influential external scatters, percentage window-wall, etc. They determine

the magnitude of certain parameters and their spread. Further differentiation embraces

the frequency range and the bandwidth with respect to the coherence bandwidth of the


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Introduction

6

given channel. Concerning the frequency most elaborated outdoor-indoor models are

designed for frequencies around 1.8GHz, the operation frequency of PCN (Personal

Communication Networks). Regarding the bandwidth, it must be said that, although the

behaviour of the channel varies heavily over a vast range from 2.4GHz to 60GHz, the

channel might be regarded as wideband. This can be explained with the broad coherence

bandwidth of the interface compared with the current maximum available data rate. In the

literature distinguished wideband and narrowband measurements are taken with respect

to the outdoor and indoor environments.

The challenge of this work is to expunge the disadvantages of the already

developed outdoor-indoor models, which use either time consuming site-specific

calculations or very simple (semi-) empirical propagation formulas. The former are

unable to transform given outdoor pdfs into their indoor counterparts, whereas the latter

neglect strong diffracted waves acting severely in the primary base station facing rooms.

Within the core research, an important output of the Radio Environment work area is the

development of such an interface model for outdoor-indoor propagation. An

approximated deterministic approach has been chosen here to be able to match existing

semi-empirical, deterministic and stochastic outdoor models to the appropriate indoor

models. The model developed allows one to predict the transformed indoor field

parameters from the known outdoor field-state, including their pdfs. This method is a

trade-off between calculation time, accuracy and the ability to transform pdf's. Another

enhancement pertains to the frequency range that is extended to 2.4GHz, 5.2GHz and

60GHz. The frequency around 2GHz is exploited by PCN. HIPERLAN captures the

frequency around 5.2GHz, although it might be extended to 17GHz. The 60GHz


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Introduction

7

frequency band is restricted to indoor applications yet, but an exhaustive study might

allow outside base stations to cover larger indoor areas. The physical picture drawn at

this frequency is quite different from the lower frequencies since it approaches the optical

boundary, and penetration losses increase enormously. Therefore the model developed

applies mainly to frequencies below 10GHz, where some comments for the 60GHz case

are added.

Chapter 1 gives a broad survey about already existing outdoor-indoor models

treating in depth parameters of interest. In Chapter 2 all the propagation allotments are

handled and summarized to give the necessary basis for the actual outdoor-indoor model,

which is exhaustively treated in Chapter 3. In Chapter 4 this model is then applied to two

completely different signal-strength predicting models. Finally conclusions and further

vistas are drawn in Chapter 5. Appendix I (Graphics) includes all relevant graphics,

which would otherwise have overloaded the actual thesis, and in Appendix II (Formulas)

all needed formulas are derived. To enable the reader to follow and prove the given

formulas and graphics, Appendix III (Matlab) embodies the Matlab source-code used

throughout this work.


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Chapter 1

8

1. Available Outdoor-Indoor Models

1.1. Introduction

Network Operators require a thorough knowledge of the channel characteristic as power

distribution, its statistics, e.g. Rayleigh or log-normal, the maximum fading margins and

several probabilities of occurrence, e.g. Angle of Arrival (AOA), Time of Arrival (TOA)

or polarization. Furthermore general tendencies are of interest, e.g. power behaviour with

varying floors or the influence of open windows, moisture walls, etc. The fading statistics

are confirmed to be Rayleigh or Rice for the small-scale fading and log-normal for the

large-scale fading [9]. The fading margins are given either implicitly through the

magnitude or spread of the parameters, as in the COST 231-Motley Model [13], or

explicitly as a result of precise site-specific computations [12]. The latter method is

unnecessarily accurate since the precise location of the power drop is not required, but

rather its existence and extent. Thus they should be used to verify more approximated

models. Other parameters of interest are discussed in the following.

1.2. Path-Loss Models

1.2.1 Linear Path-Loss Model

The most frugal model with regard to the set of parameters is the Linear Path-Loss Model

proposed by Horikoshi [4]. It assumes the excess penetration loss in dB to be

approximately linearly dependent on the angle of incidence. The absolute loss in terms of

the angle of incident and perpendicular loss 0L is given as:

( )( )log20LL o0 = , where ( ) incidence0atfieldincidenceatfield

=

. ( )1.1

The model gives best predictions for normal incidence but fails for grazing angles.


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Chapter 1

9

1.2.2 Angle dependent Path-Loss Model

The European COST 231 project [5] extrapolated an empirical formula out of numerous

measurement campaigns varying the building type, the distance and the angle of

incidence. The all embracing formula yields the loss between the transmitter location and

a reference point just inside the building:

( ) ( ) ( )( )2/GHz sin1dlog20flog2032.4L ++++= Gee WW . ( )2.1

is now the grazing angle of the impinging wave. d is the physical distance between

transmitter and external building wall just outside the reference point, where free-space

and LOS conditions are assumed. eW is the loss for the perpendicularly illuminated outer

wall and is gauged to be 4-10dB. GeW , in order of magnitude of about 20dB, is an

additional loss for perfectly grazing angles (see 1.4.). Additional terms accounting for the

floor-gain inside the building are omitted here.

1.2.3. COST 231 Keenan and Motley Model

Within the framework of COST 231 the Keenan and Motley outdoor-indoor propagation

model was amended and floor-gain corrections were added to give the following formula:

( ) ==

+++=J

j

jwjw

I

i

ifif LkLkdn1

,,

1

,,0 log10LL ( )3.1

n is given as the power decay index, d is the distance, 0L is the path loss at 1m

distance, ifL , and jwL , are the loss for floor i and wall j , respectively. I and J are the

number of penetrated floors and walls.


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Chapter 1

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1.3. Field-strength predicting Methods

1.3.1. Ray tracing

Ray tracing and cognate methods are powerful in the sense that they can predict

arbitrarily accurate with increasing site precision. One obvious drawback is that the static

character of this approach does not solve the entire field distribution at one instant in the

given space. Rather, it follows certain optical paths, which have to be truncated

depending on the accuracy required. Huge sites and high precision usually result in

formidable simulation times. A second severe drawback is the arduousness of including

diffracted rays, even though a whole theory, the Geometrical Theory of Diffraction, was

developed. Ray tracing naturally leads to penetration loss overestimation for grazing

angles and underestimation for angles > 60 . The reason for the former is the missing

diffraction term, whereas the latter is due to the neglected finite wall-thickness. Incoming

rays sense the window gaps to be wider than they actually are. And finally the ray tracing

philosophy is restricted to high frequencies, thus small wavelengths with regard to the

obstacles.

1.3.2. Method of Moments (MoM)

A breakthrough was recently achieved by the research-group around B. De Backer [12]

who were able to combat the MoMs most striking disadvantage: inefficient evaluation

techniques and towering memory consumption. This allows one to handle even large sites

in a passable computation time. The idea behind this approach is to solve the whole field-

distribution numerically. First of all the site is split into a set of linear segments along

which the field components are expanded into a series of pulse and overlapping triangle

functions. Galerkin testing is applied to achieve a system of linear equations. They can be


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Chapter 1

11

dramatically eased using some neglecting approximations and transforming it into a

sparse matrix. Finally well known linear algebra is applied to solve the set of equations.

Unlike ray tracing the MoM is not hampered by any high frequency limitation.

1.4. Parameter Dependencies and Tendencies

1.4.1. Grazing Angle

It is remarkable to note that the penetration loss for perfectly grazing angle does not

approach infinity as Fresnels Theory postulates, but reaches a constant level of around

27.5 dB almost independent of frequency [5]. This can be attributed to diffraction and

scattering by any external scatters like window edges.

1.4.2. Penetration Loss Model Parameter

The explicitly given penetration losses for normal or grazing incident angles in equation

( ) ( )2.1,1.1 and ( )3.1 are not real physical losses, but are extracted from empirical

measurements and embrace all participating propagation effects including multiple

reflection and diffraction.

1.4.3. Frequency dependent Loss

A general agreement on penetration loss in dependency of the chosen frequency has not

been found yet. The reason is that buildings, the material and general premises differ too

much from one measurement campaign to another. It has been reported [9] that as

frequency increases the penetration loss does not necessarily also increase, but might

succumb to serious fluctuations. Therefore, for increasing frequencies additional path loss

can be compensated by decreasing building penetration.


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Chapter 1

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1.4.4. Receiver Height inside a Building

Most of the papers cited make clear statements concerning the influence of the signal

strength in dependency of the receiver height inside the building. Most influential are the

shadowing clutters in front of the building. Trees let the receiver field strength decrease

from tree-height to the first floor. Above the obstruction height, when LOS conditions are

given, the power lever gradient is expected to level off. Measurements reported in [9] and

[10] show an augmentation of around 2dB/floor up to the surrounding hindrance-height

after which it remains nearly constant.

1.4.5. Moisture Effects

Network operators in regions with frequent or torrential rainfalls should incorporate an

additional penetration loss coefficient for a sufficient confidence level of the operating

system. It could be shown [7] that due to higher reflection the penetration losses of a wet

wall are raised by 10 percent compared with a dry wall.

1.4.6. Penetration Loss Statistics

Also in [7] the fading margin inside a building is evaluated. For it the outdoor log-normal

and the penetration loss statistic is considered. The assumed large number of independent

random processes that determine the penetration loss, e.g. material, permittivity,

moisture, incident angle, thickness, scatters, etc., presume one to expect the statistic to be

roughly log-normal, too. Since both effects arise independently the overall statistics is

log-normal with zero mean and a standard deviation given by:

22

npenetratiooutdoor += . ( )4.1

The fade margin at the cell boundaries with given outage probability is gained through:

( )/Qpoutage = . ( )5.1


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Chapter 2

13

2. Propagation Allotments

2.1. Introduction

To find a tractable approach to the outdoor-indoor propagation model, first the objective

has to be clarified and then the solution methods scrutinized. The aim of the Radio

Environment work area of the Mobile VCE is to develop a Simulation Platform for real-

time and real-site studies [1]. Its backbone is a meticulous database including site specific

details from building to window and door positions. Any arbitrary number of users can be

assigned to a certain number of base stations using all imaginable transmission features,

e.g. different modulations, power control, hand-over etc. The claim for real-time ability

coping with the mountainous amount of computations makes it impossible to use either

straightforward solutions of Maxwells equations or the methods mentioned in the

previous chapter, e.g. MoM or ray-tracing. Since measurements are available, empirical

models ought to be constituted in the first stage. The parameters needed are extracted

from fitted regression curves and inserted into the above-given formulas. The detriments

are apparent since the parameters are confined to the measurement-site, probabilities are

not transformable and the whole physical picture behind the penetration is basically not

understood. Therefore, before a practical model is elaborated in the second stage, all

eventual propagation components are examined to form an approximated deterministic

model, which overcomes the aforementioned disadvantages.

Using a versatile outdoor wave propagation model for three-dimensional terrain

[14] the field strength, polarization state and angle of arrival, as well as their pdfs, at a

given wall surface can be predicted. Assuming the field states are known over the

windowed-wall surface being considered, it is possible to decompose the field into TE


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Chapter 2

14

and TM components with respect to the plane of incidence. The TE wave is linearly

polarized with the electric field vector perpendicular to the plane of incidence, whereas

the TM wave has its electric field vector in the plane of incidence. The impinging wave is

partly reflected, partly absorbed and partly transmitted (Table 1). The specular and non-

specular reflected components as well as the scattered and backward diffracted ones

contribute to the total outdoor-model. The specular and non-specular transmitted and

forward-diffracted components are captured by the outdoor-indoor-model (Figure 1). All

these propagation processes arise from the same physical principles obeying Maxwells

equations. Some of them, e.g. scattering and propagation through periodic structures,

show similar physical behavior, but are listed separately to make use of theory already

developed.

Reflected part

Specular reflection (Snells Law) Non-specular reflection due to periodic structures (Floquets

Theorem) Scattering (Gaussian Scattering Matrix) Backward diffraction (UTD)

Absorbed part

Due to the structures conductivity, which results in a complex

permittivity /= jreal assuming a time-harmonic

electromagnetic field

Transmitted part

Specular transmission (Snells Law)

Non-spec. transmission due to periodic structures (FloquetsTheorem)

Scattering due to exterior wall periodicity and internal wall lattices Diffraction (UTD)

Table 1: Synopsis of the propagation effects

In order to thoroughly understand the outdoor-indoor propagation mechanism a

characteristic window-wall configuration was chosen (Figure 2 and Figure 3). Figure 2

depicts the top-view of a horizontal cross-section of such wall, where the left and the


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Chapter 2

15

right part of the picture correspond to a solid and an internally periodic wall, respectively.

The periodic wall typically consists of a thin outer and inner wall and reinforcing

concrete cross girder. Figure 3 clarifies the notation for the angles used throughout the

following work. The main transmission phenomena, including specular and non-specular

propagation, scattering and diffraction, are now examined separately.

Figure 1: Decomposition of the propagation allotments

Figure 2: Horizontal cross-section of a typical Wall-Window configuration showing both solid

and periodic wall structures on the left and right part of the picture, respectively

Outdoor Channel

Reflection at theexterior wall

Reflection at the

internally periodic wallsScattering at the exterior

wall

Backward-Diffraction atthe exterior wall-edges

Field-state at the wall-surface:

Transmission through

the window and wall

Transmission through

the internally per iodic

walls

Transmitted scattered

components

Forward-Diffraction atthe window-wall-

configuration

Indoor Channel

OUTDOOR-INDOOR

CHANNEL

E = E

TE

+ E

TM

h1Outer Wall (

W)

2h2Periodic Structure (

Wd

1,

ad

2)

h1Inner Wall (

W)

Mode n=0, specular reflection

Mode n=1

Mode n=-1

Mode n=0, specular transm.

Mode n=1

Mode n=-1

Specular impinging waveOuter-Wall

Exterior edgeWindow alignedwall face

Window (sing/dbl)

Interior edge 1 Interior edge 2

w

Window Frame

y x

z


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Chapter 2

16

Figure 3: Elevation and azimuthal decomposition for window and wall

2.2. Transmission Coefficients

The transmission coefficients for a single and double glazed window and a lossy wall are

easily obtained using the transmission line model. For the sake of computational ease the

generic case of a 5-layered dielectric is assumed as depicted in Figure 4, where the

thickness and permittivity of the individual layers is set according to the penetrated

object mentioned above.

Figure 4: Generic 5-layer structure used for derivation of the propagation formulas.

y

x

z

k

Normal to the

wall surface

Elevation angle with

respect to the x-z-plane

Azimuthal angle with

respect to the x-z-plane

Azimuthal angle with

respect to the plane ofincidence or impinging anglewith respect to the normal z

Air, semi-infinite thickness

Dielectric, thickness t

Air, thickness d

Dielectric, thickness t

Air, semi-infinite thickness


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Chapter 2

17

In the case of single glazing dis put equal to zero, tto half the actual pane-thickness and

1.019 = j . The double-glazing requires d to be put to the pane-distance and tto the

pane-thickness. Similarly, for the lossy wall d is put to zero, t to the half of the wall-

thickness and 9.05.3 = j . Both permittivities are given in [15] for 1.8GHz and have

to be corrected for higher frequencies through measurements. The derivation of the

transmission formula can be gleaned from Appendix II; merely some important impacts

are discussed herein.

It is remarkable to note that, in the case of single and double-glazing, the mutual

cancellation of the multiple reflected waves leads to severe fluctuations. The single

glazing case is shown in Figure 5 with the normalized transmitted TE power vs. the

impinging angle in parametrical dependency of the pane thickness 2tfor all frequencies

concerned. The curves are shifted by 10dB and 20dB for f=5.2GHz and f=60GHz,

respectively. It can be seen already that an increase of the pane-thickness of 1mm can

result in a power drop of 5dB. For double-glazing a pane-thickness of 1.5mm and normal

incidence were assumed. Figure 6 depicts that case with the normalized transmitted TE

power in dependency of the pane-separation. The wall attenuates the electromagnetic

wave of approximately 1.1dB/cm, 2.2dB/cm and 26.6dB/cm for 2.4GHz, 5.2GHz and

60GHz, respectively. The wall-attenuation for 60GHz is so vigorous that the penetration

scenario severely depends on fluctuating short-time effects like open or closed windows,

moving people inside, etc. Additionally, the free-space propagation loss becomes

intolerably high, limiting the range of application to a few hundred meters.


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Chapter 2

18

Figure 5: TE transmitted power vs. impinging angle for single glazing; f=2.4GHz (not shifted),

f=5.2GHz (shifted by 10dB), f=60GHz (shifted by 20dB) pane-thickness 2t: 0.5mm,

1.0mm, 1.5mm, 2.0mm

Figure 6: TE transmitted power vs. pane separation for double glazing; f=2.4GHz (not shifted),

f=5.2GHz (shifted by 10dB), f=60GHz (shifted by 20dB) pane-thickness 2t: 1.5mm


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Chapter 2

19

2.3. Non-specular Transmission due Interior Periodic Structures

Buildings typically have walls constructed from concrete blocks or bricks. Reinforcing

grids or slabs form the periodicity in concrete walls. Bricks, possibly hollow, and cement

mould a much subtler periodic structure, which becomes relevant for the propagation

mechanisms at higher frequencies. Both wall types show general interior periodic

structures as depicted in Figure 7 and Figure 2, right. This leads to additional

transmission in directions other than the specular one, due to the excitation of higher-

order space harmonics, which can carry a significant amount of power depending on the

angle of incidence. The main impact is that ray-tracing and plain point-to-point path-loss

models lose their applicability. They have to be completed by the additional rays

emanating from the inner wall surface.

To deal with this effect, the generic structure in Figure 7 has been proposed [15],

what is mathematically examined in Appendix II.

Figure 7: Top view of a horizontal cross-section of an internally periodic wall.

d

Mode n=0, specular reflection

Mode n=1

Mode n=-1

Mode n=-1

Mode n=0, specular transmission

Mode n=1

Specular impinging wave


26/106

Chapter 2

20

A. Concrete wall:

Assuming a commonly available 6thick concrete block with d=15cm, it can be shown

that, depending on the frequency and the angle of incidence, a different number of

excited space harmonics is coupled to the air and propagates into non-specular directions:

)2arcsin(sin 0kd

nn

+= ( )1.2

n angle of the non-specular components

0 angle of the impinging wave

n number of coupled space harmonics

d periodicity of the structurek wave number

For a fixed impinging angle 30= and a frequency 5.2GHz, the following propagation

directions can be calculated:

2 = imaginary, hence evanescent

1 = 62.2

0= 30.0

1 = 6.6

2 = -15.6

3 = -40.8

4 = imaginary, hence evanescent

Those angles can also be obtained using Figure 8, which depicts the case for 5.2GHz. It is

the graphical realization of formula ( )1.2 . The vertical line at0

= 30.0 crosses the

family of lines corresponding to the appropriate coupled space harmonics at the

propagating outbound angles.


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Chapter 2

21

Using Floquets Theorem and some basic propagation formulas the power carried by the

individual specular and non-specular components can easily be calculated. Figure 9

shows the transmitted power (red line) for each n and the relative transmitted power with

respect to the transmitted specular component (black line) for the 5.2GHz case. It is

important to note that the graph below depicts the power carried by the space harmonics

as a function of the inbound angle and does not say anything about the actual propagation

direction of the space harmonics. The numbers on the right hand side of Figure 9 indicate

the coupled space-harmonics. The black reference lines clearly indicate that for

impinging angles between 20 and 60 the non-specular components carry, beside the

high absolute value, up to 30dB more power than the specular one.

Figure 8: The Outbound angles of the coupled Space Harmonics for f=5.2GHz in

dependency of the Inbound angles.


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Chapter 2

22

B. Bricked wall:

It can be said that the non-specular components can be neglected for a bricked wall with a

frequency less than 20GHz, whereas for frequencies above 20GHz the non-specular

components start to carry a notable amount of energy. This fact is important for

predicting indoor propagation models for indoor communications at 60GHz.

Figure 9: Relative radiated Power of the accordant Space Harmonics depending on the inbound

angle

n = 0

n = +1

n = +2

n = +3

n = +4

n = +5

n = -5

n = -4

n = -3

n = -2

n = -1


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Chapter 2

23

2.4. Scattering due to Surface Roughness

The wavelength for 2.4GHz, 5.2GHz and 60GHz are =12.5cm, =5.7cm and

=0.5cm, respectively. Applying the Frauenhofer-criterion for flat surfaces yields:

h

h

>

>

32cos

8cos4

A rough estimation for bricked and concrete walls gives: h=2 1mm. Therefore, the

angle has to be:

>0 degrees (arbitrary) for f=2.4GHz,

>26 degrees for f=5.2GHz and

>86 degrees for f=60GHz

the surface to be considered flat. Are those conditions violated, the wall radiates:

(1) coherent scattering for highly correlated surfaces

(2) diffuse scattering for random surfaces.

Since no scattering is expected for the 2.4GHz case and some scattering for angles


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Chapter 2

24

2.5. Scattering due to Wall Interior Metallic Lattices and Meshes

Most European buildings are reinforced with consecutively arranged metallic lattices

(Figure 10, left). Furthermore, plasterboard or wall covering plaster is often reinforced

with thin wire mesh (Figure 10, right). This results in attenuation and non-specular

transmission. The periodic nature of the structure allows decomposition of the scattered

field into a two-dimensional series including a specular component and a double sum of

grating lobes. For a one-layered mesh the same approach as for the internally periodic

wall is taken (see section 2.3.). The formulas differ only in the dielectric constant of the

periodic medium, which is highly conducting in this case.

Figure 10: Common metallic lattice (left) and Common reinforcing wire mesh (right).

As a consequence of some parametric calculations for metallic lattices it can be said that

the dominant propagation mode is the specular one. Assuming a rod diameter of 1cm, a

lattice periodicity of w=10cm and normal incidence for the TE-case the attenuation

amounts to 2dB for both frequencies 2.4GHz and 5.2GHz (Figure 11). Again, the case for

60GHz is omitted here due to strong general wall losses. Figure 12 depicts the

dependency of the transmitted TE power vs. the lattice-periodicity w for the specular and

three non-specular space-harmonics for the frequencies concerned. For w>10cm the

strongest component is constantly attenuated by 2dB.

wd

h w

w


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Chapter 2

25

Figure 11: Transmitted Power of the induced space-harmonics for a metallic mesh at 2.4GHz

(circle) and 5.2GHz (star)

Figure 12: Transmitted Power of the induced space-harmonics vs. lattice-periodicity at 2.4GHz

(dashed) and 5.2GHz (solid)


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Chapter 2

26

2.6. Diffraction

Diffraction mainly occurs at window-wall transitions. The geometrical optics solution

leads to discontinuities across the shadow and reflection boundaries. The uniform theory

of diffraction eliminates the discontinuity of the electric and magnetic fields across these

boundaries. Unfortunately, closed simple solutions exist merely for the perfectly

conducting wedge case, whereas the conducting case is sufficiently solved only for non-

oblique incidence. To meet calculation time limits approximations have to be done.

1. The diffracted part is concentrated around the specular and non-specular

transmitted and reflected directions.

2. We assume that half wall-thickness is about one wavelength.

3. The closed window and the lossy wall weaken the diffracted rays depending on

the impinging angle and the wall and window type.

Due to the first assumption, remote diffraction can be neglected. For a fixed position of

the receiver in the room, only the diffraction around the adjacent two or three optical

boundaries is taken into account. To back up this approach it is essential to know that due

to interior multiple reflections and power leakage through the wall, the power level in

even the remote parts of the room never drop below a certain threshold. Therefore,

diffraction is not used to account for the power level in the shadow regions, rather to

compensate the discontinuities. The interference between the diffracted waves of the

adjacent optical boundaries gives a realistic picture about power drops due to

reciprocative cancellation.


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Chapter 2

27

The second assumption allows the wall to be considered as a half-plane. The exact

or asymptotic solution of the diffraction problem for an impedance wall takes into

account its lossy character and coupling between the wall-faces. In fact the wall can be

regarded as a perfectly conducting half-plane, since the wave inside the wall decays as

heavily as it does for the perfectly conducting half-plane. For the same reason, the

coupling-effect between the wall-faces is neglected here. It should be noted that both the

perfectly conducting half-plane and the perfectly conducting edge retrieve similar results

for the inbound and outbound angles concerned. A further interesting fact reveals that the

entire set of diffraction problems leads to the modified Fresnel Integral, which has a

tractable asymptotic solution. This has been used throughout this work to give a simple

denouement of the window-wall diffraction.

The third assumption demands the unsteadiness between the fields transmitted

through the window and wall be compensated for. Consequently, the diffraction

coefficient has to be multiplied by the difference of both real transmission coefficients.

The diffraction coefficient is obtained via the method mentioned above, using the

approximated Fresnel Integral.

The mathematical background can be found in [16] and [17], the formulas and a

more profound treatment in Section 3-D and Appendix II (Diffraction). The uniform

diffraction solution for the non-specular propagation occurring for internally periodic

walls is discarded here due to the cumbersome theory. Therefore, only the specular

propagating component is corrected with the uniform solution.


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Chapter 3

28

3. The Propagation Model

3.1. Introduction

All the participating components given in Chapter 2 have now to be combined to give an

overall prediction of the wave propagation from outdoor to indoor. Before this is done

lets recapitulate the allotments to be included for the frequencies of interest.

f=2.4GHz

Specular transmitted component through window and wall with

appropriate losses.

5 non-specular transmitted modes if applicable.

2dB loss per mesh-layer if applicable.

Diffraction correction for the specular transmitted window and wall

components.

f=5.2GHz

Specular transmitted component through window and wall with

appropriate losses.

11 non-specular transmitted modes if applicable.

2dB loss per mesh-layer if applicable.

Diffraction correction for the specular transmitted window and wall

components.

f=60GHz

Specular transmitted component through the window.

Diffraction correction for the specular transmitted window component.


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Chapter 3

29

3.2. Deterministic Transformation

The linearity of the electromagnetic field allows one to decompose it into its TE and TM

components with respect to the wall-surface and to treat them separately. The generic

propagation formula is now given through:

),(),,,(),( outoutoutdooroutoutininininindoor EE = ( )1.3

where

=

TM

outdoorindoor

TE

outdoorindoor

outdoorindoor

,

,

,E

EE and

=

TM

TE

0

0

( )

=

TMTE

TMTE

TMTE

D

LT

n,

,

,11

ndiffractio

lattice

ontransmissi

K

K

K

The mean power loss is then easily obtained: = ( ) 21log10 . The

previous section provided the individual figures to be put into equation ( )1.3 , which has

been summarized below. It should be borne in mind that aforementioned calculations

assume a non-oblique plane of incidence to ease the calculations for the periodicity,

hence 90, .

A. Specular Transmission

),(),( ,, outinoutinTMTE

inin

TMTE TT = ( )2.3

inin , refer to the variable indoor angle

outout , refer to the fixed impinging outdoor angle

),( is exclusively one for both arguments equal to zero

TMTET , transmission coefficient for window or wall


36/106

Chapter 3

30

B. Non-Specular Transmission

),(),(),( ,,,,

nininnininoutout

TMTE

ninin

TMTE TT = ( )3.3

C. Lattice or Mesh

),(0.2),( ,,,

nininninininin

TMTE dBnL = ( )4.3

n number of consecutive lattices or meshes (n=0 for 60GHz)

D. Diffraction

( ) ( )ininout

inin

inTMTE ddD ,,, m= ( )5.3

( ) ( ) inkjinoutinoutinininoutin ekaKad =

,,, sgn,

( )( )outinoutina m= 21cos2,

2=k

( )( )( )

12

1

2

415.1arctan 2

++

++

xx

exK

xxj

for all 0x . ( )6.3

( )xK represents the approximated modified Fresnel integral, which can be

simplified for 5.3>x into the first term of its asymptotic expansion:

( )

jx

xK1

2

1. ( )7.3

The most frequently [17] utilised diffraction term is given through equation ( )7.3 , which

is exclusively valid in the remote shadow regions. It can be applied to outdoor

propagation since part of the signal reaches the shadowed receiver via hilltop or roof

diffraction. Unlike the outdoor environment, the indoor environment always provides

enough signal strength to neglect just these terms, whereas the discontinuities have to be

smoothed since the receiver can be in their region. Equation ( )6.3 should be used.


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Chapter 3

31

3.3. Transformation of the Probability Functions

The approach developed allows one to transform, at least numerically, the expected

outdoor power distribution and the pdfs of the angles of arrival into the indoor power

and angular distributions. In the following the index orefers to outdoor variables and i

to indoor variables. It should be noted that these statistics do not refer to the signal itself,

rather to its describing parameters.

The generic global power delay-azimuthal-elevation spectrum can be expressed as

( ) { } ),,(,,|E,,,),,( ** fdttP = EEEE . ( )8.3

),,( f is the joint probability function of the delay, azimuth and co-elevation and

{ } ,,|E *EE the expected power conditioned on the delay, azimuth and co-elevation.

To get the appropriate power dependencies one merely has to integrate:

=

=

=

ddPP

ddPP

ddPP

),,()(

),,()(

),,()(

( )9.3

Outdoor measurements have shown [18] that the processes arise quite independently

though a certain dependency cannot be denied. Using this approximation, one obtains for

the outdoor case,

{ } { } { } { }oooooooooo

ooooooooo

oooooooooo

ooo

ooo

ffff

PPPP

|E|E|E,,|E

)()()(),,(

)()()(),,(

****EEEEEEEE

=

( )10.3

The expression of the single functions in ( )10.3 was obtained through many

measurements, i.e. [18], and is given below.


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Chapter 3

32

A. Delay Spectrum:

( ) ooo eP oo

/ , where

o equals the Delay Spread ( )s31K

'/

)(o

oo

ef oo

, where'

o equals the standard deviation ( )oo 17.1'

From ( )8.3 the expected power { }oo |E *EE is obtained as)/1/1(*

'

|E ooo

eoo

EE .

B. Azimuthal Spectrum:

ooo eP oo

/2)(

, where

o equals the Azimuthal Spread ( )105K

( )2'2/

)(ooo

ef oo

, where'

o equals the standard deviation ( )oo 38.1

'

Again, the expected power is obtained as { } ( )( ) ooooeoo

/22/*

2'

|E

EE .

C. Elevation Spectrum:

No measurements are available for this case. Even a long distance between the outdoor

Base Station and the wall surface cannot assure that both, the azimuthal and elevation

distribution, resemble. The reason is that in this case, i.e. Micro cells or larger, most of

the energy propagates via roof-top diffraction, where the last roof provides the strongest

component to the street-canyon or the wall-surface. This diffracted wave is being

reflected not often enough to guarantee a Gaussian distribution. Therefore, in case of

NLOS and Micro-Cells or larger the statistic is expected to resemble the tail of the

diffraction term given in ( )7.3 . The LOS-case would give a peak with a fringe similar to

the shifted ( )7.3 . The Pico-Cell statistic is expected to change from case to case but is

more likely to resemble a Gaussian distribution due to the large number of scatters in the

vicinity of transmitter and receiver.


39/106

Chapter 3

33

Since the outdoor statistics are now defined, a transformation rule from outdoor to indoor

for the assumed independent components has to be found.

A. Delay Spectrum:

+= oi , where we assume o


40/106

Chapter 3

34

The next step is to transform the conditioned outdoor power { }oo |E *EE , which might be

written in another form:

{ } ( )

( )( )ooooeA A

ooo

/22/*2'

|E

=EE.

( )12.3

( )AoA is the maximum impinging power and Ao the corresponding azimuthal angle. To

obtain ( ){ }nii |E*EE several steps have to be performed. First, o is substituted by

( )ni

through ( ) ( ) ( )( )kdnon

i /2sinarcsin += in equation ( )12.3 . Second, ( )A

oA is multiplied

by the transmission coefficient for the nth

coupled harmonic assuming an impinging angle

ofA

o . Third, some assumptions about the indoor spread and deviation have to be done.

For the case assumed above of no diffraction, these coefficients remain constant.

Diffraction, however, leads to a broadening of the indoor wave, which comes along with

an increase of both the spread and deviation. The increase severely depends on the

frequencies, where higher frequencies cause less spread. The figures to be put have to be

estimated to give best agreement with measurements.

The indoor power spectrum is now calculated merging ( )8.3 , ( )11.3 and ( )12.3 :

( ) ( ) ( )( )( )( ) ( )( ) ( )( )

( )( ) ( )( )2//2sinarcsin22

/2sin1

cos)(

kdn

eTAPn

i

n

ikdnA

o

nA

o

n

iii

nii

=

C. Elevation Spectrum:

As soon as the outdoor elevation statistic is given the same approach as for the azimuthal

spectrum can be taken. Usually there is no periodicity for this case, what allows one to

put n to zero in the aforementioned formulas.


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Chapter 3

35

Figure 13 compares the indoor power spectra with the outdoor power spectra. Since the

interface introduces negligible delay the outdoor and indoor delay spectra resemble, thus

are omitted here. The indoor elevation spectrum is assumed to resemble ( )7.3 with LOS

condition, Figure 13 above. Of big interest is the indoor azimuth spectrum for internally

periodic walls, Figure 13 below. The formula provided above gives the appropriate power

spectra of the space-harmonics induced. It can be seen that already the 4th

and 5th

space

harmonics are expected to carry negligible power.

Figure 13: Outdoor (left) and Indoor (right) Normalized Power Spectra for f=5.2GHzUpper: PowerElevation Spectrum (axis in degree)

Lower: PowerAzimuth Spectrum (axis in degree)


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Chapter 3

36

3.4. Outdoor Transmitter and Indoor Receiver

Let us assume an outdoor transmitter and an indoor receiver. Furthermore the transmitter

ought to be remote enough to consider the impinging wave as a plane wave. Due to

multipath propagation there exists a certain amount of impinging waves with different

angles of incidence and time delays.

Figure 14: Antenna array consisting of M antenna elements

If the receiver consists of an antenna array as depicted above in Figure 14, the received

field-strength can be expressed as follows:

)()(),(),,,()( tdddttt dtransmittereceivedarray NEchE += , ( )13.3

where

=

)()(

)()(

)()(

)(1

1

1

tEtE

tEtE

tEtE

tM

zz

M

yy

M

xx

received

array

L

L

L

E ( )14.3

is the matrix of the received spatial signal components of the appropriate antenna element

(M number of antenna elements forming the antenna-array),

=M

zz

M

yy

M

xx

cc

cc

cc

L

L

L

1

1

1

),( c ( )15.3

is the array steering matrix for the spatial components,

Antenna array consisting of

M antenna elements

x

y

x

z


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Chapter 3

37

=

zz

yy

xx

h

h

h

t

00

0

00

),,,( h with ( )16.3

=

=L

l

llll tath

1

)()()(),,,(),,,( and { }zzyyxx ,,

is the time-dependent radio channel delay-azimuthal-elevation spread function for a

linear medium, whereL is the number of appearing paths and la the channel response of

the lth

path. N(t) is the noise vector implying the independent complex white Gaussian

noise components of the antenna elements. In general, the channel-spread function can be

resolved in its participating components, e.g.

),,,(),,,(),,,(),,,( indoorinterfaceoutdoor tttt hhhh = . ( )17.3

Simply multiplying the components in the frequency domain can perform the

convolution. Assuming the receiver is not deep in the indoor environment, the last

formula ( )17.3 can be drastically eased to

),(),,,(),,,( interfaceoutdoor hhh = tt . ( )18.3

If the antenna is a vertically aligned uniform linear antenna array with /2 element

spacing the steering matrix takes the following form:

=

)()(

00

00

),(1

M

zz cc L

L

L

c with sin)1()()( = mjmm

z efc , ( )19.3

where )(mf is the complex field pattern of the mth array element.


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Chapter 4

38

4. Application

4.1. Introduction

The theory and formulas provided in the previous Chapters 2 and 3 give sufficient insight

into the physical nature of the outdoor-indoor propagation process, yet are quite useless

regarding an engineering benefit. A method has to be elaborated to use the acquired

physical knowledge and to apply given formulas. This Chapter provides therefore two

approaches, which can be used for simulation platforms or rough power estimations.

4.2. The Generic CellTo cover the large number of possible window-wall-configurations a rough grid is laid

over a building dividing the surface into cells. These cells should at least be small enough

to cover typical configurations and at most big enough to allow the field strength over the

cell to be assumed constant. Some typical configurations would be: (1) wall, (2) wall with

interiorly periodic structure, (3) wall with lattice, (4) single window, (5) double window,

(1)-(3) with single window, (1)-(3) with double window. The formulas can now

theoretically be applied to a three-dimensional measure cell as depicted in Figure 15. The

depth of this measure cell should be big enough to cover a room or parts of it. The height

should embed the height of the basic window/wall-cell and the width should seize

diffracted rays. The measure-cell should not be confused with the basic window/wall-

cell, since the latter captures the structure of the building whereas the first allows one to

calculate the power-distribution in a room by overlapping the shares of the appropriate

measure-cells. The data-base for a chosen environment is now scanned and all occurring


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Chapter 4

39

cell configurations computed. The time-consuming calculation is done once and the

obtained power distribution being tabled.

Figure 15: Proposed measurement cell configuration

In practice, however, the three-dimensional calculation is reduced to two dimensions,

thus the power is available in the (x,z)-plane. Once the power is computed in each

measure cell for each basic window/wall-configuration, these cells are overlapped. The

idea of overlapped measure-cells is reflected in Figure 16, whereas Figure 17 shows the

top-view of merely one floor. Once the power shares are added up the overall power-

distribution can be predicted quite precisely in a room or in a whole floor. It should be

borne in mind that this overlapping does NOT include multiple reflected rays within the

room. Therefore, in Figure 17 it is presumed that the room is open-end. Figure 18

displays the three-dimensional power-distribution for a single measure-cell consisting of

a wall cell and Figure 19 for a window/wall cell. Both distributions are needed for the

room proposed in Figure 17. Finally in Figure 20 the overall power-distribution in the

room resulting from all the single measure-cells can be seen.

Cell width: 2m

Measure cell width: 6m

Measure cell

depth: 5m

Typical Cell Configurations:

Plain Wall (concrete/brick, different thickness)

Internally periodic Wall (usually brick)

Single/Double glazed Window

Wall with Window (comprising the above mentioned configurations)

y

x

z


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Chapter 4

40

Figure 16: Overlapped measure-cells (grid) for adjacent basic window/wall cells (gray)

Figure 17: Top view of a room consisting of different basic cells

Basement

1st

floor

2nd

floor

30Basic Wall Cell

Basic Wall/Window Cell

Basic Wall/Window Cell

Basic Wall Cell


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Chapter 4

41

Figure 18: Specular Propagation in a Cell consisting of a plain Wall (f=5.2GHz, constant Loss of -

13dB, Impinging Angle 30 degree)

Figure 19: Specular Propagation and Diffraction in a Cell consisting of a plain Wall with window(f=5.2GHz, Impinging Angle 30 degree, averaged)

Figure 20: Specular Propagation and Diffraction in a room proposed in Figure 17 consisting of the

measure cell power distribution of Figure 18 and Figure 19.


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Chapter 4

42

From Figure 20 the window/wall-diffracted components from the single windows

can conspicuously be seen, there the room is assumed open-end. To overcome this open-

end room problem, first the specular components are multiple reflected in the room

using ray tracing methods and later the diffracted part is added. The advantage of this

method is that, if the impinging angle is fixed, the relative power distribution remains

constant. Hence, if the distribution in dB was computed for an impinging wave with unity

field strength, the impinging field strength in dB has merely to be added. A further

advantage is that the entire site has been reduced to a small number of tractable cells.

Furthermore, it allows one to calculate the average power in the cell. This can be used to

get an approximated power margin in the cell, room or even floor. The disadvantage is

that as soon as the impinging angle changes all the calculations have to be redone.

Furthermore, it is cumbersome to calculate the power distribution in the secondary

penetrated rooms in the same floor or adjacent floors, where this approach simply fails.

4.3. The modified COST 231 Motley ModelThe aforementioned problems are solved with loss in accuracy assuming that diffraction

plays a dominant role exclusively in the primary penetrated rooms, i.e. the Base Station

facing rooms. This allows using the Cost 231 Motley penetration loss model for both

primary and secondary penetrated rooms, where the primary room is corrected with an

diffraction term. To save calculation time this term can be approximated considering

merely the adjacent two or three optical boundaries. The adopted micro cell Cost 231

Motley model is itself based on measurements for frequencies around 1.8GHz with an

averaged output. Therefore, the assumed attenuation loss table for this model has to be re-

completed with measurements for all frequencies concerned unless it is interpolated with


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theoretical curves. Using the latter, i.e. the theoretical interpolation, a very gross

estimation yields the corrections summarized in Table 2. The interpolation was roughly

performed by estimating the input parameter in equations ( )1.3 through ( )5.3 with given

losses for f=1.8GHz. Afterwards the dependencies of these parameters from the

frequency were applied, e.g. the alteration of the permittivity. The parameters obtained

were finally inserted back into equations ( )1.3 through ( )5.3 to give the appropriate

losses for 2.4GHz, 5.2GHz and quite inaccurately for 60GHz. In fact these figures are

easily obtained through elementary measurements and there is no need to use possibly

incorrect figures. Table 2 is merely given for comparison with measurements performed

later and to demonstrate its applicability.

Absolute losses in dB for frequencies

Object f=1.8GHz

(given)f=2.4GHz f=5.2GHz f=60GHz

Thick concrete, no windows 13 17 36 400

Glass wall 2 13 15 15

Wall with window

For a given wall-window-ratio the

appropriate figure can be estimated

213 1317 1536 15400

Additional losses in dB relative to the tabled

f=1.8GHz case

Thick concrete, no windows 0 4 23 390

Glass wall 0 11 13 13

Wall with window

For a given wall-window-ratio the

appropriate figure can be estimated

0 411 1323 13390

Table 2: dB-correction for higher frequencies


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Once the losses of all the materials are obtained, either through measurements or

theoretically, the figures are put into the model formula:

( ) ( ) GnLndLdLL fwallwallindoorwalloutdoorMotleyCost +++= internal,external,231 cos/ ( )1.4

( )zyxDsLL MotleyCostMotleyCost ,,231modified,231 += . ( )2.4

The parameters are defined as:

L path loss in dB

( )outdoordL path loss up to the building

external,wallL penetration loss of the external wall (Tabled)

external angle of incidence

specific internal attenuation

indoord distance travelled inside the building

walln number of penetrated internal walls

internal,wallL penetration loss of the internal wall (Tabled)

fn number of penetrated floors

G gain per floor (0dB micro cells, 2dB else)

s switch (1 for primary penetrated rooms, 0

elsewhere)

( )zyxD ,, diffraction loss in primary penetrated

rooms.

The original Cost 231 Motley model ( )1.4 requires the approximate position of the

receiver within the building since only the number of penetrated walls are of importance.

The modified model needs a precise position in the primary penetrated rooms to give


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exact predictions about possible power-drops caused by diffraction. However, as

formulated in Shannons information theory, the less information given, the less that can

be obtained from it, and vice versa. Hence, if the precise position of the receiver is not

known, a specific or general diffraction margin has to be used depending on the general

appearance of the external wall. This margin hardly depends on the window/wall

materials itself, but on the number of possible diffraction sources, e.g. window-wall

transitions. Some often-necessary margins were calculated and are given in Table 3. It

has been distinguished between two frequencies (2.4GHz & 5.2GHz) and additionally

between the number of illuminated wall-surfaces. The actual altering parameter is the

number of diffractive sources, i.e. the number of irradiated windows.

Frequency

in GHz

Number of illuminated

wall-surfaces

Number of windows per

wall-surfaceAverage diffraction

margin in dB

1 1.3

2 1.9

4 2.81

6 3.5

1 2.4

2 3.4

4 4.7

2.4

2

6 5.7

1 8.8

2 10.9

4 13.41

6 15.7

1 8.8

2 11.4

4 14.4

5.2

2

6 15.7

Table 3: Average diffraction margins for several window-constellations

Table 3 reveals that the most influential parameter appears to be the frequency with up to

10dB difference. This is in accordance with the expectation of a rising number of fades

with increasing frequency. The number of diffractive sources, expressed through the


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Chapter 4

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number of illuminated walls and windows per wall, appears to be less influential. Here

the average margin increases slowly, almost monotonically with 0.5dB and 1dB per

window for 2.4GHz and 5.2GHz, respectively. For link-budget calculations network

operators should make extensive use of Table 3, which offers them the possibility of

accounting for occurring signal fades. Furthermore, the weak dependence of the margin

from the number of diffractive sources can be used to give rough margins mainly

depending on the frequency. Table 3 suggests to use a margin of D=3.2dB for 2.4GHz

and a margin of D=12.4dB for 5.2GHz.

Figure 21: Standard deviation of the diffracted field vs. impinging angle for an assumed case withf=5.2GHz, two illuminated right-angled wall-surfaces with 6 windows each.

Figure 21 depicts the averaged deviation of the diffracted field from a purely

optical field vs. impinging angle for 5.2GHz, two illuminated right-angled wall-surfaces


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Chapter 4

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with 6 windows each. Disregarding normal and grazing incidence, it can be seen that

diffraction causes almost uniform deviation that fluctuates with less than 1dB around a

mean value of 15.7dB. The physical reason behind this is that an incident ray is diffracted

in all directions independently from the impinging angle. The power-drops do not depend

on the magnitude of the diffracted rays, rather on their mutual interference, which occurs

for all impinging angles.

The original Cost 231 Motley outdoor-indoor model includes diffraction via

increased outer-wall penetration losses. The values were obtained through numerous

measurement campaigns. These were averaged over a large number of sites, buildings,

floors and rooms. The tolerated fault is obvious: In reality primary penetrated rooms

suffer a much higher diffraction fade than secondary penetrated rooms, where the fade is

actually much less than predicted. The model introduced in ( )2.4 overcomes this

inaccuracy. It distinguishes between primary and secondary penetrated rooms through an

additional diffraction margin for the former ones. This can be backed up with the fact that

the diffractive impact weakens with increasing penetration depth. It must be noted that

now the outer-wall penetration losses differ from the original Cost 231 Motley model.

Disadvantageous is that both Cost 231 Motley models ( )1.4 and ( )2.4 fail as

soon as the indoor environment appears to be highly reflective or highly obstructive. The

models give overestimation loss for the former and underestimation for the latter. To

overcome this problem an additional gain has to be added for a highly reflecting

environment depending on the passed rooms and floors. For the case of highly

obstructing, the corners act as signal sources. Thus, all corners have to be included into

the overall model.


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Chapter 5

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5. Conclusions

5.1. Conclusion

The outdoor-indoor model developed embraces the most important propagation effects

through a windowed wall, which are specular transmission, non-specular transmission,

attenuation due to internal lattices and diffraction. The general path-loss-coefficient was

obtained following an approximated deterministic approach. This loss is dependent on the

impinging and emitting angles that requires knowledge about the outdoor conditions and

the indoor position of the receiver. If these figures are available, either an indoor ray-

launching model for precise predictions or the suggested cell philosophy can be used. The

former method is extremely time-intensive in terms of computation-time extensive since

any change in the parameters requires a complete re-calculation. The latter requires re-

calculations once the impinging angle changes. A trade-off between those methods is the

modified Cost 231 Motley model, which is used in its original formulation for the

secondary penetrated rooms added with a diffraction correction coefficient for primary

penetrated rooms. This coefficient depends most on the frequency and less on the number

of diffraction sources, i.e. the number of windows in a wall, and is calculated for some

illuminating constellations.

Furthermore, the model allows transformation of the known outdoor pdfs to

calculate the appropriate indoor pdfs. For a given outdoor delay-azimuth-elevation

power spectrum the transformation rule is given, where a spread of the spectrum is

caused due to diffraction.


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5.2. Further Outlook

As mentioned in the introduction the engineers effort to gain dBm, whether in coding or

prediction accuracy, reaches saturation. The meticulous methods used today to predict

field-distribution probably wont be necessary in a couple of decads. But until this

turning point some enhancements could be achieved. In principle, research can be

classified into two categories. If you appear to be in the first one then you do research to

please yourself, yet nobody can apply it. The second way to do it is to get a good

applicable idea and then call the fuss around it research.

Following the first approach, the spread of the indoor azimuthal and elevation

spectrum introduced by diffraction should be obtained with the help of generic

calculations. Furthermore, a closed diffraction formula for oblique incidence in case of

non-perfectly conducting edges would save many measurements. And finally, the TM-

case for periodic structures should be studied.

The second approach should concentrate more on the random character of the

interface channel, caused by site-specific irregularities. A more recent challenge would

be to verify the suggested models through measurements that have already been carried

out under the Radio Environment work area of the Mobile VCE. Unfortunately, they

havent been processed yet, which leaves the engineering approach developed in this

thesis still a theoretical piece of art.


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6. Appendix I (Graphics)

6.1. Introduction

The large amount of graphics surely would have disturbed the readability of the actual

workout, the reason why they were ta

baca master thesis outdoor indoor 23651

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