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The Distortion of Ultra-Wideband Signals in the Environment

PhD Viva Presentation

Anastasios Karousos

Supervisors:Dr. Costas TzarasDr. Tim Brown

A. Karousos 2

Presentation Outline

UWB Communications

Radio Wave Propagation

Signal Prediction

Conclusions

Introduction

UWB Radio

Benefits / Challenges

Propagation Mechanisms

TD Representation

Multiple Interaction Phenomena

Results Ray-Trace Algorithm

Outdoor/Indoor Results

UWB Measurements

TD Ray-Trace

A. Karousos 3

UWB Communications

A. Karousos 4

Introduction

• Wired communications (telephone lines, optical fibres) are costly and complex

WHEREAS

• Wireless technology (mobile, satellite, WLAN) offers simplicity and mobility

HOWEVER

• Frequency crowding in the available spectrum

• Interference issues

prohibits proper exploitation of wireless systems

A. Karousos 5

UWB Radio

• FCC: “an intentional radiator that, at any point in time, has a fractional bandwidth equal or greater than 0.20 or has a bandwidth equal to or greater than 500 MHz, regardless of the fractional bandwidth”

100

101

102

−100

−90

−80

−70

−60

−50

−40

Frequency (GHz)

EIR

P S

pect

ral D

ensi

ty (

dBm

/MH

z)

FCC Spectral MaskEC Spectral MaskOfcom recommendations

The issued spectral masks from FCC and EC, as well as Ofcom’s recommendations for unlicensed radio transmission

• The fractional bandwidth is:

• The bandwidth is the frequency band which is bounded by the points that are 10 dB below the highest radiation emission

• Similar regulation from EC

medianLH

LHFC f

BffffB

)(2

A. Karousos 6

Benefits of UWB

• The increased bandwidth offers more capacity and higher data-rates – Shannon law (noise-like signals with small power are more preferable than high-powered NB signals)

• Multipaths are not an ‘enemy’; multipaths can be resolved, enhancing system’s performance

• Low probability-of-detection (LPD), proper for covert and secure communications (essential for the military)

• Location and tracking applications

• Ground penetration radars for geophysical prospecting, archaeology, medicine

• Low-cost and low-complexity equipment (almost true)

• Spectrum sharing

A. Karousos 7

Challenges

• A RAKE receiver with 50 or more fingers, would be necessary to exploit the multipath diversity

• Use of fast ADC, which may consume a lot of power

• Timing synchronisation is also important. A small timing mismatch would degrade the system’s performance

• The complex propagation effects of the channel would introduce distortion in the signal, preventing an optimal operation

• Channel models are treated as tap-delay lines, where signal distortion is assumed either known ‘a priori ’ or negligible

A. Karousos 8

Radio Wave

Propagation

A. Karousos 9

Radio Wave Propagation

• A traversing signal is reflected, diffracted, scattered or transmitted through the objects of the environment

• Since we use impulses, it is more natural and more efficient to treat such phenomena directly in the time-domain

• Parameters like number of multipaths, delay and power of every path are easily obtained

• TD closed-form solutions should be found through inverse Fourier or Laplace transform integrals to describe such phenomena

• The received signal is the convolution of the transmitted signal in the time-domain with TD coefficients. The numerical IFFT will be used for comparison results

A. Karousos 10

Reflection

• Fresnel reflection coefficients

• The received reflected field in the TD is written as:

• where

• and α , κs,h and Κs,h depend on the electrical parameters of the medium and the impinging angle

)(*)(*)()()( , shsir tttrtesAte

tK

hs

hshshs

hsetKtr

2/12,

,,,

,

12

)()(

3.8 3.9 4 4.1 4.2−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (nsec)N

orm

alis

ed A

mpl

itude

rIFFT

rTD

3.8 3.9 4 4.1 4.2−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (nsec)

Nor

mal

ised

Am

plitu

de

rIFFT

rTD

Reflection of a Gaussian doublet on a wall with

εr=5, σ=0.1 S/m and θ=45°.

Soft polarisation on top and hard polarisation on the bottom.

Time shiftSpreading factor

A. Karousos 11

Diffraction

• Waves ‘bend’ around objects – Huygens-Fresnel principle

• Diffraction theory is based on the solution of the Fresnel-Kirchhoff integrals – computational intensive

• Uniform Theory of Diffraction (UTD) describes accurately such phenomena for a number of obstacles, by treating the waves as rays, similarly to Geometrical Optics

• An incident ray results into infinite number of diffracted rays,placed on the surface of a cone (Keller’s cone)

• The diffracted field will be given by:

)(*)(*)()()( sid tttdtesAte

TD-Diffraction Coefficient

A. Karousos 12

Time-Domain Diffraction Coefficients

cLandwhere

tuttc

Ltd EdgeKnife

/2/cos2

)()2/cos(2

)(

2/

n

aandn

a

na

naandifor

caLnttc

nLtdwhere

tdtrtdtr

tdtdtrtrtd

iii

ii

hnshos

hnshoshs

Wedge

22

,2

,2

4,...,1

/)(sin2,)2sin(22

)(

)(*)()(*)(

)()(*)(*)()(

/

4

/

3

/

2

/

1

22

4,3,

21,,,

Transmitter Receiver

s1

knife-edge

s0

φ

φ'

Transmitter Receiver

s1

wedge

s0

φ

φ'

o-fa

ce n-face

where and

for

where

and

and

A. Karousos 13

Diffracted Pulses

18.5 18.6 18.7 18.8 18.9 19 19.1 19.2 19.3 19.4

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (nsec)

Nor

mal

ised

Am

plitu

de

rifft

rTD

18.5 18.6 18.7 18.8 18.9 19 19.1 19.2 19.3 19.4

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (nsec)

Nor

mal

ised

Am

plitu

de

rifft

rTD Diffracted pulse on a non-perfectly

conducting wedge with εr=4.4, σ=0.018 S/m and αint=π/3.

Diffracted pulse on an absorbing knife-edge

A. Karousos 14

Layer (Slab) Model

• Walls are not infinite in width, but finite

• The wave is partially reflected and refracted on the boundary interfaces

• These multiply reflected signals can carry significant energy

• Proper knowledge would avoid ISI and increases performance

• Easy-to-use and accurate formulations, predicting a large number of internal reflections

d

θi

Ei

Et1

Et2Et3Et4

Er1Er2Er3Er4

Assumed path of total transmitted

wave

Assumed path of total reflected

wave

z εr, μr

A. Karousos 15

Time-Domain Coefficients

)2/(,sin/2

)(14

)()(

)(*)()()(

02

02,

,2,

2,

,,

rr

n

at

hs

hsnhs

annhsR

hsRa

Rdhs

acdand

ntuean

KnteKth

trthethtr

1 1.5 2 2.5 3 3.5

x 10−8

−4000

−2000

0

2000

4000

6000

IFFTTD Solution

0.97 0.98 0.99 1 1.01 1.02

x 10−8

−3000

−2000

−1000

0

1000

2000

3000

4000

5000

6000

1.53 1.54 1.55 1.56 1.57 1.58 1.59

x 10−8

−700

−600

−500

−400

−300

−200

−100

0

100

200

300

2.65 2.7 2.75 2.8 2.85 2.9 2.95 3

x 10−8

−0.2

−0.1

0

0.1

Time (10 s)

Am

plitu

de (

Vol

ts)

−8

1 1.5 2 2.5 3 3.5

x 10−8

−6000

−5000

−4000

−3000

−2000

−1000

0

1000

2000

3000 IFFTTD Solution

−8Time (10 s)

Am

plitu

de (

Vol

ts)

1.8 1.81 1.82 1.83 1.84 1.85

x 10−8

−60

−40

−20

0

20

40

60

80

100

120

2.21 2.22 2.23 2.24 2.25 2.26

x 10−8

−3

−2

−1

0

1

2

3

4

5

6

7

0.97 0.98 0.99 1 1.01 1.02

x 10−8

−7000

−6000

−5000

−4000

−3000

−2000

−1000

0

1000

2000

3000

0

2,,2

,

,2,

2,

,

2/,

)(14

)(

14

)(

/2/)(

n

anhshs

hs

hsnanhs

hs

hsT

Tad

hs

ntueaKKn

nteK

th

cdthet

TD Reflection Coefficient:

TD Transmission Coefficient:

Reflection (top) and transmission (bottom) of a hard polarised Gaussian doublet on a wall with

εr=4.4, θ=0° and d=20 cm.

and

A. Karousos 16

Multiple-Diffraction Phenomena

• UTD multiple-diffracted waves cannot be calculated as a concatenation of single-diffraction incidences, especially when the objects are in the transition zones of the previous objects

• Higher-order diffracted fields are needed for accurate prediction

• A new slope-UTD algorithm that only includes second order diffraction terms is implemented into the time-domain

• It incorporates the derivative and the derivative of the slope coefficient in the TD

A. Karousos 17

L-parameters

• The L-parameters enforce continuity in the field prediction

• The L-parameters for the amplitude and slope terms are given by

• They depend on the value of the field at the previous object and the value of the field if the current object was absent

• They are a function of frequency

3/2

2

)(/)(/)(

)()()(

nk

nk

jksnkrmnmn

nkmnmnnkmnk

jksnkrmnmn

nkmnmnmnk

esAnsEnssEsLs

esAsEssEL

A. Karousos 18

Time-Domain Approach

• The multiply diffracted field in the TD is generally written as:

• eder(t) is the directional derivative, which equals to:

• For the knife-edge case, the derivative and the derivative of the slope coefficient are given by:

)/(*)();(*)()(*)()( 111/1111 cstsAtdtetdtete NNNderNderNNNN

)/(*)()(*)();(*)()( 22

22,22221 csts

sAtdtetdtete N

N

NNslopederN

derN

derNN

derN

)(

)(

)2/(sin12

)2/cos(22

)(

)()(

)2sin(22

),;(

2

2

,

2/3/

tut

acLtt

acLtd

tut

aLtd

slopederEdgeKnife

derEdgeKnife

Amplitude term Slope term

A. Karousos 19

• The TD derivative of the diffraction coefficient for a non-perfectly conducting wedge is

• When differentiating with respect to φ, the derivative of ros,h(t) is set to zero, whereas in the other case, i.e. differentiating with respect to φ/, rns,h(t) is set to zero

• di/(t) and dider(t;φ,φ/) are given by:

Wedge Slope-Terms

),;(*)()(*)(),;(*)()(*)(),;(

),;(*)(*)()(*)(*)()(*)(*)(),;(/

4,/4,

/3,

/3,

/2

/1,,

/1,,

/1,,

/,

tdtrtdtrtdtrtdtrtd

tdtrtrtdtrtrtdtrtrtdder

hnsder

hnsder

hosder

hosder

derhnshos

derhnshosshn

derhos

derhs

)()(

/222

),;(

)()(

)cot(22

)(

2/3

2

//

2/1/

tut

cLntnca

td

tut

an

ctd

i

iideri

i

iii

A. Karousos 20

Derivative of the Slope-Term

• The derivative of the slope-term in the TD is given by:

• where

)(*)();(*)(

)(*)();(*)()()(*)(*)(

);(*)(*)();(*)(*)()(*)(*)()(

sec,4,

/4,

sec,3,3,

sec,2

sec,1,,

/1,,1,,

int1,,

,,

tdtrtdtr

tdtrtdtrtdtdtrtr

tdtrtrtdtrtrtdtrtrtd

slopehns

slopederhns

slopehos

slopederhos

slopeslopehnshos

slopederhnshos

slopehns

derhos

derhns

derhos

slopederhs

)()(

))(sin2(23tan1)2sin(

2)(

)()(costan)(sin2),;(

)(tan)2sin(2

)(

2

22

1/

sec,

21

2

//

1int

tut

caLntt

tacLnaatd

tut

tataLnatd

tutacLntd

i

i

iii

iislopei

i

i

ii

iislopei

ii

ii

A. Karousos 21

Grazing Incidence

0 1 2 3 4 5

x 10−8

−300

−200

−100

0

100

200

300

400

500

600

700

Magnification of thesignal

TD UTD

IFFT UTD

3.96 3.97 3.98 3.99 4 4.01 4.02 4.03

x 10−8

−300

−200

−100

0

100

200

300

400

500

600

700

Transmitter Receiver

2m 2m 2m 2m 2m2m

Am

plitu

de (

V/m

)

Time (10 s)−8

0 1 2 3 4 5

x 10−8

−2

−1

0

1

2

3

4

x 104

TD UTD

IFFT UTD

Magnification of thesignal

3.96 3.97 3.98 3.99 4 4.01 4.02 4.03

x 10−8

−2

−1

0

1

2

3

4

x 104

Transmitter Receiver

Time (10 s)−8

2m 2m 2m 2m 2m 2m

Am

plitu

de (

V/m

)

Diffraction for the grazing incidence of five absorbing knife-edges, which are spaced 2m apart

Diffraction for the grazing incidence of five metallic wedges with internal angle π/5 radsand are spaced 2m apart

A. Karousos 22

Transition Regions

• The approximation on the L-parameters introduces an error in the prediction, especially close to the shadow boundaries

• Also the path response in such a scenario is very sharp and a more tedious convolution is needed

0 1 2 3 4 5 6 7

x 10−8

−200

−150

−100

−50

0

50

100

150

200

250

300

TD UTD

IFFT UTD

Magnification of thesignal

The predicted signalif dt is reduced

4.97 4.98 4.99 5 5.01 5.02 5.03 5.04

x 10−8

−150

−100

−50

0

50

100

150

200

250

300

4.97 4.98 4.99 5 5.01 5.02 5.03 5.04

x 10−8

−150

−100

−50

0

50

100

150

200

250

300

Time (10 s)A

mpl

itude

(V

/m)

−8

hTx h

Rxh

1

αint

h2

αint

h3

αint

h4

αint

3m

Transmitter

3m 3m 3m 3m

o−fa

ce n−face o−f

ace n−face o−

face n−face

o−fa

ce n−face

Shadow Boundary 12

Shadow Bound

ary 01

Shadow Boundary 23Shadow Boundary 34

Receiver

Propagation Path

A diffracted path close to the shadow boundaries

The error decreases as the time resolution is finer

A. Karousos 23

Cascade of Different Objects

• The algorithm can be applied for different objects in the path

• The source transmits a pulse every 5 ns and in each transmissiontime, the height of middle object increases by 1 m, with initial height 0 m

0 0.2 0.4 0.6 0.8 1

x 10−7

−60

−40

−20

0

20

40

60

80

TD UTD

IFFT UTD

hwαintTransmitter

2m

2 m 2 m

2m 2m 2m

Receiver

8.6 8.65 8.7

x 10−8

−15

−10

−5

0

5

10

15

20

25

4.85 4.9 4.95 5 5.05 5.1

x 10−8

−6

−4

−2

0

2

4

6

6.75 6.8 6.85 6.9

x 10−8

−40

−20

0

20

40

60

Time (10 s)−8

Am

plitu

de (

V/m

)

• The outer objects are knife-edges with height 2 m and the middle object is a non-perfectly conductive wedge with εr=10, σ=0.1 S/m and internal angle π/5 rads

A. Karousos 24

Signal Prediction

A. Karousos 25

Ray-Trace Algorithm

• A novel 3D ray-trace model was constructed based on the database preprocessing

• It operates in two stages, the preprossecing of the surrounding and the actual ray-trace

• The positions of the buildings are read from a GIS file

• The environment is then discretised into tiles and segments and the angles between them are calculated and stored into a file

A. Karousos 26

Path Search

• The Tx is inserted and its angles with the environment elements are computed

• The actual ray-trace commences. If certain conditions are fulfilled, reflection or diffraction occurs

• The path search is reduced into a search in a look-up table and the construction of the tree of the predicted paths

• If the Tx position is altered, only the top level will change, and therefore similar operations are avoided

• It combines image theory with ray-launching

A. Karousos 27

Comparison Results - Outdoor

528.4 528.6 528.8 529 529.2

181.3

181.4

181.5

181.6

181.7

181.8

181.9

182

182.1

182.2

182.3

x−coordinates (km)

y−co

ordi

nate

s (k

m)

error (dB)

−20

−15

−10

−5

0

5

10

15

20

25

30

0 100 200 300 400 500 600 700 80040

60

80

100

120

140

160

Receiver Point

Pat

h Lo

ss (

dB)

MeasurementPrediction

0 100 200 300 400 500 600 70050

60

70

80

90

100

110

120

130

140

Receiver Point

Pat

h Lo

ss (

dB)

MeasurementPrediction

530.4 530.6 530.8 531 531.2 531.4

181.6

181.7

181.8

181.9

182

182.1

182.2

182.3

182.4

182.5

182.6

x−coordinates (km)

y−co

ordi

nate

s (k

m)

error (dB)

−30

−20

−10

0

10

20

30

40

A. Karousos 28

Comparison Results - Outdoor• Measurements were conducted in various locations in London at 2.1 GHz

• The small scale effects were cancelled out by averaging

• The Tx and Rx were set at various heights (0.5 ~ 3 m)

• The ray-trace prediction tracks the changes of the received signal quiteaccurately

• Errors occur due to the simplification of the buildings shapes, the approximation of their effective electrical parameters, movement in the measuring channel (lorries, buses) and errors in the translation of the measurements on the map

9.714.720.50.5Kingsland

8.251.071.51.5Kingsland

8.38-3.031.51.5Holborn

11.46-2.370.53Holborn

9.25-4.460.53Portland

8.46-3.811.53Portland

Std (dB)Mean Error (dB)Rx Height (m)Tx Height (m)PlaceComparison results for the ray-trace predictions

A. Karousos 29

Comparison Results - Indoor

0 10 20 30 40 50 60 70 80 9050

55

60

65

70

75

80

85

90

Point

Pat

h Lo

ss (

dB)

Line 1 Line 2 Line 3 Line 4

MeasurementsPrediction

0 50 100 15040

50

60

70

80

90

100

Point

Pat

h Lo

ss (

dB)

Line 1 Line 2 Line 3

MeasurementsPrediction

Corridor NLOS

A. Karousos 30

Comparison Results - Indoor

• The channel response for various locations in the CCSR building was measured for the frequency of 4.5 GHz

• The radiation patterns of the antennas were measured in the anechoic chamber and taken into account

• The predictions are quite accurate for most of the cases

• Incorrect electrical parameters, errors in the modelling of the building, clutter inside the rooms, but also problems with the measuring apparatus that were diagnosed after the postprocessingof the data may have increased the prediction error (especially in the NLOS scenario)

8.37-0.50NLOS

5.750.04Corridor

Std (dB)Mean Error (dB)ScenarioComparison results for the ray-trace predictions

A. Karousos 31

UWB Propagation Measurements

• The channel response for the 3 GHz – 6 GHz band was measured with a VNA for the CCSR building

• The increased bandwidth offers less fractional margin

0 10 20 30 40 50 60 70 80 9045

50

55

60

65

70

75

80

85

90

PointP

ath

Loss

(dB

)

Line 1 Line 2 Line 3 Line 4

UWBNB

0 50 100 150

40

50

60

70

80

90

100

Point

Pat

h Lo

ss (

dB)

Line 1 Line 2 Line 3

UWBNB

CorridorNLOS

A. Karousos 32

TD Ray-Trace

30 35 40 45 50 55 60 65 70 750

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (nsec)

Nor

mal

ised

Am

plitu

de

MeasurementPrediction

5 10 15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (nsec)

Nor

mal

ised

Am

plitu

de

MeasurementPrediction

40 45 50 55 60 65 70 75 80 850

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (nsec)

Nor

mal

ised

Am

plitu

de

MeasurementPrediction

Rx close to the Tx Rx half way along the corridor

Rx in a deep NLOS position

A. Karousos 33

TD Prediction vs. Measurement

20 40 60 80 100 120 14045

50

55

60

65

70

75

80

85

Point

Pat

h lo

ss (

dB)

MeasurementPrediction

50 55 60 65 70 75 8045

50

55

60

65

70

75

80

85

Measured path loss (dB)

Pre

dict

ed p

ath

loss

(dB

)

10 20 30 40 50 60 70 8055

60

65

70

75

80

Point

Pat

h lo

ss (

dB)

MeasurementPrediction

55 60 65 70 7555

60

65

70

75

80

Measured path loss (dB)

Pre

dict

ed p

ath

loss

(dB

)

Corridor NLOS

A. Karousos 34

Conclusions

• TD formulations can offer correct prediction of the received signal

• They need to be described in closed-form solutions

• Import of these solutions in a deterministic tool gives fairly accurate results

• Novel ray-trace that can be used for indoor/outdoor scenarios and narrowband/ultra wideband radio

• Limitations on the knowledge of the environment characteristics (accurate dimensions, electrical properties of the walls, objects/clutter in the channel) induce an error in the prediction that is unavoidable

A. Karousos 35

Thank you for your attention.

Is there anything you may like to ask?

A. Karousos 36

Back Up

Slides

A. Karousos 37

UWB Waveforms

• They need to spread the power effectively and efficiently in the frequency-domain, avoiding interference issues.

• Fast rise and fall times, zero DC component for effective radiation.

• Such pulses are Gaussian, Rayleigh, Laplacian, cubic, orthogonal prolate spheroidalwaveforms etc.

0 2 4 6 8 10 12 14−30

−25

−20

−15

−10

−5

0

Frequency (GHz)

Nor

mal

ised

Mag

nitu

de (

dB)

Gaussian pulseGaussian monocycleGaussian doubletDamped sine wave

−1 −0.5 0 0.5 1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (nsec)

Nor

mal

ised

Am

plitu

de

Gaussian pulseGaussian monocycleGaussian doubletDamped sine wave

A. Karousos 38

Modulation of UWB Radio

• Single-band modulation, where the whole band is used or multiband modulation, where the band is partitioned into smaller parts

• In single-band, modulation is different than narrowband case; information is transmitted by generating pulses at specific time instances

• Binary phase shift keying (BPSK), pulse amplitude modulation (PAM), on-off keying (OOK), pulse position modulation (PPM), pulse interval modulation (PIM), pulse shape modulation (PSM)

• Multiband modulation is a carrier based modulation, where the frequency band is divided into smaller bands with at least 500 MHz bandwidth

• It offers flexibility in conforming to local regulations, by turning bands on or off, an ability in avoiding strong NB interferers and advanced spectral efficiency

• Possible multiband modulation techniques are MB-UWB, MB-OFDM and DS-UWB

A. Karousos 39

Single-band Modulation

• Modulation is inserted either in the polarity of the pulse or in the position of the pulse inside the frame or in both of them

• Time dithering is used for smoothing the strong spectral lines, due to the frame repetition time

0 1 2 3 4 5 6 7−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (nsec)

Nor

mal

ised

Am

plitu

de

BPSKPPM

0 2 4 6 8 10−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (nsec)

Nor

mal

ised

Am

plitu

de

TH−PPMDS−PPMDS−TH−PPM

A. Karousos 40

Multiband UWB

0 10 20 30 40 50−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (ns)

Nor

mal

ised

Am

plitu

de

MB-UWB

MB-OFDM

• MB-UWB: signals with 500 MHz bandwidth, shifted in the appropriate band

• MB-OFDM: each band is divided into subcarriers and it is transmitted according to a time-frequency code

• DS-UWB: two bands with 1.75 GHz (3.1-4.85 GHz) and 3.5 GHz (6.2-9.7 GHz) bandwidth respectively

A. Karousos 41

Inverse Techniques

• The TD solution can be found from the FD one, using inverse Fourier transform integrals, i.e.

• We can have an one-sided integral which is

• However, since the interaction mechanisms are causal functions, the analytic function can be written as

• where H[f(t)] is the Hilbert transform of f(t)

deFtf tj)(

21)(

0

)(1)(~

deFtf tj

)()()(~ tfjHtftf

• Therefore, the real part is the wanted solution in the time-domain

A. Karousos 42

Lossy Slab

1 1.5 2 2.5 3 3.5

x 10−8

−6000

−5000

−4000

−3000

−2000

−1000

0

1000

2000

3000 IFFTTD Solution

−8Time (10 s)

Am

plitu

de (

Vol

ts)

1.8 1.81 1.82 1.83 1.84 1.85

x 10−8

−60

−40

−20

0

20

40

60

80

100

120

2.21 2.22 2.23 2.24 2.25 2.26

x 10−8

−3

−2

−1

0

1

2

3

4

5

6

7

0.97 0.98 0.99 1 1.01 1.02

x 10−8

−7000

−6000

−5000

−4000

−3000

−2000

−1000

0

1000

2000

3000

1 1.5 2 2.5 3 3.5

x 10−8

−4000

−2000

0

2000

4000

6000

8000

IFFTTD Solution

−8Time (10 s)

Am

plitu

de (

Vol

ts)

1.08 1.09 1.1 1.11 1.12 1.13

x 10−8

−4000

−2000

0

2000

4000

6000

8000

1.9 1.91 1.92 1.93 1.94 1.95 1.96

x 10−8

−15

−10

−5

0

5

10

15

20

25

30

2.31 2.32 2.33 2.34 2.35 2.36 2.37

x 10−8

−0.5

0

0.5

1

1.5

Reflection of a soft polarised Gaussian doublet on a wall with

εr=4.4, σ=0.018 S/m , θ=π/8 and d=20 cm.

Transmission of a soft polarised Gaussian doublet through a wall with

εr=4.4, σ=0.018 S/m , θ=π/8 and d=20 cm.

A. Karousos 43

Shadow Boundaries

• The incident shadow boundary (ISB) signifies the boundary between the LOS and NLOS areas

• The reflection shadow boundary (RSB) signifies the boundary between the areas where reflection can or cannot exist

• These boundaries depend on the relative position of the source with respect to the edge

Reflection Shadow Boundary Incident

Shadow

Bounda

ry

φ'

φRSB

φISB

A. Karousos 44

Derivative of the reflection coefficient

• The derivative of the reflection coefficient can be easily obtained by differentiating rs,h(t)

• Therefore, it will be

• where for the o-case, ψ=π/2-φ/ and the minus corresponds to soft polarisation and the plus to hard one, whereas, for the n-case, ψ=π/2-nπ+φ and the signs are the opposite from above

• Finally

)()1(

12)(

)1(2);( ,)2/1(4

,

,2,

2,

,, tue

atattr hsatK

hs

hshs

hs

derhs

hs

2/32sin)1(sin

r

rs

2sincos

)1(sin

rr

rhand

of 44/44

The Distortion of Ultra-Wideband Signals in the Environment PhD Viva Presentation Anastasios Karousos Supervisors: Dr. Costas Tzaras Dr. Tim Brown

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