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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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