Self study presentation ‘Int. equation’kom.aau.dk/~pe/education/menu/9sem/AP_MM7_18... ·...

Cneter for PersonKommunikation 12/09/2018

(c) Patrick Eggers 1

APNET

(c) Patrick Eggers12/09/2018 1

Antennas & Propagation, 9sem WCS

MM7 : Ray tracing and UTDPatrick Eggers

13/9-2018, A3-207, 8.15-12.00

APNET

(c) Patrick Eggers

Self study presentation ‘Int. equation’• Part1 : Boundary conditions / materials

– Dielectric interface -> show derivation of expression for reflection coefficient (Verticalpolarization)

– PEC, PMC: what is it/ what does it ‘do’ (EM wise)

• Remember wrt exercises: we need some documentation back from you (written form, showing understanding of some of the core aspects)

12/09/2018 2

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Contents• I: MANAGEMENT (What we do with all those

rays)– Data base

• Raster• Vector• Content (materials, detail)

– Ray tracing– Ray launcing– 2D,2½D vs full 3D

• II : ‘The ENGINE’ (How we do it pr single ray)– UTD & Diffraction

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Objects -> polygons• Facets - objects

– # facets– # vertices– Coordinates of vertices– Material types (,, + surface roughness)– Possible object composition (window vs brick ratio

etc)• Scenery – data base

– # objects– Placement/coordinate of objects– # facets for ground– Ground data like for objects



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Ray tracing (’tracking’ possible exact)• Connecting paths Tx-Rx• Image = efficient for for small problems

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Ray shooting &bouncing (launching ’blindly’)

• Foreward (direct) tracing from Tx -> Rx• Ray tubes -> diverge -> large overhead of

’spill rays’ (as is shooting ’in blind’)• Tree branches need ’death criteria’ -> acc.

Techniques. + RECEPTION AREA

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Ray disturbances - tracking• Example : limit possibilities to most dominating

contributions1. Direct ray2. Single reflection3. Double reflection4. Single diffraction5. Triple reflection6. Single reflection + single diffraction7. Double diffraction8. Double reflection + single diffraction9. (x flections or possible scattering = diffuse

reflection)

– Transmission (penetration ? If out to indoors )

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Class 1:4 in urban scenario

www.awe-communications.com



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Class 5:8 in urban scenario

www.awe-communications.comMore components -> more detail and extension/ ‘contrast’

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Search tree

Verifying path loss and delay spread predictions of a 3D ray tracing propagation model in urban environmentTerhi Rautiainen1, Gerd Wölfle2, Reiner Hoppe356th IEEE Vehicular Technology Conference (VTC) 2002 - Fall, Vancouver (British Columbia, Canada), Sept. 2002

• Determination of all visible objects

• Computation of the angles

• Recursively processing of angular conditions

• Tree structure– Fast and

efficient

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Building data base• Structure• Resolution (raster, fx 10m)• Content (matrials, detail (windows metal

etc))• Complexity (2D, 2½D, 3D)

Fast 3-D Ray Tracing for the Planning of Microcells by Intelligent Preprocessing of the Data BaseR. Hoppe, G. W¨olfle, and F. M. Landstorfer3rd European Personal and Mobile Communications Conference (EPMCC) 1999, Paris, Mar. 1999

Raster Vector

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Data base accuracy




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Material data base


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Propagation models


”..most cases one propagation path contributes more than 90% of the total energy..”

Only power..’sell’ dispersion ’capability’ of full ray tracing to gain simplicity

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Dominat path field strength – empirical input• Path length d• Path loss exponents before and after breakpoint p• individual interaction losses f(φ,i) for each

interaction i of all n interactions• Gain due to waveguiding wk at c pixels along the

path• Gain gt of base station antenna• Power pt of transmitter

Break point pathlosswaveguideinteractions


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Computation time

• (1 GHZ PENTIUM® III, desktop relevant year 2002)

• Scenario Helsinki Downtown

• No. of buildings 1150

• Area 2 km2

• Resolution 8 m -> raster

• Database preprocessing (only once) 312 min

• Prediction time: Tx above rooftop 20 s -> why?/horizon

• Prediction time: Tx below rooftop 10 s -> why?/horizon




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Computation time 2007


Detail limited/radial Horizon accuracy limited Tradoff .. Some detail + horizon

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Example accuracy : Helsinki


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Helsink : pre/’post’diction difference


Blue ->over estim. loss Yellow -> over est. loss More green?

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Helsinki : statistical evaluation




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Example urban pathloss


Notice street guidance!, i.e. not solely range dependant loss

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Delay spread prediction• Path length -> delay spread (ISI)• Direction -> angular spread (space corr)

Simulates not enough Dispersion, long effectsPossible cause?

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Network planning

Okumura-HataRay based (site specific)notice ’spill-over’ on cell areas

http://www.awe-communications.com/indexw.html

Path loss -> coverage

Islands!

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Analytical Diffraction (‘look around corners’)

• Fresnel single diffraction (double diffraction)

• Multi diffraction special cases – half screen– Skimming incidence

– Harmonic structures



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Numerical method distinctions

• Old MM12 Surface aperture integration– Integral equation method (IE)

• MM8 Field aperture (integration, differentiation)– Fresnel-Kirchhoff theory – physical optics (PO)– Parabolic equation methods (PE)

• MM7 Ray techniques– Uniform / geometric theory of diffraction (UTD,

GTD)– Slope Diffraction – High-order GTD

James H. Whitteker, DIFFRACTION MODELLING FOR TERRESTRIAL MOBILE COMMUNICATION SYSTEMS, IEEE AP2000 Conf, Davos, Switzerland 9-14 April 2000 (CD-ROM)

Far field propagation techniques – focus on shadow region = diffraction :

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2D radial viewDiffraction sketch

MM8 : Field aperture PO (no back scatter)

MM7 : Ray UTD

MM12 : Surface aperture IE(incl. all effects incl back scatter)

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Basics• Geometric Optics (GO)

– Reflection/refraction (penetration), propagation– Concept of wave propagation along beams (waves

or rays)• is small, and therefore, wave number k is high • Wave observed far from the source. (amplitude changes

slowly in the propagation direction, phase varies quickly) • Geometric Theory of Diffraction (GTD)

– High freq. harmonic (asymptotic ( -> 0 or ω -> ∞) solution to Maxwells equations for specific objects (canonical : wedge, cylinder, ..)

– Modify GO to eliminate obvious errors (e.g. Diffraction)

• Uniform Theory of Diffraction (UTD)– Complements GTD, where GTD is invalid (i.e.

provide continuous solutions)

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Maxwell equations

No magnetic charges

Charges produce electric field

Changing magnetic flux produces electric field

Electric current and changing electric flux produce magnetic field

• Charge neutrality, = 0• No direct current, j = 0• Nonmagnetic materials, r = 1 ( = 0)

www.itn.liu.se/meso-phot/presentations/2006_surface_plasmons.ppt

Differential form -> exploited in techniques like FDTD



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Maxwell harmonic form equations• i.e. Rays : principle ’single frequency’

(narrowband) techniques

ss EjH

ss HjE

0 sE

0 sH

www.itn.liu.se/meso-phot/presentations/2006_surface_plasmons.ppt

Harmonic form : d/dt -> jω

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GO : Beams / rays• The beam direction : steepest change of phase in

every point, also direction of Poynting vector (i.e. of the direction of the energy flow) – Preservation of power– (infinitely) facet dS1 is chosen of the wave surface and a

beam is led through every point of the edge of this facet : i.e. a beam tube

– energy propagates along the beams, it cannot leave the tube through the side walls. In the lossless medium, the power passing facets dS1 and dS2 is identical

• variable s is curvilinear coordinate along the beam

– not valid where the beams cut (-> infinitely high field intensity). occur in the focus and on the surface called causticshttp://www.urel.feec.vutbr.cz/~raida/multimedia_en/chapter-2/2_3A.html

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Geometrical Theory of Diffraction (GTD)• Ray Theory• Solves some GO difficulties

Incident ray

Q1 Q2

Diffractedrays

Surface diffraction

'

)2( n

Diffracted raysIncident ray

Edge diffraction

sdQ

Observationdirection

Shadow boundary

Shadow boundary

http://gea.df.uba.ar/giambiagi/material/altintas02.ppt

Canonical shapes : wedge, cylinder

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GTD Postulates

The total field at an observation point P is decomposed into GO and diffracted components

The behavior of the diffracted field is based on the following postulates of GTD:1. Wavefronts are locally plane and waves are TEM.2. Diffracted rays emerge radially from an edge.3. Rays travel in straight lines in a homogeneous medium4. Polarization is constant along a ray in an isotropic medium5. The diffracted field strength is inversely proportional to the cross sectional area of the flux tube6. The diffracted field is linearly related to the incident field at the diffraction point by a diffraction coefficient



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GTD calculationProperties: Conceptionally simple Local phenomena Tracing of diffracted rays Pinpoints flash points Predicts non-zero field in shadow

regions A higher order approximation than GO

in terms of frequency Uniform versions yield smooth and

continuous fields at and around shadow boundaries (transition regions)

Disadvantages: Requires searching for diffraction

points on the edge Requires finding of attachment and

launching points and geodesics on the surface

Fails at caustics where many diffracted rays merge

dGOGTD EEE

sjhsd

incd esADQEE )()( ,

fieldDiffractedE d :

factorspread:)(sA

factorphase:sje

coeff.ndiffractioDyadic:,hsD

http://gea.df.uba.ar/giambiagi/material/altintas02.ppt

GTD formulation

B/W gray

•notation is borrowed from optics: s = soft or parallel polarization; h = hard or perpendicular polarization

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GTD, UTD half plane I

Diffracted ray

Etotal = EGO+Ed(GTD or UTD)

|E(GO)|

jkses

1

|Ed(GTD)|

|Ed(UTD)| Geometrical Optics (’B or W’)Geometrical theory of diffraction(smoother B vs W region Transition, but singularity)Uniform theory of diffraction(fix of GTD at singularity)

Cyl. Wave due to half plane

=0 -> ½Theoretical exactFor single diffraction

Cylindrical amplitude attenuationRadius proportionalTo phase shift

Darks

’White’

’Black’

E0

Incident plane wave

Amplitude term!

EE0

1

+

-

½

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GTD, UTD half plane II

y+y-

xx- x+

y

E GO=E

i @ x

-

y+

y-

y

E GO=E

i @ x

+

y+

y-

y

Ed y+y-

y

E tot

al=

E d+

E GO

y+y-0.

5

UTD diffracted field = difference between total field and GO

Dif. term incl sign

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GTD, UTD single diffraction I

s0 sEd(s)Ei

Billedet kan ikke vises.

0

0;sss

ssAesADEsE jksid

A is spreading factor : determines wave attenuation D is diffraction coefficient : ’partial offset’ attenuations

423121

4/

22, DRDRDD

kneD

j

´

4 diffraction components : for edge component and reflection (R=reflectioncoef.) of the surface of wedge – for either of the two sides of the wedge

R1 R2

Extend complexity now, soEi = incident spherical field

00

0

seEE

jks

i

Sphericalamplitudedecay

n = shape factor’collaps’ of wedge

Control transitionCylin.<->sphericaldiff wave

Observation, launch angles

Polarisation dependant



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GTD Valid Outside Transition Region• Repetitive application of GTD

Fresnelzone

Shadowboundary

Incidentplanewave

y

x

axis. about

isRegion Transition ofWidth

blocked.completelyor free completely is

zone Fresnel when validis GTDpoint,n observatio tozone Fresnel

by definedregion Transition

xx

Example : If x 10 m and f 1GHz, x 3 1.7 m.

x

GTD is not valid inthe transition region

eeweb.poly.edu/faculty/bertoni/docs/08Diffraction.ppt

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GTD, UTD single diffraction II

D is transition function across 4 boundariesR is reflection coefficient on front/back side of wedge (often 0, +/- 1)

;2

2cos2

;2)(

2cot

2

2

0

0

4..1

2

Nna

ssssLdteeXjXF

aLkFn

D

X

jtjX

Fresnel like integral, distance factor L .X = 0 at boundaryand increase awayfrom it

N picked such that 2πnN± - β = ±π is best satisfied

Term added to bringContineous transition

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Example : UTD polarimetric Dif. Coef.

PerfectElectricConductor R=-1 vs R=1

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D2 example @ singularity φ-φ’=π: I

1,00

0

2

2

4/2

2

22

0

0

14/4/

1

½

22,;

2sin2

2cot

0;2

sin22

cos2

;2

2/1)(

X

ssjkjks

iD

j

XjXjj

X

sseeADEE

Dkn

eDLkFn

D

Na

ssssL

eXeX

XjXF

Cotangent singularity at boundary : Set φ-φ’=π - є

Cot singularity cancel w FCalculation on next slide!!



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D2 example @ singularity φ-φ’=π: II

1,00

0

222

0

04/4/

000

22

4/4/4/

000

0

02

0

04/

00

2

½

222

22

2222

2sin2

2cot

22

2

0

00

2

0

0

0

0

X

ssjk

sssskjjjssjk

sssskX

jXjjjssjk

jksjjks

jksiD

sse

ess

ssknkn

essss

eE

eXeXnkn

essss

eE

esss

sss

sskFnkn

es

eE

eADEE

Highest order terms diminishes fastest

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UTD half plane III at transition zone

Dark

Fullyabsorbing

n=2 (wedge-> half screen)R1=R2=0,D1=D2->Damplitude = 2D2D1+D2 collapse into one

;12/sin2

2/sin2/sin2

222

24/

Lk

LkFk

eDj

ampl

Transition zone = Hyperbola, when s0=s0>>s simplifies to parabola (FresnelZone, focals at edge & )

s0

s

2

x

kxy

UTD validity: Succeeding edges outside transition zone of previous ones

Cot((π ± (φ-φ’)/(2·2))=cos(..)/sin(..)= -> 1/sin(..) ≈ 1/..| small argument

Transition zone DEFINTION

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UTD multi screenSkimming incidence : all = 0 and on line ; test case

Plane waveCorrect attenuation is 1/(3N+1)

Cylindrical wave

UTD attenuation is (½)N : power law -> needs slope term for correctness

Correct attenuation is 1/(N exponential decay

1 N

Self study presentation ‘Int. equation’kom.aau.dk/~pe/education/menu/9sem/AP_MM7_18... ·...

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