© 2000 by H. L. BertoniPolytechnic University, Brooklyn, NY1 XII. Site Specific Predictions Using Ray Methods General considerations Ray tracing using.

© 2000 by H. L. Bertoni Polytechnic University, Brooklyn, NY1

XII. Site Specific Predictions Using Ray Methods

• General considerations• Ray tracing using 2D building database • Ray tracing from a 3D building database

• Slant plane / vertical plane method • Full 3D method• Vertical lane Launch (VPL) method

• Ray tracing for indoor predictions• Using ray methods to predict statistics of delay and angle

spread


Goals and Motivation

• Goal – Make propagation predictions based on the actual shape of the

buildings in some region

• Motivation– Achieve a desired quality of service in high traffic density

areas

– Install systems without adjustment

– System simulations and studies

– Predict higher order channel statistics


Ray Techniques for Site Specific Predictions

• Numerical solvers (finite difference, finite element and moment methods) not practical for urban dimension

• Ray techniques are the only viable approach

• Predictions using 2D building data base

Pin/cushion vs. image method

• Prediction using 3D building data base

Vertical plane/slant plane - enhanced 2D methods

Full 3D method

Vertical plane launch - approximates full 3D method


Physical Phenomena and Database Requirements

• Physical phenomena that can be accounted for– Ground reflection and blockage

– Specular reflection at building walls

– Diffraction at building corners, roofs

– Diffuse scattering from building walls (for last path segment)

• Database requirements for predictions– Terrain

– Buildings decomposed into groups of polyhedrons that are :

Stacked (wedding cake buildings) or side-by-side

Polygonal base with vertical sides

Some codes assume flat roofs

Vector vs pixel (area element) data base

– Reflection coefficients at walls, diffuse scattering coefficient


Specular vs Diffuse Reflection from Walls

• Complex construction leads to scattering– Mixture of construction materials

– Architectural details

– Windows - glass, frame

• Simplifying approximations for large distances

r1

s1 s2

r2

Specular reflection ~ 1/ (r1 + r2)2

Diffuse reflection ~ A/ (s1 s2)For all construction, | ( )| 1 for 90°


Modeling Limitations

• Cannot accurately predict phase of ray fields– Position accuracy of building data base ~ 0.5 m

– Do not know wall construction - uncertainty in magnitude and phase of reflection coefficient

• Local scattering contributions not computed– Do not consider vehicles, street lights, signs, people, etc.

– Most codes do not include diffuse scattering

• Cannot predict fast fading pattern in space– Predict small area average by summing ray powers

• Can be used to predict statistical parameters

Ai exp jkLi 2 Ai Aj

exp jk Li Lj Ai 2


Ray Tracing Using a 2D Building Database

• Building are assumed to be infinitely high– Almost all models neglect transmission through the building

– 2D ray tracing around building in the horizontal plane

• Rays that are considered– Multiple specular reflections from the building walls

– Single or double diffraction at the vertical edge of a building

– Ground reflection

– Diffuse scattering from the building walls

• Advantages:– Account for low base station antennas among high rise buildings

– Computationally efficient

• Limitations:– Less accurate in an area of mixed building heights

– Fails for rooftop base stations


Two Dimensional Ray Tracing Technique

Rx Rx

Rx

Rx

Tx

No DiffractionSingle DiffractionDouble Diffraction

Rays are traced to corners, which act as a secondary sources for subsequent trace.


Reflected ray paths found from multiple Rays traced outward from the source imaging of the source in the building walls at angular separation, << w/R,

must determine if the ray from an image must use capture circle to find rays passes through the actual wall, or through that illuminate the receiver (or the analytic extension of the wall. equivalent procedure). Dia = L

Image vs Pin Cushion Method for 2D Rays

Rx

Tx

Rx

Image Method Pin Cushion Method

Tx

Rx


Footprints of Buildings in the High-Rise Section of Rosslyn, Virginia


Comparison of Measured and, 2D computed Path Gain for Low Base Station at TX4b

f = 1900MHz


Predictions for a Generic High Rise Environment

• Rectangular Street Grid

• Propagation Down Streets, Around Corners - Specular Reflection at Building Walls Diffraction at Building Corners


High Rise Buildings in Upper Manhattan, NY


Propagation Down the Urban Canyonsof High Rise Buildings

Building Building Building



y

xTXA B

RX0

RX1RX2Wy

Wy

4 2 1 3

Lx

Ly

MAIN STREET


Reflection and Diffraction Around Corners



TX

RX

12

3


Ray Path for High Rise Model

• All Path Include Direct Path + Path from Image Source to Account for Ground Reflections

• Main Street– Rm: m reflections at building on main street

• Perpendicular Streets - one turn paths– Rmn: m reflections at building on main street, n reflections on perpendicular

street + ground– RmDRn: building reflections separated by corner diffractions

• Parallel Streets - two turn paths– Rmnp: m, n, p, building reflections on main, perpendicular, parallel street– RmDRnp, RmnDRp,: building reflections + diffraction at a single corner– RmDRn DRp: building reflections + diffraction at two corners


Predictions in LOS and Perpendicular Streets

TX LOS

Distance (m)

Re

ceiv

ed

Po

we

r (d

B)

X X X X X


Turning Corners in Manhattan


Cell shape in a High Rise Environment


Vertical Plane/Slant Plane MethodB

uild

ing

He

ight

Range

Tx

Rx

cb d c

bd

0

Rx

Tx

Leftpropagationchannel

Rightpropagationchannel

Rays are traced in the vertical plane containing TX and RX to account forpropagation over buildings.

Rays are traced in the slant planecontaining TX and RX to account forpropagation around buildings.


Slant/Vertical Plane Predictionfor Aalborg, Denmark at 955MHz

T. Kurner, D.J. Cichon and W. Wiesbeck, “Concepts and Results for 3D Digital Terrain-basedWave Propagation Models: An Overview,” IEEE Jnl. JASC 11, Sept. 1993


Missing Rays in Slant Approximation

• Unless the building faces are perpendicular to the vertical plane, reflected rays lie outside of the vertical plane

• Multiply reflected rays will not lie in the slant plane

• Neglects rays that go over and around building

• Missing rays cause significant errors for high base station antenna


Transmitter and Receiver Locations forCore Rosslyn Propagation Predictions


Slant/Vertical Plane Prediction for Rooftop Antenna at 900MHz


Ray Tracing Using a 3D Building Database

• Rays that are considered:– Can account for all rays in 3D space– Some programs consider diffuse scattering– Some simplification is made, i.e. flat roofs and/or vertical walls

• Rays that are not considered:– Often unable to include rays that undergo more than one diffraction– Usually does not include transmission into the buildings

• Advantages:– Very robust model, works for many building environments

• Limitations:– Limited to a maximum of 2 diffractions (unable to account for

multiple rooftop diffraction)– Computationally very inefficient


3D Predictions of Path Gain for Elevated Base Station at TX6 and f=908MHz


Limitation of Regular 3D Ray Tracing MethodEach segment of each edge is a source of a cone of diffracted rays


Vertical Plane Launch (VPL) Method

• Finds rays in 3D that are multiply reflected and diffracted by buildings• Assumes building walls are vertical to separate the trace into horizontal and vertical components• Pin cushion method gives the ray paths in the horizontal plane• Analytic methods give the ray paths in the vertical direction• Makes approximation: rays diffracted at a horizontal edge lie in the vertical plane of the incident ray, or the vertical plane of the reflected rays


Physical Approximation of the VPL Method

Treats rays diffracted at horizontal edges as being in the vertical planesdefined by the incident or reflected rays (replaces diffraction cone bytangent planes)

Cone ofdiffracted rays

Vertical planecontaining forwarddiffracted rays

Vertical planecontaining backdiffracted rays

Vertical plane containing reflected and backdiffracted rays


VPL Method for Approximate 3D Ray Tracing


Reflections and Rooftop Diffractions for VPL Method Form a Binary Tree

1

2

3

4

5

6

7

8

9

10

Diffraction Edge

Reflection


Transmitter and Receiver Locations forCore Rosslyn Propagation Predictions


Measurements and VPL Predictions forRooftop Antenna (TX6 and f=908MHz)

-120

-115

-110

-105

-100

-95

-90

-85

-80

-75

-70

1001 1051 1101 1151 1201 1251 1301 1351

Receiver Number

Pat

h G

ain

(dB

)

Measurements

Predictions

Diffuse

Without diffuse: = -0.75 dB = 5.43 dBWith diffuse: = -0.74 dB = 5.44 dB


Measurements and VPL Predictions for Street Level Antenna (TX1a and f=908MHz)

Without diffuse: = -0.42 dB = 8.92 dB

With diffuse: = 0.49 dB = 8.34 dB

-130

-120

-110

-100

-90

-80

-70

-60

-50

1001 1051 1101 1151 1201 1251 1301 1351

Receiver Number

Pat

h G

ain

(d

B)

Measurements

No Diffuse

With Diffuse


Tx and RX Locations in Munich


Measurements and VPL Predictions in MunichRoute 1, f=900MHz, = 0.40 dB, s = 8.67 dB

-150

-140

-130

-120

-110

-100

-90

-80

-70

1 26 51 76 101 126 151 176 201 226 251 276 301 326 351

Receiver Number

Pa

th G

ain

(d

B)

Measurements

Predictions


Diffraction at Building Corners

• Important to correctly model shape of building corners• Luebbers diffraction coefficient used by many to model

diffraction at building corners– Heuristic coefficient for lossy dielectric wedges– Developed for forward diffraction over hills– Exhibits nulls in the back diffraction direction that are not physical

• Building corners are not dielectric wedges, e.g., fitted with windows, metal framing

• Need a single diffraction coefficient to use for all corners


Reflection Away From Glancing Is Influenced by Wall Properties

For low base station (BS) antenna, reflection from glass doors at Corner A influences received signal on street L-M.


Measurements Along Street L-M Show Influence of Corner A on Ray Results


Some Examples of Building Corner Construction and Diffracted Rays

Walls with windows


Comparison of Diffraction Coefficients (900 MHz)


Comparison of Power Predictions With Helsinki Measurements at 2.25 GHz


Comparison of DS Predictions With Helsinki Measurements at 2.25 GHz


Summary of Prediction Errors on Different Routes in Helsinki for Low Antennas


Conclusions

• Site specific predictions are possible with accuracyAverage error ~ 1 dB

RMS error ~ 6 - 10 dB

• Requires multiple interactions for accurate predictionsSix or more reflections required for best accuracy

Double diffraction at vertical edges is sometimes needed

• Lubbers diffraction coefficient needs modification


Ray Tracing Inside Buildings

• Ray tracing over one floor

• Propagation through the clear space between furnishings and ceiling structure

• Propagation between floors


2-D codes for Propagation Over One Floor

• Transmission through walls• Specular reflection from walls• Diffraction at corners


Effects of Floors & Ceilings

• Drop ceilings taken up with beams, ducts, light fixtures, etc.

• Floors covered by furniture

• Propagation takes place in clear space between irregularities

W


Modeling Effect of Fixtures

d 2d 3d nd (n+1)d Nd x

y

w/2

Line Source

-w/2

Assume the excess path loss for a point source is the same as that of a line source perpendicular to the direction of propagation.

Represent the effects of the furnishings and fixtures by apertures of width w in a series of absorbing screens separated by the distance d.

Use Kirchhoff-Hyugens method to find the field in the aperture of the n + 1 screen do to the field in the aperture of the n screen.

The field in the aperture of the first screen is the line source field.


Modeling Effect of Fixtures - cont.

H(xn 1,yn 1) cos n cosn H (xn ,yn )jke jkr

4rdyn

w / 2

w / 2

dzn

where r n2 zn

2 n +zn

2

2n

with n xn1 xn 2 yn1 yn 2

For small angles cos n cosn 2. Then for integration over zn becoms

(cos n cosn )H (xn, yn )jke jkr

4r-

dzn jke jkn

2n

H (xn ,yn ) exp( jkz n2 2n )dzn

d 2d 3d nd (n+1)d Nd x

y

w/2

Line Source

-w/2


Modeling Effect of Fixtures - cont.

Since exp( jkzn2 2n )dzn

e j / 4 2n

k

Therefore H (xn 1,yn 1) e j / 4

H (xn, yn )

w / 2

w / 2

e jkn

n

dyn

At the first apeture the field of the incident cylindirical wave is

H(d,y1) exp( jk0) 0 where 0 d2 y12

The excess path gain E(R) at a distance R Nd is the defined as the

ratio of the average of H (Nd,yN )2 over the aperture to the

the magnitude squared of the line source field ( 1 Nd ), or

Thus E (R)Nd1

wH (Nd,yN )

2dyN

w / 2

w / 2


Excess Path Gain E(R) Propagation Through Clear Space of 1.5 - 2 m

Distance in m

Exc

ess

Pat

h G

ain

in d

B


Rays Experiencing Only Reflection and Transmission

Path Gain : PG PRe c PTrans

For free space : PGO 4R

2

For rays experiencing reflection and transmission :

PG 4R

2

E (R) p ( p )p

2Tn (n )

n

2

where R is the unfolded path length of the ray


Predictions at 900 MHz in a University Building

Diffraction at far corners of hallway is responsible for the received signal when the direct rays go through many walls.


Propagation Between Floors Can Involve Paths That Go Outside of the Building

RX

TX

9.20 m2.62 m

2.1 m 7.50 m

1.3 m

1.3 m

Propagation can take place via paths that go outside the building via diffraction or reflection from adjacent buildings. Stair wells, pipe shafts, etc. are also paths for propagation between floors.

Direct propagation between floors has losses:

~ 5 - 8 dB for wooden floors

~ 10 dB for reinforce concrete

> 20 dB for concrete over metal pans


Predicted vs Measured Path Gain in Hotel

Number of floors between Tx and Rx

Path

Gai

n (d

B)


Summary of Propagation in Buildings

• Ray codes for coverage over on floor– Need to account for 2 or 3 reflections and 1 diffraction event

– Can achieve low errors (< 6 dB)

• Propagation through clear space can give excess loss at lower frequencies

• Propagation between floors can involve paths that lie outside of buildings


Predicting Statistics of Channel Parameters

• Need high order channel statistics (e.g. delay spread DS and angle spread AS) for advanced system design Measurements are expensive and time consuming

• Not sure if measurements for one link geometry, city,

apply elsewhere

• Monte Carlo simulation using site specific predictions

allow different link geometry, cities to be examined

• Simulations allow modifications of building database

• Relate statistics of channel parameters to the statistical

properties of the building distribution


Space-Time Ray Arrivals From a Mobile as Measured at an Elevated Base Station

1800MHz in Aalborg, Denmark


Delay Spread (DS) and Angular Spread (AS)Obtained from the Ray Simulation

Delay Spread

Angle Spread (approximate expression for small spread)

From mth ray from the jth mobile

mobile) to direction from (measured station base at arrival of angle

delay time arrival

amplitude

jm

jm

jmA

DS( j ) Am

( j )

m 2

m( j ) m

( j ) 2

Am( j ) 2

m

where m( j )

Am( j)

m 2

m( j)

Am( j ) 2

m

AS ( j) Am

( j )

m 2

m( j) m

( j ) 2

Am( j ) 2

m

where m( j )

Am( j )

m 2

m( j )

Am( j ) 2

m


Standard and Coordinate Invariant Methods of Computing AS

Standard method : ray arrival angle n measured from direction to mobile

AS (n )2 An2

n

An2

n

where (n )An2

n

An2

n

Coordinate invarient method : ray arrival angle n measured from any x - axis

Define the vector : un (cosn , sinn )

AS 180

un U2An

2

n

An2

n

180

1 U2

where U (un )An2

n

An2

n


Summary of DS/AS Measurements


Greenstein Model of Measured DS in Urban and Suburban Areas

DST1km Rkmwhere T1km is 0.3-1.0 s and

10logis a Gaussian random variable

with standard deviation 2 - 6

Greenstein, et al., “A New Path Gain/Delay Spread Propagation Model for Digital Cellular Channels,” IEEE Trans. VT 46, May 1997.


Direction of Arrival and Time Delay Computed for a Mobile Location in Seoul, Korea


Distribution of Building Heights in Three Cities


Comparison of the CDF’s of Delay Spreadfor Mobiles in Three Cities

( hBS is 5m above the tallest building)


Comparison of the CDF’s of Angular Spreadfor Mobiles in Three Cities

( hBS is 5m above the tallest building )


Scatter Plots of DS/AS vs Distance for Munich


Scatter Plot of DS versus Distance for Seoul

50 100 150 200 250 300 350 400 4500

20

40

60

10.67 degree/km

Distance(m)

Angle Spread(degree)

AS of a mobileLinear Fitting

50 100 150 200 250 300 350 400 4500

0.5

1

1.5x 10-6

0.61 usec/km

Distance(m)

Delay Spread(sec)

Seoul

DS of a mobile Linear Fitting Greensteins's median DS

A

ngle

Spr

ead

D

elay

Spr

ead


Log Normal CDF of Delay SpreadsSeoul and Munich

-14 -12 -10 -8 -6 -4 -2 00.01

0.02

0.05

0.10

0.25

0.50

0.75

0.90

0.95

0.98

0.99

0.997

Delay Spread (dB usec)

Normal Probability Plot: HBS = Hmax + 2m

Seoul Std. = 3.37 dB

Munich Std. = 3.73 dB


Effect of Building Height Distribution on DS/AS for Modified Seoul Database

BS Height Medain DS(usec) Median AS(degree)Original H=+5m 0.13 10.7

H=+2m 0.14 10.9H=95% 0.18 20.7H=80% 0.19 24

4-7 Story Building H=+5m 0.17 16.1H=+0m 0.18 23.3H=95% 0.15 35.5H=80% 0.17 37.2

12 Story Flat Bd. H=+5m 0.14 17.7H=-5.2m 0.12 47.6

5 Story Flat Bd. H=+5m 0.15 13.9H=-5.2m 0.12 47.3

4-7 Story Bd. H=+5.2m 0.17 15.4(Rayleigh Dist.)

2-3 Story H=2m 0.23 64.4


Correlation Coefficients of DS and AS vs Distance Range and Antenna Heights

r1 r2 r3 r4 All rxSeoul H=+5m 0.32 0.45 0.66 0.66 0.53

H=+2m 0.23 0.44 0.63 0.71 0.52H=95% 0.38 0.46 0.47 0.61 0.49

Munich H=+5m 0.59 0.47 0.63 0.72 0.6H=+2m 0.57 0.45 0.63 0.72 0.59H=95% 0.53 0.46 0.54 0.48 0.5


Footprint of Buildings and Locations of Base Stations ( ) and Mobiles ( )


DS/AS of LOS and Cross Roads for Modified Seoul at 8m/2m Height


Conclusions

• Site specific predictions are possible with accuracy

Average error ~ 1 dB, RMS error ~ 6 - 10 dB

• Requires multiple interactions for accurate predictions 6 or more reflections, double diffraction at vertical edges

• Site specific prediction can be used for Monte Carlo

simulation of statistical channel characteristics

Delay Spread is not strongly dependent on path geometry

or building statistic

Angular Spread at base station depends strongly on antenna

height and building height distribution

Weak correlation between Delay Spread and Angular Spread

• Further work needed on reflection and diffuse scattering

at the building walls

© 2000 by H. L. BertoniPolytechnic University, Brooklyn, NY1 XII. Site Specific Predictions Using Ray Methods General considerations Ray tracing using.

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