Transcript EL 675 UHF Propagation for Wireless Applications (4)

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
© 2000 by H. L. Bertoni
1
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
2
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
3
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
4
Polytechnic University, Brooklyn, NY
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
q
Specular reflection ~ 1/ (r1 + r2)2
Diffuse reflection ~ A/ (s1  s2)
For all construction, | (q )|  1 for q  90°
© 2000 by H. L. Bertoni
5
Polytechnic University, Brooklyn, NY
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
 Ai exp jkLi 
2



  Ai Aj exp jk Li  Lj    Ai

2
• Can be used to predict statistical parameters
© 2000 by H. L. Bertoni
6
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
7
Polytechnic University, Brooklyn, NY
Two Dimensional Ray Tracing Technique
Rx
Rx
Rx
Rx
Tx
Rays are traced to corners,
which act as a secondary
sources for subsequent
trace.
© 2000 by H. L. Bertoni
No Diffraction
Single Diffraction
Double Diffraction
8
Polytechnic University, Brooklyn, NY
Image vs Pin Cushion Method for 2D Rays
Image Method
Pin Cushion Method
Reflected ray paths found from multiple
imaging of the source in the building walls
Rays traced outward from the source
at angular separation, Dq << w/R,
Rx
Rx
Rx
Tx
Tx
must determine if the ray from an image
passes through the actual wall, or through
the analytic extension of the wall.
© 2000 by H. L. Bertoni
must use capture circle to find rays
that illuminate the receiver (or
equivalent procedure). Dia = LDq
9
Polytechnic University, Brooklyn, NY
Footprints of Buildings in the High-Rise Section
of Rosslyn, Virginia
© 2000 by H. L. Bertoni
10
Polytechnic University, Brooklyn, NY
Comparison of Measured and, 2D computed
Path Gain for Low Base Station at TX4b
f = 1900MHz
© 2000 by H. L. Bertoni
11
Polytechnic University, Brooklyn, NY
Predictions for a Generic High Rise Environment
• Rectangular Street Grid
• Propagation Down Streets, Around Corners
- Specular Reflection at Building Walls Diffraction
at Building Corners
© 2000 by H. L. Bertoni
12
Polytechnic University, Brooklyn, NY
High Rise Buildings in Upper Manhattan, NY
© 2000 by H. L. Bertoni
13
Polytechnic University, Brooklyn, NY
Propagation Down the Urban Canyons
of High Rise Buildings
y
Building
x
Building
MAIN STREET
A
TX
Building
B
RX0
4
Building
Building
1
RX2
Wy
Ly
2
Building
Building
Building
3
RX1
Wy
Building
Lx
© 2000 by H. L. Bertoni
14
Polytechnic University, Brooklyn, NY
Reflection and Diffraction Around Corners
Building
Building
Building
1
2
3
TX
Building
Building
Building
RX
© 2000 by H. L. Bertoni
15
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
16
Polytechnic University, Brooklyn, NY
Predictions in LOS and Perpendicular Streets
LOS
Received Power (dB)
TX
XXX
XX
Distance (m)
© 2000 by H. L. Bertoni
17
Polytechnic University, Brooklyn, NY
Turning Corners in Manhattan
© 2000 by H. L. Bertoni
18
Polytechnic University, Brooklyn, NY
Cell shape in a High Rise Environment
© 2000 by H. L. Bertoni
19
Polytechnic University, Brooklyn, NY
Vertical Plane/Slant Plane Method
Building Height
Rx
c
b
c
d
Tx
b
d
Rx
0
Range
Left
propagation
channel
Tx
Rays are traced in the slant plane
containing TX and RX to account for
propagation around buildings.
Rays are traced in the vertical plane
containing TX and RX to account for
propagation over buildings.
© 2000 by H. L. Bertoni
Right
propagation
channel
20
Polytechnic University, Brooklyn, NY
Slant/Vertical Plane Prediction
for 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
© 2000 by H. L. Bertoni
21
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
22
Polytechnic University, Brooklyn, NY
Transmitter and Receiver Locations for
Core Rosslyn Propagation Predictions
© 2000 by H. L. Bertoni
23
Polytechnic University, Brooklyn, NY
Slant/Vertical Plane Prediction for Rooftop
Antenna at 900MHz
© 2000 by H. L. Bertoni
24
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
25
Polytechnic University, Brooklyn, NY
3D Predictions of Path Gain for Elevated Base Station
at TX6 and f=908MHz
© 2000 by H. L. Bertoni
26
Polytechnic University, Brooklyn, NY
Limitation of Regular 3D Ray Tracing Method
Each segment of each edge is a source of a cone of diffracted rays
b
b
a
a
g
© 2000 by H. L. Bertoni
27
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
28
Polytechnic University, Brooklyn, NY
Physical Approximation of the VPL Method
Treats rays diffracted at horizontal edges as being in the vertical planes
defined by the incident or reflected rays (replaces diffraction cone by
tangent planes)
Vertical plane
containing forward
diffracted rays
Vertical plane
Vertical
plane containing
containing
back
reflected
diffracted
rays and back
diffracted rays
Cone of
diffracted rays
© 2000 by H. L. Bertoni
29
Polytechnic University, Brooklyn, NY
VPL Method for Approximate 3D Ray Tracing
© 2000 by H. L. Bertoni
30
Polytechnic University, Brooklyn, NY
Reflections and Rooftop Diffractions for VPL
Method Form a Binary Tree
8
9
4
5
7
Diffraction Edge
Reflection
10
6
3
1
2
© 2000 by H. L. Bertoni
31
Polytechnic University, Brooklyn, NY
Transmitter and Receiver Locations for
Core Rosslyn Propagation Predictions
© 2000 by H. L. Bertoni
32
Polytechnic University, Brooklyn, NY
Measurements and VPL Predictions for
Rooftop Antenna (TX6 and f=908MHz)
-70
-75
Path Gain (dB)
-80
-85
-90
-95
-100
-105
Measurements
Predictions
Diffuse
-110
-115
-120
1001
1051
1101
1151
1201
1251
1301
1351
Receiver Number
Without diffuse: h = -0.75 dB
s = 5.43 dB
With diffuse: h = -0.74 dB
s = 5.44 dB
© 2000 by H. L. Bertoni
33
Polytechnic University, Brooklyn, NY
Measurements and VPL Predictions for
Street Level Antenna (TX1a and f=908MHz)
-50
-60
Path Gain (dB)
-70
-80
-90
-100
-110
Measurements
-120
No Diffuse
With Diffuse
-130
1001
1051
1101
1151
1201
1251
1301
1351
Receiver Number
Without diffuse: h = -0.42 dB
s = 8.92 dB
With diffuse: h = 0.49 dB
s = 8.34 dB
© 2000 by H. L. Bertoni
34
Polytechnic University, Brooklyn, NY
Tx and RX Locations in Munich
© 2000 by H. L. Bertoni
35
Polytechnic University, Brooklyn, NY
Measurements and VPL Predictions in Munich
Route 1, f=900MHz,
= 0.40 dB, s = 8.67 dB
-70
Measurements
-80
Predictions
Path Gain (dB)
-90
-100
-110
-120
-130
-140
-150
1
26
51
76
101 126 151 176 201 226 251 276 301 326 351
Receiver Number
© 2000 by H. L. Bertoni
36
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
37
Polytechnic University, Brooklyn, NY
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.
© 2000 by H. L. Bertoni
38
Polytechnic University, Brooklyn, NY
Measurements Along Street L-M Show
Influence of Corner A on Ray Results
© 2000 by H. L. Bertoni
39
Polytechnic University, Brooklyn, NY
Some Examples of Building Corner
Construction and Diffracted Rays
Walls
with
windows
© 2000 by H. L. Bertoni
40
Polytechnic University, Brooklyn, NY
Comparison of Diffraction Coefficients
(900 MHz)
© 2000 by H. L. Bertoni
41
Polytechnic University, Brooklyn, NY
Comparison of Power Predictions With
Helsinki Measurements at 2.25 GHz
© 2000 by H. L. Bertoni
42
Polytechnic University, Brooklyn, NY
Comparison of DS Predictions With Helsinki
Measurements at 2.25 GHz
© 2000 by H. L. Bertoni
43
Polytechnic University, Brooklyn, NY
Summary of Prediction Errors on Different
Routes in Helsinki for Low Antennas
© 2000 by H. L. Bertoni
44
Polytechnic University, Brooklyn, NY
Conclusions
• Site specific predictions are possible with accuracy
Average error ~ 1 dB
RMS error ~ 6 - 10 dB
• Requires multiple interactions for accurate predictions
Six or more reflections required for best accuracy
Double diffraction at vertical edges is sometimes needed
• Lubbers diffraction coefficient needs modification
© 2000 by H. L. Bertoni
45
Polytechnic University, Brooklyn, NY
Ray Tracing Inside Buildings
• Ray tracing over one floor
• Propagation through the clear space between furnishings
and ceiling structure
• Propagation between floors
© 2000 by H. L. Bertoni
46
Polytechnic University, Brooklyn, NY
2-D codes for Propagation Over One Floor
• Transmission through walls
• Specular reflection from walls
• Diffraction at corners
© 2000 by H. L. Bertoni
47
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
48
Polytechnic University, Brooklyn, NY
Modeling Effect of Fixtures
y
w/2
Line Source
-w/2
d
2d
3d
nd
(n+1)d
Nd
x
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.
© 2000 by H. L. Bertoni
49
Polytechnic University, Brooklyn, NY
Modeling Effect of Fixtures - cont.
y
w/2
Line Source
-w/2

d
2d
3d
nd
 w/2
(n+1)d
Nd
x
 jk r
jke
H(x n 1 ,y n 1 )    cosa n  cosn H (x n ,y n )
dyn dzn
4 r
 w / 2
2
where
z
r   n2  z2n   n + n
2 n
with
 n  x n1  x n   y n1  y n 
2
2
For small angles cos
a n  cosn  2. T hen for int egrat ion over
zn becoms

jke jk r
jke jkn
 (cosa n  cosn )H (x n, yn ) 4 r dzn  2 H (x n ,y n )  exp( jkz2n 2n )dzn
-
n


© 2000 by H. L. Bertoni
50
Polytechnic University, Brooklyn, NY
Modeling Effect of Fixtures - cont.
Since

 exp( jkzn2 2n )dzn  e  j / 4

T herefore H (xn 1 ,y n 1 ) 
e j / 4

2 n
k
w/2
 H (x , y )
n
w/2
n
e  jkn
n
dyn
At t he first apet ure t he field of the incident cylindirical wave is
H(d,y1 )  exp( jk  0 )
where  0  d 2  y12
0
T he excess path gainE(R) at a distanceR  Nd is the defined as the
ratio of t he average ofH (Nd,y N )
2
over t he apert ure to the
 1( Nd ), or
t he magnitude squared of t he line source field
T hus
© 2000 by H. L. Bertoni

 1 w/2
2
H (Nd,y N ) dyN 
E (R)  Nd


 w w/2
51
Polytechnic University, Brooklyn, NY
Excess Path Gain E(R)
Excess Path Gain in dB
Propagation Through Clear Space of 1.5 - 2 m
Distance in m
© 2000 by H. L. Bertoni
52
Polytechnic University, Brooklyn, NY
Rays Experiencing Only Reflection and
Transmission
P ath Gain:
PG  PRe c PTrans
  
For free space: PGO 
 4 R 
2
For rays experiencing reflect ion and transmission
:
2
2
2
  
PG 
E (R)  p (q p )  Tn (qn )
 4 R 
p
n
where R is the unfolded pat h length of t he ray
© 2000 by H. L. Bertoni
53
Polytechnic University, Brooklyn, NY
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.
© 2000 by H. L. Bertoni
54
Polytechnic University, Brooklyn, NY
Propagation Between Floors Can Involve Paths
That Go Outside of the Building
2.62 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.
9.20 m
TX

1.3 m
Direct propagation between floors
has losses:
~ 5 - 8 dB for wooden floors
1.3 m
~ 10 dB for reinforce concrete

RX
2.1 m
© 2000 by H. L. Bertoni
> 20 dB for concrete over metal
pans
7.50 m
55
Polytechnic University, Brooklyn, NY
Path Gain (dB)
Predicted vs Measured Path Gain in Hotel
Number of floors between Tx and Rx
© 2000 by H. L. Bertoni
56
Polytechnic University, Brooklyn, NY
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 (s < 6 dB)
• Propagation through clear space can give excess loss at lower
frequencies
• Propagation between floors can involve paths that lie outside of
buildings
© 2000 by H. L. Bertoni
57
Polytechnic University, Brooklyn, NY
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
© 2000 by H. L. Bertoni
58
Polytechnic University, Brooklyn, NY
Space-Time Ray Arrivals From a Mobile as
Measured at an Elevated Base Station
1800MHz in Aalborg, Denmark
© 2000 by H. L. Bertoni
59
Polytechnic University, Brooklyn, NY
Delay Spread (DS) and Angular Spread (AS)
Obtained from the Ray Simulation
From mth ray from the jth mobile
Am  j   amplitude
 m  j   arrival time delay
  j   angle of arrival at base station (measured from direction to mobile)
m
Delay Spread
2
( j)
DS


 Am(j )  m(j )   (mj )
m


2
( j) 2
m
A
 Am( j)  (mj)
2
where  (mj ) 
m
m
 Am
(j ) 2
m
Angle Spread (approximate expression for small spread)
A
( j) 2
m
( j)
AS

m

 
( j)
m
A
( j) 2
m
( j)
m

2
2
where  (mj ) 
m
© 2000 by H. L. Bertoni
 Am(j )  (mj )
m
 Am
(j ) 2
m
60
Polytechnic University, Brooklyn, NY
Standard and Coordinate Invariant Methods of
Computing AS
Standard met hod: ray arrival angle n measured from direct ion t o mobile
AS 
(
2
n
A
2
2
n
 ) An
n
   (n )An
2
where
n
n
A
2
n
n
Coordinate invarient met hod
: ray arrival anglen measured from any -xaxis
D efine t he vector
: un  (cos n , sin  n )
AS 
 180
  
u
A
2
n
 U An2
2
n
n
n
where U   (u n )An
2
n
© 2000 by H. L. Bertoni


180
2
1 U
  

A
2
n
n
61
Polytechnic University, Brooklyn, NY
Summary of DS/AS Measurements
© 2000 by H. L. Bertoni
62
Polytechnic University, Brooklyn, NY
Greenstein Model of Measured DS in Urban and
Suburban Areas
DS  T1km Rkm 
where T1km is 0.3-1.0 s and
10log
is a Gaussian random variable
wit h 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.
© 2000 by H. L. Bertoni
63
Polytechnic University, Brooklyn, NY
Direction of Arrival and Time Delay Computed
for a Mobile Location in Seoul, Korea
© 2000 by H. L. Bertoni
64
Polytechnic University, Brooklyn, NY
Distribution of Building Heights in Three Cities
© 2000 by H. L. Bertoni
65
Polytechnic University, Brooklyn, NY
Comparison of the CDF’s of Delay Spread
for Mobiles in Three Cities
( hBS is 5m above the tallest building)
© 2000 by H. L. Bertoni
66
Polytechnic University, Brooklyn, NY
Comparison of the CDF’s of Angular Spread
for Mobiles in Three Cities
( hBS is 5m above the tallest building )
© 2000 by H. L. Bertoni
67
Polytechnic University, Brooklyn, NY
Scatter Plots of DS/AS vs Distance for Munich
© 2000 by H. L. Bertoni
68
Polytechnic University, Brooklyn, NY
Scatter Plot of DS versus Distance for Seoul
Delay Spread
)
c
e
s
(
-6
Seoul
x 10
d
a 1.5
DS of a mobile
e
r
Linear Fitting
p
1
Greensteins's median DS
S
Angle Spread
y
a) 0.5
le
ee
Dr
0
g
50
e
d
(
d 60
a
e
r
p 40
S
e 20
l
g
n
A 0
50
© 2000 by H. L. Bertoni
100
150
200
250
300
Distance(m)
AS of a mobile
Linear Fitting
100
150
0.61 usec/km
350
400
450
10.67 degree/km
200
250
300
Distance(m)
69
350
400
450
Polytechnic University, Brooklyn, NY
Log Normal CDF of Delay Spreads
Seoul and Munich
Normal Probability Plot: HBS = Hmax + 2m
Seoul Std. = 3.37 dB
Munich Std. = 3.73 dB
0.997
0.99
0.98
0.95
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
-14
© 2000 by H. L. Bertoni
-12
-10
-8
-6
Delay Spread (dB usec)
70
-4
-2
0
Polytechnic University, Brooklyn, NY
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
10.9
H=95%
0.18
20.7
H=80%
0.19
24
4-7 Story Building H=+5m
0.17
16.1
H=+0m
0.18
23.3
H=95%
0.15
35.5
H=80%
0.17
37.2
12 Story Flat Bd. H=+5m
0.14
17.7
H=-5.2m
0.12
47.6
5 Story Flat Bd. H=+5m
0.15
13.9
H=-5.2m
0.12
47.3
4-7 Story Bd.
H=+5.2m
0.17
15.4
(Rayleigh Dist.)
2-3 Story
© 2000 by H. L. Bertoni
H=2m
0.23
71
64.4
Polytechnic University, Brooklyn, NY
Correlation Coefficients of DS and AS vs
Distance Range and Antenna Heights
Seoul
Munich
H=+5m
H=+2m
H=95%
H=+5m
H=+2m
H=95%
© 2000 by H. L. Bertoni
r1
0.32
0.23
0.38
0.59
0.57
0.53
r2
0.45
0.44
0.46
0.47
0.45
0.46
72
r3
0.66
0.63
0.47
0.63
0.63
0.54
r4
0.66
0.71
0.61
0.72
0.72
0.48
All rx
0.53
0.52
0.49
0.6
0.59
0.5
Polytechnic University, Brooklyn, NY
Footprint of Buildings and Locations of Base
Stations ( ) and Mobiles ( )
© 2000 by H. L. Bertoni
73
Polytechnic University, Brooklyn, NY
DS/AS of LOS and Cross Roads for
Modified Seoul at 8m/2m Height
© 2000 by H. L. Bertoni
74
Polytechnic University, Brooklyn, NY
Conclusions
• Site specific predictions are possible with accuracy
Average error ~ 1 dB, RMS error ~ 6 - 10 dB
• Requires multiple interactions for accurate predictions6 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. Bertoni
75
Polytechnic University, Brooklyn, NY