Ray Tracing A radio signal will typically encounter multiple objects and will be reflected,...
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Transcript of Ray Tracing A radio signal will typically encounter multiple objects and will be reflected,...
Ray Tracing
A radio signal will typically encounter multiple objects and will be reflected, diffracted, or scattered
These are called multipath signal components
• Represent wavefronts as simple particle
• Geometry determines received signal from each signal component
• Typically includes reflected rays, can also include scattered and diffracted rays
• Requires site parameters• Geometry• Dielectric properties
• Error is smallest when the receiver is many wavelengths from the nearest scatterer and when all the scatterers are large relative to a wavelength
• Accurate model under these conditions
• Rural areas
• City streets when the TX and RX are close to the ground
• Indoor environments with adjusted diffraction coefficients
• If the TX, RX, and reflectors are all immobile, characteristics are fixed
• Otherwise, statistical models must be used
Two – Ray Model
Used when a single ground reflection dominates the multipath effects.
Approach:
• Use the free – space propagation model on each ray
• Apply superposition to find the result
c
x x'j j
r j f tray
G u t e R G u t er t Re e
x x'
2 2
22 4
l
l
l
x x'
c
l time delay of the ground reflection relative to the LOS ray
a bG G G l
product of the transmit and receive antenna field radiation patterns in the LOS direction
r c dG G G product of the transmit and receive antenna field radiation patterns corresponding to x and x’, respectively
R = Ground reflection coefficient
c
x x'j j
r j f tray
G u t e R G u t er t Re e
x x'
2 2
22 4
l
l
l
c
x x'j j
r j f tray
G u t e R G u t er t Re e
x x'
2 2
22 4
l
l
l
Delay spread = delay between the LOS ray and the reflected ray
x x'
c
l
c
x x'j j
r j f tray
G u t e R G u t er t Re e
x x'
2 2
22 4
l
l
l
If the transmitted signal is narrowband wrt the delay spread
uB u t u t 1
c
x x'j j
r j f tray
G u t e R G u t er t Re e
x x'
2 2
22 4
l
l
l
jr
r t
G R G eP P
x x'
22
4l
l
x x'
2
l phase difference between the two received signal components
d = Antenna separation
h t = Transmitter height
h r = Receiver height
t r t rx x' h h d h h d 2 22 2l
t r t rx x' h h d h h d 2 22 2l
When d is large compared to h t + h r :
x x'
2
lExpand into a Taylor series
t rh hx x'
d
4
2l
The ground reflection coefficient is given by
sin ZR
sin Z
rr
cosZ
2
vertical polarization
rZ cos 2 horizontal polarization
r 15 for ground, pavement, etc...
For very large d:
l rx x' d , , G G , R 0 1l
t rt rr t t
G G h hh hP P P
d d d
2 22
2
4
4l l
r t t rP dBm P dBm log G log h h log d 10 10 1010 20 40l
t r
r t
G h hP P
d
2
2
l
• As d increases, the received power
• Varies inversely with d 4
• Independent of
f = 900 MHz
R = - 1
h t = 50 m
h r = 2 mG l = 1
G r = 1
P t = 0 dBm
The path can be divided into three segments
1. d < h t
• The two rays add constructively
• Path loss is slowly increasing
• Path loss td h
2 2
1
t r
t rt
d h h
for h hd h
22
2 2 2
1 1
l
l
2. h t < d c
• Wave experiences constructive and destructive interference
• Small – scale (Multipath) fading
• If power is averaged in this area, the result is a piecewise linear approximation
3. d c < d
• Signal power falls off by d – 4
• Signal components only combine destructively
t rh hx x'
d
4
2l
To find d c , set
t rc
h hd
4
• In segment 1, d < h t power falls off by
• In segment 2, h t < d < d c power falls off by – 20 db/decade
• In segment 3, d c < d, power falls off by – 40 db/decade
• Cell sizes are typically much less than d c and power falls off by t/ h 21
t/ h 21
Problem 2 – 5
Find the critical distance, d c , under the two – ray model for a large macrocell in a suburban area with the base station mounted on a tower or building (h t = 20 m), the receivers at height h r = 3 m, and f c = 2 GHz. Is this a good size for cell radius in a suburban macrocell? Why or why not?
Solution
c. m
f
8
9
3 100 15
2 10
t rc
h hd . km
. 4 4 20 3
1 60 15
Ten – Ray Model (Dielectric Canyon)
• Assumptions:
• Rectilinear streets
• Buildings along both sides of the street
• Transmitter and receiver heights close to street level
• 10 rays incorporate all paths with 1, 2, or 3 reflections
• LOS (line of sight)
• GR (ground reflected)
• SW (single wall reflected)
• DW (double wall reflected
• TW (triple wall reflected)
• WG (wall – ground reflected)
• GW (ground – wall reflected)
Overhead view of 10 – ray model
i
i c
xjj
i x i j f tray
i i
R G u t eG u t er t Re e
x
22
92
1014
l
l
l
x i = path length of the i th reflected ray
ii
x
c
lix
G Product of the transmit and receive antenna gains of the i th ray
Assume a narrowband model such that
iu t u t for all i
i
i
ji x
r ti i
R G eGP P
x
22
9
14l
l
ii
x
2l
• Power falloff is proportional to d - 2
• Multipath rays dominate over the ground reflected rays that decay proportional to d - 4
General Ray Tracing
• Models all signal components– Reflections– Scattering– Diffraction
• Requires detailed geometry and dielectricproperties of site– Site specific
• Similar to Maxwell, but easier math• Computer packages often used• The GRT method uses geometrical optics to trace
the propagation of the LOS and reflected signal components
• Diffraction occurs when the transmitted signal "bends around" an object in its path
• Most common model uses a wedge which is asymptotically thin
• Fresnel knife – edge diffraction model
Diffraction
Shadowing: Diffraction and Spreading
For h small wrt d and d', the signal must travel an additional distance d
h d d 'd
d d '
2
2
The phase shift is
dv
d d 'v h
d d '
22
2
2
d d 'v h
d d '
2 is called the Fresnel – Kirchhoff
diffraction parameter
Approximations for the path loss relative to LOS are
. v
L v dB log . . v . v
log . e v
log . . . . v v .
.log v .
v
10
0 9510
2
10
10
20 0 5 0 62 0 8 0
20 0 5 0 1
20 0 4 0 1184 0 38 0 1 1 2 4
0 22520 2 4
Scattering
c
s s'j
s j f tG er t Re u t e
ss'
2
2
3
24
r t sP dBm P dBm log G log log
log log s log s'
10 10 10
10 10 10
10 20 10
30 4 20 20
• Okumura model• Empirically based (site/freq specific)• Awkward (uses graphs)
• Hata model• Analytical approximation to Okumura model
• Cost 136 Model: • Extends Hata model to higher frequency (2 GHz)
• Walfish/Bertoni:• Cost 136 extension to include diffraction from
rooftops
Simplified Path – Loss Model
r t
dP P K
d
0
r t
dP dBm P dBm K dB log
d
10
0
10
K = dimensionless constant that depends on the antenna characteristics and the average channel attenuation
d 0 = reference distance for the antenna far field
= path – loss exponent
LOS, 2 – ray model, Hata model, and the COST extension all have this basic form
Generally valid where d > d 0
d 0 = 1 – 10 m indoors
= 10 – 100 m outdoors
K dB logd
100
204
General approach:
• Take data at three values of d
• Solve for K, d o , and