Transcript EL 675 UHF Propagation for Wireless Applications (C)

IV. Propagation Characteristics
Observed in Macro / Micro Cells
• Ray model of multipath propagation
• Effects caused by multipath for narrowband
(CW) signals
• Shadow fading
• Range dependence in macrocells and
microcells
July, 2003
1
©2003 by H.L.Bertoni
Direct Observation of Multipath at
the Mobile and at the Base Station
• Direction of arrival measurements at the mobile
• Time delay measurements
• Measurement of space-time rays
• Ray model of propagation
July, 2003
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©2003 by H.L.Bertoni
Angles of Arrival at a Street Level
- CW Measurement at 900 MHz in Tokyo using 22º spot beam antenna From base station
Rows of
buildings
Mobile locations
along street
Received signal versus azimuth for various elevations
T. Taga, "Analysis for Mean Effective Gain of Mobile Antennas in Land Mobile Radio Environments", IEEE Trans., VT 39, May 1990, p. 117.
July, 2003
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©2003 by H.L.Bertoni
Received Power Envelope P(t) for
Omnidirectional Subscriber Antennas
Paris, France
Red Bank, NJ
Rays come in clusters that decay rapidly. Successive clusters have lower amplitudes.
D.M.J. Devasirvatham, "Radio Propagation Studies in a Small
City for Universal Portable Communications,” Proc. of the
IEEE VTC'88, pp. 100-104,1988.
J. Fuhl, J-P. Rossi and E. Bonek, ”High-Resolution 3-D
Direction-of-Arrival Determination for Urban Mobile Radio,
" IEEE Trans. Ant. and Prop., vol. 45, pp. 672- 682, 1997.
July, 2003
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©2003 by H.L.Bertoni
Delay Spread for Continuous Time Signals
Mean Excess D elay

T0 
 tP t dt
0

 Pt dt
0
RMS Delay Spread

 R2 MS 
2
t

T
P t dt


0

0

 Pt dt
0
T.S. Rappaport, Wireless Communications, Prentice Hall PTR, Upper Saddle River,
NJ, p.163, 1996.
July, 2003
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©2003 by H.L.Bertoni
CDF of
for Outdoor Links
- Measured at 1800 MHz for many subscriber location in Sweden
- Signals received at base station by horizontal and vertical antennas for
vertical subscriber antenna
RMS delay spread somewhat
larger in urban areas than
in suburban areas.
Co and cross Polarization
have nearly the same RMS
delay.
RMS delay of the average
power delay profile is
approximately the same as
the mean RMS delay spread.
July, 2003
M. Nilsson, B. Lindmark, M. Ahlberg, M. Larsson and C. Beckmanm,
"Measurements of the Spatio-Temporal Polarization Characteristics of a Radio
Channel at 1800 MHz,” Proc. IEEE Vehicular Technology Conference, 1999.
6
©2003 by H.L.Bertoni
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.
July, 2003
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©2003 by H.L.Bertoni
Space-Time Rays Measured at Street Level
- 890 MHz Measurement in Paris -
- Azimuth and time delay
of arriving rays
- Measured with system
having 0.1 s time resolution
- Street runs North and South
- Many rays arrive along
the street direction
J. Fuhl, J-P. Rossi and E. Bonek, "High-Resolution 3-D
Direction-of-Arrival Determination for Urban Mobile Radio,”
IEEE Trans. Ant. and Prop., vol. 45, pp. 672- 682, 1997.
July, 2003
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©2003 by H.L.Bertoni
Space-Time Rays at an Elevated Base Station
- 1800 MHz measurements in Aalborg, Denmark - Rays arrive at base station
from a limited range of
angles
- Rays are grouped into
clusters
- Time delay between clusters
~ 1 s, representing
scattering
from more distant buildings
- Time delay within a cluster
~ 100 ns
July, 2003
K.I. Pedersen, et al., "Analysis of Time, Azimuth and Doppler Dispersion
in Outdoor Radio Channels,” Proc. ACTS, 1997.
9
©2003 by H.L.Bertoni
Delay Spread (DS) and Angle Spread (AS) for
Discrete Arrivals
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
A
(j ) 2
m
( j)
DS

m


(j )
m

( j)
m
A
( j) 2
m

2
 Am( j)  (mj)
2
where  (mj ) 
m
A
m
(j ) 2
m
m
Angle Spread (approximate expression for small spread)
A
( j) 2
m
( j)
AS

m

 
( j)
m
( j)
m
A
( j) 2
m
m
July, 2003

2
(j )
( j)
A

 m m
2
where  (mj ) 
m
A
(j ) 2
m
m
10
©2003 by H.L.Bertoni
Coordinate Invariant Method for
Computing AS
Coordinate invariant met hod
:
Ray arrival angle n measured from any x-axis
Define the vect or
: un  (a x cos n  a y sin  n )
AS 
180
  
 u n  U An2
2
 An2 
n
n
where U   (u n )An2
n
July, 2003
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
180
2
1 U
  

2
A
 n
n
©2003 by H.L.Bertoni
CDF of RMS Angle Spreads
- Measured at 1800 MHz for many subscriber locations in Sweden
- Signals received at base station by horizontal and vertical antennas for
vertical subscriber antenna
RMS angle spread is larger
in urban areas than in in
suburban areas.
Co- and cross polarization
have nearly the same RMS
angle spread.
M. Nilsson, et al., "Measurements of the
Spatio-Temporal Polarization Characteristics of
a Radio Channel at 1800 MHz,” Proc. IEEE
Vehicular Technology Conference, 1999.
July, 2003
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©2003 by H.L.Bertoni
Ray Model for Street Level Mobiles
Rays arrive from all directions in the horizontal plane and up to 45º in the
vertical direction
DL ~ 3 km
Dt ~ 10 s
Base Station
D L ~ 30 m
D t ~ 100 ns
Ray paths shown for propagation from base station to subscriber
Reverse directions of arrows for propagation from subscriber to base station
July, 2003
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©2003 by H.L.Bertoni
Ray Model of Received Voltage and Power
Complex received voltage envelope at position
x along t he st reet
V(x)e j(x )   An e  jk Ln e jn
n
where
An  amplit ude of t he ray cont ribut ion
Ln  pat h length of ray
 n  addit ional phase changes upon reflection,
scat tering
k  2 /   2 f /c
Received power
PR (x)  V (x)e
j(x ) 2
   An Am e j (n m )e  jk (Ln Lm )
n
July, 2003
m
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©2003 by H.L.Bertoni
Ray Fields Are Locally Like Plane Waves
n
Narrow family
of rays
x
Phase Front
Ln(x)
For narrow bundle of rays,An and  n are approximat ely const ant
over a distance of several wave lengt hs.
Over a small region of space t he phase front is approximat ely a
plane perpendicular to t he direction
v n of the cent ral ray.
July, 2003
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©2003 by H.L.Bertoni
Relation to Plane Wave Interference
P hase variat ion for small displacement
s about a locat ionx,
is approximat ely that of a plane wave
kLn (x  s)  kLn 0  kv n   sa x   kLn0  ksv n x
wherev n x is the x component of the unit vector
v n and
kLn 0 is t he phase of t he central ray
Received voltage is t hen
V(x)e j(x )   An e j( n  kLn 0 ) exp jks v n x 
n
T his expression is like t hat found for plane waves having
com plex am plit udeAn e
July, 2003
j ( n kL n 0 )
16
and v n x  cos n
©2003 by H.L.Bertoni
Small Area Average Power
Received power PR (x)  V (x)e
j ( x ) 2
   An Am e j ( n  m )e  jk ( Ln Lm )
n
m
T he spatial averagePR (x) of t he power overx is
1
2W
W
 P (x  s)ds 
R
W
 A A e
n
n
j(  n  m )  jk ( Ln 0  Lm0 )
e
m
m
P rovided 2W  1 k v n  v m x
1
Hence
2W
W
 exp jksv
W
n
1
2W
W
 exp jksv
W
1
for n  m,
2W
n
 v m x ds
W
 exp jksv
n
W
 v m x ds  0.
 v m x ds  n,m and PR (x)   An2
n
T hus t he spatial average power is equal t o the sum of the ray powers.
July, 2003
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©2003 by H.L.Bertoni
Summary of the Ray Model of Propagation
• Propagation to or from the mobile can take place along
multiple paths (rays)
• Multiple rays give RMS delay spreads ~ 0.5 s at R = 1 km
• Rays arrive at the mobile from all directions in the horizontal
plane, and up to 45o in the vertical plane
• Rays at the base station arrive in a wedge of width ~ ±10o
• Interference effects of multipath contributions over distances
~ 10 m are like those of plane waves
July, 2003
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©2003 by H.L.Bertoni
Effects Caused by Multipath
for CW Excitation
• Fast fading at street level
• Correlation at mobile and base station
• Other effects
– Doppler spread
– Slow time fading
– Cross polarization coupling
July, 2003
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©2003 by H.L.Bertoni
Multipath Arrivals Set Up a Standing Wave
Pattern in Space
July, 2003
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©2003 by H.L.Bertoni
Interference Effects of Multiple Rays
1
2

j(  n  m )  jk (Ln  Lm ) 
V(x)   An e
e    An Am e
e

 n m

n
Scat tered rays coming from all directions result: in
 jk Ln
j n
1. Spatial fading- as subscriber moves a dist ance Dx ~  ,
the phases k(Ln - Lm ) change by ~ 2
2. Doppler spread- a subscriber moving wit h velocituysees
1 d
u
an apparent frequency changes

k Ln  cos
2 dt

3. Frequencyfading - t he phase k(Ln - Lm )   c (Ln - Lm )
changes wit h frequency
4. Slow time fading- m oving scat terers change some
Ln 's
July, 2003
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©2003 by H.L.Bertoni
Received Signal as Omni Antenna Moves
Through Standing Wave Pattern
- Rapid Fluctuation of 20dB or more
- Separations between minima ~ 0.2 m
- Wavelength at 910 MHz is  = 0.33 m
- Slow fluctuation of the small area average
Small area average
1 L2
V (x)   V (x  s)ds
L L 2
M. Lecours, I.Y. Chouinard, G.Y. Delisle and J. Roy, ”Statistical Modeling of the Received Signal Envelope in a
Mobile Radio Channel,” IEEE Trans. on Veh. Tech., Vol. VT-37, pp. 204-212, 1988.
July, 2003
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©2003 by H.L.Bertoni
Rayleigh and Rician
Cumulative Distribution Function (CDF)
1.0
Define the random
varriable
Median value
 0.939
0.8
r  V(x) V (x)
For line- of - sight
(LO S) paths, r is
CDF
0.6
approximately Rician
For non- LOS
0.4
Rayleigh CDF
Rician CDF
0.2
K5
pat hs, r is
approximately Rayleigh
July, 2003
0
0
0.5
1.0
1.5
2.0
r
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©2003 by H.L.Bertoni
2.5
Complex Autocorrelation Function
Measures t he degree to which the signalV (x)e j (x ) received at one antenna
is predict ed by t he signalV (x  s)e j (x s) received at a second antenna
separated by a distances .
Ergodic assumption: St atist ical dependence over different em bodiements
is same as averaging over many locat ions
x.
For complex signals
 1
C(s)  
2W
W


1
 V (x)e j (x )V (x  s)e  j(x s)dx 2W  V(x)2 dx

 

W
W
where 2W   is t he correlation window,assumed to be cent ered at
x  0.
July, 2003
W
24
©2003 by H.L.Bertoni
Autocorrelation Function for Ray Fields
If t he voltage is t he sum of ray fields
V (x)e j (x )   An e jk Ln (x )e jn
n
Over dist ances of 10-20, we m ay approxim at eLn (x)  Ln 0  x(v n )x . T hen
1
2W
W
 V (x)e 
V (x  s)e j (x s)dx 
j (x )
W
  An Ame
n
Similarly
so that
e
j(  n  m )  jk (Ln0  Lm0 )  jk s(v m )x
e
e
m
1
2W
 1

2W
W
 exp jkxv
W


v

dx


n
m x

nm    An2 e jk s(v )
n x
n
W
 V (x) dx   An2
2
W
C(s)   An2e  jk s(v n ) x
n
July, 2003
e
m
   An Am e
n
j( n  m )  jk(Ln0 L m0 )  jk s(v m ) x
n
A
2
n
n
25
©2003 by H.L.Bertoni
C(s) Measured Street Level
Measurements made at
f = 821 MHz
 = 0.365 m
Signal de-correlated
after s >/4
Sample Number
0.26
1
2
4
s (m)
S-B. Rhee and G.I. ZYsman, "Results of Suburban Base Station Spatial Diversity Measurements
in the UHF Band," IEEE Trans. on Comm., vol. COM-22, pp. 1630-1636, 1974.
July, 2003
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©2003 by H.L.Bertoni
Correlation at Elevated Base Station
Ray theory for sm all
M :
CR(s)
sinks M sin  
C(s) 
ks M sin 
For   0, C(s) 1
For   90o
C(s) 
sinks M 
ks M
has first zero at
s   2 M
If  M  5 o   36 rad
thens  6 
July, 2003
Measured at 900 MHz in Liverpool, England
F. Adachi, et al., "Cross correlation between the envelopes of 900 MHz signals
received at a mobile radio base station site," IEE Proc., vol. 133, Pt. F, pp. 506512, 1980.
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©2003 by H.L.Bertoni
Summary of Fading at Both Ends of Link for an
Elevated Base Station
xB
xM
Mobile in Clutter
S
xB
/2
July, 2003
Signal
Signal
Elevated Base Station
/2
S
28
xM
©2003 by H.L.Bertoni
Measured Doppler Spread
f = 1800 MHz
K.I. Pedersen, et al., "Analysis of Time, Azimuth and Doppler Dispersion in Outdoor
Radio Channels,” Proc. ACTS, 1997.
July, 2003
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©2003 by H.L.Bertoni
Frequency Fading Due to Multipath
(910 MHz in Toronto)
Individual term s in t he
expression forV (x) go
t hrough 2 phase change
for frequency changesDf
sat isfying
2Df
Li  L j   2

c
solving forDf
c
Df 
Li  L j 
For differences in pat h
length Li  L j   1.2 km
Df  0.25 M Hz
July, 2003
E.S. Sousa, et al, “Delay Spread Measurements for the Digital Cellular
Channel in Toronto,”IEEE Trans. on VT, VT-43, pp. 837-847, 1994.
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©2003 by H.L.Bertoni
Slow Time Fading Measured by
a Stationary Subscriber (900 MHz)
For a wave incident on a
moving scatterer at angle 
relative to the velocity u of
the scatterer, the scattered
wave will undergo 2 phase
change in time such that
uDt ~ .
At walking speed u = 1
m/s, and at 900 MHz,
Dt ~ 0.33 sec.
N.H. Shepherd, et al., "Special Issue on Radio
Propagation,” IEEE Trans. On
Veh.Tech., vol. VT-37, pp. 45, 1988.
July, 2003
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©2003 by H.L.Bertoni
Local Scattering Produces
Cross-Polarization
EV
EV
EV
EV
EH
July, 2003
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EV
EH
©2003 by H.L.Bertoni
Cross Polarization Coupling Measured at Base
Stations in Sweden
Measured ratios of the
sector average power
received in the horizontal
and vertical polarized
fields (H/V) at 1800 MHz.
The error limits represent
one standard deviation
Lotse, et al., "Base Station Polarization
Diversity Reception in Macrocellular
Systems at 1800 MHz", Proc. VTC 96,
pp. 1643 - 1646
July, 2003
Environment
Kungsholmen,
urban
Kista,
suburban
Veddesta,
suburban
33
Mobile
configuration
Roof-mounted
Portable, outdoors
Portable, inside van
Portable, indoors
Roof-mounted
Portable, outdoors
Portable, inside van
Portable, indoors
Roof-mounted
Portable, outdoors
Portable, inside van
Portable, indoors
Horizontal-to
-vertical power
ratio (dB)
-7  2
-4  2
-3  2
-1  4
-8  2
-2  1
-1  1
-3  1
-13  1
-6  1
-7  1
-7  1
©2003 by H.L.Bertoni
Cross Correlation of Complex and Real Signals
Cross correlat ion of two complex functions wit h zero mean
CR 
E U (x)V  (x)

E U (x)
2

E V (x)
2

Cross correlat ion of two real functions wit h non
- zero mean
CR 
E U (x)  U (x) V (x)  V (x)

E U (x)  U (x)
 E V (x) 
2

V (x)

2
E  is the expectation value or average.
July, 2003
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©2003 by H.L.Bertoni
Fast Fading Patterns of Horizontal and Vertical
Polarization Are Uncorrelated
Cross correlations of
the signals received by
horizontally and
vertically polarized base
station antennas for a
roof mounted mobile
antenna. Integration
taken as the mobile
travels over a travel
distance 2W = 10
Lempiainen, et al.,"Experimental Results of
Cross Polarization Discrimination and Signal
Correlation Values for a Polarization Diversity
Scheme", Proc. VTC 97, pp.1498-1502.
July, 2003
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©2003 by H.L.Bertoni
Summary of Multipath Effects
• Multipath arrivals set up a standing wave pattern in space
that is perceived as fast fading by a moving mobile
• Fast fading approximates Rayleigh statistics on Non-LOS
links
• Interference patterns have correlation length of /4 at the
mobile, and 6 or greater at an elevated base station
• Multipath causes frequency fading, Doppler spread and slow
time fading
• The scattering processes that create multipath also cause
depolarization of the waves
July, 2003
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©2003 by H.L.Bertoni
Statistical Properties of the
Shadow Fading
• Separating the shadow fading from fast fading and range
dependence
• Statistical distribution of shadow fading
• Correlation distance of shadow fading
• Correlation of shadow fading for signals from different base
stations
July, 2003
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©2003 by H.L.Bertoni
How to Find Shadow Fading From
Drive Test Measurements
• Drive tests conducted over many small areas of
length > 20 at different distances R from base station
• Find Uk(R) = 10log  V(x)2  for each small area k = 1, 2, ...
• Plot Uk(R) versus log R and fit data with a least squares line
having dependence of the form
U LS (R)  10log A 10n log R
• For each sector compute
Uk (R) U LS (R). For the resulting
set of numbers form the distribution function
PU k ( R)  U LS ( R)
• The distribution function is typically found to be Gaussian
July, 2003
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©2003 by H.L.Bertoni
Separating Shadow Fading from Range
Dependence
Small area average power plotted versus logR
Uk ULS
Least Squares Fit
ULS  10log PT  10log A  n10log R
corresponds to power law
P  PT A / R n
Small Area Average
July, 2003
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©2003 by H.L.Bertoni
CDF of Shadow Fading Measured Simultaneously
at Two Frequencies (955 MHz and 1845 MHz)
Fading distributions of small
area averages normalized to
Standard deviation  for:
Small area averages
Uk(955)
Uk(1845)
U k U LS 
CDF





8.0dB
8.1dB
Difference
Mean
Uk(955)
- Uk(1845)
10.5

3.3dB
Straight line plots for dist orted scale
indicate t hatUk ULS   is Gaussian
Morgensen, et al., “Urban Area Radio Propagation Measurements at 955
and 1845 MHz for Small and Micro Cells,” Proc. Of Globecom, 1991
July, 2003
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U
k
U LS  
©2003 by H.L.Bertoni
Interpreting the Shadow Fading Statistics
U
k
U  dB
Uk (955) U(955)
Uk (1845) U(1845)
±3.3 dB
±8 dB
x
At each frequency the shadow loss fluctuates by ±8 dB about its average
Shadow loss at the two frequencies are highly correlated, differing from each
other by only ± 3.3 dB (correlation coefficient C = 0.92)
Shadow loss has weak frequency dependence.
July, 2003
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©2003 by H.L.Bertoni
Multiple Distance Scales of Signal Variation
Shadow Fading Uk U
Small Area Average
Signal Strength (dB)
Overall AverageU
Distance
/2
• Travel distances ~ /2 -- Fast fading
• Travel distances ~ 10 m ~ 20 -- Shadow fading
• Entire cell out to ~ 20 km -- Range dependence A/R n
July, 2003
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©2003 by H.L.Bertoni
Shadow Fading Statistics
• For many small areas (sectors) k = 1, 2, ... at the same
distance R from the base station
• Treat  V(x)2  over each small area as a random variable
• Define new random variable Uk = 10log  V(x)2 
• Probability distribution of Uk about its mean value U
is typically found to be the Gaussian distribution
pU  U 
1
2  SF

exp U  U  /2 2SF
2

2SF
• In cities SF  8 -10 dB
• Note: if V(x) is Rayleigh distributed, then
July, 2003
43
V(x) 
2
V (x)


4
©2003 by H.L.Bertoni
2
Autocorrelation of the Shadow Fading at
900MHz
Suburban Environment
250 m
Urban Environment
Decorrelation Distance
5m
M.Gudmundson, “ Correlation Model for Shadow Fading in Mobile Radio Systems,” Electronics Letts., vol. 27 pp. 2145-2146, 1991.
July, 2003
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©2003 by H.L.Bertoni
Cross Correlation of the Shadow Loss for Links
to Two Different Base Stations

C( )
A. Mawira, ”Models for the Spatial
Correlation Functions of the (Log)Normal Component of the Variableity of VHF/UHF Field Strength in
Urban Environment,”
IEEE 0-7803-0841-7/92, 1992.
July, 2003

45
©2003 by H.L.Bertoni
Propagation Model for Shadow Fading
Street and
side walks
As the subscriber moves along street, the received signal passes over
buildings of different height, or misses the last row of buildings
Full width of Fresnel
zone near one end of link
:
2w F  2 s
For 900 M Hz at m id st reet
s = 20 m ,  = 1 3 m
2w F  5.2 m
about the widt h of a house.
Shadow loss is not sensit ive
t o frequency.
July, 2003
Subscriber
From base station
46
©2003 by H.L.Bertoni
Summary of Shadow Fading Statistics
• Shadow fading has lognormal distribution (power in dB has a
normal distribution)
• Shadow fading has weak frequency dependence
• Correlation length of the shadow fading is on the order of
building dimensions in cities and on street length in suburban
areas
• There is correlation of the fading to different base stations
when they are located in the same direction from the mobile
July, 2003
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©2003 by H.L.Bertoni
Range Dependence of the Received Signal
• High base station antenna measurements for macrocells
( for R out to 20 km )
• Low base station antenna measurements for microcells
( for R out to 2 km )
– Line of sight(LOS) paths
– Obstructed paths
July, 2003
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©2003 by H.L.Bertoni
Range Dependence of Macrocells & Microcells
• Early system using macrocells (R < 20 km)
– Base station antennas well above buildings
n
– Isotropic propagation with range variation A/R
– Hexagonal tessellation of plane
– Frequency reuse independent of antenna height
• Modern systems using microcells (R < 2 km)
– Base station antenna near (or below) rooftops
– Anisotropic propagation- A, n depend on:
• Direction of propagation relative to street grid
• Base station antenna height, location relative to buildings
– Cell shape is open issue
July, 2003
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©2003 by H.L.Bertoni
Scale of City Blocks Compare to Cell Size
FLUSHING
EAST
ELMHURST
JACKSON HEIGHTS
FLUSHING
CORONA
MEADOWS
ELMHURST
UTOPIA
HILLCREST
REGO PARK
0km
July, 2003
1
2
3
4
50
©2003 by H.L.Bertoni
Measurements of Propagation Characteristics in
Different Cities for High Base Station Antennas
• Field Strength and Its Variability in VHF and UHF
Land-Mobil Radio Service
July, 2003
51
©2003 by H.L.Bertoni
Range Dependence Measured in Tokyo
Y. Okumura, E. Ohmori, T. Kawano and K. Fukuda, “Field Strength and Its Variability in VHF and UHF Land-Mobile
Radio Service,” Re. Elec. Com. Lab., vol. 16, pp. 825-873, 1968.
July, 2003
52
©2003 by H.L.Bertoni
Range Dependence Measurements in
Philadelphia at 820 MHz
Base station in a high rise
Building environment
Base station in a residential
environment
G.D. Ott and A. Plitkins, “Urban Path-Loss Characteristics at 820 MHz,” IEEE Trans. Veh. Tech., vol. VT-27, pp.
189-197, 1978.
July, 2003
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©2003 by H.L.Bertoni
Range Dependence for Composite of Five Base
Station Sites in Philadelphia at 820 MHz
P ower law variation
PdB m  PT dB m  10logA  n10logR
or
P  PT A R
n

P at h loss index
n  3.68
G.D. Ott and A. Plitkins, “Urban Path-Loss Characteristics
at 820 MHz,” IEEE Trans. Veh. Tech., vol. VT-27, pp. 189197, 1978.
July, 2003
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©2003 by H.L.Bertoni
Definition of Path Loss and Path Gain
P ower Received
P ower T ransmit t ed
( PG is always less than 1 )
PG  P at h Gain 
P ower T ransmit t ed 1

P ower Received PG
( PL is always greater than 1 )
PL  P at h Loss 
When expressed in dB,PGdB  10logPG  L where
L  10logPL
If P  PT A / R n , then PGdB  10logA 10nlogR and
L  10logA  10nlogR
July, 2003
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©2003 by H.L.Bertoni
Hata-Okumura Model for Median Path Loss
•
Urban area:
L50 = 69.55 + 26.16 log fc - 13.82 log hb- a(hm) + (44.9-6.55 log hb) log R
where
fc
frequency (MHz)
L50
mean path loss (dB)
Hb
base station antenna height
a(hm) correction factor for mobile antenna height (dB)
R
distance from base station (km)
– The range of the parameters for which Hata’s model is valid is
150  fc  1500 MHz
30  hb  200 m
1  hm  10 m
1  R  20 km
July, 2003
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©2003 by H.L.Bertoni
Hata-Okumura Model (cont.)
• Urban area (cont.):
– For a small or medium-sized city:
a(hm)=(1.1 log fc - 0.7) hm - (1.56 log fc - 0.8 ) dB
– For a large city:
a(hm)=8.29(log 1.54 hm)2 - 1.1 dB, fc  200 MHz
or
a(hm)=3.2(log 11.75 hm)2 - 4.97 dB, fc  400 MHz
• Suburban area:
   f c 2

L50  L50 urban - 2log
 5.4  dB



28

 

• Open Area:
L50 = L50(urban) - 4.78 (log fc)2+18.33 (log fc) -40.94
July, 2003
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©2003 by H.L.Bertoni
Range index of Hata-Okumura Model
n = ( 44.9 - 6.55 loghb ) / 10
3.84
2.98
20
July, 2003
200
58
hb (m)
©2003 by H.L.Bertoni
Measurement of Path Loss for
Low Base Station Antennas of Microcells
July, 2003
59
©2003 by H.L.Bertoni
Drive Routes for Microcell Measurements
in San Francisco
• LOS drive route
• Staircase drive route
• Zig-Zag drive route
– Transverse paths - directly over buildings
– Lateral paths - to side streets perpendicular to the LOS street
July, 2003
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©2003 by H.L.Bertoni
Mission District of San Francisco
July, 2003
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©2003 by H.L.Bertoni
Drive Routes In the Mission District
July, 2003
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©2003 by H.L.Bertoni
Received Signal on LOS Route in Mission
f = 1937 MHz, hBS= 3.2 m, hm = 1.6 m
Telesis Technology Laboratories, Experimental License Progress Report to the FCC, August, 1991.
July, 2003
63
©2003 by H.L.Bertoni
Received Signal on Staircase Route in
the Sunset District vs. Distance Traveled
f = 1937 MHz, hBS= 8.7 m, hm = 1.6 m
Telesis Technology Laboratories, Experimental License Progress Report to the FCC, August, 1991.
July, 2003
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©2003 by H.L.Bertoni
Regression Fit to Received Signal Versus R
on Staircase Route in Sunset District
Telesis Technology Laboratories, Experimental License Progress Report to the FCC, August, 1991.
July, 2003
65
©2003 by H.L.Bertoni
Received Signal on Zig-Zag Route in
the Sunset District vs. Distance Traveled
f = 1937 MHz, hBS= 8.7 m, hm = 1.6 m
Telesis Technology Laboratories, Experimental License Progress Report to the FCC, August, 1991.
July, 2003
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©2003 by H.L.Bertoni
Regression Fit to Received Signal Versus R on the
Transverse Portions of the Zig-Zag Route
Telesis Technology Laboratories, Experimental License Progress Report to the FCC, August, 1991.
July, 2003
67
©2003 by H.L.Bertoni
Regression Fit to Received Signal Versus R
on the Lateral Portions of the Zig-Zag Route
Telesis Technology Laboratories, Experimental License Progress Report to the FCC, August, 1991.
July, 2003
68
©2003 by H.L.Bertoni
Comparison of Regression Fits on
Different Paths in Sunset
H.H. Xia, et al., “Microcellular Propagation Characteristics for Personal Communications in Urban and
Suburban Environments,” IEEE Trans. Veh. Tech., vol. 43, no. 3, pp. 743-752, 1994.
July, 2003
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©2003 by H.L.Bertoni
Har-Xia-Bertoni Model for
Low Base Station Antennas
• Expressions fit to regression lines for:
– 900 MHz and 1900 MHz
– hBS = 3.2, 8.7 and 13.4 m
– hm = 1.6 m
• Separate expressions for:
– LOS paths
– Obscured paths in residential environment
– Obscured paths in high rise environment
July, 2003
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©2003 by H.L.Bertoni
Har-Xia-Bertoni Model for LOS Paths
f G  frequencyin GHz
Rk  distance in km
4hb hm
Rbk 
1000
hm  1.6 m
Near - in segment ( Rk  Rbk )
LRk   81.14  39.40 log f G  0.09 log hb  15.80  5.73log hb  log Rk
Far - out segment ( Rk  Rbk )
LRk   48.38  32.10 log Rbk   45.70 log f G  25.34  13.90 log Rbk  log hb
 32.10  13.90 log hb  log Rk
July, 2003
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©2003 by H.L.Bertoni
Har-Xia-Bertoni Model for Obscured Paths in
Residential Environments
f G  frequencyin GHz
Rk  distance in km
Dh  height of base station above (below )buildings in m
Combined staircaseand transversepaths :
LRk   138.31 38.88log f G   13.74  4.58log f G  sgn Dh  log1  Dh 
 40.06  4.35sgn Dh  log1  Dh  log Rk
Lateral Paths :
LRk   127.39  31.63log f G   13.05  4.35log f G  sgn Dh  log1  Dh 
 29.18  6.70sgn Dh  log1  Dh  log Rk
July, 2003
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©2003 by H.L.Bertoni
Har-Xia-Bertoni Model for Obscured Paths
in High Rise Environments
fG  frequency in GHz
Rk  distance in km
hb  height of base st at ion above ground in m
Combined st aircase paths and transverse paths
LRk   143.21 29.74log f G  0.99loghb  47.23 3.72loghb logRk
Lateral paths
LRk   135.41 12.49log fG  4.99loghb  46.84 2.34loghb logRk
July, 2003
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©2003 by H.L.Bertoni
Comparison of Hata and Har Models
For base stat ion antenna heights outside measurement
limit s of bot h models
Dh = 9 m
For f  1 GHz
hBS = 20 m
hm = 1.6 m
Hata urban area
L  69.55 26.16log1000 13.82log20 44.9  6.55log20logRk
 130.0  36.4logRk
Har combined st aircase and transverse (resident ial)
L  138.31 13.74log(1 9)  40.06 4.35log(1 9)logRk
 124.6  35.7logRk
T wo models go into each other for middle height base station ant ennas
July, 2003
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©2003 by H.L.Bertoni
Summary of Range Dependence
• Range dependence over large distances takes the form
(PR/PTr) = A/Rn in watts or
10log (PR/PTr) = 10logA + 10nlogR in dB
• The slope index n ranges between 3 and 4 for base station
antennas above the rooftops, and is the same for all cities
• Simple formulas fit to measurements give the path gain or
path loss as a function of antenna height and frequency
• Measurements made with high base station antennas match
continuously with measurements made with low antennas
July, 2003
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©2003 by H.L.Bertoni