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8/14/2019 1 Channel Models 2004
1/22
Channel models
Propagation channel
physical medium between antennas
Radio channel
propagation channel + transmitter and
receiver antennas
Digital channel
includes the modulation and demodulation
Radio wave propagation
In this course we concentrate on radiochannels
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Radio wave propagation
BS
Pt
Pr1
Pt
Pr2
Radio wave propagation - fading
Line-of-Sight (LOS)
Reflection ()
Scattering (>>object)
= signalwavelength
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Too complicated to use in practice
Other, simpler solutions are used
Maxwells equations
Radio wave propagation
Radio wave propagation
Usually separated in to three groups
Path loss
Shadow fading
Multipath fading
Propagation effects
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Radio wave propagation
Path loss
Shadow fading
Multipath fading
PrxPtr
d=vt
v
Prx/Ptr
d=vt
Very slow
Slow
Fast
Ptr= transmitted powerPrx = received power
Radio wave propagation
shadow fading gainsg
distance dependent
average path gain
pg
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Radio wave propagation
BS
Pt
Pr1
Pt
Pr2
Radio wave propagation
Mobile unit is distance raway from antenna
Distance dependence:
Distance dependent path loss (gp)
Shadow fading gain (gs) The multipath gain (gm)
RECEIVED POWER
rx tx p s mP P g g g = + + +
in dB scale
rx tr p s m tr P gP g g g P = =
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Radio wave propagation
Radio wave propagation (dB)
RECEIVED POWER in dB scale (No bars)
Definition of decibel (dB), dbW and dBm
1010log
gain in dB
= input power
= output power
outdB
in
dB
in
out
PG
P
G
P
P
=
=
rx tx p s mP P g g g = + + +
10
dBW = decibel-Watt
10 log1 W
WdBW
PowerPower =
10
dBm = decibel-milliWatt
10 log
1 mW
mWdBm
PowerPower =
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Radio wave propagation
Separated in to three groups
Path loss
Shadow fading
Multipath fading
Propagation effects
Distance power loss
Average path loss
10 2log ,
in dB
p pg C r =
2
2;
4p tr rx
Cg C G G
r
= =
2
2
4
rx tr tr rx
tr p tr
P P G G
rC
P g P r
=
= =
Carrier wavelength =r = propagation distance
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Shadowing
Shadowing
Shadowing
A terminal moving behind a hill, etc.
At or above 300 MHz, the amount of diffracted energy is
low shadows will be distinct
Signal will fluctuate shadow fading
Shadowing gain can be estimated
Included in Geographical Information Systems (GIS)planning tools
Finer details not known
maps have resolution of 50-100 m
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Shadowing
Path loss
Shadow fading
PrxPtr
d=vt
v
Prx/Ptr
d=vt
Very slow
Slow
Ptr= transmitted powerPrx = received power
log-normal
Shadowing
Shadowing
A common model log-normal, probability density
function
log-standard deviation 8-12 dB
2
2
( )
21( )
2
i avg
i
g g
i
i
p g e
=
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Shadowing
ShadowingA common model log-normal, probabilitydensity function
Model parametersobained
empirically.
dB power normally
distributed
Shadowing
Shadowing
log-normal
rx tr p tr
C
P g P r= =
Prx/Ptr
d=vt
Very slow
Slow
log-normal
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8/14/2019 1 Channel Models 2004
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Shadowing
Autocorrelation between dB-samples of the signal level
taken at sample rate 1/T in a mobile moving at speed v,
given by
where = correlation of two shadow fading gains,
X(r) andX(r+D)
2( )k
XR k a= /T Da =
D
Shadowing
hb =
Antenna
height
hm =
Mobile
height
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Shadowing
Okumura-Hata
Multipath fading
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Multipath fading
Multipath fading
Looking more microscopic model:
Fast multipath fading dependent on phase differencesbetween wave components
Shadow fading is slow (wavelengths 10-100 m),multipath fading very rapid (wavelengths 0.5-1 m)
Multipath fading is narrowband phenomenon, when thedelay of the multipath components < the symbol durationof the transmitted signals
For wideband signals, the received power fluctuationshave considerably lower amplitude.
Multipath fading
Line-of-Sight (LOS)
Reflection ()
Scattering (>>object)
= signalwavelength
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Effects of multipath fading
Intersymbol interference
Multipath model
Random number of multipathcomponents, each with
Random amplitude Random phase
Random Doppler shift
Random delay
Each component varies with time
Model is time-varying impulseresponse
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Multipath model
Response of a channel at time ttoimpulse at t-
Each component varies with time
Model is time-varying impulse
response
Multipath model
Response of a channel at time tto impulse at t-
t = time when impulse is observed
t-= time when impulse was put into the channel
= how long ago impulse was put into channel
( ) ( )1
, ( ) ( ( ))nN
j tn n
n
c t t e t
==
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Multipath model
Response of a channel at time tto impulse at t-
n = changes slowly
n = changes quickly
Amplitude fading
( ) ( )1
, ( ) ( ( ))nN
j t
n n
n
c t t e t
=
=
Multipath fading
Narrowband signals central limit theorem used
Received signal hasNcomponents
Herex(t) andy(t) uncorrelated Gaussian processes
(N large and incoming components have the same
statistical properties).
{ } ( )( )1 1 1
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )N N N
j t
n n n n
n n n
z t t e x t jy t x t jy t x t jy t
= = =
= = + = + = +
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Multipath fading
Amplitude
Phase
2 2( ) ( ) ( )t x t y t = +
( )( ) arctan
( )
x tt
y t =
Multipath fading
The joint probability density function
2-D Gaussian
Joint probability density function of
has uniform distribution over the interval
independent of
( ) and (t)t
2 22
2( , )
2
Marginal distribution of
p e
=
2 2- 2
2Rayleigh dist
rp() = e ibu
tion
( )t
( )t [0,2 ]
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Multipath fading
First two moments of
Compute the density of the power of
Then
[ ] 2
( )2
2 14
E
Var
=
=
( )t
2( ), (t)= ( )t t
0
0
1( )p e
=
2 2
0 ( ) 2E E = = =
ll signalcomponents have
the same energy.
The Resource Management Problem
ll signalcomponents have
the same energy
If there is a strong
component
one can compute( ) ( ) ( )z t x t jy t = + +
2 2 2( ) 2
0 2 2
0
( )
zero-order Bessel function
amplitude of the dominant, constant signal
(line-of-sight)
p I e
I
+ =
Nakami-Rice or just Rice distribution
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Multipath fading time series models
Jakes model in fading
Multipath fading Jakes model
N0 low-frequency oscillators with frequency
= Doppler shifts
m=cos(2n/N), n=1,2,...,N0, +
m are used to generate signals with frequency-shifted from a carrier frequency c using modu-lation methods. The amplitudes are =1 except mwhich is = .
n chosen so that the probability distribution ofthe resultant phase is close to uniform didtri-
bution (1/2).N0=8.
1/ 2
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Multipath fading time series models
and others
Slow correlation in fading
{ }
[ ] [ ]
1 2 1
2 2
2
1 2 1
( ) ( 1) ( 2) ( ) ( 1),
( ) ,
, , 1.8384,0.8395, 0.9634 , 2.01,
Sample instanst are with respect to spatial sample interval ,
0.1 m
s s s s s
s e
T T
e
s
s
g k a g k a g k e k b e k
Var e k
a a b
k x
x
= + +
=
= =
=