7. channel models
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7. Channel Models. 2. Medium Scale Fading : due to shadowing and obstacles. 3. Small Scale Fading : due to multipath. 1. Large Scale Fading : due to distance. Signal Losses due to three Effects:. Wireless Channel. - PowerPoint PPT PresentationTRANSCRIPT
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7. Channel Models
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Signal Losses due to three Effects:
1. Large Scale Fading: due to
distance
2. Medium Scale Fading: due to shadowing and
obstacles 3. Small Scale Fading: due to
multipath
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Wireless Channel
Several Effects:• Path Loss due to dissipation of energy: it depends on distance only• Shadowing due to obstacles such as buildings, trees, walls. Is caused by
absorption, reflection, scattering …• Self-Interference due to Multipath.
transm
rec
PP
10log10
distancelog10
Frequencies of Interest: in the UHF (.3GHz – 3GHz) and SHF (3GHz – 30 GHz) bands;
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Path Loss due to Free Space Propagation:
Transmit antenna
Receive antenna
2
4rec transmP Pd
wavelength cF
d
Path Loss in dB:
10 10 1010log 20log ( ( )) 20log ( ( )) 32.45transm
rec
PL F MHz d kmP
1.1. Large Scale Fading: Free Space
For isotropic antennas:
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2. Medium Scale Fading: Losses due to Buildings, Trees, Hills, Walls …
pp LEL
The Power Loss in dB is random:
approximately gaussian with dB126
expected value
random, zero mean
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00
10log10}{ LddLE p
Path loss exponent
Reference distance• indoor 1-10m• outdoor 10-100m
Free space loss at reference distance
dB
Average Loss
10 0log ( / )d d
0pE L L
10110 010210
20dB
10 Values for Exponent :
Free Space 2Urban 2.7-3.5Indoors (LOS) 1.6-1.8Indoors(NLOS) 4-6
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• Okumura: urban macrocells 1-100km, frequencies 0.15-1.5GHz, BS antenna 30-100m high;
• Hata: similar to Okumura, but simplified• COST 231: Hata model extended by European study to 2GHz
Empirical Models for Propagation Losses to Environment
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3. Small Scale Fading due to Multipath.
a. Spreading in Time: different paths have different lengths;
time
Transmit Receive
0( ) ( )x t t t
0t
0( ) ( ) ...k ky t h t t
1 2 30t
2138
100 10 sec3 10c
Example for 100m path difference we have a time delay
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Typical values channel time spread:
channel
0( ) ( )x t t t
1 2 MAX0t
0t
1
Indoor 10 50 sec
Suburbs 2 10 2 secUrban 1 3 secHilly 3-10 sec
n
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b. Spreading in Frequency: motion causes frequency shift (Doppler)
time
time
Transmit Receive
Frequency (Hz)
Doppler Shift
v
cf
2( ) cj F tTx t X e
2( ) cj F F tRy t Y e
for each path
cF F
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time
Transmit Receive
v
Put everything together
time
)(tx )(ty
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Re{.}
tFj Ce 2 tFj Ce 2
)(th
)(tw
)(tgT
LPF
)(tgR
LPF
( )x t ( )y t
2 ( )( )( )( ) Re ( ) cj F tFy t x t ea t
Each path has … …shift in time …
…shift in frequency …
… attenuation…
(this causes small scale time variations)
paths
channel
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2.1 Statistical Models of Fading Channels
Several Reflectors:
Transmit
v
( )x t
t ( )y t
t
1
2
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For each path with NO Line Of Sight (NOLOS):
2 ( )( )( ) Re ( )c kj F tk
kk
Fy t a e x t
v( )y t average time delay
• each time delay
• each doppler shift
k
DF F
cos( )v t
t
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)2 ( )( 22( ) Re ( )c k cFF j F j F tj t
kkky t e e x t ea
2 ( )2( ) ( )c kj F Fj F tk
k
r t a e e x t
Assume: bandwidth of signal <<
( ) ( )kx t x t … leading to this:
Some mathematical manipulation …
k/1
2( ) Re ( ) cj F ty t r t e
( ) ( ) ( )r t c t x t
with 2 ( )2( ) c kj F Fj F t
kk
c t a e e random, time varying
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Statistical Model for the time varying coefficients
2 ( )2
1
( ) c kM
j F Fj F tk
k
c t a e e
randomBy the CLT is gaussian, zero mean, with:( )c t
*0( ) ( ) (2 )DE c t c t t P J F t
D Cv vF Fc
with the Doppler frequency shift.
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Each coefficient is complex, gaussian, WSS with autocorrelation
*0( ) ( ) (2 )DE c t c t t P J F t
( )c t
and PSD
20
2 1 if | |( ) (2 ) 1 ( / )
0 otherwise
DDD D
F FFS F FT J F t F F
with maximum Doppler frequency.DF
( )S F
DF F
This is called Jakes spectrum.
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Bottom Line. This:
time
v
time
)(tx )(ty
11( )c t
( )c t
N( )Nc t
( )y t)(tx
… can be modeled as:
delays
1
N
time time
time
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For each path
( ) ( )c t P c t
• unit power• time varying (from
autocorrelation)
• time invariant• from power distribution
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Parameters for a Multipath Channel (No Line of Sight):
Time delays: L 21 sec
Power Attenuations: LPPP 21 dB
Doppler Shift: DF Hz
)()()( txtcty
( ) ( )c t P c t
)(tc WSS with Jakes PSD
Summary of Channel Model:
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Non Line of Sight (NOLOS) and Line of Sight (LOS) Fading Channels1. Rayleigh (No Line of Sight). Specified by:
Time delays
Power distribution
],...,,[ 21 NT
],...,,[ 21 NPPPP
Maximum Doppler DF
0)}({ tcE
2. Ricean (Line of Sight) 0)}({ tcE
Same as Rayleigh, plus Ricean Factor
Power through LOS
Power through NOLOS
TotalLOS PK
KP
1
TotalNOLOS PK
P
1
1
K
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Simulink Example
-K-
TransmitterGain
B-FFT
SpectrumScope
RectangularQAM
Rectangular QAMModulatorBaseband
-K-
Receiver Gain
RayleighFading
Multipath RayleighFading Channel
-K-ChannelAttenuation
BernoulliBinary
Bernoulli BinaryGenerator
Rayleigh Fading Channel Parameters
M-QAM Modulation
Bit Rate
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Set Numerical Values:
modulation
power
channel
CD FcvF Recall the Doppler Frequency:
carrier freq.
sec/103 8 m
velocity
Easy to show that: GHzChkmHzD FvF /
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Channel Parameterization
1. Time Spread and Frequency Coherence Bandwidth2. Flat Fading vs Frequency Selective Fading3. Doppler Frequency Spread and Time Coherence4. Slow Fading vs Fast Fading
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1. Time Spread and Frequency Coherence Bandwidth
Try a number of experiments transmitting a narrow pulse at different random times
)()( ittptx
)(tp
We obtain a number of received pulses
( ) ( ) ( ) ( ) ( )i i i iy t c t p t t c t p t t
1tt 1 2
it t1 2
0
0
Nt t1 2 0
)( 11 itc2 2( )ic t
( )ic t
transmitted
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Take the average received power at time it t
1 2 0
1P2P P
2|)(| tcEP
MEAN
RMS
0
10
20
Received Power
time
More realistically:
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This defines the Coherence Bandwidth.Take a complex exponential signal with frequency . The response of the channel is:
)(2)()( MEANtFjetcty
If
)(tx F
1|| RMSF 2 ( )( ) ( ) MEANj F ty t c t e
then
i.e. the attenuation is not frequency dependent
Define the Frequency Coherence Bandwidth as
15c
RMS
B
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15c
RMS
B
frequencyCoherence Bandwidth
Channel “Flat” up to the Coherence Bandwidth
This means that the frequency response of the channel is “flat” within the coherence bandwidth:
Frequency CoherenceSignal Bandwidth <>
Frequency Selective Fading
Flat Fading Just attenuation, no distortion
Distortion!!!
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Example: Flat Fading
Channel : Delays T=[0 10e-6 15e-6] secPower P=[0, -3, -8] dBSymbol Rate Fs=10kHzDoppler Fd=0.1HzModulation QPSK
Spectrum: fairly uniform
Very low Inter Symbol Interference (ISI)
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Example: Frequency Selective Fading
Channel : Delays T=[0 10e-6 15e-6] secPower P=[0, -3, -8] dBSymbol Rate Fs=1MHzDoppler Fd=0.1HzModulation QPSK
Spectrum with deep variations
Very high ISI
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3. Doppler Frequency Spread and Time Coherence
Back to the experiment of sending pulses. Take autocorrelations:
)()()( * ttctcEtR
Where:
1tt 1 2
it t1 2
0
0
Nt t1 2 0
)( 11 itc2 2( )ic t
( )ic t
1( )R t2 ( )R t
( )R t
transmitted
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Take the FT of each one:
( )S F
DF F
This shows how the multipath characteristics change with time.It defines the Time Coherence:
)(tc
916C
D
TF
Within the Time Coherence the channel can be considered Time Invariant.
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Summary of Time/Frequency spread of the channel
Time Spread
Frequency Spread ),( FtS
F
t
RMS
DF
Frequency Coherence
15c
RMS
B
Time Coherence
916C
D
TF
mean
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Stanford University Interim (SUI) Channel Models
Extension of Work done at AT&T Wireless and Erceg etal.
Three terrain types:• Category A: Hilly/Moderate to Heavy Tree density;• Category B: Hilly/ Light Tree density or Flat/Moderate to Heavy Tree density• Category C: Flat/Light Tree density
Six different Scenarios (SUI-1 – SUI-6).Found in
IEEE 802.16.3c-01/29r4, “Channel Models for Wireless Applications,” http://wirelessman.org/tg3/contrib/802163c-01_29r4.pdfV. Erceg etal, “An Empirical Based Path Loss Model for Wireless Channels in Suburban Environments,” IEEE Selected Areas in Communications, Vol 17, no 7, July 1999