7. Channel Models. Signal Losses due to three Effects: 1. Large Scale Fading: due to distance 2....
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Transcript of 7. Channel Models. Signal Losses due to three Effects: 1. Large Scale Fading: due to distance 2....
7. Channel Models
Signal Losses due to three Effects:
1. Large Scale Fading: due to
distance
2. Medium Scale Fading: due to shadowing and
obstacles3. Small Scale Fading: due to
multipath
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
P
P10log10
distancelog10
Frequencies of Interest: in the UHF (.3GHz – 3GHz) and SHF (3GHz – 30 GHz) bands;
Path Loss due to Free Space Propagation:
Transmit antenna
Receive antenna
2
4rec transmP Pd
wavelength c
F
d
Path Loss in dB:
10 10 1010log 20log ( ( )) 20log ( ( )) 32.45transm
rec
PL F MHz d km
P
1.1. Large Scale Fading: Free Space
For isotropic antennas:
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
00
10log10}{ Ld
dLE 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 2
Urban 2.7-3.5
Indoors (LOS) 1.6-1.8
Indoors(NLOS) 4-6
• 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
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 10sec
3 10c
Example for 100m path difference we have a time delay
Typical values channel time spread:
channel
0( ) ( )x t t t
1 2 MAX0t
0t
1
Indoor 10 50 sec
Suburbs 2 10 2 sec
Urban 1 3 sec
Hilly 3-10 sec
n
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
time
Transmit Receive
v
Put everything together
time
)(tx )(ty
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
2.1 Statistical Models of Fading Channels
Several Reflectors:
Transmit
v
( )x t
t ( )y t
t
1
2
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
)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
Statistical Model for the time varying coefficients
2 ( )2
1
( ) c k
Mj F Fj F t
kk
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 C
v vF F
c with the Doppler frequency shift.
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.
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
For each path
( ) ( )c t P c t
• unit power• time varying (from
autocorrelation)
• time invariant• from power distribution
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:
Non Line of Sight (NOLOS) and Line of Sight (LOS) Fading Channels
1. 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
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
Set Numerical Values:
modulation
power
channel
CD Fc
vF Recall the Doppler Frequency:
carrier freq.
sec/103 8 m
velocity
Easy to show that: GHzChkmHzD FvF /
Channel Parameterization
1. Time Spread and Frequency Coherence Bandwidth
2. Flat Fading vs Frequency Selective Fading
3. Doppler Frequency Spread and Time Coherence
4. Slow Fading vs Fast Fading
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
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:
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
1
5cRMS
B
1
5cRMS
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!!!
Example: Flat Fading
Channel : Delays T=[0 10e-6 15e-6] sec
Power P=[0, -3, -8] dB
Symbol Rate Fs=10kHz
Doppler Fd=0.1Hz
Modulation QPSK
Spectrum: fairly uniform
Very low Inter Symbol Interference (ISI)
Example: Frequency Selective Fading
Channel : Delays T=[0 10e-6 15e-6] sec
Power P=[0, -3, -8] dB
Symbol Rate Fs=1MHz
Doppler Fd=0.1Hz
Modulation QPSK
Spectrum with deep variations
Very high ISI
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
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
9
16CD
TF
Within the Time Coherence the channel can be considered Time Invariant.
Summary of Time/Frequency spread of the channel
Time Spread
Frequency Spread ),( FtS
F
t
RMS
DF
Frequency Coherence
1
5cRMS
B
Time Coherence
9
16CD
TF
mean
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.pdf
V. 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