wireless channels path loss and shadowing - metu...
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EE 728 METU AOY 1
Wireless Channels
Path Loss and Shadowing
A. Özgür Yılmaz - METU
EE 728 METU AOY 2
Wireless channel susceptible to
Noise
Interference
Channel impediments
Impediments change over time unpredictably due to
User movement
Environment dynamics
Channel impediments
Path loss and shadowing (~deterministic, large scale)
Multipath (~statistical, small scale)
EE 728 METU AOY 3
Free space propagation, line of sight (LOS) attenuation
An isotropic tx antenna with power Watts
Power density at distance d
If tx antenna has directivity (field radiation pattern)
Rx antenna gathers a portion of the radiated power proportional to its cross-sectional area.
Path Loss and Shadowing
tP
d2
2/
4mW
d
Pt
24 d
PG t
t
rt
t Ad
PG
24
EE 728 METU AOY 4
From EMT
Friis transmission formula
2
2
)4( fd
cGGPP rttr
Received
power
time
4
2
rr GA
EE 728 METU AOY 5
Remarks
Gains depend on antenna physical properties.
Other losses (atmosperic absorption) sometimes
effective
Path loss
Usually in dB
Used directly for satellite communications and
radio links
1
2
2
)4(
dPL
Lrttr PGGPP /
dBadBLdBrdBtdBtdBr PPGGPP )()()()()()(
EE 728 METU AOY 6
Transmitted signal
Equivalent lowpass representation of
bandpass signals
complex envelope, equivalent lowpass signal
Received signal
)(tu
EE 728 METU AOY 7
With free space path loss
Link gain comprised of transmit and receive
antenna gains
Delay due to the distance traveled by the EM
waves
})(4
Re{)( )(2
tfjletu
fd
Gctr
tG
rG
lG
2
2
)4( fd
cGGPP rttr
EE 728 METU AOY 8
Path loss (usually antenna gains excluded)
fd
cP
fd
c
P
PGP
dBL
r
tlL
4log20
4
10,
2
EE 728 METU AOY 9
Example
EE 728 METU AOY 10
Atmospheric attenuation
Oxygen, water
Rain, fog
Height dependent
http://www.rfcafe.com/references/electrical/atm_absorption.htm
EE 728 METU AOY 11
http://www.tscm.com
EE 728 METU AOY 12
Ray Tracing
Many objects in surroundings
Reflection (EMW on an object larger than wavelength)
Diffraction (path obstructed by a surface with sharp
irregularities)
Scattering (medium densely consists of objects smaller than
wavelength)
Multipath
signal
components
EE 728 METU AOY 13
Solve Maxwell’s equations with boundary
conditions
Too complex
Everything should be perfectly known
Simplification necessary
Ray tracing
Assume a finite number of reflectors with known
location and dielectric properties
EE 728 METU AOY 14
Two-ray model
x'x
Ground reflection coefficient Ground reflection coefficient
c
xx
c
l , bal GGG dcr GGG
tfj
xxj
r
lj
l cexx
etuGR
l
etuGtr
2
/)'(2/2
'
)()(
4)(
EE 728 METU AOY 15
If transmitted signal is slowly changing in
relation to ,
/)'(2,'4
22
lxxxx
eGR
l
GPP
jrl
tr
2222' dhhdhhlxx rtrt
10,2
1122 xxx
d
hhlxx rt2
'
d
hh rt
4
)()(),()( tutututu
EE 728 METU AOY 16
Asymptotic case
d is large
For earth and road surfaces
Receiver power falls off as
Independent of frequency since combination of
two rays effectively forms an antenna array
(antenna array gain does not necessarily
decrease with frequency)
0,' dlxx
rl GG
1R
4d
EE 728 METU AOY 17
mhmh
R
GG
MHz
rt
rl
2,50
1
1
900
EE 728 METU AOY 18
Example
EE 728 METU AOY 19
Ten-ray model
For urban microcells
Flat city with 90 degrees intersecting linear streets
(rectilinear streets)
Buildings along both sides of streets
Building-lined streets act as dielectric canyon to
the propagating signal.
Since signal energy is dissipated with each
reflection, more than 3 reflections can be
generally ignored.
EE 728 METU AOY 20
Typical power falloff
Some empirical studies obtained power falloff
proportional to
*
2 d
62, d
EE 728 METU AOY 21
Generalized ray tracing
Diffracted and scattered rays also taken into account
Leads to a complicated path loss model.
Simplifications needed
Local mean received power (LMRP)
Ray tracing depends on exact tx/rx locations (phase)
Only a mean received power usually required for link quality
Cellular systems utilize LMRP for power control and handoff
EE 728 METU AOY 22
Empirical Path-Loss Models
Most wireless systems operate in complex propagation environments
Cannot be accurately modeled by free space prop. or ray tracing
Path-loss models developed over the years to predict path loss in typical wireless environments
Large urban macrocells
Urban microcells
Inside buildings, …
Never forget: these are just models!
EE 728 METU AOY 23
These models based on empirical measurements
Over a given distance
In a given frequency range
For a particular geographical area or building
One must be careful in using these models for other scenarios.
Path loss, shadowing, multipath all contribute to received power in empirical measurements
Averaging to remove multipath effects
Local mean attenuation over several
Repetitions throughout the environment
Repetitions in similar environments
EE 728 METU AOY 24
Okumura Model
Large urban macrocells, 1-100kms
150-1500MHz
Base station-to-mobile measurements in Tokyo
Empirical formulas
Others obtained from Okumura’s empirical plots
Corrections proposed later
Path
loss
Median
attenuation
Antenna
height gains
Gain due to
type of
environment
EE 728 METU AOY 25
Hata model
Closed-form formula for Okumura’s model
Frequency in MHz, distance in km
Correction factor for the mobile antenna height
based on the size of the coverage area
Small-to-medium size cities
Larger cities
Other environments
K ranges from 39.54(countryside) to 40.94(desert)
MHz300cf
EE 728 METU AOY 26
Hata well approximated Okumura for
Hata does not model well the current cellular
systems with smaller cell sizes and higher
frequencies, indoor environments
COST 231 Extension to Hata
1.5-2GHz, 1-20kms
0dB for medium-sized cities, suburbs; 3dB for
metropolitan areas
Piecewise Linear (Multislope) Model
Empirical measurements are fitted to piecewise
linear functions
km1d
m10hm1m,200hm30 rt
MC
EE 728 METU AOY 27
EE 728 METU AOY 28
Indoor Attenuation Factors
Penetration through Walls
Floors
Objects
Glass, …
All these factors significantly affect indoor path loss
Floors Depends on building material
Attenuation largest for the 1st passed floor (10-20dB)
Decreases with subsequent floors (6-10dB, a few dB for larger than 4 floors)
Rappaport has details
Floor 0
1
2
EE 728 METU AOY 29
Partition losses (walls)
Losses by different studies vary widely
Very hard to make generalizations
FAF: floor attenuation factor
PAF: partition attenuation factor
EE 728 METU AOY 30
Simplified Path-Loss Model
Simplified models necessary for system design
K unitless constant depending on antenna
characteristics and average channel attenuation
reference distance for antenna far field
path-loss coefficient
0d
EE 728 METU AOY 31
Obstacles between transmitter and
receiver
Signal attenuated
Shadowing
EE 728 METU AOY 32
Random variation of received power due to blockage from objects in signal path
The exact locations and impact of the blocking objects are usually unknown => statistical models
The most common model: log-normal pdf
Gain in dB is normal.
Bad reception
Good reception
EE 728 METU AOY 33
physically impossible
Log-normal model captures the underlying
physical model most correctly when
),(log10, 210 dBdB
NP
P
P
P
r
tdB
r
t
rt PP 1
0dB
EE 728 METU AOY 34
Mathematical justification for log-normal
Attenuation due to an object
Attenuation due to many objects
CLT after taking logarithm
Shadowing is a random process
Assumption: WSS
Covariance between shadow fading at two
points separated by distance
ie
i
i
e
EE 728 METU AOY 35
Decorrelation distance is where
correlation drops to 1/e of max
Shadowing r.p.
White noise passed through a first-order IIR filter
(AR)
cX
EE 728 METU AOY 36
Combined Path Loss and Shadowing
Combination of
simplified path loss
Zero mean shadow fading creating variations in
received power
),0(~,log10log10 2
01010 dB
Nd
dK
P
PdBdB
dBt
r
dB
Slowly
changing
Rapidly
changing
EE 728 METU AOY 37
Outage probability under path loss and
shadowing
Outage: event that the received power falls below
a predetermined power level
Outage probability idea can be used to find the
cell coverage area in cellular networks.
EE 728 METU AOY 38
Example
900MHz, , K=-31.54dB, varianceof log-normal shadowing 13.29 71.3
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