cours2 - fundamentals of propagation modelling (dr mischa dohler)
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8/2/2019 Cours2 - Fundamentals of Propagation Modelling (Dr Mischa DOHLER)
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research & development
Fundamentals of
Propagation ModellingPathloss, Shadowing & Fading
Dr Mischa DohlerSenior ExpertFT R&D
21 November 2006
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MastersPHY Mischa Dohler 2/42 research & development France Telecom Group
Who am I working for?
4200 researchers, technicians and engineers on 17 sites worldwide
San FranciscoBoston France
(8 labs)London WarsawBeijing Guangzhou
New Delhi
Tokyo
Seoul
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MastersPHY Mischa Dohler 3/42 research & development France Telecom Group
My Contact Details
My preferred mode of communication is email: mischa.dohler@orange-ftgroup.com
mischa@ieee.org
However, you can also call me on: office: +33 4 76 76 45 14
mobile: +33 6 74 70 86 75
You can also visit me for discussions at: France Tlcom R&D
28 Chemin du Vieux Chne
38243 Meylan Cedex
France
You can see my research interests by: googelling me
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MastersPHY Mischa Dohler 4/42 research & development France Telecom Group
My Recommendations
Some good books related to this lecture are: Simon Saunders Antennas & Propagation
William Jakes Microwave Mobile Communications
Kaveh Pahlavan Wireless Information Networks
Some good articles related to this lecture are: A. Neskovic, N. Neskovic, and G. Paunovic, "Modern Approaches in Modeling of
Mobile Radio Systems Propagation Environment," IEEE Comm. Surveys, 2000.
H. L. Bertoni, et al., "UHF Propagation Prediction for Wireless PersonalCommunications," Proc. IEEE, Sept. 1994, pp. 1333-1359.
V. Erceg et al., "Urban/Suburban Out-of-Sight Propagation Modeling, IEEECommun. Magazine, June 1992, pp. 56-61.
Some good online articles related to this lecture are: http://www.deas.harvard.edu/~jones/es151/prop_models/propagation.html
http://www.ictp.trieste.it/~radionet/2000_school/lectures/carlo/linkloss/INDEX.HTM
and then there is always http://en.wikipedia.org/
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Some Important Basics
Introduction to Wireless Channels
Pathloss, Shadowing, Fading
The Big Picture
1
2
3
Lecture's Outlook
4
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1Some Important Basics
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Scenario [1/2]
We consider the following scenario
Base Station: BS
Mobile Station: MS
Line-of-Sight: LOS
non-LOS: nLOS
MS
(LOS)
BS
MS
(nLOS)
3. Scattering
1.Free-Space
Propagation
2. Reflection
4. Diffraction
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Scenario [2/2]
and would like to understand why the received power is like this:
1000 2000 3000 4000 5000 6000 7000 8000 900010000-120
-110
-100
-90
-80
-70
-60
-50
Distance [log of meter]
ReceivedPower[dBW]
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Presupposed Basics [1/4]
To really understand these phenomena, one needs a profoundknowledge in Physics and Mathematics.
From the world of Physics, I would like you to be familiar with: formulation of electromagnetic propagation
reflection, scattering and diffraction
Many subsequent processes are random; hence, be familiar with: notions of statistics (PDF, CDF)
moments, mean, variance, etc.
dependence, correlation, etc.
Many processes are in addition stochastic; hence, be familiar with: notions of coherence, etc.
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MastersPHY Mischa Dohler 10/42 research & development France Telecom Group
Presupposed Basics [2/4]
Just to make sure, some revisions on statistics: a random process (left) leads to a histogram (middle) and a mathematical
abstraction in form of the probability density function, PDF (right)
the most important factors about the PDF are mean, std/variance, and shape
in nature, unbounded PDFs are Gaussian and bounded PDFs are uniform
typical half-bounded PDFs: Rayleigh, Rice, Nakagami, lognormal, Gamma, etc.
0 1000 2000 3000 4000 5000 6000 7000 8000
.
.
.
0 0.5 1 1.5 2 2.50
20
40
60
80
100
120
140
160
180
200
0 0.5 1 1.5 2 2.5 3 3.5 40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2
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MastersPHY Mischa Dohler 11/42 research & development France Telecom Group
Presupposed Basics [3/4]
Just to make sure, some revisions on electromagnetic (EM) waves: E & H are in-phase and occur together; hence, only E-field is considered normally
E-wave oscillates: in time with angular frequency = 2f = 2/T
in space with spatial frequency k = 2/
f is the frequency in [Hz], T the period in [s], and = c/f the wavelength in [m]
E = E0 cos(t kr); for convenience, we write E = E0 ej (t kr)
E
x
y
z
r >> =90
H
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Presupposed Basics [4/4]
Just to make sure, some revisions on decibels: unit was introduced by A. Graham Bell, who experimented with human hearing
he noted that we (as well as nature and machines) feel 'logarithmically'
We hence have the following units: 10 log10(X) = X in dB
10 log10(1 mW) = 0 dBm
10 log10(1 W) = 0 dBW
0 dBW = 30 dBm
This unit is VERY common in Engineering: dBi relates the actual radiated signal power to the one of a isotropic antenna
dBc relates the signal power at a given spectral point to the one of the carrier
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2Introduction to Wireless Channels
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Sources of Signal Distortions
A useful signal can get distorted by: noise (thermal, shot): additive
interference (self, other): additive
wireless channel: multiplicative
Simplified, we can hence write for the received signal: received = channel * transmitted + noise + interference
Note! noise and interference is always bad news, the channel not always (cf MIMO)
modern communication systems are dominated by interference and channel transmitting a stronger signal does not counteract the channel; why?
for the additive components, important is the ratio between signal power andnoise + interference powers (SNR, SIR, SINR)
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Propagation Mechanisms: free space propagation (distance dependent)
reflection and refraction (from surfaces, into buildings)
diffraction (from roof edges)
scattering (from surrounding trees)
Propagation Conditions: line-of-sight (LOS) (great visibility between Tx & Rx)
non LOS (nLOS) (no direct visibility between Tx & Rx)
obstructed LOS (oLOS) (small obstacle in-between Tx & Rx)
Distortions: Doppler effect (caused by mobility in the channel)
multipath propagation (signals arriving via different paths)
Wireless Channel Taxonomies [1/7]
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Propag. Mechanisms Overview [2/7]
Note! all 5 effects result from the same set of equations: Maxwell's Equations
the equations are very complicated and not useful for every problem
for different ratios between object size and wavelength, different effects occur
Occurrence (given surface undulations h, object size dand wavelength ): free-space propagation: always occurs for any dand
reflection/refraction: >> h, d>>
diffraction: in the order of the curvature of the edge
scattering: or < h
In this course, we will not deal with diffraction and scattering, and
only briefly dwell on free-space propagation and the effect of reflection.
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Friis' Transmission Equation: , assuming
PRxto be received and PTxtransmitted powers
GRxto be receive and GTxtransmit antenna gains
dthe distance between Tx and Rx, and = c/f the wavelength
perfect matching of Tx and Rx antennas, no multipath and aligned polarisation
In dB, we hence get: Prx=Ptx+Gtx+Grx+148dB 20log(f) 20log(d)
PRxdecreases
with -20dB/dec:
Propag. Mechanisms Free-Space [3/7]
2
4
=
dGGPP RxTxTxRx
PRx[dBm]
d [log]100m1km 10km
-20
-40
-60
gradient of -20dB/dec
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Fresnel's Reflection Equation: , assuming
Rto be the generally complex reflection coefficient,
which depends on the impinging angle and the involved materials
since is often not known, an average reflection coefficient is given
What is the power loss in dB, if the average reflection coefficient is R= 0.3 on a dry day: -10.5 dB
R= 0.6 on a rainy day: -4.4 dB
The average Rwill also have a variance. With an increasing numberof consecutive reflections, let's say N= 10: What happens to the average overall reflection coefficient?
What happens to the variance of this overall reflection coefficient?
Propag. Mechanisms Reflection [4/7]
2RPP TxRx =
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LOS (opposite for nLOS) has the following properties: advantage: strong signal disadvantage LOS: strong interference
oLOS is something in-between LOS and nLOS.
Propagation Conditions Overview [5/7]
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Doppler Formula: , where
c= 3 108 m/s is the speed of light, and
vis the summed speed of the Tx and/or Rx and/or (!) reflecting objects
e.g., little movement in the channel (left), more movement in the channel (right):
Distortions Doppler Effect [6/7]
+=c
vff originalperceived 1
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-25
-20
-15
-10
-5
0
5
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-25
-20
-15
-10
-5
0
5
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Assume we send two symbols of duration Ts; then, objects along theellipses with Tx & Rx in the foci, yield same propagation delays: intra-symbol interference: - overlap of symbol replicas within symbol
duration (same colour below)
- this leads to mutual cancellation
inter-symbol interference: - overlap of symbol replicas belonging to
different symbols (grey shading below)
Distortions Multipath Propag. [7/7]
symbol#1
symbol#2
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We incorporate now all effects we encountered, to arrive at:
where the r's are the respective distances, the v's the respective speeds
the R's the respective reflection coefficients, E0 is measured at 1 meter distance
and MPCiis the number of multipath components which has been reflected itimes
Summed Contributions [1/3]
( )( ) ( )( )
( )( )
( )( )
+
=
+
++
=
++
+
=
+++==
refl.i MPCk
)(/)(12
,1
,0
i
)(/)(12
2,
2,1,0
i
)(/)(12
1,
1,0
)(/)(12
0
0
i
,,
2,2,
1,1,00
)(
1)(
...)(
1)()(
)(
1)(
)(
1
...refl.twicerefl.once)LOS()(
trkctvfj
ki
i
l
li
trkctvfj
i
ii
trkctvfj
i
i
trkctvfj
MPCntotal
kikic
iic
iicc
e
tr
mtRE
etr
mtRtRE
etr
mtREe
tr
mE
EtE
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The resulting signal strength and hence power are random, becausethe following components in the previous equation are random: trajectory / location
number of MPCs
number of reflections per MPC
reflections coefficient per reflection
speeds (Tx, Rx, clutter) This is very complex! Luckily, rearranging the equation, we can
decompose it into 3 multiplicative fading components:
large-scale fading (pathloss)
medium-scale fading (shadowing)
small-scale fading (fading, fast fading)
Summed Contributions [2/3]
n
j
n
l
l
ki
totalneAtR
tr
mEtE
)(
)(
1)(
,0
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Summed Contributions [3/3]
The sum in dB (i.e. product in linear scale!) of pathloss (blue),shadowing (red), fading (green) is our total channel (black).
1000 2000 3000 4000 5000 6000 7000 8000 900010000-140
-120
-100
-80
-60
-40
-20
0
20
Distance [log of meter]
ReceivedPower[dBW]
fading +
shadowing +
pathloss =
total channel
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3Pathloss, Shadowing and Fading
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Pathloss Overview [1/5]
Pathloss has the following characteristics: function of distance (as well as frequency, environment, antenna heights)
it is a 'deterministic' effect
is obtained by averaging over 1000
1000 2000 3000 4000 5000 6000 7000 8000 900010000-120
-110
-100
-90
-80
-70
-60
-50
Distance [log of meter]
R
eceivedPower[dBW]
example gradient:-20 dB/dec
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Pathloss Degrees of Modelling [2/5]
Free-space pathloss model: loss of -20dB/decade distance
very simple model, but not very realistic
application in satellite channels and over short LOS distances
Single-slope pathloss model:
n= 1.5 (waveguides), n= 24 (LOS + clutter), n= 46 (nLOS + clutter) simple and more accurate model, but correct reference point d0has to be found
application in WLANs, interference power in cellular systems, etc.
Dual-slope pathloss model: d < dbreakpoint: n1 = 2 (normally), d > dbreakpoint: n2= 26 (nLOS + clutter)
simple and more accurate model, but requires strong LOS + once refl. component
application in long-range WLANs and cellular systems
( ) ( )2
00
=
d
ddPdP
( ) ( ) ( )ndddPdP 00 =
( ) ( ) ( ) ( ) ( ) ( )21
,00n
BPBP
n
dddPdPdddPdP ==
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Pathloss Degrees of Modelling [3/5]
Deterministically simulated pathloss behaviour: ray-tracing type tools determine field behaviour for given scenario
very complex modelling approach, and not necessarily a better model
application for very specific models (close to head, within mobile phone, etc)
Empirically-fitted pathloss model:
real measurements taken with P(d0) and n, n1, n2 fitted to give best match difficult to obtain, very simple model and fairly realistic
application in simulators, planning and optimisation tools, etc
Really measured pathloss behaviour: real measurements taken and used for planning and optimisation tools
complex and memory-consuming model, but very accurate
used by all operators and within available commercial tools
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Pathloss Important Models [4/5]
Two-Ray Pathloss Model (dual-slope model):
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Pathloss Important Models [5/5]
Okumura-Hata Pathloss Model (empirically-fitted model):
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Shadowing Overview [1/2]
Shadowing has the following characteristics: function of the environment (as well as frequency, distance, antenna heights)
random effect due to randomly appearing and disappearing waves
is obtained by averaging over 40 and subtracting the pathloss
1000 2000 3000 4000 5000 6000 7000 8000 900010000-50
-40
-30
-20
-10
0
10
20
Distance [log of meter]
R
eceivedPower[dBW]
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Shadowing Modelling Approach [2/2]
The reasoning behind the distribution of shadowing is as follow: each arriving MPC is the result of a random amount of multiple random reflections
the power is hence
this term determines the shadowing behaviour, i.e. the (dis)appearance of waves
Due to its random nature, we want to determine its distribution: take logarithm of power, i.e.: Gaussian
distribution of G:
find distribution of P, i.e. , by using :
this distribution is referred to as lognormal distribution
Lognormal distribution has zero-mean and STD [dB] =
typical values are dB = 4-10dB (microcell), 6-18dB (macrocell)
2iRP
== 22 lnlnln ii RRPG
GeP =
p
gpgpdfppdf
== )ln()(
10ln/10=dB
2
2
22
1)(
=
x
G exp
2
2
ln
2
1
2
1)(
=
x
P ex
xp
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Fading Overview [1/4]
Fading has the following characteristics: function of the environment and frequency
random effect due to randomly wave additions/cancellations
is obtained by subtracting the pathloss and shadowing (no averaging!)
1000 2000 3000 4000 5000 6000 7000 8000 900010000-50
-40
-30
-20
-10
0
10
Distance [log of meter]
R
eceivedPower[dBW]
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Fading Modelling Approach [2/4]
Eliminating pathloss and shadowing, the complicated equation,expressing the total received field, turns:
where An is the random amplitude of the n-th MPC,
and n is the random phase of the n-th MPC.
For large N's, each sum tends to a Gaussian distribution, i.e.
which is referred to as a complex Gaussian distribution.
As Engineers, we are interested in the envelope and power of E.
+= n
nn
n
nn
n
j
ntotal AjAeAEn sincos
),0(),0(),0( 222 CN + jEtotal
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Fading Modelling Approach [3/4]
The envelope follows a Rayleigh distribution:
The power follows a central-chi-squared distribution:
Typical distributions (usually referred to envelope): Rayleigh (fits well under nLOS)
Nakagami (fits well under weak LOS)
Rice (fits well under strong LOS)
( ) ( )
2
22
2222 )(,,0,0
=+=
x
Vtotal exxpEV NN
( ) ( )22
2
22222
21)(,,0,0
x
Ptotal expEP=+= NN
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Fading Modelling Approach [4/4]
The fading patterns for these cases is shown below:
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-40
-30
-20
-10
0
10
Distance [meter]
ReceivedPower[dB
W]
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-40
-30
-20
-10
0
10
Distance [meter]
ReceivedPower[dBW]
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-40
-30
-20
-10
0
10
Distance [meter]
ReceivedPower[dBW]
Rayleigh(nLOS)
many bit errors
Nakagami(weak LOS)
less bit errors
Rice(strong LOS)
almost no errors
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4The Big Picture
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Advantages & Disadvantages
Pathloss: adv.: limits interference powers
disadv.: limits desired signal power
Shadowing: adv.: limits interference, facilitates capture effect in ad hoc networks
disadv.: limits signal power, is difficult to predict
Fading: adv.: (facilitates increase of capacity in MIMO channels)
disadv.: causes errors, requires strong channel code
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Simulation Platforms
Type of simulator: link-level (point-to-point): fading ("channel model")
system-level (entire system): pathloss + shadowing ("pathloss model")
Example of Ad Hoc Network: Link Level Simulator: 1. Rayleigh fading to determine BER/PER versus
SNR without shadowing/pathloss for givenchannel code, modulation and packet length.
System Level Simulator: 2. Randomly place nodes which determinesdistance between them.
3. Obtain for given distance the deterministic
pathloss and random shadowing loss.4. For given transmit power, obtain with theselosses the received power, and hence SNR.
5. Obtain PER from step 1 and re-run from step 2with new locations/packets/etc.
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Some Thoughts
Designing modern communicationsystems is a cross-community exercise(IT, telecom, etc).
The world of computing and wirelesssystems converges. For instance,
IPv6 is designed to work over awireless system too.
The wireless channel is fundamental tothe system design of any wirelesssystem.
Although not along yourspecialty and interest, thislecture will prove vital to you.
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Acronyms
A list of some important acronyms used in the lecture: BER Bit Error Rate
CDF Cumulative Distribution Function
LOS Line-of-Sight
MIMO Multiple-Input Multiple Output (channel)
MPC Multi-Path Component
n/oLOS non/obstructed LOS PER Packer Error Rate
PDF Probability Distribution Function
Rx, Tx Receiver, Transmitter
SI(N)R Signal-to-Interference(-plus-Noise) Ratio
SNR Signal-to-Noise Ratio
STD Standard Deviation
WLAN Wireless Local Area Network
UMTS Universal Mobile Telecommunications Systems
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Advanced Topics
If you really want to get into channel modelling, here some importanttopics which I didn't have time to deal with:
c/nc-2-2n, Gamma, negative exponential distributions, etc.
power delay profile
time-selective channel (fast versus slow)
coherence time frequency-selective channel (selective versus flat)
coherence bandwidth
Bello functions
spatial channel modelling
MIMO channels
ultra-wideband channel
IEEE & ETSI BRAN standard models
top related