cours2 - fundamentals of propagation modelling (dr mischa dohler)

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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My Contact Details

My preferred mode of communication is email: [email protected]

[email protected]

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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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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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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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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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)


n

j

n

l

l

ki

totalneAtR

tr

mEtE

)(

)(

1)(

,0


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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


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


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


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


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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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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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

cours2 - fundamentals of propagation modelling (dr mischa dohler)

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