Fundamentals of Propagation Modellingperso.citi.insa-lyon.fr/jmgorce/coursMASTRIA/Cours2...research...

research & development

Fundamentals ofPropagation ModellingPathloss, Shadowing & Fading

Dr Mischa DohlerSenior ExpertFT R&D

21 November 2006

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 DelhiTokyo

Seoul


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 Télécom R&D

28 Chemin du Vieux Chêne

38243 Meylan Cedex

France

� You can see my research interests by:� googelling me ☺


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 Personal

Communications," Proc. IEEE, Sept. 1994, pp. 1333-1359.� V. Erceg et al., "Urban/Suburban Out-of-Sight Propagation Modeling, IEEE

Commun. 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/


� Some Important Basics

� Introduction to Wireless Channels

� Pathloss, Shadowing, Fading

� The Big Picture

1

2

3

Lecture's Outlook

4


1Some Important Basics


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-SpacePropagation

2. Reflection

4. Diffraction


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]

Rec

eive

d P

ower

[dB

W]


Presupposed Basics [1/4]

� To really understand these phenomena, one needs a profound knowledge 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.



� 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 80000

0.5

1

1.5

2

2.5

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

µ

2σ



� 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 ω = 2πf = 2π/T

in space with spatial frequency k = 2π/λ

� f is the frequency in [Hz], T the period in [s], and λ = c/f the wavelength in [m]� E = E0 cos(ωt – kr); for convenience, we write E = E0 ej‧(ωt – kr)

Eθθθθ

x

y

z

r >> λλλλθ=90°

Hφφφφ



� 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

� …


2Introduction to Wireless Channels


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 and noise + interference powers (SNR, SIR, SINR)


� 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]


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 d and wavelength λ):� free-space propagation: always occurs for any d and λ

� reflection/refraction: λ >> ∆h, d >> λ� diffraction: λ in the order of the curvature of the edge

� scattering: λ ≈ 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.


� Friis' Transmission Equation: , assuming

� PRx to be received and PTx transmitted powers

� GRx to be receive and GTx transmit antenna gains

� d the distance between Tx and Rx, and λ = 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)

� PRx decreases with -20dB/dec:

Propag. Mechanisms – Free-Space [3/7]

2

4

⋅⋅⋅=d

GGPP RxTxTxRx πλ

PRx [dBm]

d [log]100m 1km 10km

-20

-40

-60gradient of -20dB/dec


� Fresnel's Reflection Equation: , assuming

� R to be the generally complex reflection coefficient,

� which depends on the impinging angle φ and the involved materials

� since φ 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 R will also have a variance. With an increasing number of 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 ⋅=


� 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]


� Doppler Formula: , where

� c = 3‧108 m/s is the speed of light, and

� v is 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


� Assume we send two symbols of duration Ts; then, objects along the ellipses 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


� 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 MPCi is the number of multipath components which has been reflected i times

Summed Contributions [1/3]

( )( ) ( )( )

( )( )

( )( )∑ ∑ ∏

∑

∑

∑∑∑

∈ ∈

⋅−+⋅

=

⋅−+⋅

⋅−+⋅⋅−+⋅

⋅⋅⋅=

+⋅⋅⋅⋅+

⋅⋅⋅+

⋅=

+++==

refl.i MPCk

)(/)(12

,1,0

i

)(/)(12

2,2,1,0

i

)(/)(12

1,1,0

)(/)(12

00

i

,,

2,2,

1,1,00

)(

1)(

...)(

1)()(

)(

1)(

)(

1

...refl. twicerefl. once)LOS()(

trkctvfj

ki

i

lli

trkctvfj

iii

trkctvfj

ii

trkctvfj

MPCntotal

kikic

iic

iicc

etr

mtRE

etr

mtRtRE

etr

mtREe

tr

mE

EtE

π

π

ππ


� The resulting signal strength and hence power are random, because the 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

jn

ll

kitotal

neAtRtr

mEtE ϕ)(

)(

1)(

,0



� 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


Rec

eive

d P

ower

[dB

W]

fading +

shadowing +

pathloss =

total channel


3Pathloss, Shadowing and Fading


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 λ

1000 2000 3000 4000 5000 6000 7000 8000 900010000-120

-110

-100

-90

-80

-70

-60

-50


Rec

eive

d P

ower

[dB

W]

example gradient:-20 dB/dec


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 = 2…4 (LOS + clutter), n = 4…6 (nLOS + clutter)

� simple and more accurate model, but correct reference point d0 has to be found� application in WLANs, interference power in cellular systems, etc.

� Dual-slope pathloss model:� d < dbreakpoint : n1 = 2 (normally), d > dbreakpoint : n2 = 2…6 (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

BPBPn dddPdPdddPdP ⋅=⋅=


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


Pathloss – Important Models [4/5]

� Two-Ray Pathloss Model (dual-slope model):


Pathloss – Important Models [5/5]

� Okumura-Hata Pathloss Model (empirically-fitted model):


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 λ and subtracting the pathloss

1000 2000 3000 4000 5000 6000 7000 8000 900010000-50

-40

-30

-20

-10

0

10

20


Rec

eive

d P

ower

[dB

W]


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 σdB = 4-10dB (microcell), 6-18dB (macrocell)

∏∝ 2iRP

∑∏ =∝= 22 lnlnln ii RRPG

GeP =p

gpgpdfppdf

∂∂⋅== )ln()(

10ln/10⋅= σσ dB

2

2

22

1)(

−⋅= σ

πσ

x

G exp

2

2

ln

2

1

2

1)(

−⋅⋅= σ

πσ

x

P ex

xp


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


Rec

eive

d P

ower

[dB

W]


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 φn 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.

∑∑∑ ⋅⋅+⋅=⋅∝′ ⋅

nnn

nnn

n

jntotal AjAeAE n ϕϕϕ sincos

),0(),0(),0( 222 σσσ CΝΝN →⋅+⊂′ jEtotal



� 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

−⋅=+⊂′= σ

σσσ

x

Vtotal ex

xpEV NN

( ) ( ) 222

22222

2

1)( ,,0,0 σ

σσσ

x

Ptotal expEP−

⋅=+⊂′= NN



� 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]

Rec

eive

d P

ower

[dB

W]

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-40

-30

-20

-10

0

10

Distance [meter]

Rec

eive

d P

ower

[dB

W]

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-40

-30

-20

-10

0

10

Distance [meter]

Rec

eive

d P

ower

[dB

W]

Rayleigh (nLOS)

many bit errors

Nakagami(weak LOS)

less bit errors

Rice (strong LOS)

almost no errors


4The Big Picture


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


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 given channel code, modulation and packet length.

� System Level Simulator: 2. Randomly place nodes which determines distance between them.

3. Obtain for given distance the deterministic pathloss and random shadowing loss.

4. For given transmit power, obtain with these losses the received power, and hence SNR.

5. Obtain PER from step 1 and re-run from step 2 with new locations/packets/etc.


Some Thoughts

� Designing modern communication systems is a cross-community exercise (IT, telecom, etc).

� The world of computing and wireless systems converges. For instance, IPv6 is designed to work over a wireless system too.

� The wireless channel is fundamental to the system design of any wireless system.

� Although not along your specialty and interest, this lecture will prove vital to you.


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


Advanced Topics

� If you really want to get into channel modelling, here some important topics which I didn't have time to deal with:

� c/nc-χ2-2n, 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

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