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Basic of Propagation TheoryS-72.333
Physical Layer Methods in WirelessCommunication Systems
Fabio BelloniHelsinki University of Technology
Signal Processing Laboratory
fbelloni@wooster.hut.fi
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Outline Introduction
Free-Space Propagation- Isotropic Radiation
- Directional Radiation
- Polarization
Terrestrial Propagation: Physical Models
- Reflection and the Plane-Earth Model
- Diffraction and diffraction losses
Terrestrial Propagation: Statistical Models Indoor propagation Conclusions
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Introduction The study of propagation is important to wireless communication
because it provides
1) prediction models for estimations the power required to close acommunication link reliable communications.
2) clues to the receiver techniques for compensating theimpairments introduced through wireless transmission.
The propagation effects and other signal impairments are oftencollected and referred to as the channel.
Channel models for wireless communications may be defined as
Physical modelsand Statistical Models. RX signal is the combination of many propagation models
multipathand fading.
In addition to propagation impairments, the other phenomena thatlimit wireless communications are noiseand interference.
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Free-Space Propagation
The transmission is characterized by- the generation, in the transmitter (TX), of an electric signal
representing the desired information,
- propagationof the signal through space,
- a receiver (RX) that estimates the transmitted information fromthe recovered electrical signal.
The antenna converts between electrical signals and radio waves,and vice versa.
The transmission effects are most completely described by the
Maxwells equations. Here we assume a linear medium in which all the distortions can becharacterized by attenuation or superposition of different signals.
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Isotropic Radiation
An antenna is isotropic if it can transmit equally in all directions.
It represents an ideal antenna and it is used as reference to whichother antennas are compared.
RXTX
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Isotropic Radiation The power flux density of an isotropic source that radiates power
PT watts in all directions is
R =PT
4R2
Wm2
where 4R2 is the surface area of a sphere.
The power captured by the receiving antenna (RX) depends on thesize and orientation of the antenna with respect to the TX
PR = R Ae =PT
4R2Ae
where Ae is the effective areaor absorption cross section.
Effective area of an isotropic antenna in any direction: Aisoe =2
4 .
The antenna efficiency is defined as = AeA
where A is the
physical area of the antenna.
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Isotropic Radiation The link between TX and RX power for isotropic antennas is
PR =
4R
2PT =
PT
LP
where LP = 4R 2 is the free-space path loss between twoisotropic antennas.
The path loss depends on the wavelength of transmission. The sensitivity is a receiver parameter that indicates the minimum
signal level required at the antenna terminals in order to providereliable communications.
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Directional Radiation Real antenna is not isotropic and it has gainand directivity which
may be functions of the azimuth angle and elevation angle .
n
N1
z
x
y
0
2 1
3 dB
beamwidth
M ain
Lobe
TX
Side
Lode
Peak
AntennaGain
Back
Lobe
Antenna
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Directional Radiation Transmit antenna gain: GT(, ) =
Power flux density in direction(,)Power flux density of an isotropic antenna
.
Receive antenna gain: GR(, ) = Effective area in direction(,)Effective area of an isotropic antenna . Principle of reciprocity signal transmission over a radio path is
reciprocal in the sense that the locations of the transmitter andreceiver can be interchanged without changing the transmission
characteristics.
Maximum transmit or receive gain
G
Ae=
4
2
Side-lode and back-lobe are not considered for use in thecommunications link, but they are considered when analyzinginterference.
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The Friis Equation: Link Budget In case of non-isotropic antenna, the Free-Space loss relating the
received and transmitted power is
PR =PT GT GR
LP= PT GT GR
4R
2(1)
or, as a decibel relation,
PR(dB) = PT(dB) + GT(dB) + GR(dB) LP(dB)where X(dB) = 10log10(X).
Closing the link means that the right hand side of eq.(1) providesenough power at the receiver to detect the transmitted informationreliably RX sensitivity.
The Friis equation (Link Budget), as presented so far, does notinclude the effect of noise, e.g. receiver noise, antenna noise,
artificial noise, multiple access interference,...
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The Friis Equation: Link Budget Let us assume the receiver noise as dominant an let us model it by
the single-sided noise spectral density N0.
To include the noise, the Link Budget may now be expressed as
PR
N0=
PT GT GR
LP k Te(2)
where N0 = k Te, k is the Boltzmanns constant and Te is theequivalent noise temperature of the system.
In satellite application, eq.(2) is written as CN0
= EIRP Lp + GT k:
C
N0 =
PR
N0 received carrier-to-noise density ratio (dB/Hz)
EIRP = PT GT TX Equivalent Isotropic Radiated Power (dBW) G
T= GR
Te RX gain-to-noise temperature ratio (dB/K)
Lp
Path loss (dB)
k Boltzmanns constant23 November 2004 Belloni,F.; Basic of Propagation Theory; S-72.333 11
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Polarization
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Polarization The electric field may be expressed as
E = Ex
u x + Eyu y. In the phasor domain we can write E = cos()u x + sin()eju y.
- & = 0 Linear polarization,- = 4 & = 2 Right-hand (-) and Left-hand (+) circular pol.
Examples:- VP: = 2 & = 0
E = u y,
- HP: = 0 & = 0 E = u x,
- RHCP: =
4 & =
2 E =1
2u x j1
2u y,- LHCP: = 4 & =
2
E = 1
2
u x +j 12u y,
In time domainE(t) = cos()cos(wt)u x + sin()cos(wt + )u y.
Scattering effects tend to create cross-polarization interference.23 November 2004 Belloni,F.; Basic of Propagation Theory; S-72.333 13
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Polarization
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Polarization
Projection matrix:
Er
El
= 1
2
1 j
1
j
Ex
Ey
where Er and El are the right and left circular bases, respectively.
Axial ratio: R = |El||Er||El|+|Er| =
1 Left-Hand Circular Pol.
0 Linear Pol.
1 Right-Hand Circular Pol.if R
(0, 1) Left-Hand Elliptical Pol. and if R
(
1, 0) Right-HandElliptical Pol.
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Polarization Example: verify, by using the axial ratio, that a left-hand circular
polarization can be identified by setting = 4 & =2 .
Ex = cos() =12
Ey = sin() ej = j 1
2
Er
El
= 1
2
1 j1 j
12
j 12
=
01
R =|El| |Er|
|El|+ |Er|=
1 0
1 + 0
= 1
Left-Hand Circular Polarization!
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Terrestrial Propagation: Physical Models They consider the exact physics of the propagation environment
(site geometry). It provides reliable estimates of the propagation
behavior but it is computationally expensive. Basic modes of propagation:- Line-of-Sight (LOS) transmission clear path between
transmitter (TX) and receiver (RX), e.g. satellite communications.
- Reflection bouncing of electromagnetic waves fromsurrounding objects such as buildings, mountains, vehicles,...
- Diffraction bending of electromagnetic waves around objectssuch as buildings, hills. trees,...
- Refraction electromagnetic waves are bent as they move fromone medium to another.
- Ducting physical characteristic of the environment create awaveguide-like effect.
RX signal is the combination of this models multipathand fading.23 November 2004 Belloni,F.; Basic of Propagation Theory; S-72.333 17
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Reflection and the Plane-Earth Model
Plane-Earth propagation equation: PR = PTGTGRhThR
R2 2
- Assuming R hT, hR the equation is frequency independent,- inverse fourth-power law,
- dependence of antennas height.
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Diffraction When electromagnetic waves are forced to travel through a small
slit, they tend to spead out on the far end of the slit.
Huygenss principle: each point on a wave front acts as a pointsource for further propagation. However, the point source does notradiate equally in all the directions, but favors the forward direction,
of the wave front.23 November 2004 Belloni,F.; Basic of Propagation Theory; S-72.333 19
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Diffraction Fresnel zones are important in order to understand the basic
propagation phenomena.
Rule of thumb: in order to obtain transmission under free-spacecondition, we have to keep the "first-Fresnel zone" free of obstacles.
R = |T QR| |T OR| (q1)
2 R q2 h =
qd1d2d1+d2
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Diffraction Losses
3 2 1 0 1 2 3
5
0
5
10
15
20
25
Diffraction parameter ()
Path
lossrela
tive
to
the
freespace
(dB)
A perfectly absorbing screen is placed between the TX and RX. When the knife-edge is even with the LOS, the electric field is
reduced by one-half and there is a 6-dB loss in signal power.23 November 2004 Belloni,F.; Basic of Propagation Theory; S-72.333 21
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Terrestrial Propagation: Statistical Models
By measuring the propagation characteristics in a variety ofenvironments (urban, suburban, rural), we develop a model based
on the measured statistics for a particular class of environments. In general, they are easy to describe but they are not accurate. The statistical approach is broken down into two components:
- median path loss;- local variations;
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Terrestrial Propagation: Statistical Models Median path loss: investigations motivate a general propagation
model such as PTPR
= rn
, where r is the distance between TX and
RX, n is the path-loss exponent and the parameter represents aloss that is related to frequency , antenna heights, ...
Environment n
Free-Space 2
Flat Rural 3
Rolling Rural 3.5
Suburban, low rise 4
Dense Urban, Skyscrapers 4.5
Local variations: the variation about the median can be modelled
as a log-normal distribution (shadowing).23 November 2004 Belloni,F.; Basic of Propagation Theory; S-72.333 23
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Indoor propagation To study the effects of indoor propagations has gained more and
more importance with the growth of cellular telephone.
Wireless design has to take into account the propagationcharacteristics in high-density location.
Wireless Local Area Networks (LANs) are being implemented toeliminate the cost of wiring of rewiring buildings.
Indoor path-loss model
LP(dB) = (dB) + 10 log10
rr0
n+
Pp=1
WAF(p) +
Qq=1
FAF(q)
- WAF Wall Attenuation Factor- FAF Floor attenuation Factor- r dinstance TX and RX- r0
reference distance (1 m)
- Q and P number of floors and walls, respectively.23 November 2004 Belloni,F.; Basic of Propagation Theory; S-72.333 24
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Conclusions The link budget may be improved by using directional instead of
isotropic antennas.
There is a trade off between the accuracy and the computationalcomplexity for propagation models.
The polarization of electromagnetic waves is an important issue forwireless communication.
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References Haykin, S.; Moher, M.; Modern Wireless Communications ISBN
0-13-124697-6, Prentice Hall 2005.
https://ewhdbks.mugu.navy.mil/POLARIZA.HTM http://www.walter-fendt.de/ph11e/emwave.htm Paraboni, A.; Antenne, McGraw-Hill 1999.
Saunders, S.; Antennas and Propagation for WirelessCommunication Systems, Wiley, 2000.
Vaughan, R.; Andersen, J.B.; Channels, Propagation and Antennasfor Mobile Communications , IEE, 2003.
Bertoni, H.; Radio Propagation for Modern Wireless Systems,Prentice Hall, 2000.
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https://ewhdbks.mugu.navy.mil/POLARIZA.HTMhttp://www.walter-fendt.de/ph11e/emwave.htmhttp://www.walter-fendt.de/ph11e/emwave.htmhttps://ewhdbks.mugu.navy.mil/POLARIZA.HTM7/30/2019 Basic Propagation Theory
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Homeworks Let us assume a right-hand circular polarization with Ex = 1 and
Ey =
j. Compute the loss in dB in a wireless link when the
horizontal component is attenuated by 6-dB. In case of physical models for terrestrial propagation, which are the
basic models of propagation. Explain briefly each of them.
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