Propagation

Mechanism

PROF. MICHAEL TSAI

2011/9/29

Propagation Mechanism

• Free-space propagation

• Reflection

• Diffraction

• Scattering

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d

ARX

Free-space loss

If we assume RX antenna to be isotropic:

Attenuation between twoisotropic antennas in freespace is (free-space loss):

��� ��

4��

��

�� �� � �4��

�

3

Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson

Free-space lossFriis’ law

Received power, with antenna gains GTX and GRX:

Valid in the far field only

��� � ������

� � �� (�)�� � ��

�

4��

�����

���|�� � � ��|�� + ��|�� − L� ��|�� � + ���|��

� ��|�� + ��|�� − 10 log��� �

!

+ ���|��

4

2Lad R =

Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson

Free-space lossWhat is far field?

Rayleigh distance:

2

λ

where �" is the largest dimension ofthe antenna.

λ / 2 -dipole

λ / 2

Parabolic

2r

�� �2�"

�

�" � �/2

� � �/2

�" � 2%

�� �8%

�

5

Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson

Reflection and transmission (1)

Θi Θr

Θt

ε1

ε 2

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Reflection and transmission (2)

• Snell’s law– Reflection angle

– Transmission angle

• Transmission and reflection: distinguish TE and TM waves

Θ � Θ�

sinΘ+

sin��

,�

,

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Reflection and transmission (3)

Brewsterangle

Phase inverted

grazing angle

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The d-4 law (1)

• For the following scenario

• the power goes like

• for distances greater than

��� � - �������.�.��

�

�/ �"0 14.�.��

�

9

88Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson

The d-4 law (2)

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Diffraction, Huygen’s principle

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Diffraction

• Single or multipleedges

• makes it possible togo behind corners

• less pronouncedwhen the wavelengthis small compared toobjects

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Scattering

Specularreflection

Scattering

Rough surface

Specularreflection

Smooth surface

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Kirchhoff theory – scattering by rough surfaces

for Gaussian surface distribution

2

standard deviation of height

angle of incidence

2 3456 � 27833+6 exp −2 <�=6 sin>

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Waveguiding

Waveguiding effectsoften result in lowerpropagation exponents

n=1.5-5

This means lower pathloss along certainstreet corridors

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