Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson
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
6
84Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson
Reflection and transmission (2)
• Snell’s law– Reflection angle
– Transmission angle
• Transmission and reflection: distinguish TE and TM waves
Θ � Θ�
sinΘ+
sin��
,�
,
7
85Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson
Reflection and transmission (3)
Brewsterangle
Phase inverted
grazing angle
8
87Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson
The d-4 law (1)
• For the following scenario
• the power goes like
• for distances greater than
��� � - �������.�.��
�
�/ �"0 14.�.��
�
9
89Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson
Diffraction, Huygen’s principle
11
90Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson
Diffraction
• Single or multipleedges
• makes it possible togo behind corners
• less pronouncedwhen the wavelengthis small compared toobjects
12
95Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson
Scattering
Specularreflection
Scattering
Rough surface
Specularreflection
Smooth surface
13
96Slides for “Wireless Communications” © Edfors, Molisch, Tufvesson
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>
14