The correlation of multi-propagation paths is an indicator for the effectiveness of diversity reception, transmission and MIMO. The penetration of the waves into buildings is limited to distinct passages through windows, and decorrelation is introduced through multiple reflections inside. This is analysed.

1. Path Correlation
through Penetration to Buildings
•
Dr. Joseph Shapira
1

2. Contents
•
1.
2.
3.
4.
5.
6.
•
1.
2.
Propagation modes
Sources of waves impinging on the outer wall
Reflection and transmission through walls
Transmission through apertures
Propagation within a room
Coupling into inner rooms
Indoors-generated transmission
Paths’ correlation
Correlation between impinging sources
Correlation between offspring branches
diffractions of each penetration mode)
(reflections
and
•
2

3. Propagation modes
1.
2.
3.
4.
•
5.
6.
Impinging waves
Wall penetration
Aperture penetration
1
Transmission through
multiple walls
Propagation within the room
Coupling to inner rooms
5
4
3
6
2
3

4. Sources of waves impinging on the outer
wall
1.
2.
3.
4.
Direct (LOS)
1.
Remote source – plane wave. Full correlation between source
antennas.
2. Near source (across the street). Full de-correlation at edges of the
aperture dD ≥ λR
d – source antennas spacing; D –
aperture; R- distance
Remote reflector – each reflector is a remote source. The distance
between the reflectors – d, determines the correlation between
them.
Over the roof, and around-the-wall diffraction – these are line
sources. Create a single ray in the plane of the line.
Propagation along the street (waveguide propagation). Impinges on
the wall at low grazing angle, high attenuation. Reflectors or line
diffractors across the street, generate wave impinging near normal
incidence and may be stronger.
4

5. Transmission through the wall –
the angular filter
Γ
T
T
Γ
H polarization
V polarization
(incidence in horizonthal plane)
5

6. Window penetration
•First Fresnel zone
s2
d=
4λ
•Diffraction zone – attenuated by
•ceiling and furniture clutter
W Wi = exp{ − αd }
•Transition zone W =  A 


Wi  λd 
2
 λ 


2πh 

h
2
λd
h>
4s
holds for
•W,Wi flux density, i incident
1st Fresnel zone
Edge diffraction
6

7. The window penetration depth
cos 2 ϑ
Free space penetration depth
filter
d ' = ( s 2 4λ ) cos 2 ϑ
d
d
'
7

8. Wall reflection loss
Reflection loss [dB]
-5.00
88
80
72
64
56
48
40
32
8
24
-3.00
16
Reflection loss [dB]
0
-1.00
V polarization
TE, eps=3
TM, eps=6
-7.00
-9.00
TM, Eps=3
H polarization
-11.00
TE, eps=6
TM, eps=10
TE, eps=10
-13.00
-15.00
Angle from zenit, degrees
8

9. Room reflections
• The reflection loss is not trivial
• Up to 10 dB per reflection.
• The direct ray is dominant
θ
180−θ
Γ6
• Scattering from objects near the
• UE (e.g person) competes with
• high order reflection
180+θ
Γ
4
−θ
Γ2
9

10. Reference to reported observations
•
Mischa Dohler et. Al. :MiMO channel measurements, IEEE
Communications Magazine • March 2007
•
•
•
Most contributions are LOS. Then only single bounce
counts. Others, and diffractions, are too small
Propagation along corridor – key-hole effect. DOA is only
along the corridor axis.
Clustered multipath are correlated
10

11. Direction-of-arrival measurements
A. Molisch. The BS was placed across the street against the building
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12. Indoor-generated transmission
• Reciprocity imples dominance of direct + 1st reflection
• Within the same room– scattering rich.
• Through walls to other rooms – angular filter through each
wall. However, multiple rays may have equal strength (due to
complexity of environment, e.g. corridor propagation etc.). A
range of richness dimensions.
• Indoors to outdoors – by reciprocity,
•
same as out-indoors.
12

13. Correlation analysis
•LOS remote source penetrates the wall/ window as a plane wave. Full
correlation.
•Edge diffraction of the window is directive. The diffraction of both
edges overlap too far to meet the de-correlation condition≥ λR
dD
•Over-the-roof diffraction is coherent in the horizontal plane.
•Around-the-corner diffraction is coherent in the vertical plane.
•The outer wall/ window does not change the correlation of the
penetrating waves. However, it acts as an angular filter, limiting the
range of incidence.
•Indoor reflections are attenuated. Only direct and 1 st bounce count. The
correlation of the incoming waves does not change.
13

14. Correlation analysis - 2
• The indoor multipath is mainly of order 1 – 2 (diffraction by a
close-by object may add).
• The degree of source depends on the number of angularly
separated reflection/ scattering that hit the wall with similar
strength through the wall angular filter. This may typically be
1 – 2.
• The MIMO degree is then
Most
then
then
rarely
1–1
1–2
2–2
higher
14

15. Dr Joseph Shapira
Comm&Sens Ltd
jshapira@netvision.net.il
www.comm-and-sens.com
15