Download Polarization Model at 60 GHz

April 2009
doc.: IEEE 802.11-09/0431r0
Polarization Model for 60 GHz
Date: 2009-04-02
Authors:
Name
Affiliati
ons
Address
Phone
email
Alexander Maltsev
Intel
+78314162461
[email protected]
Roman Maslennikov
Intel
Artyom Lomayev
Intel
Alexey Sevastyanov
Intel
Alexey Khoryaev
Intel
Turgeneva str., 30, Nizhny
Novgorod, 603024, Russia
Turgeneva str., 30, Nizhny
Novgorod, 603024, Russia
Turgeneva str., 30, Nizhny
Novgorod, 603024, Russia
Turgeneva str., 30, Nizhny
Novgorod, 603024, Russia
Turgeneva str., 30, Nizhny
Novgorod, 603024, Russia
Submission
Slide 1
[email protected]
[email protected]
[email protected]
[email protected]
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Abstract
This contribution presents a polarization model proposal for 60 GHz
WLAN Systems
Submission
Slide 2
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Polarization Model
•
•
•
Polarization impact for 60 GHz is significant because even NLOS (reflected)
signals remain strongly polarized (i.e. coupling between orthogonal
polarization modes is low) and cross-polarization discrimination (XPD) is high
even for NLOS signals.
The polarization of signals is changed by reflections and different types of
antenna polarizations provide different received power for various signal
clusters (e.g., LOS, first-order reflection, second-order reflection).
Therefore, support of polarization characteristics in 60 GHz WLAN channel
models is very important.
Submission
Slide 3
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Polarization Impact Modeling
• Polarization is a property of EM waves describing the
orientation of electric field E and magnetic intensity H
orientation in space and time. The vector H due to
properties of EM waves can always be unambiguously
found if E orientation and the direction of propagation is
known. So the polarization properties are usually described
for E vector only.
• In order to support polarization impact in the channel
model, polarization characteristics of antennas and
polarization characteristics of the propagation channel
should be introduced.
Submission
Slide 4
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Antenna Polarization Properties
•
•
•
In the far field zone, the electric vector E is a function of the radiation direction
(defined by the azimuth angle  and elevation angle  in the reference coordinate
system) and decreases as r-1 with increase of the distance r.
z
Vector E is perpendicular to the
propagation direction r and can

be
decomposed
into
two
k
E
orthogonal components: E and
Eφ that belong to the planes of
E
constant φ and constant  angles,

respectively.
r
Knowledge of E and Eφ of the
radiated signal (which may be
functions of φ and ) fully
describes
polarization
φ
characteristics of the antenna in
the far field zone.
x
Submission
Slide 5
Alexander Maltsev, Intel Corporation
y
April 2009
doc.: IEEE 802.11-09/0431r0
Polarization Description Using Jones Vector
• Wave polarization can be described using Jones calculus introduced in
optics to describe polarized light. In general case Jones vector is
composed from two components of electric filed of EM wave.
• The Jones vector e is defined as the normalized two-dimensional
electrical field vector E. The first element of the Jones vector is
reduced to the real number. The second element of this vector defines
phase difference between orthogonal components of the E field.
• For example, for antenna polarization model the orthogonal
components of Jones vector are defined for E and Eφ components
respectively.
Submission
Slide 6
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Examples of Antennas Polarization Description
Using Jones Vector
Antenna Polarization Type
Corresponding Jones Vector
1
 
0
0
 
1
Linear polarized in the -direction
Linear polarized in the φ-direction
1 
 
 j
1 1 
2   j 
1
2
Left hand circular polarized (LHCP)
Right hand circular polarized (RHCP)
Submission
Slide 7
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Polarization Characteristics of Propagation
Channel
• With the selected E field bases (E and Eφ components) for TX and RX
antennas, the propagation characteristics of each ray of the propagation
channel may be described by channel polarization matrix H.
• In this case, transmission equation for one ray channel may be written as:
y  e HRX HeTX x
• Where x and y are transmitted and received signals, eTX and eRX are
polarization (Jones) vectors for TX and RX antennas, respectively.
• Components of polarization matrix H will define gain coefficients between
E and Eφ components at the TX and RX antennas.
• Matrix H includes the attenuation of the signal due to reflection. To
separate the reflection attenuation (reflection coefficient) impact, matrix H
may be normalized by its largest singular value.
Submission
Slide 8
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Polarization Characteristics of Propagation
Channel (Cont’d)
•
•
•
•
•
For LOS signal path matrix HLOS is the identity matrix.
For NLOS (reflected) paths, H has more complex structure.
The model for NLOS channel polarization matrix is defined based on the
following considerations:
It is known that reflection coefficients are different for E field components
belonging (parallel) to the plane of incidence and for perpendicular to the
plane of incidence. Also these coefficients depend on the incident angle. The
theoretical coupling between parallel and perpendicular components is zero for
plane interfaces but due to non-idealities (roughness) some coupling always
exists.
Therefore, the polarization matrix for the given first-order reflected signal path
may be found as a product of a matrix that rotates E vector components from
the coordinate system associated with TX antennas to the coordinate system
associated with incident plane. Next, a matrix with reflection coefficients (and
cross-polarization coupling coefficients) is applied followed by a rotation of
the coordinate system associated with RX antenna.
Submission
Slide 9
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Polarization Channel Matrix for First Order Reflections
Incident plane
Reflection surface
• The figure shows an example of the first
order reflected signal path.
• Equation shows a structure of the channel
propagation matrix for the case of the first
order reflected signals.
• The reflection matrix R includes reflection
coefficients R and R|| for perpendicular and
parallel components of the electric field E 
and E || respectively.
• Elements 1 and 2 in matrix R are crosspolarization coupling coefficients
RX

 inc
k
n
E
LOS
E
 tx
TX
r – direction of wave propagation
n – normal to the incident plane
1   cos tx  sin  tx 
 cos rx  sin  rx   R  inc 
H ref 1  


  


R






sin

cos

 sin  tx  cos tx 
2
||
inc 
rx
rx 



 
 
recalculation
of polarizati on
vector from the
plane of incidence basis
to RX coordinates
Submission
recalculation
of TX polarizati on
vector to the plane
of incidence basis
reflection
matrix
R
Slide 10
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Polarization Channel Matrix for Second Order
Reflections
• To obtain polarization channel matrix for the second order reflections,
additional rotation and reflection matrices are added.
1 
 cos rx  sin  rx   R  2 inc 
H ref 2  








R

2
||
2 inc
  sin  rx  cos rx  

2 nd reflection
1   cos tx  sin  tx 
 cos p  sin  p   R 1inc 


  








sin

cos

R

 sin  tx  cos tx 
p
p 
2
||
1inc 




1st reflection
Submission
Slide 11
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Polarization Impact Model Development Methodology
• To develop polarization model the following methodology is proposed:
– Define elements of reflection matrix R. It may be found from experiments [1] or
theory (Fresnel formulas)
– Perform ray-tracing of interesting environments (conference room, cubicle
environment, and living room) with taking into account geometry and
polarization characteristics of the propagation channel
– Define channel polarization matrices H for different types of clusters and make
statistical models approximating empirical distributions of matrices elements
[1] K. Sato et al, “Measurements of Reflection and Transmission
Characteristics of Interior Structures of Office Building in the 60 GHz Band”,
IEEE Trans. Antennas Propag., vol. 45, no. 12., pp.1783-1792, Dec. 1997.
Submission
Slide 12
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Example of Polarization Characteristics for Conference
Room Channel Model
• To demonstrate the proposed approach, reference results were generated for
the conference room channel model.
• The R and R|| elements of the reflection matrix R were obtained using
Fresnel formulas. The cross-coupling elements 1 and 2 of matrix R were
taken equal to zero.
• 3D ray tracer with polarization support was used to generate multiple
realizations of channel polarization matrices H for different types of
clusters (with taking into account the information about the reflection
incident angles and rotation angles needed to perform all geometrical
transformations).
Submission
Slide 13
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Reflection Coefficients Dependence on Incident Angle
– The figure shows graphs of reflection coefficients vs. incident angle for
parallel and perpendicular polarizations for the interface between regions
with the refraction indices n1 = 1 and n2 = 2.
– Reflection coefficients
are calculated using
Fresnel formulas:
R 
sin 0  inc 
sin  0  inc 
R|| 
tg inc  0 
tg inc  0 
 0  arcsin nn12  sin inc 
where inc is an incident angle
Submission
Slide 14
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Channel Polarization Matrix Coefficients
Distribution for the First Order Wall Reflections
– For the first order reflected
signals from walls the plane of
incidence is horizontal.
– Since zero cross-polarization
coupling coefficients were used
in the ray-tracing model, there is
no coupling between horizontal
and vertical polarized signals.
– The reflection coefficients may
be both positive and negative to
correctly
model
circular
polarization.
– The obtained results may be used
to generate final statistical
models (by approximating the
graphs and taking into account
major statistical dependences).
Submission
Slide 15
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Channel Polarization Matrix Coefficients
Distribution for the First Order Ceiling Reflections
– For the first order reflected signals
from ceiling the plane of incidence
is vertical.
– Also there is no coupling between
E and Eφ components.
– The signs of reflection coefficients
(diagonal elements) has changed
relatively to the case of the first
order reflections from walls.
– If circularly polarized antennas are
used then TX and RX antennas
with different handedness will
have
approximately
matched
polarization characteristics. (The
same applies to the first order wall
reflections).
Submission
Slide 16
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Channel Polarization Matrix Coefficients
Distribution for the Second Order Walls Reflections
•
•
•
Submission
Slide 17
For the second order reflected
signals from walls the plane of
incidence is horizontal.
Also there is no coupling
between different polarizations.
Both reflection coefficients
(diagonal
elements)
have
approximately
same
distributions.
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Channel Polarization Matrix Coefficients Distribution
for the Second Order Wall-Ceiling Reflections
•
•
Submission
Slide 18
The second order reflections
from wall-ceiling go through
two reflections from wall and
ceiling or from ceiling and
wall.
As a result, there is a non-zero
“geometrical” coupling in
matrix H (coupling between
components E and Eφ of the
TX and RX antennas) even
though
cross-polarization
coupling coefficients or matrix
R are taken to be equal to zero.
Alexander Maltsev, Intel Corporation
April 2009
doc.: IEEE 802.11-09/0431r0
Conclusion for Polarization Model
• The concept to introduce polarization characteristics into the channel
model is proposed.
• The proposed approach based on calculation of channel polarization
matrix H for each cluster in the channel model with taking into
account reflection properties of the surfaces (reflection matrix R) and
ray tracing geometry
• As an example, the polarization model for the conference room is
considered.
Submission
Slide 19
Alexander Maltsev, Intel Corporation