An attempt was made to calculate the depolarization effects of rain on linearly or elliptically polarized millimeter waves. Results are given in graphs and tables

Bostian, C. W.

Marshall, R. E.

Stutzman, W. L.

Wiley, P. H.

English

NASA Technical Reports Server

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"Polarization Effects in Millimeter Wave Propagation Through Rain:
A Review of Present Theory and a Discussion of Current Experiments"
by P.H. Wiley, C.W. Bostian, W.L. Stutzman, and R.E. Marshall
I. Introduction .
Over the past 60 years the need for an ever increasing number of
communications channels has steadily pushed the upper limit of usable
frequencies from the tens of kilohertz"region, to about 12 GHz. Today,
we are faced with the need to develop reliable.systems at frequencies
above 12 GHz to meet the communications needs of the present and the
near future. However, the mastering of this part of the frequency
spectrum will require overcoming difficulties more severe than those
encountered at lower frequencies. The dominant factor affecting propa-
gation along a ground path at frequencies above 12 GHz is rain. Rain-
fall attenuation and scattering increase so much as frequency is in-
creased above 12 GHz that they are the greatest single problem facing
the designer of communications systems to operate at these millimeter
wavelengths. It is obvious that attenuation and scattering can greatly
reduce the magnitude of a wave propagating through heavy rain but this
is not the only effect. An arbitrarily polarized wave will be depolarized,
or have its polarization changed,as it passes through a rain-filled space.
The gross attenuation of millimeter waves as a function of rainfall rate
has been studied in detail both theoretically and experimentally, but the
dependence of attenuation on the polarization of the wave has received
little attention. Semplak at Bell Labs has measured the differential
attenuation which rain produces between two orthogonal components of a
https://ntrs.nasa.gov/search.jsp?R=19720020510 2020-03-11T18:22:58+00:00Z
-2-
linearly polarized wave and hence verified that rain causes depolarization
of a \\rave which is transmitted with the particular polarization that he
chose. However, the depolarization which would be experienced by a wave
transmitted with any other polarization cannot;be inferred from his
measurements. As yet, no experiment has been done which provided data
sufficient to calculate the depolarization by rain of an arbitrary linearly
or elliptically polarized millimeter wave. It would be valuable to have
actual data on how a wave with arbitrary polarization is affected by rain
for several reasons as listed in Figure 1. First, a system could be de-
signed utilizing a polarization for which the average attenuation is a
minimum. Second, the two orthogonal polarizations exhibiting the minimum
conversion of energy between them could be operated as separate communi-
cations channels and would have the least possible cross-polarization inter-
ference. Third, polarization diversity to increase reliability could be
provided using the two polarizations whose respective fading levels have
the least correlation. Fourth, a great deal could be learned about the
rain itself.
II. How Should Depolarization Effects Be Studied Experimentally?
In order to gain an insight into what measurements are necessary in
order to completely define the depolarization properties of a medium such
i as rain we can turn to the general theory of depolarization as proposed
i 2by Beckmann. This theory rests on the fact that a wave with any arbitrary
polarization can be expressed as the sum of two waves with orthogonal linear
polarizations. Therefore we will toiow how any wave is depolarized if we
measure the depolarization of two orthogonal linearly polarized waves. As
-3-
shown in Figure 2 ET represents the electric field vector of a transmitted
arbitrarily polarized plane wave at a particular instant of time. ET
can be resolved into components E~ and E™ along the x and y axes respectively.
As £„ propagates toward the receiver, a part of its energy will be converted
to a y-polarized wave which is called IL . The remainder of the energy of
readies the receiver will still be x-polarized and is denoted by
ER r. Similarly E~ produces a cross-polarization component ER and a
\ direct component ER . Hence each component of the received wave is com-
posed of the sum of a direct wave and a cross-polarized wave. This relation
1
 is put into equation form in Figure 3. The x component of the received wave
is called ED and is equal to EL plus ED . The y component E~D is equalKX KXX Kyx Ky
: to Ep plus IL ' The T's or polarization coefficients defined in Figure 3Kyy
] allow these equations to be rewrittten in terms of the transmitted waves E™
J i _
: 1 and E^y- The measurement of the polarization coefficients is straightforward.
} Making IL = 0 allows a direct determination of r and r while making
".[ ij ' Jv-A. -^J
Err, = 0 permits; measurement of r and r .ix i yx yy
As a conse,quence of Beckmann's theory of depolarization, every medium
I
will pass either one polarization unchanged, or two polarizations unchanged,
or it will pass all polarizations unchanged; there are no other possibilities.
If raindrops were spherical and if multiple scattering and sidescatter were
negligible, then a rain-filled space would pass all polarizations unchanged.
This result was obtained -in 1908 by Gustav Mie whose work laid the foundation
for later developments. ' Figure 4 shows the polarizations resulting from
scattering from a single spherical raindrop. Note that in the direction of
propagation linear polarization is produced when the incident wave is linearly
polarized and therefore no depolarization occurs.
; -4-
i
; Although no depolarization \i/ould occur if raindrops were spherical,
i it has been established by high speed photography that raindrops are not
spherical but oblate, and that the oblateness increases with drop size.
I
Figure 5 represents a cross-sectional view of an oblate raindrop showing
the major axis and the minor axis which are both perpendicular to the direction
of propagation. This distorted raindrop will no longer pass all polarizations
unchanged, but since- the drop has symmetry about both its major axis and
its minor axis it will not depolarize any wave with linear polarization
• parallel to either axis. .Hence two polarizations are passed unchanged and
the major and minor axes.are -called the principal axes of the drop since
they define the incident polarization for which no depolarization occurs.
In Figure 5 E, and E~ will not be depolarized, but they will suffer unequal
attenuation. The cross-section of the drop seen by E, is larger than the
cross-section seen by E~, and therefore E~ will suffer more attenuation by
the raindrop than will I",. Oguchi was the first to calculate the dif-
ference in attenuation suffered by waves polarized parallel to the principal
axes of an oblate raindrop. The table in Figure 6 shows the expected attenu-
ation at 8.6 mm wavelength for waves polarized parallel to the major and
minor axes as a function of the rain rate in millimeters per hour. As can
be seen, the difference increases from 0.4 db/km at 12.5 mm/hr to 4.6 db/km
at 150 mm/hr. These theoretical predictions made by Oguchi have been veri-
fied experimentally by Semplak.
Although, perhaps, it is not obvious at first, it is the difference in
the attenuations along the principal axes of the drop which causes all
polarizations not parallel to one of these axis to be depolarized. This
-5-
is illustrated in Figure 7 where EL represents a transmitted wave whose
polarization is not parallel to either principal axis. F~ can be expressed
as a component E, along the major axis and E- along the minor axis. As
F, and IL propagate, they will be attenuated but their direction will not
be changed since they are parallel to the principal axis. E~,' and E~f
represent E, and IL at the time they reach the receiver. Since E", has
-L Lt _L '
been attenuated more than E?, E,' will be proportionally smaller thanh J-
E-1 and the resultant IL will not be parallel to ET. Hence £„ has been
depolarized or rotated in the direction of the minor axis. The maximum
depolarization of E~ will occur when IL makes an angle of +_ 45° with
respect to the minor axis of the drop. This means that if the minor axis
of the raindrop were vertical then the transmitted wave should be polarized
at +_ 45° from the vertical in order for the maximum depolarization to
be observed. If the transmitted wave were vertically polarized then no
polarization would be observed and the polarization coefficients could
not be evaluated. The medium would appear not to depolarize when in fact
any polarization except vertical or horizontal would be strongly depolarized.
In reality the minor axis of the raindrop is canted at some angle with
respect to vertical and so a vertically transmitted wave would still be
depolarized to some degree. However, since according to Thomas the average
raindrop canting angle is only about 15° a much greater depolarization would
be observed for a transmitter at +_ 45° from the vertical. Another conclusion
can be drawn from the relation between the position of the principal axes
and depolarization. Since the amount of depolarization depends on the posi-
tion of the principal axes and since the canting angle is almost entirely
-6- . .
dependent on \\tind velocity, depolarization should bear a strong correlation
to wind velocity. There should be little or no correlation between depolari-
zation and rain rate alone unless the position of the principal axes is
taken into account.
III. Description of a Current Experiment
At the present time an experiment funded by NASA is being constructed
. on the campus of Virginia Polytechnic Institute and State University to de-
termine how a wave with arbitrary polarization is depolarized by rainfall.
The experiment will be conducted at a frequency of 17.65 GHz and will measure
the differential attenuation and cross-polarization levels of two orthogonal
linearly polarized waves. The relative phase of both the direct and the
cross-polarized component of each wave will also be measured although it is
believed to be small. From this data the polarization coefficients will
be computed and a prediction of the depolarization of an arbitrarily polarized
wave by rain will be possible.
For the experiment, a path length of 1.43 km was chosen since it is
long enough for the desired effects to be observable, but short enough so
that the rainfall will be likely to be constant along it. The ground
clearance at midpath is 80 ft which represents an angle of about 2 degrees
from the center of the beam. The antennas will be 48 inch parabolic dishes
with a beam width of one degree and hence only the sidelobes will intercept
the ground at midpath. This means that any multipath signal will be more
than 50 dB below the main signal, and therefore multipath propagation will
cause no errors in the cross-polarization measurements which should be no
more than 40 dB below the main signal.
-7-
ii
' The transmitter for the experiment has an output of 50 MW which is
:,' divided by a 3 dB coupler and fed to separate transmitting antennas. The
two transmitting antennas will be linearly polarized at +45° and -45° re-
i
spectively in q'rder to produce the maximum depolarization effect.
i
Two receiving antennas will also be oriented at +_45° and coupled to
separate receivers. When both polarizations are transmitted simultaneously,
the differential attenuation betiveen them will be recorded. If, however,
only one polarization is transmitted, the attenuation of the direct signal
and the conversion to the orthogonal polarization will be recorded.
The rainfall will be measured with tipping-bucket raingauges in incre-
ments of 0.01 inches. Simultaneously, the number of raindrops falling per
unit area will be recorded with a special sensing device. These two measure-
ments will not only give the rainfall rate but will allow computation of
the size of the average raindrop. This should eliminate errors due to the
use of incorrect raindrop size distributions in the computations. Since
a high correlation of wind velocity to depolarization is expected, three
wind recorders will be provided along the path to record wind speed and
direction. An additional weather measurement, the temperature .of the
rain itself, will be recorded since the complex permittivity of water is
a function of temperature."'
All the data generated by the experiment will be converted to digital
form, preprocessed, and stored on tape by an on-line digital computer. The
computer will also make periodic system reliability checks and will vary
the switching speed of the transmitter as the rainfall rate changes.
-8-
Based on the computations by Oguchi of the differential'attenuation
per kilometer encountered by waves polarized parallel to the principal
axes of an oblate raindrop, we are able to predict the levels of the
cross-polarization signals which will be observed for a frequency of
17.65 GHz and a path length of 1.43 km. According to Thomas the ratio
of the rainfall attenuation at 17.65 GHz to that at 35 GHz is as shown
in part (a) of Figure 8. This ratio varies from 0.33 for a rain rate
: of 12.5 mm/hr to 0.44 for a rate of 150 mm/hr. Using these ratios Oguchi's
!
! differential attenuation at 35 GHz for a one kilometer path can be con-
• verted to the differential attenuation at 17.65 GHz for a 1.43 km path as
shown in part (b) of Figure 8. Once the differential attenuation for
waves polarized along the major axis and the minor axis is known, the
I
expected conversion of energy from a polarization of +45° to a polariza-
tion of -45° can 'be computed as a function of the canting angle of the
raindrops. The ratio of the cross-polarized signal received at -45° to
|' the main signal received at +45° will determine one of the polarization
coefficients. Figure 9 shows the method used to compute the expected
•: level of the cross-polarized signal. E™ represents the polarization of
I the transmitted1 wave at an angle of +45° from the vertical. R, and R_
i
denote the directions of the major and minor axis respectively of the
raindrop. EL is resolved into a component E™ along R, and a component
ET- along R-. Components ET-, and ET~ are attenuated by different amounts
as they propagate and when the received signal components E~R, and E~R? are
added to make the received signal ER, we find that ER now has a cross-
polarized component ER perpendicular to E- and a main component E™,, parallel
to Ep. Figure 10 shows the level of £„ in db beloiv £,„, for several rainfall
-9-
rates and for values of 6 of 0° and +15°. As can be seen the expected
level ranges from about -40 db to -15 db. We expect the cross-polarization
discrimination of our antennas to be 35 - 40 db, so we should be able to
measure depolarization for rain rates as low as 10 - 20 mm/hr. From our
data we should be able to predict the depolarization of any arbitrarily
polarized millimeter wave as a function of rainfall rate and wind velocity.
This research is being sponsored by a NASA grant under contract
number NCR 47-004-091. ''"
-10-
References
i 1. Semplak, R. A., "Effect of Oblate Raindrops on Attenuation at 30.9
Ghz," Radio Science, vol. 5, no. 3, March 1970, pp. 559-564.
i 2. Beckmann, Petr., The Depolarization of Electromagnetic Waves, Boulder,
Colorado: The Golem Press, 1968, pp. 10-35.
3. Oguchi, T., "Attenuation of Electromagnetic Waves Due to Rain with
i Distorted Raindrops," J. Radio Res. Labs (Tokyo) vol. 7, no. 33,
September 1960, pp. 467-485.
4. Thomas, David T.,"Cross Polarization Distortion in Microwave Radio
Transmission Due to Rain," Radio Science, vol. 6, no. 10, October
1971, pp. 833-840.
; 5. Setzer, David E., "Computed Transmission Through Rain at Microwave
•
!
 and Visible Frequencies," B.S.T.J., vol. 49, no. 8, October 1970,
pp. 1873-1892.
-11-
1. Polarization with minimum attenuation could be used.
2. Polarization multiplexing could be employed using 2
polarizations with minimum cross-polarization inter-
ference .
3. Polarization diversity could be optimized by using
2 polarizations with the least simultaneous fading.
4. Data concerning the structure of rain would be
obtained.
Figure 1. Benefits of a Depolarization
Study of Arbitrarily Polarized Waves.
-12-
Receiver
Rxx
Figure 2 Expressing depolarization of an arbitrary wave
as the sum of the depolarizations of two ortho-
gonal linearly polarized \vaves.
-13-
E
*
 F
r = Ryx
~ — r = Rxy
Then
n = r c"Rx: STY ^ T + r
^
 T
* yx
measure
r
^efficients xx = ,
T xy when = 0
•* v/\.
rr- , r
V
-14-
elliptical
polarization
linear
polarization
linear
polarization
A
elliptical
polarization
linear
polarization
elliptical
polarization
incident
linear
polarization
elliptical
polarization
Figure 4 Scattering From a Spherical Raindrop
-15-
Minor Axis
Major Axis
Figure 5 Oblate Raindrop
-16-
Attenuation db/kn
I Rain Rate
/ mm/hr
/
12.5
25
50
100
150
Major
Axis
3.21
6.20
12.0
22.1
31.6
Minor
Axis
2.81
5.46
10.3
18.9
27.0
Figure 6 Attenuation of waves polarized parallel
to the major axis and the minor axis of
an oblate raindrop.
-17-
Minor
Axis
Major
Axis
Figure 7 Depolarization by differential attenuation
-18-
Rain Rate mm/hr
12.5
25
50
100
150
Attenuation db/km
35 GHz
3
6
12
22
• 32
17.65 GHz
1
2
• 4
9
14
Attenuation at
Attenuation at
0.33
0.33
0.33
0.41
0.44
17.65 GHz
35 GHz
.
: Rain Rate mm/hr
12.5
25
50 .
100
150
it
Attenuation a1
minor axis
2.81
5.46
10.3
18.9
27.0
: ^i;rnj7 *"*km
major axis
3.21
6.20
12.0
22.1
31.6
Attenuation ai
minor axis
1.33
2.58
4.88
11.10
17.00
L l 7 fi q da- L / . U O i a
1.43^
major axis
1.52
2.94
5.69
12.97
19.90
Figure 8 Computation of the differential attenuation at 17.65 GHz based
' on the attenuation at 35 GHz.
-19-
Vertic
+45C
Figure 9 Method used in computation .of cross-polarized signal level
-20-
Canting angle = 0 = Oe
Rain
Rate
12.5
25
50
100
150
%
1.41
1.41
1.41
1.41
1.41
\
I
I
1
1
1
^2
1
1
1
1
1
I
ER/ETi 4
0.858
0.743
0.570
0.279
0.142
E R /E
2 2
0.840
0.713
0.520
0.225
0.101
**1
0.858
0.743
0.570
0.279
0.142
ER2
0.840
0.713
0.520
0.225
0.101
ERM
1.20
1.03
0.770
0.356
0.171
ERX
0.012
0.021
0.036
0.038
0.029
DY /T:
I\A/ IJ-QX t
- 40.0
- 33.8
- 26.6
- 19.4
- 15.5
Canting angle = 0 = 15°
Rain
Rate
12.5
25
50
100
150
ET
1
1
1
1
1
\
0.866
0.866
0.866
0.866
0.866
\
0.5
0.5
0.5
0.5
0.5
ER / ETl 4
0.858
0.743
0.570
0.279
0.142
^4 %
0.840
0.713
0.520
0.225
0.101
ERl
0.429
0.371
0.285
0.139
0.071
ER2
0.726
0.616
0.450
0.195
0.087
ERM
0.843
0.719
0.532
0.238
0.110
ERX
0.008
0.014
0.023
0.024
0.010
•wy
- 40.4
- 34.2
- 27.2
- 20.0
- 16.2
Figure 10 Expected Cross-Polarization Levels


Polarization effects in millimeter wave propagation through rain: A review of present theory and a discussion of current experiments

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