CP44 1
UK Study Group 3
30 March 2001
Attached is a copy of a paper to be presented at CLIMPARA ’01, immediately preceding
the WP 3J/3M meetings in May/June 2001.
This paper includes further development of the model for rain scatter interference (mode
(2) propagation) intended to update Recommendation P.620, as a result of the WRC2000
request to include earth station elevation angle as an input parameter, and further to clarify
the parameter d.
It is intended to submit an input to WP 3M based on this work.
MODELLING RAIN SCATTER INTERFERENCE: A FRESH ANALYSIS
Chris J Gibbins
Radio Communications Research Unit
Rutherford Appleton Laboratory
Chilton, Didcot, Oxfordshire, OX11 0QX, UK
Tel: 44-1235-446584, Fax: 44-1235-446140, E-mail: C.J.Gibbins@rl.ac.uk
Abstract
Efficient exploitation of the available radio
frequency spectrum is usually achieved through
different services sharing the same frequency bands,
facilitated by an evaluation of the likely levels of
interference which may be generated by one service
into another. Such interference may be influenced
by a variety of atmospheric and meteorological
processes acting on the propagation medium,
including anomalous transhorizon propagation
caused by ducting in clear air and by scattering from
rain coupling into the antenna beam of a victim
receiving station. As pressure grows for access to
available spectrum, it becomes of increasing
importance to estimate interference levels more
precisely, with particular reference to the
configurations of systems to be protected.
This protection is achieved through the process of
coordination, whereby initial estimates of the likely
levels of interference are used to determine a
distance within which a more detailed evaluation of
interference is carried out. For interference due to
scattering from rain, this initial estimate makes use
of a number of simplifying assumptions which can
no longer be sustained. This paper re-examines the
current model for rain scatter interference and
develops an improved formulation in which the
parameters of a victim receiving station are more
properly taken into account. Comparisons are given
between predictions from the new formulation and
experimental measurements of rain scatter
interference.
Keywords:
Interference
Rain
Attenuation,
Rain
Scatter,
Introduction
A basic precept to efficient spectrum management is
the requirement for diverse services to share the
available radio frequency spectrum in a way which
maximizes access and utilization and minimizes
interference. Of the many scenarios where such
different services share the same spectrum, one of
the most ubiquitous is that between terrestrial and
satellite-based radio communications systems, where
it is of paramount importance that sensitive earth
station receiving systems, operating to satellites in
the geostationary orbit (GSO), are protected from
harmful interference from terrestrial transmitters
using the same frequency bands.
Protection of earth stations from such interference is
usually ensured through the complex (and costly)
coordination
procedure
involving
detailed
evaluations of propagation losses between terrestrial
transmitting stations and receiving earth stations, and
in order to reduce the amount of work involved in
this process, initial estimates are made of the size of
the area around the earth station, beyond which
interference levels can be considered negligible.
Internationally, this is achieved using the procedures
in Appendix S7 of the Radio Regulations, which
take into account a wide range of factors that may
contribute to, or mitigate against, the likelihood of
harmful interference effects. Included in this is an
evaluation of the propagation conditions along the
path between an earth station and a hypothetical
terrestrial station, which is based on the models in
ITU-R Recommendation P.620 [1] for clear-air
propagation (mode (1)) and scattering from rain
(mode (2)). These models were developed for
sharing between earth stations with high-gain
antennas and terrestrial transmitting stations with
low-gain antennas.
The current model for rain scatter interference is
based on a number of simplifications, including an
assumption that the earth station operates with an
elevation angle of 20º to the GSO satellite. With the
increasing deployment of satellite communications
systems worldwide, this assumption is no longer
valid, and in Resolution 74, the World
Radiocommunication Conference, WRC 2000,
requested the ITU-R to develop refinements to
propagation mode (2) to address elevation angle
dependency for incorporation into Appendix S7 [2,
3]. Accordingly, a new formulation for the path loss
due to rain scatter is being developed in which the
earth-station elevation angle is an input parameter, in
order to provide more realistic estimates of rain
scatter interference.
Within the area established by the coordination
procedure, more detailed evaluations of path losses
are carried out for specific and identified sources of
interference, generally using the methods in
Recommendation P.452-9 [4]. Although the rain
scatter method in Recommendation P.452 does not
make the same simplifying assumptions as in
Recommendation P.620, there exist some constraints
to its application, amongst which are a restriction to
systems in which one antenna is still considered to
2
be low gain and which is modeled with a Gaussian
beam radiation pattern. This precludes use of the
many antenna radiation patterns which have been
developed specifically for frequency-sharing studies,
and also of application to scenarios in which both
interfering and victim station antennas may have
high gain, for example with earth stations sharing bidirectionally-allocated frequency bands. The model
being developed here has the potential to be
extended to incorporate any antenna radiation pattern
and be applied to any sharing scenario.
Overview of the Rain Scatter Process
The transmission loss between a transmitting
terrestrial station (TS) and a receiving earth station
(ES) due to coupling by rain scatter is described by
the bistatic radar equation (BRE), in which the
received power scattered from a volume element V
is given by:
Pr 
Pt Gt G r 2A
4 
2 2 2
rt rr
 V
Pr 
4 2 
GtAdrr
rt2
2
3

d G r  sin d
 
0
(3)
0
Assuming a Gaussian antenna gain pattern for the
receiving antenna:
   2

G r    G rmax exp    ln 2
  3 



(3)
where 3 is the 3 dB beamwidth, noting that the
product Grmax  32  constant  4 ln 2  e , where e is
the antenna aperture efficiency, and since, from
rt
Figure 1, drr 
d , the received power can
sin  s
be written
Pr 
(1)
where Pt is the transmitted power, Gt, Gr are the
transmitting terrestrial and receiving earth station
antenna gains, λ is the wavelength, η is the average
scattering cross-section per unit volume, A is the
attenuation outside the scattering volume, and rt, rr
are the distances from the transmitting and receiving
antennas to the scattering volume. The geometry of
scattering by a rain cell is shown in Figure 1.
Pt 2
Pt 2 e
32
2

Gt    A 
d
rt sin  s
(4)
For Rayleigh scattering, applicable to scattering
from high-altitude ice crystals and from rain at
frequencies below about 8 GHz, the cross-section
per unit volume, , is related to the radar reflectivity
ZR, defined as the sum of the 6th power of the
scattering-particle diameters, per unit volume:

5 2
K Z R M  10 18
4
mm2/m3
(5)
where λ is in metres and M is a polarization
decoupling factor (M = 1 for matched polarizations).
K
2

m2  1
2
m2  2
(6)
where m is the complex permittivity of water, and
2
K  0.9 at frequencies below about 10 GHz,
decreasing slowly to about 0.8 at 40 GHz.
Figure 1: Geometry of scattering from rain cell.
Integrating over the volume within the rain cell, the
total received power is

Pr  Pr 

Pt 2
Pt 2
4 
4 3 all
space
3

Gt G rA
all space
Gt G rA
rt2 rr2
rt2 rr2
dV
(2)
rr2
The integration in Eq.(4) is carried out over all
angles between the terrestrial station antenna
boresight and the common volume. It is more
convenient, however, to integrate over the height h
of the beam intersection within the rain cell, and to
consider only scattering in the vertical plane, i.e.
forward or back scattering only. Then, if dl is the
incremental length within the common volume,
sin drr dd
after transforming into polar coordinates with the
earth station at the origin.
If the earth station antenna beam is much narrower
than the terrestrial antenna beam at the common
volume, then, to a first approximation, Gt, , A and rt
are independent of  and , and the received power
simplifies to
dl  rt
d
dh

sin  s sin 
(7)
where  is the elevation angle of the earth station. If
the reflectivity term depends on height, i.e.
Z h   Z R F h 
(8)
where ZR is the reflectivity due to rainfall at the
ground, then the bistatic radar equation can be
written as:
Pr  3 e

K
Pt
32 2
2
Z R M  10 18
rt2
C
(9)
where C is the effective scatter transfer function,
which includes all dependencies on height:
C

Gt h Ah F h 
dh
sin 
(10)
For rain, the reflectivity factor in the Rayleigh region
is related to the rainfall rate by:
Z R  400R1.4
mm6/m3
(11)
where R is the rainfall rate in mm/h.
Concatenating all constants, the ratio of received to
transmitted power can then be rewritten
logarithmically in terms of the path loss:
P 
L  10 log t 
 Pr 
 199  20 log r  20 log f  10 log Z R
(12)
 Ag  10 log S  10 log M  10 log C
  
h  hm
C ice  exp     1   R c
cos

sin 
 
hm  d c tan 

hc
where  = 0.230, to convert attenuation from dB to
nepers.
1 is the rain attenuation outside the common
volume towards the Earth station and 2 is the rain
attenuation outside the common volume towards the
terrestrial station:


 d 
 R rm 1  exp   e 


 rm 

  d e  hR cot 

1  
exp  
rm

 
 R rm 

  exp   d e 
 r 


 m



 r  de
 R rm 1  exp  
rm



2  

 r 

 R rm 1  exp   r 
 m 


for hm  hR

(17)


 for hm  hR



 for forward scatter

for back scatter
(18)

1.6  1  cos T  
 
4 f  10  
2

 
3 
 10
(13)


1

cos


1.7
T 
5 f  10)  
 
2

 

where T is the azimuth of the terrestrial station
relative to the earth-station beam azimuth, at the
scatter volume (T = 0 for forward scatter and 180
for back scatter).
Referring to the parameters shown in Figure 2, the
effective scatter transfer function comprizes two
components – for scattering from rain below the rain
height, hR, and for scattering from ice above the rain
height:
C  C rain  Cice

 dh
 y 
sin


 sin 
hh
 g T h exp   R  m
hm

Figure 2: Schematic of rain scatter.
 R  kR is the specific attenuation due to rain in
the rain cell, in dB/km, and rm is a scaling distance
for rain attenuation outside the common volume, and
describes the decrease in rainfall rate away from the
rain cell centre:
rm  600 R 0.5 10  R 1
0.1 9
(14)
(19)
 is the elevation angle of the earth-station antenna
  

C rain  exp     1  2  

  cos 
hc
(16)
dh
g T h  exp  6.5 h  h R 
sin 
where f is the frequency in GHz, Ag is the attenuation
along the path due to atmospheric gases, and S is an
additional allowance for the deviation from Rayleigh
scattering at frequencies above 10 GHz, which is
given in dB by
10 log S  R 0.4
4

 

main beam and
(15)
d c  h  hm  / tan  for forward scatter
y
(20)
h  hm  / tan  for back scatter

h is the height of the intersection of the terrestrial
station horizon ray with the earth station antenna
main beam (km), and dc is the diameter of the rain
cell:
d c  3.3R 0.08
(21)
gT(h) is the numerical antenna gain component of the
terrestrial station in the direction of an integration
element dx, along the earth-station main beam (see
Figure 2).
Note that when the entire common volume of the
intersection between the two antenna beams lies
below the rain height, hR, only the integral Crain
contributes and Cice becomes zero. Conversely,
when the entire common volume lies above the rain
height, Crain vanishes and only Cice contributes.
From Eq. (15), the attenuation outside the common
volume can be written as


 1
 
  10 log exp  0.23
 2  

 cos 20
  (25)


 1.063 1  2
Neglecting the first term and considering only the
attenuation outside the common volume in the
direction of the terrestrial station, this has been
simplified to yield the following expression:
2  638 kR 0.5  10  R 1
0.1 9
The effective scatter transfer function reduces to
C
The Method in Recommendation ITU-R P.620-4
In order to evaluate the integrals in Eqs. (15) and
(16), some simplifying assumptions were made to
derive the mode(2) procedure in Recommendation
P.620-4 [2] (see Figure 2):
 the distance along the earth-station main beam
from the edge of the rain cell to the rain height,
da = D0 – Da, was replaced by the distance ds =
D0 – D, assuming that for scatter heights up to
and just above hR, attenuation would occur
within the entire rain cell;
 the earth-station antenna main-beam elevation
angle was assumed to be  = 20, so that
da  ds 




dc
cos 20 
With these assumptions, the expression for the
transmission loss due to rain scatter becomes:
 10 log Ab  2  10 log C  E  Ag
 d

 R s
1  10 5.16






(27)
6.5  hR  for   hR
E
for   hR
0
(28)
  6r  50 2  10 5 .
(22)
the terrestrial antenna gain, gT, was assumed to
be constant within the rain cell and hence
removed from within the integral;
only the back-scatter component was considered
in the expression for Crain and in the term
10logS;
the second integral, Cice, was replaced with a
simple empirical expression for scattering from
ice;
the polarization decoupling factor, M, was
assumed to be unity.
L  173  20 log r  20 log f  14 log R  g T
2.24
 Rds
The effect of scattering from ice above the rain
height is described by the following empirical
expression, derived from the decrease in reflectivity
above the rain height of 6.5 dB/km, multiplied by a
factor which approximates the distance above the
rain height (equivalent to h – hR in this paper):
where
 3.5R 0.08 km
(26)
(23)
where the deviation from Rayleigh scattering is
given by:
1.7

0.005  f  10  R 0.4 for 10  f  40
10 log Ab  

for f  10
0
(24)
The coordination distance is then determined by
finding the distance r at which the transmission loss
equals the required loss, i.e., the loss necessary to
protect the earth station from harmful interference.
To this distance is added a factor
d 
hR
2 tan 
(29)
to account for the additional distance between the
rain cell and the earth station, to yield the total
distance between stations, within which detailed
interference evaluations are to be performed.
Development of an Improved Model
The effective scatter transfer function includes all
the elevation-angle dependencies, and this was
evaluated only for an earth-station elevation angle of
20 in the development of the current model in
Recommendation P.620. Since there is now a
requirement to include elevation angle as an input
parameter, the integrals in Eqs. (15) and (16) have
been re-examined. The limits of integration depend
on the region within the rain cell at which the
intersection between the earth-station antenna main
beam and the terrestrial station antenna main beam
occurs:
5
for hR  hm
hm

hc  hR
for hm  hR  hm  d c tan 
h  d tan  for h  h  d tan 
c
R
m
c
 m
(30)
The height of the beam intersection point, hm, is
determined by the geometry of the scenario being
considered, and may be expressed in general in
terms of the earth-station elevation angle ,, the
terrestrial station elevation angle  and the angle 
subtended at the Earth’s centre by the two stations
separated by the range distance rs (see Figure 2):
hm  cos 2   2 cos     cos  cos  cos 2 
rE

 rE
sin     
(31)
which, for a terrestrial station with zero elevation
angle, i.e.  = 0, reduces to
 cos2   2 cos    cos   1 
hm  rE 
 1 (32)
sin   




where   rs / rR radians, rE = 8500 km is the
effective radius of the Earth and the distance from
the terrestrial station to the edge of the rain cell is
given by r  rs  d e .
The integral in Eq. (15), for scatter below the rain
height, can be evaluated thus:
hc
Cb 

 exp  0.23
hm

R
1
1  dh


sin

tan
  sin 

h  hm 

4.34
sin  

1  exp  0.23hc  hm 

 R 1  cos   
1

cos  

(33)
and the integral in Eq. (16), for scatter above the rain
height, is similarly derived:
hm  d c tan 
Ca 

hc
exp  1.5h  h R 






and, considering only the back scatter case, the
attenuation outside the common volume towards the
terrestrial station is expressed as:

 r 
2   R rm 1  exp   
 rm 

(36)
Combining these together, the attenuation outside
the common volume, for scatter below the rain
height, is

 

b  exp   0.23 1  2 
cos




(37)
Similarly the attenuation outside the common
volume for scatter above the rain height is given by:

h  hm 
 
a  exp  0.23 1   R c

cos

sin  


(38)
The term hc is given by Eq. (30) for the three
scattering regions – above the rain height for
scattering from ice only, below the rain height for
scattering only from raindrops and the region
spanning the rain height with scattering from both
rain and ice. The scatter transfer function can then
be expressed logarithmically as
10 log C  10 logb Cb  a Ca 
(39)
and the transmission loss becomes
L  173  20 log rs  20 log f  14 log R
 10 log C  10 log Ab  g T  Ag
(40)
In this formulation, the loss (and consequently the
coordination distance) is determined as a function of
the total separation between stations, and thus the
additional factor in Eq. (29) is no longer necessary.
dh
sin 
  hc  h R 

exp  
0.67 
0.67  

sin    hm  d c tan   h R
exp  
0.67
 



hm 
 for hm  h R
 R rm 1  exp  


 rm tan  

  hm  h R  

(35)
1  
 
exp  

  rm tan   
 R rm 
 for hm  h R

exp   hm  

  rm tan   

(34)
The attenuation outside the common volume towards
the earth station can be written in terms of the beam
intersection height within the common volume, hm:
Comparison with Recommendation P.620-4
Figure 3 shows the transmission loss at 18 GHz
calculated at a rainfall rate of 25 mm/h from the
above model, as a function of range, for two
elevation angles and two rain heights, compared with
the loss predicted from Recommendation P.620-4.
For ranges up to about 100 km, the two models are
comparable. Above this range, however, the new
model predicts losses which are generally higher for
a given range, or alternatively shorter ranges (and
hence shorter coordination distances) for a given
6
loss. Significantly higher losses are predicted at the
higher elevation angles, whereas Rec. P.620-4 does
not distinguish between different elevation angles.
The dip in transmission losses at 20 elevation angle
results from the increased coupling due to scattering
from the ice layer in the vicinity of the 0 isotherm.
however, the beam intersection point rises to above 2
km at elevation angles below 5 and to the vicinity
of 5 km around elevation angles near 10 - 15. As
the beam intersection point increases in height
towards the rain height, the transmission loss
decreases, and then begins to increase as the
intersection point moves through the rain height and
into the ice layer above, where the reflectivity
decreases by –6.5 dB/km.
The coordination distances as a function of
frequency resulting from the new model, for a
required transmission loss of 150 dB at a rainfall rate
of 20 mm/h, are compared with those from
Recommendation P.620-4 in Figure 5, for two
elevation angles of 20 and 70. There are actually
two curves shown for Recommendation P.620-4, for
the two elevation angles arising from application of
Eq. (29). In these examples, the coordination
distances from the new model are smaller than those
from Recommendation P.620 for frequencies up to
about 20 GHz, while at higher frequencies, the new
model actually predicts slightly longer distances at
the higher elevation angles.
Figure 3: Transmission loss vs. range from the new
model compared with Rec. P.620-4.
The dependence on elevation angle is further
examined in Figure 4, which shows the transmission
losses calculated at 18 GHz and a rainfall rate of 25
mm/h and two rain heights, at two ranges of 100 and
300 km.
Figure 5: Coordination distances calculated as a
function of frequency, for a transmission loss of 150
dB at a rainfall rate of 20 mm/h.
Comparison with Recommendation P.452-9
Figure 4: Elevation-angle dependence of rainscatter model at 18 GHz and 25 mm/h.
At 100 km separation between the terrestrial station
and the earth station, the beam intersection point lies
below the rain height for all elevation angles, and the
transmission loss varies only slowly, decreasing as
the elevation angle increases. At 300 km separation,
The rain scatter model in Recommendation P.452
does not make the assumption that the terrestrial
antenna gain is constant throughout the rain cell, but
considers a two-part representation in which the
main beam is approximated by a narrow beam
Gaussian distribution while the antenna sidelobes are
modeled with a broad Gaussian distribution.
Analytical expressions for the integrals can be
derived, in terms of error functions, for the three
regions within the rain cell delineated by Eq.(30).
The mode (2) procedure in Recommendation P.452
additionally considers statistical distributions for
both rainfall rates and rain heights, calculating the
loss at each value of rain height in the statistical
distribution and at each value of rainfall rate in the
distribution, assigning to this the joint probability of
7
occurrence. The losses are histogrammed in 1 dB
steps and within each bin the percentages of
occurrence are summed, to yield the overall
cumulative distribution of transmission loss. This
effectively convolves together the probabilities of
occurrence of both rainfall rates and rain heights.
Figure 6 shows the calculated transmission loss at 18
GHz as a function of range for 0.01% of time,
between an earth station with an elevation angle of
10 and a terrestrial station, for a climate with a
rainfall rate of 59 mm/h exceeded for 0.01% of time
and a rain height of 3 km. The steps in the curves
for Recommendation P.452 arise from the
histogramming procedure.
The decrease in transmission loss predicted from
Recommendation P.452, which arises through
increased coupling as the beam intersection moves
through the rain height, is spread out over a wide
range of distances because of the range of rain
heights taken into account. Both the new model and
Recommendation P.620 consider only a single value
for the rain height. In order to effect a more realistic
comparison between the models, a rain height
constant at all probabilities was also considered, and
the comparison with the new model shows very good
agreement, at least up to about 250 km in this
example. There is a difference between the new
model and Recommendation P.452 assuming a
constant rain height of ~3.5 dB at ranges greater than
about 250 km, which is not at present understood.
Figure 6: Transmission losses for 0.01% of time
calculated from Recs. P.452 and P.620, compared
with the new model. Frequency = 18 GHz, 0.01%
rainrate = 59 mm/h, rain height = 3 km.
The predictions from Recommendation P.620 in this
example show a general underestimation of the
transmission loss for ranges up to about 200 km
(which would suggest unnecessarily longer
coordination distances), and an overestimation at
ranges beyond this. The point of inflexion at about
270 km arises from the ice scatter factor, E,
contributing to the loss, and suggests that the
approximation in Eq. (28) is less efficient than the
proposed new model.
Comparison with Experimental Measurements of
Rain Scatter
Figure 7 shows experimental measurements of the
transmission loss due to rain scatter measured over
two years on a 131 km long bistatic link from
Chilbolton to Baldock at 11.2 GHz, from the COST
210 database [7], together with the predicted losses,
based on the simultaneously-measured rainfall rate
distribution, from Recommendations P.452-9 and
P.620-4, together with those from the new model,
based on the measured rainfall rate distributions. In
general, the comparison is good in all cases.
Figure 7: Comparison between model predictions
and measured rain scatter losses on a bistatic link
between Chilbolton and Baldock at 11.2 GHz
(Station separation = 131 km).
In this example, as in the other examples given
above, the terrestrial station is constrained to an
elevation angle of  = 0, i.e. pointing towards the
horizon – which is the geometry considered by
Recommendation P.620 and Appendix S7.
However, as indicated in Eq. (31), the new model
can readily be extended to cases where both stations
have non-zero elevation angles, and Figure 8 shows
a comparison between the model predictions and
measurements on a short path bistatic link, with a
station separation of 26 km, in which the transmitter
had an elevation angle of  = 15 and the receiver
had an elevation angle of  = 27. For the new
model predictions, the free-space path loss and
gaseous attenuations were adjusted to account for the
longer pathlength from stations to the beam
intersection. The new model gives very good
agreement, whereas Recommendation P.620
performs poorly since it is not designed for this
geometry.
The r.m.s difference between the measured losses
and those predicted by the different models are listed
in Table 1, from which it can be seen that there is
little significant difference between any of the
models for the Chilbolton – Baldock path, while the
new model provides a significant improvement for
the shorter, higher-frequency path.
8
comparisons with experimental measurements made
on bistatic links over both long and short paths
indicate good agreement.
Figure 8: Comparison between model predictions
and measured rain scatter losses on a bistatic link
between Nordheim and Darmstadt at 29.6 GHz
(Station separation = 26 km).
TABLE 1
R.m.s. differences (in dB) between
measurements and models
Rec.
Rec.
New
Path
P.452
P.620
Model
Chilbolton 1.1
1.1
0.9
Baldock
Nordheim 5.4
14.3
1.5
Darmstadt
The model is being developed further to include a
convolution with the statistical probability of
occurrence of the rain height, following the mode (2)
procedure in Recommendation P.452-4, and to
consider more properly the antenna radiation
patterns for both the transmitting station and the
receiving station. With the availability of high-speed
processors and sophisticated mathematical software
packages, numerical integration of the effective
scatter transfer function including practical antenna
radiation patterns for both transmitting and receiving
stations, such as that in Recommendation P.620,
becomes quite feasible, and the model can, in
principle, be extended to cover any geometry of
transmitting and receiving antenna beams which
intersect within a rain cell.
Acknowledgements
This work was supported
Radiocommunications Agency.
1.
2.
3.
For a majority of cases, the new model yields shorter
coordination distances than those determined using
current procedure in Recommendation P.620-4,
especially for those applications being actively
considered at present and in the near future, although
somewhat longer coordination distances may result
for systems operating with high elevation angles at
higher frequencies.
The model can additionally be applied to scenarios
in which both transmitting and receiving stations
operate with non-zero elevation angles, and
the
UK
References
Conclusions
A new model has been developed for rain scatter
interference in which the elevation angle of the earth
station being protected is taken into account. The
model is based on a symbolic integration of the
effective scatter transfer function, including
scattering both from rain below the rain height and
from ice above the rain height.
As in
Recommendation P.620-4, the model assumes that
the terrestrial station antenna gain is constant
throughout the rain cell, and can thus be removed
from the integral in the scatter transfer function.
This assumption has been tested and found to be
generally valid, by carrying out a numerical
integration of the scatter transfer function using the
antenna radiation pattern in Recommendation P.620
(Appendix 4 to Annex 1) [8].
by
4.
5.
6.
7.
8.
Recommendation ITU-R P.620-4: “Propagation
data required for the evaluation of coordination
distances in the frequency range 100 MHz to
105 GHz”, Geneva, 2000.
WRC 2000, Resolution 74 [COM4/1]: “Process
to keep the technical bases of Appendix S7
current”, Istanbul, 2000.
Recommendation ITU-R SM.[Doc.1/1004]:
“Determination of the coordination area around
an earth station in the frequency bands between
100 MHz and 105 GHz”, Geneva, 2000.
Recommendation ITU-R P.459-4: “Prediction
procedure for the evaluation of microwave
interference between stations on the surface of
the Earth at frequencies above about 0.7 GHz”,
Geneva, 2000.
CCIR Report 724-2: “Propagation data required
for the evaluation of coordination distance in the
frequency range 1 – 40 GHz”, Reports of the
CCIR, 1990, Annex to Volume V, Propagation
in Non-Ionized Media, Geneva, 1990.
CCIR Report 569-4:
“The evaluation of
propagation factors in interference problems
between earth stations on the surface of the
Earth at frequencies above about 0.5 GHz”, ibid.
COST 210: “Influence of the atmosphere on
interference between radio communications
systems at frequencies above 1 GHz”, Final
Report EU13407EN, CEC, Luxembourg, 1991.
ITU-R Document 3M/160: “Proposed revision
of the mode (2) coordination method in
Recommendation ITU-R P.620-4”, June 2000.
9