Seybold J.S. Introduction to RF Propagation

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Step 3: Calculate the horizontal projection of L

Step 4: Find the 0.01% rainfall rate for rain region K from Table 10.2.

Step 5: Calculate the speciﬁc attenuation for the frequency, polarization, and

rain rate.

Step 6: Compute the horizontal reduction factor.

Step 7: Compute the vertical adjustment factor.

Since z>q,

Since latitude > 36,

and

Step 8: Compute the effective path length

Step 9: Compute the 0.01% fade depth.

001

7 75 4 971 38 52

.. .=◊ = dB

=◊=3 925 1 267 4 971.. .km

001

180

40 9 1 0

1 40 9 31 1

3 925 7 75

045

1 267

sin .

+∞

()

◊

-◊ +

()

c=0

◊

()

427 074

40 9

3 925

cos .

.km

◊

tan

37 0

427 074

51 28 degrees

001

2427

1078

427 411

0381

0 695

◊

()

-◊

()

=0 072 42 7 75

1 082

dB km

001

= mm h

()

=565 409 427. cos . . km

262 SATELLITE COMMUNICATIONS

Step 10: Compute the fade depth for 0.1% probability.

For these locations and angles,

and the expression for the 0.1% fade is

Thus the uplink rain fade can be expected to exceed 14.8 dB 0.1% of the

year.

Using a similar approach for the downlink, yields

The central angle is

from which the slant range is found,

and then the elevation angle to the satellite can be determined

The 20-GHz regression coefﬁcients are

for circular polarization, the regression coefﬁcients are

The 0.01% attenuation is

And ﬁnally the 0.1% fade depth is 16.85 dB.

Thus the downlink rain fade can be expected to exceed 16.85 dB 0.1%

of the year. In this case, the uplink and downlink fades are comparable. The

001

43 25

.= dB

k ==0 072 1 083., .a

0 075 1 099

0 069 1 065

., .

= 57 7. degrees

sDL

= 36 850,km

= 27 7. degrees

26 80

090

degrees degrees

0 655 0 033 0 1 0 045 38 52 0 1 0 1 40 9

38 52

001

14 8

. . ln . . ln . . sin .

()

∞

()()

b=0

RAIN FADES 263

30-GHz uplink has slightly less attenuation even though it has the lower ele-

vation angle.This is due to the more moderate rain region in New York.The

rain in Miami is heavy enough to cause the lower-frequency (20-GHz)

downlink at the greater elevation angle to still have a slightly larger rain

fade.

To determine the overall link availability, the weather in Miami and New

York are treated as independent. Furthermore, it is clear that if either end

fades out, the link will drop. The probability of the link being out is one

minus the probability of both links being operational, which, since they are

independent, is simply the product of their probabilities.

䊐

11.7.2 Crane Rain Attenuation Model for Satellite Paths

The Crane global model [10, 11] is similar to the ITU model in that it also

employs the concept of rain regions for determining expected rain rates and

that the attenuation is a function of the range rate. It differs in that the data

are slightly different and the attenuation model is considerably different.

Crane provides rain data for a variety of rain probabilities, but does not use

an availability adjustment factor like the ITU model. Even so, experience

shows that the models generally produce results that are in reasonably close

agreement.

The process of determining the linear regression coefﬁcients for the

speciﬁc attenuation due to rain is the same as for the ITU. In fact, the same

coefﬁcients are used. The difference is that the speciﬁc rain rate for the

desired availability must be used. The rain rates versus probability are given

in Table 10A.4 for each of the Crane rain regions.

For ground-to-space links, the height of the rain cell must be taken into

account, just as it is with the ITU model. Crane uses rain cell height data that

are a function of latitude and probability [12]. As seen in Table 11.2, for 30

degrees latitude, the rain heights are

Crane gives a procedure for doing a logarithmic interpolation over

availability [13]:

(11.26)

Figure 11.6 shows the interpolated rain cell height for several different lati-

tudes. For other latitudes, values from Table 11.2 should be used in (11.26).

Hp h

()

001 1

0 001ln .

394 1==.%km for

001

5 35 0 001==..%km for

PPP

outage UL DL

=- = ¥

1 1 999 10 0 002

.~.

264 SATELLITE COMMUNICATIONS

RAIN FADES 265

TABLE 11.2 Crane Model Rain Cell Heights for

Different Latitudes

Latitude, North

Rain Height (km)

or South (deg) 0.001% 1%

£2 5.3 4.6

4 5.31 4.6

6 5.32 4.6

8 5.34 4.59

10 5.37 4.58

12 5.4 4.56

14 5.44 4.53

16 5.47 4.5

18 5.49 4.47

20 5.5 4.42

22 5.5 4.37

24 5.49 4.3

26 5.46 4.2

28 5.41 4.09

30 5.35 3.94

32 5.28 3.76

34 5.19 3.55

36 5.1 3.31

38 5 3.05

40 4.89 2.74

42 4.77 2.45

44 4.64 2.16

46 4.5 1.89

48 4.35 1.63

50 4.2 1.4

52 4.04 1.19

54 3.86 1

56 3.69 0.81

58 3.5 0.67

60 3.31 0.51

62 3.14 0.5

64 2.96 0.5

66 2.8 0.5

68 2.62 0.5

≥70 2.46 0.5

Source: Table 4.1 from Ref. 12, courtesy of John Wiley & Sons.

The approximate path length in rain is then

(11.27)

where

is the effective rain cell height

is the effective station height

z is the elevation angle

is the 4/3 earth radius, 8500 km

HHR

RSe

()

tan tanzz

266 SATELLITE COMMUNICATIONS

99 99.1 99.2 99.3 99.4 99.5 99.6 99.7 99.8 99.9 100

0.5

1.5

2.5

3.5

4.5

5.5

Crane Rain Cell Height vs. Availability

Availability (%)

Rain Cell Height (km)

99.95 99.955 99.96 99.965 99.97 99.975 99.98 99.985 99.99 99.995 100

0.5

1.5

2.5

3.5

4.5

5.5

Crane Rain Cell Height vs. Availability

Availability (%)

Rain Cell Height (km)

∞

>70

∞

>70

∞

Figure 11.6 Rain cell height versus availability at 30 degrees latitude, for the Crane

global model.

The expression for terrestrial path rain attenuation is employed to determine

the horizontal path attenuation.

(11.28)

and

(11.29)

where d(RR) is a function of the rain rate,

(11.30)

d is link distance in km,

(11.31)

and

(11.32)

The total slant-path attenuation due to rain is then given by

(11.33)

where

(11.34)

The overall attenuation on an earth–space path ends up being a function of

the rain rate (availability), frequency and elevation angle, just as it does with

the ITU model. Figure 11.7 shows plots of the expected rain attenuation on

an earth–space path versus availability, for several elevation angles and

operating frequencies using the Crane model in rain region E.

When applying the Crane global model to slant paths with elevation angles

less than about 10 degrees, depending upon the availability and the rain cell

height, it is possible to compute a slant-path distance, d, that is greater than

22.5 km. Since this is beyond the valid range of the Crane model, the values

for Atten(RR,d) and hence A

are invalid. This can lead to bogus attenuation

L HR RHH HH HR

se eR S R S Se

()()

()

+-- +

()()

222

2sin sinzz

Atten

zRR=◊ -

()()

a 0 026 0 03..ln

RR=◊

()

083 017

026 003

..ln

d RR RR

()

38 06. . ln km

Atten k RR

ee e

RR d

yRR

zRR RR

=◊

()

◊

()

◊

()

◊

()

22 5

083 017..ln

. km

Atten k RR e y d RR

=◊ -

()

◊

d10dB km,

RAIN FADES 267

estimates that can increase as the availability decreases. The author has found

that a viable work around for this circumstance is to replace Atten(RR,d) by

Atten(RR,22.5) in the expression for A

whenever d > 22.5 km.

Example 11.4. A ground station must communicate with a high-ﬂying aircraft

with 99.9% rain availability. The aircraft is ﬂying at 50,000ft and may appear

at elevation angles as low as 15 degrees. What fade margin should be used if

the ground station is located in Southern California and the frequency of oper-

ation is 10 GHz?

The aircraft altitude ensures that it will be ﬂying above any heavy rainfall,

so this problem may be treated as a satellite rain attenuation problem. South-

ern California is in Crane rain region F and it is assumed that the latitude is

32 degrees, that the earth station altitude is near sea level, and that circular

polarization is used.

The regression coefﬁcients for circular polarization at 10 GHz are readily

found to be

k ==0 009485 1 270., .a

268 SATELLITE COMMUNICATIONS

90 91 92 93 94 95 96 97 98 99 100

5 Deg El Crane-E

15 Deg El Crane-E

30 Deg El Crane-E

85 Deg El Crane-E

Rain Attenuation on an Earth-Space Path

Availability

Rain Attenuation (dB)

Figure 11.7 Rain attenuation values versus availability for different elevation angles

at 30 GHz using the Crane model in rain region E, at 30 degrees latitude.

using values from Table 10A.2 and t=45 degrees for circular polarization.

The 99.9% rain rate is found in Table 10A.4:

The rain height is found by interpolating values from Table 11.2 for 32 degrees:

The path distance in rain is given by

The next step is to compute d(RR):

Since d >d(RR), the horizontal path attenuation is given by

where

and

The resulting attenuation is then

The total slant-path attenuation due to rain for 99.9% availability is then given

where

Atten

Atten = 245.dB

y = 0 2175.

z =-0 0305.

Atten k RR

ee e

yRR

zRR RR

=◊

()

◊

()

◊

()

083 017..ln

d 53 2799..

()

= km

d ª

()

2 4 27 0

15 15 2 4 27 0 8500

15 87

tan tan .

.km

01 376

528 376

0 001

01 427.% .

ln .

ln . .

()

= km

RR = 53.mmh

RAIN FADES 269

The result is

It is clear that the dry climate in California combined with a lower frequency

considerably reduces the impact of rain on link operation. 䊐

11.7.3 The DAH Rain Attenuation Model

The DAH rain attenuation model, developed by Dissanayake, Allnut, and

Haidara [14, 15] and also sometimes called the USA model, is a modiﬁcation

of the ITU model presented earlier. The essential difference of the DAH

model is that it accounts for the fact that rain is nonhomogeneous in both the

vertical and horizontal directions. The DAH model can be implemented using

the following 10-step procedure [14].

Step 1: Compute the freezing height of the rain (analogous to the rain height

for the ITU model) using the station latitude, f.

(11.35a)

(11.35b)

Step 2: Determine the slant path below the freezing rain using the same pro-

cedure as the ITU model.

For q<5 degrees,

(11.36a)

Otherwise,

(11.36b)

where

q is the elevation angle

is the station height ASL in km

()

sin q

fr s

()

sin sinqq

=- -

()

≥∞5 0 0 075 23 23.. ,ff

=∞<<∞50 23, f

= 246.dB

L HR RHH HH HR

Se eR S R S Se

()()

()

+-- +

()()

222

2sin sinzz

270 SATELLITE COMMUNICATIONS

Step 3: Determine the horizontal projection of the slant-path length, just as

was done for the ITU model.

(11.37)

Step 4: Determine the speciﬁc attenuation due to rain for 0.01% availability

and the desired frequency and polarization, the same as for the ITU model.

(11.38)

Step 5: Compute the horizontal path adjustment factor for 0.01% of the time

using the same expression as was used for the ITU model.

(11.39)

where L

is in km and f is in GHz.

Step 6: Calculate the adjusted rainy path length.

(11.40a)

(11.40b)

where

(11.41)

Step 7: Compute the vertical adjustment factor analogous to the ITU model.

(11.42)

where

(11.43a)

(11.43b)

cf=≥∞036for

cf f=- <∞36 36for

001

1311 045

sin .

()

()()

tan

001

Lrh

fr s

()

sin q

zqfor

Lrh

()

001.

cos q

zqfor

001

1078 0381

+--

()

kR=

()

001.

dB km

()

cos q

RAIN FADES 271