Seybold J.S. Introduction to RF Propagation

Подождите немного. Документ загружается.

The earth station is at 20 degrees latitude and the geostationary satellite is

by deﬁnition at 0 degrees latitude, so y=20 degrees in Figure 11.2. It is known

that h = 42,242 km and r

= 6378 km, so

implies that r

= 36,314 km. Using this value for r

, the elevation angle can now

be determined from

which yields q=66.6 degrees. 䊐

11.5 ATMOSPHERIC ATTENUATION

When considering atmospheric absorption on a slant path, the variation of the

atmosphere with altitude must be considered. While temperature, pressure,

and water vapor content may be constant for terrestrial paths over limited dis-

tances, a slant path will cross a continuum of conditions as it passes up through

the atmosphere. Mathematically, this can be treated as if the atmosphere

were made up of discrete layers. When the slant path completely exits the

troposphere such as for an earth-to-space link, the attenuation estimate may

be based on the entire columnar oxygen and water vapor content of the

atmosphere. In this case, the total length of the path is no longer a factor in

computing atmospheric loss, since only the length of the segment that is within

the atmosphere contributes to the attenuation.

The ITU provides a detailed model, called the line-by-line model for deter-

mining the speciﬁc attenuation of the atmosphere [6]. The most accurate esti-

mate of slant-path attenuation is obtained by integrating the results of the ITU

line-by-line speciﬁc attenuation over altitude [6]. Because of its complexity, it

is not often employed in practice, but instead a curve ﬁt, also provided in Ref.

6, is used to predict the speciﬁc attenuation with less than a 15% error. For

most applications, this simpliﬁed calculation presented in Ref. 6 is sufﬁcient.

Figure 11.3 shows a plot of the slant-path attenuation versus frequency for

several elevation angles that was generated using the simpliﬁed approach. The

simpliﬁed approach uses standard atmosphere speciﬁc attenuations, equiva-

lent heights, and the elevation angle of the path to provide an estimate of total

attenuation that is within 10% of the more detailed computation. This method

is valid for elevation angles between 5 and 90 degrees, ground station altitudes

between 0 and 2 km, and frequencies that are more than 500 MHz away from

the centers of the resonance lines (shown in Figure 11.4). The path attenua-

tion is given by

cos

sin

()

cos y

252 SATELLITE COMMUNICATIONS

ATMOSPHERIC ATTENUATION 253

Figure 11.3 Atmospheric absorption for an earth–space path.

–1

–2

0 100 200 300 400 500 600 700 800 900 1000

Frequency, f(GHz)

Zenith attenuation (dB)

Figure 11.4 Zenith attenuation due to atmospheric gases. Curve A: Mean global ref-

erence atmosphere (7.5 g/m

at sea level). Curve B: Dry atmosphere. (Figure 3 from

Ref. 6, courtesy of the ITU.

(11.8)

The speciﬁc attenuations for oxygen and water vapor (g

and g

, respectively)

are the same values used for terrestrial links from Figure 10.1, q is the eleva-

tion angle, and h

and h

are the equivalent oxygen and water vapor heights,

respectively.

For 1 £ f £ 56.7GHz,

For 56.7 < f < 63.3GHz,

For 63.3 £ f < 98.5GHz,

For 98.5 £ f £ 350GHz,

The equivalent water vapor height is given by

for f £ 350 GHz.

This method is valid for ground terminal altitudes of 2 km and below. For

slant paths to high-altitude aircraft or satellites, the entire troposphere is

traversed and the expected attenuation varies only with the geographical

location (environmental conditions) and frequency.Therefore the atmospheric

loss does not depend on the actual link distance.

Example 11.2. Determine the gaseous absorption on a 20-degree slant path

to a satellite if the frequency is 20GHz. Assume standard atmospheric param-

eters and that the ground station is at sea level.

fff

()

165 1

161

22 23 2 91

333

183 3 4 58

190

325 1 3 34

222

hff

362

5 542 1 76414 10 3 05354 10

6 815

118 75 0 321

=- ¥+ ¥ +

()

.. .

362

42 2

0 039581 1 19751 10 9 14810 10

1 0 028687 2 07858 10

90 6

-¥+¥

-+◊

()

.. .

10= km

hfff

23253

5 386 3 32734 10 1 87185 10 3 52087 10

83 26

60 1 2

=- ¥+ ¥ - ¥

()

-- -

.. . .

()

qsin

254 SATELLITE COMMUNICATIONS

The easiest method to determine the expected attenuation is to interpolate

between the 10- and 30-degree curves in Figure 11.3. By interpolating, the

attenuation can be estimated to be about 1.4 dB for the entire path. 䊐

11.6 IONOSPHERIC EFFECTS

The ionosphere has many effects on electromagnetic waves, which apply

primarily below 10 GHz and are pronounced below 1 GHz. The effects of the

ionosphere correlate with sun spot activity and the diurnal cycle. Possible

effects include: fading, which can be signiﬁcant (20 dB or more); depolarization

or Faraday rotation, time delay; and dispersion (differential time delay). Table

11.1 provides a summary of ionospheric effects for several frequencies at a

30-degree elevation angle.

Faraday rotation is an angular rotation of the polarization vector. For cir-

cular polarization, the only impact is to change the angle between the two sets

of polarization axes, which can degrade the cross-polarization isolation and

increase the cross-polarization loss if the antennas are not perfectly circularly

polarized. This is only signiﬁcant in systems that have a signiﬁcant axial ratio

loss to begin with (see Chapter 3 for more details). The relative insensitivity

of circular polarization to Faraday rotation is one reason circular polarization

is often used in satellite communications, particularly below 10 GHz. If linear

polarization is used, for maximum energy transfer the antenna polarization

axes must be aligned, which can be difﬁcult for space communication even

without the effect of Faraday rotation.

Propagation delay may be important in some time critical systems such as

navigation or GPS. If two carriers are available, however, it is possible to use

the 1/f

relationship to estimate the additional propagation delay and remove

it. This is done with GPS receivers that use both the L1 and L2 frequencies.

This was one of the techniques that military GPS used to outperform civilian

GPS. Recent changes to the GPS satellite constellation and operating doctrine

have made dual frequency operation and the accompanying delay correction

available to civilian systems as well.

It is interesting that most of the refraction values in the table are on the

order of minutes and seconds, not degrees. Only at the HF frequencies is the

refraction signiﬁcant enough to bend the rays back to earth. The remaining

effects are negligible below 1 GHz, with the exception of scintillation.

11.7 RAIN FADES

As discussed in Chapter 10, hydrometeors can cause attenuation, scattering,

and depolarization of electromagnetic waves. Rain cell models such as Crane

or ITU are employed to predict the rain fade depth that will occur with a given

RAIN FADES 255

256 SATELLITE COMMUNICATIONS

TABLE 11.1 Ionospheric Effects for Several Different Frequencies at 30-Degree Elevation Angle

Frequency

Effect Dependence 0.1 GHz 0.25 GHz 0.5 GHz 1 GHz 3 GHz 10 GHz

Faraday rotation 1/f

30 rotations 4.8 rotations 1.2 rotations 108° 12° 1.1°

Propagation delay 1/f

25 ms4ms1ms 0.25 ms 0.028 ms 0.0025 ms

Refraction 1/f

<1° <0.16° <2.4¢<0.6¢<4.2≤<0.36≤

Variation in the 1/f

20¢ 3.2¢ 48≤ 12≤ 1.32≤ 0.12≤

direction of arrival

(rms)

Absorption (auroral ª1/f

5 dB 0.8 dB 0.2 dB 0.05 dB 6 ¥ 10

-3

dB 5 ¥ 10

-4

and/or polar cap)

Absorption (mid- 1/f

<1dB <0.16 dB <0.04 dB <0.01 dB <0.001 dB <1 ¥ 10

-4

latitude)

Dispersion 1/f

0.4 ps/Hz 0.026ps/Hz 0.0032 ps/Hz 0.0004 ps/Hz 1.5 ¥ 10

-5

ps/Hz 4 ¥ 10

-7

ps/Hz

Scintillation

See Rec. See Rec. See Rec. See Rec. >20 dB ª10 dB ª4dB

ITU-R P.531 ITU-R P.531 ITU-R P.531 ITU-R P.531 Peak-to-peak Peak-to-peak Peak-to-peak

Values observed near the geomagnetic equator during the early night-time hours (local time) at equinox under conditions of high sunspot number.

Source: Table 1 from Ref. 1 courtesy of the ITU.

probability. The depth of a rain fade is correlated with rain rate and highly

correlated with the transmit frequency. The rain fade depth, duration, and fre-

quency of occurrence are highly dependent upon geographical location and

even at a given location can vary considerably year-to-year. The modeling of

rain fades for satellite links is similar to that for terrestrial links, albeit a little

more complex, since the model must account for the variation in rain density

with altitude. Rain statistics (for terrestrial or satellite links) tend to be cyclo-

stationary on a month-to-month basis, meaning that the statistics for a partic-

ular month are consistent from year-to-year, but the statistics from one month

to the next are not.

11.7.1 ITU Rain Attenuation Model for Satellite Paths

The amount of fading due to rain is a function of the frequency and is highly

correlated with rain rate. By using rain statistics for a given region, it is possi-

ble to determine the probability that a given fade depth will be exceeded. The

rain availability of a communication link is the complement of the probabil-

ity of the link fade margin being exceeded. The ITU [7] provides global rain

statistics by dividing the earth into rain regions and assigning a rain rate to

each region along with the probability of that rain rate being exceeded. The

ITU model used here employs only the 0.01% rain statistics and then applies

an adjustment factor to the predicted rain fade depth for other probabilities.

For ground-to-space and ground-to-airborne links, the statistical height of

the rain cell must be taken into account [1, 8]. The assumption is that for

ground-to-airborne links, the airborne platform altitude is above the tropo-

sphere. When this assumption holds, the slant-path rain attenuation is no

longer a function of the link distance. The latest ITU recommendation [8] ref-

erences a text ﬁle of rain cell height data as a function of latitude and longi-

tude. A less accurate, but nonetheless widely employed, method of computing

the expected rain cell height as a function of latitude and the rainfall rate is

to use the expression from an earlier recommendation [9]. For latitudes less

than 36 degrees, the rain cell height is assumed to be 4 km. For higher latitudes,

the rain cell height is taken to be

(11.9)

In central Florida then, the nominal rain cell height is 3.6 km.

The ITU [1] gives a 10-step procedure for computing the rain attenuation

on a satellite path. That procedure is paraphrased here.

Step 1: Determine the rain height, h

Step 2: Determine the length of the slant path that is below the top of the rain

cell.

For q<5°,

=- - ∞

()

4 0 075 36. latitude

RAIN FADES 257

(11.10)

Otherwise,

(11.11)

where h

is the surface height where the antenna is located.

Step 3: Calculate the horizontal projection of L

(11.12)

Step 4: Find the 0.01% rainfall rate for the location. For Florida, rain region N,

(11.13)

Step 5: Calculate the speciﬁc attenuation for the desired frequency, polariza-

tion, and rain rate using the interpolated linear regression coefﬁcients that

are found from (10.3) and (10.4).

(11.14)

Step 6: Compute the horizontal reduction factor, r

0.01

for 0.01% of the time.

(11.15)

where L

is in km and f is in GHz.

Step 7: Calculate the vertical adjustment factor v

0.01

for 0.01% of the time.

(11.16)

For z> q,

(11.17)

Otherwise,

(11.18)

()

sin q

()

001.

cos q

tan

001

degrees

001

1078 0381

+--

()

kR=

()

001.

dB km

001

= mm h

Gsl

()

cos q

()

sin q

()

sin sinqq

258 SATELLITE COMMUNICATIONS

If latitude < 36 degrees,

Otherwise,

Then,

(11.19)

Step 8: The effective path length is then computed as

(11.20)

Step 9: The 0.01% rain fade depth is next computed from

(11.21)

Step 10: To determine the maximum fade depths for other probabilities in the

range from 0.001% to 5%, the availability adjustment factor is applied.

If p ≥ 1% or if |latitude| ≥ 36 degrees,

(11.22)

If p < 1% and |latitude| < 36 degrees and q>25 degrees,

(11.23)

Otherwise,

(11.24)

The maximum fade is then given by

(11.25)

The overall expected attenuation on an earth–space path ends up being a func-

tion of the rain rate (availability), frequency, and elevation angle only. Figure

11.5 shows plots of the expected rain attenuation on an earth–space path

versus availability, for several elevation angles and operating frequencies using

pAp

()

---

()()()(

001

0 655 0 033 0 045 1

001

. . ln . ln sin

b=- - ∞

()

0 005 36 1 8 4 25. . . sinlatitude q

b=- -

()

0 005 36. latitude

b=0

RE001.

=g dB

LLv

001.

001

1311 045

sin .

()

()()

q c

c=0

c= -36 degrees latitude

RAIN FADES 259

the ITU model in rain region N. As the required availability increases, so does

the amount of rain-fade margin that is needed.

Example 11.3. Consider a geostationary satellite that uses a 30-GHz uplink

and a 20-GHz downlink. If the uplink is located in New York City, the down-

link is in Miami and the satellite is at 90 degrees longitude, determine the

99.9% fade margin for both the downlink and the uplink if circular polariza-

tion is used. What is the overall probability of a communications outage?

First, the satellite and ground station locations are used to determine the

elevation angles to the satellite. New York is in rain region K, its latitude is

approximately 40 degrees, and its longitude is about 74 degrees. For the uplink,

then the earth lat/long parameters are;

the satellite lat/long parameters are;

==090degrees degrees,

==40 74deg , degrees rees

260 SATELLITE COMMUNICATIONS

90 91 92 93 94 95 96 97 98 99 100

5 Deg El ITU-N

15 Deg El ITU-N

45 Deg El ITU-N

85 Deg El ITU-N

Rain Attenuation on Earth-Space Path

Availabilit

Rain Attenuation (dB)

Figure 11.5 Required rain attenuation margin values versus availability for different

elevation angles at 30 GHz using the ITU model in rain region N, at 30 degrees

latitude.

and, using (11.4),

Next, the uplink slant range is found using (11.5):

The elevation angle is determined using (11.6),

Using information from Table 10A.2, the speciﬁc attenuation regression coef-

ﬁcients for the uplink are

Using the uplink elevation angle of 40.9 degrees and a tilt angle of 45 degrees

for circular polarization, the regression coefﬁcients for the uplink are found

from (10.3) and (10.4) to be

Next, the 10-step procedure is applied.

Step 1: Find the rain height.

Step 2: Determine the length of the slant path that is below the rain height.

()

37 0

40 9

565

sin .

.km

=- - ∞

()

=4 0 075 36 3 7..latitude km

HH VV

0 177

1 011

0 187 1 021

0 167 1 0

., .

= 40 9. degrees

cos

, sin .

()

42 378 42 6

37 930

076

sUL

()

=42 378 1

6 378

42 378

6 378

42 378

42 6 37 930

cos . , km

= 42 6. degrees

RAIN FADES 261