Seybold J.S. Introduction to RF Propagation

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242 RAIN ATTENUATION OF MICROWAVE AND MILLIMETER-WAVE SIGNALS

TABLE 10A.1 Linear Regression Coefﬁcients for Determination of Speciﬁc

Attenuation Due to Rain as a Function of Polarization

Frequency (GHz) k

1 0.0000387 0.0000352 0.912 0.880

2 0.000154 0.000138 0.963 0.923

4 0.000650 0.000591 1.121 1.075

6 0.00175 0.00155 1.308 1.265

7 0.00301 0.00265 1.332 1.312

8 0.00454 0.00395 1.327 1.310

10 0.0101 0.00887 1.276 1.264

12 0.0188 0.0168 1.217 1.200

15 0.0367 0.0335 1.154 1.128

20 0.0751 0.0691 1.099 1.065

25 0.124 0.113 1.061 1.030

30 0.187 0.167 1.021 1.000

35 0.263 0.233 0.979 0.963

40 0.350 0.310 0.939 0.929

45 0.442 0.393 0.903 0.897

50 0.536 0.479 0.873 0.868

60 0.707 0.642 0.826 0.824

70 0.851 0.784 0.793 0.793

80 0.975 0.906 0.769 0.769

90 1.06 0.999 0.753 0.754

100 1.12 1.06 0.743 0.744

120 1.18 1.13 0.731 0.732

150 1.31 1.27 0.710 0.711

200 1.45 1.42 0.689 0.690

300 1.36 1.35 0.688 0.689

400 1.32 1.31 0.683 0.684

Source: Table 1 from Ref. 10, courtesy of the ITU.

APPENDIX 10A: DATA FOR RAIN ATTENUATION MODELS

DATA FOR RAIN ATTENUATION MODELS 243

TABLE 10A.2 Interpolated Regression Coefﬁcients for 1–40 GHz

f(GHz) k

1 3.87 ¥ 10

-5

0.912 3.52 ¥ 10

-5

0.88

2 1.54 ¥ 10

-4

0.963 1.38 ¥ 10

-4

0.923

3 3.576 ¥ 10

-4

1.055 3.232 ¥ 10

-4

1.012

4 6.5 ¥ 10

-4

1.121 5.91 ¥ 10

-4

1.075

5 1.121 ¥ 10

-3

1.224 1.005 ¥ 10

-3

1.18

6 1.75 ¥ 10

-3

1.308 1.55 ¥ 10

-3

1.265

7 3.01 ¥ 10

-3

1.332 2.65 ¥ 10

-3

1.312

8 4.54 ¥ 10

-3

1.327 3.95 ¥ 10

-3

1.31

9 6.924 ¥ 10

-3

1.3 6.054 ¥ 10

-3

1.286

10 0.01 1.276 8.87E-3 1.264

11 0.014 1.245 0.012 1.231

12 0.019 1.217 0.017 1.2

13 0.024 1.194 0.022 1.174

14 0.03 1.173 0.027 1.15

15 0.037 1.154 0.034 1.128

16 0.043 1.142 0.039 1.114

17 0.05 1.13 0.046 1.101

18 0.058 1.119 0.053 1.088

19 0.066 1.109 0.061 1.076

20 0.075 1.099 0.069 1.065

21 0.084 1.091 0.077 1.057

22 0.093 1.083 0.085 1.05

23 0.103 1.075 0.094 1.043

24 0.113 1.068 0.103 1.036

25 0.124 1.061 0.113 1.03

26 0.135 1.052 0.123 1.024

27 0.147 1.044 0.133 1.017

28 0.16 1.036 0.144 1.011

29 0.173 1.028 0.155 1.006

30 0.187 1.021 0.167 1

31 0.201 1.012 0.179 0.992

32 0.216 1.003 0.192 0.985

33 0.231 0.995 0.205 0.977

34 0.247 0.987 0.219 0.97

35 0.263 0.979 0.233 0.963

36 0.279 0.971 0.247 0.956

37 0.296 0.962 0.262 0.949

38 0.314 0.954 0.278 0.942

39 0.332 0.947 0.294 0.935

40 0.35 0.939 0.31 0.929

244 RAIN ATTENUATION OF MICROWAVE AND MILLIMETER-WAVE SIGNALS

TABLE 10A.3 ITU Rainfall Rates

for Different Probabilities and Rain Regions

Percentage

of Time (%) A B C D E F G H J K L M N P Q

1.0 <0.1 0.5 0.7 2.1 0.6 1.7 3 2 8 1.5 2 4 5 12 24

0.3 0.8 2 2.8 45 2.4 4.5 7 4 13 4.2 7 11 15 34 49

0.1 2 3 5 8 6 8 12 10 20 12 15 22 35 65 72

0.03 5 6 9 13 12 15 20 18 28 23 33 40 65 105 96

0.01 8 12 15 19 22 28 30 32 35 42 60 63 95 145 115

0.003 14 21 26 29 41 54 45 55 45 70 105 95 140 200 142

0.001 22 32 42 42 70 78 65 83 55 100 150 120 180 250 170

Rainfall intensity exceeded (mm/h).

Source: Table 1 from Ref. 11, courtesy of the ITU.

DATA FOR RAIN ATTENUATION MODELS 245

TABLE 10A.4 Crane Rain Rates for Different Probabilities and Rain Regions

Percent A B B1 B2 C D1 D2 D3 E F G H

of Year RR RR RR RR RR RR RR RR RR RR RR RR

5 0 0.2 0.1 0.2 0.3 0.2 0.3 0 0.2 0.1 1.8 1.1

3 0 0.3 0.2 0.4 0.6 0.6 0.9 0.8 1.8 0.1 3.4 3.3

2 0.1 0.5 0.4 0.7 1.1 1.2 1.5 2 3.3 0.2 5 5.8

1 0.2 1.2 0.8 1.4 1.8 2.2 3 4.6 7 0.6 8.4 12.4

0.5 0.5 2 1.5 2.4 2.9 3.8 5.3 8.2 12.6 1.4 13.2 22.6

0.3 1.1 2.9 2.2 3.4 4.1 5.3 7.6 11.8 18.4 2.2 17.7 33.1

0.2 1.5 3.8 2.9 4.4 5.2 6.8 9.9 15.2 24.1 3.1 22 43.5

0.1 2.5 5.7 4.5 6.8 7.7 10.3 15.1 22.4 36.2 5.3 31.3 66.5

0.05 4 8.6 6.8 10.3 11.5 15.3 22.2 31.6 50.4 8.5 43.8 97.2

0.03 5.5 11.6 9 13.9 15.6 20.3 28.6 39.9 62.4 11.8 55.8 125.9

0.02 6.9 14.6 11.3 17.6 19.9 25.4 34.7 47 72.2 15 66.8 152.4

0.01 9.9 21.1 16.1 25.8 29.5 36.2 46.8 61.6 91.5 22.2 90.2 209.3

0.005 13.8 29.2 22.3 35.7 41.4 49.2 62.1 78.7 112 31.9 118 283.4

0.003 17.5 36.1 27.8 43.8 50.6 60.4 75.6 93.5 130 41.4 140.8 350.3

0.002 20.9 41.7 32.7 50.9 58.9 69 88.3 106.6 145.4 50.4 159.6 413.9

0.001 28.1 52.1 42.6 63.8 71.6 86.6 114.1 133.2 176 70.7 197 542.6

Source: Table 3.1 from Ref. 2, courtesy of John Wiley & Sons.

246

Introduction to RF Propagation, by John S. Seybold

CHAPTER 11

Satellite Communications

11.1 INTRODUCTION

There are numerous applications of satellite systems, including remote sensing

(SAR, IR, visual), communication links for telephone, aircraft, and military

purposes, mobile communications such as satphones, Iridium, and so on, direct

broadcast satellite TV, navigation systems such as GPS, and communication

eavesdropping for intelligence collection. While each of these objectives have

their own unique requirements, all satellite systems share certain characteris-

tics and operate in the same kind of environment. It is also essential that all

man-made satellites be able to communicate with their terrestrial control sta-

tions regardless of their primary mission.

Satellite communication links entail a signal traversing the entire

atmosphere and therefore can suffer signiﬁcantly due to atmospheric factors,

depending upon the frequency. In addition, the distances involved are consid-

erable, so the free-space loss is much larger than it is for terrestrial links. The

costs of reaching orbit dictates that satellite aperture size and transmit power

are at a premium, making reliable link design a challenge.

In this chapter, many of the channel impairments that have been previously

discussed are revisited and it is shown how they are applied to satellite com-

munication links. First the various types of satellite orbits and their charac-

teristics are brieﬂy examined, followed by determination of the range to the

satellite. Computation of the actual line-of-sight or slant-range distance to the

satellite is somewhat complicated by the curvature of the earth. Once the dis-

tance to the satellite has been determined and the free-space loss calculated,

other link impairments must be considered. These include atmospheric atten-

uation (gaseous absorption, rain, clouds, and fog), and ionospheric effects. A

considerable amount of time is spent on the atmospheric absorption and rain

attenuation, even though they have been covered in earlier chapters. This is

for two reasons: (a) At the frequencies of interest for most satellite links, rain

and atmospheric attenuation can be signiﬁcant, and (b) The computation of

these losses is somewhat different than for the terrestrial case.

The unique aspects of antennas for satellite communications are discussed,

including sky noise and radome effects. It is also imperative that a satellite link

analysis takes into account the fact that many of the atmospheric losses are

absorptive in nature and therefore raise the apparent receiver noise ﬂoor, by

effectively increasing the sky temperature. This often-overlooked effect can

cause errors of several dB in computing link performance for low-noise

receivers.

Scintillation is a form of fast fading that can be attributed to multipath from

variations in the ionosphere or the troposphere. While the mechanisms of

these two types of scintillation are different, the effect on the communication

link is similar: A variation in signal strength that may cause tracking, detec-

tion, and AGC problems. Tropospheric scintillation can be problematic for

nearly horizontal paths, but is rarely a concern for satellite paths. Tropospheric

scintillation is due to variations in temperature and humidity and can apply to

frequencies as high as 30 GHz. Since the lower atmosphere is usually hori-

zontally stratiﬁed, this effect is most pronounced at low elevation angles [1].

Ionospheric scintillation only affects signals below 10 GHz, but is not sensitive

to elevation angle. Other ionospheric phenomena that are of concern for satel-

lite links include propagation delay, dispersion, and Faraday rotation.

Foliage can also be a signiﬁcant signal attenuator. In some cases the losses

due to foliage are so large that the designer simply treats them as blockages.

In the case of a mobile system, this results in brief outages or reduced data

throughput. For static systems, this approach renders some locations unsuit-

able. A prime example of this is that North American homes with large trees

blocking their line of sight to the southwestern sky cannot receive Direct TV.

11.2 SATELLITE ORBITS

Satellite orbits are loosely grouped into four categories: low earth orbit

(LEO), medium earth orbit (MEO), geosynchronous orbit (GEO), and high

earth orbit (HEO). Figure 11.1 shows the relationships among the different

orbits [2].

The corresponding orbital altitudes (above the earth’s surface) are

LEO, 500–900 km

MEO, 5000–12,000 km

GEO, 36,000 km*

HEO, 50,000 km

These deﬁnitions are not universal and may be applied rather casually. HEO

satellites have an elliptical orbit, which may be very near the earth at its low

SATELLITE ORBITS 247

* More precisely, 35,786km from Ref. 2, pp. 19 and 35.

point (perigee) and will have a period greater than one sidereal day (23.9344 h,

one earth rotation). HEO is often used for scientiﬁc applications.

Geosynchronous satellite orbits have an orbital period of exactly one side-

real day and move about in a relatively small angular window, depending upon

the orbital inclination. If a geosynchronous orbit has an inclination angle of

zero relative to the equator, then the satellite will remain directly above the

earth’s equator and appear virtually stationary from the earth’s surface. This

special case of geosynchronous orbit is called geostationary orbit (GSO). GEO

(and GSO) satellites have little or no relative motion, while all others pass

through the sky and produce signiﬁcant Doppler shift on any electromagnetic

waves that are transmitted to or received from the earth.

With the exception of geostationary satellites, the free-space loss will vary

with time as the satellite orbits the earth. The direction and magnitude of the

Doppler shift will also vary with time as the satellite passes overhead. The

Doppler shift depends upon the frequency of operation and is given by

(11.1)

where f

is the center frequency and v

is the relative velocity between the

satellite and the earth terminal.

While geostationary satellites have the advantage of minimal Doppler shift,

the corresponding higher orbital altitude produces a much longer time delay

and greater free-space loss than the lower orbits. Geosynchronous satellites,

while not stationary, tend to move at a lower rate (relative to the earth) than

LEOs, MEOs, and HEOs, which relaxes the Doppler and angular tracking

requirements. The time delay can be a concern for satellite communications,

248 SATELLITE COMMUNICATIONS

HEO

GEO

Figure 11.1 Satellite orbits.

especially for HEOs and GEOs. For GEO orbits where the round trip is

72,000 km, the corresponding delay is approximately 240 ms. The greater path

loss and signal delay for GEO satellites relative to LEOs and MEOs are

somewhat offset by the reduced tracking requirements.

11.3 SATELLITE OPERATING FREQUENCY

Satellite communications occur from frequencies of tens of MHz, to 40 GHz

and beyond. The higher frequencies permit much greater bandwidth, which

permits greater data ﬂow and can reduce power requirements. This is a

signiﬁcant consideration as bandwidth demands increase and the electro-

magnetic spectrum becomes more crowded. Higher frequencies also permit

greater antenna gain for a given aperture size. Conversely, lower frequencies

have less propagation losses (gaseous, clouds, rain) as well as less free-space

loss and are better able to penetrate buildings and foliage. Any regulatory

restrictions in the geographic areas covered by the satellite must also be taken

into account. Thus the choice of operating frequencies includes many

considerations.

A recent trend has been toward ka-band satellites, which use 30-GHz uplink

and 20.2-GHz downlink frequencies. The wide separation in frequency makes

transmit-to-receive isolation easier to attain. The reason for this migration to

higher frequencies is spectral crowding, antenna aperture size restrictions, and

an improved understanding of rain attenuation in the ka band due in large

part to the ACTS experiment [3]. Higher frequency (and satellite power) is

what has made direct broadcast television possible. It was not that long

ago that having satellite TV required a fairly large C-band antenna in the

backyard.

Literally on the opposite end of the spectrum are the amateur radio satel-

lites (more correctly, satellite payloads because they usually piggy back on

a larger satellite). The amateur satellites often use 140-MHz uplinks and

30-MHz downlinks, or 440-MHz uplinks and 145-MHz downlinks.The primary

motivation for these frequency selections is the wide availability and low cost

of amateur equipment in these bands. This permits the satellite to service the

largest possible segment of the amateur community. All amateur satellites

are LEOs because the path loss of the higher orbits would make low-cost

communications very difﬁcult. By using LEOs, low-power and omnidirection

antennas can be used to communicate (albeit brieﬂy) from one ground station

to another. Leo satellites also permit worldwide usage.

11.4 SATELLITE PATH FREE-SPACE LOSS

The largest path loss element in a satellite link is of course the free-space loss,

which is a function of the distance between the ground station and the

satellite and the frequency or wavelength. The distance to the satellite is a

SATELLITE PATH FREE-SPACE LOSS 249

function of the satellite altitude and elevation angle at which it is viewed

(due to the earth’s curvature) [4]. Figure 11.2 shows the geometry, where

is the earth’s radius (6378km)

h is the satellite height above the center of the earth

q is the elevation angle at which the satellite appears

The law of sines provides the relationships needed to solve for r

(11.2)

where the central angle is given by

(11.3)

If the elevation angle, q, is not known, the central angle can be found using

the expression [4]

qq=+

cos sin

()

sin

hr r

sin

()

250 SATELLITE COMMUNICATIONS

Figure 11.2 Satellite slant-path geometry.

(11.4)

where

is the earth station latitude

is the earth station longitude

is the subsatellite latitude

is the subsatellite longitude

With the central angle known, the slant-path distance and elevation angle are

readily found using

(11.5)

and

(11.6)

Alternatively, one may use the slant range to the satellite (if known) and its

height, to solve for the elevation angle using the law of cosines. Note that the

actual earth radius is used in this calculation, not the 4/3’s approximation [4].

The 4/3’s earth approximation is only appropriate for terrestrial paths that are

nearly horizontal and simply aids in ﬁnding the radio horizon. The effect of

refraction on the elevation angle is negligible for slant paths with elevation

angles greater than 2–3 degrees [5].

In the case of a GEO satellite, the height is ﬁxed, so the communication

distance becomes a function of the elevation angle, which is, in turn, a

function of the location (latitude, longitude) of the earth terminal. With

GEO

= 42,242 km,

(11.7)

This distance is then used in the Friss free-space loss equation to determine

the free-space path loss to the satellite.

Example 11.1. What is the elevation angle and path distance between a

geostationary satellite and its earth terminal if the earth terminal is located at

20 degrees latitude? You may assume that the satellite and earth station are

at the same longitude, -90 degrees.

GEO

sin cos sin

sin

cos

sin

()

cos y

cos cos cos cos sin siny

()

() ()

()

() ()

LLll LL

esse es

SATELLITE PATH FREE-SPACE LOSS 251