Topic XII: Introduction in Satellite Mobile Communications
Lecture 12: Satellite Fixed Links
Below we will consider communication links between fixed earth stationary stations
with large aperture antenna for cafellly local observations and geostationary satellites
located in orbits 20,000-40,000 km above the Earth and orbiting the Earth at the same
angular speed as the Earth’s rotation. In such systems, the dominant companents of
the propagation loss is simply the free space loss. Beyond this, the radio wave
propagation phenomena can be separated into three independent effects caused by
ionosphere, troposphere and Earth’s terrain, as shown in Fig. 12.1 [1].
As for local effects of terrain obstructions, such as hills, trees, buildings,
located in the vicinity of the ground station, they are same as between the high and
low terminal antennas in rural, suburban and urban environments descussed in
Lectures 2-7 in the context of stationary and mobile personal wireless systems. Let us
consuder two other kinds of links passing through the troposphere and ionosphere.
12.1. Effects of Troposphere in Sattelite Communication Links
Tropospheric effects involve interactions between the radio waves and the lower layer
of Earth’s atmosphere, including effects of the gases composing the air and
hydrometeors such as rain.
2
12.1.1. Attenuation of radio waves
The troposphere consists of a mixture of particles, having a wide range of sizes and
characteristics, from the molecules in atmospheric gases to raindrops and hail. The
main processes caused the total wave loss (in dB) are the absorption and the
scattering, that is, Ltot  Labs  Lscat .
Absorption occurs as the result of conversion from radio wave energy to
thermal energy within an attenuating particle, such as a gas molecule or a raindrop
(see Fig. 12.2).
Scattering occurs from redirection of the radio waves into various directions,
so that only a fraction of the incident energy is transmitted onwards in the direction of
the receiver (see Fig. 12.3). This process is frequency-dependent, since wavelengths
shich are long when compared to the particles’ size will be only weakly scattered. The
main influenced particles in radio links passing through the troposphere are
hydrometeors, including raindrops, fog and clouds. For such kinds of obstructions of
radio wave energy the scattering effects are only significant to systems operating
above around 10 Ghz. The absorption effects alsp rise with frequency of radio waves,
although not so rapidly. Below we will consider rain effects as the case of
hydrometeors, as most important in determining communication system reliability.
For other effects, see [2-4].
Rain attenuation. The attenuation of radio waves caused by rain increases with
the number of raindrops along the radio path, the size of the drops and the length of
the path trough the rain (see Fig. 12.4). If such parameters, as the drops’ density and
size in a given region are constant, then the received power Pr at the receiver with a
given antenna decreases exponentially with range r through the rain, that is,
3
Pr  Pr (0) expr
(12.1)
where  is the reciprocal of the distance required for the power to drop by a factor e 1 .
Expressing this as a propagation loss in dB gives
L  10 log
Pt
 4.343r
Pr
(12.2)
It is more convenient to estimate the total loss via the specific attenuation in the dB/m,
that is,
L
 4.343
r

(12.3)
The  value is given by the following relationship [1]:

   N ( D)  C( D)dD
(12.4)
D0
where N(D) is the number of drops of diameter D per metre of path length (so-called
the drop size 1D distribution) C(D) is the effective attenuation cross-section of a drop
[dB/m], which depends on frequency of radio wave.
In real situations in troposphere the drop size distribution N ( D) is not constant
and we must take into account the range dependence of the specific attenuation, e.g.,
   (r ) and integrate it over the whole radio path length rR to find the total path loss:
rR
L    (r )dr
(12.5)
0
There is only one way to resolve this equation, to take a particular drop size
distribution and integrate the result. Usually the following distribution is used [1]
 D
N ( D)  N 0exp

 Dm 
(12.6)
where N 0 and Dm are parameters, with Dm depending on the rainfall rate, R,
measured on the ground in millimetres per hour, and with N 0  8  103 m2 mm1 and
4
Dm  0122
.
 R 0.21mm
(12.7)
As for the attenuation cross-section C(D) from (12.4), it can be found using so-called
the Rayleigh approximation, which is valid for lower frequencies, that is, for the case
when the average drop size is smaller compared to the incident wavelength. In this
case only absorption in the drop occurs and
C( D) 
D3

(12.8)
At higher frequencies attenuation increases more slowly tending towards a constant
value known as the optical limit. At these frequencies, scattering forms a significant
part of attenuation which can be described using the Mie scattering theory. This must
be applied for the cases when the wavelength is of a similar size to the drops since
resonance phenomena are produced. In general, Eq. (12.4) can be solved directly using
expression (12.5). However, in more practical situations an empirical model is usually
used, where  (r ) is assumed to depend only on R, that is:
  aR b
(12.9)
where a and b depend on frequency and average rain temperature and  has units
dB/km. Table 12.1 shows values for a and b at various frequencies f at 20 0 C for
horizontal polarization of radio wave. A more complete set of curves of  versus f is
shown in Fig. 12.5. The path length rR used to multiply (12.9) to find rain attenuation
is the total rainy stant path length, as shown in Fig. 12.6. All heights depicted in Fig.
12.6 are measured above mean sea level; h R is the effective rain height, usually the
same with that, at which the temperature is 0 0 C . It depends on the latitude and
location area of the ground station [1]. Using geometry presented in Fig. 12.6, one
can easy obtain the rain path length (for   50 ) as
5
rR 
hR  hS
sin 
(12.10)
For paths in which the elevation angle  is significantly less than 90 0 , it is necessary
to account for the variation in the rain in the horizontal direction. This allow us to
reduce to the finite size of rain clouds, i.e., to the areas called the rain cells (Fig.
12.7). In this case of finite rain sizes, the path length is reduced by using a reduction
factor s. If so, the rain attenuation is
L  srR  aR b srR
(12.11)
Also rain varies in time over various scales: seasonal, annual, diurnal. All of these
temporal variations are usually accounted by use (12.11) to predict the rain attenuation
not exceeded for 0.01% of the time L0.01 in terms of R0.01 , the rainfall rate exceeded
0.01% of the time in an average year (i.e., around 53 minutes), and then correcting this
attenuation according to the percentage level. Thus
L  aR0b.01 s0.01rR
(12.12)
where the following empirical expression for s0.01 is used:
s0.01 
1
rR sin 
1
35 exp 0.01R0.01 
(12.13)
The attenuation can then be corrected to the relevant time percentage P using
LP  L0.01  012
.  P  ( 0.5460.043 log P )
(12.14)
The reference rainfall rate R0.01 is strongly dependent on the geographical location:
from around 30 mm/hour at the Northern Europe and 50 mm/hour at the Southern
Europe (Mediterranean) up to 160 mm/hour at the Equator.
The effect of rain fading may be reduced by applying site diversity, where two
ground stations are separated at the range so that the paths to the satellite are separated
6
by greater than the extent of a typical rain cell. the signal is then switched between the
earth stations, according to which one saffers from least attenuation over given time
period. The probability of both links suffering deep rain fades at the same time can
then made very small.
Gaseous absorption. As was mentioned in Topic I, gaseous molecules in
atmosphere may absorb energy from radio waves passing through them, thereby
causing attenuation. This attenuation is greatest for polar molecules such as
water H 2 O (see Fig. 12.8). The oppositely charged ends of such molecules, as seen
from Fig. 12.8, cause them to align with an ambient electric field. Since electric field
of radio wave is changing in direction twice per cycle, realignment of such molecules
occurs continuously, so a significant loss may result. At higher frequencies this
realignment occurs faster, so the absorption loss has general tendency to increase with
frequency.
Non-polar molecules, as oxygen O2 may also absorb wave energy due to the
existence of magnetic moments. Here also the increase of absorption is observed with
increase of wave frequency. But here several resonance peaks of absorption each
corresponding to different modes of molecule vibration, the lateral, the longitudinal
etc., are occur. The main resonance peaks of H 2 O and O2 are given in Table 12.2.
the oxygen peak at around 60 GHz is actually a complex set of closely spaced peaks
which prevent the use of the band 57-64 GHz for practical satellite communication.
The specific attenuation in dB/km for water vapour,  w , and for oxygen,  o , is given
in Fig. 12.9 for a standard set of atmospheric conditions. The total atmospheric
attenuation La for a particular path is then found by integrating the total specific
attenuation over the total path lenth rT in the atmosphere:
7
rT
rT
0
0
La    a (l )dl     w (l )   o (l )dl
[dB]
(12.15)
This integration calculated for the total zenith (  900 ) attenuation is presented in
Fig. 12.10 by assuming an exponential decrease in gas density with height. The
attenuation for an inclined paths with an elevation angle   10 0 can then be found
from the zenith attenuation Lz as:
La 
Lz
sin 
(12.16)
We must note that atmospheric attenuation results in an effective upper frequency
limit for mobile-satellite communications.
12.1.2. Tropospheric refraction
The refractive index n of the earth’s atmosphere is slightly greater than 1, with a
typical value at the Earth’s surface of around 1.0003. Since the value is so close to 1,
it is common to express the refractive index in N-units, which is the difference
between the actual value of the refractive index and unity in parts per million:
N  (n  1)  106
(12.17)
This equation defines the atmospheric refractivity N. Thus the ground surface value of
N  N S  300 N-units. N varies with pressure, temperature and with water vapour
pressure of the atmosphere. Also this quantity vary with location and height, the
dominant variation of N is vertical with height above the Earth’s surface: N reduces
towards zero (n becomes close to unity) as the height is increased. The variation is
approximately exponential within the first few tens of kilometres of the Earth’s
atmosphere, i.e., within the region is called the troposphere:
8
 h
N  N S exp  
 H
(12.18)
where h is the height above sea level, and N S  315 and H=7.35 km are standard
reference values. This refractive index variation with height causes the phase velocity
of radio waves to be slightly slower closer to the Earth’s surface, such that the ray
paths are not straight, but tend to curve slightly towards the ground. In other words the
elevation angle  1 of initial ray at any arbitrary point B (see Fig. 12.11) changes at
angle  2 . The same situation will be at the next layer of atmosphere with other
refractive index n. Finally the ray launched from the Earth’s surface propagate over
the curve, the radius of curvature at any point  is given in terms of the rate of
change of n with height:
 cos  1 dn 
  

 n dh 
1
(12.19)
The resulting ray curvature illustrated by Fig. 12.12. For small heights, the standard
atmosphere of Eq. (12.18) can be approximated as linear, as shown in Fig. 12.13,
according to the following equation:
N  NS 
NS
h
H
(12.20)
The refractivity thus has nearly constant gradient of about -43 N-units per kilometre. If
so, the curvature of the ray trajectory is constant (this follows from (12.19) for
dn/dh=const). A common way to take this factor into account is to introduce instead
the real Earth’s radius the effective Earth’s radius:
Reff  k e RE
where RE  6375 km and k e is the effective Earth radius factor, given by
(12.21)
9
ke 
1
RE (dn / dh)  1
(12.22)
The median value for is taken to be 4/3, so the effective radius for 50% of the time is
about 8500 km. Since the variation of refractive index is mostly vertical, rays
launched and received with the relatively high elevation angles used in satellite fixed
links will be mostly unaffected. Nevertheless, the effective radius of the Earth must be
accounted for cases when calculating ideal antenna pointing angle for the ground
facility (see Fig. 12.14). Variations in the refractive index gradient with time may lead
to some loss in effective antenna gain of ground station due to misalignment and can
be corrected by using automatic steering.
12.1.3. Tropospheric scintillation
Due to turbulent flows caused the turbulent structiure of wind in the troposphere, the
mainly horizontal layers of equal refractive indexes in it become mixed, leading to
rapid refractive index variations over small distances, so-caled, the small-scale
variations, as well as over short time intervals, so-called rapid refractive index
variations. Waves travelling through these layers with rapid variations of index
therefore vary fastly and randomly in amplitude and phase. This effect is called dry
tropospheric scintillation.
Another source of of tropospheric scintillation, which is called wet, is rain; it
leads to a wet component of scintillation, which tends to be slower than the dry
effects. Because scintillation is not an absorptive effect, the mean level of the radio
signal is essentially unchended. This phenomenon change dramatically the phase and
amplitude fluctuations both in the space and time domains. Moreover, this
phenomenon is strongly frequency-dependent: the shorter wavelengths will encounter
10
more severe fluctuations of signal amplitude and phase resulting from a given scale
size. The scale size can be determined by experimental monitoring the scintillation of
signal on two nearby paths and by examing the cross-correlation between the
scintillation on the paths. If the effects are closely correlated, then the scale size is
large compared with the path spacing [5]. Figure 12.15a shows an example of the
signal measured simultaneously at three frequencies during a scintillation event. It is
clear that there is some absorption taking place, but these changes are relatively
slowly. In order to extract the scintillation component, the data is filtered with a highpass filter having cut-off frequency around 0.01 Hz; the results shown in Fig. 12.15b
according to [7, 8].
At the same time, the mugnitude of the scintillation in [7, 8] is measured by its
standard deviation, or intensity (in dB), measured over one minute intervals, as shown
in Fig. 12.16. It is clear that curves presented there for three frequencies are similar.
Additional investigations have shown that the distribution of the signal fluctuations
(in dB) is approximately a Gaussian distribution, whose standard deviation is the
intensity.
As was shown in [5], the dissipation of turbulent air masses in the troposphere
occurs according to low which describes this dissipation of energy spectrum from
large turbulencies to small at the rate of f
8 / 3
at frequencies above around 0.3 Hz.
This is evident in Fig. 12.17. The scintillation intensity (standard deviation) can be
described by the following expression [1]:
 pre 
 we f 7 /12 g( D)
(sin ) 1.2
[dB]
(12.23)
where f is the carrier frequency,  is the elevation angle of the ground antenna,  we is
the scintillation intensity due to weather conditions (temperature, atmospheric
11
pressure, water vapour pressure), and g(D) the parameter of averaging of the
scuntillation across the aperture of the ground-based antenna. The latter parameter
leads to reduction in the scintillation intensity for large aperture diameter D.
Scintillations are most noticeable in warm, humid climates and is greatest during
summer days. One way to reduce the scintillation phenomenon is to use an antenna
with a wide aperture, since this produces averaging of the scintillation across the
slightly different paths taken to each point across the aperture.
Another approach is to use spatial diversity of two antennas, where the signals
from two antennas are combined to reduce the overal fade depth (see Fig. 12.18). Best
results are produced using vertically separated antennas due to the tendency for
horizontal stratification of the troposphere.
12.1.4. Signal depolarisation in the troposphere
To understand this aspect, let us define the wave polarisation phenomenon. The
alignment of the electric field vector E of a plane wave relative to the direction of
propagation defines the polarisation of the wave. If E lies in the plane perpendicular
to the plane of wave propagation, but the magnetic field H is horizontal and lies in the
plane of wave propagation (with vector k) then the wave is said to be verically
polarised; conversely, when E is horizontal, but H is perpendicular to k and E, the
wave is said to be horizontally polarised. Both of them are lineary polarised, since the
electric field vector E has a single direction along the whole of the propagation axis
(vector k). If two plane lineary polarised waves of equal amplitude and orthogonal
polarisation (vertical and horizontal) are combined with a 90 0 phase difference, the
resulting wave will be circularly polarised (CP), in which the motion of the electric
field vector will describe a circle centered on the propagation vector (all kinds of
12
wave polarization is presented in Fig. 12.19). The field vector will rotate by 360 0 for
every wavelength traveled. Circularly polarised waves are most commonly used in
satellite communication, since they can be generated and received using antennas
which are oriented in any direction around their axis without loss of power.They may
be generated as either right-hand circularly polarised (RHCP) or left-hand circularly
polarised (LHCP), depending on direction of vector E rotation relative to clockwise
(see Fig. 12.19). In the most general case, the components of two waves could be of
unequal amplitude, or at the phase angle other than 90 0 . The result is an ellliptically
polarised wave, where vector E still rotates at the same rate as for circular polarised
wave, but varies in amplitude with time. In the case of ellipical polarisation, the
parameter axis ratio, AR  E maj / E min , is usually introduced (see Fig. 12.19). AR is
defined to be positive for left-hand polarisation and negative for right-hand
polarisation. Now let us return to the situation of wave field polarisation in the
tropospheric propagation channel.
The wave polarisation is also changed during passing through an anisotropic
medium such as a rain cloud (see Fig. 12.20) As follows from illustration, a purely
vertical polarised wave may obtain the additional horizontal component, or the righthand circularly polarised (RHCP) wave may obtain the additional left-hand circularly
polarised (LHCP) component. The extent of this depolarisation may be measured by
the terms cross-polar discrimination (XPD) and cross-polar isolation (XPI), which
can be defined by the following field ratios:
XPD  20 log
E ac
E ax
(12.24)
XPI  20 log
E ac
E bx
13
where the E-field components defined in Fig. 12.21. Essentially, XPD expresses how
much of a signal in a given polarisation is transformed into the opposite polarisation
caused by the medium, while XPI shows how much two signals of opposite
polarisations transmitted simulteneously will interfere with each other at the receiver.
Raindrops are a major source of tropospheric depolarisation and their shape may be
approximated by an oblate spheroids. The typical shape of a raindrop depends on its
size, as shown in Table 12.3 according to [2, 6], where D is diameter of a sphere with
the same volume as the raindrop.
Depolarisation is strongly correlated with rain attenuation, and standard
models of depolarisation use this fact to predict XPD directly from the attenuation.
One such model gives [1]
XPD=a-blogL
(12.25)
where L is the rain attenuation (in dB), and a and b are constants: a=35.8 and b=13.4
[1]. This is accurate prediction model for frequencies above 10GHz. Hydrometeors
and tropospheric scintillation can be the additional source of signal depolarisation in
fixed satellite communication links.
12.2. Ionospheric Effects in Fixed Satellite Communication Links
12.2.1. Ionosphere
The ionosphere is a region of ionised plasma (ionised gas which consists both neutral
atoms and molecules and charge particles, electrons and ions) which surrounds the
Earth at a distance ranging from 50 km to 500-600 km where is continuously extends
to magnetosphere (700-2000 km). The ions and electrons are created in ionosphere by
14
Sun’s electromagnetic radiation, solar wind and cosmic rays which are the sources of
atoms and molecules ionization. Since the Sun’s radiation penetrates deeper into the
Earth’s atmosphere at zenith, the ionosphere extends closest to the Earth around the
equator and is more intense on the daylight side. Figure 12.22 shows how the
ionosphere separates into four distinct layers: D, E, F1 and F2, during the day and how
these layers continuously transform during the night into the E and F layers.
The key parameter which affects on radio communications is the electron
concentration N measured in free electrons number per cubic metre. The variation of
N with height in the ionosphere for a typical day and night as shown in Fig. 12.23
according to [9]. the electron content of the ionosphere changes the effective
refractive index encountered by radio waves transmitted from the Earth, changing
their direction by increasing wave velocity. Depend on special conditions, which are
determined by wave frequency, elevation angle of ground-based antenna, electron
content, etc., the wave may fail to escape from the Earth and may appear to be
reflected back to earth, although the process is actually refraction (see Fig. 12.24). The
refractive index of an ordinary wave depends on both N and the wave frequency f
according to
n02  1 
f c2
f2
(12.26)
where f c is the critical frequency of plasma at the given height, given by
f c  8.9788 N
[Hz]
(12.27)
Apparent reflection from the ionosphere back to Earth, as shown in Fig. 12.24, can
occur whenever the wave frequency is below f c , so useful frequencies for satellite
communications need to be well above this f c . The greatest critical frequency
normally encountered is around 12 MHz. This is the other extreme of an overal l
15
atmospheric “window” which is bounded at the high-frequency end by atmospheric
absorption at hundreds of gigahertz. Even well above 12 MHz, however, a number of
ionospheric effects are important in satellite communications, as described below in
the following sections.
12.2.2. Faraday rotation
A lineary polarised wave becomes rotated during its passage through the ionosphere
due to the combiled effects of the free electrons and the Earth’s magnetic field. This
phenomenon is called Faraday rotation. The angle associated with this rotation
depends on the frequency and the total number of electrons encountered along the
radio path, according to
2.36  10 20

Bav N tot
f2
(12.28)
where f is in hertz and Bav  H av is the average magnetic field of the Earth at the
ionospheric altitudes [Weber per square metre]; a typical value is
Bav 
7  10 21 Web  m2 . The parameter N tot in (12.28) is the total number of electrons
contained in a column of cross-sectional area 1 m 2 and length equal to the path
length, i.e., the total electron content, N tot :
rT
N tot   Ndr
[electrons  m 2 ]
(12.29)
0
The total electron content for a zenith path varies over the range to electrons per
square metre, with the peak taking place during the daytime.
If lineary polarised waves are used, extra path loss will result due to
depolarisation which results polarisation mismatch between the satellite and groundbased antennas. There are some ways to minimise this extra path loss. In fact, as was
16
mentioned above by use of circular polarised waves we exclude the depolarisation
effect. Moreover, one can vary physically or electronically the receive antenna
polarisation or aligning the antennas to compensate for an average value of the
rotation, provided that the resulting mismatch loss is acceptable.
12.2.3. Group delay
The effect of refraction of radio wave passing through the ionosphere means that the
resulting phase shift differes from the expected phase shift based on the physical path
length. This can be considered as a change in the apparent path length, r [m] :
r 
40.3
N tot
f2
(12.30)
Typical values for a 4 GHz zenith path system are between 0.25 and 25 m. The change
in path length can equivalently be considered as a time delay,  [ s] :

40.3
N tot
cf 2
(12.31)
12.2.4. Dispersion
The change in effective path length arising from the group delay described above
would not be problematic in itself if it were applied equally to all
frequencies.However, the delay time, as can be seen from (12.31), is frequency
dependent. So a transmitted pulse occupying a wide bandwidth will be smeared when
it arrives at the receiver, with the higher frequencies arriving earlier. The dispersion is
defined as the rate of change of the delay with respect to frequency, i.e.,
d
80.6
  3 N tot
df
cf
[s/Hz]
(12.32)
17
The differential delay associated with opposite extremes of a signal occupying a
bandwidth is then
  
80.6
f  N tot
cf 3
(12.33)
12.2.5. Ionospheric scintillation
There is a wind presented in the ionosphere, just as in the troposphere, which causes
rapid variations in the local electron density, particularly close to sunset. These
density variations cause changes in refraction of the radio wave in the earth-satellite
channel and hence of signal levels. Portions of the ionosphere then act like lenses,
cause focusing and defocusing and divergence of the wave and hence lead to signal
level variations, i.e., the signal scintillation. The key characteristics of ionospheric
scintillations, which must be accounted, are the follows:
- Low-pass power spectrum, roll-off as f
3
, corner frequency is as in
troposphere about 0.1 Hz.
- Strong correlation between scintillation occurrence and sunspot cycle.
- Size of disturbances proportional to carrier frequency of power 1.5, i.e.,
~ f c3/ 2 .
18
Summary of Ionospheric Effects:
Let us summarise now ionospheric effects described above. For this purpose
we depict the magnetude of various ionospheric effects in Table 12.4. The first row
describes the Faraday rotation in angle degrees, second row presents time delay in
microseconds, and the last row describes frequency dispersion in picoseconds ( 10 9 s )
per one megahertz. As follows from depicted magnetudes, all the effects becomes
negligible with increase of radio frequency. This is why, higher frequencies over the
range of 20 to 50 GHz are usually used constructing fixed earth-satellite
communication links.
19
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[3] Marshall, J. S., and W. M. K. Palmer, “The distribution of raindrops below
10GHz”, NASA Reference Publication 1108, 1983.
[4] Maral, G., and M. Bousquet, Satellite Communication Systems, Techniques and
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