Optical limits
7.2.5 Tropospheric Scintillation
When the wind blows, the mainly horizontal layers of equal refractive index in the tropo-sphere tend to become mixed due to turbulence, leading to rapid refractive index variations over small distances or scale sizes and over short time intervals. Scintillation also occurs at optical frequencies, where it is more commonly known as the twinkling of stars. Waves travelling through these rapid variations of index therefore vary in amplitude and phase. This
10 20 30 40 50 60 70 80 90 100 200 300
10−1 100 101 102
Frequency [GHz]
Total zenithal absorption [dB]
Dry air
With water vapour
Figure 7.10: Total one-way zenith attenuation in dry air and including water vapour
148 Antennas and Propagation for Wireless Communication Systems
is dry tropospheric scintillation. Another source of tropospheric scintillation is rain; rain leads to a wet component of variation, which tends to occur at slower rates than the dry effects.
Scintillation is not an absorptive effect in that the mean level of the signal is essentially unchanged. The effect is strongly frequency-dependent in that shorter wavelengths will encounter more severe variations resulting from a given scale size. The scale size can be determined by monitoring the scintillation on two nearby paths and examining 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. Figure 7.12(a) 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 this changes relatively slowly. In order to extract the scintillation component, the data is filtered with a high-pass filter having a cut-off frequency of around 0.01 Hz, yielding the results shown in Figure 7.12(b). The magnitude of the scintillation is measured by its standard deviation, or intensity (in decibels), measured usually over 1 min intervals as shown in Figure 7.13. Notice the close similarity between the curves at the three frequencies.
The distribution of the fluctuation (in decibels) is approximately a Gaussian distribu-tion, whose standard deviation is the intensity. The physics of the air masses in the troposphere leads to a well-defined roll-off of the spectrum, reducing at the rate of f8=3 at frequencies above around 0.3 Hz [Tatarski, 61]. This is evident in Figure 7.14.
The scintillation intensity pre may be predicted from an ITU-R model [ITU, 618] as follows:
pre ¼reff7=12gðDÞ
ðsinÞ1:2 ½dB ð7:19Þ
where f is the carrier frequency, is the elevation angle, ref depends on the weather conditions (temperature, atmospheric pressure and water vapour pressure) and g(D) accounts for averaging of the scintillation across the aperture of the antenna, which leads to a reduction in the scintillation intensity for large-aperture diameter D.
Scintillation is most noticeable in warm, humid climates and is greatest during summer days. One way to reduce the effect of scintillation is to use an antenna with a wide aperture,
Troposphere
Earth h
Apparent direction of satellite
Real direction of satellite
Figure 7.11: Ray bending due to tropospheric refractivity
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0 1000 2000 3000 4000 5000 6000 7000 8000 9000
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1 0
Measured data
Time [s]
Relative power [dB]
12.5 GHz
20 GHz
30 GHz
0 500 1000 1500 2000 2500 3000 3500 4000 4500
−2
−1 0 1 2 3 4 5 6 7 8
Filtered with 10mHz cutoff [dB]
Time [s]
Relative power [dB]
12.5 GHz 20 GHz
30 GHz
(a)
(b)
Figure 7.12: Measured signals at 12.5, 20 and 30 GHz during a scintillation event: (a) raw measurements, (b) after high-pass filtering. The filtered signals are offset by 3 dB for clarity, and all actually have 0 dB mean. Details of the measurement set-up are given in [Howell, 92] and further data analysis is described in [Belloul, 98]
150 Antennas and Propagation for Wireless Communication Systems
because 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, where the signals from two antennas are combined to reduce the overall fade depth (Chapter 16 gives more details). Best results for a given antenna separation are produced using vertically separated antennas due to the tendency for horizontal stratification of the troposphere.
7.2.6 Depolarisation
The polarisation state of a wave passing through an anisotropic medium such as a rain cloud is altered, such that a purely vertical polarised wave may emerge with some horizontal components, or an RHCP wave may emerge with some LHCP component, as shown in Figure 7.15. The extent of this depolarisation may be measured by the terms cross-polar discrimination (XPD) or cross-polar isolation (XPI). These are defined (in decibels) by the following field ratios:
XPD¼ 20 logEac
Eax ð7:20Þ
XPI¼ 20 logEac
Ebx ð7:21Þ
0 1000 2000 3000 4000 5000 6000 7000 8000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Standard deviation over one minute intervals [dB]
Time [s]
Standard deviation [dB]
Figure 7.13: Scintillation intensity, calculated from Figure 7.12. The curves increase in order of increasing frequency
Satellite Fixed Links 151
where the E terms are the electric fields defined as shown in Figure 7.16. Essentially, XPD expresses how much of a signal in a given polarisation is scattered into the opposite polarisation by the medium alone, while XPI shows how much two signals of opposite polarisations transmitted simultaneously will interfere with each other at the receiver. Rain-drops are a major source of tropospheric depolarisation and their shape may be approximated by an oblate spheroid. In still air, the drops tend to fall with their major axis parallel to the ground. If there is a horizontal wind component, however, the axis tilts through a canting angle (Figure 7.17). All of the drops in a given rain cloud will be subject to similar forces, so there is an overall imbalance in the composition of the cloud.
10−2 10−1 100
10−4 10−3 10−2 10−1 100
Spectrum
Power spectral density [dB Hz 2−1]
Frequency [Hz]
f−8/3
Figure 7.14: Power spectrum of tropospheric scintillation at 20 GHz
VP
RHCP
VP+HP
RHCP+LHCP
Medium
Figure 7.15: Depolarisation in an anisotropic medium
152 Antennas and Propagation for Wireless Communication Systems
A wave passing through such raindrops will tend to have the component of the electric field parallel to the major axis attenuated by more than the orthogonal polarisation and will therefore emerge depolarised. The typical shape of a raindrop depends on its size, as shown in Table 7.3, where D is the 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 the XPD directly from the attenuation. One such model [NASA, 83] takes the form
XPD¼ a b log L ð7:22Þ
where L is the rain attenuation [dB] and a and b are constants. Representative values for these constants are a¼ 35:8 and b ¼ 13:4, resulting in the curve as shown in Figure 7.18. This is a reasonably accurate approach for frequencies above 10 GHz. Depolarisation may also have other causes:
hydrometeors other than rain, particularly, needle-shaped ice crystals;
tropospheric scintillation;
ionospheric scintillation (Section 7.3.4).