** Rec. ITU-R S.1525-1 **
RECOMMENDATION ITU-R S.1525-1
**Impact of interference from the Sun into a geostationary-satellite orbit fixed satellite service link**
(Question ITU-R 236/4)
(2001-2002)
The ITU Radiocommunication Assembly,
*considering*
a) that Sun transits are a natural phenomena in geostationary-satellite orbit fixed-satellite service (GSO FSS) networks, which occur over a period of 3 9 days twice a year, depending on the antenna diameter;
b) that GSO FSS earth station operators and customers plan for the Sun transits and implement appropriate means to minimize their impact;
c) that GSO FSS earth station operators should have a methodology available to analyse the magnitude of the interference from the Sun and the timing of the interference events,
*recommends*
**1** that, in designing GSO FSS links, the methodology given in Annex 1 may be used to assess the level of carrier-to-noise ratio (*C*/*N*) degradation of a GSO link resulting from Sun transit;
**2** that GSO FSS earth station operators may use the method in Annex 2 to predict the date and time of a Sun transit at an earth station.
ANNEX 1
**Calculation of the level of interference from the Sun into a GSO FSS link**
Sun transits occur twice a year near the spring and autumn equinoxes when the Sun passes close to the main beam of the receiving GSO earth station. During these Sun transits, the microwave radiation from the Sun acts as a source of interference, increasing the effective noise temperature of
the satellite link and therefore degrading the link performance. If the amount of degradation exceeds the clear-sky margin of the link, then the link will suffer an outage – usually termed a Sun-outage.
For frequencies below about 30 GHz, emission from the Sun can be considered as having three components: the thermal emission from the “quiet” Sun, a slowly-varying component related to the number and size of sunspots, and occasional intense bursts of emission due to Sun flares. All three components are time-varying, and so it is extremely difficult to use the Sun as a reference source for accurate evaluation of the performance of earth station antennas.
In the satellite communication bands, the thermal emission from the quiet Sun decreases with increasing frequency. The emission is generally unpolarized.
Sunspots are magnetic regions on the Sun, appearing as dark spots on its surface. They typically last for several days, although very large ones may last for several weeks. Although the number of sunspots varies greatly from day to day, there is an underlying pattern with a period of approximately 11 years. Every 11 years, the Sun undergoes a period of activity called the “Sun maximum”, followed by a period of quiet called the “Sun minimum”. During the Sun maximum there are many sunspots, Sun flares, and coronal mass ejections, all of which can affect communications and the weather on Earth. There is a rough correlation between the total solar flux and the number of sunspots. As this increased flux is associated with several small areas of the Sun’s surface, it is unsafe to assume a uniform brightness distribution across the face of the Sun. In fact, if the GSO earth station has an antenna beamwidth smaller than the apparent diameter of the Sun, then it could experience varying levels of interference during a single Sun transit event. Emission due to sunspots is somewhat circularly polarized, although this effect is diluted by the random polarization of the thermal emissions from the quiet Sun.
Sun flares or bursts may double or triple the Sun flux, occasionally reaching factors of 100 times the usual level. In the satellite communication bands, most events are fairly short – 5 min to about an hour. Occurrence is unpredictable, but as already noted the events are more frequent around the Sun maximum. Typically there could be a couple of events per day.
The apparent diameter of the Sun at microwave frequencies is slightly larger than the optical diameter. Also, the Earth-Sun distance varies slightly during the year, resulting in a variation in the apparent diameter of the Sun and thus in apparent brightness temperature. However these effects are small compared with other uncertainties (such as the sunspot number), and may thus be neglected. A reasonable estimate of the apparent diameter of the Sun at the equinox is 0.53.
Although the foregoing material indicates that significant and unpredictable variations exist in the effective level of the Sun flux in the satellite communication bands, a number of simple models have been proposed for the average level. These models are adequate for assessment of the typical levels of interference which can be expected during Sun transits. One expression for the brightness temperature of the quiet Sun at microwave frequencies is:
where:
* T*_{Sun} : equivalent brightness temperature (K)
*f* : frequency (GHz)
: factor to account for the polarization of the emissions from the Sun, which could be taken to be 0.5 for the reasons given above.
This model gives a value of around 21 000 K for the quiet Sun at a frequency of 4 GHz. By comparison, a typical value at sunspot maximum would be 90 000 K.
## 1 General approach
The Sun transit of a GSO receiver is a phenomenon that can be easily assessed as the geometry is well known. The method described in detail in Recommendation ITU-R BO.1506 which evaluates the impact of solar inteference into broadcasting-satellite service (BSS) links may be used also in the case of FSS links. That Recommendation fully describes the Sun transit effect on GSO FSS link budgets. The impact of Sun transit is not a fade but an increase of the system noise temperature that can be significant for some low margin, low noise GSO links.
## 2 Application of the methodology to different antenna sizes
The detailed approach described in Recommendation ITU-R BO.1506 has been applied to different antenna sizes.
Two possible approaches could be used to generate the solar noise temperatures for the off-axis angle and the azimuth angle as seen at the focal point of an FSS earth station antenna:
– Full simulation of the motion of the Sun, using for example the algorithm developed in Annex 2.
– A simplified approach based on the fact that the declination angle of the Sun changes at approximately 0.4 per day at the equinoxes and its hour angle changes at approximately 0.25 per min.
The results in Figs. 1 to 6 are typical of those produced using these methods. In all the cases the initial noise temperature used is 150 K and the antenna patterns used are according to Recommendation ITU-R S.465 at 11 GHz.
The impact on a link performance depends on the size of the antenna and the initial noise temperature of the link. For large antennas with high gain, the degradation of the *C*/*N* can be up to 15 dB (as shown in Fig. 2) but occurs fewer times than for small antennas with wider beams (e.g. Fig. 6).
As was expected the results show that the depth of the degradation of the *C*/*N* is a function of the antenna size and the duration of the Sun transit increases as the antenna diameter decreases.
## 3 Variation during a day
Computations have been done to show a time profile of the degradation of *C*/*N* as a function of the time of the day close to the equinox period. The time step is set to 1 s.
ANNEX 2
**Simplified method to calculate the Sun transit period for a GSO earth station**
GSO FSS earth station operators have accepted that Sun interference is a natural phenomenon that occurs for a short period 0 to 21 days before or after the equinoxes, depending on whether the station is located in the Northern or Southern Hemisphere.
Most operators use simplified algorithms such as the one given below, which does not require a specific carrier link budget, to estimate the day and times when a Sun transit will occur. With this information, they can take proactive action to mitigate the effects of Sun interference.
## 2 Satellite ephemeris data
Satellite operators use a number of different mathematical models to represent the movement of a satellite. A simplified approach was developed by one GSO satellite operator whereby, instead of computing all physical effects acting on a satellite, these effects are defined in terms of three equations. This approximation contains 11 parameters obtained with a least-squares curve fit. It has been demonstrated that this simplified model approximates the full prediction results to better than 0.01° for a period of up to seven days.
In this approach, the three equations that predict the satellite’s position at any relative time, *t*, from the start of the epoch are:
Satellite east longitude:
*L* = *L*_{0} + *L*_{1}*t* + *L*_{2}*t*^{2} + (*L*_{c} + *L*_{c}_{1}*t*) cos(*Wt*) + (*L*_{s} + *L*_{s}_{1}*t*) sin(*Wt*) + (*K*/2) (*l*_{c}_{2}_{ }– *l*_{s}_{2}) sin(2*Wt*) – *K l*_{c}*l*_{s} cos(2*Wt*) (1)
Satellite geocentric latitude:
* l* = (*l*_{c} + *l*_{c}_{1}*t*) cos(*Wt*) + (*l*_{s}_{ }+ *l*_{s}_{1}*t*) sin(*Wt*) (2)
Satellite radius:
*r*_{sat} = *r*_{g} (1 – 2*L*_{1}/3(*W* – *L*_{1})) (1 + *KL*_{c}* *sin(*Wt*) – *KL*_{s} cos(*Wt*)) (3)
where:
*W* = *L*_{1} + 360/*t*_{r} degrees/day
*t*_{r} : rotation period of the Earth, in days
*r*_{g} : nominal radius of GSO satellite orbit (km)
*K* = /360
*t* : time in days
and the eleven parameters are:
*L*_{0} : mean longitude (East of Greenwich) (degrees)
*L*_{1} : drift rate (degrees/day)
*L*_{2} : drift acceleration (degrees/day/day)
*L*_{c} : longitude oscillation-amplitude for the cosine term (degrees)
*L*_{c}_{1} : rate of change of longitude, for the cosine term (degrees/day)
*L*_{s} : longitude oscillation-amplitude for the sine term (degrees)
*L*_{s}_{1} : rate of change of longitude, for the sine term (degrees/day)
*l*_{c} : latitude oscillation-amplitude for the cosine term (degrees)
*l*_{c}_{1} : rate of change of latitude, for the cosine term (degrees/day)
*l*_{s} : latitude oscillation-amplitude for the sine term (degrees)
*l*_{s}_{1} : rate of change of latitude, for the sine term (degrees/day).
With the satellite position defined as a function of time in terms of a geocentric system aligned with the Greenwich Meridian, the satellite position with respect to the earth station and the appropriate pointing angles are calculated as follows:
*r* = *r*_{sat}_{ }– *r*_{sta} (4)
*r*_{x} = *r*_{sat }cos(_{sat}) cos(_{sat} – _{sta}) – *R*_{a} (5)
*r*_{y} = *r*_{sat }cos(_{sat}) sin(_{sat} – _{sta}) (6)
*r*_{z} = *r*_{sat}* *sin(_{sat}) – *R*_{z} (7)
where:
_{sat}_{ }: satellite latitude (geocentric)
_{sat}_{ }: satellite longitude
_{ }_{sta}_{ }: station longitude East of Greenwich
_{ }*R*_{a}_{ }: station radial distance from Earth rotational axis
*R*_{z}_{ }: station axial distance above Earth equatorial plane.
The calculation of the earth station coordinates are generally known in terms of its geodetic latitude, longitude and height above a reference ellipsoid (altitude). This reference ellipsoid is based on an equatorial radius and a flattening constant.
The earth station position is calculated in terms of the radial distance from the rotational axis of the Earth *R*_{a} and the axial distance north of the equatorial plane of the Earth, *R*_{z}_{, }which are calculated as follows:
*R*_{a} (*R* *h*) cos(_{sta}) (8)
*R*_{z} [*R*(1 – *f** *)^{2} *h*] sin(_{sta}) (9)
(10)
where:
*h* : geodetic height of the earth station above the ellipsoid (km)
_{sta} : geodetic latitude of the Earth station
*f* : flattening of the Earth ellipsoid
*R*_{equ} : equatorial radius of Earth ellipsoid.
From the above, the azimuth and elevation pointing is determined as follows:
Earth station azimuth angle:
*AZ *= arctan (*r*_{y}_{ }/*r*_{North}) (11)
Earth station elevation angle:
*EL*_{geometric}_{ }= arctan (*r*_{zenith}_{ }/(*r*_{North}^{2} + *r*_{y}^{2})^{1/2}) (12)
where:
*r*_{North} = *r*_{x}_{ }sin(_{sta}) + *r*_{z} cos(_{sta}) (13)
*r*_{zenith} = *r*_{x} cos(_{sta}) + *r*_{z}_{ }sin(_{sta}) (14)
## 3 Predicted Sun transit periods
In order to calculate the timing of the interference from the Sun, earth station pointing angles in terms of the equatorial coordinate system (ECS) are required, which will be described in more detail in the following paragraph.
This is the same coordinate system used for polar antenna mounts. The hour angle and declination in the ECS are calculated from AZ and EL above as:
Declination = arcsin(sin(*EL*) · sin(_{sta}) + cos(*EL*) · cos(_{sta}) · cos(*AZ*))
## 3.1 Coordinate system for calculating Sun transit
The calculations for Sun interference are based on the equatorial coordinate system, where the Earth’s equator is the reference plane and the vernal equinox is the reference direction. The vernal equinox or The First Point of Aries, is the intersection of the ecliptic (mean plane of the Earth’s orbit) with the celestial equator, at which the Sun crosses the equator from south to north. The Earth’s centre is the origin of this system, which is illustrated in Fig. 9.
Declination and right ascension give the coordinates of the Sun. Declination is the angle between the equatorial plane and the Sun. Right ascension is the angle, measured counterclockwise relative to celestial north in the equatorial plane from the vernal equinox to the current position of the Sun. The hour angle is the angular difference between the observer’s longitude and the longitude of the Sun.
## 3.2 Calculating the coordinates of the Sun
Time is measured with respect to the period of the Earth’s rotation in terms of the Sun day, which is the period between successive Sun passages through the observer’s meridian. Since the Earth also circles the Sun in a one-year period, the Sun day is not the true period of the Earth’s rotation. The Earth travels 1/365 of the way around its orbit in one day, but the Earth has to rotate slightly more than one complete turn relative to a fixed star during this interval.
Sidereal time is based on the Earth’s rotation with respect to a fixed star. Variations in the Earth’s rotation, due to precession and nutation, affect the length of the sidereal day. Precession is the circular movement of the Earth’s North Pole around the ecliptic pole. The radius of this circle is (usually terms the obliquity of the ecliptic) approximately 23.5 and a period of 26 000 years is required to complete one revolution. Nutation is a complicated oscillation of the Earth’s North Pole about the mean North Pole. The difference between the mean sidereal time and apparent sidereal time is called the equation of the equinox.
The right ascension and declination of the Sun, as well as the Earth’s rotation relative to the vernal equinox are related to Universal Time (UT). Universal Time, which is the basis for civil timekeeping, is closely related to the mean diurnal motion of the Sun and is directly related to sidereal time. Local apparent sidereal time (LAST) is the hour angle of the true equinox, the intersection of the true equator and the ecliptic of the date, which is affected by the nutation of the Earth’s axis. Local mean sidereal time (LMST) is the hour angle of the mean equinox or the intersection of the mean equator with the ecliptic of the date, which is affected by the precession of the Earth’s axis.
The right ascension and declination of the Sun can be derived from the obliquity of the ecliptic, W, and the ecliptic longitude, *L*_{Sun}, as shown in Fig. 10 as:
*L*_{Sun} = *L*_{mean} + 1.915 sin(*M*_{e}) + 0.020 sin(2 *M*_{e})
where the mean longitude of the Sun is:
*L*_{mean} = 280.460 + 0.9856474 *d*
and the mean anomaly of Earth’s orbit is:
*M*_{e}_{ }= 357.528 + 0.9856003 *d*
The time *d* is expressed in terms of Julian days (JD) referenced to 1200 UT, 1 January 2000, which is Julian day 2 451 545 and *d* = *JD* – 2 451 545.
From the law of sines in spherical trigonometry the declination, *D*, is:
and the right ascension, *RA*, is:
For this purpose, the declination of the Sun can be approximated by:
*D*_{Sun} = 23.5 sin(360 ( *p* – *x*)/365)
where 23.5 is the approximate obliquity of the ecliptic, *p* is the day of the year and the value *x* is 80 for the vernal equinox and 83.5 for days near the autumnal equinox. Because the number of days from the vernal to autumnal equinox is not equal, the value *x* takes on these two different values.
One condition for Sun transit is when the declination of the Sun is very close to the declination of the satellite as derived above in terms of the equatorial coordinate system. The approximate date for Sun transit, *P*_{0}, can be obtained to the nearest integer of *p*, by substituting the declination angle for *D*_{Sun} in the equation above.
## 3.3 Calculating the right ascension of the Sun
Using the value of *P*_{0}_{ }as the starting point of an iterative calculation that increments the Julian day, the calculation proceeds until:
|*D*_{Sun} – Declination | 0.17
where:
At the time that the declination of the Sun and the earth station declination angle are very close, the value of right ascension of the Sun is obtained from:
Another condition for Sun transit is coincidence of the right ascension of the Sun and the satellite. The declination of the satellite look angle is a fixed value; however, the equivalent right ascension of the satellite varies with time as follows:
*RA*_{sat} = *LAST* – Hour angle
or
*LAST* = *RA*_{sat} + Hour angle
where the hour angle was calculated previously above. In terms of Greenwich apparent sidereal time (GAST):
*GAST* = *LAST* – _{sta}
therefore, equating *RA*_{sat} = *RA*_{Sun} and substituting the value *RA* from above:
*GAST* = *RA* + Hour angle – _{sta}
The time in Coordinated Universal Time (UTC) can then be computed from:
*GAST* = 100.4602346 + 0.985647348 (*JDO*_{sat} – 2 451 545) + 15.041068 *UT*
or
where *JDO*_{sat} is the Julian date at midnight, that is, it must be a half integer.
It was found through measurements conducted at an operating earth station that the above method can estimate the peak Sun transit to 15 s.
While the above calculations provide an accurate estimation of the time of a Sun transit for an earth station, the actual number of days and the length of the time that significant levels of Sun interference will be experienced at a particular earth station will depend on the signal characteristics, performance objectives, and link margins for each carrier. The following sections derive approximate values for the number of affected days, maximum duration per day, and the total duration of the Sun transit effects at each equinox.
### 3.5.1 The number of affected days
Because the declination angle of the Sun changes at approximately 0.4 per day at the equinoxes, the number of affected days at each equinox can be approximated by:
where 0.48 is the approximate optical diameter of the Sun and the earth station antenna half power beamwidth, _{3dB} (degrees) is estimated as:
_{3dB}_{ }= 70 /*d*_{ant}
where:
* d*_{ant}_{ }: antenna diameter
: wavelength in the same units.
For an 11 m antenna at a frequency of 11 GHz, _{3dB} = 0.17, and so Sun transits through the 3 dB beamwidth of the antenna would typically occur on 1 or 2 successive days at each equinox.
### 3.5.2 The maximum duration
Because the hour angle of the Sun changes at approximately 0.25 per minute, the maximum duration of a Sun transit can be approximated by:
For the 11 m antenna, _{3dB} = 0.17, and so the maximum duration of a Sun transit through the antenna 3 dB beamwidth would be approximately 2.5 min.
### 3.5.3 Total duration at each equinox
When a large number of parallel lines intersect a circle, the average length of the intersection is *D*/4, where *D* is the diameter of the circle. The total length of the intersections is *D*^{2}/4*p*, where *p* is the separation between the parallel lines.
From this last expression, and since the declination angle of the Sun changes at approximately 0.4 per day at the equinoxes and its hour angle changes at approximately 0.25 per min, the total duration of the Sun transits at each equinox can be approximated by:
Total duration (_{3dB} + 0.48°)^{2} / (4 0.4° 0.25°)
For the 11 m antenna, _{3dB} = 0.17, and so the total duration of Sun transits through the antenna 3 dB beamwidth would be approximately 3.5 min at each equinox. |