1、 Rec. ITU-R SF.765-1 1 RECOMMENDATION ITU-R SF.765-1 Intersection of radio-relay antenna beams with orbits used by space stations in the fixed-satellite service (1992-2002) The ITU Radiocommunication Assembly, considering a) that Recommendation ITU-R SF.406 specifies the maximum e.i.r.p. of line-of-
2、sight radio-relay system transmitters operating in the frequency bands shared with the fixed-satellite service (Earth-to-space); b) that the examination of the compliance of radio-relay stations operating below 15 GHz with Recommendation ITU-R SF.406 requires the calculation of the angle between the
3、 direction of the radio-relay antenna beam and the direction towards the geostationary-satellite orbit; c) that the effect of atmospheric refraction should be taken into account in the above calculation, recommends 1 that the material contained in Annex 1 should be taken into consideration when plan
4、ning radio-relay systems; 2 that the method described in Annex 2 should be used for the calculation of the angle between the direction of the radio-relay antenna beam and the direction towards the geostationary-satellite orbit. NOTE 1 For their own protection, highly sensitive radio-relay receivers
5、operating in frequency bands between 1 and 15 GHz shared with space radiocommunication services (space-to-Earth) should avoid directing their antennas towards the geostationary-satellite orbit (see Note 2 of Recommendation ITU-R SF.406). The method given in this Recommendation can also be used for s
6、uch purpose. Annex 1 General considerations concerning the intersection of radio-relay antenna beams with orbits used by space stations in the fixed-satellite service 1 Introduction The exposure of the antenna beams of radio-relay systems to emissions from communication satellites is geometrically p
7、redictable when such satellites have circular orbits with recurrent earth tracks but is only predictable statistically for inclined circular orbits of arbitrary periods. A phased system of these recurrent earth-track satellites can be made to follow a single earth-track and such systems are of incre
8、asing interest for communication. Geostationary satellites are a special case, since the equator constitutes the earth-track of all equatorial orbits. 2 Rec. ITU-R SF.765-1 At any Earth location from which the satellites of a single-earth-track system could be seen, successive (non-stationary) satel
9、lites would follow a fixed arc through the sky, from horizon to horizon. Moreover, except for inclined orbits, this arc would be independent of longitude and be symmetrical relative to North/South. Subsequent portions of this Annex consider exposure conditions relative to a circular equatorial orbit
10、 (including the special case of the orbit of a geostationary satellite) and also the probability of exposure to unphased satellites (non-recurrent earth-track). Some indication of the extent to which existing antennas of radio-relay systems are directed towards the orbit of a geostationary satellite
11、, has been provided by several administrations. It is shown that although the overall percentage of antenna beams which intersect the geostationary orbit is about 2%, this percentage will be substantially higher if one takes into account the beam extending to 2 from its axis, and the effect of refra
12、ction. Examination of the compliance of existing radio-relay stations with Recommendation ITU-R SF.406 indicates that the percentage of stations having an antenna-beam direction within 2 of the geostationary-satellite orbit is in the order of 10% in some countries. Furthermore, it cannot be assumed
13、that substantial segments of the orbit in any range of longitude are free from illumination by the antennas of radio-relay systems. 2 Some characteristics of the antenna beams of terrestrial radio-relay systems Line-of-sight radio-relay systems use antennas with gains of the order of 40 dB and half-
14、power beam-widths of the order of 2. Trans-horizon systems generally use antennas with higher gain and narrower beams, say 50 dB and 0.5. In either case, path inclinations are less than 0.5 on the average and rarely in excess of 5. When all of a negatively inclined beam strikes the Earth, there woul
15、d be no exposure to an orbit. For horizon-centred beams, the upper half could have exposure. When passive reflectors are used, spill-over also should be considered. Since the beams are close to the Earth and traverse a considerable thickness of atmosphere, diffraction and refraction should be taken
16、into account in making precise calculations of exposure. 3 Directions to circular equatorial orbits It is well known from geometric considerations that the azimuth angle, A (measured clockwise from North) and the angle of elevation, e, of a satellite in a circular equatorial orbit can be expressed b
17、y: A = arctan ( tan /sin ) (1) += coscos21/)1coscos(arcsin2KKKe (2) where: K : orbit radius/Earth radius : Earth latitude of the terrestrial station : difference in longitude between the terrestrial station and the satellite. Rec. ITU-R SF.765-1 3 Eliminating between these two equations leads to: +=
18、 tan1)1(tantanarccos2221KKeKeA (3) If necessary, azimuths and elevations to any single-earth-track inclined orbit system, of given height, inclination and equatorial crossings could be determined by an extension of this analysis. For such systems, however, the orbit directions would depend both on l
19、atitude and longitude of the terrestrial station. An antenna directed at the orbit of a non-geostationary satellite (or other single earth-track orbit) will be certain to have intermittent exposure. For a circular equatorial orbit (other than the orbit of the geostationary satellite) with m satellit
20、es, antennas having an interference beamwidth of radians will have interference for a fraction of the time given approximately by: P = m /(2) (4) For the special case of the orbit of a geostationary satellite, P will be either zero or unity. 4 Unphased satellite systems In this case it is possible t
21、o derive only an average probability of exposure to a satellite. Thus, for a system of n orbits of equal height and equal inclination angle, i, it can be shown that the average probability of exposure is given by: P = m n /(8 cos ) arccos (sin ( /2)/sin i arccos (sin ( + /2)/sin i (5) when (i /2), a
22、nd where: m : number of satellites in each orbit : latitude of intersection between the antenna beam and the orbital sphere. In most of the cases encountered in practice, when i , calculations can be made by means of the following equation: =222sinsin8 inmP (6) The relative error of the calculations
23、 made by means of equation (6) does not exceed 0.25% of those made with equation (5). For the particular case of the polar orbit, i = /2, and the above expression reduces to: )cos8/(2= nmP (7) 5 Geometric relations between the directions of radio-relay antennas and the geostationary-satellite orbit
24、The geostationary-satellite orbit is particularly important, not only from the point of view of the exposure of radio-relay systems to beams from satellites, but also because of the limitations imposed by Recommendation ITU-R SF.406 on the directions of radio-relay antennas to protect reception by g
25、eostationary satellites. 4 Rec. ITU-R SF.765-1 Equation (3) can be expressed as: )cos(arccostantanarccos1eeKA= (8) where: A : azimuth (or its complement at 360) measured from the South in the Northern Hemisphere and from the North in the Southern Hemisphere K : orbit radius/Earth radius, assumed to
26、be 6.63 e : geometric angle of elevation of a point on the geostationary-satellite orbit : latitude of the terrestrial station. For a given station latitude and for a given angle of elevation the values of the angle A, for the two orbit points, are measured from both sides of the meridian. 5.1 The e
27、ffects of atmospheric refraction The usual effect of atmospheric refraction is to bend the radiowave ray towards the Earth; the beam of a radio-relay antenna having an angle of elevation , may reach a satellite with an angle of elevation e where: e = (9) and e and are algebraic values, and is the ab
28、solute value of the correction due to refraction. The extent of bending depends on the climate of the region where the station is situated (refractive index, gradient of the index, etc.), on the altitude of the station and the initial angle of elevation ; the variation of as a function of is particu
29、larly rapid at a low negative value of . The value of may exceed several tenths of a degree, and this is particularly important for stations at medium or high latitudes, where a slight change in the angle of elevation results in a considerable change of the azimuth to each of the two corresponding p
30、oints on the geostationary-satellite orbit. Moreover, this correction varies in time with atmospheric conditions. At a given point of latitude and for a given angle of elevation, the azimuth to the orbit will in time scan a certain angular zone. To apply Recommendation ITU-R SF.406, whereas a mean v
31、alue of refraction will provide substantial protection, to provide full protection it is desirable to consider the maximum and minimum values of bending due to refraction, so as to determine the azimuths of the extremities of this angular zone. This can be done on a statistical basis. Equation (8) m
32、ay be used to determine the extreme azimuths of the angular zone, on the basis of extreme angles of elevation e1and e2. It is not always easy to determine the bending as a function of the climate, the altitude of the station and the angle of elevation , since the assumption of a reference atmosphere
33、 of exponential type is not always applicable and the probability of the formation of atmospheric ducts is by no means negligible, especially in certain hot maritime areas. Where a hypothetical atmosphere of exponential type is admissible and where the ground index, N, and the gradient N of the inde
34、x between 0 and 1 000 m are related, the curves showing correction as a function of the angle of elevation can be calculated. Determining the maximum and minimum corrections 1and 2is then equivalent to the assessment of the maximum and minimum of N (or N ) corresponding to the particular case under
35、consideration. Rec. ITU-R SF.765-1 5 The influence of the altitude of the station is very difficult to assess. For positive angles of elevation, the radio beam quickly leaves the atmosphere, the bending is relatively slight and the influence of altitude is probably reduced. On the other hand, for ne
36、gative angles of elevation, a beam crossing the horizon passes twice through the densest layers of the atmosphere; the bending is thus greater and its variation with altitude at constant angle of elevation is likely to be much greater. However, there are no accurate data in this connection. Provisio
37、nally, and to provide protection under all conditions, one should adopt the following rules: 5.1.1 in those geographical areas where propagation data are available which will enable the amount of bending to be determined on a statistical basis, the maximum bending (for instance the bending not excee
38、ded for 99.5% of the time) and the minimum bending should be derived from these data; 5.1.2 where such data are not available, the following approximation may be used. Limits of refractive index assuming an exponential reference atmosphere can be calculated from the sea-level radio refractivity, N0,
39、 and the gradient, N (as found in worldwide charts). A range for N0between 250 and 400 (N at sea level between 30 and 68, respectively) is representative of minimum and maximum values throughout a large part of the world and throughout the year. Establishing these limits permits the calculation of c
40、urves for 1and 2as a function of angle of elevation of the antenna and station height. The refraction correction, , can be calculated by the following integration: nrnnnd)(/cot21=(10) This integration is performed under the condition of Snells law for polar coordinates, which follows: n(r) r cos = n
41、(r1) r1 cos 1(11) where: n(r) = 1 + a exp b(r r0) r0: Earth radius (6 370 km) 1= r0+ h (h: station height) 1: elevation angle at the station n1: refractivity at the station height 2: refractivity at the orbit a = N0 106b = ln N0/(N0+ N ) N0= 400 and N = 68 for maximum bending 0= 250 and N = 30 for m
42、inimum bending. This integration has been carried out and the calculation results are presented in Fig. 1. Numerical formulae which give a good approximation to this function are described in Note 2 of Annex 2, 4, to this Recommendation. 6 Rec. ITU-R SF.765-1 D01-scRec. ITU-R SF.765-1 7 5.2 Use of a
43、 graphical method for determination of azimuths to be avoided A graphical method which takes into account the influence of the actual local horizon can be used to determine azimuths to be avoided. The approximations it makes limit its application to stations located below about 70 latitude. Its azim
44、uthal accuracy is approximately 0.1 with better results for low angles of elevation. This method, illustrated in Fig. 2, is based on the consideration of the apparent orbit of a geostationary satellite, taking into account the effect of refraction, the latitude of the terrestrial station, antenna el
45、evation angle and the influence of the local optical (real) horizon. D02-sc8 Rec. ITU-R SF.765-1 To plot the apparent (refracted) orbit, it is necessary to raise the trace of the geometric orbit at each point by a quantity , which is a function of the geometric orbit elevation and the station height
46、. This can be done by plotting the point whose elevation is and azimuth is C( (), where C( ) is given by equation (14) of Annex 2 and ( ) is max( ) or min( )in Note 2 of Annex 2. The method may be summarized as follows: 5.2.1 On Fig. 2 draw a straight line passing through the origin and the point co
47、rresponding to the latitude of the station in question. (This implies an approximation of the orbit by a straight line in this small region.) The reference azimuth (0 on Fig. 2) for a zero geometric angle of elevation is calculated using equation (8). 5.2.2 Draw a horizontal line corresponding to th
48、e angle of elevation planned for the antenna. 5.2.3 Raise the trace of the geometric orbit at each point by the quantity (a function of e) to account for the maximum and minimum refraction expected. This means that there will be two new traces, one corresponding to minimum bending and the other to m
49、aximum bending. 5.2.4 Draw the local horizon in the region of the azimuth concerned. For preliminary studies, the method can be simplified by replacing the real local horizon by a mean, approximate horizon. 5.2.5 Using a compass set to a radius of 2, find on the straight line of the constant angle of antenna elevation, the centre of a circle tangential to the trace corresponding to minimum
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