1、 Rec. ITU-R S.1713-1 1 RECOMMENDATION ITU-R S.1713-1 Methodology to calculate the minimum separation angle at the Earths surface between a non-geostationary HEO-type FSS satellite in its “active” arc and a geostationary satellite (Question ITU-R 241/4) (2005-2007) Scope This Recommendation provides
2、methodologies to calculate the minimum separation angle anywhere on the Earths surface between a high Earth orbit (HEO) satellite in its “active” arc and: a) all visible locations in the GSO arc; b) a specific GSO satellite. The first methodology (see Annex 3) is useful for determining if a HEO syst
3、em complies with the equivalent power flux density (epfd) limits in frequency bands where Radio Regulations Article 22 epfd limits apply. The second (see Annex 5) is useful for interference assessment between a specific GSO network and a HEO-type FSS satellite. The ITU Radiocommunication Assembly, c
4、onsidering a) that in the great majority of HEO satellite system designs, the apogee for each satellite occurs at the highest latitude point in its orbit, and each satellite transmits only while it is within an “active” arc around the apogee; b) that the key parameter to determine the worst case of
5、interference between a HEO system and a GSO system is the minimum separation angle at which an active HEO satellite is seen by any earth station operating with a GSO satellite; c) that the angle subtended at the Earths surface between a HEO satellite and a point in the GSO varies with the latitude a
6、nd longitude of the point on the Earths surface. Thus the separation angle at an earth station in a GSO network between the satellite to which it is operating and a HEO satellite varies with the latitude and longitude of that earth station; d) that the determination of the minimum separation angle b
7、etween a HEO system and a GSO network would facilitate rapid preliminary assessments of the potential for a HEO system to share a band with GSO systems; e) that in frequency bands where Radio Regulations (RR) Article 22 epfd limits apply, non-GSO systems, including HEO systems, are obliged to meet t
8、he epfd limits everywhere on the Earths surface taking into account downlinks from every visible location in the GSO arc (whether or not a GSO satellite currently exists at the worst-case longitude); f) that for HEO systems described in considering a) operating in frequency bands where RR Article 22
9、 epfd limits apply, the maximum epfd corresponds to the minimum separation angle at the Earths surface between a HEO satellite in its active arc and the worst-case GSO longitude and 2 Rec. ITU-R S.1713-1 occurs when a HEO satellite is at the beginning or end of its active arc (i.e. lowest latitude p
10、oint in the active arc); g) that in frequency bands where RR Article 22 epfd limits do not apply, frequency sharing between a HEO system and a specific GSO network generally requires calculation of the minimum separation angle at the Earths surface between a HEO satellite in its active arc and the l
11、ocation of the specific GSO satellite; h) that for HEO systems described in considering a), the calculation indicated in considering g) results in a minimum separation angle at the Earths surface between a HEO satellite in its “active” arc and the specific GSO satellite that does not necessarily occ
12、ur when the HEO satellite is at the beginning or end of its “active” arc, recommends 1 that the methodology described in Annex 1 may be used to compute the separation angle at which a given HEO satellite in its active arc is “seen” from a given earth station operating with a given GSO satellite, and
13、 then to compute the minimum separation angle at the Earths surface taking into account all possible earth station locations and all possible GSO satellite longitudes; 2 that Annex 2 may be used to determine the increase in noise temperature of the GSO link due to interference from the HEO satellite
14、; 3 that the methodology described in Annex 5 may be used to compute the minimum separation angle at which a given HEO satellite in its “active” arc is “seen” from a given earth station operating to a specific GSO satellite. NOTE 1 Annex 3 applies iteratively the methodologies contained in Annexes 1
15、 and 2 to determine the minimum separation angle at which an active satellite in a given HEO system can be seen by any earth station operating to any GSO satellite, and thus calculates the worst case of increase in noise temperature of the GSO link. NOTE 2 Annex 4 gives examples of the application o
16、f Annexes 1 to 3. NOTE 3 Annex 6 gives examples of the application of Annex 5. Annex 1 Method for calculating the minimum angle, subtended at the Earths surface, between a HEO satellite within its active arc and the visible portion of the geostationary orbit Figure 1 is a two-dimensional illustratio
17、n of the path taken by a satellite orbiting the Earth. In general this will be an elliptical orbit, where one of the two focal points is coincident with the Earths centre of gravity, O, and the orbit plane is inclined with respect to the Earths Equatorial plane. (The GSO is a special case, in which
18、the ellipse becomes a circle in the Equatorial plane.) Rec. ITU-R S.1713-1 3 FIGURE 1 Plane geometry of an elliptical orbit In most HEO systems a satellite in such an orbit will transmit (and receive) only while it is within a limited arc containing the apogee, A, and hence will cause (or suffer) in
19、terference only while it is within that arc, which is commonly termed the active arc. The great majority of HEO systems are designed so that the apogee is the highest latitude point within the orbit, and in such cases the maximum interference levels potentially occur when a satellite is at the begin
20、ning or the end of its active arc. The length of the active arc varies from system to system. In Fig. 1 the start of the active arc is shown as s, and the end as e. The orbit dynamics are such that the satellite travels rapidly in the region of the perigee, P, and relatively slowly in the region of
21、the apogee. (In fact the area swept out by radius vector, r, per unit of time, i.e. (r2/2)(/t), is constant throughout the orbit.) Step 1: The first step here is to determine the length Os from the basic orbit characteristics. Information normally provided to ITU-R concerning a HEO system includes t
22、he following: apogee height (AB (km); perigee height (PL (km); eccentricity,e; inclination; i degrees; true anomaly of start (and end) of active arc (angle POs in Fig. 1, i.e. 180 ). As an alternative to the true anomalies of s and e, the time periods for the satellite to travel from s to apogee and
23、 from apogee to e are often given, e.g. 4 h. In such cases the value of may be deduced, either by setting up a time-step simulation to determine it, or by integration based on the fact that (r2/2)(/t) is constant, but both options are relatively complex. For ITU-R studies it is usually more convenie
24、nt for either the true anomaly of s (or e), or angle , to be given explicitly, and this is assumed here; however, the electronic version of the EXCEL spreadsheet appended to this Recommendation contains a visual basic routine to determine from the time before apogee at which the satellite reaches s
25、(or the time after apogee at which the satellite reaches e). It may be noted that the information required by RR Appendix 4 to be supplied when any filing for a non-GSO satellite system is submitted to the Radiocommunication Bureau includes the apogee and perigee heights and the eccentricity, but cu
26、rrently the active arc limits, which are relevant only for non-GSO systems of the HEO class, are not listed in the data to be supplied. However, for non-GSO systems (implicitly including HEOs) planned to use bands in which RR Article 22 epfd limits apply, one of the parameters required by RR Appendi
27、x 4 is the minimum height above the Earths surface at which any satellite in the system transmits. For a HEO satellite this is sC in Fig. 1. From Fig. 1, using the equation of an ellipse and plane trigonometry, a quadratic equation for x in terms of AB, PL, e and may be formed, and solved for x, and
28、 length Os may then be found from triangle Oms. 4 Rec. ITU-R S.1713-1 FIGURE 2 Plane triangle extracts It is unlikely that a GSO link would be designed to operate with elevation (el) lower than 5, for which EG works out to be 41 124.624 km. el may exceed 5, but EG clearly exceeds that length. Hence
29、the condition for E to be “visible” to G is 35 786 km EG 41 124.624 km E is visible to s but E is obscured from sby the Earth. E0is on the contour for which sis at 0 elevation. Then triangle OsE0is right-angled, and hence sE0= (Os)2 (6 378)2)0.5.So the condition for E to be visible to s issE (Os)2 (
30、6 378)2)0.5. Step 2: The next step is to find the latitude of s and its longitude relative to the simultaneous apogee longitude, which may be done using Fig. 3. This is a three-dimensional representation of the orbit, using the same symbols as in Fig. 1 so Os is as calculated in Step 1. By applying
31、the spherical Cosine Rule to spherical triangles OBCD and CODF in Fig. 3, and then applying the spherical Sine Rule to spherical triangle ONBC, it may be deduced that the longitude of s relative to A (C) and its latitude (C) are given by: )sin(/)(sin(cosFOCand)cos(/)(tan(tanFOD11cCCi =Rec. ITU-R S.1
32、713-1 5 FIGURE 3 Geographical coordination of start of HEO active arc Step 3: Having found the latitude and instantaneous relative longitude of s, the corresponding interference separation angle () at any earth station, E, operating to any geostationary satellite, G, may be calculated using Fig. 4,
33、in which points C, O, F, N and s are identical to those in Fig. 3. Thus in Fig. 4 the latitude of E is Eand its longitude relative to the longitude of A is E, and the longitude of G relative to the longitude of A is G. Then, since C,E, C, E, G, OE (Earths radius), OG (GSO radius) and Os are known or
34、 have been calculated, by applying the spherical Cosine Rule to spherical triangle ONCE, and then applying the plane Cosine Rule to plane triangle OsE, the length sE may be calculated; by applying the spherical Cosine Rule to spherical triangle OCFJ, and then applying the plane Cosine Rule to plane
35、triangle OsG, the length sG may be calculated; and by applying the spherical Cosine Rule to spherical triangle OEJK, and then applying the plane Cosine Rule to plane triangle OEG, the length EG may be calculated. And finally in plane triangle EsG, since the three sides sE, sG and EG have now been ca
36、lculated, the angle may be found by using the plane Cosine Rule. 6 Rec. ITU-R S.1713-1 FIGURE 4 Geometry of interference from HEO satellite at start of active are to GSO network earth station (i.e. path sE) Thus, by employing this procedure, the interference separation angle, , may be calculated for
37、 any GSO downlink (i.e. for an earth station in any geographical location receiving from a GSO satellite on any longitude), if the HEO inclination angle, apogee height, perigee height, eccentricity, and either the true anomaly or the time relative to apogee of the start (or end) of the active arc ar
38、e known. To find the minimum value of a simple computer program may be written to cycle through a range of combinations of E, Eand G, employing the above procedure to calculate for each combination, and then select the lowest value. Since interference can occur only for combinations of E, Eand Gfor
39、which E is visible to both G and s (see Fig. 4), but all such combinations must be investigated, it is convenient to arrange for the simple program to include wide ranges of the three variables and then to exclude from the reckoning any combinations where E is obscured by the Earth from either G or
40、s or both G and s. This is illustrated in the plane triangle extracts from Fig. 4 shown in Fig. 2. Rec. ITU-R S.1713-1 7 Annex 2 Calculation of increase in GSO link noise due to interference from a HEO satellite at the start of its active arc From Fig. 4 it can be seen that interference from a HEO s
41、atellite at s to the link between a geostationary satellite at G and an earth station at E will enter that earth stations receiver via a side lobe of its antenna pattern. The corresponding increase in noise temperature of the GSO link is given by: dB)(log10)()4(log20)100)(log101TkGd/E/T/T += where:
42、T/T: link noise increase expressed as a percentage E1: e.i.r.p. density of carrier transmitted by HEO satellite (dB(W/Hz) d: length of interference path sE (m) : wavelength (m) = (0.3)/f where f is the HEO carrier frequency (GHz) G(): receive gain of earth station antenna at frequency f and at off-a
43、xis angle (dBi) T: noise temperature of GSO link (K) k: Boltzmanns constant, i.e. 10log(k) = 228.6 dB(W/Hz/K). T may be either the noise temperature of the GSO downlink alone, or the GSO system noise temperature referred to the earth station receiver input, depending on how it is preferred to expres
44、s T/T. For the calculation of G(), since the methodology in this Annex relates to interference between non-GSO and GSO systems it is appropriate to employ the gain patterns prescribed in Recommendation ITU-R S.1428, where G() is expressed in terms of D/ and D is the antenna diameter (m). Annex 3 Ite
45、rative implementation of the methodology in Annex 1 In the attachment (“MinseparationHEOangle”) to this Annex the procedure developed in Annex 1 is implemented in an EXCEL spreadsheet, which contains Visual Basic routines to cycle through all combinations of earth station latitude and longitude and
46、GSO satellite longitude for which both the GSO satellite and the start of a HEO system active arc are simultaneously visible, and thus identify the minimum separation angle at any earth station for which mutual interference could occur. For the convenience of the user the simple steps described in A
47、nnex 2 are incorporated into the spreadsheet to provide an output giving the maximum value of T/T due to that interference if required. As is evident from the examples in Annex 4, the spreadsheet covers all types of orbit in which a limited active arc is employed, provided that the arc does not inte
48、rsect any line between the GSO and the Earths surface at latitude 81.3. The only input data required are the following parameters of the HEO system: height of apogee (km); height of perigee (km); 8 Rec. ITU-R S.1713-1 eccentricity (as a decimal fraction); orbit inclination angle (degrees); one (or m
49、ore) of three parameters to define the start s (or end “e“) of the active arc, i.e.: either geocentric angle between s and apogee (degrees), or time taken for a satellite to move between s and apogee (h)1, or height of s (km). If the user wishes the corresponding value of T/T to be calculated the following additional input parameters are needed: maximum HEO satellite e.i.r.p. density (dB(W/Hz); and the following parameters of the GSO link: diameter
