1、 Rec. ITU-R S.1529 1 RECOMMENDATION ITU-R S.1529 Analytical method for determining the statistics of interference between non-geostationary-satellite orbit fixed-satellite service systems and other non-geostationary-satellite orbit fixed-satellite service systems or geostationary-satellite orbit fix
2、ed-satellite service networks (Question ITU-R 231/4) (2001) The ITU Radiocommunication Assembly, considering a) that emissions from the earth stations as well as from the space stations of satellite systems (geostationary-satellite orbit fixed-satellite service (GSO FSS), non-GSO FSS, non-GSO mobile
3、-satellite service (MSS) feeder links) in the FSS may result in interference to another such system when both systems operate in the same frequency bands; b) that when non-GSO satellite systems are involved, the statistical behaviour of interference, especially that related to short-term events, con
4、stitutes an important factor in interference evaluation studies; c) that it is desirable to have reliable and precise tools for determining the statistical behaviour of interference between systems that have co-frequency links when the interference environment involves non-GSO satellite systems; d)
5、that computer simulation methods (see Recommendation ITU-R S.1325) may require an excessively long computer time to ensure that all interference events are taken into account and thus statistically significant results are obtained, recommends 1 that the analytical method given in Annex 1 should be c
6、onsidered as a possible method for use in obtaining aggregate interference cumulative probability distributions for assessing the interference between systems that have co-frequency links when the interference environment involves non-GSO satellite systems. ANNEX 1 An analytical method for assessing
7、 interference in interference environments involving non-GSO satellite systems 1 Introduction Most of the existing methods to assess interference involving non-GSO satellite systems are based on direct computer simulation. These methods are usually time consuming and require a new lengthy simulation
8、 run each time a change is made in some of the system and system parameters. Also, in complex situations, involving a large number of earth stations and non-GSO satellites, 2 Rec. ITU-R S.1529 these methods may require a very long computer time to produce statistically significant results. This Anne
9、x presents an analytical method, that can be implemented through numerical techniques, intended to perform the evaluation of interference sensitivity to system and system parameters without requiring lengthy computer simulation runs. Also, as opposed to results generated through simulation, the resu
10、lts obtained with the analytical approach correspond to an infinite number of simulated days, and therefore, in this sense, they do not present the need for long running times, as may be required in computer simulation methods to assure statistically significant results. The method is based on the k
11、nowledge of the probability density function (pdf) of the position of a single satellite placed in an orbit with an arbitrary inclination. To illustrate the applicability of the proposed method to complex interference environments, results for some specific situations are presented. Comparisons of t
12、he results obtained using the proposed method and those generated by a widely used commercially available simulation software have indicated that the proposed method can generate reliable and precise results with less required computer time. 2 Methodology Let us consider an interference environment
13、involving several, say n, non-GSO systems. The approach being considered in this Recommendation to assess interference in such an environment takes into account the fact that, once the position of one particular satellite (here referred to as reference satellite) in each constellation is known, the
14、aggregate interference levels affecting the receivers of any interfered-with system in the environment (considering that all systems parameters are given) can be uniquely determined. It further assumes that the positions of these reference satellites are characterized by statistically independent ra
15、ndom vectors. Based on these assumptions, desired and interfering signal power levels can be seen as random variables that are deterministic functions of the positions of the reference satellites, and therefore their pdfs can be determined once the pdfs modelling the positions of each of the n refer
16、ence satellites are known. As an example, consider the situation illustrated in Fig. 1. This Figure shows two non-GSO satellite systems, both having circular orbits and arbitrary satellite constellations. Satellites of system 1 move on surface E1 and satellites of system 2 move on surface E2. Refere
17、nce satellites for both systems are also indicated. In this example the downlink aggregate interference from system 1 satellites into a given earth station in system 2 is considered. Given that reference satellite Siof system i ( i = 1, 2) is located at longitude iand latitude ithe positions of all
18、other satellites in both constellations can be uniquely determined as a function of the two location vectors T),(111=x and .),(222T=x Therefore, considering for instance that the earth station antenna always points to the nearest satellite in the constellation of its system, and that all other syste
19、ms parameters, such as satellite and earth station antenna radiation patterns, e.i.r.p., etc. are known, then both the downlink aggregate interference I and the desired signal level C at the considered earth station can be computed for each pair of values of the vectors ,),(Tiii=x , ,iii= Figure 5a
20、shows the results obtained for the probability distribution estimates with the proposed method and through a computer simulation run corresponding to 58 simulated days (6101 time steps with a 5 s time step). The required computer time was around 45 min for both methods, in a 200 MHz PC machine. Fig.
21、 5b and 5c display, in an expanded view, the regions of Fig. 5a corresponding, respectively, to lower levels of interference (side lobe interference) and higher levels of interference (close to in-line interference). It can be noted from these Figures that a good agreement between the results genera
22、ted by the two methods was obtained in the range of lower levels of interference. Considering the higher levels of interference, that occur for a very a small percentage of time, we note that several values of z, although showing a positive probability in the proposed method, did not occur in the si
23、mulation results. This suggests that an increase in the number of simulated days might be required to better cover all the possibilities for the system satellites locations. These differences are also reflected in Fig. 6, which shows the obtained cumulative distribution curves in the range of higher
24、 levels of interference. Note that a difference of 1.5 dB can be observed for the values of Z corresponding to probabilities on the order of .1014 16 Rec. ITU-R S.1529 1529-05a108106104110280 60 40 20Z (dB)Solid line: analytical methodDotted line: simulationProbabilityFIGURE 5aProbability distributi
25、on estimates obtained with the proposed approachand by computer simulation (58 simulated days, 5 s time step)1529-05b80 75 70 60Z (dB)65Solid line: analytical methodDotted line: simulationProbabilityFIGURE 5bProbability distribution estimates obtained with the proposed approachand by computer simula
26、tion - Lower levels of interference(58 simulated days, 5 s time step)0.00010.00100.01000.1000Rec. ITU-R S.1529 17 1529-05c108106104110235 30 25 20Z (dB)Solid line: analytical methodDotted line: simulationProbabilityFIGURE 5cProbability distribution estimates obtained with the proposed approachand by
27、 computer simulation - Higher levels of interference(58 simulated days, 5 s time step)1529-0610710610510410335 30 25 20Z (dB)P(z Z)Solid line: analytical methodDotted line: simulationFIGURE 6Cumulative distribution estimate function obtained with the proposed approachand by computer simulation - Hig
28、her levels of interference(58 simulated days, 5 s time step)18 Rec. ITU-R S.1529 For the simulation results shown in Fig. 7, the number of simulated days was increased from 58 to 290 and the time step was reduced from 5 to 2 s, resulting in computer simulation time of approximately 9 h and 22 min in
29、 a 200 MHz PC machine. Note the improvement in the quality of the simulation results. 1529-07108106104110235 30 25 20Z (dB)Solid line: analytical methodDotted line: simulationProbabilityFIGURE 7Probability distribution estimates obtained with the proposed approachand by computer simulation - Higher
30、levels of interference(290 simulated days, 2 s time step)It is worth pointing out here that, as opposed to results generated through simulation, the results obtained with the proposed analytical approach correspond to an infinite number of simulated days, and therefore, in this sense, they do not pr
31、esent the reliability problem associated with computer simulation methods. For a given interference environment, the computer time required by the proposed method depends on how fine is the quantization of the reference satellites - planes (similar to the size of the time step in computer simulation
32、 methods). Finer quantization trades computer time for higher precision in the numerical results. This is illustrated in Fig. 8 which shows the differences in the probability distribution estimates obtained with the proposed method when the grid element used in the non in-line interference regions o
33、f the - plane is increased from the 0.09 0.09 square used in the previous example to a 0.15 0.15 square, while the same size was maintained for the grid elements in the in-line interference regions. The corresponding reduction in computer time was from 45 min to around 15 min. Rec. ITU-R S.1529 19 1
34、529-081081061041021010180 60 40 20Z (dB)Solid line:in-line interference region: quantization grid = 0.01 0.01non in-line interference region: quantization grid = 0.09 0.09Dotted line:in-line interference region: quantization grid = 0.01 0.01non in-line interference region: quantization grid = 0.15 0
35、.15ProbabilityFIGURE 8Probability distribution estimates obtained with the proposedapproach for different grid quantizationsExample 2 Let us consider two non-GSO systems, LEO 1 and LEO 2. Satellite system LEO 1 has the same orbital dynamics (orbital inclination, number of planes, number of satellite
36、 per planes, altitude, etc.) as the LEO D system. Satellite system LEO 2 has the same orbital dynamics as the LEO F system. This second example considers the uplink interference from LEO 1 earth stations into a LEO 2 satellite. This situation is illustrated in Fig. 9. In this Figure, each earth stat
37、ion is assumed to have four antennas (beams), pointed to the LEO 1 satellites corresponding to the four highest elevation angles that satisfy the minimum elevation angle constraint (the constellation contains a total of 48 satellites). Considering that all feeder-link earth stations transmit the sam
38、e power, the aggregate uplink interference power reaching a LEO 2 satellite (say, satellite i), located at a given point, is proportional to the quantity: Ge5Ge5=10102,)( )(eaNjNkijijkjeijisidGGz where: )(, ijisG : receiving antenna gain of satellite i in a direction ij(degrees) off the main beam ax
39、is )(, ijkjeG : earth station transmitting antenna gain in a direction ijk(degrees) off the main beam axis dij: range between satellite i and the earth station j. 20 Rec. ITU-R S.1529 Note that the random variable ziis a function of the given location of the considered LEO 2 interfered-with satellit
40、e and the random location of the LEO 1 reference satellite. In the equation above Neand Na represent, respectively, the number of earth stations and the number of antennas (per earth station) tracking a LEO 1 satellite with an elevation angle higher than the prescribed minimum value. 1529-09ijijijkE
41、jij0ij0ijkEjFIGURE 9Uplink interference geometryLEO 1 networkearth stationLEO 1 networkearth stationLEO 1satelliteconstellationLEO 2 i-thsatelliteThe LEO 1 earth station antenna transmitting radiation pattern was the same as in Example 1. The LEO 2 satellite receiving antenna radiation pattern was c
42、onsidered to have the same form as that in Example 1 but with Gmax= 12 dBi and 0= 52. The minimum operating elevation angle for the LEO 1 earth stations was assumed to be 5. Concerning the earth station switching strategy, it was assumed that each LEO 1 gateway contains four earth station antennas t
43、hat track LEO 1 satellites with elevation angles higher than the prescribed minimum value, 5. Results were obtained for a total of 120 LEO 1 earth stations (worldwide). The considered set of earth station locations is illustrated in Fig. 10 together with the location of the interfered-with LEO 2 sat
44、ellite (black cross). The location of the LEO 2 satellite was chosen so that the number of visible earth stations is maximized (number of visible earth stations equal to 65). This way the number of interference entries to be considered is maximum. Rec. ITU-R S.1529 21 1529-10FIGURE 10LEO 1 earth sta
45、tion distribution and LEO 2 satellite location (24.5 E, 44.5 N)This example illustrates the ability of the proposed analytical method to handle complex interference environment. Figure 11 illustrates the CDF obtained with the proposed approach for the variable z, corresponding to the aggregate uplin
46、k interference from LEO 1 earth stations into a LEO 2 satellite (120 LEO 1 earth stations worldwide). Simulation results were not obtained in this case. 1529-1110810610410210210170 60 30 20Z (dB)P(z Z)50 40FIGURE 11Cumulative distribution estimate function obtained with the proposed approach for the
47、 variable z,corresponding to the aggregate uplink interference from LEO 1 earth stationsinto a LEO 2 satellite (120 LEO 1 earth stations worldwide)22 Rec. ITU-R S.1529 10 Applying the analytical method to repeated track non-GSO satellite systems When applying the methodology described in the previou
48、s sections to assess the statistical behaviour of interference when repeated track non-GSO satellite systems are involved, it is more adequate to have the position of the reference satellite given in terms of its mean anomaly M and the longitude of the orbit ascending node when the satellite is at t
49、he perigee rather than in terms of its longitude and latitude, as before. In this case, the position of the reference satellite is represented by the vector ,),( = MMTx . Let then ),( Gpxdenote the pdf function of the vector .x Here again, the idea is to model M as a random variable and measure the probability )( MP by the fraction of the period T (period of the satellite revolution) during which M(t) takes values in the interval . Under th
