等效功率通量密度（equivalent power flux density，EPFD）是衡量非静止轨道（non-geostationary orbit，NGSO）星座系统对静止轨道（geostationary orbit，GSO）星座系统干扰的一项重要评价指标，通常采用外推卫星轨道位置、统计不同EPFD值出现时间占比的方法获得其概率分布。对于如Starlink等的巨型星座，沿用传统外推方法计算EPFD存在仿真时间长、计算效率低等问题。为此，该文提出了一种计算EPFD概率分布的方法。通过在某一区域内不同位置放置基准卫星生成星座快照，以获取所以可能的卫星分布。同时，通过基准卫星的卫星出现概率表征快照概率，计算不同快照产生的EPFD，进而获得EPFD的概率分布。仿真结果表明，该文方法可同时适用于卫星数量较少的传统星座及超大规模的巨型星座，仿真结果与传统外推方法具有相同的准确度，但计算效率更高。
EPFD (equivalence power flux density) is an important indicator for evaluating the interference of a NGSO (non-geostationary orbit) constellation system to a GSO (geostationary orbit) system. The EPFD probability distribution is usually obtained by extrapolating the satellite orbit position and compile statistics the occurrence time proportion of various EPFD values. For mega-constellation systems like Starlink, the traditional extrapolation method to calculate EPFD will involve long, inefficient simulations. This paper presents a simplified method to calculate the EPFD probability distribution. Constellation snapshots are generated by placing reference satellites at various locations in a region to obtain all possible satellite distributions. The snapshot probabilities are then characterized by the occurrence probabilities of the reference satellites, and the EPFD generated for various snapshots used to obtain the EPFD probability distribution. Simulations show that this method can be applied to both traditional constellations with fewer satellites and to mega-constellations. These simulations have the same accuracy as the traditional method, but with higher computational efficiencies.
[1] World Radio Comunication Conferences. Equivalent power flux density (EPFD) limits:WRS16/15-C[S]. Geneva:International Telecommunication Union, 2016.
[2] 葛侠. 卫星导航系统集总EPFD计算与分析[J]. 无线电工程, 2010, 40(12):35-37, 64. GE X. Research on aggregate EPFD from all RNSS systems[J]. Radio Engineering, 2010, 40(12):35-37, 64. (in Chinese)
[3] International Telecommunication Union. Radio regulations[M]. Geneva:International Telecommunication Union, 2016.
[4] International Telecommunication Union. Functional description to be used in developing software tools for determining conformity of non-GSO stationary-satellite orbit fixed-satellite service systems or networks with limits contained in Article 22 of the Radio Regulations recommendation ITU-R S.1503-3[S]. Geneva:International Telecommunication Union, 2018.
[5] SpaceX. Legal Narrative:SAT-LOA-20190704-00057[Z]. Washington DC, USA:Federal Communications Commission, 2020.
[6] 刘帅军, 徐帆江, 刘立祥, 等. Starlink星座覆盖与时延分析[J]. 卫星与网络, 2020(7):50-52. LIU S J, XU F J, LIU L X, et al. Analysis of Starlink constellation coverage and time delay[J]. Satellites & networks, 2020(7):50-52. (in Chinese)
[7] MIHAI A. SpaceX Gen2 non-geostationary satellite system:SAT-LOA-20200526-00055[Z]. Washington DC, USA:Federal Communications Commission, 2020.
[8] PORTILLO I D, CAMERON B G, CRAWLEY E F. A technical comparison of three low earth orbit satellite constellation systems to provide global broadband[J]. Acta Astronautica, 2019, 159(6):123-135.
[9] 章罗娜, 马忠成, 饶建兵, 等. 低轨卫星互联网发展趋势及市场展望[J]. 国际太空, 2020(11):28-31. ZHANG L N, MA Z C, RAO J B, et al. Development trend and market prospect of low orbit satellite Internet[J]. Space International, 2020(11):28-31. (in Chinese)
[10] LIN Z Q, JIN J, YAN J, et al. Fast calculation of the probability distribution of Interference involving Multiple Mega-constellations[C]//The 5th Space Information Networks Symposium. Shenzhen:Springer Science and Business Media Deutschland GmbH, 2020:18-34.
[11] RAVISHANKAR C, GOPAL R, BENAMMAR N, et al. Next-generation global satellite system with mega-constellations[J]. International Journal of Satellite Communications and Networking, 2021, 39(1):6-28.
[12] 代建中, 冯旭哲. 低轨卫星系统频谱干扰及其规避仿真与分析[J]. 信息技术, 2021, 45(2):79-84, 91. DAI J Z, FENG X Z. Simulation and analysis of spectrum interference and mitigation of LEO satellite system[J]. Information Technology, 2021, 45(2):79-84, 91. (in Chinese)
[13] 靳瑾, 李娅强, 张晨, 等. 全球动态场景下非静止轨道通信星座干扰发生概率和系统可用性[J]. 清华大学学报(自然科学版), 2018, 58(9):833-840. JIN J, LI Y Q, ZHANG C, et al. Occurrence probability of co-frequency interference and system availability of non-geostationary satellite system in global dynamic scene[J]. Journal of Tsinghua University (Science and Technology), 2018, 58(9):833-840. (in Chinese)
[14] ZHANG C, JIN J, KUANG L L, et al. Blind spot of spectrum awareness techniques in nongeostationary satellite systems[J]. IEEE Transactions on Aerospace and Electronic Systems, 2018, 54(6):3150-3159.
[15] ZHANG C, JIANG C X, JIN J, et al. Spectrum sensing and recognition in satellite systems[J]. IEEE Transactions on Vehicular Technology, 2019, 68(3):2502-2516.
[16] ZHANG C, JIN J, ZHANG H, et al. Spectral coexistence between LEO and GEO satellites by optimizing direction normal of phased array antennas[J]. China Communications, 2018, 15(6):18-27.
[17] REN Z X, LI W, JIN J, et al. A GEO satellite position and beam features estimation method based on beam edge positions[J]. Journal of Communications and Information Networks, 2019, 4(4):87-94.
[18] LIN Z Q, JIN J, YAN J, et al. A method for calculating the probability distribution of interference involving mega-constellations[C]//71st International Astronautical Congress, Dubai:International Astronautical Federation, 2020.
[19] International Telecommunication Union. Analytical method to calculate visibility statistics for NGSO satellites as seen from a point on the earth's surface:Recommendation ITU-R S.1257[S]. Geneva:International Telecommunication Union, 2002.
