Co-Frequency Interference Analysis and Dynamic Simulation Validation of Satellite-Direct-to-Device Systems Against Terrestrial IMT Networks in Cross-Border Scenarios
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摘要: 针对手机直连卫星(Satellite-Direct-to-Device, SD2D)系统对邻国边境IMT网络产生的同频下行干扰，该文推导了保护IMT终端和基站所需的PFD (Power Flux Density)和EPFD (Equivalent Power Flux Density)限值，并构建了动态仿真框架进行验证。仿真基于典型低轨星座，并按ITU-R推荐的信道传播、地物遮挡及天线辐射模型建立；综合考虑同频波束隔离、波束调度与建链策略等工程约束，采用分段搜索算法确定满足IMT保护要求的最小隔离距离及其对应的PFD/EPFD统计值。基线仿真及其稳定性验证结果表明，在I/N 门限−6 dB、百分位99.5%的保护准则下，典型系统 Starlink-1满足边境 IMT 终端/基站保护所需最小隔离距离的基线值为195 km/290 km，稳定性验证范围为195–210 km/290–300 km；Starlink-2对应基线值为272 km/420 km，稳定性验证范围为266–290 km/370–420 km。敏感性测试显示：地物遮挡可显著降低终端侧干扰并压缩所需隔离距离，但对基站侧影响有限；保护百分位仅改变从样本中提取“尾部事件”的统计口径；最低工作仰角、极化复用、同频波束数以及建链策略等参数会改变活跃波束的选择与分布，从而导致隔离距离呈现非线性、甚至非单调变化。Abstract:
Objective Satellite-Direct-to-Device (SD2D) systems that reuse terrestrial IMT spectrum may generate harmful downlink interference to incumbent IMT networks in adjacent administrations, especially in cross-border deployments where SD2D downlinks overlap the receiver bands of both IMT user equipment (UEs) and IMT base stations (BSs). Therefore, a practical coexistence methodology is needed to (i) translate IMT receiver protection criteria into explicit power-flux-density (PFD) or equivalent-power-flux-density (EPFD) constraints and (ii) validate these constraints under realistic spatiotemporal dynamics so that they can be mapped to enforceable geographic coordination measures such as border isolation distances. The study focuses on the dominant interference path (SD2D downlink to IMT receivers) and establishes a traceable workflow from deterministic PFD/EPFD limits to dynamic Monte Carlo validation and the resulting minimum border isolation distances. Methods A cross-border scenario is modeled where Country A deploys an SD2D system and Country B operates a terrestrial IMT network. Two representative downlink frequencies, 1995 MHz and 2190 MHz, are evaluated for two SpaceX-related configurations, Starlink-1 and Starlink-2. The IMT network is modeled with ITU-R/3GPP-compliant characteristics, using I/N protection criteria with a threshold of −6 dB and a target percentile κ (baseline κ=99.5%) for both IMT UEs and BSs. Satellite transmit antennas use the ITU-R S.1528 reference pattern; IMT-BS receive antennas use the ITU-R F.1336 sector pattern; IMT-UEs are modeled as omnidirectional. A back-lobe blocking attenuation model is applied to both satellite and BS patterns to capture rear-side shielding. Propagation follows the ITU-R P.619 model with free-space loss as a conservative baseline, and an optional clutter-loss term is introduced via a shielding probability. Deterministic protection limits are obtained by back-calculating the maximum permissible aggregate PFD for IMT-UE protection and the maximum permissible aggregate EPFD for IMT-BS protection. A dynamic simulator then validates these limits and searches for the required minimum border isolation distances (Fig.4 ). Co-channel beam isolation is optimized through the C/I complementary cumulative distribution function (CCDF), and a segmented-search algorithm determines the minimum UE- and BS-side isolation distances together with κ-percentile PFD/EPFD statistics.Results and Discussions The deterministic-limit derivation yields a maximum permissible aggregate PFD of −102.72 dBW/m2/MHz at 2190 MHz (IMT-UE) and a maximum permissible aggregate EPFD of −129.53 dBW/m2/MHz at 1995 MHz (IMT-BS) (Fig.3 ). For Starlink-1, the C/I design target gives a minimum beam-isolation angle pair of (12°, 12°) (Fig.5 ). Dynamic simulation shows that under the representative baseline setting and the I/N threshold of −6 dB and κ=99.5%, the minimum isolation distance is 195 km for UE-protection and 290 km for BS-protection (Fig.6 ,Fig.7 ,Table 4 ). The coordination distance is therefore 290 km, and the κ-percentile simulated PFD/EPFD matches the deterministic limits with a residual margin below 0.5 dB. For Starlink-2, the optimized isolation angles increase to (15°, 15°), and under the same baseline setting, the required distances rise to 272 km (UE) and 420 km (BS) (Table 5 ). The baseline distances reported above should be interpreted as representative values under the specified simulation configuration, rather than strictly converged unique results. Stability verification shows that, under different sampling intervals, simulation durations, and random seeds, the UE/BS-side distances mainly fall within 195–210 km/290–300 km for Starlink-1 and 266–290 km/370–420 km for Starlink-2 (Table 7 ). Sensitivity results for Starlink-1 further show that the isolation distance is governed by the upper tail of the aggregate I/N distribution (Table 6 ). Tightening κ from 99.5% to 100% increases the UE/BS-side distances from 195/290 km to 304/560 km. Clutter shielding substantially reduces the UE-side distance, e.g., to 173 km at a shielding probability of 0.5, but has little effect on BS protection. Polarization reuse increases the UE/BS-side distances to 222/360 km, while increasing the number of co-channel beams to 16 raises the BS-side distance to 330 km. The minimum service elevation and link-establishment strategy are dominant operational factors: changing the elevation threshold from 10° to 35° shifts the required distances from 340/460 km to 101/150 km, while switching from Sat-MaxElevation to UE-MaxElevation reduces them to 80/180 km.Conclusions The proposed workflow converts IMT receiver protection criteria into deterministic PFD/EPFD limits and validates them with a spatiotemporal simulator. Under the I/N threshold of −6 dB and κ=99.5%, the baseline and stability tests jointly indicate representative UE/BS coordination-distance ranges of 195–210 km/290–300 km for Starlink-1 and 266–290 km/370–420 km for Starlink-2, rather than unique, strictly converged values. Sensitivity tests further show that the κ-percentile only changes the statistical criteria for extracting "tail events" from the samples, and clutter shielding mainly benefits UEs, whereas minimum elevation, polarization reuse, co-channel-beam number, and link-establishment strategy can reshape worst-case geometry and drive large (sometimes non-monotonic) changes in the required distances. The framework provides a traceable bridge from receiver criteria to enforceable border coordination measures. -
表 1 SD2D系统轨道参数配置
系统 高度(km) 轨道倾角(°) 轨道面 单面星位① RAAN 间隔(°) 各壳层星位数 星位总数/卫星总数 Starlink-1 525 53 28 120 12.9 3360 8640 /8640 340 53 48 110 7.5 5280 Starlink-2 335 26 96 60 3.75 5760 46800 /15000 ②334 32 96 60 3.75 5760 333 38 96 60 3.75 5760 332 43 96 60 3.75 5760 331 48 96 60 3.75 5760 330 53 96 60 3.75 5760 329 60 48 60 7.5 2880 328 69 48 60 7.5 2880 327 76 48 60 7.5 2880 326 96.87 60 60 6 3600 注：①星位 (orbit slots) 指每个轨道面内预设的可部署位置。②关于 Starlink-2 的轨道配置，SpaceX 声明其实际在轨部署卫星总数将不超过 15000 ，小于预设星位总数46800 ，以灵活调整星座构型[18]。故本文在仿真时，固定总卫星数15000 颗，并按各壳层星位数占比进行均匀缩放：335/334/333/332/331 km 每壳层 1846 颗；330 km壳层 1847 颗；329/328/327 km: 每壳层 923 颗；326 km 壳层1154 颗。
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表 2 SD2D系统主要技术参数
参数 Starlink-1/Starlink-2 频带 698– 2690 MHz/1429 -2690 MHz卫星发射带宽 5 MHz 卫星天线发射极化 右旋圆极化 单波束发射功率 4.79–14.79 dBW
(12.79 dBW @2190 /1995 MHz)单波束EIRP 38.89–48.89 dBW
(46.89 dBW @2190 /1995 MHz)卫星天线方向图 ITU-R S.1528[19] 单星同频波束数量 ($ J $) 6 最低工作仰角 ($ {\varepsilon }_{\min } $) 20°/10° 建链策略 Sat-MaxElevation 径向和横向尺寸 ($ {L}_{\text{r}},{L}_{\text{t}} $) $ {L}_{\text{r}}={L}_{\text{t}}= $1.6 m 第一旁瓣比值 (SLR) 20 dB 旁瓣级数设计参数 (l) 2
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表 3 IMT系统主要技术参数
参数 取值 基站部署类型 乡村宏基站 (Rural-macro) 小区半径 > 3 km (@ 1–2 GHz，典型值 5 km) 基站天线高度 30 m (@ 1–2 GHz) 基站扇区数量 3 基站接收机噪声系数 5 dB 频率复用系数 1 基站天线类型 Non-AAS, ITU-R F.1336[21] 基站天线设计参数 $ {\varphi }_{3} $=65°, $ \beta $=3°, 线极化±45°, $ {L}_{\text{f}} $=3 dB, $ {G}_{0} $=18 dBi, $ {k}_{\text{p}} $=0.7, $ {k}_{\text{h}} $=0.7, $ {k}_{\text{v}} $=0.3 终端部署密度(单扇区
同频发射终端数量)3 终端天线高度 1.5 m 终端天线类型 全向天线 终端天线设计参数 最大增益–3 dBi，线性极化±45º 终端人体损耗 4 dB 终端噪声系数 9 dB
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表 4 Starlink-1干扰 IMT 终端和基站的动态仿真数值结果 ($ {\left(\mathrm{I}/\mathrm{N}\right)}_{\mathrm{th}} $= –6 dB, κ=99.5%)
$ d $ (km) IMT 终端 IMT 基站 I/N (dB) PFD 统计值
(dBW/m²/MHz)裕量ξ(dB) I/N (dB) EPFD 统计值
(dBW/m²/MHz)裕量ξ(dB) 0 11.35 –85.37 –17.35 17.25 –106.27 –23.25 100 2.46 –94.26 –8.46 11.25 –112.28 –17.25 195 –6.12 –102.84 0.12 1.47 –122.06 –7.47 290 –13.71 –110.43 7.71 –6.37 –129.90 0.37
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表 5 Starlink-2干扰 IMT 终端和基站的动态仿真数值结果 ($ {\left(\mathrm{I}/\mathrm{N}\right)}_{\mathrm{th}} $= –6 dB, κ=99.5%)
$ d $ (km) IMT 终端 IMT 基站 I/N (dB) PFD 统计值
(dBW/m²/MHz)裕量ξ(dB) I/N (dB) EPFD 统计值
(dBW/m²/MHz)裕量ξ(dB) 0 10.73 –85.99 –16.73 16.74 –106.79 –22.74 100 4.19 –92.53 –10.19 13.81 –109.72 –19.81 272 –6.16 –102.88 0.16 –0.55 –124.07 –5.45 420 –14.15 –110.87 8.15 –6.21 –129.74 0.21
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表 6 关键参数变化对 Starlink-1 干扰IMT系统仿真结果的敏感性测试
参数 波束隔离角 链路数量 $ {\left(\mathrm{I}/\mathrm{N}\right)}_{\text{UE}} $
($ @d $=0)$ {\left(\text{PFD}\right)}_{\text{UE}} $
($ @d $=0)$ d_{\min }^{\text{UE}} $ $ {\left(\mathrm{I}/\mathrm{N}\right)}_{\text{BS}} $
($ @d $=0)$ {\left(\text{EPFD}\right)}_{\text{BS}} $
(@$ d $=0)$ d_{\min }^{\text{BS}} $ 基线(默认配置) (12°, 12°) 9010 11.35 –85.37 195 17.25 –106.27 290 κ=100% (12°, 12°) 9010 14.77 –81.95 304 19.95 –103.58 560 $ {P}_{\text{shield}} $=0.2 (12°, 12°) 9010 11.07 –85.37 193 17.25 –106.27 290 $ {P}_{\text{shield}} $=0.5 (12°, 12°) 9010 10.43 –85.37 173 17.25 –106.27 290 $ {P}_{\text{shield}} $=0.8 (12°, 12°) 9010 9.06 –85.37 141 17.25 –106.27 290 $ {P}_{\text{shield}} $=1.0 (12°, 12°) 9010 –8.35 –85.37 0 17.25 –106.27 290 极化复用 (12°, 12°) 15817 12.41 –84.31 222 18.78 –104.75 360 同频波束数=1 (12°, 12°) 7839 11.68 –85.04 207 17.23 –106.30 270 同频波束数=16 (10°, 10°) 16962 11.75 –84.97 192 17.57 –105.96 330 最低仰角=10° (15°, 15°) 2597 9.75 –86.97 340 16.30 –107.23 460 最低仰角=35° (12°, 12°) 36608 12.92 –83.79 101 15.79 –107.74 150 建链策略 2
(UE-MaxElevation)(10°, 10°) 75836 14.19 –82.53 80 12.83 –110.70 180 建链策略 3
(Sat-Random)(12°, 12°) 6379 9.89 –86.83 180 16.59 –106.94 270 建链策略 4
(UE-Random)(15°, 15°) 4169 8.68 –88.04 192 14.92 –108.61 340
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表 7 采样间隔、仿真时长与随机种子稳定性验证结果
系统 ($\Delta $t, T, Seed) ($ d_{\min }^{\text{UE}} $, $ d_{\min }^{\text{BS}} $) Starlink-1 (10, 1, 1)(基线) (195, 290) Starlink-1 (5, 1, 1) (206, 300) Starlink-1 (1, 1, 1) (200, 300) Starlink-1 (10, 3, 1) (206, 300) Starlink-1 (10, 1, 11) (210, 300) Starlink-1 (10, 1, 21) (202, 290) Starlink-2 (10, 1, 1)(基线) (272, 420) Starlink-2 (5, 1, 1) (266, 370) Starlink-2 (1, 1, 1) (275, 410) Starlink-2 (10, 3, 1) (290, 390) Starlink-2 (10, 1, 11) (290, 390) Starlink-2 (10, 1, 21) (280, 410)
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