空间引力波探测中星间伪码测距建模与仿真分析

孙晨颖; 姚未来; 梁新栋; 贾建军

doi:10.11999/JEIT250121

空间引力波探测中星间伪码测距建模与仿真分析

doi: 10.11999/JEIT250121 cstr: 32379.14.JEIT250121

孙晨颖^{1, 2},
姚未来^{1, 2},
梁新栋³,
贾建军^{1, 2, 3, ,}

1.
中国科学院上海技术物理研究所上海 200083
2.
中国科学院大学北京 100049
3.
国科大杭州高等研究院杭州 310024

基金项目: 国家重点研发计划(2023YFC2205401)

详细信息

作者简介:
孙晨颖：女，博士生，研究方向为空间引力波探测中星间长基线测距与通信技术

姚未来：男，博士生，研究方向为空间引力波探测激光干涉仪及精密锁相环

梁新栋：男，副研究员，研究方向为空间激光精密测量、空间引力波探测技术

贾建军：男，研究员，研究方向为空间主动光电与量子精密测量、空间大口径望远镜、空间引力波探测技术

通讯作者:
贾建军　jjjun10@mail.sitp.ac.cn

中图分类号: TN927; TP873
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- 被引次数: 0
出版历程
- 收稿日期: 2025-02-28
- 修回日期: 2025-04-25
- 网络出版日期: 2025-05-10
- 刊出日期: 2025-06-30

Modeling and Simulation Analysis of Inter-satellites Pseudo-code Ranging for Space Gravitational Wave Detection

SUN Chenying^{1, 2},
YAO Weilai^{1, 2},
LIANG Xindong³,
JIA Jianjun^{1, 2, 3
, ,}

1.
Shanghai Institute of Technology and Physics of Chinese Academy of Sciences, Shanghai 200083, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou 310024, China

Funds: National Key R&D Program of China (2023YFC2205401)

摘要

摘要: 为满足空间引力波探测中时延干涉算法(TDI)对米级精度星间距数据的需求，基于激光链路建立星间绝对距离测量系统。该文以空间引力波探测太极计划为背景，通过分析空间引力波探测中星间测距的实现原理，设计了基于伪随机码(PRN)低深度相位调制的星间测距模型，分析了测距精度的主要影响因素，并基于直接数字合成器(DDS)模拟外差干涉信号，进行了伪码测距系统的FPGA仿真验证。仿真结果表明，采用该模型可获得的理论测距精度可达厘米量级，达到了空间引力波探测的米级精度需求。该激光测距方案对卫星导航和天基引力波探测的工程应用具有参考价值。
- 空间引力波探测 /
- 星间测距 /
- 伪码测距
Abstract: Objective Inter-satellite laser interferometry for space gravitational wave detection is constrained by orbital dynamics and other perturbations, which cause continuous variations in inter-satellite distances. Therefore, laser frequency noise becomes the dominant noise source in the inter-satellite interferometry system. To suppress this noise, the Time Delay Interferometry (TDI) algorithm is applied during data post-processing, where a virtual equal-arm interferometer is synthesized by shifting and combining data streams. However, accurate TDI combinations depend on precise knowledge of absolute inter-satellite distances at the picometer level. Any deviation in these measurements may propagate into errors in the final processed data. To address this issue, an inter-satellite ranging scheme based on Pseudo-Random Noise (PRN) is proposed. This method enables both inter-satellite ranging and data communication, providing theoretical support for autonomous satellite navigation as well as inter-satellite ranging and communication in space-based gravitational wave missions. Methods To reduce power consumption and spacecraft mass, the inter-satellite ranging task is implemented using existing laser links for scientific measurement. Only a small fraction of the available power is allocated to the ranging subsystem to avoid degrading the phase stability of science measurements. A low-depth Binary Phase-Shift Keying (BPSK) modulation scheme based on PRN is proposed to enable laser ranging and data communication as auxiliary functions of the high-precision inter-satellite interferometry system. The ranging system architecture incorporates a Digital Phase-Locked Loop (DPLL) for carrier synchronization and a Delay-Locked Loop (DLL) for PRN code synchronization. Theoretical limitations of ranging accuracy are systematically analyzed, including contributions from shot noise, integration time, inter-code interference, optical data bit encoding, and the impulse response of the DPLL. These analyses guide improvements in both the DPLL and DLL designs. A Direct Digital Synthesizer (DDS) is used to generate the heterodyne signal. Simulation verification of unidirectional ranging, bidirectional ranging and inter-satellite data communication is performed on a Field Programmable Gate Array (FPGA) platform. Results and Discussions The simulation results (Table 2, Table 3) demonstrate that the optimization methods proposed in (Fig.9, Fig.11) effectively reduce the effects of data encoding and inter-code interference on the ranging accuracy of the delay-locked tracking loop, respectively. As shown in (Table 4), in a single delay-locked tracking loop, the dominant factor limiting ranging accuracy is data bit encoding for optical communication when the local PRN code is absent; otherwise, shot noise becomes the primary source of error. (Fig.16) illustrates the distortion of the PRN code caused by the phasemeter pulse response, and shows that Manchester encoding significantly mitigates this distortion. The final simulation results after applying all optimization techniques are summarized in (Table 5). With a modulation depth of approximately 0.4 rad, corresponding to an equivalent optical power of less than 4%, the Root Mean Square (RMS) errors for both unidirectional and bidirectional ranging are approximately 3 cm at a measurement rate of 3 Hz with an 80 MHz sampling frequency. For unidirectional ranging with data streams encoded at 19 kbps and 39 kbps, the corresponding RMS ranging errors are approximately 5 cm and 20 cm, respectively. Bidirectional ranging supports data transmission only at 19 kbps, yielding an RMS error of approximately 6 cm. When the phase modulation depth is reduced to 0.2 rad (corresponding to an equivalent optical power below 1%), the RMS ranging error is approximately 6 cm; if 19 kbps data are transmitted simultaneously, the RMS error increases to approximately 12 cm. These simulation results confirm that sub-meter absolute distance resolution is achievable under all tested conditions. Conclusions Based on the Taiji plan, an absolute distance measurement scheme utilizing low-depth phase modulation of PRN codes is proposed. A receiver model based on a DPLL and a DLL is established. The limiting factors affecting inter-satellite ranging accuracy are analyzed, leading to improvements in the ranging model. The simulation results, following comprehensive optimizations, show that the primary limiting factors of ranging accuracy are unavoidable shot noise and the encoding of data bits for optical communication. At a clock sampling rate of 80 MHz, with a PRN code phase modulation depth of 0.4 rad, the bidirectional ranging RMS error is approximately 6 cm when communication data is encoded at 19 kbps. When the modulation depth is reduced to 0.2 rad, the RMS error increases to approximately 12 cm while transmitting 19 kbps data concurrently. These simulation results demonstrate a clear improvement over meter-level accuracy, and the ranging model offers valuable insights for space gravitational wave detection and satellite autonomous navigation. Given the complexity of clock synchronization, it is assumed in this study that the clocks of the transmitter and receiver are fully synchronized. Further research will address clock synchronization issues, and electrical and optical experiments will be conducted to assess the performance of the proposed architecture in future work.
- Space gravitational wave detection /
- Inter-satellite ranging /
- Pseudo-code ranging

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图 1 星间激光测距实现原理简图

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图 2 调制深度与调制功率占比关系图

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图 3 相位调制0.4 rad的载波时域图

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图 4 数字锁相环路设计框图

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图 5 伪码捕获与跟踪实现框图

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图 6 散粒噪声对伪码时序和相关运算的影响

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图 7 数据编码信号结构图

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图 8 不同数据速率下伪码的相关值

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图 9 数据编码改进示意图

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图 10 码间串扰下伪码的时间序列图及伪码相关图

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图 11 码间串扰改进示意图

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图 12 不同积分长度下伪码的相关值

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图 13 DLL跟踪环路测距性能仿真框图

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图 14 DLL跟踪环路在不同情况下的测距精度

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图 15 曼彻斯特编码前后DPLL输出PRN的失真情况

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图 16 接收系统DPLL与DLL测距性能仿真框图

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表 1 散粒噪声与载噪比理论预估值

接收功率 ${P_S}\left( {{\text{pW}}} \right)$	相位噪声 $ \vartheta _{}^{{\mathrm{sn}}}\left( {{\text{μ rad/}}\sqrt {{\text{Hz}}} } \right) $	载噪比 $ C/N^{{\mathrm{sn}}}\left( {{\text{dB}} \cdot {\text{Hz}}} \right) $
1767.53	19.24	94.32
757.51	29.38	90.64

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表 2 不同数据速率对应的DLL测距精度(m)

数据速率(kbps)	积分器个数	测距精度
19.53	1	0.0634
19.53	2	0.0196
39.06	1	0.1408
39.06	2	0.0769

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表 3 存在本地PRN码时不同散粒噪声下对应的DLL测距精度(m)

散粒噪声 (μrad/Hz^1/2)	无本地PRN	有本地PRN	减去本地PRN
0	1.1005×10^–9	0.3231	2.3550×10^–9
20	0.0323	0.3326	0.0327
30	0.0359	0.3390	0.0359

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表 4 单独DLL在不同情况下的测距精度(m)

散粒噪声 (μrad/Hz^1/2)	本地PRN码	数据速率(kbps)
散粒噪声 (μrad/Hz^1/2)	本地PRN码	0	19.53	39.06
0	无	1.1005×10^–9	0.0196	0.0350
0	有	2.3550×10^–9	0.0722	0.0769
20	无	0.0323	0.0516	0.0502
20	有	0.0327	0.0834	0.0834
30	无	0.0359	0.0536	0.0509
30	有	0.0359	0.0821	0.0848

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表 5 不同条件对应DPLL与DLL的测距精度(m)

调制深度(rad)	数据速率 (kbps)	单向/ 双向测距	载噪比(dB-Hz)
调制深度(rad)	数据速率 (kbps)	单向/ 双向测距	81.94	87.96	93.98
0.4	0	单	0.0302	0.0257	0.0061
0.4	0	双	0.0332	0.0336	0.0158
0.4	19	单	0.0547	0.0456	0.0111
0.4	19	双	0.0646	0.0642	0.0310
0.4	39	单	0.2033	0.1611	0.0422
0.2	0	单	0.0599	0.0452	0.0116
0.2	0	双	0.0632	0.0498	0.0123
0.2	19	单	0.1076	0.0812	0.0211
0.2	19	双	0.1236	0.0897	0.0235

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参考文献(22)

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