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

SUN Chenying; YAO Weilai; LIANG Xindong; JIA Jianjun

doi:10.11999/JEIT250121

Volume 47 Issue 6

Jun. 2025

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Article Navigation > Journal of Electronics & Information Technology > 2025 > 47(6): 1826-1836

SUN Chenying, YAO Weilai, LIANG Xindong, JIA Jianjun. Modeling and Simulation Analysis of Inter-satellites Pseudo-code Ranging for Space Gravitational Wave Detection[J]. Journal of Electronics & Information Technology, 2025, 47(6): 1826-1836. doi: 10.11999/JEIT250121

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SUN Chenying, YAO Weilai, LIANG Xindong, JIA Jianjun. Modeling and Simulation Analysis of Inter-satellites Pseudo-code Ranging for Space Gravitational Wave Detection[J]. Journal of Electronics & Information Technology, 2025, 47(6): 1826-1836. doi: 10.11999/JEIT250121

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

doi: 10.11999/JEIT250121 cstr: 32379.14.JEIT250121

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)

Received Date: 2025-02-28
Rev Recd Date: 2025-04-25

Available Online: 2025-05-10

Publish Date: 2025-06-30

Abstract

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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References(22)

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