Ground electronics verification of inter-satellites laser ranging in the Taiji program
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摘要:
在空间引力波探测太极计划中，激光干涉测距系统是获取引力波信号的直接手段，为了消除激光频率不稳定性对其的影响，需利用时间延迟干涉技术降低噪声的干扰。时间延迟干涉是一种数据后处理方法，要实现该技术的数据构型，需对卫星臂长实现精确的绝对距离测量。本文从太极计划的需求分析出发，分别从信源编码设计、延迟环设计以及数据处理算法等方面介绍测距系统的设计方案。在信源编码中，文章通过分析m序列、gold序列、Weil码三种伪随机码的自、互相关性优劣以及长度选取上的灵活性，最终选择了Weil码并筛选出其自相关性最优的移位-截取组合，将其作为测距系统所用的伪随机码。同时，基于该测距系统，搭建了一套地面电子学验证实验装置，以模拟信号传输的物理过程并验证系统性能。实验主体装置采用一块基于Xilinx公司K7芯片的自研FPGA板卡用以模拟卫星通信测距过程以及实现锁相环、延迟环等功能。实验将24.4 kbps的16位信息码与1.5625 Mbps的1024位Weil码进行BPSK调制，采样频率为50 MHz，通过10~60 m的射频同轴电缆进行传输后，使用质心法对采集数据进行优化，随后测定该距离。实验结果表明：在60 m范围内，测距精度优于1.6 m。实验证明了测距系统原理及设计的可行性，为下一步的光学系统验证奠定了技术基础。
Abstract:In the Taiji program, laser interferometry is utilized to detect the tiny displacement produced by the gravitational wave signals. Due to the large-scale unequal arm, the laser frequency noise is the largest noise budget in the space interferometer system. To reduce the influence of laser frequency noise, a technology called the Time Delay Interferometry (TDI) is utilized to deal with it. The TDI is a kind of data post-processing method, which forms the new data stream by the method of the time delay to initial data. But the premise of TDI needs to obtain accurate absolute arm length between satellites. Thus, for that requirement, we discuss the ranging system scheme and implement a ground electronics verification experiment. The ranging system is based on Direct Sequence Spread Spectrum (DS/SS) modulation, and it mainly includes three parts, which are the signal structure, a Delay Locked Loop (DLL), and a data processing algorithm. In DS/SS modulation, types of pseudo-random code can make a difference to the quality of correlation and the ranging accuracy. Therefore, to design the optimal pseudo-random code, we compare the correlation and flexibility in choosing lengths of the m sequence, gold sequence, and Weil code. Weil code that has a shift-cutoff combination with the best autocorrelation is chosen as the ranging code. The ground electronics verification experiment is set up for simulating the physical process of signal transmission and verifying system performance. The main device of the experiment is a FPGA card based on the K7 chip from Xilinx, which is used to simulate the function of communication and ranging between satellites. Meanwhile, we change the length of the Radio Frequency (RF) coaxial cable to correspond to different ranges. The experimental process can be summarized as follows. Firstly, 16-bit data at 24.4 kbps and 1024-bit Weil code at 1.5625 Mbps are modulated with Binary Phase Shift Keying (BPSK) in the 50 MHz sampling frequency. Then the signal is transmitted through RF coaxial cables of 10 to 60 m in length. In receiving end, the signal is consolidated by DLL and the ranging information is collected. To measure the range accurately, we use a centroid method to optimize the collected data. The results show that the ranging accuracy is better than 1.6 m within 60 m. In conclusion, this experiment proves the principle of the scheme and its feasibility, laying a technical foundation for optical system verification in the future.
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图 1 星间绝对距离测量与通信原理图
Figure 1. Principle diagram of the inter-satellites absolute ranging and laser communication system
图 4 最优移位-截取点的Weil码自相关图像
Figure 4. The autocorrelation figure of Weil codes in the optimal shift-cutoff combination
图 7 延迟、超前路的相关值对比
Figure 7. The comparison of the correlation value between delay and ahead signals
图 11 不同长度射频线的实验结果。（a）10 m；（b）12 m；（c）20 m；（d）30 m；（e）50 m；（f）60 m
Figure 11. Experiment results with different length cables. (a) 10 m; (b) 12 m; (c) 20 m; (d) 30 m; (e) 50 m; (f) 60 m
表 1 伪随机码自相关性对比
Table 1. Autocorrelation comparison of pseudorandom codes
伪随机码 处理（取最优） 码长 最大自相关旁瓣绝对值 dB值 m序列（本原多项式系数2011） 无 1023 0.000977 −120.39 遍历插1或0 1024 0.0469 −86.782 gold序列（本原多项式系数2011、
2157）无 1023 0.06354 −84.136 遍历插1 1024 0.082 −81.929 遍历插0 1024 0.0859 −81.526 Weil码 无 1031 0.0611 −84.544 遍历截取7位 1024 0.0625 −84.288 
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表 2 实验结果附表
Table 2. Attached table of experimental results
真实值/m 实验平均值/m 均方差（测距精度）/m 10 9.03 0.86 12 11.13 1.21 20 19.24 1.24 30 30.18 1.59 50 50.14 1.35 60 61.23 1.26
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表 3 相关峰移动点数在50 MHz采样频率下对应的距离
Table 3. Distances corresponding to the number of shifts of the correlation peak at the 50 MHz sampling frequency
相关峰移动点数 光速时对应距离/m 70%光速对应距离/m 1 6 4.2 2 12 8.4 3 18 12.6 4 24 16.8 5 30 21.0 6 36 25.2 7 42 29.4 … … … 12 72 50.4 14 84 58.8
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