基于椭圆球面波函数波形成型的测控信号设计

许志超; 陆发平; 康家方; 安琪; 张治霖; 杨东凯

doi:10.13700/j.bh.1001-5965.2024.0068

基于椭圆球面波函数波形成型的测控信号设计

doi: 10.13700/j.bh.1001-5965.2024.0068

许志超^{1, 2, 3},
陆发平^{2, 3},
康家方^{2, 3},
安琪^{2, 3},
张治霖^{2, 3},
杨东凯^1, ,

1.
北京航空航天大学电子信息工程学院，北京 100191
2.
海军航空大学，烟台 264001
3.
山东省信号与信息处理重点实验室，烟台 264001

基金项目:

博士后创新人才支持计划(BX20200039)；山东省“泰山学者”建设工程专项(ts20081130)

详细信息

通讯作者:
E-mail：edkyang@buaa.edu.cn

中图分类号: V443.1；TN975
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- 文章访问数: 332
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- 被引次数: 0
出版历程
- 收稿日期: 2024-01-30
- 录用日期: 2024-02-29
- 网络出版日期: 2024-04-10
- 整期出版日期: 2026-04-30

Design of tracking telemetry and command signal based on prolate spheroidal wave functions waveform forming

XU Zhichao^{1, 2, 3},
LU Faping^{2, 3},
KANG Jiafang^{2, 3},
AN Qi^{2, 3},
ZHANG Zhilin^{2, 3},
YANG Dongkai^{1
, ,}

1.
School of Electronic and Information Engineering，Beihang University，Beijing 100191，China
2.
Naval Aviation University，Yantai 264001，China
3.
Key Laboratory on Signal & Information Processing of Shandong Province，Yantai 264001，China

Funds:

China National Postdoctoral Program for Innovative Talents (BX20200039); Special Fund Project of “Mount Taishan Scholars” Construction Project in Shandong Province (ts20081130)

More Information

Corresponding author: E-mail：edkyang@buaa.edu.cn

摘要

摘要:
如何提高信号波形功率效率、信息传输效率是目前测控系统(TT&C)波形设计面临的难题之一。研究发现具有双正交性、最佳时频能量聚集性、频谱可控性等基础特性的椭圆球面波函数(PSWF)非常适合测控系统信号波形，并将PSWF引入测控系统信号波形设计，提出基于PSWF波形成型的四维统一扩频测控系统信号波形设计方法。该方法利用高能量聚集度PSWF作为波形成型函数，具有更高的功率效率和信息传输速率、更优的抗干扰和抗截获能力，能够为测控系统信号波形设计提供一种更优的波形方案。仿真结果表明：相对于传统基于矩形脉冲函数的测控系统信号，在相同系统误码性能的条件下，所提方法信息传输速率可提升1倍，扩频增益提升为3.44 dB。
- 椭圆球面波函数 /
- 波形成型 /
- 测控信号 /
- 功率效率 /
- 信息传输速率
Abstract:
Enhancing the signal waveform's power efficiency and information transmission efficiency is one of the issues in tracking, telemetry, and command (TT&C) system waveform design. It is found that the basic characteristics such as biorthogonal, optimal time-frequency energy aggregate, and spectral controllable of prolate spheroidal wave functions (PSWFs) make it be a reliable candidate for TT&C signal waveform design. In this paper, PSWF are introduced into TT&C signal waveform design, and a four-dimensional unified spread spectrum TT&C signal waveform design method based on PSWF waveform shaping is proposed. This new idea, by using high-energy aggregation PSWF as waveform shaping functions, can obtain higher power efficiency and information transmission rate, better anti-interference and anti-interception capabilities. It provides a better waveform scheme for the design of TT&C signal waveforms. For instance, the suggested approach can boost the spread spectrum gain by 3.44 dB and the information transmission rate by one when compared to conventional TT&C signals based on rectangular pulse functions under the same system error performance.
- prolate spheroidal wave functions /
- waveform forming /
- tracking telemetry and command signal /
- power efficiency /
- information transmission rate

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图 1 PSWF的时域波形

Figure 1. Waveform of PSWF in time domain

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图 2 PSWF的功率谱

Figure 2. PSD of PSWF

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图 3 接收机带宽造成的信噪比损失

Figure 3. Signal-to-noise ratio loss from receiver bandwidth

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图 4 PSWF波形与码片干扰示意图

Figure 4. Schematic diagram of PSWF function waveform and code chip interference

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图 5 基于PSWF波形成型的扩频测控系统调制端模型

Figure 5. Modulation end model of spread spectrum TT&C based on PSWF waveform shaping

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图 6 基于PSWF波形成型的扩频测控系统解调端模型

Figure 6. Demodulation end model of spread spectrum TT&C system based on PSWF waveform shaping

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图 7 调制信号时域波形

Figure 7. Modulation signal waveform in time domain

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图 8 信号波形功率谱密度

Figure 8. PSD of modulation signal waveform

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图 9 信号CCDF曲线

Figure 9. CCDF of signal waveform

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图 10 频谱效率与扩频因子倒数的关系

Figure 10. Relationship between spectrum efficiency and the reciprocal of spreading factor

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图 11 理论和仿真误码率曲线

Figure 11. Error rate curve of theoretic and simulate results

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图 12 系统抗干扰能力误码率仿真曲线

Figure 12. Curves of system anti-interference ability

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图 13 接收机带宽造成的信噪比损失

Figure 13. SNR loss from receiver bandwidth

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图 14 原理样机实验测试系统

Figure 14. Principle prototype experimental test system

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图 15 硬件射频信号实测结果

Figure 15. Test results of hardware RF signals

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表 1 模板信号与接收码元信号的相关值

Table 1. Correlation values of template signal and received symbol signal

函数	相关值
函数	0阶PSWF	1阶PSWF
0阶PSWF	0.9994	4.6×10⁻⁴
1阶PSWF	4.6×10⁻⁴	0.9989

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表 2 设计方案参数

Table 2. Design scheme parameters

参数	数值
码片时长/s	9.775×10⁻⁵
成型波形	0阶、1阶PSWF
传输带宽/MHz	2.046
信息速率/(Kbit·s⁻¹)	2
扩频码码长/码片	2 046
码元时长/s	0.002

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表 3 设计方案参数对比

Table 3. Comparison of parameters in design scheme

类型	成型函数	码片时长/s	传输带宽/MHz	信息速率/(Kbit·s⁻¹)	码元时长/s	扩频码码长/码片
基于矩形脉冲函数波形成型的测控信号	矩形脉冲函数	9.775×10⁻⁵	2.046	2	0.001	1023
基于PSWF波形成型的测控信号	0阶、1阶PSWF	9.775×10⁻⁵	2.046	2	0.002	2 046

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表 4 样机系统参数设置

Table 4. Prototype system parameter settings

信源/KB	采样频率/(MSa·s⁻¹)	载波频率/GHz	信道条件
46（368 000 bit）	5.115（5倍过采样）	2	短距离室内传输

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