一种具有多普勒容忍性的通感一体化波形设计

王佳欢 范平志 时巧 周正春

王佳欢, 范平志, 时巧, 等. 一种具有多普勒容忍性的通感一体化波形设计[J]. 雷达学报, 2023, 12(2): 275–286. doi: 10.12000/JR22155
引用本文: 王佳欢, 范平志, 时巧, 等. 一种具有多普勒容忍性的通感一体化波形设计[J]. 雷达学报, 2023, 12(2): 275–286. doi: 10.12000/JR22155
WANG Jiahuan, FAN Pingzhi, SHI Qiao, et al. Doppler resilient integrated sensing and communication waveforms design[J]. Journal of Radars, 2023, 12(2): 275–286. doi: 10.12000/JR22155
Citation: WANG Jiahuan, FAN Pingzhi, SHI Qiao, et al. Doppler resilient integrated sensing and communication waveforms design[J]. Journal of Radars, 2023, 12(2): 275–286. doi: 10.12000/JR22155

一种具有多普勒容忍性的通感一体化波形设计

doi: 10.12000/JR22155
基金项目: 国家自然科学基金(62020106001, 62131016, 62071397)
详细信息
    作者简介:

    王佳欢,博士生,主要研究方向为通感一体化波形设计

    范平志,教授,博士生导师,主要研究方向为雷达/通信信号设计及其应用、高移动车辆无线通信、无线大数据、信息理论与编码

    时 巧,助理教授,主要研究方向为雷达通信一体化波形设计

    周正春,教授,博士生导师,主要研究方向为编码理论、通信/雷达波形设计、电子信息对抗

    通讯作者:

    周正春 zzc@swjtu.edu.cn

  • 责任主编:崔国龙 Corresponding Editor: CUI Guolong
  • 中图分类号: TN95

Doppler Resilient Integrated Sensing and Communication Waveforms Design

Funds: The National Natural Science Foundation of China (62020106001, 62131016, 62071397)
More Information
  • 摘要: 针对现有联合设计的通感一体化波形对运动目标探测性能不足的问题,该文提出了一种具有多普勒容忍性的通感一体化波形联合设计方案。首先,基于脉冲串模糊函数,推导了构造多普勒容忍波形等价于波形在相关区内具有极低的积分旁瓣电平。基于此,构建了以最小化一体化波形的加权积分旁瓣电平为优化准则,以发射波形的能量、峰均功率比以及与通信波形之间的相位差为约束条件的优化问题,从而实现具有多普勒容忍性的通感一体化波形的构造。由于该优化问题的非凸性,该文提出一种基于优化最小化的迭代优化算法对其进行求解。数值仿真实验表明,相比传统一体化波形,该文提出的一体化波形具有更高的多普勒容忍性和更低的误符号率,在保证通信质量的前提下显著提升了通感一体化系统对运动目标的探测性能。

     

  • 图  1  通感一体化模型图

    Figure  1.  ISAC model

    图  2  算法收敛曲线

    Figure  2.  Convergence curve of the proposed algorithm

    图  3  基于MM的一体化波形在不同参数下的SER比较

    Figure  3.  SER comparison under various parameters based on MM-based ISAC waveform

    图  4  基于MM和基于LFM的一体化波形SER性能比较

    Figure  4.  SER comparison between MM-based and LFM-based ISAC waveform

    图  5  非周期自相关函数

    Figure  5.  Aperiodic auto-correlation functions

    图  6  模糊函数

    Figure  6.  Ambiguity functions

    表  1  基于FFT/IFFT快速计算${\boldsymbol{a}}_n^{(t)}$[30]

    Table  1.   Compute ${\boldsymbol{a}}_n^{(t)}$ based on FFT/IFFT[30]

     1. 输入:$ {\boldsymbol{x}}_n^{(t)} $, $ \{ {\omega _l}\} _{l = - L + 1}^{L - 1} $,执行:
     2. ${\boldsymbol{fx} } = {\rm{fft} }({[{\boldsymbol{x} }_n^{(t)},{ {\bf{0} }_{1 \times L} }]^{\rm{T} } })$
     3. ${\boldsymbol{r} } = {\rm{ifft} }({\left| { {\boldsymbol{fx} } } \right|^2})$
     4. $ {\boldsymbol{c}} = {\boldsymbol{r}} \circ {[0,{\omega _1}, \cdots ,{\omega _{L - 1}},0,{\omega _{L - 1}}, \cdots ,{\omega _1}]^{\text{T}}} $
     5. ${\boldsymbol{\mu}} = {\rm{fft} }({\boldsymbol{c} })$
     6. ${\bf{tmp} } = {\rm{ifft} }\left( {\mu \circ ({\boldsymbol{fx} })} \right)$
     7. ${\boldsymbol{Rx} }_n^{(t)} = {\bf{tm} }{ {\bf{p} }_{1:L} }$
     8. ${\lambda }_{J}=\mathop {\max }\limits_{k}\{ {\omega }_{k}(L-k):k=1,2,\cdots ,L-1\}$
     9. ${\lambda _u} = \dfrac{1}{2}\left( { { \mathop {\max }\limits_{1 \le i \le L} }{\mu _{2i} } + { \mathop {\max }\limits_{1 \le i \le L} }{\mu _{2i - 1} } } \right)$
     10. $ {\boldsymbol{a}}_n^{(t)} = - {\boldsymbol{R}}{{\boldsymbol{x}}^{(t)}} + ({\lambda _J}L + {\lambda _u}){{\boldsymbol{x}}^{(t)}} $
     11. 输出:$ {\boldsymbol{a}}_n^{(t)} $
    下载: 导出CSV

    表  2  二分法求$ {\boldsymbol{\delta}} $

    Table  2.   Bisection method for ${\boldsymbol{ \delta }}$

     1. 初始化:设置搜索区间$ ({\delta _L},{\delta _U}) $。设置$ {\delta _L} = 0 $以及
      $ {\delta _U} = \dfrac{{{\alpha _U}}}{{\min \{ |{a_{n,l}}| \ne 0,l = 1,2, \cdots ,L\} }} $, 令$ \delta \in ({\delta _L},{\delta _U}) $
     2. While $ |{\delta _U} - {\delta _L}| > {\text{eps}} \cdot |{\delta _U}| $
     3.  $ \delta = ({\delta _L} + {\delta _U})/2 $
     4.  If $ {\text{sign}}({f_L}(\delta )) = {\text{sign}}({f_L}({\delta _U})) $
     5.    $ {\delta _U} = \delta $
     6.  or
     7.    $ {\delta _L} = \delta $
     8.  End if
     9. End while,输出:$ \delta $
    下载: 导出CSV

    表  3  基于MM算法的一体化波形设计

    Table  3.   MM-based algorithm for ISAC waveform design

     1. 输入:$ \alpha $, $\epsilon$, $ {\omega _l} $, $ {{\boldsymbol{e}}_n} $,以及$ {\boldsymbol{x}}_n^{(0)} = {{\boldsymbol{e}}_n} $
     2.  for $ t = 0,1,2, \cdots $执行
     3.   计算 $ {\boldsymbol{a}}_n^{(t)} $(根据表1执行)
     4.   计算 $\bar {\boldsymbol{x} } _n^{(t + 1)}$(根据式(40))
     5.   计算 ${\boldsymbol{x} }_n^{(t + 1)} = \Pi (\bar {\boldsymbol{x} } _n^{(t + 1)})$(根据式(41))
     6.  end for (当收敛时)
     7. 输出:$ {\boldsymbol{x}}_n^{(t + 1)} $
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-07-20
  • 修回日期:  2022-10-13
  • 网络出版日期:  2022-10-27
  • 刊出日期:  2023-04-28

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