基于分式二次规划的互模糊函数赋形方法

杨晨 吴蕾 杨威 姜卫东 刘永祥

杨晨, 吴蕾, 杨威, 等. 基于分式二次规划的互模糊函数赋形方法[J]. 雷达学报(中英文), 2024, 13(1): 174–186. doi: 10.12000/JR23126
引用本文: 杨晨, 吴蕾, 杨威, 等. 基于分式二次规划的互模糊函数赋形方法[J]. 雷达学报(中英文), 2024, 13(1): 174–186. doi: 10.12000/JR23126
YANG Chen, WU Lei, YANG Wei, et al. Cross-ambiguity function shaping through fractional quadratic programming[J]. Journal of Radars, 2024, 13(1): 174–186. doi: 10.12000/JR23126
Citation: YANG Chen, WU Lei, YANG Wei, et al. Cross-ambiguity function shaping through fractional quadratic programming[J]. Journal of Radars, 2024, 13(1): 174–186. doi: 10.12000/JR23126

基于分式二次规划的互模糊函数赋形方法

doi: 10.12000/JR23126
基金项目: 国家自然科学基金(61871384),湖南省科技创新计划自主项目(2022RC1092),国防科技大学自主创新科学基金项目(22-ZZCX-043)
详细信息
    作者简介:

    杨 晨,硕士生,主要研究方向为认知雷达波形设计

    吴 蕾,硕士生,主要研究方向为雷达信号处理

    杨 威,博士,副教授,主要研究方向为认知雷达目标探测与识别

    姜卫东,博士,研究员,主要研究方向为雷达系统、雷达信号处理、雷达目标识别

    刘永祥,博士,教授,主要研究方向为雷达目标识别、雷达目标微动特性

    通讯作者:

    杨威 yw850716@sina.com

  • 责任主编:崔国龙 Corresponding Editor: CUI Guolong
  • 中图分类号: TN957

Cross-ambiguity Function Shaping Through Fractional Quadratic Programming

Funds: The National Natural Foundation of China (61871384), The Science and Technology Innovation Program of Hunan Province (2022RC1092), The Science Technology Innovation Program of National Defense University (22-ZZCX-043)
More Information
  • 摘要: 在开展认知雷达波形设计时,由于发射波形与接收滤波器的非匹配体制,互模糊函数赋形相比传统模糊函数赋形优化自由度更高。该文针对强杂波条件下微弱运动目标检测问题,以最大化信干噪比为优化准则,提出了一种联合发射相位编码序列与接收滤波器设计的互模糊函数赋形方法。在恒模约束下,优化问题被建模为二次分式规划形式;然后通过引入辅助变量,并利用共轭梯度法求解Stiefel流形空间上的最小化问题,非凸优化据此转化为恒模约束二次优化问题;通过交替循环和类幂迭代算法求得最优解。此外考虑到发射波形受硬件限制而难以实现严格恒模,该文构建了一种低峰均比约束二次优化问题模型,并利用最近邻向量法求得最优解。最后,不同参数下的仿真与实测数据实验表明,该文赋形方法相较于传统方法具有较高的信干噪比增益和收敛速度。

     

  • 图  1  干扰能量分布

    Figure  1.  Interference energy distribution

    图  2  本文算法目标函数响应值收敛曲线

    Figure  2.  The convergence curve of objective function response value in the proposed algorithm

    图  3  不同方法下SINR值随迭代次数变化

    Figure  3.  SINR versus the iteration times of different algorithms

    图  4  5种算法生成CAF

    Figure  4.  CAF generated by five different algorithms

    图  5  5种算法生成CAF距离单元($r = 1,2,3$; $N{\text{ = 50}}$)截面图

    Figure  5.  Distance cut ($r = 1,2,3$) of the CAF generated by five algorithms ($N{\text{ = 50}}$)

    图  6  5种算法SINR值随发射波形码长变化曲线

    Figure  6.  SINR of five different algorithms versus code length

    图  7  不同PAR约束下发射波形实部虚部

    Figure  7.  The real and imaginary parts of transmitting waveform under different PAR constraints

    图  8  不同PAR约束下SINR值随运行时间变化

    Figure  8.  SINR versus the iteration time under different PAR constraints

    图  9  不同k取值下信干噪比随运行时间变化曲线

    Figure  9.  SINR with respect to running time under different values of k

    图  10  海南地区某机场实测数据距离-多普勒图

    Figure  10.  Range-Doppler diagram of real measured data from an airport in Hainan

    图  11  实测数据运用算法1运行结果

    Figure  11.  Results of applying Alg. 1 to the real measured data

    1  基于PML的恒模发射波形与接收滤波器联合互模糊函数设计

    1.   CAF shaping for CM transmit waveforms and receive filters based on PML

     输入:干扰能量分布矩阵${\boldsymbol{\sigma }}$,噪声能量${{\boldsymbol{\sigma }}_n}$,目标散射系数${\alpha _{\rm target}}$
     输出:优化发射波形x,优化接收滤波器h
     1 Initialization: 初始化发射波形${{\boldsymbol{x}}_0}$,初始化接收滤波器${{\boldsymbol{h}}_0}$,参
     数$\lambda $,参数$\mu $。迭代终止条件${\varepsilon _1}$, ${\varepsilon _2}$
     2 while ${\text{error } } \ge {\varepsilon _1}$ do
     3   式(13)、式(14)更新A, B
     4   共轭梯度法在Stiefel流形空间求解U
     5   条件式(29)更新$\mu $
     6   式(28)更新$\lambda $
     7   式(22)更新Q
     8   求Q最大特征值$\gamma $,并更新${\boldsymbol{\hat Q}}$
     9   while ${\text{error } } \ge {\varepsilon _2}$ do
     10    式(26)进行类幂内层迭代
     11   end while
     12   式(11)计算接收滤波器h
     13 end while
     14 return ${\boldsymbol{x}},{\boldsymbol{h}}$
    下载: 导出CSV

    2  低PAR约束下最近邻向量问题求解方法

    2.   Nearest vector method with low PAR

     输入: 发射波形${ {\boldsymbol{x} } }^{(s)}$,发射波形能量约束E,发射波形PAR约束
     $\rho $,矩阵$ {\boldsymbol{\hat Q}} $
     输出:发射波形${ {\boldsymbol{x} }^{(s + 1)} }$
     1 Initialization: 单位化${{\boldsymbol{x}}^{(s)}}$, $\xi = \sqrt {E\rho /N} $, $k = 0$
     2 选取${{\boldsymbol{x}}^{(s)}}$中模长最小的$\left( {N - k} \right)$个元素的索引构成集合${{\mathcal{M}}}$,若
     ${{\mathcal{M}}}$不唯一,$k = k + 1$,重复步骤2
     3 if $\forall m \in {{\mathcal{M}}}$, $ x_m^{(s)} = 0 $ do
     4  if $m \in {{\mathcal{M}}}$ do
     5   $x{_m^{(s + 1)} } = \sqrt {\left( {E - k{\xi ^2} } \right)/\left( {N - k} \right)}$
     6  else do
     7   $x_m^{{(s + 1)} } = \xi { {\rm{e} }^{ {\text{j} }\arg x_m^{{(s)} } } }$
     8  return ${{\boldsymbol{x}}^{(s + 1)}}$
     9 else do
     10 $\varpi = \sqrt {\left( {E - k{\xi ^2} } \right)/\sum\limits_{m \in { {\mathcal{M} } } } { { {\left| {x_m^{{(s)} } } \right|}^2} } }$
     11 if $\forall m \in {{\mathcal{M}}}$, $\varpi x_m^{{(s)} } > \xi$ do
     12  $k = k + 1$,返回步骤2
     13 else do
     14  if $m \in {{\mathcal{M}}}$ do
     15   $x{_m^{(s + 1)} } = \varpi x_m^{(s)}$
     16  else do
     17   $x_m^{{(s + 1)} } = \xi { {\rm{e} }^{ {\text{j} }\arg x_m^{{(s)} } } }$
     18  end
     19 end
     20 end
     21 return ${{\boldsymbol{x}}^{(s + 1)}}$
    下载: 导出CSV

    表  1  不同码长下5种算法性能统计

    Table  1.   Performance statistics table of five algorithms under different code length

    码长N收敛时SINR (dB)收敛时运行时间(s)
    所提方法We-CAFUniAFSIMISOCREWcyclic所提方法We-CAFUniAFSIMISOCREWcyclic
    308.51.78.36.98.254.02.739.065.531.7
    4012.54.310.59.311.3159.819.7155.8290.3162.2
    5014.75.111.510.913.3256.931.9365.4346.9256.3
    6015.56.212.111.114.6304.168.6346.1358.0288.6
    7017.17.213.612.415.6477.4161.9426.2372.2342.8
    8017.47.814.613.316.1691.0238.6687.8664.4506.9
    9018.28.715.714.416.7745.8373.0721.5807.1622.5
    10018.69.616.015.717.4820.9477.91113.81066.4822.5
    下载: 导出CSV

    表  2  实测数据实验下的雷达参数

    Table  2.   Radar parameters in real measured data experiment

    参数数值
    采样率1 GHz
    带宽400 MHz
    脉冲重复频率2000 Hz
    脉冲宽度10 μs
    高度1.5 km
    俯仰角30°
    方位角
    波束宽度
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-07-11
  • 修回日期:  2023-09-08
  • 网络出版日期:  2023-10-07
  • 刊出日期:  2024-02-28

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