面向多任务动态场景的雷达与干扰空时协同波束联合优化方法

廖晓容 孙国皓 钟苏川 余显祥 李明

廖晓容, 孙国皓, 钟苏川, 等. 面向多任务动态场景的雷达与干扰空时协同波束联合优化方法[J]. 雷达学报(中英文), 2024, 13(3): 613–628. doi: 10.12000/JR23243
引用本文: 廖晓容, 孙国皓, 钟苏川, 等. 面向多任务动态场景的雷达与干扰空时协同波束联合优化方法[J]. 雷达学报(中英文), 2024, 13(3): 613–628. doi: 10.12000/JR23243
LIAO Xiaorong, SUN Guohao, ZHONG Suchuan, et al. Joint optimization of radar and jammer space-time cooperative beamforming for a multitasking dynamic scene[J]. Journal of Radars, 2024, 13(3): 613–628. doi: 10.12000/JR23243
Citation: LIAO Xiaorong, SUN Guohao, ZHONG Suchuan, et al. Joint optimization of radar and jammer space-time cooperative beamforming for a multitasking dynamic scene[J]. Journal of Radars, 2024, 13(3): 613–628. doi: 10.12000/JR23243

面向多任务动态场景的雷达与干扰空时协同波束联合优化方法

doi: 10.12000/JR23243
基金项目: 国家自然科学基金(62201371),四川省自然科学基金(2022NSFSC1952),衢州市大科创项目(2022D013)
详细信息
    作者简介:

    廖晓容,硕士生,主要研究方向为组网雷达信号处理、资源分配

    孙国皓,博士,副研究员,主要研究方向为认知雷达信号处理、分布式雷达信号处理、机载/星载雷达信号处理、天域态势感知

    钟苏川,博士,副教授,主要研究方向为随机动力系统、随机信号处理等

    余显祥,博士,副教授,主要研究方向为雷达波形设计与处理、最优化理论算法以及阵列信号处理等

    李 明,博士,主要研究方向为机载雷达信号处理、阵列信号处理、干扰抑制技术

    通讯作者:

    孙国皓 sghsjw2005@126.com

  • 责任主编:易伟 Corresponding Editor: YI Wei
  • 中图分类号: TN974

Joint Optimization of Radar and Jammer Space-time Cooperative Beamforming for a Multitasking Dynamic Scene

Funds: The National Natural Science Foundation of China (62201371), Sichuan Provincial Natural Science Foundation (2022NSFSC1952), Municipal Government of Quzhou (2022D013)
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  • 摘要: 现代雷达对抗形势复杂多变,体系与体系的作战已成为基本特点,而体系整体性能关乎着战场的主动权乃至最终的胜负。通过优化体系中雷达与干扰波束资源可以提升整体性能,获得在空间、时间域优效的低截获探测性能,然而空时域协同波束联合优化是一个复杂多参数耦合的非凸问题。该文针对空时域多任务动态场景,建立了以雷达探测性能为优化目标,以干扰性能以及能量限制为约束条件的优化模型。为求解该模型,该文提出了基于迭代优化的空时协同波束联合设计方法,即以雷达发射、接收、多干扰机发射波束交替迭代优化。其中,针对多干扰机协同优化的不定矩阵二次约束二次规划(QCQP)问题,该文基于可行点追踪-连续凸逼近(FPP-SCA)算法,在SCA算法的基础上,通过引入松弛变量与惩罚项,保证算法在合理松弛度下的可行性,解决了矩阵不定情况下难以获得可行解的问题。仿真表明,在一定的干扰机能量约束下,该文所提方法在保证雷达高性能探测目标且不受干扰情况下,同时实现了多干扰机在空时域干扰对方每个平台以掩护我方雷达探测的效果;相比传统算法,在动态场景中基于FPP-SCA算法的协同干扰具有更优效果。

     

  • 图  1  多任务场景示意图

    Figure  1.  Schematic diagram of the multitask scene

    图  2  基于迭代的波束资源联合优化算法总体框架

    Figure  2.  The overall framework of the joint optimization algorithm of beamforming resources based on iteration

    图  3  各平台相对地面的位置及运动路线

    Figure  3.  The position and movement route of each platform relative to the ground

    图  4  各平台相对雷达的位置及运动路线

    Figure  4.  The position and movement route of each platform relative to the radar

    图  5  各时刻的目标函数优化过程

    Figure  5.  The optimization process of the objective function at each moment

    图  6  各时刻的雷达波束权矢量

    Figure  6.  The beamforming vectors of radar at each moment

    图  7  各时刻干扰机发射波束权矢量(功率归一化)

    Figure  7.  Transmit beamforming vectors of jammers at each moment (power normalization)

    图  8  侦察平台各角度上的接收功率

    Figure  8.  The received power of the reconnaissance platforms at all angles

    图  9  对方雷达各角度上的接收功率

    Figure  9.  The received power of the opposing radars at all angles

    图  10  对方平台在干扰机方向的接收功率

    Figure  10.  The received power of the opposing platforms in the direction of the jammers

    图  11  雷达探测目标的信干噪比

    Figure  11.  The signal-to-interference plus noise ratio of the target detected by our radar

    图  12  雷达波束权矢量

    Figure  12.  The radar beamforming vectors

    图  13  对方平台在各方向上的接收功率

    Figure  13.  The received power of the opposing platforms at all angles

    1  基于FFP-SCA算法的干扰机发射波束权矢量优化过程

    1.   Optimization process of jammers’ transmit beamforming vectors based on FFP-SCA algorithm

     步骤1 初始化:
     设迭代次数$q = 0$,初始化M维向量${{\boldsymbol{z}}_0}$;
     步骤2 循环执行:
      (1) 求解下式凸优化问题:
      $ \begin{gathered} \mathop {\min }\limits_{{{\boldsymbol{w}}_{{{\mathrm{t}}}}},{\boldsymbol{s}}} {\text{ }}{\boldsymbol{w}}_{\rm{t}}^{\rm{H}}{\boldsymbol{H}}{{\boldsymbol{w}}_{\text{t}}} + \mu \sum\limits_{m = 1}^{K + L + N} {{s_m}} \\ {\text{s}}{\text{.t}}{\text{.}}\left\{ \begin{aligned} & {{\text{ }}2{{\mathrm{Re}}} \left\{ {{\boldsymbol{z}}_q^{\text{H}}( - {{\boldsymbol{P}}_k}){{\boldsymbol{w}}_{\rm{t}}}} \right\} \le - {\beta _k} + {\boldsymbol{z}}_q^{\text{H}}( - {{\boldsymbol{P}}_k}){{\boldsymbol{z}}_q} + {s_k},{\text{ }}k = 1,2, \cdots ,K} \\ & {{\text{ }}2{{\mathrm{Re}}} \left\{ {{\boldsymbol{z}}_q^{\text{H}}( - {{\boldsymbol{Q}}_l}){{\boldsymbol{w}}_{\rm{t}}}} \right\} \le - {\beta _l} + {\boldsymbol{z}}_q^{\text{H}}( - {{\boldsymbol{Q}}_l}){{\boldsymbol{z}}_q} + {s_{K + l}}{\text{, }}l = 1,2, \cdots ,L} \\ & {{\text{ }}{\boldsymbol{w}}_{\rm{t}}^{\rm{H}}{{\boldsymbol{R}}_n}{{\boldsymbol{w}}_{\rm{t}}} \le {\rho _n} + {s_{K + L + n}},{\text{ }}n = 1,2, \cdots ,N} \\ & {{\text{ }}{s_m} \ge 0,{\text{ }}m = 1,2, \cdots ,K + L + N} \end{aligned} \right.\end{gathered} $
        得到当前最优解$ {\boldsymbol{w}}_{\rm{t}}^{\text{*}} $;
      (2) 将第q次得到的$ {\boldsymbol{w}}_{\rm{t}}^{\text{*}} $赋值给${{\boldsymbol{z}}_{q + 1}}$;
      (3) 令$q = q + 1$;
     直到目标函数收敛,循环结束。
    下载: 导出CSV

    2  基于迭代的空域波束资源联合优化算法

    2.   Joint optimization algorithm of beamforming resources based on iterative optimization in the spatial domain

     步骤1 初始化:
      设置场景数据(如平台位置、阵元个数、阵元间距等),给定$ {{\boldsymbol{w}}_{o{\rm t}}} $, $ {{\boldsymbol{w}}_{n{\rm t}}} $初值;
     步骤2 执行循环:
      (1) 求解式(17),得到当前最优解$ {\boldsymbol{w}}_{o{\rm r}}^{\text{*}} $:对矩阵${{\boldsymbol{B}}^{ - 1}}{\boldsymbol{A}}$进行特征值分解,最大特征值对应的特征向量即所求$ {\boldsymbol{w}}_{o{\rm r}}^{\text{*}} $;
      (2) 求解如式(22)所示的凸优化问题,得到当前最优解${\boldsymbol{w}}_{o{\rm t}}^{\text{*}}$;
      (3) 根据算法1,得到当前最优${\boldsymbol{w}}_{n{\rm t}}^{\text{*}}$;
     直到目标函数收敛和优化变量收敛,循环结束;
     步骤3 输出结果:
     最终波束权矢量$ {\boldsymbol{w}}_{o{\rm r}}^{\text{*}} $, $ {\boldsymbol{w}}_{o{\rm t}}^{\text{*}} $和$ {\boldsymbol{w}}_{n{\rm t}}^{\text{*}} $的值即为波束资源联合优化的最优结果。
    下载: 导出CSV

    3  基于迭代的空时协同波束资源联合优化方法

    3.   Joint optimization method of space-time cooperative beamforming resources based on iterative optimization

     步骤1 初始化:
      设置场景数据(如平台运动轨迹、阵元个数、阵元间距等),给定$ {{\boldsymbol{w}}_{o{\rm t}}}(\tau ) $, $ {{\boldsymbol{w}}_{n{\rm t}}}(\tau ) $初值。
     步骤2 执行循环:
      (1) 固定当前$ {{\boldsymbol{w}}_{o{\rm t}}}(\tau ) $, $ {{\boldsymbol{w}}_{n{\rm t}}}(\tau ) $,化简并求解式(2),得到最优$ {{\boldsymbol{w}}_{o{\rm r}}^*}(\tau ) $;
      (2) 固定当前$ {{\boldsymbol{w}}_{o{\rm r}}}(\tau ) $, $ {{\boldsymbol{w}}_{n{\rm t}}}(\tau ) $,化简并求解式(2),得到最优$ {{\boldsymbol{w}}_{o{\rm t}}^*}(\tau ) $;
      (3) 固定当前$ {{\boldsymbol{w}}_{o{\rm r}}}(\tau ) $, $ {{\boldsymbol{w}}_{o{\rm t}}}(\tau ) $,采用FPP-SCA算法求解式(35),得到最优$ {{\boldsymbol{w}}_{n{\rm t}}^*}(\tau ) $;
      直到目标函数和优化变量收敛,循环结束;
     步骤3 输出结果:
     当前波束权矢量$ {\boldsymbol{w}}_{o{\rm r}}^ * (\tau ) $, $ {\boldsymbol{w}}_{o{\rm t}}^ * (\tau ) $和$ {\boldsymbol{w}}_{n{\rm t}}^ * (\tau ) $的值即为运动平台的波束资源联合优化最优结果。
    下载: 导出CSV

    表  1  各时刻的平台坐标(km)

    Table  1.   The coordinates of each platform at each time (km)

    平台 $\tau = 1$时刻 $\tau = 2$时刻 $\tau = 3$时刻 $\tau = 4$时刻
    目标 (5,100) (10,100) (15,100) (20,100)
    对方雷达 (10,75) (16,70) (22,65) (28,60)
    侦察平台1 (60,90) (60,85) (60,80) (60,75)
    侦察平台2 (60,60) (60,55) (60,50) (60,45)
    我方雷达 (0,0)
    干扰机1 (–3,20)
    干扰机2 (12,10)
    干扰机3 (20,10)
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-12-25
  • 修回日期:  2024-03-22
  • 网络出版日期:  2024-04-23
  • 刊出日期:  2024-06-28

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