基于交替方向惩罚法的低精度量化MIMO雷达恒模波形设计方法

万环 余显祥 全智 廖斌

万环, 余显祥, 全智, 等. 基于交替方向惩罚法的低精度量化MIMO雷达恒模波形设计方法[J]. 雷达学报, 2022, 11(4): 557–569. doi: 10.12000/JR22072
引用本文: 万环, 余显祥, 全智, 等. 基于交替方向惩罚法的低精度量化MIMO雷达恒模波形设计方法[J]. 雷达学报, 2022, 11(4): 557–569. doi: 10.12000/JR22072
WAN Huan, YU Xianxiang, QUAN Zhi, et al. Constant modulus waveform design for low-resolution quantization MIMO radar based on an alternating direction penalty method[J]. Journal of Radars, 2022, 11(4): 557–569. doi: 10.12000/JR22072
Citation: WAN Huan, YU Xianxiang, QUAN Zhi, et al. Constant modulus waveform design for low-resolution quantization MIMO radar based on an alternating direction penalty method[J]. Journal of Radars, 2022, 11(4): 557–569. doi: 10.12000/JR22072

基于交替方向惩罚法的低精度量化MIMO雷达恒模波形设计方法

doi: 10.12000/JR22072
基金项目: 国家自然科学基金(62171292),广东省自然科学基金(2020A1515010410, 2022A1515010188)
详细信息
    作者简介:

    万 环(1992-),女,江西南昌人,博士。主要研究方向为阵列信号处理、雷达波形设计以及最优化理论算法等

    余显祥(1991-),男,四川人,博士。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。目前发表IEEE Trans期刊论文10余篇

    全 智(1978-),男,广西柳州人,深圳大学特聘教授,博士生导师,国家优秀青年科学基金获得者。主要研究方向为远距离宽带无线通信系统、射频系统校准与测试、数据驱动的信号处理等。担任IEEE Transactions on Signal Processing等期刊编委

    廖 斌(1983-),男,江西萍乡人,深圳大学特聘研究员,博士生导师。主要研究方向为阵列信号处理、自适应信号处理、雷达信号处理等。担任IEEE Transactions on Aerospace and Electronic Systems等期刊编委

    通讯作者:

    廖斌 binliao@szu.edu.cn

  • 责任主编:梁军利 Corresponding Editor: LIANG Junli
  • 中图分类号: TN958

Constant Modulus Waveform Design for Low-resolution Quantization MIMO Radar Based on an Alternating Direction Penalty Method

Funds: The National Natural Science Foundation of China (62171292), Guangdong Basic and Applied Basic Research Foundation (2020A1515010410, 2022A1515010188)
More Information
  • 摘要: 在MIMO雷达中配备大量有源天线单元可以获得优异的波束形成性能,但会导致系统能耗大、电路复杂及成本高等问题。采用低精度的DAC组件可有效克服上述问题,但现有基于无限精度DAC条件所设计的MIMO雷达波形往往难以直接适用于低精度DAC系统。为此,该文提出了一种离散相位约束下基于最小化积分副主瓣比的低精度量化MIMO雷达恒模波形设计方法。该方法首先采用丁克尔巴赫(Dinkelbach)算法将目标函数二次分数形式转换成减法形式,再利用交替方向惩罚法求解非凸恒模离散相位约束问题。最后通过数值仿真与其他方法进行对比,分析了所提方法的发射方向图与积分副主瓣比性能,验证了该方法的有效性。

     

  • 图  1  配置低精度DAC组件的MIMO雷达发射端系统结构图

    Figure  1.  System structure diagram of MIMO radar transmitter with low-resolution DACs

    图  2  1比特与2比特波形元素可行域(红点)

    Figure  2.  Feasible areas of 1 bit and 2 bit waveform entries (red dots)

    图  3  极低精度1比特量化的对称单主瓣波形序列相位分布图

    Figure  3.  1-bit quantized waveform for single symmetrical mainlobe element phase diagram

    图  4  极低精度1比特对称单主瓣波形方向图和ISMR与迭代次数关系图

    Figure  4.  1-bit quantized waveform for single symmetrical mainlobe beampattern and the relationship between ISMR versus iteration number

    图  5  极低精度1比特量化的对称双主瓣波形方向图和ISMR与迭代次数关系图

    Figure  5.  1-bit quantized waveform for two symmetrical mainlobe beampattern and the relationship between ISMR versus iteration number

    图  6  低精度(2~5比特)量化的对称单主瓣波形方向图和ISMR与迭代次数关系图

    Figure  6.  Low precision quantized waveform for symmetrical single mainlobe beampattern and the relationship between ISMR versus iteration number

    图  7  低精度(2~5比特)量化的对称双主瓣波形方向图和ISMR与迭代次数关系图

    Figure  7.  Low precision quantized waveform for two symmetrical mainlobe beampattern and the relationship between ISMR versus iteration number

    图  8  低精度(2~5比特)量化的非称双主瓣波形方向图和ISMR与迭代次数关系图

    Figure  8.  Low precision quantized waveform for two asymmetrical mainlobe beampattern and the relationship between ISMR versus iteration number

    表  1  丁克尔巴赫交替方向惩罚法的低精度量化MIMO雷达恒模波形设计算法

    Table  1.   MIMO radar constant modulus waveform design algorithm with low-precision quantized based on DADPM

     输入:${\boldsymbol{s}}_B^{(0)}$, ${\xi ^{(0)}}$, B, $\delta $, $\nu $, $\epsilon$;
     输出:${\boldsymbol{s} }_B^{ \star }$;
     步骤1:设置 $k = 0$;
     步骤2:初始化:${\varrho ^{(0)}}$, ${{\boldsymbol{p}}^{(0)}}$;
     步骤3:计算${{\boldsymbol{\varXi}} ^{(k)}} = {{\boldsymbol{\varOmega}} _{\text{s}}} - {\xi ^{(k)}}{{\boldsymbol{\varOmega}} _{\text{m}}}$;
     步骤4:设置 $t = 0$;
     步骤5:更新${\boldsymbol{\tilde s}}_B^{(t + 1)}$与${\boldsymbol{s}}_B^{(t + 1)}$,分别通过解问题(16)与问题(23);
     步骤6:更新${\varrho ^{(t + 1)}}$和${{\boldsymbol{p}}^{(t + 1)}}$,通过式(28)与式(29);
     步骤7:更新内循环迭代次数,令$t = t + 1$;
     步骤8:重复步骤5—步骤7,直到满足式(32)中任一停止条件,存
         储${\boldsymbol{s}}_B^{(t + 1)}$;
     步骤9:令${\boldsymbol{s}}_B^{(k + 1)} = {\boldsymbol{s}}_B^{(t + 1)}$,计算${\xi ^{(k + 1)}} = {\text{ISMR}}({\boldsymbol{s}}_B^{(k + 1)})$;
     步骤10:更新外循环迭代次数,令$k = k + 1$;
     步骤11:重复步骤2—步骤10,直到$f({{\boldsymbol{s}}}_{B}^{(k+1)},{\xi }^{(k+1)})\le \epsilon$;
     步骤12:返回 :问题(8)的解${\boldsymbol{s} }_B^{{\star} } = {\boldsymbol{s} }_B^{(k + 1)}$。
    下载: 导出CSV

    表  2  主瓣对称下极低精度量化波形算法性能统计表

    Table  2.   Performance statistics table of the extreme low precision quantized waveform algorithm for symmetrical mainlobe

    主瓣对称情况下方法最小ISMR (dB)最大ISMR (dB)平均ISMR (dB)运算时间(s)
    单主瓣双主瓣单主瓣双主瓣单主瓣双主瓣单主瓣双主瓣
    ADMM-$\infty $bit–15.7192–7.682511.17829.4329–15.1842–7.30312.35272.0368
    QADMM-1bit–4.1057–3.995310.1032–1.3280–4.2891–3.98722.38652.1003
    ADMM-1bit–7.1965–6.72442.3044–4.6130–5.3700–5.13293.14572.6269
    GLAS1-1bit–7.6930–7.7134–6.9940–6.6514–7.3283–7.14670.01060.0104
    GLAS2-1bit–7.6170–8.3327–6.5995–7.6447–7.0952–7.99700.07360.0748
    SDR-1bit–5.9636–7.0137–5.5988–6.7182–5.7154–6.825637.825038.0630
    BCD-1bit–6.8706–3.0849–2.0389–0.2157–6.8327–3.05870.19720.1964
    DADPM-1bit–8.8275–3.9973–2.5693–1.7831–8.6527–3.98128.51478.3249
    下载: 导出CSV

    表  3  低精度量化的对称主瓣波形算法性能统计表

    Table  3.   Performance statistics table of the low precision algorithm for symmetrical mainlobe

    主瓣对称情况下算法最小ISMR (dB)最大ISMR (dB)平均ISMR (dB)运算时间(s)
    单主瓣双主瓣单主瓣双主瓣单主瓣双主瓣单主瓣双主瓣
    QADMM-2bit–5.5427–4.324511.02377.7345–5.4178–4.07842.38142.1377
    QADMM-3bit–6.3020–4.956011.05327.7081–6.0587–4.65642.34682.1597
    QADMM-4bit–6.5840–5.109111.08637.6597–6.1687–4.97902.15272.3519
    QADMM-5bit–6.6815–5.149011.10277.6038–6.2214–5.00742.25272.4368
    ADMM-$\infty $bit–15.7192–7.682511.17829.4329–15.1842–7.30312.35272.0368
    DADPM-2bit–9.0532–5.0738–4.8751–4.9024–8.7875–4.70158.77568.2487
    DADPM-3bit–9.5309–5.8123–9.4311–5.7812–9.1178–5.47258.78748.1834
    DADPM-4bit–9.6694–6.2968–9.6103–6.1025–9.2789–6.10348.87438.2981
    DADPM-5bit–10.1160–6.5541–9.9715–6.3251–9.8321–6.27538.89758.3546
    下载: 导出CSV
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  • 收稿日期:  2022-04-24
  • 修回日期:  2022-08-15
  • 网络出版日期:  2022-08-24
  • 刊出日期:  2022-08-28

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