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间隙波导技术及其空间应用

陈翔 孙冬全 崔万照

王伟, 李梦良, 王福来, 饶彬, 程旭. 一种抗间歇采样转发干扰的全极化雷达发射波形优化方法[J]. 电子与信息学报, 2023, 45(11): 3877-3886. doi: 10.11999/JEIT221469
引用本文: 陈翔, 孙冬全, 崔万照. 间隙波导技术及其空间应用[J]. 电子与信息学报, 2023, 45(1): 168-180. doi: 10.11999/JEIT211291
WANG Wei, LI Mengliang, WANG Fulai, RAO Bin, CHENG Xu. An Optimization Method for Transmitting Waveform of Polarimetric Radar Against Interrupted Sampling Repeater Jamming[J]. Journal of Electronics & Information Technology, 2023, 45(11): 3877-3886. doi: 10.11999/JEIT221469
Citation: CHEN Xiang, SUN Dongquan, CUI Wanzhao. Gap Waveguide Technology and its Space Applications[J]. Journal of Electronics & Information Technology, 2023, 45(1): 168-180. doi: 10.11999/JEIT211291

间隙波导技术及其空间应用

doi: 10.11999/JEIT211291
基金项目: 国家自然科学基金(61901359, 61901320)
详细信息
    作者简介:

    陈翔:男,高级工程师,博士,研究方向为航天器微波毫米波技术

    孙冬全:男,副教授,博士,研究方向为微波毫米波电路、天线理论及技术

    崔万照:男,研究员,博士,研究方向为航天器微波技术

    通讯作者:

    孙冬全 dqsun87@163.com

  • 中图分类号: TN81

Gap Waveguide Technology and its Space Applications

Funds: The National Natural Science Foundation of China (61901359, 61901320)
  • 摘要: 间隙波导(GW)是一种基于非接触电磁带隙(EBG)结构的新型人工电磁(EM)材料,其独特的非接触结构和宽带电磁屏蔽特性在构建新型电磁传输线及屏蔽结构方面显示出极大的优势和灵活性,为微波毫米波部件、电路及天线等领域带来了新的研究视角和实现途径,近年来引起了广泛关注。该文首先简要介绍了间隙波导概念和原理,分析了其技术优势;进一步,根据不同的研究及应用领域分类,全方位地归纳总结了间隙波导技术相关的国内外研究进展情况;最后,结合空间技术背景和发展需求,探讨了间隙波导在空间微波毫米波技术中的应用前景,提出了基于间隙波导技术的非接触式无源互调干扰控制方法及堆叠集成毫米波电路系统两个重要的应用方向。该文工作可为间隙波导技术相关研究和应用提供一定的借鉴与参考。
  • 近年来,随着电子技术的不断发展,雷达所处的电磁工作环境正呈现复杂化和激烈化态势[1]。尤其是数字射频存储器(Digital Radio Frequency Memory, DRFM)的出现和日臻完善,给雷达抗干扰带来了极大挑战[2-4]。间歇采样转发干扰(Interrupted Sampling Repeater Jamming, ISRJ)作为DRFM衍生出的新型相参干扰样式,通过巧妙地对截获雷达信号进行分段转发,在雷达接收端脉压后形成与目标回波相似的密集假目标串[5],达到对干扰方实施压制和欺骗的双重效果。由于ISRJ具有响应速度快、工程实现简单的特点,传统方法往往难以有效抑制[6,7]。因此,针对ISRJ的对抗技术成为当前抗干扰领域研究的热点问题。

    目前,针对ISRJ的抑制方法可分为3个类别:第1类采用发射端波形设计的方法,具体做法是在发射端设计稀疏多普勒特性波形和正交LFM-相位编码波形,然后在接收端进行滑窗抽取检测和分段滤波来实现对ISRJ的识别和抑制[8,9]。第2类采用接收端的信号处理方法,即基于干扰信号不同于目标回波的特征,在雷达接收端实现对ISRJ的滤除或抑制[10-12],该类方法大多依赖于对ISRJ的相关参数的估计[13];此外,也有学者通过深度学习对回波信号进行处理[14,15],在显著抑制干扰的同时摆脱了对参数估计的依赖。第3类方法综合采用发射端和接收端的联合设计[6,7,16-19],以提高抗干扰的自由度,简化接收端处理的复杂程度,代表性工作包括:文献[6]提出了一种抗ISRJ的联合设计算法,通过对非凸优化问题的求解实现了对ISRJ的显著抑制;文献[7]将模型扩展至多脉冲情形,并有效地解决了干扰机高速运动时的波形失配问题。

    但需要指出的是,以文献[6]和文献[7]为代表的抗ISRJ联合设计方法中,性能准则“信干噪比”中的“信”并未考虑目标特性对发射信号的调制作用。但在宽带雷达条件下,目标常常不能再看作一个点目标,而是在距离维上具有多个散射中心的扩展目标[19]。另外,值得注意的是,作为表征电磁波矢量性的参数,极化信息的利用可以显著提高雷达系统的目标检测[19]、识别[20]和抗干扰能力[21,22]。在抗干扰方面,文献[21]在空域-极化域显著地抑制了多干扰源欺骗干扰;文献[22]利用正交极化高分辨距离像间的互相关系数作为鉴别量,达到了大于90%的正确鉴别概率。这充分说明了极化信息的引入对有效解决抗干扰问题具有重要价值。

    针对现有技术的不足和短板,本文将在抗干扰设计中引入极化信息,并修正波形优化性能指标中信干噪比的数学形式,进而深入研究宽带全极化雷达的抗ISRJ发射波形和接收滤波器联合设计问题。实验结果表明,引入极化信息和考虑扩展目标对信号的调制作用显著提高了ISRJ的抑制性能。

    假设雷达在一个相干处理间隔(Coherent Processing Interval, CPI)内发射K个相位编码脉冲信号,发射波形序列的表达式为s=[sT1,sT2,,sTK]TCNK×1,其中()T表示转置运算。不失一般性,序列中的第k个脉冲表示为

    sk=[sk(1),sk(2),,sk(N)]TCN×1,k=1,2,,K (1)

    其中,N表示相位编码信号的码长。并且K个相位编码脉冲信号满足恒模条件。

    宽带雷达条件下,第k个脉冲的目标冲激响应矩阵(Target Response Impulse Matrix, TIRM)表示为[19]

    Hk(θ)=(H0(θ)00H1(θ)H0(θ)00HQ1(θ)HQ2(θ)00HQ1(θ)000HQ1(θ)),Q=MN+1 (2)

    其中,θ表示对应的目标方位角(Target Aspect Angle, TAA)。

    假定目标在一个CPI内保持特性不变,则有H1(θ)=H2(θ)==HK(θ),则K个目标回波可以表征为

    sT=H(θ)s (3)

    其中,H(θ)=diag(H1(θ),H2(θ),,HK(θ))CMK×NK

    需要指出的是,H(θ)对方位角扰动十分敏感,故本文将给定方位角的先验范围[θmin,θmax],并取该方位角范围内TIRM的均值作为目标特性,以此来增加系统设计的鲁棒性[19],即

    ¯H(θ)=1KHKHi=1H(θi) (4)

    其中,KH为对方位角区间[θmin,θmax]离散化的份数。

    ε=[εH,εV]T为全极化雷达发射天线的Jones矢量,则ε可以写为

    ε=[cosαsinαsinαcosα][cosβjsinβ] (5)

    其中,α[π/2,π/2]为极化旋转角,β[π/4,π/4]为极化椭圆角。假设雷达发射和接收信号共用一副天线,且一个CPI内不改变天线的极化方式,则有接收天线极化η=ε。则全极化雷达接收到的回波序列表示为

    xT=(ηHTε)¯H(θ)s=(εHTε)¯H(θ)sCMK×1 (6)

    其中,T为目标的极化散射矩阵。

    另外,ISRJ可用矩阵J=Diag(j)CN×N表示[7],则对应于第k个发射脉冲的ISRJ信号可表示为

    sJk=(WJJk)sk=JMsk (7)

    其中,WJM×N且有

    WJ[p,q]={1 , p=q0 , pq (8)

    其中,p=1,2,,M, q=1,2,,N,等价于在干扰矢量j后补MN0。同目标特性相似,假定干扰特性在一个CPI内也保持不变,即有J1=J2==JK=J,则雷达在一个CPI内接收到的K个ISRJ信号可综合表示为

    sJ=[sTJ1,sTJ2,,sTJK]T=Cs (9)

    其中,CK个ISRJ信号对应的干扰特性矩阵,有C=diag(WJJ,WJJ,,WJJ)CMK×NK。可以看出,C是由K个发射脉冲干扰特性矩阵拼接而成的分块对角矩阵。则全极化雷达接收到的干扰回波序列为

    xJ=(ηHεJ)sJ=(εHεJ)sJCMK×1 (10)

    其中,εJ为干扰机天线极化方式的Jones矢量。

    设接收滤波器为w=[wT1,wT2,,wTK]TCMK×1,则不失一般性,雷达回波经接收滤波器处理后的输出结果为

    r=(εHTε)wH¯H(θ)s+(εHεJ)wHsJ+wHv (11)

    其中,vCMK×1为复加性高斯白噪声序列。

    rkxTh(n)为第k个目标回波xTk和相应接收滤波器hk的互相关函数,即

    rkxTh(n)=Mm=1(xTHk(m)hHk(m+n)+xTVk(m)hVk(m+n)), n=1M,2M,,0,,M2,M1 (12)

    则目标回波与接收滤波器的互模糊函数为

    χxTh(n,f)=Kk=1rkxTh(n)exp(jkf) (13)

    其中,f=2πfdTp, fd为多普勒频移,Tp为雷达的脉冲重复周期。干扰信号与接收滤波器的互模糊函数为

    χxJh(n,f)=Kk=1rkxJh(n)exp(jkf) (14)

    联合设计的目的,一方面在于在干扰机高速运动的情况下,目标回波能够最大限度地匹配目标特性,而在一定的多普勒频移区间内保持较高的脉压增益。另一方面,尽可能地让多普勒频移区间内干扰信号与接收滤波器之间的互模糊函数能量保持为零,从而对ISRJ的形成抑制。综合以上要求,对多普勒频移区间(f1, f2)进行离散化处理后,构造如式(15)的目标函数分量:

    ξ=Ll=1(N1n=1N,n0|Kk=1(rkxTHhH(n)+rkxTVhV(n))exp(jkf)|2+M1n=1M|Kk=1(rkxJHhH(n)+rkxJVhV(n))exp(jkf)|2) (15)

    其中,fl=f1+(l1)Δf,l=1,2,,LL为离散化份数,Δf=(f2f1)/(L1)为等份划分后的频率间隔。

    另外,由于非匹配滤波体制的使用,在对目标回波进行接收滤波处理时,脉压峰值将存在峰值损耗,即存在信噪比损失(Signal-to-Noise Ratio Loss, SNRL)。由矩阵的相容性,有

    (16)

    其中,\left\| \cdot \right\|表示向量或矩阵的2-范数。由此可定义SNRL的表达式为

    {\text{SNRL}} = 20\lg \frac{{\left\| {\boldsymbol{T}} \right\|\left\| {\boldsymbol{w}} \right\|\left\| {\overline {{\boldsymbol{H}}(\theta )} } \right\|\left\| {\boldsymbol{s}} \right\|}}{{\left| {({{\boldsymbol{\varepsilon}} ^{\text{H}}}{\boldsymbol{T\varepsilon}} )\cdot {{\boldsymbol{w}}^{\text{H}}}\overline {{\boldsymbol{H}}(\theta )} {\boldsymbol{s}}} \right|}} (17)

    故可给目标回波施加如式(18)的峰值约束条件,保证脉压峰值具备一定的稳定性,即

    \begin{split} {g_1}({\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon}} ) =& {\left| {({\boldsymbol{h}}_{\text{H}}^{\text{H}}{{\boldsymbol{x}}_{{\text{TH}}}} + {\boldsymbol{h}}_{\text{V}}^{\text{H}}{{\boldsymbol{x}}_{{\text{TV}}}}) - {a_{{\text{max}}}}} \right|^2} \\ & = {\left| {({{\boldsymbol{\varepsilon}} ^{\text{H}}}{\boldsymbol{T\varepsilon}} )\cdot {{\boldsymbol{w}}^{\text{H}}}\overline {{\boldsymbol{H}}(\theta )} {\boldsymbol{s}} - {a_{{\text{max}}}}} \right|^2} \end{split} (18)

    代入恒模约束条件{\boldsymbol{s}} = NK,以及{{\boldsymbol{w}}^{\text{H}}}{\boldsymbol{w}} = {M_{\boldsymbol{w}}},其中{M_{\boldsymbol{w}}}为接收滤波器能量,则有

    {a_{{\text{max}}}} = \sqrt {NK{M_{\boldsymbol{w}}}} \left\| {\boldsymbol{T}} \right\|\left\| {\overline {{\boldsymbol{H}}(\theta )} } \right\|{10^{ - \frac{\mu }{{20}}}} (19)

    然后,为进一步抑制干扰信号,同样对干扰施加峰值约束,以将干扰信号的脉压峰值尽可能降低,即

    \begin{split} {g_2}({\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon}} ) & = {\left| {({\boldsymbol{h}}_{\text{H}}^{\text{H}}{{\boldsymbol{x}}_{{\text{JH}}}} + {\boldsymbol{h}}_{\text{V}}^{\text{H}}{{\boldsymbol{x}}_{{\text{JV}}}}) - {a_{{\text{min}}}}} \right|^2} \\ & = {\left| {({{\boldsymbol{\varepsilon}} ^{\text{H}}}{{\boldsymbol{\varepsilon}} _{\text{J}}})\cdot {{\boldsymbol{w}}^{\text{H}}}{{\boldsymbol{s}}_{\text{J}}} - {a_{{\text{min}}}}} \right|^2} \end{split} (20)

    综上,能量约束下天线极化方式、发射波形序列和接收滤波器序列的联合优化问题可以表示为

    \left. \begin{split} & \mathop {{\text{min }}}\limits_{{\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon}} } \varGamma ({\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon}} ) = \xi ({\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon}} ) + {\gamma _1}{g_1}({\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon}} ) \\ & \quad + {\gamma _2}{g_2}({\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon}} )\\ & \text{s}\text{.t}\text{.}\;\;{{\boldsymbol{w}}}^{\text{H}}{\boldsymbol{w}}={M}_{w}\text{,}\left|{s}_{k}(n)\right|=1,k=1,2,\cdots, K,\\ & \quad n=1,2,\cdots ,N \end{split}\right\} (21)

    其中,{\gamma _1}{\gamma _2}表示对应的峰值约束权值,需要指出的是,为保证惩罚力度,{\gamma _1}{\gamma _2}通常取较大数值[23],这样才能有效地滤波器的输出,同时抑制干扰信号。至此,本节完成了宽带全极化雷达抗ISRJ问题的数学建模。

    对于式 \left(21\right) ,本文将采用交替迭代的方法进行分解,具体做法为:在给定发射波形序列{{\boldsymbol{s}}^{(0)}}和Jones矢量{{\boldsymbol{\varepsilon}} ^{(0)}}初始值的基础上,先固定 {{\boldsymbol{s}}^{(i)}} {{\boldsymbol{\varepsilon}} ^{(i)}},可求解 {{\boldsymbol{w}}^{(i + 1)}} ;再固定{{\boldsymbol{w}}^{(i + 1)}}{{\boldsymbol{\varepsilon}} ^{(i)}},可求解{{\boldsymbol{s}}^{(i + 1)}};最后固定{{\boldsymbol{s}}^{(i + 1)}}{{\boldsymbol{w}}^{(i + 1)}},求解{{\boldsymbol{\varepsilon}} ^{(i + 1)}},重复上述流程,直至达到设定的收敛条件,上述迭代过程的数学形式依次可表示为

    {{\boldsymbol{w}}^{(i + 1)}} = {\text{arg min }}\varGamma \left( {{{\boldsymbol{s}}^{(i)}},{\boldsymbol{w}},{{\boldsymbol{\varepsilon}} ^{(i)}}} \right) (22)
    {{\boldsymbol{s}}^{(i + 1)}} = {\text{arg min }}\varGamma \left( {{\boldsymbol{s}},{{\boldsymbol{w}}^{(i + 1)}},{{\boldsymbol{\varepsilon}} ^{(i)}}} \right) (23)
    {{\boldsymbol{\varepsilon}} ^{(i + 1)}} = {\text{arg min }}\varGamma \left( {{{\boldsymbol{s}}^{(i + 1)}},{{\boldsymbol{w}}^{(i + 1)}},{\boldsymbol{\varepsilon}} } \right) (24)

    其中,{{\boldsymbol{s}}^{(i)}},{{\boldsymbol{w}}^{(i)}}{{\boldsymbol{\varepsilon }}^{(i)}}分别表示第i次迭代后发射波形序列{\boldsymbol{s}}、接收滤波器序列{\boldsymbol{w}}和Jones矢量{\boldsymbol{\varepsilon}} 的最优解。收敛条件方面,可设置\left| {{\varGamma ^{(i + 1)}}({\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon}} ) - {\varGamma ^{(i)}}({\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon}} )} \right|/ \left| {{\varGamma ^{(i)}}({\boldsymbol{s}},{\boldsymbol{w}},{\boldsymbol{\varepsilon }})} \right| < {\eta _\varGamma }作为算法的收敛条件[24,25]{\eta _\varGamma }为预设值。下面将分别求解迭代过程中接收滤波器{{\boldsymbol{s}}^{(i + 1)}}、发射波形{{\boldsymbol{w}}^{(i + 1)}}和Jones矢量{{\boldsymbol{\varepsilon}} ^{(i + 1)}}对应的子问题。

    根据式 \left(21\right) 和式 \left(22\right) ,在迭代求解的第i步,固定发射波形{{\boldsymbol{s}}^{(i)}}和Jones矢量 {{\boldsymbol{\varepsilon}} ^{{\text{(}}i{\text{)}}}} ,求解{{\boldsymbol{w}}^{(i + 1)}}的问题为

    \begin{split} & \mathop {{\text{min }}}\limits_{\boldsymbol{w}} \varGamma ({\boldsymbol{w}}) = \xi \left( {{{\boldsymbol{s}}^{(i)}},{\boldsymbol{w}},{{\boldsymbol{\varepsilon}} ^{(i)}}} \right) + {\gamma _1}{g_1}\left( {{{\boldsymbol{s}}^{(i)}},{\boldsymbol{w}},{{\boldsymbol{\varepsilon}} ^{(i)}}} \right) \\ & \quad + {\gamma _2}{g_2}\left( {{{\boldsymbol{s}}^{(i)}},{\boldsymbol{w}},{{\boldsymbol{\varepsilon}} ^{(i)}}} \right)\\ & {\text{s}}{\text{.t}}{\text{. }}{{\boldsymbol{w}}^{\text{H}}}{\boldsymbol{w}} = {M_{\boldsymbol{w}}}\\[-10pt] \end{split} (25)

    为了便于对目标函数进行优化,分别定义目标回波矩阵{{\boldsymbol{S}}_{{\text{T}}l}}和ISRJ矩阵{{\boldsymbol{S}}_{{\text{J}}l}}

    \begin{split} & {{\boldsymbol{S}}}_{\text{T}l}\left[p,q\right]\\ & =\left\{ \begin{aligned} & {s}_{\text{T}k+1}\left(M - n\right)\text{exp}\left({\rm{j}}\left(k + 1\right){f}_{l}\right),q - \left(p - Mk\right)=n\\ & 0,\;{\text{其他}} \end{aligned}\right. \end{split} (26)
    \begin{split} & {{\boldsymbol{S}}}_{\text{J}l}\left[p,q\right]\\ & =\left\{\begin{aligned} & {s}_{\text{J}k+1}\left(M - n\right)\text{exp}\left({\rm{j}}\left(k + 1\right){f}_{l}\right),q - \left(p - Mk\right)=n\\ & 0,\; 其他\end{aligned}\right. \end{split} (27)

    其中,l = 1,2, \cdots ,L, n = 0,1, \cdots ,M - 1, p = 1, 2, \cdots ,MK, q = 1,2, \cdots ,2M - 1, k = {\text{quo}}(p - 1,M)表示\left\lfloor {\dfrac{{p - 1}}{M}} \right\rfloor, \left\lfloor \cdot \right\rfloor 表示向下取整操作,于是,优化问题(25)可以等效写为

    \begin{split} & \mathop {{\text{min }}}\limits_{\boldsymbol{w}} \varGamma ({\boldsymbol{w}}) = {{\boldsymbol{w}}^{\text{H}}}{\boldsymbol{Pw}} - 2{\text{Re}}\left( {{{\boldsymbol{p}}^{\text{H}}}{\boldsymbol{w}}} \right)\\ & {\text{s}}{\text{.t}}{\text{. }}\;{{\boldsymbol{w}}^{\text{H}}}{\boldsymbol{w}} = {M_{\boldsymbol{w}}} \end{split} (28)

    其中

    \begin{split} {\boldsymbol{P}} =& \sum\limits_{l = 1}^L {\left( {{{\left| {{\boldsymbol{{\varepsilon}} ^{\text{H}}}{\boldsymbol{T\varepsilon}} } \right|}^2}{{\boldsymbol{S}}_{{\text{T}}l}}{\boldsymbol{W}}{\boldsymbol{S}}_{{\text{T}}l}^{\text{H}} + {{\left| {{{\boldsymbol{\varepsilon}} ^{\text{H}}}{{\boldsymbol{\varepsilon}} _{\text{J}}}} \right|}^2}{{\boldsymbol{S}}_{{\text{J}}l}}{{\boldsymbol{S}}_{{\text{J}}l}}^{\text{H}}} \right)} \\ & + {\gamma _1}{\left| {{{\boldsymbol{\varepsilon}} ^{\text{H}}}{\boldsymbol{T\varepsilon}} } \right|^2}{{\boldsymbol{s}}_{\text{T}}}{{\boldsymbol{s}}_{\text{T}}}^{\text{H}} + {\gamma _2}{\left| {{{\boldsymbol{\varepsilon}} ^{\text{H}}}{{\boldsymbol{\varepsilon}} _{\text{J}}}} \right|^2}{{\boldsymbol{s}}_{\text{J}}}{{\boldsymbol{s}}_{\text{J}}}^{\text{H}}\\[-1pt] \end{split} (29)
    {\boldsymbol{p}} = {\gamma _1}{a_{{\text{max}}}}{{\boldsymbol{\varepsilon}} ^{\text{H}}}{\boldsymbol{T\varepsilon}} \cdot {{\boldsymbol{s}}_{\text{T}}} + {\gamma _2}{a_{{\text{min}}}}{{\boldsymbol{\varepsilon}} ^{\text{H}}}{{\boldsymbol{\varepsilon}} _{\text{J}}}\cdot {{\boldsymbol{s}}_{\text{J}}} (30)

    {\text{Re(}} \cdot {\text{)}}表示取实部操作,{\boldsymbol{W}}表示维度为2M - 1的对角方阵(除了第M个对角元素等于0之外,其余对角元素为1,且对角元素以外的元素均为0)。

    根据文献[7],式 \left(28\right) 中的最优解为

    {{\boldsymbol{w}}^{(i + 1)}} = - \sqrt {\frac{{{M_{\boldsymbol{w}}}}}{{{{\left\|u\left( {{{\boldsymbol{w}}^{(i)}}} \right)\right\|}^2}}}} u\left( {{{\boldsymbol{w}}^{(i)}}} \right) (31)

    其中

    u\left( {{{\boldsymbol{w}}^{(i)}}} \right) = \left( {{{\boldsymbol{P}}^{(i)}} - {\text{tr}}\left( {{{\boldsymbol{P}}^{(i)}}} \right){{\boldsymbol{I}}_{MK}}} \right){{\boldsymbol{w}}^{(i)}} - {{\boldsymbol{p}}^{(i)}} (32)

    根据式 \left(21\right) 和式 \left(23\right) ,固定接收滤波器序列{{\boldsymbol{w}}^{(i + 1)}}和Jones矢量{{\boldsymbol{\varepsilon}} ^{(i)}},求解{{\boldsymbol{s}}^{(i + 1)}}的问题形式可以表示为

    \begin{split} & \mathop {{\text{min }}}\limits_s \varGamma ({\boldsymbol{s}}) = \xi \left( {{\boldsymbol{s}},{{\boldsymbol{w}}^{(i + 1)}},{{\boldsymbol{\varepsilon}} ^{(i)}}} \right) + {\gamma _1}{g_1}\left( {{\boldsymbol{s}},{{\boldsymbol{w}}^{(i + 1)}},{{\boldsymbol{\varepsilon}} ^{(i)}}} \right) \\ & \quad + {\gamma _2}{g_2}\left( {{\boldsymbol{s}},{{\boldsymbol{w}}^{(i + 1)}},{{\boldsymbol{\varepsilon}} ^{(i)}}} \right)\\ & {\text{s}}{\text{.t}}{\text{. }}\;\left| {{s_k}(n)} \right| = 1,k = 1,2,\cdots,K,n = 1,2, \cdots ,N \\[-10pt] \end{split} (33)

    为求解式(33),定义接收滤波器矩阵{{\boldsymbol{R}}_l}

    \begin{split} & {{\boldsymbol{R}}}_{l}\left[p,q\right]\\ & =\left\{ \begin{aligned} & {w}_{k+1}\left(n\right)\text{exp}\left(j\left(k + 1\right){f}_{l}\right), q + \left(p - Mk\right) = M + n\\ & 0, {\text{其他}}\end{aligned}\right. \end{split} (34)

    其中,l = 1,2, \cdots ,L, n = 1,2, \cdots ,M, p = 1,2, \cdots ,MK, q=1,2,\cdots ,2M-1,\;k=\text{quo}(p-1,M)

    于是,式 \left(33\right) 可以等效为

    \begin{split} & \mathop {{\text{min }}}\limits_{\boldsymbol{s}} \varGamma (s) = {s^{\text{H}}}{\boldsymbol{Qs}} - 2{\text{Re}}\left( {{{\boldsymbol{q}}^{\text{H}}}{\boldsymbol{s}}} \right)\\ & \text{ s}\text{.t}\text{.}\;\left|{s}_{k}(n)\right|=1,k=1,2,\cdots,K,n=1,2,\cdots ,N \end{split} (35)

    其中

    \begin{split} {\boldsymbol{Q}} =& \sum\limits_{l = 1}^L \left( {{\left| {{{\boldsymbol{\varepsilon}} ^{\text{H}}}{\boldsymbol{T}}{\boldsymbol{\varepsilon}} } \right|}^2}{{\overline {{\boldsymbol{H}}(\theta )} }^{\text{H}}}{{\boldsymbol{R}}_l}{\boldsymbol{W}}{{\boldsymbol{R}}_l}^{\text{H}}\overline {{\boldsymbol{H}}(\theta )} \right. \\ & \left.+ {{\left| {{{\boldsymbol{\varepsilon}} ^{\text{H}}}{{\boldsymbol{\varepsilon}} _{\text{J}}}} \right|}^2}{{\boldsymbol{C}}^{\text{H}}}{{\boldsymbol{R}}_l}{{\boldsymbol{R}}_l}^{\text{H}}{\boldsymbol{C}} \right) \\ & + {\gamma _1}{\left| {{{\boldsymbol{\varepsilon}} ^{\text{H}}}{\boldsymbol{T}}{\boldsymbol{\varepsilon}} } \right|^2}{\overline {{\boldsymbol{H}}(\theta )} ^{\text{H}}}{\boldsymbol{w}}{{\boldsymbol{w}}^{\text{H}}}\overline {{\boldsymbol{H}}(\theta )} \\ & + {\gamma _2}{\left| {{{\boldsymbol{\varepsilon}} ^{\text{H}}}{{\boldsymbol{\varepsilon}} _{\text{J}}}} \right|^2}{{\boldsymbol{C}}^{\text{H}}}{\boldsymbol{w}}{{\boldsymbol{w}}^{\text{H}}}{\boldsymbol{C}} \end{split} (36)
    {\boldsymbol{q}}={\gamma }_{1}{a}_{\text{max}}{({{\boldsymbol{\varepsilon}} }^{\text{H}}{\boldsymbol{T}}{\boldsymbol{\varepsilon}} )}^{\text{H}}{\overline{{\boldsymbol{H}}(\theta )}}^{\text{H}}{\boldsymbol{w}}+{\gamma }_{2}{a}_{\text{min}}{({{\boldsymbol{\varepsilon}} }^{\text{H}}{{\boldsymbol{\varepsilon}} }_{\text{J}})}^{\text{H}}{{\boldsymbol{C}}}^{\text{H}}{\boldsymbol{w}} (37)

    对于问题式(35),有最优解为[7]

    {{\boldsymbol{s}}^{(i + 1)}} = - {\text{exp}}\left( {{\text{j}} \cdot {\text{arg}}\left( {v\left( {{{\boldsymbol{s}}^{(i)}}} \right)} \right)} \right) (38)

    其中

    v\left( {{{\boldsymbol{s}}^{(i)}}} \right) = \left( {{{\boldsymbol{Q}}^{(i)}} - {\text{tr}}\left( {{{\boldsymbol{Q}}^{(i)}}} \right){{\boldsymbol{I}}_{NK}}} \right){{\boldsymbol{s}}^{(i)}} - {{\boldsymbol{q}}^{(i)}} (39)

    根据式 \left(21\right) 和式 \left(24\right) ,固定接收滤波器序列{{\boldsymbol{w}}^{(i + 1)}}和发射波形序列{{\boldsymbol{s}}^{(i + 1)}},求解Jones矢量{{\boldsymbol{\varepsilon}} ^{(i + 1)}}的问题为

    \begin{split} \mathop {{\text{min }}}\limits_{\boldsymbol{\varepsilon}} \varGamma {\text{(}}{\boldsymbol{\varepsilon}} {\text{)}} = & \xi \left( {{{\boldsymbol{s}}^{(i + 1)}},{{\boldsymbol{w}}^{(i + 1)}},{\boldsymbol{\varepsilon}} } \right) \\ & + {\gamma _1}{g_1}\left( {{{\boldsymbol{s}}^{(i + 1)}},{{\boldsymbol{w}}^{(i + 1)}},{\boldsymbol{\varepsilon}} } \right) \\ & + {\gamma _2}{g_2}\left( {{{\boldsymbol{s}}^{(i + 1)}},{{\boldsymbol{w}}^{(i + 1)}},{\boldsymbol{\varepsilon}} } \right) \\ \text{ s}\text{.t}\text{. }{{\boldsymbol{\varepsilon}} }^{\text{H}}{\boldsymbol{\varepsilon}} =1& \end{split} (40)

    由于Jones矢量{\boldsymbol{\varepsilon}} 的未知量个数恒定为2,可采用网格法求解。具体地,将\alpha \in [ - {\pi}/2,{\pi}/2]等分为{L_\alpha }份,将\beta \in [ - {\pi}/4,{\pi}/4]等分为{L_\beta }份,算法遍历{L_\alpha }\cdot {L_\beta }次后求得最优解{{\boldsymbol{\varepsilon}} ^{(i + 1)}}

    综合以上发射波形序列{\boldsymbol{s}}、接收滤波器序列{\boldsymbol{w}}和Jones矢量{\boldsymbol{\varepsilon}} 的交替迭代求解方法,即可完成抗ISRJ的恒模互补波形最优化设计。为进一步缩短算法收敛所需的时长,可在不牺牲算法性能的前提下,引入平方迭代框架(SQUAREd iterative Method, SQUAREM)实现算法收敛速度的显著提升[25]。使用平方迭代框架后,宽带全极化雷达的恒模互补波形设计算法流程如算法1所示。

    算法1 宽带全极化雷达抗ISRJ恒模互补波形设计流程
     输入:目标脉冲响应矩阵\overline {{\boldsymbol{H}}(\theta )}、干扰特性矩阵{\boldsymbol{C}}、初始{\boldsymbol{s}},{\boldsymbol{w}}
        {\boldsymbol{\varepsilon}}
     输出:最优发射波形序列{{\boldsymbol{s}}^\nabla }、接收滤波器序列{{\boldsymbol{w}}^\nabla }和Jones矢量{{\boldsymbol{\varepsilon}} ^\nabla }
     1 重复
     2 将{{\boldsymbol{w}}^{(i)} }代入式(31)计算{{\boldsymbol{w}}_1},将{{\boldsymbol{w}}_1}代入式(31)计算{{\boldsymbol{w}}_2}
     3   {{\boldsymbol{r}}_1} = {{\boldsymbol{w}}_1} - {{\boldsymbol{w}}^{(i)} }, {{\boldsymbol{v}}_1} = {{\boldsymbol{w}}_2} - {{\boldsymbol{w}}_1} - {{\boldsymbol{r}}_1} , {\alpha _1} = - {{\boldsymbol{r}}_1}/{{\boldsymbol{v}}_1}
     4   将{ {\boldsymbol{w} }^{(i)} } - 2{\alpha _1}{ {\boldsymbol{r} }_1} + {\alpha _1}^2{{\boldsymbol{v}}_1}代入式(31)计算{{\boldsymbol{w}}^{(i + 1)}}
     5   若 \varGamma \left( {{{\boldsymbol{s}}^{{\text{(}}i{\text{)}}}},{{\boldsymbol{w}}^{(i + 1)}},{{\boldsymbol{\varepsilon }}^{{\text{(}}i{\text{)}}}}} \right) > \varGamma \left( {{{\boldsymbol{s}}^{{\text{(}}i{\text{)}}}},{{\boldsymbol{w}}^{{\text{(}}i{\text{)}}}},{{\boldsymbol{\varepsilon}} ^{{\text{(}}i{\text{)}}}}} \right) ,循环
     6     {\alpha _1} \leftarrow \left( {{\alpha _1} - 1} \right)/2
     7     将{{\boldsymbol{w}} ^{{\text{(}}i{\text{)}}}} - 2{\alpha _1}{{\boldsymbol{r}}_1} + {\alpha _1}^2{{\boldsymbol{v}}_1}代入式(31)计算{{\boldsymbol{w}}^{{\text{(}}i + 1{\text{)}}}}
     8   结束
     9   将{{\boldsymbol{s}}^{{\text{(}}i{\text{)}}}}代入式(38)计算{{\boldsymbol{s}}_1},将{{\boldsymbol{s}}_1}代入式(38)计算{{\boldsymbol{s}}_2}
     10   {{\boldsymbol{r}}_2} = {{\boldsymbol{s}}_1} - {{\boldsymbol{s}}^{{\text{(}}i{\text{)}}}}, {{\boldsymbol{v}}_2} = {{\boldsymbol{s}}_2} - {{\boldsymbol{s}}_1} - {{\boldsymbol{r}}_1},{\text{ }}{\alpha _2} = - {{\boldsymbol{r}}_2}/{{\boldsymbol{v}}_2}
     11   将{{\boldsymbol{s}}^{ {\text{(} }i{\text{)} } } } - 2{\alpha _2}{{\boldsymbol{r}}_2} + {\alpha _2}^2{{\boldsymbol{v}}_2}代入式(38)计算{s^{{\text{(}}i + 1{\text{)}}}}
     12   若\varGamma \left( {{{\boldsymbol{s}}^{{\text{(}}i + 1{\text{)}}}},{{\boldsymbol{w}}^{{\text{(}}i + 1{\text{)}}}},{{\boldsymbol{\varepsilon}} ^{{\text{(}}i{\text{)}}}}} \right) > \varGamma \left( {{{\boldsymbol{s}}^{{\text{(}}i{\text{)}}}},{{\boldsymbol{w}}^{{\text{(}}i + 1{\text{)}}}},{{\boldsymbol{\varepsilon}} ^{{\text{(}}i{\text{)}}}}} \right),循环
     13     {\alpha _2} \leftarrow \left( {{\alpha _2} - 1} \right)/2
     14     将{ {\boldsymbol{s} }^{ {\text{(} }i{\text{)} } } } - 2{\alpha _2}{{\boldsymbol{r}}_2} + {\alpha _2}^2{ {\boldsymbol{v} }_2}代入式(38)计算{{\boldsymbol{s}}^{{\text{(}}i + 1{\text{)}}}}
     15   结束
     16   使用网格法迭代求解{{\boldsymbol{\varepsilon}} ^{{\text{(}}i + 1{\text{)}}}}
     17   i \leftarrow i + 1
     18 达到收敛条件,结束
    下载: 导出CSV 
    | 显示表格

    计算复杂度方面,第 i 次迭代求解{{\boldsymbol{w}}^{{\text{(}}i + 1{\text{)}}}}{{\boldsymbol{s}}^{{\text{(}}i + 1{\text{)}}}}的运算量主要来自对矩阵{\boldsymbol{P}}{\boldsymbol{Q}}的计算,求解{{\boldsymbol{\varepsilon}} ^{{\text{(}}i + 1{\text{)}}}}的运算量则可忽略不计。使用式(29)、式(36)给出的定义式运算的计算复杂度分别为{{O}}(LK{M^3}){{O}}(LKN{M^2})。若直接计算式(32)、式(39)中的第1项和第2项,可大幅度降低算法复杂度。经由证明,求解{\text{tr}}({\boldsymbol{P}}){\text{tr}}({\boldsymbol{Q}})的复杂度为{{O}}(LK{M^2}),故本文算法经简化后的计算复杂度为{{O}}(LK{M^2}),而引入平方迭代框架不改变计算复杂度。

    本节设计了基于实测目标数据的实验验证。目标数据采用佐治亚理工学院T-72坦克全极化雷达 \mathrm{X} 波段实测数据[26],测量信号为中心频率{f_0} = 9.6{\text{ GHz}}的步进频脉冲信号,覆盖带宽为660 MHz,雷达俯仰角固定为30.42°,方位角范围为[0^\circ , 360^\circ ]。具体来说,数据库中,转台方位角的变动步长为0.05°,每个数据文件中宽带雷达共进行 79 次扫描,因此,单个文件的方位角变化范围为3.90°,同时,相邻数据文件中心方位角间相差4.25°。这表明在 79 次扫描之后,存在 0.35°的测量盲区。高分辨测量中,单个 \mathrm{T}\mathrm{I}\mathrm{R}\mathrm{M} 的距离支撑长度为Q = 37[19]。非特别说明,仿真中求平均采用的方位角范围[{\theta _{{\text{min}}}},{\theta _{{\text{max}}}}][161.55^\circ ,162.75^\circ ]

    本小节固定雷达的天线极化方式,分析本文方法的有效性。仿真参数设置为:雷达和干扰机均采用垂直极化 {\boldsymbol{\varepsilon}} = {[0,1]^{\text{T}}} ,雷达参数方面,发射波形时宽为T = 81.28{\text{ ns}},发射脉冲个数为K = 4,发射信号的码长为N = 40,回波点数为M = 76,对应信号带宽B = 0.5{\text{ GHz}},占空比{D_{\text{t}}} = 1\% ;干扰机参数方面,设置ISRJ占空比为{D_{\text{J}}} = 20\% ,ISRJ转发周期为{T_{\text{J}}} = 20{\text{ ns}};目标方面,极化散射矩阵设置为[1,{\text{0}}{\text{.1}}{{\text{e}}^{{{ - {\rm{j}}\pi }}/3}};{\text{0}}{\text{.1}}{{\text{e}}^{{{ - {\rm{j}}\pi }}/3}},{{\text{e}}^{{{{\rm{j}}\pi }}/3}}],信噪比损失因子为\mu = 1{\text{ dB}},权重因子{\gamma _1} = {\gamma _2} = 100,峰值约束关系为{a_{{\text{min}}}} = {a_{{\text{max}}}} \times {10^{ - 4}},并将[{f_1},{f_2}]=[ - 0.3,0.3]离散化为L = 10份,预设收敛精度为{\eta _\varGamma }={10^{ - 7}},设置信噪比为15{\text{ dB}},信干比为 - 15{\text{ dB}}

    图1(a)图1(b)分别给出了目标函数\varGamma、信噪比损失\mu 随迭代次数的取值变化情况。可以看出,本文算法具有收敛性。图2给出了优化后的目标回波、 \mathrm{I}\mathrm{S}\mathrm{R}\mathrm{J} 的脉压结果及归一化模糊函数能量图。从图2(a)可以看出,本文方法的目标回波主瓣峰值约为 - 7{\text{ dB}},文献[7]方法的目标回波主瓣峰值约为 - 12{\text{ dB}};由图2(b)可见,本文方法的干扰峰值约为- 29{\text{ dB}},文献[7]方法的干扰峰值约为 - 24{\text{ dB}}。这表明,本文方法较好地实现了波形对目标特性的匹配和对ISRJ的抑制。对比图3(a)图3(b)可以看出,目标回波的模糊函数在给定的频移区间内保持了良好的多普勒容忍性;而ISRJ的模糊函数也实现了对给定频移区间的干扰抑制。针对算法的鲁棒性,图4给出了不同方位角区间[{\theta _{{\text{min}}}},{\theta _{{\text{max}}}}]对目标回波脉压峰值的影响,对比TIRM精确已知的情况,跨度1.2°的方位角区间[161.55^\circ ,162.75^\circ ]性能下降约2 dB、跨度3.9°的方位角区间[161.55^\circ ,165.45^\circ ]性能下降约4 dB、跨度10.0°的方位角区间[161.55^\circ , 171.55^\circ ]性能下降约4.5 dB。由此表明:先验方位角范围越大,本文所提算法的脉压增益下降越大,但鲁棒性随之增强。图5给出了不同脉冲数K和信噪比损失\mu 时,本文算法重复1000次独立实验后旁瓣峰值随信干比的变化情况。图5(a)表明,随信干比增加,旁瓣峰值呈现下降-稳中略升-下降-稳定的趋势,当信干比较大时,回波几乎仅含有目标回波。图5(b)表明,旁瓣峰值呈现单调下降至稳定的趋势,当信噪比很大时,回波几乎不含噪声,而信干比固定,因而趋于稳定。

    图 1  目标函数和信噪比损失的收敛情况
    图 2  目标回波和干扰的脉压性能比较
    图 3  目标回波和干扰的互模糊函数性能比较
    图 4  不同方位角范围的鲁棒性算法的归一化脉压峰值
    图 5  旁瓣峰值随信干比和信噪比的变化曲线

    本小节引入天线极化矢量优化,分析极化优化对目标回波和ISRJ脉压性能的影响。仿真过程中设置N = M = 80,将极化旋转角\alpha \in [ - {\pi}/2,{\pi}/2]、极化椭圆角\beta \in [ - {\pi}/4,{\pi}/4]等分为50份,步长分别为0.02{\pi}, 0.01{\pi},其他参数设置同4.1节。干扰机天线极化方式依次考虑以下几种设置:60°线极化{{\boldsymbol{\varepsilon}} _{\text{J}}} = {\left[ {\dfrac{{\sqrt 2 }}{2}{{\text{e}}^{{\text{j}}\frac{{\pi}}{3}}},\dfrac{{\sqrt 2 }}{2}{{\text{e}}^{{\text{j}}\frac{{\pi}}{3}}}} \right]^{\text{T}}}、左旋圆极化{{\boldsymbol{\varepsilon}} _{\text{J}}} = \left[ \dfrac{{\sqrt 2 }}{2}{{\text{e}}^{{\text{j}}\frac{{5{\pi}}}{6}}}, \dfrac{{\sqrt 2 }}{2}{{\text{e}}^{{\text{j}}\frac{{\pi}}{3}}} \right]^{\text{T}}、右旋圆极化{{\boldsymbol{\varepsilon}} _{\text{J}}} = {\left[ {\dfrac{{\sqrt 2 }}{2}{{\text{e}}^{ - {\text{j}}\frac{{\pi}}{6}}},\dfrac{{\sqrt 2 }}{2}{{\text{e}}^{{\text{j}}\frac{{\pi}}{3}}}} \right]^{\text{T}}}

    图6依次给出了干扰机在3种不同极化工作方式下,进行天线极化矢量优化前后的目标回波脉压归一化幅度图。可以看出,经极化矢量优化后目标回波脉压结果对比优化前旁瓣平均下降了13~19 dB。图7则给出了干扰机在不同极化工作方式下,进行天线极化矢量优化前后的ISRJ信号脉压归一化幅度图。可以看出,经极化矢量优化后目标的ISRJ信号脉压峰值对比优化前有不同程度的下降,其中在干扰机采用60°线极化时,干扰脉压峰值近似相同,整体水平却有所下降;在干扰机采用左旋圆极化和右旋圆极化时,干扰脉压后整体下降至非常低的水平(此时近似被完全滤除)。综上说明了经优化后的天线极化矢量在获得更好目标位置检测能力的同时,显著抑制了间歇采样干扰信号,进一步增强了宽带场景下的雷达探测能力。

    图 6  不同干扰机天线极化方式设置条件下目标回波脉压幅度图
    图 7  不同干扰机天线极化方式设置条件下ISRJ回波脉压幅度图

    为进一步验证本文方法在宽带全极化雷达条件下抗ISRJ的有效性,本节考虑干扰机高速运动,即设置干扰机与雷达间距离为{d_{\text{J}}} = 1100{\text{ m}},干扰机速度{v_{\text{J}}} = 30{\text{ m}}/{\text{s}};目标距离雷达d = 600{\text{ m}},目标速度v = 40{\text{ m}}/{\text{s}},其余参数同4.1节,对比本文方法与文献[7]方法在目标探测和干扰抑制方面的差异。

    图8给出了不同脉冲数K对应的回波脉压效果。根据图8(a)可以看出,在K = 2时,本文方法对目标回波有约 - 9{\text{ dB}}的脉压增益(较文献[7]方法高出约8{\text{ dB}});从图8(b)可看出在K = 4时目标回波增益较文献[7]方法高出约6 dB;从图8(c)则可看出在K = 6时目标回波增益较文献[7]方法高出约4 dB。而对于ISRJ信号,则在3种场景下都近似被完全滤除,图8结果进一步表明,本文方法相比文献[7]的目标探测性能更好,同时对ISRJ信号起到了显著的抑制效果。

    图 8  不同脉冲数条件下本文方法与文献[7]方法的脉压结果对比

    本文对宽带全极化雷达发射波形、接收滤波器和天线极化进行联合优化以实现间歇采样转发干扰的抑制。对于多分量非凸优化问题,基于交替迭代求解方法,依次对最优发射波形、接收滤波器和天线极化进行了有效求解。对比现有方法,本文方法不仅实现了发射波形-目标的相互匹配,还充分利用了目标和干扰机的极化域信息,使得脉压后显著抑制了ISRJ并保证良好的目标回波增益,同时其多普勒容限显著增强了算法对高速干扰机的适用性,对解决高分辨场景下抗间歇采样转发干扰问题具有一定的实际意义和应用价值。而下一步将重点研究 \mathrm{I}\mathrm{S}\mathrm{R}\mathrm{J} 参数不确定条件下的波形鲁棒性设计问题,以降低对先验信息的精度要求。

  • 图  1  间隙波导理论和实际模型

    图  2  典型的间隙波导传输线

    图  3  近年来所提出的几种重要的新型间隙波导非接触EBG结构

    图  4  基于间隙波导技术的新型毫米波传输线

    图  5  基于间隙波导的非接触法兰及扩展应用

    图  6  基于间隙波导技术的新型无源器件

    图  7  基于脊间隙波导传输线的无基片功率放大器

    图  8  间隙波导阵列天线

    图  9  S频段折叠小型化非接触式低PIM法兰及PIM实测结果

    图  10  基于间隙波导技术的堆叠式毫米波电路系统

    表  1  间隙波导国内外研究领域分类

    研究领域细节分类
    非接触EBG结构理论分析;新型非接触EBG;其他
    GW传输线经典GW传输线及应用;新型GW传输线及应用;过渡、互联方法
    GW的微波毫米波
    技术应用
    无源器件:非接触法兰、滤波器、耦合器、移相器、旋转关节等;有源电路:无基片有源电路;
    天线:缝隙阵列天线、GW喇叭天线、其他新型天线等;
    其他:电路封装、快速测试、3D打印、先进制造等
    下载: 导出CSV
  • [1] 徐常志, 靳一, 李立, 等. 面向6G的星地融合无线传输技术[J]. 电子与信息学报, 2021, 43(1): 28–36. doi: 10.11999/JEIT200363

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  • 收稿日期:  2021-11-18
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