Time-inversion technique based correction of complex radome radiation beam distortion

An Teng-Yuan; Ding Xiao; Wang Bing-Zhong

doi:10.7498/aps.72.20221767

Abstract

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1. 引　言
2. 理论分析
3. 计算及验证
3.1 无天线罩辐射波束指向角偏差验证
3.2 天线罩辐射波束指向角偏差缩小验证
3.3 天线罩辐射波束畸变改善论证
4. 结　论

References

Abstract

In the electromagnetic wave radiated by radome, there often occur pointing angle deviation, beam distortion and other phenomena, due to the complex electromagnetic medium composition, special contour and complex working environments. For conventional optimization methods, harsh and complex situations increase its workload, especially in the case that the specific location parameter information is unknown. In this paper, a method with time-inversion technique for correcting the radiation beam distortion of the complex radome is proposed. With the time-inversionl method, the concrete parameters of different positions for the radome and the surrounding environment information are not necessary to be determined in advance. The derivation shows that the environmental information is eliminated adaptively by the conjugate convolution operation, and it is proved by numerical operation that the signal of maximum radiation gain in target angle is time-inversion signal. Then based on the adaptive focusing properties of time-inversion electromagnetic waves, a top wedge radome and an icing working radome are taken as the case study. The equal amplitude phase shifting serves as the control group to highlight the advantages of time-reversal. In the end, the results show that the radiation beam pointing error can be reduced from ±10° to ±0.9° within ±45° scanning range for the top wedge radome in C-band. And the annihilated main beam can be converged again for the radome in the icing state. In addition, all the improvements are in a broadband range, and the robustness of the entire radome system is enhanced by increasing target angle energy caused by the increasing the directionality of the array radiation and the narrowing the 3 dB beamwidth. This paper provides an effective method of analyzing the complex radomes and radio wave propagations in complex media.

Keywords:

PACS:

04.30.-nk
42.68.ay
41.20.Jb	(Electromagnetic wave propagation; radiowave propagation)

Authors and contacts

Institute of Applied Physics, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding author: Ding Xiao, xding@uestc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 62171093).

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1. 引　言

天线罩罩体一般由天然或人工复合材料构成, 这些介质材料的损耗以及与空气介电常数的差异, 会影响罩内天线的辐射功率. 此外, 电磁波在透过特殊外形罩体时, 不同位置的介质层对应的电磁波入射角和极化角不同, 会出现不同的传输系数和插入相位延迟, 从而导致波束偏转、方向图畸变^[1,2]. 为了有效分析天线罩内外电波传播特性, 研究者们最初提出了利用多次反射级数求和的分析方法^[3]. 此后, 随着机载天线罩的发展并结合数值计算技术, 提出了射线追踪分析方法^[4-9], 如, 以几何光学为基础的射线跟踪法^[5], 基于物理光学理论的等效口径法^[6]、口径积分法^[7]、平面波谱法^[8]以及感应积分法^[9]等多种方法. 其中, 除口径积分法^[10]外, 其他方法均受到口径和罩体外形的限制, 且计算量较大. 此外, 还有矩量法^[11]以及各种基于矩量法的混合方法^[12]. 上述方法在分析和优化天线罩的过程中, 都需要预先建立罩体外形的曲面方程, 确定阵列天线单元的具体位置. 进而通过计算传输系数、插入相位延迟等参数, 对罩体进行变厚度处理^[13]或对单元性能单独调控等处理, 但这些方法往往在窄带分析上具有较好的效果^[14]. 但是, 对于特殊轮廓天线罩^[15], 或罩体上有非均匀堆积物^[16,17]时, 天线罩部分区域的曲率变化剧烈, 传统射线追踪方法分析结果误差较大. 建立复杂的模型以及引入不同算子优化的过程又会不可避免地引入大量迭代操作, 使计算量陡增. 此外, 近年来出现了大量人工电磁材料与天线罩相融合的技术, 如, 在电磁对抗中占据优势的频率选择表面(FSS)的天线罩^[18], 以及为了更好地调控电磁波而提出的智能反射表面^[19-21]. 总体而言, 亟需一种具有较强自适应性, 能应对不同尺寸的天线罩, 以及对复杂变化的罩体模型进行宽带分析的新方法.

时间反演技术最初由Fink团队应用于声学检测^[22]. 它的核心是将接收到的宽带信号做时间上的反转, 然后再发射. 由于时间反演电磁波在各类不同电磁环境下均具有时间-空间同步聚焦的电磁特性^[23], 因此, 利用时间反演的时空同步聚焦特性, 时间反演近年来和能量传输^[24]、目标追踪^[25]、自适应波束聚焦阵列^[26]以及智能表面和波束赋形等方向^[27]相结合, 进行了一系列的研究. 电子科技大学的研究者在文献[28]中利用平面电磁波照射偶极子阵列, 使用时间反演技术实现了偶极子阵列辐射方向图的自适应回溯. 更深入研究发现, 丰富的多径信息可使上述聚焦效果更加明显^[23], 且宽频带的时域信号通过时间反演会带来宽频带的聚焦效果^[29].

据此, 我们设想将时间反演技术引入到天线罩分析中, 通过相对简单的时间反演操作取代繁琐的建模迭代计算, 尤其是在罩体的具体结构参数未知、罩体轮廓复杂以及外界复杂电磁环境等情况下. 同时期望实现宽频带的辐射波束纠正和增益提升. 本文除了提出基于时间反演技术的复杂天线罩辐射波束畸变纠正的分析和优化方法外, 还建立了全波仿真模型. 通过无覆盖阵列作为对比, 在宽频带范围内验证了顶部劈尖天线罩和结冰工作天线罩对辐射波束畸变的纠正效果.

2. 理论分析

有别于天线罩的其他分析和优化方法, 时间反演技术能够充分考虑罩内天线阵各阵元间的耦合效应, 天线阵与天线罩的耦合效应, 以及外界复杂电磁环境对天线罩的影响. 这些信息被包含在天线的接收信号中, 并在对该接收信号反演并重新发送的过程中起到预处理的作用^[30].

为此, 建立图1所示的理论分析模型, 即任意天线罩覆盖任意阵列天线. 其中天线罩的曲率、外形以及所处的电磁环境未知, 下方阵列天线为N元线阵. 分析认为:

$图 1 基于时间反演的天线罩下阵列辐射方法\r\nFig. 1. Radiation method of array antenna under radome based on time reversal.$

图 1 基于时间反演的天线罩下阵列辐射方法

Fig. 1. Radiation method of array antenna under radome based on time reversal.

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第1步　从目标方向(θ_d, ϕ_d)向天线罩照射一束平面波, 该平面波的时域波形不受限制, 但工作频段需覆盖罩内阵列天线, 此时域信号为s(t).

第2步　目标方向的平面波经过复杂电磁环境以及天线罩后被阵列天线接收, 此时各阵元接收信号为y_i(t), i = 1, 2, ···, N. 因此, 阵列得到的时域信号可记为

${\boldsymbol{y}}(t) = \left[ {{y_1}(t),{y_2}(t), \cdots ,{y_N}(t)} \right] .$

(1)

由于信道信息未知, 故假设目标方向为(θ_d, ϕ_d), 此时不同阵元接收信号的信道响应为^[31-33]

$\begin{split} {{\boldsymbol{P}}_{{{r}}x}}({\theta _{\text{d}}},{\varphi _{\text{d}}},t) =\;& [ {\boldsymbol{p}}({{\boldsymbol{r}}_1},{\theta _{\text{d}}},{\varphi _{\text{d}}},t),{\boldsymbol{p}}({{\boldsymbol{r}}_2},{\theta _{\text{d}}},{\varphi _{\text{d}}},t), \cdots ,\\ &{\boldsymbol{p}}({{\boldsymbol{r}}_N},{\theta _{\text{d}}},{\varphi _{\text{d}}},t) ]^{\text{T}},\\[-10pt]\end{split}$

(2)

其中r_i表示阵元所处的空间位置. 当天线罩以及外界环境可视为线性时不变系统时, 上述接收信号可写为

${\boldsymbol{y}}(t) = s(t) * {{\boldsymbol{P}}_{rx}}{({\theta _{\text{d}}},{\varphi _{\text{d}}},t)^{\text{T}}},$

(3)

其中*代表前后两式做卷积运算.

第3步　将每个阵元所接收的信号做时间反演操作, 得到反演信号为y_i(–t), i = 1, 2, ···, N. 于是, 第2步中的接收信号y_i(t)变为

${\boldsymbol{y}}( - t) = s( - t) * {{\boldsymbol{P}}_{rx}}{({\theta _{\text{d}}},{\varphi _{\text{d}}}, - t)^{\text{T}}}.$

(4)

第4步　将所得反演信号通过对应的阵元同时发射.

假设外界环境以及罩体对阵元的辐射响应为P_tx(r_i, θ, ϕ, t), 根据天线单元的互易性以及空间的时不变性, 有P_tx = P_rx. 此时天线罩远场辐射电场可写为

${F_{tr}}(\theta ,\varphi ,t) = {\boldsymbol{y}}{( - t)^{\text{T}}} * {{\boldsymbol{P}}_{tx}}(\theta ,\varphi ,t).$

(5)

将(5)式通过傅里叶变换转换到频域进行分析, 辐射电场可重写为

$\begin{split} &{F_{tr}}(\theta ,\varphi ,\omega ) = {\left[ {{{\boldsymbol{y}}^ * }(\omega )} \right]^{\text{T}}}{{\boldsymbol{P}}_{tx}}(\theta ,\varphi ,\omega ) \\=\;& {s^ * }(\omega ){\left[ {{\boldsymbol{P}}_{rx}^*({\theta _{\text{d}}},{\varphi _{\text{d}}},\omega )} \right]^{\text{T}}}{{\boldsymbol{P}}_{tx}}(\theta ,\varphi ,\omega ).\end{split}$

(6)

可以看出, 此时天线罩的辐射仅取决于P_tx和P^*_rx的内积. 换言之, 时间反演操作能够预处理未知且复杂的电磁环境信息和阵列本征辐射信息等. 在后续的分析中可以发现, 数学上的卷积巧妙地使得这部分复杂信息在反演信号发射过程中自适应消除.

第5步　天线罩辐射波束的纠正.

对于天线罩内的阵列天线, 任意激励信号c(ω)在目标方向得到的增益可记为^[34]

$G({\theta _{\text{d}}},{\varphi _{\text{d}}},\omega ) = \frac{{{{{{\left| {F({\theta _{\text{d}}},{\varphi _{\text{d}}},\omega )} \right|}^2}} / (}{Z_0})}}{{{P_{{\text{in}}}}/(4{\text{π }})}},$

(7)

其中Z₀为自由空间波阻抗, P_in= c^T(ω)c^*(ω)为阵列的总输入功率. 假设天线罩内阵列将激励信号完全辐射, 由(7)式得

$\begin{split}& G({\theta _{\text{d}}},{\varphi _{\text{d}}},\omega ) \\ =\;& \frac{{4{\text{π }}}}{{{Z_0}}}\frac{{{c^{\text{T}}}(\omega ){{\boldsymbol{P}}_{tx}}({\theta _{\text{d}}},{\varphi _{\text{d}}},\omega ){\boldsymbol{P}}_{tx}^{\text{H}}({\theta _{\text{d}}},{\varphi _{\text{d}}},\omega ){{\boldsymbol{c}}^ * }(\omega )}}{{{{\boldsymbol{c}}^{\text{H}}}(\omega ){\boldsymbol{c}}(\omega )}}. \end{split}$

(8)

其中(·)^H表示厄密共轭. 根据厄密共轭的特性可以发现, 当且仅当 $\boldsymbol c (\omega) = \gamma^* \boldsymbol P^*_{tx} (\theta_{\rm d},\phi_{\rm d}, \omega)$ 时, 在目标方向取得最大增益G_max:

${G_{\max }}({\theta _{\text{d}}},{\varphi _{\text{d}}},\omega ) = \frac{{4{\text{π }}}}{{{Z_0}}}{\left\| {{{\boldsymbol{P}}_{tx}}({\theta _{\text{d}}},{\varphi _{\text{d}}},\omega )} \right\|^2},$

(9)

其中γ表示任意的非零复数因子; $\left\| . \right\|$ 表示L²的范数. 明显可见, 当γ= s(ω)时, 目标方向取得最大增益的阵列激励为

${{\boldsymbol{c}}_{{\text{optimal}}}}(\omega ) = {s^*}(\omega ){\boldsymbol{P}}_{rx}^*({\theta _{\text{d}}},{\varphi _{\text{d}}},\omega ).$

(10)

即当天线罩以及环境信息固定后, 发射从目标方向接收到的时间反演信号, 可使得该阵列在目标方向上得到最大增益. 这个最大增益在数值上是其他任何分析优化方法无法超过的.

通过上述分析, 得到如下结论:

1)时间反演技术可以规避传统优化中提取天线罩所带来的复杂信道和辐射源本征信息的复杂操作.

2)时间反演技术能够提高目标角度的增益, 具有将已经偏离的主波束向目标方向纠正的能力, 在一定范围内能实现精确扫描.

3)时间反演技术结合时域信号的宽带特性, 能实现宽频带的波束纠正.

3. 计算及验证

3.1 无天线罩辐射波束指向角偏差验证

为了突出覆盖天线罩对阵列辐射的影响, 首先针对无天线罩覆盖时, 阵列天线使用传统移相扫描和时间反演方法所得的阵列辐射性能进行对比. 选用文献[35]提出的宽带贴片天线为辐射源, 它的工作频率范围为5—6 GHz, 以25 mm阵元间距(对应6 GHz的0.5倍波长)排布成8元线阵, 阵列天线位于xoy平面沿x轴排布, 如图2所示.

$图 2 8元线阵\r\nFig. 2. 8-element linear array.$

图 2 8元线阵

Fig. 2. 8-element linear array.

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由于计算模型中天线阵是线阵, 因此目标方向(θ_d, ϕ_d)中ϕ_d的取值为0. 以(+30°, 0°)为目标角度, 以阵列天线中阵元2和阵元8的接收和发射为例. 各个阵元接收到从目标方向(+30°, 0°)的发射信号, 其中阵元2和阵元8接收到的信号分别为y₂(t)和y₈(t), 如图3(a)所示. 利用时间反演方法, 将各个阵元所得接收信号进行时间反转, 其中阵元2和阵元8得到的反演信号分别为y₂(–t)和y₈(–t), 如图3(b)所示.

$图 3 目标角度为(+30°, 0°)时, 阵列天线单元2和单元8的接收信号和反演信号　(a)接收信号(b)时间反演信号\r\nFig. 3. Received signal and time reversal signal of array antenna element 2 and element 8 when the target angle is (+30°, 0°): (a) The received signal; (b) the excitation signal by time reversal.$

图 3 目标角度为(+30°, 0°)时, 阵列天线单元2和单元8的接收信号和反演信号　(a)接收信号(b)时间反演信号

Fig. 3. Received signal and time reversal signal of array antenna element 2 and element 8 when the target angle is (+30°, 0°): (a) The received signal; (b) the excitation signal by time reversal.

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此外, 以目标角度(0°, 0°), (+15°, 0°), (+30°, 0°), (+45°, 0°)为例, 对比了无覆盖阵列天线传统方法与时间反演方法的阵列辐射结果, 展示于表1和表2中.

表 1 无覆盖阵列天线传统方法与时间反演方法的阵列辐射结果

Table 1. Radiation results of array antenna by traditional method and time reversal.

目标/(°)	传统方法				本文方法
	实际波束指向/(°)		目标方向增益/dBi		实际波束指向/(°)		目标方向增益/dBi
	5 GHz	6 GHz	5 GHz	6 GHz	5 GHz	6 GHz	5 GHz	6 GHz
0	0	0	13.2	11.4	0	0	13.8	14.9
+15	+14.7	+14.8	11.7	10.4	+14.8	+14.9	13.8	14.7
+30	+29.3	+29.6	13.5	14.2	+29.5	+29.7	13.6	14.2
+45	+43.1	+43.4	13.0	13.2	+43.4	+43.9	13.1	13.2

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表 2 无覆盖阵列天线传统方法与时间反演方法的阵列辐射3 dB宽度对比结果

Table 2. The 3 dB beamwidth of array antenna radiation by traditional method and time reversal.

	目标/(°)	传统方法		本文方法
	目标/(°)	5 GHz	6 GHz	5 GHz	6 GHz
3 dB波束宽度/(°)	0	15.0	12.6	14.9	12.6
	+15	15.6	13.1	15.4	13.1
	+30	17.2	14.7	17.0	14.8
	+45	20.2	17.5	20.1	17.3

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可以看出, 相较于传统等幅移相馈电, 时间反演方法对各个扫描角偏差进行了纠正, 最大纠正角度达到了0.5°. 此外, 各个目标角度的增益都有约0.1 dB的提升, 3 dB波束宽度最大减小了0.1°. 受阵列规模的限制, 通过时间反演方法得到的实际波束指向和目标指向仍然有一些差距, 但是与传统方法相对比, 其指向角偏差已有明显的改善.

3.2 天线罩辐射波束指向角偏差缩小验证

对于天线罩覆盖下的阵列天线辐射性能, 首先验证本方法对顶部劈尖天线罩辐射波束指向角偏差的缩小. 如图4所示, 阵列天线位于xoy平面沿x轴排布, 在阵列天线上方40 mm处放置一个顶部劈尖天线罩^[36]. 天线罩介质层的相对介电常数是4.3, 且上下表面之间夹角是10°, 天线罩在x轴和y轴进行大尺寸延伸以确保罩内辐射不会沿介质层边缘绕射.

$图 4 顶部劈尖天线罩计算模型示意图\r\nFig. 4. Schematic diagram of calculation model of top wedge radome.$

图 4 顶部劈尖天线罩计算模型示意图

Fig. 4. Schematic diagram of calculation model of top wedge radome.

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由于计算模型中天线阵是线阵, 因此目标方向(θ_d, ϕ_d)中ϕ_d的取值为0, 随机对两个目标方向(+45°, 0°)和–30°, 0°)进行考察.

图5(a), (c), (e)和(g)分别展示了通过传统移相扫描方式, 阵列天线辐射透过顶部劈尖天线罩后的波束指向. 图5(b), (d), (f)和(h)则分别展示通过本文所提时间反演方法, 阵列天线辐射透过顶部劈尖天线罩后的波束指向. 相较于3.1节无天线罩阵列辐射情况, 此时, 使用传统移相馈电方式, 顶部劈尖天线罩的辐射波束指向角偏差严重恶化. 在图5(a)和图5(c)计算案例中设计的目标方向是(–30°, 0°), 使用传统移相扫描波束指向最大偏差达到了11.0°. 特别地, 当目标方向是(+45°, 0°)时, 在目标方向已无明显的辐射特征, 其主瓣明显衰弱或淹没在众多旁瓣中. 而采用时间反演技术后, 天线罩辐射波束的普遍性偏差得以改善, 而且这个改善是宽带范围内的提升, 如前述的最大10°偏差被缩小到0.8°.

$图 5 时间反演和传统方法归一化辐射方向图对比(颜色条表示辐射场的相对场强(归一化模值))　(a)目标角度–30°, 5 GHz 传统相扫辐射方向图; (b) 目标角度–30°, 5 GHz 时间反演辐射方向图; (c)目标角度–30°, 6 GHz 传统相扫辐射方向图; (d) 目标角度–30°, 6 GHz 时间反演辐射方向图; (e)目标角度+45°, 5 GHz 传统相扫辐射方向图; (f) 目标角度+45°, 5 GHz 时间反演辐射方向图; (g)目标角度+45°, 6 GHz 传统相扫辐射方向图; (h) 目标角度+45°, 6 GHz 时间反演辐射方向图\r\nFig. 5. Comparison of normalized radiation pattern between time reversal and traditional methods: (a) The 5 GHz traditional phase scan radiation pattern when the target angle is –30°; (b) the 5 GHz time reversal radiation pattern when the target angle is –30°; (c) the 6 GHz traditional phase scanning radiation pattern when the target angle is –30°; (d) the 6 GHz time reversal radiation pattern when the target angle is –30°; (e) the 5 GHz traditional phase scanning radiation pattern when the target angle is +45°; (f) the 5 GHz time reversal radiation pattern when the target angle is +45°; (g) the 6 GHz traditional phase scanning radiation pattern when the target angle is +45°; (h) the 6 GHz time reversal radiation pattern when the target angle is +45°.$

图 5 时间反演和传统方法归一化辐射方向图对比(颜色条表示辐射场的相对场强(归一化模值))　(a)目标角度–30°, 5 GHz 传统相扫辐射方向图; (b) 目标角度–30°, 5 GHz 时间反演辐射方向图; (c)目标角度–30°, 6 GHz 传统相扫辐射方向图; (d) 目标角度–30°, 6 GHz 时间反演辐射方向图; (e)目标角度+45°, 5 GHz 传统相扫辐射方向图; (f) 目标角度+45°, 5 GHz 时间反演辐射方向图; (g)目标角度+45°, 6 GHz 传统相扫辐射方向图; (h) 目标角度+45°, 6 GHz 时间反演辐射方向图

Fig. 5. Comparison of normalized radiation pattern between time reversal and traditional methods: (a) The 5 GHz traditional phase scan radiation pattern when the target angle is –30°; (b) the 5 GHz time reversal radiation pattern when the target angle is –30°; (c) the 6 GHz traditional phase scanning radiation pattern when the target angle is –30°; (d) the 6 GHz time reversal radiation pattern when the target angle is –30°; (e) the 5 GHz traditional phase scanning radiation pattern when the target angle is +45°; (f) the 5 GHz time reversal radiation pattern when the target angle is +45°; (g) the 6 GHz traditional phase scanning radiation pattern when the target angle is +45°; (h) the 6 GHz time reversal radiation pattern when the target angle is +45°.

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为了全面地展示本文方法的有效性, 计算了更多的目标方向, 如表3和表4所列. 需要指出, 表3和表4还分别展示了传统移相扫描方式和本文所提方法下天线罩在目标方向的辐射增益和3 dB波束宽度. 可以发现, 本文的方法不但能够纠正天线罩辐射波束指向角偏差, 还能改善在指向角处的辐射增益, 这与表达式(9)和(10)的理论分析吻合. 从表4可以看出, 在–30°—+30°范围内, 目标方向的增益提高, 方向性变强, 同时3 dB波束宽度变窄. 在(+30°, 0°)为目标角度的情况下, 5 GHz对应的波束宽度缩减了10°, 因此利用本文方法能使得天线罩辐射具有更好的抗干扰能力.

表 3 顶部劈尖天线罩下传统方法与时间反演阵列辐射结果

Table 3. Results of array radiation by traditional method and time reversal under the top wedge radome.

目标/(°)	传统方法				本文方法
	实际波束指向/(°)		目标方向增益/dBi		实际波束指向/(°)		目标方向增益/dBi
	5 GHz	6 GHz	5 GHz	6 GHz	5 GHz	6 GHz	5 GHz	6 GHz
–45	–31.5	–31.7	8.7	9.2	–44.3	–44.2	12.3	12.9
–30	–19.0	–20.5	5.5	10.7	–29.2	–29.3	15.3	16.6
–15	–5.7	–6.1	12.8	11.4	–14.6	–14.7	16.3	17.0
0	+8.3	+8.6	13.2	11.4	+0.3	–0.2	16.8	17.2
+15	+23.7	+25.1	11.7	10.4	+14.3	+14.6	16.2	17.0
+30	+42.2	+38.7	8.4	13.2	+30.6	+29.1	13.6	15.9
+45	无较强主瓣				+42.0	+43.3	14.5	15.1

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| 显示表格

表 4 顶部劈尖天线罩下传统方法与时间反演阵列辐射3 dB波束宽度对比结果

Table 4. The 3 dB beam width of array antenna radiation by traditional method and time reversal under top wedge radome.

	目标/(°)	传统方法		本文方法
	目标/(°)	5 GHz	6 GHz	5 GHz	6 GHz
3 dB波束宽度/(°)	–45	17.1	13.9	19.5	18.8
	–30	16.5	14.5	16.3	14.1
	–15	15.6	12.8	14.9	12.8
	0	16.2	13.2	13.4	12.9
	+15	19.0	14.7	17.5	13.0
	+30	26.1	14.1	16.1	14.0
	+45	无较强主瓣		19.3	13.8

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3.3 天线罩辐射波束畸变改善论证

特殊外形轮廓的一个具体表现就是结冰状态的天线罩. 接着, 以结冰状态天线罩为例, 对天线罩辐射波束畸变改善进行论证. 如图6所示, 此时天线罩下层仍与xoy面平行, 上层模拟结冰状态, 假设上层表面以 $z = 10 \times \sin (\dfrac{{x{\text{π }}}}{{50}})$ 的函数关系波动. 天线罩在x轴和y轴进行了大尺寸延伸以确保罩内辐射不会沿介质层边缘绕射.

$图 6 表面积冰天线罩覆盖在阵列天线\r\nFig. 6. Rrray antenna under the ice on the radome surface.$

图 6 表面积冰天线罩覆盖在阵列天线

Fig. 6. Rrray antenna under the ice on the radome surface.

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图7(a)和图8(a)分别为目标方向是(±45°, 0°)时, 利用传统移相扫描方式, 结冰天线罩的辐射情况: 它们在目标方向辐射被严重削弱, 主瓣产生明显分裂, 出现了若干辐射旁瓣, 导致了天线罩辐射波束畸变. 图9(a)则展示了一个极端畸变情形, 在目标方向(0°, 0°)时, 天线罩辐射主瓣几乎消失. 图7(b)、图8(b)和图9(b)则分别给出了利用本文方法, 结冰天线罩的辐射情况. 与传统移相扫描方式相比, 使用本文方法后, 结冰天线罩的辐射畸变得到明显的改善, 它们体现在辐射主瓣重新汇聚在目标方向且在目标方向上有较高的辐射增益, 此外传统方式的旁瓣也得到有效抑制.

$图 7 目标波束指向–45°时传统方法和时间反演方法在远场的实际增益图　(a)传统方法增益图; (b)时间反演方法增益图\r\nFig. 7. Realized gain pattern of target angle –45° (linear): (a) The pattern of traditional method; (b) the pattern of time reversal.$

图 7 目标波束指向–45°时传统方法和时间反演方法在远场的实际增益图　(a)传统方法增益图; (b)时间反演方法增益图

Fig. 7. Realized gain pattern of target angle –45° (linear): (a) The pattern of traditional method; (b) the pattern of time reversal.

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$图 8 目标波束指向+45°时传统方法和时间反演方法在远场的实际增益图　(a)传统方法增益图; (b)时间反演方法增益图\r\nFig. 8. Realized gain pattern of target angle +45° (linear): (a) The pattern of traditional method; (b) the pattern of time reversal.$

图 8 目标波束指向+45°时传统方法和时间反演方法在远场的实际增益图　(a)传统方法增益图; (b)时间反演方法增益图

Fig. 8. Realized gain pattern of target angle +45° (linear): (a) The pattern of traditional method; (b) the pattern of time reversal.

下载: 全尺寸图片幻灯片

$图 9 目标波束指向0°时传统方法和时间反演方法在远场的实际增益图　(a)传统方法增益图; (b)时间反演方法增益图\r\nFig. 9. Realized gain pattern of target angle 0° (linear): (a) The pattern of traditional method; (b) the pattern of time reversal.$

图 9 目标波束指向0°时传统方法和时间反演方法在远场的实际增益图　(a)传统方法增益图; (b)时间反演方法增益图

Fig. 9. Realized gain pattern of target angle 0° (linear): (a) The pattern of traditional method; (b) the pattern of time reversal.

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4. 结　论

电磁波在复杂媒质中的传播一直是电磁场领域研究的热点和难点, 传播媒质的电磁参数, 传输信道特征往往影响着其中传播的电磁波. 本文推导时间反演电磁波传输特性, 发现反演信号在数学上的卷积巧妙地消除了媒质、信道信息, 使得不依赖传播媒质电磁参数, 传输信道特征仍旧能够获取电磁波传输特性. 进一步, 本文以解决复杂天线罩辐射波束畸变问题为案例, 提出了基于时间反演技术的复杂天线罩波束畸变纠正方法, 并对其进行计算验证.

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图 1 基于时间反演的天线罩下阵列辐射方法

Figure 1. Radiation method of array antenna under radome based on time reversal.

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图 2 8元线阵

Figure 2. 8-element linear array.

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图 3 目标角度为(+30°, 0°)时, 阵列天线单元2和单元8的接收信号和反演信号　(a)接收信号(b)时间反演信号

Figure 3. Received signal and time reversal signal of array antenna element 2 and element 8 when the target angle is (+30°, 0°): (a) The received signal; (b) the excitation signal by time reversal.

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图 4 顶部劈尖天线罩计算模型示意图

Figure 4. Schematic diagram of calculation model of top wedge radome.

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Figure 5. Comparison of normalized radiation pattern between time reversal and traditional methods: (a) The 5 GHz traditional phase scan radiation pattern when the target angle is –30°; (b) the 5 GHz time reversal radiation pattern when the target angle is –30°; (c) the 6 GHz traditional phase scanning radiation pattern when the target angle is –30°; (d) the 6 GHz time reversal radiation pattern when the target angle is –30°; (e) the 5 GHz traditional phase scanning radiation pattern when the target angle is +45°; (f) the 5 GHz time reversal radiation pattern when the target angle is +45°; (g) the 6 GHz traditional phase scanning radiation pattern when the target angle is +45°; (h) the 6 GHz time reversal radiation pattern when the target angle is +45°.

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图 6 表面积冰天线罩覆盖在阵列天线

Figure 6. Rrray antenna under the ice on the radome surface.

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图 7 目标波束指向–45°时传统方法和时间反演方法在远场的实际增益图　(a)传统方法增益图; (b)时间反演方法增益图

Figure 7. Realized gain pattern of target angle –45° (linear): (a) The pattern of traditional method; (b) the pattern of time reversal.

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图 8 目标波束指向+45°时传统方法和时间反演方法在远场的实际增益图　(a)传统方法增益图; (b)时间反演方法增益图

Figure 8. Realized gain pattern of target angle +45° (linear): (a) The pattern of traditional method; (b) the pattern of time reversal.

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图 9 目标波束指向0°时传统方法和时间反演方法在远场的实际增益图　(a)传统方法增益图; (b)时间反演方法增益图

Figure 9. Realized gain pattern of target angle 0° (linear): (a) The pattern of traditional method; (b) the pattern of time reversal.

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表 1 无覆盖阵列天线传统方法与时间反演方法的阵列辐射结果

Table 1. Radiation results of array antenna by traditional method and time reversal.

目标/(°)	传统方法				本文方法
	实际波束指向/(°)		目标方向增益/dBi		实际波束指向/(°)		目标方向增益/dBi
	5 GHz	6 GHz	5 GHz	6 GHz	5 GHz	6 GHz	5 GHz	6 GHz
0	0	0	13.2	11.4	0	0	13.8	14.9
+15	+14.7	+14.8	11.7	10.4	+14.8	+14.9	13.8	14.7
+30	+29.3	+29.6	13.5	14.2	+29.5	+29.7	13.6	14.2
+45	+43.1	+43.4	13.0	13.2	+43.4	+43.9	13.1	13.2

DownLoad: CSV

表 2 无覆盖阵列天线传统方法与时间反演方法的阵列辐射3 dB宽度对比结果

Table 2. The 3 dB beamwidth of array antenna radiation by traditional method and time reversal.

	目标/(°)	传统方法		本文方法
	目标/(°)	5 GHz	6 GHz	5 GHz	6 GHz
3 dB波束宽度/(°)	0	15.0	12.6	14.9	12.6
	+15	15.6	13.1	15.4	13.1
	+30	17.2	14.7	17.0	14.8
	+45	20.2	17.5	20.1	17.3

DownLoad: CSV

表 3 顶部劈尖天线罩下传统方法与时间反演阵列辐射结果

Table 3. Results of array radiation by traditional method and time reversal under the top wedge radome.

目标/(°)	传统方法				本文方法
	实际波束指向/(°)		目标方向增益/dBi		实际波束指向/(°)		目标方向增益/dBi
	5 GHz	6 GHz	5 GHz	6 GHz	5 GHz	6 GHz	5 GHz	6 GHz
–45	–31.5	–31.7	8.7	9.2	–44.3	–44.2	12.3	12.9
–30	–19.0	–20.5	5.5	10.7	–29.2	–29.3	15.3	16.6
–15	–5.7	–6.1	12.8	11.4	–14.6	–14.7	16.3	17.0
0	+8.3	+8.6	13.2	11.4	+0.3	–0.2	16.8	17.2
+15	+23.7	+25.1	11.7	10.4	+14.3	+14.6	16.2	17.0
+30	+42.2	+38.7	8.4	13.2	+30.6	+29.1	13.6	15.9
+45	无较强主瓣				+42.0	+43.3	14.5	15.1

DownLoad: CSV

表 4 顶部劈尖天线罩下传统方法与时间反演阵列辐射3 dB波束宽度对比结果

Table 4. The 3 dB beam width of array antenna radiation by traditional method and time reversal under top wedge radome.

	目标/(°)	传统方法		本文方法
	目标/(°)	5 GHz	6 GHz	5 GHz	6 GHz
3 dB波束宽度/(°)	–45	17.1	13.9	19.5	18.8
	–30	16.5	14.5	16.3	14.1
	–15	15.6	12.8	14.9	12.8
	0	16.2	13.2	13.4	12.9
	+15	19.0	14.7	17.5	13.0
	+30	26.1	14.1	16.1	14.0
	+45	无较强主瓣		19.3	13.8

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Vol. 72, Issue 3 - 2023-02-05

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