复杂动态海面与目标电磁散射及回波仿真研究现状与展望

郭立新; 魏仪文

doi:10.12000/JR22202

复杂动态海面与目标电磁散射及回波仿真研究现状与展望

DOI: 10.12000/JR22202

郭立新^,,
魏仪文^,

西安电子科技大学物理学院西安 710071

基金项目: 国家自然科学基金(62231021, U21A20457, 61871457)

详细信息

作者简介:
郭立新，博士，教授，主要研究方向为雷达、通信环境电波传播与散射和目标光电特性理论及应用

魏仪文，博士，副教授，主要研究方向为复杂超电大地海环境散射特性、回波仿真及SAR成像

通讯作者:
郭立新 lxguo@xidian.edu.cn

魏仪文 ywwei@xidian.edu.cn

责任主编：许小剑 Corresponding Editor: XU Xiaojian
中图分类号: O45
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出版历程
- 收稿日期: 2022-10-10
- 修回日期: 2023-01-13
- 网络出版日期: 2023-02-22
- 刊出日期: 2023-02-28

Status and Prospects of Electromagnetic Scattering Echoes Simulation from Complex Dynamic Sea Surfaces and Targets

GUO Lixin^,,
WEI Yiwen^,

School of Physics, Xidian University, Xi’an 710071, China

Funds: The National Natural Science Foundation of China (62231021, U21A20457, 61871457)

More Information

Corresponding author: GUO Lixin, lxguo@xidian.edu.cn; WEI Yiwen, ywwei@xidian.edu.cn

摘要

摘要: 海洋表面是一种高度不规则和时空不重复的复杂动态体系。海杂波是雷达电磁信号照射到海面产生的大量散射体回波的叠加，受风力、洋流、海浪等的影响呈现非均匀性和非平稳性。海杂波信号对海上目标的探测具有一定的干扰作用，尤其是高海情条件下，海浪起伏更加剧烈，目标信号极易淹没在强海杂波信号中，严重限制着雷达对海上目标的检测能力。海杂波及目标电磁散射特性研究是提升复杂海洋环境下目标检测能力的基础，以电磁波与实际复杂动态海面及目标电磁散射机理为基础，形成实际海洋环境下目标回波数据，对海杂波及目标雷达回波特征分析，实测数据集的补充，均存在重大意义。为了让更多相关研究者获得基于物理机理的复杂海环境与目标回波仿真方法近些年的发展和未来趋势，该文总结了回波仿真的3类方法，并针对海面与目标仿真场景特点，分析了3类方法的优劣和适应性，给出了部分仿真结果；还介绍了一些基于实测的回波数据集，可方便学者对回波特性进行分析；最后对复杂海面与目标回波仿真方法和特性研究的发展趋势进行了展望。
- 电磁散射 /
- 海杂波 /
- 海面回波分析 /
- 合成孔径雷达(SAR)成像 /
- 目标识别
Abstract: The ocean surface is a complicated dynamic system with considerable irregularity and nonrepetition in space and time. Sea clutter is the superposition of a large number of scatterer echoes generated by the radar electromagnetic signal irradiated to the sea surface, which is affected by wind, currents, waves, etc. and shows nonuniformity and nonsmoothness. The sea clutter signal has a certain interference effect on the detection of sea targets, especially under high sea conditions when the waves are furious, and the target signal is readily drowned out by the strong sea clutter signal, severely limiting the radar’s detection capability on sea targets. The investigation of sea clutter and target electromagnetic scattering properties serves as the foundation for improving the target detection capability in difficult marine environments. The formation of target echo data in the actual marine environment is of great significance for the analysis of sea clutter and target radar echo characteristics, as well as the supplementation of the actual measurement data set based on electromagnetic waves and the actual complex dynamic sea surface and target electromagnetic scattering mechanism. This study summarizes three key categories of echo simulation methods, analyzes the benefits, disadvantages, and adaptability of several categories of methods for the characteristics of the sea surface and target simulation scenarios, and provides some simulation results in order to make recent advancements and future trends of physics-based complex sea environment and target echo simulation methods more accessible to relevant researchers. It also introduces some echo datasets based on real measurements, which can facilitate scholars’ analysis of echo characteristics. Lastly, the trend toward developing complex sea surface and target echo simulation methods and characteristics for research is presented.
- EM scattering /
- Sea clutter /
- Sea echo analysis /
- SAR imaging /
- Target detection and recognition

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1. 引言

由于脉冲雷达发射的大功率信号在城市环境下容易干扰电台等其他通讯设备，可以借助通信信号来探测目标。近年来出现的多载波调制(Multi-Carrier Modulation, MCM)技术^[1]引起了人们的关注，由此发展而来的正交频分复用(Orthogonal Frequency Division Multiplex, OFDM)^[2]技术采用多路正交子载波进行信号调制，具有频率分集和波形分集的潜力，在通信、雷达一体化的发展背景下有着重要的研究价值。

相位编码OFDM信号具有多普勒高分辨力，用于雷达动目标检测时可以更精确地估计目标速度。不同的相位编码信号具有不同的自相关特性。霍夫曼编码可以降低信号自相关函数的整体旁瓣水平，但其包络峰均比(Peak-to-Mean Envelope Power Ratio, PMEPR)明显增大^[3]。研究表明，barker码序列具有较好的综合性能^[4]，本文将以13位barker码作为相位编码序列。

最近10年，国内外在OFDM信号特性与波形设计上取得了较好的研究成果^[5–7]，因此OFDM雷达的信号处理问题受到了研究者的关注。张卫等人^[8]利用Keystone变换在信号子载波域、快时间域和慢时间域进行联合解耦合处理，解决了目标的跨距离-多普勒单元走动问题，进而可估计出匀速运动下的多目标参数信息，但计算量较大；Lellouch等人^[9]利用回波与发射信号的载频相位信息得到了点目标距离及径向速度估计，但要求目标在一个距离门内运动，即不发生越距离单元走动现象。除此以外，还需进一步研究OFDM雷达回波处理中面临的一些特殊问题，如速度补偿和多普勒解模糊。

在信号处理领域，最大似然估计是一种渐进有效估计量，但是对于多测量的非线性模型而言其计算量较大，不利于实际应用。为了提高计算效率，本文借鉴文献[10]中MIMO雷达信号处理的思路，结合OFDM信号多载波正交结构的特点，对信号进行通道分离，形成多通道信号。通过相关处理得到不同子载波上的距离像；利用Keystone变换进行速度补偿并解多普勒模糊，对同一载波的相同距离单元进行脉冲多普勒处理，得到每个子载波对应的多普勒频谱；进一步在子载波域作相参积累，得到距离-多普勒2维谱。通过谱峰搜索和CLEAN技术^[11]的运用，从中提取出峰值位置对应的时延和多普勒参数。将其作为初值，结合观测数据的似然函数，利用牛顿迭代法获得更精确的参数估计，本文称之为近似最大似然估计。近似最大似然估计量可构成复合假设检验的重要环节，提升检测器的目标检测性能。论文组织结构如下：第2节给出了相位编码OFDM信号的回波模型；第3节给出了目标距离和速度参数的最大似然估计模型；为了提高目标运动参数估计的运算效率，第4节提出一种基于通道分离的近似最大似然估计算法；第5节利用仿真实验验证了算法的性能；第6节是总结。

2. 相位编码OFDM信号模型

设雷达发射相位编码OFDM信号为：

${s_{\rm T}\, }(t) = {{\rm{e}}^{{\,\rm{j2{{π}} }}{f_{\!\rm c}}t}}\sum\limits_{n = 0}^{N - 1} {u(t - n{T_{\rm r}}} ){\rm{rect}}\left( \frac{{t - n{T_{\rm r}}}}{{{T_{\rm r}}}}\right)$

(1)

其中， ${\rm{rect}}(t) = \left\{ \begin{array}{l}1,\;\; 0 \le t \le 1\\0,\;\; {\rm{else}}\end{array} \right.$ 表示窗函数， ${f\!_{\rm c}}$ 为雷达信号的工作频率，N是脉冲个数， ${T_{\rm r}}$ 是脉冲重复周期， $u(t)$ 为相位编码OFDM信号的复包络：

$u(t) = \sum\limits_{k = 0}^{K - 1} {\sum\limits_{m = 0}^{M - 1} {{a_{k,m}}} } {{\rm{e}}^{{\,\rm{j2{{π}} }}k\Delta ft}} \;{\rm{rect}}\left(\frac{{t - m{t_{\rm c}}}}{{{t_{\rm c}}}}\right)$

(2)

其中，K是载波个数，第k个子载波上的相位编码序列 ${a_{k,m}}$ 由M个码元组成， ${t_{\rm c}}$ 为码元宽度，B是信号总带宽，为了满足子载波间的正交性，子载波间隔 $\Delta f = B/K = 1/{t_{\rm c}}$ 。

对目标散射的回波进行下变频处理，可获得相应的OFDM基带信号：

${s_{\rm r}}(t) = {A_0}{{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}{f\!_{\rm c}}t}}{s_{\rm T}\,}(t - \tau )$

(3)

其中， ${A_0}$ 为目标散射强度， $\tau = \displaystyle\frac{{2(R - vt)}}{c} =$ ${\tau _0} \!-\! \displaystyle\frac{{2vt}}{c}$ 是匀速运动目标对应于t 时刻的时延。 ${\tau _0}{\rm{ = }}\displaystyle\frac{{2R}}{c}$ 表示 $t = 0$ 时刻的目标距离时延， $v$ 是目标的径向速度。若满足条件 $\displaystyle\frac{{2vt}}{c} \ll {t_{\rm c}}$ ，则式(3)可以简化为：

$\begin{align} {s_{\rm r}}(t) \approx & \sum\limits_{n = 0}^{N - 1} \sum\limits_{k = 0}^{K - 1} \sum\limits_{m = 0}^{M - 1} {{A_0}{a_{k,m}}{\rm{rect}}\left(\frac{{t - n{T_{\rm r}} - {\tau _0}}}{{{T_{\rm r}}}}\right)}\\ & \cdot {\rm{rect}}\left( \frac{{t - n{T_{\rm r}} - {\tau _0} - m{t_{\rm c}}}}{{{t_{\rm c}}}}\right){{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}({f_{\rm c}} + k\Delta f){\tau _0}}} \\ &\cdot {{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}k\Delta ft}}\,{{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}({f_{\rm d}} + {f_{{\rm d}k}})t}}\,{{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}k\Delta fn{T_{\rm r}}}} \end{align}$

(4)

其中，子载波间的多普勒频差 ${f_{{\rm d}k}} = \displaystyle\frac{{2vk}}{c}\Delta f$ 。记全时间 $t = n{T_{\rm r}} + \tilde t$ ，其中快时间 $\tilde t \in [0,{T_{\rm r}})$ ，则式(4)表示为：

$\begin{align} {s_{\rm r}}(\tilde t,n) =& \sum\limits_{k = 0}^{K - 1} \sum\limits_{m = 0}^{M - 1} {A_0}{a_{k,m}} {\rm{rect}}\left(\frac{{\tilde t - {\tau _0}}}{{{T_{\rm r}}}}\right)\\ & \cdot{\rm{rect}}\left( \frac{{\tilde t - {\tau _0} - m{t_{\rm c}}}}{{{t_{\rm c}}}}\right){{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}({f_{\rm c}} + k\Delta f){\tau _0}}}\\ & \cdot {{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}k\Delta f\tilde t} \;{{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}({f_{\rm d}} + {f_{{\rm d}k}}) (\tilde t + n{T_{\rm r}})}} \end{align}$

(5)

其中，第2个指数项表示不同子载波的回波信号具有不同的频率偏移；由第3个指数项可以看出，子载波分别与慢时间和快时间相耦合。

在加性高斯白噪声背景下，观测信号可以表示为：

$y(\tilde t,n) = {s_{\rm r}}(\tilde t,n) + w(\tilde t,n)$

(6)

其中， ${\rm{E}}\left( {w(\tilde t,n)} \right) = 0$ , ${\rm{Var}}\left( {w(\tilde t,n)} \right) = {\sigma ^2}$ 。

3. 最大似然估计

针对式(6)在快时间域采样，采样时刻为 $\tilde t = m{t_{\rm c}} + p{T_{\rm s}}$ ，其中， ${T_{\rm s}} = \displaystyle\frac{1}{{K\Delta f}}$ , $p \in [0,K - 1]$ , $m \in [0,M - 1]$ 。由于 ${f_{{\rm d}k}}\tilde t \ll 1$ ，式(5)进一步化简

$\begin{align} {s_{\rm r}}(p,m,n) =& \sum\limits_{k = 0}^{K - 1} {A_0}{a_{k,m}}{\rm{rect}}\left(\frac{{m{t_{\rm c}} + p{T_{\rm s}} - {\tau _0}}}{{{T_{\rm r}}}}\right)\\ & \cdot {\rm{rect}}\left(\frac{{p{T_{\rm s}} - {\tau _0}}}{{{t_{\rm c}}}}\right){{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}({f_{\rm c}} + k\Delta f){\tau _0}}} \\ & \cdot {{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}({f\!_{\rm d}} + k\Delta f) (m{t_{\rm c}} + p{T_{\rm s}})}} {{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}({f\!_{\rm d}} + {f\!_{{\rm d}k}})n{T_{\rm r}}}} \end{align}$

(7)

令 $A = {A_0}{{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}{f_{\rm c}}{\tau _0}}}$ ，则采样信号为：

${{Y}} = A{{S}} + {{W}}$

(8)

其中， ${{S}} = {[{{{s}}_0},·\!·\!·\!,{{{s}}_{N - 1}}]^{\rm T} }$ , ${{Y}} = {[{{{y}}_0},·\!·\!·\!,{{{y}}_{N - 1}}]^{\rm T}}$ ${{{y}}_n} = {\left[y({\tilde t_0},n),·\!·\!·\!,\,y({\tilde t_{MK - 1}},n)\right]^{\rm T}\ }$ ${{{s}}_n} = \displaystyle\sum\limits_{k = 0}^{K - 1} {a_{k,m}}$ ${{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} (}}{f_{\rm d}} + {f_{{\rm d}k}})n{T_{\rm r}}}}$ 　　 $\cdot{{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}k\Delta f{\tau _0}}}\left[{{\rm{e}}^{{\rm{j}}2{\rm{{{π}} }}({f_{\rm d}} + k\Delta f){{\tilde t}_0}}}\right.,·\!·\!·\!,$ $\left.{{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}({f_{\rm d}} + k\Delta f){{\tilde t}_{MK - 1}}}}\right]^{\rm T}$

记待估参数向量 ${u} = {[A,v,R]^{\rm T}}$ ，噪声的协方差矩阵R=σ²I，则观测数据Y对应的似然函数为：

$p({{Y}}\left| {{u}} \right.) = \prod\limits_{n = 0}^{N - 1} {\frac{1}{{{{\rm{{{π}} }}^{MK}}}}} {\left| {{R}} \right|^{ - 1}} {{\rm{e}}^{{\rm{ - }}{{({{{y}}_n} - A{{{s}}_n})}^{\rm H}}{{{R}}^{ - 1}}({{{y}}_n} - A{{{s}}_n})}}$

(9)

式(8)是关于A的条件线性模型，其最大似然估计为：

$\hat A = \sum\limits_{n = 0}^{N - 1} {{{s}}_n^{\rm H}{{{R}}^{ - 1}}{{{y}}_n}} {\Biggr/} \sum\limits_{n = 0}^{N - 1} {{{s}}_n^{\rm H}{{{R}}^{ - 1}}{{{s}}_n}}$

(10)

将其代入式(9)，则距离和速度参数的最大似然估计为：

$\begin{align} [\hat R,\hat v] =& \mathop {\arg \min }\limits_{[R,v]} \sum\limits_{n = 0}^{N - 1} {{{\left({{{y}}_n} - \hat A{{{s}}_n}\right)}^{\rm H}}} {{{R}}^{ - 1}}\left({{{y}}_n} - \hat A{{{s}}_n}\right)\\ =& \mathop {\arg \max }\limits_{[R,v]} {{{{\left| {\sum\limits_{n = 0}^{N - 1} {{{s}}_n^{\rm H}{{{R}}^{ - 1}}{{{y}}_n}} } \right|}^2}} \mathord{\left/ {\vphantom {{{{\left| {\sum\limits_{n = 0}^{N - 1} {{{s}}_n^H{{{R}}^{ - 1}}{{{y}}_n}} } \right|}^2}} {\sum\limits_{n = 0}^{N - 1} {{{s}}_n^{\rm H}{{{R}}^{ - 1}}{{{s}}_n}} }}} \right. } {\sum\limits_{n = 0}^{N - 1} {{{s}}_n^{\rm H}{{{R}}^{ - 1}}{{{s}}_n}} }}\\ = &\! {({\sigma ^2}KN)^{ - 1}}\! \mathop {\arg \max }\limits_{[R,v]} \Biggr| \!{\sum\limits_{n = 0}^{N - 1} {\sum\limits_{p = 0}^{K - 1} {\sum\limits_{m = 0}^{M - 1} {\sum\limits_{k = 0}^{K - 1}\! {y(p,m,n)} } } } } \\ & \cdot a_{k,m}^*{{\rm{e}}^{{\,\rm{j}}2{{π}}k\Delta f{\tau _0}}} {{\rm{e}}^{{\rm{ - j}}2{{π}}({f_{\rm d}} + k\Delta f) (m{t_{\rm c}} + p{T_{\rm s}})}} \\ & \cdot {{\rm{e}}^{{\rm{ - j}}2{{π}}({f_{\rm d}} + {f_{{\rm d}k}})n{T_{\rm r}}}} \Biggr|^{2} \end{align}$

(11)

针对该模型，通过由粗到精的网格搜索可以得到参数的估计值。记速度搜索范围为 $[ - {v_{\max }},{v_{\max }}]$ ，距离搜索范围为 $[0,{R_{\max }}]$ ，则搜索次数对应为 $U = {\rm{ceil}}\left( {2{v_{\max }}/\Delta v} \right)+ 1$ 和 $V = {\rm{ceil}}\left( {{R_{\max }}/\Delta R} \right)+ 1$ 。其中， ${\rm{ceil}}(x)$ 表示不小于x 的最小整数， $\Delta v$ 和 $\Delta R$ 表示搜索步长。算法计算复杂度为 $O\left( {UVKN{{\log }_2}(KN)} \right)$ 。

令 $\displaystyle\sum\nolimits_{k = 0}^{K - 1} {|{a_{k,m}}} {|^2} = 1$ ，由文献[12]可知，待估参数的Cramer-Rao下限为：

$\begin{align} {\rm{CRLB}}(v) =& {{{c^{\,2}}{\sigma ^2}N} \mathord{\left/ {\vphantom {{{c^2}{\sigma ^2}N} {\left( {32{{({{{π} }}{f_{\rm c}}{T_{\rm r}}{A_0})}^2}} \right.}}} \right.} {\left( {32{{({{{π} }}{f_{\rm c}}{T_{\rm r}}{A_0})}^2}} \right.}}\cdot \Bigr[{N^2}(N \!-\! 1)\\ & \left.\left.(2N \!-\! 1)/6 \!-\! {N^2}{{(N \!-\! 1)}^2}/4\right] \right)\quad\quad\quad\quad\ \end{align}$

(12)

${\rm{CRLB}}(R) = 3{c^2}{\sigma ^2}\Bigr/\left( {8{{({\rm{{{π}} }}\Delta f{A_0})}^2} N\left({K^2} - 1\right)} \right)$

(13)

4. 基于通道分离的近似最大似然估计

直接利用式(11)求最大似然估计时计算量较大，在此考虑提高运算效率的参数估计方法。式(11)中相位项 ${{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}{f_{{\rm d}k}}n{T_{\rm r}}}}$ 和 ${{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}k\Delta f(m{t_{\rm c}} + p{T_{\rm s}})}}$ 的子载波k分别与慢时间和快时间相耦合。针对不同的子载波，多脉冲联合处理时目标将在距离单元和多普勒单元上走动。鉴于此，文献[8]利用Keystone变换在信号子载波域、快时间域和慢时间域进行联合解耦合处理，解决了目标的跨距离多普勒单元走动问题，计算量约为 $3{K^3}N{\log _2}(KN)$ 。事实上，式(11)中的相位项 ${{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}k\Delta fp{T_{\rm s}}}}$ 体现了不同子载波的回波信号具有不同的频率偏移，因此可以将多载波正交结构的OFDM雷达信号进行分离，通过多通道接收的方式增大距离分辨单元，避免目标的跨距离单元走动和3维Keystone变换。当 $\left| {{f_{\rm d}} + {f_{{\rm d}k}}} \right| < {{\Delta f}}/{2}$ 时，对式(5)进行通道分离，即用参考信号 ${{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}k\Delta f\tilde t}}$ 与回波混频并经过低通滤波处理，得到各子载波通道上的信号

$\begin{align} x(\tilde t,n,k) =& \sum\limits_{m = 0}^{M - 1} {A_0}{a_{k,m}}{\rm{rect}}\left(\frac{{\tilde t - {\tau _0}}}{{{T_r}}}\right)\\ & \cdot {\rm{rect}}\left( \frac{{\tilde t - {\tau _0} - m{t_c}}}{{{t_{\rm c}}}}\right) {{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}({f_{\rm c}} + k\Delta f){\tau _0}}}\\ & \cdot {{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}{f_{\rm d}}\tilde t}} {{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}({f_{\rm d}} + {f_{{\rm d}k}})n{T_{\rm r}}}} \end{align}$

(14)

其中，快时间域的采样时刻 $\tilde t = m{t_{\rm c}} + p{T_{\rm s}}$ 。

用相位编码信号作为参考对式(14)作相关处理，得到第i个距离单元上的信号

$\begin{align} {z_k}(\tilde t,n,i) = & {\sum\limits_{m,l = 0}^{M - 1} {{A_0}{a_{k,m}}} a_{k,l}^*{\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{{T_{\rm r}} - \left| {{\tau _0} - i{t_{\rm c}}} \right|}}} \right)}\\ & \cdot {{\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{\tilde t - \left| {{\tau _0} - \left( {i + l - m} \right){t_{\rm c}}} \right|}}} \right)}\\ {} & { \cdot {{\rm{e}}^{{\rm{ - j}}2{{π}} ({f_{\rm c}} + k\Delta f){\tau _0}}}{{\rm{e}}^{{\,\rm{j}}2{{π}} {f_{\rm d}}\tilde t}}{{\rm{e}}^{{\,\rm{j}}2{{π}} ({f_{\rm d}} + {f_{{\rm d}k}})n{T_{\rm r}}}}} \end{align}$

(15)

此时，信号的距离分辨单元 $\Delta R =c/(2\Delta f)$ 相对较大，目标不易产生跨距离单元走动。当最大多普勒频差小于多普勒分辨单元，即 $(({2v})/{c})(K - 1)\Delta f <$ ${1}/(N{T_{\rm r}})$ 时，子载波和慢时间之间的耦合可以忽略，本文称之为低速运动，否则，称之为高速运动。此时，可利用Keystone变换消除子载波k与慢时间n之间的耦合，即 $({f_{\rm d}} + {f_{{\rm d}k}})n = {f_{\rm d}}h$ ，实现多普勒维对齐。解耦合后的信号

$\begin{align} {{g_k}(\tilde t,h,i) = }&{{z_k}\left(\tilde t,\frac{{{f_{\rm c}}}}{{{f_{\rm c}} + k\Delta f}}h,i\right)}\\ \approx &{\sum\limits_{m,l = 0}^{M - 1} {{A_0}{a_{k,m}}} a_{k,l}^*{\,\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{{T_{\rm r}} - \left| {{\tau _0} - i{t_{\rm c}}} \right|}}} \right)}\\ {}&{ \cdot {\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{\tilde t - \left| {{\tau _0} - \left( {i + l - m} \right){t_{\rm c}}} \right|}}} \right)}\\ {}&{ \cdot {{\rm{e}}^{{\rm{ - j}}2{{π}} ({f_{\rm c}} + k\Delta f){\tau _0}}}{{\rm{e}}^{{\,\rm{j}}2{{π}} {f_{\rm d}}\tilde t}}{{\rm{e}}^{{\,\rm{j}}2{{π}} {f_{\rm d}}h{T_{\rm r}}}}} \end{align}$

(16)

经Keystone变换后的信号在慢时间域可能出现多普勒速度模糊现象( ${f_{\rm d}} = {\tilde f_{\rm d}} + r/{T_{\rm r}}$ ，其中 $\left| {{{\tilde f}_{\rm d}}} \right| < 1/(2{T_{\rm r}})$ ，折叠因子 $r \in \{ - 8, - 7, ·\!·\!·\! ,7,8\}$ )，则式(16)改为：

$\begin{align} {{g_k}\left( {\tilde t,h,i} \right) \approx }&{\sum\limits_{m,l = 0}^{M - 1} {{A_0}{a_{k,m}}} a_{k,l}^*{\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{{T_{\rm r}} - \left| {{\tau _0} - i{t_{\rm c}}} \right|}}} \right)}\\ {}&{ \cdot {\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{\tilde t - \left| {{\tau _0} - \left( {i + l - m} \right){t_{\rm c}}} \right|}}} \right)}\\ {}&{ \cdot {{\rm{e}}^{{\rm{ - j}}2{{π}} ({f_{\rm c}} + k\Delta f){\tau _0}}}{{\rm{e}}^{{\,\rm{j}}2{{π}} {f_{\rm d}}\tilde t}}{{\rm{e}}^{{\rm{j}}2{{π}} {{\tilde f}_{\rm d}}h{T_{\rm r}}}}}\\ {}& \cdot {{\rm{e}}^{{\,\rm{j}}2{{π}} r \displaystyle\scriptsize\frac{{{f_{\rm c}}}}{{{f_{\rm c}} + k\Delta f}}h}} \end{align}$

(17)

经过折叠因子补偿后的信号

${f_k}(\tilde t,h,i) = {g_k}(\tilde t,h,i) {{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}r \displaystyle\scriptsize\frac{{{f_{\rm c}}}}{{{f_{\rm c}} + k\Delta f}}h}}$

(18)

对式(18)进行脉冲多普勒处理，即关于慢时间作相参积累，可得第k个子载波上的多普勒频谱

$\begin{align} {{F_k}(\tilde t,u,i) = }&{\sum\limits_{m,l = 0}^{M - 1} {{A_0}{a_{k,m}}} a_{k,l}^*{\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{{T_{\rm r}} - \left| {{\tau _0} - i{t_{\rm c}}} \right|}}} \right)}\\ &{ \cdot {\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{\tilde t - \left| {{\tau _0} - \left( {i + l - m} \right){t_{\rm c}}} \right|}}} \right)}\\ & \cdot {\frac{{{\rm{sin}}({{π}} s)}}{{{\rm{sin}}({{π}} s/N)}}{{\rm{e}}^{{\,\rm{j}}{{π}} \displaystyle\scriptsize\frac{{N - 1}}{N}s}}{{\rm{e}}^{{\rm{ - j}}2{{π}} ({f_{\rm c}} + k\Delta f){\tau _0}}}}\\ & \cdot{{\rm{e}}^{{\,\rm{j}}2{{π}} {f_{\rm d}}\tilde t}} \end{align}$

(19)

其中， $s = u - {\tilde f_{\rm d}}N{T_{\rm r}}$ , $u \in [0,N - 1]$ 。

进一步，关于k作相参积累可得距离-多普勒谱：

$\begin{align} {F(\tilde t,u,i) = }&{\sum\limits_{m,l = 0}^{M - 1} {{A_0}{a_{k,m}}} a_{k,l}^*{\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{{T_{\rm r}} - \left| {{\tau _0} - i{t_{\rm c}}} \right|}}} \right)}\\ {}& \cdot {{\rm{rect}}\left( {\frac{{\tilde t - {\tau _0}}}{{\tilde t - \left| {{\tau _0} - \left( {i + l - m} \right){t_{\rm c}}} \right|}}} \right)}\\ &\cdot {\frac{{{\rm{sin}}({{π}} s)}}{{{\rm{sin}}({{π}} s/N)}}\frac{{{\rm{sin}}({{π}} p)}}{{{\rm{sin}}({{π}} p/K)}}}\\ &{ \cdot {{\rm{e}}^{{\,\rm{j}}{{π}} \displaystyle\scriptsize\frac{{N - 1}}{N}s}}{{\rm{e}}^{{\,\rm{j}}{{π}} \displaystyle\scriptsize\frac{{K - 1}}{K}p}}{{\rm{e}}^{{\rm{ - j}}2{{π}} {f_{\rm c}}{\tau _0}}}{{\rm{e}}^{{\,\rm{j}}2{{π}} {f_{\rm d}}\tilde t}}} \end{align}$

(20)

其中， $p = q + K\Delta f{\tau _0}$ , $q \in [0,K - 1]$ 。

上述基于通道分离和Keystone相结合的方法是对式(11)模型的简化处理。为了进一步提高算法的估计精度，将得到的参数值作为初值，根据式(11)进行牛顿迭代，得到近似最大似然估计量。算法计算量约为 $KN{\log _2}(KN) \!+\! N{\log _2}N \!+\! 2K{\log _2}K \!+\! {K^2}N$ 。

上述模型均是以单目标为例进行讨论的。在多目标情况，可以利用CFAR检测器在距离-多普勒谱域进行谱峰搜索，根据最大峰值对应的参数估计值重构相应的子信号

$b(\tilde t,n) = \sum\limits_{k = 0}^{K - 1} {{{\rm{e}}^{{\,\rm{j}}2{\rm{{{π}} }}k\Delta f{{\hat \tau }_0}}}{{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}({{\hat f}_{\rm d}} + k\Delta f)\tilde t}}{{\rm{e}}^{{\rm{ - j}}2{\rm{{{π}} }}({{\hat f}_{\rm d}} + {{\hat f}_{{\rm d}k}})n{T_{\rm r}}}}}$

(21)

利用CLEAN技术从原信号中减去重构的子信号，然后对剩余信号继续上述的操作，直到CFAR检测不出峰值为止。算法处理流程如图1所示。

图 1 算法处理流程图

Figure 1. Algorithm processing flow chart

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5. 仿真实验

仿真参数设置如表1所示。根据表中数据并结合前文的分析可知，目标产生速度模糊的阈值是 ${v_{\rm una}}{\rm{ = }}15\;{\rm{m/s}}$ ，出现跨距离单元走动的速度临界值是 ${v_{\rm t}} \approx {\rm{4}}{\rm{.68}}\,{\rm{m/s}}$ ，速度分辨率 $\Delta {v_{\rm r}}=0.06\,{\rm{m/s}}$ ，且满足 $({{2v{T_{\rm r}}}})/{c} \ll {t_{\rm c}}$ 。由于 $\left| {{f_{\rm d}} + {f_{{\rm d}k}}} \right| \ll {{\Delta f}}/{2}$ ，多普勒频偏导致的子载频间串扰可忽略不计。在高斯白噪声背景下，2个目标距离为 ${R_1} = 10.0\;{\rm{km}}$ , ${R_2} = 1.8\ {\rm{km}}$ , ${R_{\rm{3}}} \!\!=\!\! 17.0\;{\rm{km}}$ ，径向速度 ${v_1} \!\!=\!\! 20\;{\rm{m/s}}$ , ${v_2} \!=\! {\rm{24}}\;{\rm{m/s}}$ , ${v_{\rm{3}}} \!=$ 34 m/s，对应的目标散射强度分别为 ${A_{01}} = 5$ , ${A_{02}} = 2$ , ${A_{0{\rm{3}}}} = {\rm{1}}$ 。虚警率 ${P_{\rm fa}} \!=\! {10^{ - 3}}$ ，蒙特卡洛仿真100次。

表 1 仿真参数

Table 1. Simulation parameters

参数	数值
工作频率 ${f_{\rm c}}$ (GHz)	5
带宽B (MHz)	64
脉冲重复周期 ${T_{\rm r}}$ (ms)	2
脉冲数N	250
载波数K	64

下载: 导出CSV

| 显示表格

信号经过通道分离和相关处理后，在子载波-多普勒平面的投影如图2所示。由图2可以看出，目标的多普勒频移随子载波的变化而变化，因此不能直接进行子载波域的相参积累。

图 2 原始子载波-多普勒平面投影

Figure 2. The contour of the original subcarrier-Doppler plane

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经过Keystone变换和CLEAN处理后，相应子载波-多普勒平面的投影如图3所示。可见，多普勒频移与子载波之间的耦合得到校正。

图 3 校正后的子载波-多普勒平面投影

Figure 3. The contour of the corrected subcarrier-Doppler plane

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对Keystone变换的数据在子载波域进行相参积累，获得信号的距离-多普勒2维谱如图4所示。其中图4(a)是聚焦于第1个目标的结果，图4(b)是剔除前两个目标后聚焦于第3个目标的结果。结果表明，本文所述的补偿方法能在快时间域、慢时间域以及子载波域将目标的回波能量积累起来，有利于目标检测和后续的参数估计。

图 4 回波信号的距离-多普勒2维谱

Figure 4. Echo signal range-Doppler two-dimensional spectrum

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下面考察近似最大似然估计量的性能。当 $v = 20\;{\rm{m/s}}$ , ${\rm{SN}}{{\rm{R}}_i}$ 在0～20 dB之间变化时，分别利用文献[8]所述的联合Keystone变换法、通道分离与Keystone变换组合法以及本文所提的近似最大似然估计法进行速度估计，估计量的均方根误差(RMSE)曲线如图5(a)所示。图5(b)给出了各种算法对应的计算量随脉冲数的变化情况。

图 5 各算法的参数估计精度及计算量

Figure 5. Parameter estimation accuracy and calculation amount of each algorithm

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由图5(a)可知，文献[8](点划线)与基于通道分离和Keystone相结合的方法(实线)的速度估计的RMSE曲线变化趋势类似。在相同的估计精度下，与上述两种方法相比，本文基于通道分离的近似最大似然估计法(点线)的输入信噪比 ${\rm{SN}}{{\rm{R}}_i}$ 改善约4 dB。同时，本文算法得到的RMSE非常接近Cramer-Rao下限。由图5(b)可知，在相同脉冲数下，本文算法的计算量较文献[8]的算法大幅降低。由于使用了牛顿迭代法，与基于通道分离和Keystone相结合的方法相比，计算量有所增加，但仍然远小于文献[8]中算法的计算量。因此，本文提出的基于通道分离的近似最大似然估计算法在估计精度和计算复杂度上具有综合优势。

6. 总结

本文将OFDM通信信号应用在雷达动目标探测中，在通信、雷达一体化的发展背景下有着重要的应用前景。本文参考多载频MIMO雷达通道分离得到目标高分辨距离信息的方法，将OFDM信号的多载波正交结构与脉冲多普勒处理相结合，并借助Keystone变换解决了多普勒偏移问题。为了得到更好的估计精度，利用牛顿迭代法对似然函数进行优化，得到了基于通道分离的近似最大似然估计方法。仿真结果验证了算法的综合性能。今后还可针对机动目标相干化处理以及参数估计问题展开研究，扩展OFDM雷达的应用范围。

图 1 MPI并行技术与FMM技术所得仿真结果及并行加速比

Figure 1. Simulation results and parallel acceleration ratios obtained by MPI parallel technique and FMM technique

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图 2 海面与其上方圆柱复合散射并行FDTD、串行FDTD以及MoM的比较

Figure 2. Comparison of the sea surface with its overlying cylindrical composite scattering by parallel FDTD, FDTD and MoM

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图 3 FEM计算所得粗糙面与目标复合电磁散射仿真结果

Figure 3. Simulation results of the FEM calculation of the composite scattering from the rough surface and the target

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图 4 迭代电流类方法在复合散射中应用PO-PO与FE-BI-KA仿真结果对比

Figure 4. The scattering comparation of two different current iteration methods: PO-PO and FE-BI-KA

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图 5 舰船目标和海面单双站散射

Figure 5. Scattering from ship and sea surface

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图 6 OpenGL中物体映射到计算机屏幕示意图

Figure 6. Diagram of object mapping to computer screen in OpenGL

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图 7 飞行器模型坐标示意图

Figure 7. Schematic diagram of the aircraft

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图 8 电大飞行器双站散射结果

Figure 8. Bistatic scattering of the aircraft

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图 9 OptiX射线追踪程序关系示意图

Figure 9. Schematic diagram of the relationship between OptiX ray tracing programs

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图 10 OptiX中各程序模块的关系及其数据交换示意图

Figure 10. Schematic representation of the relationship between the program modules and their data exchange in OptiX

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图 11 大型航母编队示意图

Figure 11. Diagram of a large aircraft carrier formation

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图 12 大型航母编队单双站散射结果

Figure 12. The scattering results for large carrier formations

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图 13 TDSBR与CST时域回波仿真结果对比

Figure 13. Comparison of TDSBR and CST time domain echo simulation results

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图 14 舰船与粗糙面复合散射示意图

Figure 14. Schematic of composite scattering from a ship and a rough surface

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图 15 不同带宽(或脉冲宽度下)调制高斯脉冲时域回波

Figure 15. Time domain echoes of modulated Gaussian pulses under different bandwidths / pulse widths

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图 16 不同反射次数时域散射回波

Figure 16. Scattered echoes in time domain under different number of reflections

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图 17 SBR方法验证与仿真

Figure 17. Validation and simulation of SBR method

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图 18 阿利伯克级驱逐舰与海面复合场景

Figure 18. Arleigh Burke-class destroyer with sea composite scene

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图 19 3级海况不同舰船方位下舰船以及舰船+目标的一维距离像

Figure 19. High resolution range profile of the ship and the ship+target for different ship orientations in three sea states

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图 20 不同海况下舰船与海面复合场景一维距离像对比结果

Figure 20. Comparison high resolution range profile of the ship and sea surface composite scenes under different sea conditions

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图 21 不同时刻的破碎波

Figure 21. Broking waves at different moments

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图 22 含单卷浪海面散射模型示意图

Figure 22. Schematic diagram of a sea surface scattering model with breaking waves

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图 23 SBR-PTD方法与MoM计算结果对比验证

Figure 23. Validation of the SBR-PTD against MoM

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图 24 SBR-PTD计算含单卷浪海面的后向RCS

Figure 24. RCS of single breaking wave using SBR-PTD

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图 25 波导出口处场强分布

Figure 25. Field intensity distribution at waveguide exit

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图 26 考虑蒸发波导影响下目标散射场功率分布(船头旋转角 $\varphi = 0^\circ$ )

Figure 26. Target scattered field power distribution considering the effect of evaporative waveguides (Bow rotation angle $\varphi = 0^\circ$ )

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图 27 MoM-PO海面与上方圆柱电磁散射仿真结果

Figure 27. Scattering results of sea surface and cylindrical with of MoM-PO

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图 28 复杂海面与目标散射成分分析

Figure 28. Analysis of the scattering components from complex sea surfaces and targets

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图 29 IPIX雷达编号40数据不同极化下时空二维杂波图

Figure 29. Two-dimensional spatial-temporal clutter maps for different polarizations of IPIX radar number 40 data

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图 30 部署现场平面图

Figure 30. The deployment site plan

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图 31 试验架设位置

Figure 31. The test stand location

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图 32 对海探测实验点

Figure 32. The experimental site for sea dection

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图 33 距离-方位图

Figure 33. 2D graph of range-azimuth

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图 34 灵山岛综合实验基地

Figure 34. Lingshan island integrated experimental base

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图 35 海塔平台

Figure 35. The sea tower platform

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图 36 不同参数下杂波分布的最佳模型

Figure 36. Best model for clutter distribution with different parameters

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图 37 3°擦地角U₁₀=15 m/s HH极化顺风散射系数时间序列及均值归一化杂波幅值

Figure 37. Time series of scattering coefficients and normalized clutter for HH polarization under U₁₀=15 m/s and 3° grazing angle

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图 38 入射波频率为1.5 GHz时不同风速后向散射场的多普勒谱

Figure 38. Doppler spectra of the backscattered field at different wind speeds for an incident wave frequency of 1.5 GHz

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图 39 复杂海背景下掠海低飞目标的双站RCS和归一化多普勒谱

Figure 39. Bistatic RCS and normalized Doppler spectrum of a low-flying target in a complex sea background

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图 40 复杂舰船与海面的杂波分布图、杂波概率密度分布、时间相关性

Figure 40. Complex ship and sea clutter map, clutter probability distributions and time correlation

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图 41 X波段下杂波多普勒谱( $f = 10\;{\text{GHz}}$ )

Figure 41. Doppler spectrum at X-band ( $f = 10\;{\text{GHz}}$ )

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图 42 HH极化与VV极化下电场幅度比值的时间序列

Figure 42. Time series of electric field amplitude ratios under HH polarization and VV polarization

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图 43 含多卷浪海面与目标复合多普勒谱

Figure 43. Composite Doppler spectrum of surface and target with multi breaking waves

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图 44 不同海况下掠海巡航导弹目标SAR图像

Figure 44. SAR images of missile targets at different sea states

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图 45 不同海况舰船编队SAR图像 ${\theta _{\rm{i}}} = {45^{\text{o}}}$ , ${\varphi _{\rm{i}}} = {45^{\text{o}}}$

Figure 45. SAR images of ship formations in different sea states at ${\theta _{\rm{i}}} = {45^{\text{o}}}$ , ${\varphi _{\rm{i}}} = {45^{\text{o}}}$

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图 46 不同海况舰船编队SAR图像 ${\theta _{\rm{i}}} = {45^{\text{o}}}$ , ${\varphi _{\rm{i}}} = {90^{\text{o}}}$

Figure 46. SAR images of ship formations in different sea states at ${\theta _{\rm{i}}} = {45^{\text{o}}}$ , ${\varphi _{\rm{i}}} = {90^{\text{o}}}$

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图 47 不同海况下SAR图像中目标识别结果

Figure 47. Target recognition results in SAR images under different sea states

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表 1 串行FDTD方法及并行FDTD方法计算一个样本耗时对比

Table 1. Comparison of the simulation time of a sample by the FDTD method and the parallel FDTD method

极化方式	网格数	串行时间(s)	并行时间(s)	加速比X
HH	131072	250854.42	3067.72	81.77
VV	131072	273862.33	3289.24	83.26

下载: 导出CSV

表 2 仿真算例运行时间(秒)

Table 2. Simulation time (s)

模型	SBR	CUDA-SBR	加速比x
舰船+海面双站	994.6	46.3	27.4
舰船+海面单站	776.1	25.7	30.2

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表 3 仿真算例的运行时间(秒)

Table 3. Running time of the simulation example (s)

模型	三角面片数量	SBR	OpenGL-SBR
双站：飞行器yoz面	158376	72.72	7.13
双站：飞行器xoz面	158376	81.84	8.82
单站：飞行器yoz面	158376	56.78	5.07
单站：飞行器xoy面	158376	57.09	5.12

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表 4 大型航母编队计算时间(秒)

Table 4. Simulation times for large carrier formations (s)

模型	三角面片数量	SBR	一个角度下平均计算时间
单站：大型航母编队	979025	137.250	0.7625
双站：大型航母编队	979025	47.927	/

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表 5 IPIX雷达主要性能参数

Table 5. The key parameters of IPIX radar

参数	数值
雷达频率	9.4 GHz
中频	150 MHz
脉冲宽度	20~5000 ns
发射峰值功率	8 kW
发射信号波长	3 cm
多普勒频移	34 Hz/节
脉冲重复频率(PRF)	0~2000 Hz
距离分辨率	30 m
半功率点波瓣宽度	0.9°
雷达天线高度	30 m
极化方式	HH, VV, HV, VH
擦地角	<1°
采样距离间隔	15 m

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表 6 OTB MS3的主要特性

Table 6. The main characteristics of OTB MS3

参数	数值
纬度	$34^\circ 36'55.32''{\text{S}}$
经度	$20^\circ 17'20.11''{\text{E}}$
地面高度	53 m
天线高度	56 m
离海距离	1.2 km
方位角范围	208°～ 80°N (SSW-ENE)
距离	(CNR > 15 dB)1.25～4.50 km
擦地角	(< 15 km)3.00°～0.16°
擦地角	(CNR > 15 dB)3.0°～0.7°

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表 7 雷达参数

Table 7. The key parameters of radar

技术指标	参数
工作频段	X
载频范围	9.3~9.5 GHz
带宽	25 MHz
脉冲重复频率	1.6 K, 3.0 K, 5.0 K和10.0 K
天线极化方式	HH
天线长度	1.8 m
天线工作模式	凝视、圆周扫描
天线水平波束宽度	1.2°
天线垂直波束宽度	22°

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表 8 U₁₀=10 m/s不同条件下海杂波幅度最佳拟合模型统计分布

Table 8. Best-fit model statistics distribution for sea clutter amplitude at U₁₀=10 m/s

入射角	极化	入射频率(GHz)
入射角	极化	X波段10 GHz	Ku波段15 GHz
30°	HH	WB	WB
30°	VV	WB	WB
45°	HH	WB	WB
45°	VV	K	K
60°	HH	WB	WB
60°	VV	K	K
80°	HH	RL	RL
80°	VV	RL	RL

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1. 引言
2. 相位编码OFDM信号模型
3. 最大似然估计
4. 基于通道分离的近似最大似然估计
5. 仿真实验
6. 总结

复杂动态海面与目标电磁散射及回波仿真研究现状与展望

DOI: 10.12000/JR22202

作者简介:
郭立新，博士，教授，主要研究方向为雷达、通信环境电波传播与散射和目标光电特性理论及应用

魏仪文，博士，副教授，主要研究方向为复杂超电大地海环境散射特性、回波仿真及SAR成像

通讯作者:
郭立新 lxguo@xidian.edu.cn

魏仪文 ywwei@xidian.edu.cn

计量

Status and Prospects of Electromagnetic Scattering Echoes Simulation from Complex Dynamic Sea Surfaces and Targets

Corresponding author: GUO Lixin, lxguo@xidian.edu.cn; WEI Yiwen, ywwei@xidian.edu.cn

1. 引言

2. 相位编码OFDM信号模型

3. 最大似然估计

4. 基于通道分离的近似最大似然估计

5. 仿真实验

6. 总结

计量

目录

1. 引言

2. 相位编码OFDM信号模型

3. 最大似然估计

4. 基于通道分离的近似最大似然估计

5. 仿真实验

6. 总结

期刊介绍

联系我们

复杂动态海面与目标电磁散射及回波仿真研究现状与展望

DOI: 10.12000/JR22202

作者简介: 郭立新，博士，教授，主要研究方向为雷达、通信环境电波传播与散射和目标光电特性理论及应用 魏仪文，博士，副教授，主要研究方向为复杂超电大地海环境散射特性、回波仿真及SAR成像

通讯作者: 郭立新 lxguo@xidian.edu.cn 魏仪文 ywwei@xidian.edu.cn

计量

出版历程

Status and Prospects of Electromagnetic Scattering Echoes Simulation from Complex Dynamic Sea Surfaces and Targets

Corresponding author: GUO Lixin, lxguo@xidian.edu.cn; WEI Yiwen, ywwei@xidian.edu.cn

1. 引言

2. 相位编码OFDM信号模型

3. 最大似然估计

4. 基于通道分离的近似最大似然估计

5. 仿真实验

6. 总结

计量

出版历程

目录

1. 引言

2. 相位编码OFDM信号模型

3. 最大似然估计

4. 基于通道分离的近似最大似然估计

5. 仿真实验

6. 总结

期刊介绍

联系我们

作者简介:
郭立新，博士，教授，主要研究方向为雷达、通信环境电波传播与散射和目标光电特性理论及应用

魏仪文，博士，副教授，主要研究方向为复杂超电大地海环境散射特性、回波仿真及SAR成像

通讯作者:
郭立新 lxguo@xidian.edu.cn

魏仪文 ywwei@xidian.edu.cn