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Main-lobe Deceptive Jammers with Array Radars Using Space-time Multidimensional Coding
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摘要: 随着电子技术的快速发展，雷达面临的电磁环境日益复杂。当存在主瓣有源欺骗干扰时，传统相控阵雷达自适应波束形成抗干扰失效，主瓣干扰抑制已成为雷达领域亟待解决的共性难题。该文针对来自主瓣的自卫式转发干扰，提出了一种时空多维域编码抗主瓣欺骗式干扰方法。首先，设计发射通道-脉冲-子脉冲编码，在接收端采用多普勒分多址方法实现了发射信号分离。针对目标高速运动导致的分离错位现象，提出一种基于波束形成能量差的移位数估计方法。随后，利用目标与干扰的延时相位差，设计收发联合的双重编码相位补偿方法，在发射空间频率域实现对真实目标、跨脉冲转发干扰、脉内转发干扰的区分，并且通过构建联合发射-接收权矢量，对主瓣欺骗式干扰进行空域滤波抑制。针对实际中波达角度(DOA)误差造成的抗干扰性能下降问题，构建了以最大化输出信干噪比(SINR)为目标函数的约束优化问题，基于交替迭代算法对接收权矢量，发射编码系数、接收编码系数分别进行优化。仿真实验验证了所提方法相比于其他雷达体制在抗主瓣欺骗干扰方面的有效性，其中相比于传统MIMO雷达，所提阵列时空多维域编码技术在4个主瓣干扰存在的情况下SINR可提升34 dB。Abstract: With the rapid development of electronic technology, the electromagnetic environment is becoming increasingly complex. For instance, adaptive beamforming cannot suppress main-lobe jammers for traditional phased array radars; therefore, developing measures to tackle this common problem is an urgent need in radar technology. This study addresses the problem of main-lobe deceptive jammer suppression using space-time multidimensional coding. The first step is to design a three-dimensional phase coding scheme applicable across transmit channels, pulses, and subpulses. A Doppler division multiple access technique is employed at the receiver to separate the transmit signals. To solve the problem of waveform misalignment caused by high-speed moving targets, a novel approach is proposed to estimate the compensation index according to differences in beamforming energy. Subsequently, a dual-phase compensation method that leverages the phase differences between the main-lobe deceptive jammers and the target is proposed; this method can distinguish the true target, pulse-delayed jammers, and rapidly generated jammers in the transmit spatial frequency domain. Moreover, spatial filtering is applied to suppress all the main-lobe deceptive jammers by designing an appropriate transmit-receive weight vector. Additionally, an optimization problem aiming to maximize the output Signal-to-Interference-plus-Noise Ratio (SINR) is formulated to address the problem of performance degradation due to the Direction of Arrival (DOA) Errors. Further, to solve this problem, an alternating optimization method is utilized to obtain the optimized weight vector and transmit and receive coding coefficients iteratively to improve the SINR. Simulation results demonstrate that the proposed method suppresses the main-lobe deceptive jammers more effectively than other radar frameworks. Specifically, compared to the conventional multiple-input multiple-output radar, the proposed method achieves an SINR improvement of 34 dB in the presence of four main-lobe deceptive jammers.
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图 1 发射通道-脉冲-子脉冲三维域编码示意图
Figure 1. Illustration of three-dimensional coding scheme in transmit channels, pulses, and subpulses
图 3 真假目标分布及补偿意图
Figure 3. Distribution of true and false targets and illustration of compensation
图 5 时空多维域编码信号处理流程图
Figure 5. The flowchart of signal processing with space-time multidimensional coding
图 6 单个接收通道内信号距离-多普勒结果
Figure 6. The range-Doppler result within a single receive element
图 7 通道移位数估计结果
Figure 7. Estimation of channel shift number beampattern of space-time multidimensional coding array
图 8 目标收发空间谱及收发二维波束形成方向图
Figure 8. Target transmit-receive spatial spectrum and 2D transmit-receive beampatern
图 11 误差存在情况下阵列时空多维域编码功率谱
Figure 11. Transmit-receive spatial spectrum of space-time multidimensional coding array in the presence of DOA errors
图 13 不同参数优化后SINR对比
Figure 13. Comparison of SINR after different parameter optimizations
表 1 目前主瓣干扰抑制技术对比
Table 1. Comparison of current main-lobe jammer suppression techniques
分类 方法 抗干扰原理 局限性 空域 单脉冲技术[7,8] 构建4通道单脉冲系统，分两级抗干扰 对系统误差稳健性差，低快拍时性能差 数据预处理[9,10] 采用阻塞矩阵、正交投影矩阵、特征投影矩阵等预处理矩阵抑制主瓣干扰 子空间技术[11] 将主瓣干扰斜投影到旁瓣干扰子空间抑制 时域 盲源分离[12,13] 利用基于矩阵联合对角化/特征矩阵近似联合对角化方法
分离出主瓣干扰和目标不适用于目标和干扰信号具有部分
相关特性的场景稀疏恢复[14] 将信号模型转换为欠定矩阵方程，然后通过稀疏分解基追踪算法来求解 脉冲分集[15,16] 改变信号慢时间域参数，构造脉间的信息差异来区分真、
假目标频域 频率捷变[3−5] 结合Hough变换、参差重频、压缩感知、交替迭代、脉冲变换等方法设计抗干扰捷变波形 相参积累难 极化域 极化滤波[17−19] 通过雷达收发系统极化方式与干扰信号极化方式正交，
抑制了主瓣压制干扰真、假目标间互扰对极化抗干扰
性能影响很大极化分集[20] 采用发射端极化分集、收发二维极化分集、极化编码等
方法抑制主瓣干扰分布式组网 组网/分布式[21−24] 通过数据级/信号级信息融合，进行多站协同对抗 系统时间和空间同步、目标配对、
资源调度管理难
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表 2 第1次和第2次补偿后的目标发射、接收空间频率
Table 2. Transmit and receive spatial frequencies of targets after first and second compensation
目标 第1次补偿后发射空间频率 第1次补偿后接收空间频率 第2次补偿后发射空间频率 第2次补偿后接收空间频率 真实目标 $ f_{{\theta _0},{p_0},l}^{} = \dfrac{d}{\lambda }\sin {\theta _0} - {\gamma _{\text{T}}}(l - 1) $ $ f_{{\theta _0}}^{} = \dfrac{d}{\lambda }\sin {\theta _0} - {\gamma _{\text{R}}} $ $ {\bar f_{{\theta _0},{p_0},l}} = \dfrac{d}{\lambda }\sin {\theta _0} $ $ {\bar f_{{\theta _0}}} = \dfrac{d}{\lambda }\sin {\theta _0} $ 假目标1 $ \begin{gathered} f_{{\theta _1},{p_1},l}^{} = \dfrac{d}{\lambda }\sin {\theta _1} - {\gamma _{\text{T}}}\left( {{p_1} - {p_0}} \right) \\ - {\gamma _{\text{T}}}(l - 1) \\ \end{gathered} $ $ f_{{\theta _1}}^{} = \dfrac{d}{\lambda }\sin {\theta _1} - {\gamma _{\text{R}}} $ $ \begin{gathered} {{\bar f}_{{\theta _1},{p_1},l}} = \dfrac{d}{\lambda }\sin {\theta _1} - {\gamma _{\text{T}}}\left( {{p_1} - {p_0}} \right) \\ - {\gamma _{\text{T}}}(l - 1) \\ \end{gathered} $ $ {\bar f_{{\theta _1}}} = \dfrac{d}{\lambda }\sin {\theta _1} - {\gamma _{\text{R}}} $ 假目标2 $ \begin{gathered} f_{{\theta _2},{p_2},l}^{} = \dfrac{d}{\lambda }\sin {\theta _2} - {\gamma _{\text{T}}}\left( {{p_2} - {p_0}} \right) \\ - {\gamma _{\text{T}}}(l - 1) \\ \end{gathered} $ $ f_{{\theta _2}}^{} = \dfrac{d}{\lambda }\sin {\theta _2} - {\gamma _{\text{R}}} $ $ {\bar f_{{\theta _2},{p_2},l}} = \dfrac{d}{\lambda }\sin {\theta _2} - {\gamma _{\text{T}}}\left( {{p_2} - {p_0}} \right) $ $ {\bar f_{{\theta _2}}} = \dfrac{d}{\lambda }\sin {\theta _2} $ 假目标3 $ f_{{\theta _3},{p_3},l}^{} = \dfrac{d}{\lambda }\sin {\theta _3} - {\gamma _{\text{T}}}(l - 1) $ $ f_{{\theta _3}}^{} = \dfrac{d}{\lambda }\sin {\theta _3} - {\gamma _{\text{R}}} $ $ {\bar f_{{\theta _3},{p_3},l}} = \dfrac{d}{\lambda }\sin {\theta _3} - {\gamma _{\text{T}}}(l - 1) $ $ {\bar f_{{\theta _3}}} = \dfrac{d}{\lambda }\sin {\theta _3} - {\gamma _{\text{R}}} $ 假目标4重叠
部分$ f_{{\theta _4},{p_4},l}^{} = \dfrac{d}{\lambda }\sin {\theta _4} - {\gamma _{\text{T}}}(l - 1) $ $ f_{{\theta _4}}^{} = \dfrac{d}{\lambda }\sin {\theta _4} - {\gamma _{\text{R}}} $ $ {\bar f_{{\theta _4},{p_4},l}} = \dfrac{d}{\lambda }\sin {\theta _4} - {\gamma _{\text{T}}}l' $ $ {\bar f_{{\theta _4}}} = \dfrac{d}{\lambda }\sin {\theta _4} $ 假目标4非
重叠部分$ f_{{\theta _4},{p_4},l}^{} = \dfrac{d}{\lambda }\sin {\theta _4} - {\gamma _{\text{T}}}(l - 1) $ $ f_{{\theta _4}}^{} = \dfrac{d}{\lambda }\sin {\theta _4} - {\gamma _{\text{R}}} $ $ {\bar f_{{\theta _4},{p_4},l}} = \dfrac{d}{\lambda }\sin {\theta _4} - {\gamma _{\text{T}}}(l - 1) $ $ {\bar f_{{\theta _4}}} = \dfrac{d}{\lambda }\sin {\theta _4} - {\gamma _{\text{R}}} $
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1 交替迭代的收发编码及方向图联合优化方法
1. The joint optimization of transceiver coding and beampattern using alternating iteration
输入：M, N, L, K, $ {p_0} $, $ {p_q} $, $ {\sigma _q} $, $ {\sigma _n} $ 初始化：$i = 1$, $ {{\boldsymbol{w}}^{(i - 1)}} $, $ \gamma _{\text{T}}^{(i - 1)} $, $ \gamma _{\text{R}}^{(i - 1)} $, ${\text{ }}I$ while ${{i < }}I$ 1. 依据$ \gamma _{\text{T}}^{(i - 1)} $, $ \gamma _{\text{R}}^{(i - 1)} $，通过求解优化问题$ \mathcal{P}_{\boldsymbol{w}}^{(i)} $搜索$ {{\boldsymbol{w}}^{(i)}} $； 2. 依据$ {{\boldsymbol{w}}^{(i)}} $, $ \gamma _{\text{R}}^{(i - 1)} $，通过求解优化问题$ \mathcal{P}_{{\gamma _{\text{T}}}}^{(i)} $搜索$ \gamma _{\text{T}}^{(i)} $； 3. 依据$ {{\boldsymbol{w}}^{(i)}} $, $ \gamma _{\text{T}}^{(i)} $，通过求解优化问题$ \mathcal{P}_{{\gamma _{\text{R}}}}^{(i)} $搜索$ \gamma _{\text{R}}^{(i)} $； 4. 计算当前${{\mathrm{SINR}}^{(i)}}$； 5. if $ \left| {{{\mathrm{SINR}}^{(i)}} - {{\mathrm{SINR}}^{(i - 1)}}} \right| < \varepsilon $ then 6. 令$ {{\boldsymbol{w}}}^{\ast }={{\boldsymbol{w}}}^{(i)},\;{\gamma }_{\text{T}}^{\ast }={\gamma }_{\text{T}}^{(i)},\;{\gamma }_{\text{R}}^{\ast }={\gamma }_{\text{R}}^{(i)} $，停止迭代； 7. end if 8 $i = i + 1$； end while 输出：$ {{\boldsymbol{w}}^ * } $, $ \gamma _{\text{T}}^ * $, $ \gamma _{\text{R}}^ * $.
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表 3 系统仿真参数
Table 3. System simulation parameters
参数 数值 参数 数值 发射阵元数M 8 接收阵元数N 6 载频${f_0}$ 8 GHz 脉冲重复频率${f_{\mathrm{r}}}$ 20 kHz 脉冲数K 64 发射编码系数$ {\gamma _{\text{T}}} $ 1/M 接收编码系数${\gamma _{\text{R}}}$ 1/N 脉宽${T_{\mathrm{p}}}$ 5 μs 子脉冲数L 5 带宽B 5 MHz
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表 4 真假目标参数设置
Table 4. Simulation parameters of true and false targets
参数 数值 参数 数值 真目标角度($^ \circ $) 1 真目标主值距离(km) 3 信噪比SNR (dB) 0 真目标脉冲延迟数 0 目标速度(m/s) 80 假目标角度($^ \circ $) 1, 1, 1, 1 假目标主值
距离(km)1.5, 3.0, 3.5, 6.5 假目标脉冲延迟数 2, 1, 0, 0 假目标JNR (dB) 20, 20, 20, 20
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