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Joint Design of LPI Transmit Waveform and Receive Beamforming Based on Neural Networks for FDA-MIMO
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摘要: 针对传统相控阵或多输入多输出(MIMO)体制的低截获概率(LPI)阵列雷达仅能控制特定角度的辐射能量，而无法实现特定区域(距离、角度)能量控制的问题，该文提出一种基于神经网络的频控阵-多输入多输出(FDA-MIMO)雷达低截获概率发射波形设计方法。该方法通过对FDA-MIMO雷达的发射波形和接收波束形成联合设计，在确保雷达对目标检测概率的情况下，将雷达辐射能量均匀地分散到空域当中，并尽可能降低辐射到目标位置的能量，从而减小雷达信号被截获的概率。首先，建立了最小化方向图匹配误差准则下LPI性能发射波形设计和接收波束形成的优化目标函数；然后，将目标函数作为神经网络的损失函数；最后，通过迭代训练最小化神经网络的损失函数，直至网络收敛，求解出发射信号波形和对应的接收加权矢量。仿真结果表明，该文所提方法能更好地控制雷达功率分布，相比于传统算法，控制发射方向图非目标区域的波束能量分布方面有5 dB的改善；此外，在接收端形成的接收方向图波束能量也更为集中，且在多个干扰位置均产生了–50 dB以下的零陷，具有很好的干扰抑制效果。
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关键词:
- 频控阵-多输入多输出雷达 /
- 低截获概率阵列雷达 /
- 残差神经网络 /
- 波形设计 /
- 波束形成
Abstract: Traditional Low Probability of Intercept (LPI) array radars that use phased array or Multiple-Input Multiple-Output (MIMO) systems face limitations in terms of controlling radiation energy only at specific angles and cannot achieve energy control over specific areas of range and angle. To address these issues, this paper proposes an LPI waveform design method for Frequency Diverse Array (FDA)-MIMO radar utilizing neural networks. This method jointly designs the transmit waveform and receive beamforming in FDA-MIMO radars to ensure target detection probability while uniformly distributing radar energy across the spatial domain. This minimizes energy directed toward the target, thereby reducing the probability of the radar signal being intercepted. Initially, we formulate an optimization objective function aimed at LPI performance for transmitting waveform design and receiving beamforming by focusing on minimizing pattern matching errors. This function is then used as the loss function in a neural network. Through iterative training, the neural network minimizes this loss function until convergence, resulting in optimized transmit signal waveforms and solving the corresponding receive weighting vectors. Simulation results indicate that our proposed method significantly enhances radar power distribution control. Compared to traditional methods, it shows a 5 dB improvement in beam energy distribution control across nontarget regions of the transmit beam pattern. Furthermore, the receiver beam pattern achieves more concentrated energy, with deep nulls below −50 dB at multiple interference locations, demonstrating excellent interference suppression capabilities. -
图 2 多通道混频结合低通滤波的接收框架
Figure 2. Multi-channel mixing combined with low pass filtering receiver framework
1 基于ResNet的优化算法伪代码
1. Pseudocode for optimization algorithm based on ResNet
1. ResNet I训练 网络输入：随机噪声矩阵 while未达到最大迭代次数or网络未收敛do 根据网络输出计算损失函数： $ \mathcal{L}_{1}(\boldsymbol{S}) \leftarrow\left\{\operatorname{Re}\left(\boldsymbol{S}^{\mathrm{H}} {\boldsymbol{a}}(r, \theta)\right), \operatorname{Im}\left(\boldsymbol{S}^{\mathrm{H}} {\boldsymbol{a}}(r, \theta)\right)\right\} $
$ \leftarrow\{\operatorname{Re}(\boldsymbol{S}), \operatorname{Im}(\boldsymbol{S})\} \leftarrow \boldsymbol{x}_{\text {outI }} $使用自适应优化算法(Adaptive Moment Estimation, Adam)
更新网络参数end while 输出波形$ {\boldsymbol{s}} $
$ {{\boldsymbol{s}}}=\operatorname{vec}(\boldsymbol{S})={\mathrm{e}}^{{\mathrm{j}} {\boldsymbol{x}}_{{\mathrm{outI}}}} $2. ResNet II训练 网络输入：随机噪声矩阵 while未达到最大迭代次数or网络未收敛do 根据网络输出计算损失函数：
${\mathcal{L}}_{{\mathrm{II}}}({\boldsymbol{w}}) \leftarrow \left\{ {\mathrm{Re}}\left({\boldsymbol{w}}^{\mathrm{H}}\tilde {\boldsymbol{S}} {\boldsymbol{v}}(r,\theta) \right),\;{\mathrm{Im}}\left({\boldsymbol{w}}^{\mathrm{H}}\tilde {\boldsymbol{S}}{\boldsymbol{v}}(r,\theta) \right)\right\} $
$\leftarrow {\boldsymbol{x}}_{{\mathrm{outII}}} $使用自适应优化算法Adam更新网络参数 end while 输出接收加权矢量w ${\boldsymbol{w}}={\boldsymbol{x}}_{{\mathrm{outII}}}(1:NL)+{\mathrm{j}} {\boldsymbol{x}}_{{\mathrm{outII}}} (NL+1:2NL)$ 
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表 1 仿真参数设置
Table 1. Simulation parameter setting
参数名称 符号 数值 发射阵元数 $ M $ $ 10 $ 接收阵元数 $ N $ $ 10 $ 发射波形样本数 $ L $ $ 8 $ 参考载频 $ f_{0} $ $ \text { 10 GHz } $ 频偏增量 $ \Delta f $ $ 3 \;\mathrm{kHz} $ 带宽 $ { B } $ $ 3\; \mathrm{kHz} $ 光速 $ \rm{c} $ $ 3 \times 10^{8} \;\mathrm{m} / \mathrm{s} $ 阵元间距 $ d $ $ {\mathrm{c}} /\left(2 f_{0}\right) $ 距离观测范围 $ r$ $ [0: 0.1: 100] \;\mathrm{km} $ 角度观测范围 $ \theta $ $ \left[-90^{\circ}: 0.5^{\circ}: 90^{\circ}\right] $ 目标权重 $ \omega_{k} $ $ 1 $ 旁瓣区域权重 $ \omega_{p, q} $ $ 1 $ 干扰区域权重 $ \omega_{i} $ $ 1 $ 方向图主瓣调节参数 $ \mu $ $ 4 $
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