面向FDA-MIMO近程探测器的SG-DDPG低截获点状波束设计

贾金伟; 高敏; 韩壮志; 刘利民; 尹园威

doi:10.11999/JEIT260010

面向FDA-MIMO近程探测器的SG-DDPG低截获点状波束设计

doi: 10.11999/JEIT260010 cstr: 32379.14.JEIT260010

陆军工程大学石家庄校区石家庄 050003

详细信息

作者简介:
贾金伟：男，陆军工程大学博士生，研究方向为：电子对抗、雷达信号处理、无线电引信抗干扰等

高敏：男，博士，陆军工程大学教授，博士生导师，研究方向为：无线电引信抗干扰、无线电引信设计等

韩壮志：男，博士，陆军工程大学教授，博士生导师，研究方向为：电子对抗、雷达信号处理、无线电引信抗干扰等

刘利民：男，博士，陆军工程大学教授，博士生导师，研究方向为：电子对抗、雷达信号处理等

尹园威：男，博士，陆军工程大学讲师，研究方向为：电子对抗、雷达信号处理等

通讯作者:
韩壮志　zhuangzhi_signal@163.com

中图分类号: TN974
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出版历程
- 修回日期: 2026-04-17
- 录用日期: 2026-04-17
- 网络出版日期: 2026-05-05

SG-DDPG low intercept point beam design for FDA-MIMO short-range detector

Shijiazhuang Campus, Army Engineering University, Shijiazhuang 050003, China

摘要

摘要: 点状波束可有效提高近程探测器空域低截获能力，本文聚焦于频控阵(FDA-MIMO)阵元频偏设置对波束合成的影响这一关键因素，提出了基于阶段化引导深度确定性策略梯度(SG-DDPG)强化学习算法的低截获点状波束设计技术。首先构建了波束空域低截获性能评估模型，然后设计了多维阶段化引导奖励函数，通过Actor-Critic模型运用梯度上升的方法最大化奖励值，得到当前环境下波束汇聚性能较好的阵元频偏，突破了公式法计算阵元频偏需要近程探测器落角接近垂直的技术瓶颈。仿真表明，SG-DDPG算法优化后的阵元频偏使得FDA-MIMO波束在波束汇聚性能和低截获性能明显好于其他经典频偏设置方法，并适用于近程探测器各种落角下的低截获波束设计，有效提高了近程探测器的低截获性能。
- 近程探测器 /
- 低截获 /
- 点状波束设计 /
- FDA-MIMO /
- SG-DDPG强化学习算法
Abstract: Objective Radio short-range detector is the most widely used short-range detector with the largest number of equipment in both domestic and international fields. However, in modern battlefields, the electromagnetic environment is becoming increasingly complex, and radio short-range detectors have to deal with various electromagnetic interferences. Especially, the fourth-generation jammer that implements the forwarding deception interference based on Digital Radio Frequency Memory (DRFM) is highly likely to cause failure situations such as premature detonation in radio proximity detectors. This significantly reduces the damage control capability of the radio short-range detector. Therefore, it is urgent to conduct research on the important issue of anti-forwarding deception interference for short-range detectors. Among them, improving the low interception capability of the radio detector can effectively resist the repeater deception jamming. Methods In this paper, the frequency diverse array (FDA) -multiple-input multiple-output (MIMO) technology is employed, and key factors influencing beam convergence are determined. Aiming at the design of spatial low-interception beam of short-range detector, the performance evaluation model of beam spatial low-interception is constructed. And then the FDA-MIMO low intercept point beam design technology based on Stage Guidance-Deep Deterministic Policy Gradient (SG-DDPG) algorithm is proposed. In the SG-DDPG algorithm, a multi-dimensional phased guidance reward function is designed. Through the Actor-Critic model, the gradient rise method is used to maximize the reward value, therefore the frequency offset of the array element with better beam convergence performance in the current environment is obtained. Meanwhile, the SG-DDPG algorithm applies to LPI point beam design across various radio detector fall angles, overcoming the technical bottleneck that the formula method for the array element frequency offset only applies when the radio detector’s fall angle is close to vertical. Results and Discussions The simulation shows that with the array element frequency offset optimized by the SG-DDPG algorithm, the FDA-MIMO beam exhibits a half-power beam width of 1 m in the distance dimension and 9.9° in the angular dimension. The beam convergence and LPI performance with the proposed method are significantly better than other classical frequency offset calculation methods. Thus, the proposed algorithm represents a new method for array element frequency offset optimization and LPI point beam design, effectively improving the radio detector’s LPI performance. Conclusions This paper presents an FDA-MIMO LPI point beam design method based on the SG-DDPG algorithm, with the array element frequency offset as the optimization objective. The simulation results show that: (1) The proposed method breaks through the limitation that the radio detector fall angle must be close to vertical when calculating the array element frequency offset by the formula method. The algorithm can be applied to the design of LPI beams under various radio detector fall angles, where it achieves improved LPI performance; (2) The half-beam width with the proposed method is only 1 m in the range dimension and 9.9° in the angle dimension, which is significantly better than the traditional methods. Under different fall angles, the interception area of the beam formed with the proposed method is the smallest, demonstrating the best LPI performance.
- Radio detector /
- Low probability of intercept /
- Point beam design /
- FDA-MIMO /
- SG-DDPG reinforcement learning

HTML全文

图 1 FDA的发射阵列示意图

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图 2 空域低截获性能评估原理图

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图 3 本文的逻辑简图

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图 4 SG-DDPG算法模型图

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图 5 SG-DDPG算法智能体训练累计奖励和平均奖励曲线

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图 6 波束截获面积和平均截获面积随智能体训练变化趋势图

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图 7 三维波束图

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图 8 二维俯视图

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图 9 波束在距离维的切面图

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图 10 波束在角度维的切面图

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图 11 立方指数频偏方法FDA-MIMO波束图

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图 12 对数频偏方法FDA-MIMO波束图

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图 13 本文所提算法的FDA-MIMO波束图

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图 14 在(200 m，30°)处汇聚的FDA-MIMO波束图

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图 15 在(30 m，45°)处汇聚的FDA-MIMO波束图

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图 16 在$ \left(10\text{m}，60{^{\circ}}\right) $处汇聚的FDA-MIMO波束图

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图 17 落角10°时不同高度下近程探测器波束的截获面积

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图 18 落角45°时不同高度下近程探测器波束的截获面积

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图 19 落角60°时不同高度下近程探测器波束的截获面积

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图 20 落角85°时不同高度下近程探测器波束的截获面积

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表 1 SG-DDPG算法伪代码

算法：SG-DDPG
初始化：运用随机的网络参数$ \omega $和$ \theta $分别初始化Critic训练网络$ {Q}_{\omega }\left(s,a\right) $和Actor训练网络$ {\mu }_{\theta }\left(s\right) $，复制相同的参数$ {\omega }^{\prime}\leftarrow \omega $、$ {\theta }^{\prime}\leftarrow \theta $，分别　初始化Critic目标网络$ {Q}_{{{\omega }^{-}}} $和Actor目标网络$ {\mu }_{{{\theta }^{-}}} $
迭代过程：
for回合$ e=1\rightarrow \text{E} $ do:
初始化随机过程$ N $，用于动作探索
获取环境初始状态$ {s}_{1} $
for迭代步数$ t=1\rightarrow T $ do：
根据当前策略和噪声选择动作$ {a}_{t}={\mu }_{\theta }\left({s}_{t}\right)+N $
执行动作$ {a}_{t} $，获得奖励$ {r}_{t} $，环境状态变为$ {s}_{t} $
将$ \left({s}_{t},{a}_{t},{r}_{t},{s}_{t+1}\right) $存储进经验回放池$ \mathbf{R} $
从$ \mathbf{R} $中采样N个元组$ {\left\{\left({s}_{i},{a}_{i},{r}_{i},{s}_{i+1}\right)\right\}}_{i=1,\cdots ,N} $
对每个元组，运用目标网络计算$ {y}_{i}={r}_{i}+\gamma {Q}_{{{\omega }^{-}}}\left({s}_{i+1},{\mu }_{{{\theta }^{-}}}\left({{{s}^{\prime}}}_{i}\right)\right) $
通过最小化目标损失$ L=\dfrac{1}{N}\displaystyle\sum \nolimits_{i=1}^{N}{\left({y}_{i}-{Q}_{\omega }\left({s}_{i},{a}_{i}\right)\right)}^{2} $，更新Critic训练网络
计算数据的策略梯度，更新Actor训练网络：
$ {\nabla }_{\theta }J\approx {\left.\dfrac{1}{N}\displaystyle\sum \nolimits_{i=1}^{N}{\nabla }_{\theta }{\mu }_{\theta }\left({s}_{i}\right){\nabla }_{a}{Q}_{w}\left({s}_{i},a\right)\right\| }_{a={{\mu }_{\theta }}\left({s}_{i}\right)} $
更新目标网络：
$ {\omega }^{-}\leftarrow \tau \omega +\left(1-\tau \right){\omega }^{-} $
$ {\theta }^{-}\leftarrow \tau \theta +\left(1-\tau \right){\theta }^{-} $
end for
end for

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表 2 不同简化模型的定量结果

低截获评估模型	奖惩函数	角度维半波束宽度($ {^{\circ}} $)↓	距离维半波束宽度(m)↓	截获面积($ {\text{m}}^{2} $)↓	速度(s)↓
√	×	21.2	89.3	9077	1965
×	√	13.6	2.7	3256	1352
√	√	9.9	1	1613	984

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表 3 仿真参数设置

仿真参数	值	仿真参数	值
阵元数量/个	6	点状波束期望角度/$ {^{\circ}} $	30
中心频率/GHz	10	点状波束期望距离/米	30
各阵元频偏/MHz	0、246.71、249.18、254.1、257.11、258.1(由本文所提算法生成)

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表 4 仿真参数设置

仿真参数	值	仿真参数	值
阵元数量/个	6	中心频率f₀/GHz	10
基础频偏Δf	5 KHz
立方指数频偏情形各阵元频偏/MHz	0.005、0.04、0.135、0.32、0.625、1.08
对数频偏情形各阵元频偏/Hz	0、3466、5493、6931、8047、8959
本文所提算法各阵元频偏/MHz	0、246.71、249.18、254.1、257.11、258.1

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表 5 仿真参数设置

仿真参数	值	仿真参数	值
阵元数量/个	6	中心频率f₀/GHz	10

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表 6 仿真参数设置

仿真参数	值	波束宽度	值
近程探测器落角/$ {^{\circ}} $	15、45、60、85	Log-FDA	$ 14.1{^{\circ}} $
离地高度/m	10–1000	Cub-FDA	$ 12.3{^{\circ}} $
阵元数量/个	6	SG-DDPG算法	$ 9.9{^{\circ}} $
基础频率/GHz	10	公式法(落角$ 10{^{\circ}} $)	$ 28{^{\circ}} $
公式法(落角$ 60{^{\circ}} $)	$ 16{^{\circ}} $	公式法(落角$ 45{^{\circ}} $)	$ 23{^{\circ}} $
		公式法(落角$ 85{^{\circ}} $)	$ 9.5{^{\circ}} $

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