针对载频与脉冲间隔随机捷变雷达的运动目标旁瓣快速抑制方法

魏嘉; 宁晨; 孔梓丞; 张鑫悦; 魏敬卓; 田静

doi:10.12000/JR26049

针对载频与脉冲间隔随机捷变雷达的运动目标旁瓣快速抑制方法

DOI: 10.12000/JR26049 CSTR: 32380.14.JR26049

北京理工大学信息与电子学院北京 100081

基金项目: 国家自然科学基金(62371049)，天基智能信息处理全国重点实验室基金(TJ-01-22-02, TJ-01-25-06)

详细信息

作者简介:
魏　嘉，博士生，主要研究方向为捷变雷达目标参数估计

宁　晨，博士，主要研究方向为雷达目标探测与成像

孔梓丞，博士生，主要研究方向为运动目标参数估计

张鑫悦，博士生，主要研究方向为雷达目标探测与成像

魏敬卓，博士生，主要研究方向为运动目标参数估计

田　静，教授，主要研究方向为雷达信号处理

通讯作者:
田静 tianjing1114@hotmail.com

责任主编：全英汇 Corresponding Editor: QUAN Yinghui

中图分类号: TN957
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出版历程
- 收稿日期: 2026-02-13
- 修回日期: 2026-05-08

Fast Sidelobe Suppression for Moving Targets in Random Frequency and Pulse Repetition Interval Agile Radars

School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China

Funds: The National Natural Science Foundation of China (62371049), Foundation of National Key Laboratory of Space-Based Intelligent Information Processing (TJ-01-22-02, TJ-01-25-06)

More Information

Corresponding author: TIAN Jing, tianjing1114@hotmail.com

摘要

摘要: 载频与脉冲间隔随机捷变(RFPA)雷达可通过合成宽带获得高距离分辨率。但是，在长时间相参积累过程中，运动目标容易出现距离徙动(RCM)现象，且RFPA信号固有的随机高旁瓣特性会严重降低雷达对目标的检测和估计性能。针对上述两个问题，该文提出了一种基于非均匀Keystone变换的加窗迭代自适应滤波方法(NUKT-WIAA)。首先，采用非均匀Keystone变换(NUKT)对运动目标进行RCM校正，以实现目标能量的有效积累。然后，对每个距离-多普勒单元为中心的矩形处理窗内的NUKT结果进行迭代自适应滤波(IAA)处理，实现对RFPA信号旁瓣的快速抑制。在迭代过程中，采用强散射点筛选策略提高协方差矩阵的计算效率，从而进一步降低所提算法的计算复杂度。仿真结果表明，在多目标和连续杂波场景下，NUKT-WIAA算法能够以较低的计算量和存储量同时实现对运动目标的徙动校正和旁瓣抑制。
- 载频与脉冲间隔随机捷变信号 /
- 距离徙动 /
- 旁瓣抑制 /
- 迭代自适应滤波 /
- 计算效率
Abstract: Random Frequency and Pulse Repetition interval Agile (RFPA) radars can achieve high range resolution using a synthesized wide bandwidth. However, Range Cell Migration (RCM) occurs for moving targets during long coherent integration, and the inherent randomly fluctuating high sidelobes pose a significant challenge for RFPA radars. To address these issues and enhance target detection and estimation performance, a Windowed Iterative Adaptive Approach based on the Non-Uniform Keystone Transform (NUKT-WIAA) is proposed. First, a NUKT is employed to correct the RCM caused by moving targets, effectively concentrating most of the target energy. An IAA is then applied to the NUKT results within a rectangular processing window centered on each range-Doppler cell to achieve fast sidelobe suppression of RFPA signals. A strong scatterer selection strategy is implemented during iterations to enhance the computational efficiency of the covariance matrix, thereby reducing the overall computational complexity of the proposed algorithm. Simulation results reveal that NUKT-WIAA can simultaneously achieve migration correction and sidelobe suppression for moving targets across various scenarios, multiple point targets, range-spread targets, and environments with continuous strong clutter while maintaining low computational complexity and memory usage.
- Random Frequency and Pulse repetition interval Agile signal (RFPA) /
- Range cell migration /
- Sidelobe suppression /
- Iterative adaptive approach /
- Computational efficiency

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图 1 RFPA信号的时-频示意图

Figure 1. Time-frequency diagram of RFPA signal

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图 2 NUKT预处理过程及结果

Figure 2. NUKT preprocessing process and results

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图 3 处理窗示意图

Figure 3. Schematic diagram of the processing window

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图 4 多目标场景下各算法的距离-速度像估计结果

Figure 4. Range-velocity image estimation results of each algorithm in multi-target scenarios

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图 5 杂波场景下各算法的距离-速度像估计结果

Figure 5. Range-velocity image estimation results of each algorithm in clutter scenarios

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图 6 不同目标数($ {N}_{\text{t}} $)下收敛的MSE与处理窗尺寸($ {k}_{\text{r}}\times {k}_{\text{d}} $)的关系

Figure 6. Converged MSE curves versus processing window size ($ {k}_{\text{r}}\times {k}_{\text{d}} $) for different target numbers ($ {N}_{\text{t}} $)

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图 7 不同处理窗尺寸下的MSE曲线与迭代次数的关系

Figure 7. MSE curves versus iteration number with different processing window sizes

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表 1 RFPA信号波形参数

Table 1. Parameters of RFPA signal

参数	指数
载波频率($ {f}_{\text{c}} $)	8 GHz
脉冲宽度($ {T}_{\text{p}} $)	1 μs
平均脉冲间隔($ {T}_{\text{r}} $)	20 μs
脉冲间隔捷变范围($ {T}_{\text{w}} $)	6 μs
频率捷变范围(B)	400 MHz
采样频率($ {f}_{\text{s}} $)	800 MHz
脉冲间隔概率密度分布	均匀分布
频率概率密度分布	均匀分布
脉冲个数(M)	512
LFM基带信号带宽($ {B}_{0} $)	40 MHz
最小跳频间隔	0.78 MHz

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1 NUKT-WIAA算法流程图

1. Flowchart of the NUKT-WIAA algorithm

离线计算：
步骤1：根据式(19)计算并存储$ {a}_{l,k}\left(p,q\right) $，其中，　$ p=0,1,\cdots ,L-1 $，$ q=0,1,\cdots ,K-1 $，$ l=0,1,\cdots ,L-1 $，　$ k=0,1,\cdots ,K-1 $。
在线计算：
步骤2.1：根据式(17)计算$ {\boldsymbol{Y}}_{\text{NUKT}} $。
初始化：令$ \hat{x}_{p,q}^{0}={y}_{NUKT}\left(p,q\right) $，其中，$ p=0,1,\cdots ,L-1 $，　$ q=0,1,\cdots ,K-1 $。
迭代：
1: For $ i=1,2,\cdots ,I $
2: 　If $ i=1,2 $, then
3: 　　步骤2.2：根据式(34)计算$ {u}^{i} $；
4: 　Else
5: 　　步骤2.3：根据式(33)计算$ {\gamma }^{i} $；
6: 　End If
7: 　For $ p=0,1,\cdots ,L-1 $
8: 　　　步骤2.4：根据式(35)确定集合$ {\mathbb{N}}^{i} $；
9: 　　　For $ q=0,1,\cdots ,K-1 $
10: 　　　 If $ 10\mathrm{\lg }\left({\left\| \hat{x}_{p,q}^{i-1}\right\| }^{2}\right) \lt {\zeta }_{1} $ then
11: 　　　　步骤2.5：$ \hat{x}_{p,q}^{i}=\hat{x}_{p,q}^{i-1} $；
12: 　　　 Else
13: 　　　　步骤2.6：根据式(37)确定$ {\tilde{\boldsymbol{D}}}_{p,q}^{i} $，$ {{\boldsymbol{\varLambda }}}^{i-1} $和$ {\boldsymbol{x}}^{i-1} $；
14: 　　　　步骤2.7：根据式(36)计算$ {\tilde{\boldsymbol{R}}}_{p,q}^{i} $；
15: 　　　　步骤2.8：根据式(38)计算$ \hat{x}_{p,q}^{i} $；
16: 　　　 End If
17: 　　 End For
18: End For
19: If $ \frac{1}{LK}\sum \limits_{p=0}^{L-1}\sum \limits_{q=0}^{K-1}\left\| \hat{x}_{p,q}^{i}-\hat{x}_{p,q}^{i-1}\right\| \lt {\zeta }_{2} $ then
20: 输出估计值$ \hat{x}_{p,q}^{i} $；
21: Else
22: 返回第1行；
23: End If
24: End For
输出：$ \hat{x}_{p,q}^{\text{iter}} $，其中，$ \text{iter} $表示算法达到收敛时的迭代次数。

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表 2 距离扩展目标参数

Table 2. Parameters of range-spread targets

目标索引	散射点索引	距离(m)	速度(m/s)	SNR (dB)	RCM单元	目标索引	散射点索引	距离(m)	速度(m/s)	SNR (dB)	RCM单元
R1	S1	1505.81	43.95	–6	3	R2	S9	1504.50	64.09	0	4
	S2	1505.63	43.95	0	3		S10	1504.69	64.09	25	4
	S3	1505.44	43.95	30	3		S11	1504.88	64.09	3	4
	S4	1505.25	43.95	3	3		S12	1505.06	64.09	–5	4
	S5	1505.06	43.95	–10	3	R3	S13	1504.88	69.58	–35	4
	S6	1504.88	43.95	15	3		S14	1505.06	69.58	5	4
	S7	1504.69	43.95	1	3		S15	1505.25	69.58	1	4
	S8	1504.50	43.95	17	3		S16	1505.44	69.58	7	4

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表 3 点目标参数

Table 3. Parameters of point targets

目标索引	距离(m)	速度(m/s)	SNR (dB)	RCM单元
T1	1504.69	56.76	27	4
T2	1504.88	78.74	30	4
T3	1505.44	75.07	–10	5
T4	1505.06	58.59	–17	4
T5	1505.63	36.62	0	2
T6	1504.88	38.45	–7	3
T7	1505.81	49.44	–35	3
T8	1501.50	106.20	20	6
T9	1506.88	1.83	–7	1
T10	1511.06	87.89	15	5

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表 4 距离扩展目标功率估计误差(dB)

Table 4. Power estimation errors of range-spread target(dB)

目标索引	散射点索引	MF-IAA	MF-IAF	NUKT-WIAA	目标索引	散射点索引	MF-IAA	MF-IAF	NUKT-WIAA
R1	S1	1.12	–0.25	–0.05	R2	S9	17.81	0.03	0.01
	S2	–6.93	0.13	0.18		S10	–1.57	0.00	0.00
	S3	–3.65	0.03	–0.03		S11	5.79	0.06	0.05
	S4	14.07	0.36	0.17		S12	1.16	–0.01	–0.03
	S5	29.30	0.81	0.51	R3	S13	36.34	0.88	–0.61
	S6	7.04	0.08	0.13		S14	2.71	0.05	0.03
	S7	18.98	0.66	0.00		S15	1.20	0.01	–0.01
	S8	1.47	–0.01	0.01		S16	1.07	0.00	0.05

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表 5 点目标目标功率估计误差(dB)

Table 5. Power estimation errors of point targets(dB)

目标索引	MF-IAA	MF-IAF	NUKT-WIAA
T1	–2.74	0.00	0.00
T2	–3.26	0.00	0.00
T3	1.59	–0.02	0.06
T4	1.64	0.04	0.00
T5	–0.05	0.00	0.00
T6	1.41	0.00	–0.01
T7	2.49	–0.11	0.04
T8	–0.08	0.00	0.00
T9	0.07	0.02	0.01
T10	0.08	0.00	0.00

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表 6 目标参数

Table 6. Target parameters

目标索引	距离(m)	速度(m/s)	SNR (dB)	RCM单元
T1	1504.88	–45.78	0	–3
T2	1507.31	–9.16	–10	–1
T3	1505.81	–20.14	10	–2
T4	1503.94	–16.48	2	–1
T5	1503.94	–9.16	6	–1
T6	1507.31	9.16	–5	1
T7	1506.56	9.16	7	1
T8	1505.44	21.97	4	2
T9	1504.50	16.48	–13	1
T10	1509.56	43.95	–35	3

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表 7 存储需求对比

Table 7. Storage memory comparison

算法	存储需求
MF-IAA	$ M{L}^{2}K $
MF-IAF	$ {L}^{2}{K}^{2}+LKMN $
NUKT-WIAA	$ {L}^{2}{K}^{2} $

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表 8 计算复杂度对比

Table 8. Computational complexity comparison

算法	预处理部分	迭代部分
MF-IAA	$ \mathcal{O}\left[LMN\right] $	$ \mathcal{O}\left\{\left(iter\times LK\right)\left[{\left(M{k}_{\text{l}}\right)}^{3}+\left(LK+1\right){\left(M{k}_{\text{l}}\right)}^{2}+2M{k}_{\text{l}}\right]\right\} $
MF-IAF	$ \mathcal{O}\left[LKMN\right] $	$ \mathcal{O}\left\{\left(iter\times LK\right)\left[{\left({k}_{\text{r}}{k}_{\text{d}}\right)}^{3}+\left(LK+1\right){\left({k}_{\text{r}}{k}_{\text{d}}\right)}^{2}+2{k}_{\text{r}}{k}_{\text{d}}\right]\right\} $
NUKT-WIAA	$ \mathcal{O}\left[{M}^{2}N+\left(K+1\right)LM\right] $	$ \mathcal{O}\left[\displaystyle\sum \nolimits_{i=1}^{iter}\left(LK-{G}^{i}\right)C\left({k}_{\text{r}},{k}_{\text{d}},{\alpha }^{i}\right)\right] $

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表 9 运行时间对比

Table 9. Time cost comparison

算法	迭代次数	运行时间(s)
MF-IAA	14	29037.76
MF-IAF	13	1037.46
NUKT-WIAA	7	12.59
注：计算机主要配置：英特尔CPU I9-10850K，处理器频率为3.60 GHz，内存为16 GB，软件为MATLAB profiler 2019a。

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