﻿ 一种基于脉内特征的PRI变换新方法
 舰船科学技术  2017, Vol. 39 Issue (10): 132-136 PDF

1. 江苏科技大学 电信学院，江苏 镇江 212003;
2. 中国船舶重工集团公司第七二三研究所，江苏 扬州 225001

A new PRI transform method based on intra-pulse characteristics
LE Ming-jun1, LIANG Guang-zhen2, XIONG Chong1
1. School of Electronic Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China;
2. The 723 Research Institute of CSIC, Yangzhou 225001, China
Abstract: Pulse repetition interval (PRI) transform and its improved algorithms are the classical algorithms in radar signal sorting area. With the signal environment getting more and more complex, radar signals with different modulation overlap seriously and the PRI distribute in wide ranges. In addition the pulse jitter is serious, the traditional method of sorting capability has been greatly reduced and even it will be sorted wrong. In response to these problems, further improvement should be applied in traditional improve algorithms. We propose a new sorting method which use the intra-pulse characteristics to separate pluses beforehand, which greatly reduces the complexity of the signal. It is possible to adapt the jitter problems and wide range PRI values questions in radar signal sorting and verified the validity of the new algorithm by computer simulation.
Key words: PRI transform     complex signal environment     pulse jitter     intra-pulse characteristics
0 引 言

1 PRI算法原理及脉内特征分析 1.1 传统改进PRI算法原理

 $g(t) = \sum\limits_{n = 0}^{N - 1} {\delta (t - {t_n})}\text{，}$ (1)

 $D(\tau ) =\int_{ - \infty }^\infty g(t)g(t + \tau \exp (2\pi jt/\tau ){\rm d}t \text{，}$ (2)

 $\begin{split}D(\tau ) =\sum\limits_{n = 0}^{N - 1} {\sum\limits_{m = 0}^{n - 1} {\delta (\tau - {t_n} + {t_m})} }\cdot \exp [2\pi j{t_n}/({t_n} - {t_m})]\text{。}\end{split}$ (3)

PRI变换与自相关函数的区别在于加入了相位因子 $\exp (2\pi jt/\tau )$ ，对交叠脉冲信号做自相关处理，会在真PRI处出现峰值，在真PRI整数倍处也会出现峰值，即会出现子谐波问题，PRI变换中加入的相位因子一方面可以累计真实PRI的谱峰，另一方面可以抑制PRI的高次谐波。

1）随着TOA远离时间起点，PRI变换中的相位因子的相位误差增大。

2）本应该集中在同一个PRI箱中的脉冲对由于PRI的抖动而将分布在平均PRI值附近的几个箱中。

$[{\tau _{\min }},{\tau _{\max }}]$ 为PRI的范围，并将此范围分解成K个小区间，每个小区间为一个PRI箱，则第k个PRI箱的中心为

 $\begin{array}{l}{\tau _k} = (k - \displaystyle\frac{1}{2})[({\tau _{\max }} - {\tau _{\min }})/K] + {\tau _{\min }}\text{，}\\k = 1,2, \cdots K\text{。}\end{array}$ (4)

 $\begin{array}{l}{D_{_k}} = \int {_{{\tau _k} - {b_k}/2}^{{\tau _k} + {b_k}/2}} D(\tau ){\rm d}\tau = \\[5pt]\sum\limits_{{\tau _k} - {b_k}/2 < \atop{t_n} - {t_m} < {\tau _k} + {b_k}/2} \!\!\!\!\!\!\!\!\!\!\!\!\!\!{\exp [2\pi j{t_n}} /({t_n} - {t_m})]\text{。} \end{array}$ (5)

1）观察时间原则：

 $\left| {{D_k}} \right| \geqslant \alpha \frac{T}{{{\tau _k}}} \text{，}$ (6)

2）消除谐波原则

 $\left| {{D_k}} \right| \geqslant \beta {C_k} \text{，}$ (7)

3）消除噪声原则

 $\left| {{D_k}} \right| \geqslant \gamma \sqrt {T{\rho ^2}{b_k}}\text{。}$ (8)

 ${A_k} = \max \left\{ {\alpha \frac{T}{{{\tau _k}}},\beta {C_k},\gamma \sqrt {T{\rho ^2}{b_k}} } \right\}\text{。}$ (9)

1.2 雷达脉内特征分析

 $s(n) = A\exp \{ j[\frac{{2\pi {f_0}n}}{{{f_c}}} + \varphi ]\}\text{，}$ (10)

 $s(n) = A\exp \{ j2\pi [\frac{{{f_0}n}}{{{f_c}}} + \frac{{\mu {n^2}}}{{2f_c^2}}]\} \text{，}$ (11)

 $s(n) = A\exp \{ j[\frac{{2\pi {f_0}n}}{{{f_c}}} + \varphi (n)]\}\text{，}$ (12)

 $s(n) = A\exp \{ j[\frac{{2\pi {f_k}n}}{{{f_c}}} + \varphi ]\}\text{。}$ (13)

1.2.1 单频常规信号（CW）

 $\begin{array}{l}R(k) = {A^2}E\\[3pt] \left\{ \begin{array}{l}2\exp [j2\pi {f_0}k/{f_c}] - \exp [j2\pi {f_0}(k - 1)/{f_c}]\text{，}\\[3pt] - \exp [j2\pi {f_0}(k + 1)/{f_c}]\text{。}\end{array} \right.\end{array}$ (14)

1.2.2 线性调频信号（LFM）

LFM信号的数学表达式为：

 $s(t) = Arect(\frac{t}{T})\exp [j2\pi ({f_c}t + \frac{K}{2}{t^2})]\text{，}$ (15)

 $f = {f_c} + Kt,\,\left( - \frac{T}{2} \leqslant t \leqslant \frac{T}{2}\right)\text{，}$ (16)

 图 1 典型线性调频信号 Fig. 1 Typical signal of LFM

 $|S(f)| = \frac{A}{{\sqrt {2k} }}{\{ {[c({k_1}) + c({k_2})]^2} + {[s({k_1}) + s({k_2})]^2}\} ^{1/2}}\text{，}$ (17)

 $\begin{split}\theta (f) = - \displaystyle\frac{\pi }{k}{(f - {f_c})^2}+ \arctan \left[\displaystyle\frac{{s({k_1}) + s({k_2})}}{{c({k_1}) + c({k_2})}}\right]\text{。}\end{split}$ (18)

1.2.3 相位编码信号（PSK）和频率编码信号（FSK）

PSK和FSK信号形式见式（12）和式（13），雷达信号采用PSK调制后，信号实际上是一种脉冲压缩扩谱信号，信号频谱展宽，功率谱密度降低，接收机可以利用匹配接收得到信号增益，还可以利用数字接收技术对编码序列进行改变。对于FSK信号，脉内各子码频率不同，在子码范围内，瞬时自相关码元无跳变时即为CW信号。

2 基于脉内特征的PRI变换算法

1）接收端接收包含脉内特征和到达时间的脉冲流，假设信号的脉内特征已经正确识别，首先根据脉冲的不同调制方式将脉冲流进行划分，形成脉冲子流并编号，此时脉冲流得到了稀释。

2）对各个脉冲子流进行PRI变换实现不同脉冲的信号分选，不同体制的雷达脉冲对应不同的PRI谱图。

3）对估计出的PRI进行分析与识别，以便后续处理。

 图 2 算法实现流程 Fig. 2 Algorithm implementation process

3 计算机仿真及结果分析

 图 3 PRI值估计结果 Fig. 3 Estimated results of PRI value

1）传统算法的检测结果误差为0.071 7，新算法误差仅为0.005 4，检测结果更接近真实的PRI值，而且峰值非常明显，所受抖动的影响明显小于传统改进算法；

2）由于加入了脉内特征作为分选参数，将脉冲以脉内特征为依据划分为不同的脉冲子流，再对每个脉冲子流进行处理，很大程度地稀释了脉冲，降低了数据的复杂度；

3）本文算法的结果除了包含检测出的PRI值，还有其对应的脉内特征，利于进一步分析与处理。

4 结 语

 [1] 何明浩. 雷达对抗信息处理[M]. 北京: 清华大学出版社, 2010. HE Ming-hao. Radar countermeasure information processing [M]. Beijing Tsing Hua University Press, 2010. [2] 乔宏乐, 王超, 王鹏. 基于PRI变换法的脉冲信号分选算法[J]. 火控雷达技术, 2012 (2): 34–38. QIAO Hongle, WANG Chao, WANG Peng. Pulse Signals De-interleaving Algorithm Based on PRI Transform[J]. Fire Control Radar Technology, 2012 (2): 34–38. [3] MARDIA H K. New techniques for the deinterleaving of repetitive sequences[J]. Radar & Signal Processing Iee Proceedings F, 1989, 136 (4): 149–154. [4] MILOJEVIĆ D J, POPOVIĆ B M. Improved algorithm for the deinterleaving of radar pulses[J]. Radar & Signal Processing Iee Proceedings F, 1992, 139 (1): 98–104. [5] MAHDAVI A, PEZESHK A M. A fast enhanced algorithm of PRI transform[C]// International Symposium on Parallel Computing in Electrical Engineering. 2011: 179–184. [6] 魏东升, 巫胜洪. 雷达信号脉内细微特征的研究[J]. 舰船科学技术, 1994 (3): 23–30. WEI Dongsheng, WU Shenghong. Study on the subtle characteristics of radar signal[J]. Ship Science and Technology, 1994 (3): 23–30. [7] 陈韬伟. 基于脉内特征的雷达辐射源信号分选技术研究[D]. 成都: 西南交通大学, 2010. CHEN Tao-wei. Deinterleaving technology for radar emitter signals based on the intra-pulse features [D]. Chengdou: Southwest Jiaotong University, 2010. [8] 贾立印, 张洪顺. LFM脉冲压缩雷达信号的时频分析及其应用[C]// 全国无线电应用与管理学术会议. 2008. JIA Li-yin, ZHANG Hong-shun. Time-frequency analysis of LFM pulse compression radar signal and appliance [C]// National Conference on Radio Application and Management, 2008.