吕分布时间尺度分析及实现方法研究

doi:10.12263/DZXB.20210816

电子学报 ›› 2022, Vol. 50 ›› Issue (11): 2790-2798.DOI: 10.12263/DZXB.20210816

吕分布时间尺度分析及实现方法研究

张亮¹^,², 于洪波¹, 张翔宇³^,⁴, 王国宏¹, 景洲²

^1.海军航空大学信息融合研究所, 山东烟台 264001
^2.中国人民解放军94326部队, 山东济南 250000
^3.海军航空大学航空电子与指挥系, 山东青岛 266041
^4.中北大学信息与通信工程学院, 山西太原 030023

收稿日期:2021-06-30 修回日期:2021-10-21 出版日期:2022-11-25
- 作者简介:
- 张亮男, 1987年出生于山东德州.现为海军航空大学信息融合研究所博士研究生.研究方向为雷达抗干扰.E‑mail: 332401479@qq.com
  于洪波男, 1983年出生于山东宁阳.现为海军航空大学信息融合研究所讲师.研究方向为雷达数据处理和情报分析.E‑mail: 281861081@qq.com
- 基金资助:
- 国家自然科学基金 (61731023); 山东省自然科学基金 (ZR2020QF071); 博士后科学基金 (2021M693003); 泰山学者攀登计划专项经费

LV’s Distribution Time-Scaling Analysis and the Research on Implementation Methods

ZHANG Liang¹^,², YU Hong-bo¹, ZHANG Xiang-yu³^,⁴, WANG Guo-hong¹, JING Zhou²

^1.Institute of Information Fusion，Naval Aviation University，Yantai，Shandong 264001，China
^2.Unit 94326 of PLA，Jinan，Shandong 250000，China
^3.Department of Avionics Engineering and Command，Naval Aviation University，Qingdao，Shandong 266041，China
^4.College of Information and Communication Engineering，North University of China，Taiyuan，Shanxi 030023，China

Received:2021-06-30 Revised:2021-10-21 Online:2022-11-25 Published:2022-11-19

摘要/Abstract

摘要：

吕分布（LV’s Distribution，LVD）是一种中心频率-调频斜率域信号分析工具，核心思想是对信号瞬时自相关函数进行时间尺度（Time-Scaling，TS），去除时间变量与延时变量的耦合关系. 本文从TS的角度对LVD进行了解释，在此基础上，分析了现有基于尺度傅里叶变换的TS实现方法，指出该方法存在频率混叠和频点丢失问题，并进行了修正，同时基于尺度变换和线性正则变换，进一步提出2种TS实现方法并将其应用于LVD. 试验表明，相比现有LVD实现方法，所提3种实现方法在计算复杂度、抗噪效能、检测非线性调频信号方面具备各自优势.

关键词: 吕分布, 时间尺度, 实现方法, 尺度傅里叶变换, 尺度变换, 线性正则变换

Abstract:

LV’s distribution(LVD) is a signal analysis tool in centroid frequency-chirp rate(CFCR) domain. The core idea of LVD is to remove the coupling relationship between time variables and delay variables, by performing time-scaling(TS) on signal instantaneous autocorrelation function. In this paper, LVD is reinterpreted from the perspective of TS. On this basis, the existing TS implementation method based on scaled Fourier transform(SFT) is analyzed and modified, owing to the problems of spectrum loss and frequency aliasing. At the same time, two TS implementation methods based on scale transform(ST) and linear canonical transform(LCT) are proposed and applied to LVD. Experimental results show that the proposed methods have their own advantages in computational complexity, anti-noise performance, and nonlinear frequency modulation signal detection, compared with the existing LVD implementation method.

Key words: LVD, TS, implementation methods, SFT, ST, LCT

中图分类号:

TN957

张亮, 于洪波, 张翔宇, 王国宏, 景洲. 吕分布时间尺度分析及实现方法研究[J]. 电子学报, 2022, 50(11): 2790-2798.

ZHANG Liang, YU Hong-bo, ZHANG Xiang-yu, WANG Guo-hong, JING Zhou. LV’s Distribution Time-Scaling Analysis and the Research on Implementation Methods[J]. Acta Electronica Sinica, 2022, 50(11): 2790-2798.

图/表 12

图1 Z平面频点分布图

图2 复乘次数随信号采样点数变化曲线

图3 对称参数瞬时自相关函数

图4 去耦后的对称参数瞬时自相关函数

图5 一维傅里叶变换结果

图6 第1个LFM分量吕分布

图7 多分量LFM信号吕分布

图8 皮尔逊相关系数随尺度因子变化曲线

图9 信号检测率与Rényi熵随信噪比变化曲线

图10 参数估计平均相对误差随信噪比变化曲线

图11 蝙蝠超声波时频分布

图12 蝙蝠超声波的吕分布

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吕分布时间尺度分析及实现方法研究

LV’s Distribution Time-Scaling Analysis and the Research on Implementation Methods

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