微弱LFM信号的FrFT检测能力分析

基于分数阶傅里叶变换（FrFT）检测线性调频（LFM）信号广泛应用于雷达、通信、声呐和电子战领域，但缺乏对检测灵敏度的定量分析。为此，研究了FrFT对微弱LFM信号的检测能力。根据FrFT思想和二元假设检验理论，推导了检测概率和虚警概率的数学表达式。由于表达式是关于LFM信号频谱的函数，因此区分快变信号和慢变信号对LFM的频谱进行了合理近似。基于接收机工作特性曲线分析了FrFT检测LFM信号的灵敏度。仿真比较了FrFT与传统傅里叶变换（FT）对微弱LFM信号的检测能力，结果表明FrFT对LFM信号的检测灵敏度和信号累积能力均优于FT。

Detection capability analysis of weak LFM signals based on fractional Fourier transform

Detection of linear frequency modulated(LFM) signals based on fractional Fourier transform(FrFT) is widely used in radar,communications,sonar,and electronic warfare fields.However,there is a lack of quantitative analysis of detection sensitivity.Therefore,detection ability of FrFT to weak LFM signals is studied.According to FrFT theory and binary hypothesis testing theory,mathematical expressions of detection probability and false alarm probability are deduced.Since the expression is a function of the frequency spectrum of the LFM signal,a distinction is made between the fast-varying signal and the slowly-varying signal to make a reasonable approximation to the spectrum of the LFM.And then,detection sensitivity of FrFT detecting LFM signal is analyzed based on the receiver operating characteristic curve.Comparison of detection capability between FrFT and traditional Fourier transform(FT) through simulation shows that the detection capability of FrFT is superior to that of FT.