基于分数阶傅里叶变换的反辐射导弹检测技术

提出一种应用分数阶傅里叶变换(FRFT)来检测反辐射导弹(ARM)的新方法。由于分数阶傅里叶变换可以通过快速傅里叶变换实现,且不需进行多通道相位补偿,计算量小。仿真结果表明,该方法能够在ARM信噪比低达-14dB、ARM与载机回波功率比为-27dB的情况下,准确地检测出ARM来,从而实现ARM发射的早期告警。     

海杂波FRFT域的分形特性及目标检测

通过对实测海杂波数据的仿真分析,论证了海杂波在分数阶Fourier变换域具有分形特征,而且有目标单元和无目标单元存在分数维差异,这种分数维差异在分数阶Fourier变换域存在一个最大值。基于此特征提出了基于分数阶Fourier变换域海杂波分数维差异的目标检测方法,此方法通过检测回波信号分数阶Fourier变换域分数维的变化的最大值达到检测目标的目的,这比基于时域分数维差异的方法具有更好的检测效果。最后通过对实测海杂波数据进行仿真,证实了该方法的有效性。     

基于分数阶谱相减的弱目标检测方法

提出了海杂波背景下的基于分数阶谱相减的弱运动目标检测方法。该方法通过对回波信号检测单元和参考单元分别作分数阶Fourier变换(FRFT),然后将得到的两个模值相减来构成检测统计量,达到抑制杂波、提高检测概率的目的。利用IPIX实测数据实验表明,所提方法在增加目标与杂波FRFT峰值差、提高信杂比以及检测概率等方面都明显优于仅对回波作FRFT变换。在信杂比降低到-12 dB时仍能很容易地检测出目标。设置适当的恒虚警检测门限,该检测方法能够达到更好的检测效果。     

一种改进的AR模型反辐射导弹检测算法

反辐射导弹(ARM)具有多普勒频率时变特征,其回波信号的传统功率谱为一宽带频谱,不利于对其进行检测.针对这种情况,提出一种改进的AR模型检测算法,该算法将分数阶相关理论引入到AR模型功率谱估计中,把传统的功率谱转变为分数阶谱,使ARM回波信号能量得到聚集,从而实现ARM的有效检测.仿真结果表明,该方法能够在ARM信噪比低达-16 dB的情况下,准确将ARM检测出来,实现实时告警.     

基于分数阶Fourier变换的多分量LFM信号检测

分数阶Fourier变换作为最新提出的一种分析工具,其变换域同时具有信号的时域信息和频域信息,其实质是Fourier变换的一种广义形式,较适合处理非平稳信号。文中提出一种基于分数阶Fourier变换的多分量LFM信号参数估计与分离方法。通过在分数阶Fourier域搜索峰值点来对多分量LFM信号进行检测和参数估计,同时结合逐次消去思想来分离多个未知参数的LFM信号,抑制了强信号分量对弱信号分量的遮蔽干扰。     

一种基于分数阶Fourier变换的雷达运动目标检测算法

针对雷达回波为多分量LFM信号时,时频分析存在的交叉项干扰问题,提出了一种基于分数阶Fourier变换(Fractional Fourier Transform,FRFT)的伪Wigner分布(PWD).该方法通过在参数平面按阈值进行峰值搜索确定变换域阶次,再在相应的分数阶Fourier域计算PWD,有效地抑制了交叉项的干扰,有利于更好地提取信号的时频信息.仿真实验证明了在强背景噪声下该算法的有效性.     

抽样率转换的分数阶Fourier域分析

为了节省计算量及存储空间,在一个信号处理系统中常常需要不同的抽样率及其相互之间的转换.而在分数阶Fourier域中分析信号完全可用较低的抽样频率来抽样(低于Nyquist抽样率),这就意味着建立在频域上的传统抽样率转换理论将不再适用.本文将建立在Fourier变换(频域)上的传统抽样率转换理论推广到了分数阶Fourier域,通过研究时域抽取和零值内插操作在分数阶Fourier域的表示及其含义,导出了基于分数阶Fourier变换的有理分数倍抽样率转换理论.可以看到,将分数阶Fourier变换的变换阶数取为π/2,便得到了与传统频域多抽样率理论完全一致的结果.最后,本文通过仿真对导出的分数阶Fourier域多抽样率理论进行了验证.     

基于FRFT的线性调频信号欠采样快速检测方法

采用分数阶Fourier变换对线性调频信号(Linear Frequency Modulation,LFM)进行检测与参数估计时,由于信号的特征未知,需要运用二维搜索方法确定分数阶Fourier变换的最佳旋转角度.该方法运算量巨大.为减少运算量,本文推导了欠采样前后LFM信号的分数阶Fourier变换最佳能量聚集旋转角度关系,证明了无噪LFM信号的调频率估计可以完全不受Nyquist采样定理的限制;通过推导分析欠采样含噪LFM信号在最佳分数阶Fourier域的信噪比,给出了欠采样倍数M对LFM信号检测的影响及其选取原则;最终提出一种基于欠采样理论的LFM信号快速检测方法.实验结果表明,当M选取合适时,利用原始信号的欠采样样本即可对LFM信号实现有效检测,快速确定其调频率.     

一体化电子战系统中连续波干扰抑制研究

在雷达信号和通信信号一体化电子战系统中,需要处理的雷达信号和通信信号在时频域都是重叠的,存在很强的时频耦合,给信号检测带来很大的困难。讨论了作为干扰的强通信信号对宽带雷达脉冲信号非协作检测的影响,提出了一种基于分数阶Fourier变换的干扰抑制方法。该方法利用分数阶Fourier变换对不同信号的时域聚集特性,在分数阶Fourier变换域滤除干扰,提高了信号的信干比,改善系统对宽带脉冲的检测性能,该方法对存在多个通信干扰信号时仍然适用。仿真结果表明,该方法对提高系统检测宽带雷达脉冲信号的性能是有效的。     

基于频域延时FRFT模函数对消的检测方法

在分析线性调频信号分数阶Fourier变换的频移特性的基础上,提出了一种基于频域延时FR-FT模函数对消的海面弱运动目标检测方法。此方法在基本不减弱信号的情况下有效地抑制了海杂波,在低信杂比条件下有较好的检测性能。利用IPIX实测数据仿真实验表明,所提方法在改善信杂比以及提高检测概率等方面都明显优于仅对回波作FRFT变换。文中给出的检测概率曲线表明该方法在低信杂比条件下具有较高的检测概率,证实了方法的有效性。     

一种改进的基于FrFT的SAR运动目标检测与成像方法

针对传统的基于FrFT的SAR地面运动目标检测方法的不足,该文结合分数阶Fourier域滤波、重排谱图以及CLEAN思想,提出了一种改进的方法。该方法能够以较高精度估计目标的多普勒起始频率和中心频率,并能分辨在时频平面位于同一直线的多个目标。最后给出了FrFT数值计算结果与有量纲的多普勒参数之间的转换公式。仿真结果表明了该方法的有效性。     

Closed-Form Analytical Expression of Fractional Order Differentiation in Fractional Fourier Transform Domain

In this paper, a closed-form analytical expression for fractional order differentiation in the fractional Fourier transform (FrFT) domain is derived by utilizing the basic principles of fractional order calculus. The reported work is a generalization of the differentiation property to fractional (noninteger or real) orders in the FrFT domain. The proposed closed-form analytical expression is derived in terms of the well-known confluent hypergeometric function. An efficient computation method has also been derived for the proposed algorithm in the discrete-time domain, utilizing the principles of the discrete fractional Fourier transform algorithm. An application example of a low-pass finite impulse response (FIR) fractional order differentiator in the FrFT domain has also been investigated to show the practicality of the proposed method in signal processing applications.     

A Novel Multiuser SISO-BOFDM Systems with Group Fractional Fourier Transforms Scheme

Existing multiuser (MU) schemes are mainly accomplished by MIMO techniques. In this letter, we propose a novel group fractional Fourier transform based MU SISO Biorthogonal Frequency Division Multiplexing system, in which multiple independent data streams from co-channel mobile stations (MSs) can be transmitted in the same frequency and time slot. Because the chirp bases generated by different orders based fractional Fourier transform (FrFTs), at same subchannel, are mutually approximately orthogonal, when FrFT orders are effectively allocated to different co-channel MSs, the co-channel interference can be perfectly suppressed by simple correlative detection in FrFT domain with respective optimal order, at the receiver of each MS. Finally, system simulations show the essential advantages over conventional MU schemes.     

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。     

基于分数阶傅里叶变换的Chirp浅剖精细探测方法

实现弱回波信号检测和高信噪比(SNR)浅剖图像获取是浅剖精细探测的首要任务。该文在分析分数阶傅里叶变换(FrFT)解卷积原理,推导时间量纲化变换公式的基础上,提出一种基于FrFT的浅剖精细探测新方法。该方法通过FrFT解卷积实现分数阶傅里叶域(u域)沉积层冲激响应求解,采用u域加窗滤波技术对带内噪声进行有效抑制,经时间量纲化变换实现高信噪比u域沉积层冲激响应包络信号至时域浅剖包迹的直接变换,得到高质量的浅剖图像。仿真实验和实测数据处理验证了算法的精细探测能力,算法性能优于脉冲压缩和自回归(AR)预测滤波方法。     

基于载机信号重构的反辐射导弹检测技术

针对反辐射导弹的检测问题,主要是消除载机信号的干扰。提出一种基于栽机信号重构的反辐射导弹检测技术。首先,在频域估计出载机信号的多普勒频率以及幅度后,重构载机信号,并在分数阶Fourier域消除载机信号;最后结合载机信号和反辐射导弹信号在分数阶Fourier域的差别,有效地排除载机信号残余的干扰并检测出反辐射导弹。该方法不需要估计栽机信号的相位,因此简单易行。仿真证实,该方法可以有效地消除栽机信号干扰,并能检测出反辐射导弹。     

Analysis of Chirp as windowing function through fractional Fourier transform

This article presents a new mathematical model for obtaining the fractional Fourier transform (FrFT) of Chirp function. FrFT is a parameterised transform having an adjustable transform parameter which makes it more flexible and superior over ordinary FT in several applications. It is an important tool used in signal processing for spectral analysis. The closed-form expression derived for FrFT of finite duration Chirp establishes the dependence of FrFT of Chirp on the order of FrFT and the Chirp parameter. The mathematical model obtained shows that the Chirp function can be used as an adjustable window function in the fractional Fourier domain. The main-lobe width, side-lobe level and side-lobe fall-off rate of a Chirp window can be controlled by changing the adjustable transform parameter to different values. For some particular values of fractional angle, Chirp can give better spectral parameters than the existing window functions. By varying the order of FrFT, the variations in spectral parameters of the Chirp window are obtained and studied. The performance of the Chirp window in fractional domain is also compared with some of the existing windows.     

基于分数傅里叶变换的OFDM的联合定时和频率同步

In this paper a joint timing and frequency synchronization method based on Fractional Fourier Transform (FrFT) is proposed for Orthogonal Frequency-Division Multiplexing (OFDM) system. The combination of two chirp signals with opposite chirp rates are used as the training signal, the received training signal with timing and frequency offset is transformed by FrFT and the two peaks representing two chirps in FrFT domain are detected, then the position coordinates of the two peaks are precisely corrected and substituted into an equation group to calculate timing and frequency offset simultaneously. This method only needs one FrFT calculation to implement synchronization, the computational complexity is equal to that of FFT and less than that of correlation or maximum likelihood calculation of existing methods, and estimation range of frequency offset is large, greater than half the signal bandwidth, while the simulation results show that even at low SNR it can accurately estimate timing and frequency offset and the estimation error is less than that of existing methods.     

Beamforming using the fractional Fourier transform

We present a new method of beamforming using the fractional Fourier transform (FrFT). This method encompasses the conventional minimum mean-squared error (MMSE) beamforming in the frequency domain or spatial domain as special cases. It is especially useful for applications involving chirp signals such as signal enhancement problems with accelerating sinusoidal sources where the Doppler effect generates chirp signals and a frequency shift and active radar problems where chirp signals are transmitted. Numerical examples demonstrate the potential advantage of the proposed method over the ordinary frequency or spatial domain beamforming for a moving source scenario.     

基于FrFT空间目标探测与高精度频率估计

针对空间目标探测中低信噪比下信号检测与频率精确估计的问题,提出了基于分数阶傅里叶变换(FrFT)的实现方法。首先介绍FrFT进行参数估计的基本原理,在对接收回波信号的动态特性进行分析的基础上,为满足信号检测概率和实时处理要求,设计FrFT在空间目标检测应用中的相关参数,并提出频率估计精度的改进措施,分析了目标检测和频率估计性能。仿真分析结果表明该方法满足工程要求。