Chirp-Rate Resolution of Fractional Fourier Transform in Multi-component LFM Signal

Distinguishing close chirp-rates of different linear frequency modulation （LFM） signals under concentrated and complicated signal environment was studied. Firstly, detection and parameter estimation of multi-component LFM signal were used by discrete fast fractional Fourier transform （FrFT）. Then the expression of chirp-rate resolution in fractional Fourier domain （FrFD） was deduced from discrete normalize time-frequency distribution, when multi-component LFM signal had only one center frequency. Furthermore, the detail influence of the sampling time, sampling frequency and chirp-rate upon the resolution was analyzed by partial differential equation. Simulation results and analysis indicate that increasing the sampling time can enhance the resolution, but the influence of the sampling frequency can he omitted. What＇s more, in multi-component LFM signal, the chirp-rate resolution of FrFT is no less than a minimal value, and it mainly dependent on the biggest value of chirp-rates, with which it has an approximately positive exponential relationship.

ALGORITHM FOR THE DETECTION AND PARAMETER ESTIMATION OF MULTICOMPONENT LFM SIGNALS

A novel algorithm based on Radon-Ambiguity Transform (RAT) and Adaptive Signal Decomposition (ASD) is presented for the detection and parameter estimation of multicompo-nent Linear Frequency Modulated (LFM) signals. The key problem lies in the chirplet estimation. Genetic algorithm is employed to search for the optimization parameter of chirplet. High estimation accuracy can be obtained even at low Signal-to-Noisc Ratio(SNR). Finally simulation results are provided to demonstrate the performance of the proposed algorithm.

Parameter estimation of LFM signals based on time reversal

In this paper,parameter estimation of linear frequency modulation(LFM)signals containing additive white Gaussian noise is studied.Because the center frequency estimation of an LFM signal is affected by the error propagation effect,resulting in a higher signal to noise ratio(SNR)threshold,a parameter estimation method for LFM signals based on time reversal is proposed.The proposed method avoids SNR loss in the process of estimating the frequency,thus reducing the SNR threshold.The simulation results show that the threshold is reduced by 5 dB compared with the discrete polynomial transform(DPT)method,and the root-mean-square error(RMSE)of the proposed estimator is close to the Cramer-Rao lower bound(CRLB).

Study on the Characteristics of LFM Signals, BC Signals and Their Mixed Modulation Signals

This paper proposes a linear frequency modulation (LFM signal) and biphase coding (BC signal) mixed modulation signal called LFM-BC signal. LFM-BC signal has both LFM signal and BC signal two kinds of traditional signal advantages but makes up for their shortcomings. In this paper, LFM-BC signal, LFM and BC signals are studied and compared from the time characteristic and frequency characteristic of the signal, fuzzy function, pulse compression and Doppler characteristics and low probability of interception (LPI) characteristics.

Generalized Parseval’s Theorem on Fractional Fourier Transform for Discrete Signals and Filtering of LFM Signals

This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality with lower and upper bounds associated with FRFT parameters, named as generalized Parseval’s theorem by us. These results theoretically provide potential valuable applications in filtering, and examples of filtering for LFM signals in FRFT domains are demonstrated to support the derived conclusions.

Union Resolution Performance of Frequency Modulation Parameter Based on RWT for LFM Signals

Union resolution performance of FM (frequency modulation) parameter based on Radon-Wigner transform (RWT) for multi-component LFM (linear frequency modulation) signals is studied. Firstly, the RWT output expression is offered, and the independent resolution performances of initial frequency and chirp rate are analyzed. Secondly, the RWT output approximate analytic expression is given based on quadratic Taylor's series expansion, and the contour property is analyzed. Contour can be used to picture the union resolution performance of FM parameter, and 2-D resolution performance is studied based on approximate analytic expression, and the union resolution expression of FM parameter and resolution ellipse are offered. The simulation results validate the union resolution expression, and show that the union resolution can improve the resolution performance of multi-component LFM signals, contrasted with absolute resolution performance. The paper can help the study of LFM parameter estimation and resolution performance.

Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform

This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm based on Quasi-Newton method is proposed which consists of two steps of searching, leading to a reduction in computation without loss of accuracy. And for multicomponent signals, we further propose a signal separation technique in the fractional Fourier domain which can effectively suppress the interferences on the detection of the weak components brought by the stronger components. The statistical analysis of the estimate errors is also performed which perfects the method theoretically, and finally, simulation results are provided to show the validity of our method.

基于多分量LFM信号时频分析的水声多普勒和时延估计研究

在水声多普勒因子和时延估计研究实用化的进程中,利用多分量线性调频(LFM)信号实现估计的算法研究越来越普遍。针对多分量LFM信号时频域存有交叉项时各分量参数估计不准确的问题,提出基于非完全残差与脊线段匹配的自适应模态分解方法。该方法采用非完全残差函数保留了交叉点处的部分时频信息,利用脊线段匹配方法提供更精确的预设时频脊线,改进了各分量LFM信号调频斜率和起始频率的估计精度。联合两个估计量进一步给出了多普勒因子和时延估计的算法。仿真结果表示,较现有模态分解算法,所提改进方法有效解决了估计分量过程中交叉区间断裂带来的估计误差;水声多径的条件下,该方法的多普勒因子和时延估计精度优于对比的现有方法。

The Detection of the Multi-source LFM Signal by Fractional Fourier Transform in Low SNR

The Linear Frequency-Modulated signal (LFM) has been used widely in radar signals. Using the characteristics of the linear frequency-modulated signal in fractional domain, three kinds of algorithms based on fractional domain have been put forward, that is, the maximum value detection, the energy concentration detection and the signal kurtosis detection. What's more, the detection performance of each algorithm has been analyzed qualitatively.

基于FRFT的低信噪比LFM信号参数快速估计算法

基于分数阶傅里叶变换(Fractional Fourier Transform,FRFT)对线性调频(Linear Frequency Modulated,LFM)信号参数进行估计,问题关键是确定FRFT最佳阶数,根据误差迭代思想提出新的参数估计算法,该算法利用归一化带宽和旋转角的转化关系,由估计误差推算角度差值,有效降低了运算量,不需要调频斜率正负的先验信息,改进的对数搜索算法可以进一步提高参数估计结果的稳定性和可靠性。仿真结果表明,信噪比在-8 dB以上时该方法在高效率的前提下仍具有良好的参数估计性能,平均估计误差在1%以内,估计结果接近Cramer-Rao下限,满足工程实时处理需求。

基于Z变换和改进FRI的LFM信号参数估计方法研究

为了完成线性调频(linear frequency modulation,LFM)信号的稀疏采样,并利用稀疏数据对原始信号参数进行估计,本文提出了一种基于Z变换和改进有限新息率(finite rate of innovation,FRI)的LFM信号参数估计方法。以Z变换理论为基础,设计了一种数学模型,一旦信号能够表达成该数学模型的结构形式,就能通过Z变换和零化滤波器的方法估计信号参数。然后,利用了自相关延迟的FRI结构对LFM信号采样,该结构不仅完成了LFM信号的稀疏采样,而且稀疏采样结果能够与数学模型结构相符。在理论上通过数学论证的方式证明了所提方法能够用于获取LFM信号参数信息,并通过仿真和实测数据验证了所提方法的有效性,理论和实验结果表明该方法只需要4个采样点就能实现对LFM信号的参数估计,并且实验中的参数估计误差均在3%以内,极大的提高有限新息率采样的参数估计效率。

高斯白噪声背景下的LFM信号的分数阶Fourier域信噪比分析

目标大机动运动使雷达回波表现为频率和调频率参数均未知的LFM信号。未知参数LFM信号的检测和估计采用分数阶Fourier变换来实现受到越来越多的关注,为此本文着重分析其分数阶Fourier变换的信噪比。首先推导出时限线性调频信号的分数阶Fourier变换模平方,给出了在分数阶Fourier域的峰值点与未知参数的关系,然后研究了附加白噪声LFM信号在分数阶Fourier域的统计特性,确定了其信噪比,并与理想情况(即参数频率和调频率参数已知)下线性相位匹配滤波器的输出信噪比进行了比较。

基于高斯短时分数阶傅里叶变换的多分量LFM信号检测与参数估计

该文针对线性调频信号,提出一种基于分数阶波包变换分析方法——高斯短时分数阶傅里叶变换。通过旋转角度的搜索及高斯窗口宽度的调整,能够在低信噪比条件下对多分量LFM信号进行检测,避免交叉项的出现,并能得到参数的估计值。通过推导分析给出变换结果的解析表达式,计算机仿真结果也表明了该变换的有效性。

基于改进Wigner-Hough变换的多分量LFM信号特征提取

为了解决Wigner-Hough变换对多分量线性调频(LFM)信号特征提取受噪声困扰的问题,提出采用数字图像处理中改进的Sobel算子对含噪声信号的WVD时频图进行边缘特征检测,利用Hough变换对信号特征进行提取.通过对WHT,SPWD-Hough变换以及改进WHT 3种方法进行计算机仿真比较结果表明,改进的WHT对多分量LFM信号的特征提取效果最好.

基于分数阶Fourier变换的多分量LFM信号检测与参数估计

介绍了分数阶 Fourier变换的基本原理和基本性质 ,提出了基于分数阶 Fourier变换的多分量 LFM信号检测和参数估计方法。为了解决多个 LFM分量之间的相互影响问题 ,特别是强分量掩盖弱分量的问题 ,本文还提出了一种结合逐次消去思想和分数阶 Fourier变换的多分量 LFM信号检测和参数估计算法 ,它可以解决强度相差较大的多分量 LFM信号中检测和估计弱 LFM分量参数的问题。

基于分数阶Fourier变换的LFM信号参数估计精度分析

本文采用一阶扰动分析的方法分析了基于分数阶Fourier变换的LFM信号参数估计精度,推导得到了频率估计误差均方值表达式和调频率估计误差均方值表达式,前者反比于信号时长,后者反比于信号时长的平方。结果表明,基于分数阶Fourier变换的LFM信号参数估计方法在估计精度方面达到了最优。

一种低信噪比下LFM信号参数快速估计算法

为了对线性调频(LFM)信号参数进行快速、准确的估计,提出了一种新算法.该算法根据LFM信号当能量一定时在相同时宽范围内频谱幅度平方与调频斜率成反比的特点,通过对若干组快速傅里叶变换(FFT)结果进行模值选大,同时给出了起始频率和调频斜率的估计.仿真结果表明,通过合理设置算法参数,算法可以用于信噪比低至-38 dB的LFM信号的参数估计.

基于积分二次相位函数的多分量LFM信号分析

基于二次相位函数的调频率估计算法用于多分量LFM信号时,信号间互扰严重并且会产生伪峰。针对这一问题,该文采用积分二次相位函数,提出了一种改进的多分量LFM信号分析方法,仿真实验表明:该方法相比于原方法能够有效抑制伪峰和信号间互扰,同时要求的信噪比门限低,估计均方误差更接近CRLB。

基于循环平稳分析的LFM信号盲处理结果可靠性评估

针对线性调频(LFM,Linear Frequency Modulation)信号盲处理结果的可靠性评估问题,提出了一种基于循环频率特征分析的处理算法.首先对观测信号进行调制方式识别及参数估计,并据此建立参考信号,后将观测信号与参考信号作相关运算.通过检测相关序列在零频率附近是否存在循环频率,实现对LFM信号盲处理结果的可靠性检验.文中对所提出检验算法的错误概率进行了理论推导,并以常用的离散多项式变换(DPT,Discrete Polynomial Transform)法为例进行了实证分析.仿真结果表明,相对于已有时域方法而言,本文算法无需估计信噪比,且在低信噪比条件下具有更好的统计性能.

一种高效的LFM信号参数估计方法及性能分析

该文从最大似然估计出发,得出了一种LFM信号参数估计方法,并采用一阶扰动模型分析其统计性能.该方法涵盖经典的多项相位变换法,将最大似然估计的多维搜索转化为一维搜索,但性能较多项相位变换法更优,低信噪比时仍可接近Cramer-Rao界.另外,结合基于傅里叶系数内插的快速高精度测频算法,该方法运算量与多项相位变换法相当,便于实现.仿真验证了其有效性及性能分析.