Parameter estimation method for a linear frequency modulation signal with a Duffing oscillator based on frequency periodicity

In view of the complexity of existing linear frequency modulation(LFM)signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio(SNR),a parameter estimation method for LFM signals with a Duffing oscillator based on frequency periodicity is proposed in this paper.This method utilizes the characteristic that the output signal of the Duffing oscillator excited by the LFM signal changes periodically with frequency,and the modulation period of the LFM signal is estimated by autocorrelation processing of the output signal of the Duffing oscillator.On this basis,the corresponding relationship between the reference frequency of the frequencyaligned Duffing oscillator and the frequency range of the LFM signal is analyzed by the periodic power spectrum method,and the frequency information of the LFM signal is determined.Simulation results show that this method can achieve high-accuracy parameter estimation for LFM signals at an SNR of-25 dB.

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).

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.

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.

HIGH RESOLUTION RANGE PROFILE FORMATION BASED ON LFM SIGNAL FUSION OF MULTIPLE RADARS

This paper presents a new method of High Resolution Range (HRR) profile formation based on Linear Frequency Modulation (LFM) signal fusion of multiple radars with multiple frequency bands. The principle of the multiple radars signal fusion improving the range resolution is analyzed. With the analysis of return signals received by two radars,it is derived that the phase difference between the echoes varies almost linearly with respect to the frequency if the distance between two radars is neg-ligible compared with the radar observation distance. To compensate the phase difference,an en-tropy-minimization principle based compensation algorithm is proposed. During the fusion process,the B-splines interpolation method is applied to resample the signals for Fourier transform imaging. The theoretical analysis and simulations results show the proposed method can effectively increase signal bandwidth and provide a high resolution range profile.

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。

脉冲噪声下基于Sigmoid的LFM信号参数估计

由于脉冲噪声具有的短时大幅值特性,使得基于高斯假设的信号参数估计方法无法在脉冲噪声环境下有效估计参数。针对此问题,利用α稳定分布模拟随机脉冲噪声,提出了一种基于Sigmoid-CFRFT的LFM信号参数估计方法。首先,建立了一种自适应Sigmoid函数,证明了信号经过此非线性变换后,信号的2阶矩由无界变为有界,且信号的相位信息保持不变。其次,将变换后的信号进行离散时间CFRFT,建立了数学优化模型,并使用水循环算法搜索最优值点。最后,利用了非标准SαS分布噪声的修正方法,分析了标准和非标准分布下参数估计的性能。仿真结果说明,所提方法不仅可以有效抑制脉冲噪声对LFM信号分数谱特征的影响,而且能够实现低信噪比信号参数的高精度估计。相比于现有的基于非线性变换的参数估计方法,本文方法具有更好的精度,稳定性和噪声鲁棒性。

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。

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。

LFM-BPSK复合调制信号识别与参数估计

首先介绍了相位编码与线性调频(Linear frequency modulation and binary phase shift keying,LFM-BPSK)复合调制信号的模型,并分析了其相位特征及概率密度函数,然后通过分段滤波提高信号的输出信噪比。采用二叉树方法,基于相位展开和瞬时频率对LFM-BPSK复合调制信号、BPSK信号和LFM信号进行了识别,并讨论和分析了纽曼-皮尔逊(N-P)准则下识别门限的选取。接着对LFM-BPSK复合调制信号进行参数估计;最后用Matlab对LFM-BPSK复合调制信号的识别进行了仿真验证,并对识别后的信号进行了参数估计的仿真。结果表明,本文方法在较低信噪比下仍能实现较好的识别性能和参数估计精度。

高精度LFM信号参数估计的谱校正方法

为精确估计噪声背景下线性调频(linear frequency modulation,LFM)信号的调频率和中心频率等参数,提出了一种基于Radon模糊变换(Radon-ambiguity transform,RAT)和分数阶傅里叶变换(fractional Fourier transform,FRFT)的离散谱校正估计方法。该方法将LFM信号的调频率和中心频率估计问题转化为模糊域和分数阶Fourier域上的两次一维谱峰搜索过程,并且通过对矩形窗截断的LFM信号的RAT和FRFT谱线结构分析,将能量重心谱校正法引入两次谱峰搜索过程,在不增加运算量的基础上实现了谱峰位置的超分辨率估计,较大幅度地提高了信号的参数估计精度。仿真结果显示,对于单分量LFM信号情况,该方法对信号的RAT和FRFT谱峰位置的校正误差分别降到了扫描步长的1.55%和4.94%,证明了该方法的有效性。

基于多尺度线性调频基信号稀疏分解的多分量LFM信号检测

该文针对传统的基于二次时频分析和原子追踪匹配方法处理多分量LFM信号时存在的时频干扰和等振幅交叉分解等问题,提出了一种基于多尺度线性调频基信号稀疏分解的多分量LFM信号检测方法,该方法采用多尺度的线调频基函数对多分量LFM信号进行投影分解,通过从不同的时间支撑区内投影系数最大的基函数中寻找出使分解信号能量最大的基元函数组合,逐次获得信号包含的能量最大的LFM信号分量,从基元函数连接形成的频率曲线即可获得LFM信号分量瞬时频率的估计,再对分量瞬时频率求起始时间点的频率值和曲线斜率便可得到该LFM分量的中心频率及调频斜率,仿真试验表明该文方法能精确地提取等振幅多分量LFM信号的瞬时频率,并具有很强的抗噪声干扰能力。

基于正交匹配追踪的欠采样LFM信号参数估计

受限于目前数字采样水平,对宽带线性调频(LFM)信号进行欠采样参数估计具有重要的研究价值。该文基于线性调频信号具有近似矩形的幅频特性,对其频谱的差分过程进行处理,采用正交匹配追踪算法有效提取欠采样信号频谱的边缘信息,实现在欠采样环境下的宽带线性调频信号起始频率和终止频率的估计,具有较高的估计精度,仿真实验证明了其有效性。

Evaluation of the performance of linearly frequency modulated signals generated by heterodyning two free-running laser diodes

A method to evaluate the influence of the laser linewidth on the linearly frequency-modulated(LFM)signals generated by heterodyning two free-running laser diodes(LDs)is proposed.The Pearson correlation coefficient between the instantaneous frequency of the generated LFM signal and that of an ideal LFM signal is introduced to quantify the quality of the generated LFM signal.The closed-form solution of the correlation coefficient is given,which shows that the correlation coefficient is determined by the ratio of the LFM signal bandwidth to the square root of the total linewidth of the two LDs when the observation interval is fixed.Simulation results are also given,which proves the correctness of the theoretical results.

LFM信号参数估计的插值FRFT算法

提出了一种基于分数阶傅里叶变换(fractional Fourier transform,FRFT)的线性调频(linear fre-quency modulation,LFM)信号参数估计的插值算法。首先针对FRFT的旋转角度α搜索步长问题,提出了在较大搜索步长下进行插值以得到α精估计的方法;然后针对离散分数阶傅里叶变换(digital fractional Fourier transform,DFRFT)因参数u离散化而造成的栏栅效应问题,采用相邻谱线进行插值以得到u的精估计;最后用α和u插值精估计结果对单分量LFM信号的参数进行估计。这一方法在不影响估计精度的前提下,降低了计算量和复杂度。仿真结果表明,在较低的信噪比下,LFM信号参数估计的精度仍十分逼近克拉美罗界(Cramer-Rao bound,CRB)。

基于高斯加权分数阶傅里叶变换的LFM信号参数估计

针对低占空比下传统算法参数估计性能下降的问题,提出了一种高斯加权分数阶傅里叶变换(GFRFT,Gaussian-weighted fractional Fourier transform)参数估计方法。给出了时限信号GFRFT的定义并推导了其模值平方的特性,研究了高斯白噪声背景下GFRFT的输出信噪比并给出了闭式表达式,进行了仿真实验并讨论说明了该方法的适用条件。仿真结果表明,该方法在低占空比的情况下可以有效地提高参数估计精度。

基于NP准则的LFM信号盲处理结果可靠性检验

本文研究了线性调频(LFM,Linear Frequency Modulation)信号盲处理结果的可靠性检验问题,提出了一种基于纽曼皮尔逊(NP,Neyman-Pearson)准则的检验算法.先根据调制识别结果对应的信号模型构造参考信号,通过分析不同假设下参考信号与观测信号相关累加值概率分布参数的差异,利用NP准则构建检验统计量并确定相应的门限,对LFM信号盲处理结果的可靠性进行检验.计算机仿真结果表明,本算法在较低信噪比条件下,可实现对LFM信号盲处理结果的可靠性检验.

LFM脉压雷达的随机移频干扰研究

分析了固定移频干扰对LFM脉冲压缩雷达的干扰效果,针对固定移频干扰容易被识别的缺点,提出了一种改进的移频方式——随机移频。理论分析表明随机移频干扰经脉压处理后为覆盖一定距离的似噪声干扰带,通过控制频移量的随机分布参数可改变干扰带覆盖范围、干扰带中心位置和干扰带内能量分布。由于干扰获得了部分压缩增益,较低的干扰功率就可实现遮盖干扰。仿真实验证实了理论分析的正确性和干扰的有效性。

近场宽带LFM信号被动测向和测距方法

提出了一种采用分数阶傅里叶变换的聚焦波束形成被动定位方法,实现了水声近场宽带线性调频(linear frequency modulated,LFM)信号的被动测向和测距。建立了基于球面波模型的近场宽带LFM信号接收数据模型,应用分数阶傅里叶变换(fractional Fourier transform,FRFT)将LFM信号的时变阵列流形矩阵变换为固定阵列流形矩阵,结合近场声源的聚集波束形成技术,利用多重信号分类算法实现了对多个宽带LFM信号的方位与距离联合估计。数值仿真验证了该方法对水声目标方位和距离估计的有效性,并仿真分析信噪比、声源距离、声源个数等对该算法性能的影响。