LFM signal parameter estimation in the fractional Fourier domains: Analytical models and a high-performance algorithm

The index of the peak magnitude of the fractional Fourier transform (FrFT) of linear frequency modulated (LFM) signals has been widely used as a powerful chirp-rate estimator. In this paper, we propose analytical approximations for the peak FrFT magnitude (PFM) of mono and multicomponent LFM signals, both for noiseless and noisy cases. In addition, we present a novel coarse-to-fine FrFT-based algorithm designed specifically for chirp-rate estimation of multi-component LFM signals. Our approach entails an initial coarse estimation of the chirp-rates for each component by utilizing our proposed mathematical models. By leveraging these models, we achieve improved performance and a reduced signal-to-noise breakdown threshold. Furthermore, we incorporate a unique and efficient estimate-and-subtract strategy to refine the estimated parameters using our proposed models. Rather than removing the components from the LFM signal, we utilize the derived model to identify and remove peaks in the PFM. This strategy enhances the algorithm’s capability to handle challenging scenarios. Extensive simulation results demonstrate that our proposed algorithm performs very close to the Cramér–Rao lower bound. It effectively eliminates the leakage effect between signal components, avoids error propagation, and maintains an acceptable computational cost compared to other state-of-the-art methods.     

改进的相位展开算法及其在瞬时频率估计中的应用

 研究了一种改进的相位展开算法及其在瞬时频率估计中的应用.首先讨论了噪声对相位展开的影响,发现当每个周期内的样本数为2个样本时相位展开具有最佳的性能;接着利用这个性质得到一种简单的相位展开算法,可以在较低信噪比条件下估计出信号的瞬时相位;随后把相位展开算法应用于正弦波频率估计,得到了改进的相位平均法,利用它可以在较低信噪比条件下得到宽带信号的瞬时频率曲线;最后通过MATLAB仿真对算法进行验证.     

Direction of arrival estimation of sources with intersecting signature in time–frequency domain using a combination of IF estimation and MUSIC algorithm

Time–frequency (TF) approaches are frequently employed for source localization at low signal to noise ratio. However, TF approaches fail to achieve the desired performance for sparsely sampled signals or signals corrupted by heavy noise in an under-determined scenario when sources are not TF separable. In this study, we propose a new TF method for direction of arrival (DOA) estimation of sources with closely spaced and overlapping TF signature. The proposed method uses a combination of a high-resolution time–frequency distribution and instantaneous frequency estimation method for extraction of sources with intersecting and closely spaced time–frequency signatures. Once sources are extracted, their DOAs are estimated using a well known multiple signal classification (MUSIC) algorithm. Experimental results demonstrate that the proposed source localization method achieves better performance as compared to the conventional time–frequency MUSIC algorithm.

     

基于离散小波分解和频率脊线分析的CPM信号符号速率盲估计

非合作接收条件下,连续相位调制（CPM,Continuous Phase Modulation）信号多变未知的信号体制使其符号速率盲估计一直是分析该类信号的难点之一.现有的算法大多直接基于信号的瞬时频率或循环平稳性,存在抗噪性能差,不适用于多指数CPM信号等问题.针对该问题,本文通过分析小波变换在信号分解和时频分析中的优势,提出一种综合利用离散小波（DWT,Discrete Wavelet Transform）分解和频率脊线提取的CPM信号符号速率估计的新算法.算法对比分析表明,所提算法具有更好的抗噪性能且在小数据量时也能达到较好的估计性能.     

利用DFT和迭代校正的正弦信号频率估计算法

对电磁信号的频率估计广泛应用于通信、雷达、导航和电子对抗等领域。针对正弦信号的频率精确估计,本文提出了一种利用DFT和迭代校正的频率估计算法,并与现有三种基于DFT的频率估计算法进行了性能仿真对比,分析结果表明,新算法的频率估计性能明显优于其他三种算法,可以得到非常逼近CRLB的频率估计值,迭代校正5次时,频率估计的RMSE距离CRLB不到0.07dB,而且没有估计误差平层,算法估计精度高,对频率的取值范围不敏感,性能稳定,迭代校正的复杂度较低,具有很好的应用价值。      

Diversity and channel estimation using time-varying signals and time-frequency techniques

We propose the use of time-varying (TV) signaling in modulation schemes to provide multiuser detection and multipath diversity in TV wireless channels. Specifically, we design an orthogonal linear chirp modulation scheme that is based on assigning different users with optimally designed parameters in order to reduce multiple-access interference. We also derive conditions on the parameters of the modulation signals to achieve multipath diversity. Furthermore, we propose the use of TV pilot signals with nonlinear instantaneous frequency and matched time-frequency (TF) techniques to estimate fast-fading channels with unknown state information. The proposed algorithm simplifies to the estimation of the parameters of multiple linear chirps, which we perform using the modified matching pursuit decomposition. We compare our estimation method with the use of pilot signals with linear instantaneous frequency, which we implement using the reassigned spectrogram. The proposed modulation scheme is applied to a frequency-hopped code-division multiple-access system for which we demonstrate improved performance when compared with frequency-shift-keying (FSK) modulation due to the designed multipath diversity and low multiple-access interference. Our simulations also demonstrate the increased estimation performance when pilot signals with nonlinear structures are used instead of linear structured ones to estimate TV channel parameters.     

LFM信号参数估计算法研究

初始频率和调频斜率是表征线性调频信号频率特性的基本参数,如何准确快速地估计它们具有的重要意义。针对传统LFM信号参数估计算法中繁琐的搜索和计算问题,提出了一种不需要参数搜索的快速LFM信号参数估计算法。该算法先用希尔伯特变换估计LFM信号瞬时相位,再用高阶差分估计LFM信号瞬时频率特性,最后用直线拟合LFM信号瞬时频率特性从而得到初始频率和调频斜率的估计。仿真实验验证了本文算法的有效性,说明本文算法能够给出满意的参数估计结果。     

联合STFT-迭代变权拟合的LFM信号参数估计方法

针对现有线性调频(LFM)信号参数估计方法估计精度与估计速度难以兼得,以及对信号畸变敏感的难题,提出了一种联合Rife插值改进的短时傅里叶变换(STFT)-迭代变权最小二乘线性拟合(IRLSF)参数估计的方法。使用Rife插值改进的STFT较好地保持了LFM信号瞬时频率曲线的线性特征,迭代变权处理有效地抑制了估计得到的瞬时频率中出现异常值对参数估计精度的影响。该方法无需进行复杂的计算和参数搜索,实时性好。仿真分析表明,相对于常规最小二乘线性拟合(CLSF)方法信噪比下限降低了4dB。湖试结果验证了该方法的有效性和实用性。      

基于瞬时频率估计的进动锥体目标微多普勒频率提取方法

该文针对进动锥体目标的微动特性提取,建立等效散射点模型下的微多普勒频率与目标运动参数关系。结合进动调制的微多普勒频率近似正弦变化规律的特点,提出基于瞬时频率估计和随机抽样一致性(RANSAC)的进动目标微多普勒频率提取方法。该方法将回波信号分为若干段,每一段的回波信号近似为若干线性调频(LFM)信号分量之和,通过调频Relax算法估计各信号分量的瞬时频率,并通过随机抽样一致性算法估计散射点的微多普勒曲线。基于仿真数据和电磁计算数据的实验验证了该方法的有效性及稳健性。     

多线性调频信号瞬时频率估计快速算法

对多线性调频信号的瞬时频率估计问题提出一种快速算法,该算法以特征子空间跟踪算法为基础,结合矩阵线性变换和多项式方程求根得到参数估计。该算法的优点是计算量小,其计算量仅与短时傅里叶变换相当;频率分辨力较高;多信号情况下不存在交叉项问题;当多个分量的功率差异达到14 d B时仍能有效估计瞬时频率。但是,由于采用了矩阵求逆的步骤,该算法在低信噪比环境下性能较差。仿真实验显示在信噪比不低于6 d B时,算法具有明显的优越性。     

ISAR imaging of target with complex motion based on novel approach for the parameters estimation of multi-component cubic phase signal

Inverse synthetic aperture radar (ISAR) imaging of target with complex motion is very important in the radar signal processing domain. In this case, the received signal can be characterized as multi-component cubic phase signal (CPS), and the high quality instantaneous ISAR images can be obtained by the parameters estimation approach. The match Fourier transform (MFT) has been proposed for the parameters estimation of linear frequency modulated (LFM) signal, and it has been used successfully in the field of ISAR imaging. In this paper, the third-order match Fourier transform (TMFT) is proposed as an extension of the traditional MFT for the parameters estimation of cubic phase signal, and the asymptotic statistical performance is analyzed theoretically with the derivation of asymptotic statistical results for the estimated parameters. Finally, the TMFT algorithm is used as a tool for the improvement of inverse synthetic aperture radar (ISAR) images quality of target with complex motion, and the results of simulated and real data validate the effectiveness of the TMFT algorithm.     

基于ε等级约束差分进化的多径估计算法

本文针对基于扩展Kalman滤波（EKF）的多径估计算法需要对非线性观测方程进行线性化.对初值比较敏感,造成估计性能下降的问题,提出了基于智能优化的多径估计算法.该算法将估计误差的二阶矩作为目标函数,将瞬时误差作为约束条件,同时考虑多径参数的先验信息,实现了将多径估计问题转化为具有约束条件的优化问题.然后,利用一种智能优化算法来解决该优化问题.本文采用了ε等级约束差分进化（εCRDE）算法来解决有约束条件的优化问题,并对该算法进行改进,使改进后的εCRDE算法可以实现多径参数的迭代估计.仿真结果表明,与EKF算法相比,在单一多径和2路多径情况下,基于改进εCRDE的多径估计算法都具有更好的估计性能.     

宽带CDMA中一种新的自适应信道估计方法

在衰落信道中进行相干解调必须知道瞬时的信道参数，但由于信道是时变的，所以信道估计器的频率响应和带宽应该是由衰落信道的统计特性和系统的信干比决定。利用瞬时信道估计的自相关函数，本文提出了信道估计的一种新的自适应算法。在平坦瑞利信道中的计算机仿真表明本方法在3G标准支持的所有多普勒频率范围内都能获得良好的均方误差性能。     

SOQPSK-TG信号的EM半盲载波频偏估计

针对成形偏移四相相移键控-TG(Shaped Offset Quadrature Phase Shift Keying-Telemetry Group version, SOQPSK-TG)信号在训练序列长度受限时频偏估计精度较低的问题,利用双二进制分解(Doubinary Decomposition, DBD)原理提出基于期望最大化(Expectation Maximization, EM)的SOQPSK半盲载波频偏(Carrier Frequency Offset, CFO)估计算法。为了确保EM算法收敛到预期性能范围,使用基于非线性四次方码元定时估计算法的非数据辅助频偏估计方法优化了EM算法初始点选择。仿真实验结果表明,该算法相比于使用训练序列进行数据辅助估计的方法,在不增加辅助数据数量的前提下能够进一步提升CFO估计的精度,并在较高信噪比下拥有接近序列总长度所对应的克拉美罗界(Cramér-Rao Bound, CRB)的优秀性能。     

基于插值的多普勒频偏和频率斜升联合估计算法

为解决卫星移动通信系统中突发传输在低信噪比条件下的载波快速同步问题,该文提出一种基于插值的频偏和频率斜升联合估计算法。先通过对多普勒斜升搜索结合低复杂度频偏估计获得频偏和频率斜升的粗估计结果,再以频率斜升粗估计结果为中心、计算3个频率斜升值所对应的对数似然函数并据此对频率斜升进行二次插值以获得频率斜升估计值,最后在该估计值下计算出对应的频偏估计值,完成频偏和频率斜升的联合估计。仿真结果表明,该文算法的信噪比门限较低,估计性能接近克拉美罗下界(CRLB),而且计算复杂度远低于最大似然估计算法,非常适于实际应用。     

一种集成SVD和PWVD的VCO非线性度检测新方法

针对现有压控振荡器(VCO)非线性度检测方法可靠性和普适性较差的问题,提出一种集成奇异值分解(SVD)降噪和伪魏格纳威尔分布(PWVD)瞬时频率估计的VCO非线性度检测新方法。该方法首先对待检测对象中频信号进行降噪处理,然后将降噪后的中频信号通过希尔伯特(Hilbert)变换转换为解析信号,最后利用自适应窗长的PWVD瞬时频率估计算法处理解析信号,实现中频信号的瞬时频率估计。仿真结果表明了文中方法的有效性、较强的环境适应能力和普适性。     

多径衰落信道下的OFDM时频联合同步算法

符号定时和载波频率偏差将严重影响OFDM系统的性能。基于具有重复结构的CAZAC序列,提出了一种仅利用一个CAZAC符号实现符号定时、整数倍频偏与小数倍频偏估计的同步算法。这种算法在完成粗定时同步的同时得到整数倍频偏估计,然后根据整数倍频偏估计值对定时估计进行修正,最后完成小数倍频偏估计。分析与仿真结果表明,该算法相对经典算法,不但提高了传输效率,还显著改善了OFDM系统的定时与频偏估计性能,相比CAZAC序列算法,提升了多径信道下的同步性能。     

低信噪比情况下调频信号的瞬时频率估计

提出一种基于互Wigner-Ville分布(XWVD)的瞬时频率迭代估计方法.理论分析了该方法的收敛性,通过仿真比较了各种瞬时频率估计方法在噪声下的估计方差,证明此方法在低信噪比情况下对估计线性调频信号的瞬时频率有较好的效果.并采用加窗的方法改进了此算法,仿真结果证明,改进的方法对非线性调频信号的瞬时频率进行了有效估计.     

5G卫星通信系统频偏估计算法

卫星通信系统中存在的大的多普勒频偏严重影响着系统的性能.为了提高频偏估计的性能,基于5G NR帧结构和同步信号,提出新的利用级联积分梳状(Cascaded Integrator Comb,CIC)滤波器插值的小数倍频偏估计算法.该算法分两步实现小数倍频偏估计:首先,利用结构简单、运算快速的CIC滤波器对接收主同步序列(...     

An iterative algorithm for single-frequency estimation

An algorithm for the estimation of the frequency of a complex sinusoid in noise is proposed. The estimator consists of multiple applications of lowpass filtering and decimation, frequency estimation by linear prediction, and digital heterodyning. The estimator has a significantly reduced threshold relative to existing phase-based algorithms and performance close to that of maximum likelihood estimation. In addition, the mean-squared error performance is within 0.7 dB of the Cramer-Rao bound (CRB) at signal-to-noise ratios (SNRs) above threshold. Unlike many autocorrelation and phase-based methods, the proposed algorithm's performance is uniform across a frequency range of -/spl pi/ to /spl pi/. The computational complexity of the algorithm is shown to be favorable compared with maximum likelihood estimation via the fast Fourier transform (FFT) algorithm when significant zero-padding is required.