Quasi maximum likelihood estimator of polynomial phase signals for compressed sensed data

Several papers in the literature cover parameter estimation of frequency modulated (FM) signals under reduced number of signal samples with respect to the Nyquist/Shannon criterion, i.e., within the compressive sensing (CS) framework. However, scope of these papers is mainly limited to sinusoids or sum of sinusoids. In this paper, the CS framework is extended to parameter estimation of higher order polynomial phase signals (PPSs) using the quasi-maximum likelihood (QML) estimator and robust short-time Fourier transform (STFT). The considered signal is assumed to be non-uniformly sampled PPS with smaller number of samples with respect to the Nyquist/Shannon criterion. However, the proposed technique can also be generalized to uniformly sampled signals with missing or unreliable samples.     

一种单分量PPS的快速估计算法

 提出了基于多项式-厄米多项式变换(PHPT)的多项式相位信号(PPS)参数估计算法.其基本思路是将相位系数转化为泰勒系数的估计,并用PHPT实现泰勒系数的估计.该方法为线性算法,对最低阶系数有很好估计效果,且计算复杂度比已有算法低,等效于三次FFT运算.仿真验证了该方法的有效性.     

Analysis of polynomial-phase signals by the integrated generalizedambiguity function

The aim of this work is the performance analysis of a method for the detection and parameter estimation of mono or multicomponent polynomial-phase signals (PPS) embedded in white Gaussian noise and based on a generalized ambiguity function. The proposed method is shown to be asymptotically efficient for second-order PPS and nearly asymptotically efficient for third-order PPSs. The method presents some advantages with respect to similar techniques, like the polynomial-phase transform, for example, in terms of (i) a closer approach to the Cramer-Rao lower bounds, (ii) a lower SNR threshold, (iii) a better capability of discriminating multicomponent signals     

Aliasing detection and resolving in the estimation of polynomial-phase signal parameters

A novel method for aliasing detection and resolving in the estimation of polynomial-phase signal (PPS) parameters is presented. Aliasing is detected using two high-order ambiguity functions (HAFs) of a uniformly sampled PPS embedded in noise. If aliasing occurred, we propose a way of recovering the true parameters from their aliased positions. To that end, a closed-form expression for the true parameter value is derived. As opposed to the concurrent methods, the proposed method provides much more robust results with higher order PPSs and does not require nonuniform sampling. In addition, it can be readily extended to the multicomponent PPS case. Simulations support the theoretical results.     

A fast algorithm for estimating the parameters of a quadratic FM signal

This paper describes a fast algorithm that can be used for estimating the parameters of a quadratic frequency modulated (FM) signal. The proposed algorithm is fast in that it requires only one-dimensional (1-D) maximizations. The optimal maximum likelihood method, by contrast, requires a three-dimensional (3-D) maximization, which can only be realized with an exhaustive 3-D grid search. Asymptotic statistical results are derived for all the estimated parameters. The amplitude estimate is seen to be optimal, whereas the phase parameters are, in general, suboptimal. Of the four phase parameter estimates, two approach optimality as the signal-to-noise ratio (SNR) tends to infinity. The other two have mean-square errors that are within 50% of the theoretical lower bounds for high SNR. Simulations are provided to support the theoretical results. Extensions to multiple components and higher order FM signals are also discussed.     

Tracking of unknown nonstationary chirp signals using unsupervisedclustering in the Wigner distribution space

This paper is concerned with the problems of (1) detecting the presence of one or more FM chirp signals embedded in noise, and (2) tracking or estimating the unknown, time-varying instantaneous frequency of each chirp component. No prior knowledge is assumed about the number of chirp signals present, the parameters of each chirp, or how the parameters change with time. A detection/estimation algorithm is proposed that uses the Wigner distribution transform to find the best piecewise cubic approximation to each chirp's phase function. The first step of the WD based algorithm consists of properly thresholding the WD of the received signal to produce contours in the time-frequency plane that approximate the instantaneous frequency of each chirp component. These contours can then be approximated as generalized lines in the (ω, t, t²) space. The number of chirp signals (or equivalently, generalized lines) present is determined using maximum likelihood segmentation. Minimum mean square estimation techniques are used to estimate the unknown phase parameters of each chirp component. The authors demonstrate that for the cases of (i) nonoverlapping linear or nonlinear FM chirp signals embedded in noise or (ii) overlapping linear FM chirp signals embedded in noise, the approach is very robust, highly reliable, and can operate efficiently in low signal-to-noise environments where it is hard for even trained operators to detect the presence of chirps while looking at the WD plots of the overall signal. For multicomponent signals, the proposed technique is able to suppress noise as well as the troublesome cross WD components that arise due to the bilinear nature of the WD     

分数阶傅里叶变换的多项式相位信号DOA估计

针对多项式相位信号波达方向(DOA)估计研究较少的问题,提出了一种基于分数阶傅里 叶变换(FRFT)的多项式相位信号(PPS)的DOA估计算法。该算法首先通过多项式相位变换,估 计出PPS的最高阶相位系数,从而可以消除最高阶项。运用这一降阶思想,依次消除高阶项 ,这样PPS可降为线性调频(LFM)信号,然后将宽带的LFM信号转化为分数阶Fourier域窄带的 平稳信号。在相应的分数阶Fourier域,运用求根MUSIC算法对信号进行DOA估计,从而把LFM 信号的DOA估计推广到了PPS的DOA估计。理论分析和仿真实验表明,该方法能很好地估计出P PS的DOA,并且简洁。     

Statistical properties of the LMS fourier analyzer in the presence of frequency mismatch

The statistical performances of the conventional adaptive Fourier analyzers, such as the least mean square (LMS), the recursive least square (RLS) algorithms, and so forth, may degenerate significantly, if the signal frequencies given to the analyzers are different from the true signal frequencies. This difference is referred to as frequency mismatch (FM). We analyze extensively the performance of the conventional LMS Fourier analyzer in the presence of FM. Difference equations governing the dynamics and closed-form steady-state expression for the estimation mean square error (MSE) of the algorithm are derived in detail. It is revealed that the discrete Fourier coefficient (DFC) estimation problem in the LMS eventually reduces to a DFC tracking one due to the FM, and an additional term derived from DFC tracking appears in the closed-form MSE expression, which essentially deteriorates the performance of the algorithm. How to derive the optimum step size parameters that minimize or mitigate the influence of the FM is also presented, which can be used to perform robust design of step size parameters for the LMS algorithm in the presence of FM. Extensive simulations are conducted to reveal the validity of the analytical results.     

Carrier Frequency Offset Estimation for FM and Symbiotic FM Radio Data System Hybrid Signal

The symbiotic FM radio data system(SRDS)is a radio data system that a specially designed OFDM signal co-lives with FM signal,which enables a significantly higher data rate than existing radio data systems.The cyclic prefix of the OFDM symbol has the same length as the OFDM body,which enables the analytic separation of the co-channel OFDM and FM signal at receiver side,utilizing the fact that the OFDM body and prefix is equal.In this work,we show that the OFDM body and prefix cannot be viewed as equal when there is sufficient carrier frequency offset(CFO).Thus,we propose a two-step CFO estimation algorithm for FM and SRDS hybrid signal.The first step estimates the coarse CFO by exploring the characteristics of the FM signal.Once the coarse CFO is removed,the residual CFO is small enough for FM and OFDM separation.The second step fine estimates CFO from the OFDM-only signal using its repeated PN structure after the separation.Detailed mathematical equations are formulated and simulation results are given.The results show that the proposed algorithm works fine with the simulation setup and has a final residual CFO less than 3.9Hz.     

调频遥测信号载波频率的精确估计

传统调频遥测信号载波频率估计算法对输入信号降采样后直接进行快速傅里叶变换，实现方法虽然简单，但测量精度较差，无法适应高动态、低信噪比等复杂场景。为此，提出了一种调频遥测信号载波频率的精确估计算法。两并联补偿支路先分别采用正、负调频频率对输入信号进行频率预先补偿，低通滤波后完成降采样处理，削弱调频频率的频谱影响；频率搜索状态对采样数据进行载波多普勒变化率的频率补偿，经过快速傅里叶变换、非相干积分和频谱重心搜索完成频率解算，提高载波频率的检测性能。试验与分析表明，所提算法在高动态、低信噪比等复杂场景下可显著提高调频遥测信号载波频率的估测性能。     

Improved estimation of hyperbolic frequency modulated chirp signals

This article deals with parameter estimation of product signals consisting of hyperbolic FM and chirp factors. A computationally simple algorithm that decouples estimation of the chirp parameters from those of the hyperbolic FM part is presented. It relies on a simple data transformation that removes the hyperbolic FM component, leaving one with the simpler problem of estimating chirp parameters. For the latter, the high-order ambiguity function (HAF) is adopted. Schemes for estimating the hyperbolic FM parameter are also proposed. The method improves on existing approaches and is shown to provide performance close to the Cramer-Rao bound     

单通道合成孔径雷达抗调频斜率失配干扰新方法

该文针对单通道合成孔径雷达(SAR)无法有效抑制调频斜率失配干扰的问题进行了深入的研究。根据干扰频谱与真实回波频谱的差异，该文提出了一种基于频域匹配滤波处理的合成孔径雷达调频斜率失配干扰抑制方法。该方法在准确测得干扰调频斜率的基础上，首先利用干扰信号的空间稀疏性以及低信干比(SIR)的特点，对干扰位置进行稀疏超分辨估计以获得较为精确的干扰时延相位。然后通过获得的干扰调频斜率和时延相位重建干扰信号频谱，以此为基础设计正交匹配滤波器在频域实施干扰信号的抑制，并重建无失真场景图像。最后，计算机仿真实验验证了该文所提方法的有效性。     

多项式相位信号瞬时频率变化率估计及其应用

通过定义两种新的变换——指数型相位匹配变换和复时间延迟型相位匹配变换,可实现对任意阶次的多项式相位信号(PPS)的瞬时频率变化率(IFR)估计.给出了这两种变换的基本原理和实现方法,同时分析了算法实现过程中应注意的问题.进而,研究了IFR在以下三个方面的应用:(1)PPS的参数估计问题;(2)PPS的瞬时频率估计问题;(3)构造新的时频分布,该分布对于阶次大于2的多项式相位信号具有理想的时频聚集性.最后通过计算机仿真实验验证了本文所提算法的有效性.     

Optimal simultaneous detection and estimation under a false alarmconstraint

This paper addresses the problem of finite sample simultaneous detection and estimation which arises when estimation of signal parameters is desired but signal presence is uncertain. In general, a joint detection and estimation algorithm cannot simultaneously achieve optimal detection and optimal estimation performance. We develop a multihypothesis testing framework for studying the tradeoffs between detection and parameter estimation (classification) for a finite discrete parameter set. Our multihypothesis testing problem is based on the worst case detection and worst case classification error probabilities of the class of joint detection and classification algorithms which are subject to a false alarm constraint. This framework leads to the evaluation of greatest lower bounds on the worst case decision error probabilities and a construction of decision rules which achieve these lower bounds. For illustration, we apply these methods to signal detection, order selection, and signal classification for a multicomponent signal in noise model. For two or fewer signals, an SNR of 3 dB and signal space dimension of N=10 numerical results are obtained which establish the existence of fundamental tradeoffs between three performance criteria: probability of signal detection, probability of correct order selection, and probability of correct classification. Furthermore, based on numerical performance comparisons between our optimal decision rule and other suboptimal penalty function methods, we observe that Rissanen's (1978) order selection penalty method is nearly min-max optimal in some nonasymptotic regimes     

Performance of quadratic time-frequency distributions as instantaneous frequency estimators

General performance analysis of the shift covariant class of quadratic time-frequency distributions (TFDs) as instantaneous frequency (IF) estimators, for an arbitrary frequency-modulated (FM) signal, is presented. Expressions for the estimation bias and variance are derived. This class of distributions behaves as an unbiased estimator in the case of monocomponent signals with a linear IF. However, when the IF is not a linear function of time, then the estimate is biased. Cases of white stationary and white nonstationary additive noises are considered. The well-known results for the Wigner distribution (WD) and linear FM signal, and the spectrogram of signals whose IF may be considered as a constant within the lag window, are presented as special cases. In addition, we have derived the variance expression for the spectrogram of a linear FM signal that is quite simple but highly signal dependent. This signal is considered in the cases of other commonly used distributions, such as the Born-Jordan and the Choi-Williams distributions. It has been shown that the reduced interference distributions outperform the WD but only in the case when the IF is constant or its variations are small. Analysis is extended to the IF estimation of signal components in the case of multicomponent signals. All theoretical results are statistically confirmed.     

Two-Dimensional Polynomial Phase Signals: Parameter Estimation and Bounds

This paper considers the problem of parametric modeling and estimation of nonhomogeneous two-dimensional (2-D) signals. In particular, we focus our study on the class of constant modulus polynomial-phase 2-D nonhomogeneous signals. We present two different phase models and develop computationally efficient estimation algorithms for the parameters of these models. Both algorithms are based on phase differencing operators. The basic properties of the operators are analyzed and used to develop the estimation algorithms. The Cramer-Rao lower bound on the accuracy of jointly estimating the model parameters is derived, for both models. To get further insight on the problem we also derive the asymptotic Cramer-Rao bounds. The performance of the algorithms in the presence of additive white Gaussian noise is illustrated by numerical examples, and compared with the corresponding exact and asymptotic Cramer-Rao bounds. The algorithms are shown to be robust in the presence of noise, and their performance close to the CRB, even at moderate signal to noise ratios.     

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.     

一般阵列误差情况下空时谱分析的研究

本文研究了一般阵列误差情况下的空时二维鲁棒参数估计方法.首先本文给出了一般阵列误差模型,然后基于该模型提出了空时加权子空间拟合(ST-WSF)算法,并给出了信号参数,即信号波达方向和频率的估计的Cramér-Rao下界.仿真结果进一步验证了算法的有效性.     

A new LMS-based Fourier analyzer in the presence of frequency mismatch and applications

The performance of the conventional least mean square (LMS) Fourier analyzer may degenerate significantly, if the signal frequencies given to the analyzer are different from the true signal frequencies. This difference is referred to as frequency mismatch (FM). We first analyze the performance of the conventional LMS Fourier analyzer for a single sinusoid in the presence of FM. We derive the dynamics and steady-state properties of this analyzer as well as the optimum step size parameter which minimizes the influence of the FM. Extensive simulations reveal the validity of the analytical results. Next, a new LMS-based Fourier analyzer is proposed which simultaneously estimates the discrete Fourier coefficients (DFCs) and accommodates the FM. This new analyzer can very well compensate for the performance degeneration due to the FM. Applications to estimation/detection of dual-tone multiple frequencies (DTMF) signals and analysis of real-life noise signals generated by a large-scale factory cutting machine are provided to demonstrate the excellent performance of our new Fourier analyzer.     

稀疏重构下的非线性调频信号参数估计算法

非线性调频信号广泛应用于雷达声纳领域，其具有多阶多项式相位、未知参数多的特点，给参数估计带来困难。针对此问题，本文提出一种稀疏重构下的非线性调频信号参数估计算法。该方法利用Gabor原子良好时频特性，以 范数稀疏正则最小二乘模型为目标函数，并推导了问题的二阶锥规划（SOCP）形式，最终通过求解的Gabor原子进行参数估计。算法分析信号的时频特征，完成信号的分解重构，适应于各类调频信号。仿真实验证明，本文算法对调频信号二阶与一阶相位参数估计精度都贴近CRB，而对二阶参数的估计较二次相位差分算法更适应较低信噪比。