Multicomponent Chirp Signals Research Articles

Model order estimation in multi-component chirp signals

Real datasets exhibiting non-constant frequencies, can be analyzed with the help of multi-component chirp signals adequately. This requires estimation of the number of chirp components in practice. The problem of estimation becomes difficult when the data is composed of moderate to large number of chirp components. We propose Bayesian approach to estimate the number of components of a multi-component chirp model using an approximation to the mode of the posterior distribution. This approximation is motivated from the relation between mode of the obtained posterior and the sequential least squares estimators. Extensive numerical simulations highlight superior performance of the proposed estimators than that of the estimators based on Akaike information criterion, Bayesian information criterion and asymptotic maximum a posteriori probability, for a large range of signal-to-noise ratio levels. We further illustrate the implementation of the proposed estimators through two real data examples.

On refinements to QMFD based chirp parameter estimation

Commuting matrix methods furnish a full basis of orthogonal eigenvectors for the discrete Fourier transform or its centered version needed for computing the discrete fractional Fourier transform and multicomponent chirp signal analysis. However, these approaches suffer from ill-conditioning issues at higher matrix sizes, and require a computationally expensive eigenvalue decomposition.In this paper, ill-conditioning issues associated with the QMFD approach developed previously by the authors are addressed via diagonal modification. Further symmetries of the eigenvectors are used to reduce the size of the underlying eigenvalue problem. These modifications are then incorporated into the real-arithmetic implementation of the QMFD approach that is shown to be significantly superior to the conventional implementation and the corresponding MSE of the chirp parameter estimates are shown to approach their Cramer–Rao lower bounds.

On estimating parameters of a multi-component Chirp Model with equal chirp rates

Multi-component chirp signal models with equal chirp rates appear in various radar applications, e.g., synthetic aperture radar, echo signal of a rapid mobile target, etc. Many sub-optimal estimators have been developed for such models, however, these suffer from the problem of either identifiability or error propagation effect. In this paper, we have developed theoretical properties of the least squares estimators (LSEs) of the parameters of multi-component chirp model with equal chirp rates, where the model is contaminated with linear stationary errors. We also propose two computationally efficient estimators as alternative to LSEs, namely sequential combined estimators and sequential plugin estimators. Strong consistency and asymptotic normality of these estimators have been derived. Interestingly, it is observed that sequential combined estimator of the chirp rate parameter is asymptotically efficient. Extensive numerical simulations have been performed, which validate satisfactory computational and theoretical performance of all three estimators. We have also analysed a simulated radar data with the help of our proposed estimators of multi-component chirp model with equal chirp rates, which performs efficiently in recovery of inverse synthetic aperture radar (ISAR) image of a target from a noisy data.

Frequency estimation of chirp signals based on fractional fourier transform combined with Otsu’s method

The parameters estimation of linear frequency modulation (LFM) signals, which also called chirp signals, have been widely applied in optical communication, LIDAR and many other fields. Fractional Fourier transform (FRFT) is one of the most important methods for estimating the frequency of chirp signals. However, the traditional estimation methods based on FRFT are incapable of high-precision parameter estimation for chirp signals, especially multi-component LFM signals. Therefore, we present a novel parameter estimation method based on the Otsu ratio, i.e., the interclass ratio of impulse signal to noise. An algorithm is used to determine this ratio, and then the frequency parameters of chirp signals are estimated by using the ratio as the fitness function. The parameter estimation of single-component and multi-component chirp signals is simulated. The results show that the proposed method has higher estimation accuracy than the traditional FRFT method.

RANGE AND RADIAL VELOCITY MEASUREMENT AMBIGUITY ELIMINATION WITH TRAINS OF MULTICOMPONENT SIGNALS

When designing pulse-Doppler radar, one of the key points is the choice of the pulse repetition period, which determines the boundaries of unambiguous measurement of range and radial velocity and creates contradictions in the measurement of these values. This contradiction is especially acute in the analysis of signals reflected from the propellers and turbines of aircraft. The main approaches to solving the problem of expanding the boundaries of unambiguous measurement of range and radial velocity is the use of variable pulse repetition period and the creation of signal ensembles to separate them by shape. Generation of an ensemble of sounding signals for a pulsed radar must be carried out taking into account both cross-correlation and auto-correlation properties. An approach to the generation of multicomponent signal trains with the possibility of pulse separation inside the train is proposed. Each of the pulses in the train is formed by adding a number of chirp signals, which differ in the values of amplitude and frequency deviation. As the frequency deviation increases, the amplitude of the component decreases. Reducing the cross-correlation coefficient of multicomponent signals from the formed ensemble can be achieved by increasing the number of components of each signal. The size of the signal ensemble, which can be formed on the basis of multicomponent chirp signals, depends on the requirements for the cross-correlation coefficient and auto-correlation function of the signals. It is shown that in order to expand the limits of coordinate measurement at a fixed wavelength, it is necessary to increase the number of pulses in the train. The results of the research demonstrate the potential possibility of using the proposed multicomponent chirp signal to form train of pulses with its subsequent separation.

Pulse width estimation of multi-component chirp signal based on integration decomposition of fractional Fourier transform

Signal parameter estimation is a common process in the sphere of radar signal processing. For the widely used chirp signal, the estimation of pulse width is essential in applications of signal reconnaissance, passive radar, anti-jamming, and others. An efficient pulse width estimation method for multi-component chirp signal is proposed. Different from the conventional pulse width estimation methods based on short-time time-frequency analysis, the proposed method extracts the time-varying signal feature via integration decomposition. In the proposed method, the amplitude history (AH) curve, which presents the temporal distribution of signal energy, is generated based on the intermediate data of the fractional Fourier transform integration. Then a detector is provided to locate the start and end positions of the chirp signal component in the AH curve. Monte Carlo experiments under different conditions verify the noise robustness and computational efficiency of the proposed method. In general, the proposed method provides a new perspective for extracting the time-varying feature of the signal component, and it is a useful reference for future investigations concerning integration decomposition.

ADMM–Net: A Deep Learning Approach for Parameter Estimation of Chirp Signals Under Sub-Nyquist Sampling

Parameter estimation of chirp signals plays an important role in the field of radar countermeasures. Compressed sensing (CS) based sub-Nyquist sampling and parameter estimation methods alleviates the pressure on hardware systems to acquire and process chirp signals with large time-bandwidths. In this paper, a framework based on the fractional Fourier transform (FrFT) and alternating direction method of multipliers network (ADMM-Net) is proposed to realize chirp signal parameter estimation under sub-Nyquist sampling. The whole framework is composed of multiple parallel ADMM-Nets, where each ADMM-Net is defined over a data flow graph, which is derived from the iterative procedures of the ADMM algorithm for optimizing a CS-based $p$ -order FrFT spectral estimation model. The chirp rate and central frequency of chirp signals are obtained through a two-dimensional search on the spectrum image output by the network group. Experiments demonstrate that the proposed ADMM-Net-based method can achieve higher estimation accuracy and computational efficiency at lower signal-to-noise ratios and sampling ratios than traditional CS methods. We also demonstrate that the proposed ADMM-Net-based framework has strong generalization ability for multi-component chirp signals. Furthermore, we further generalize ADMM-Net to GADMM-Net, in which the activation function is data-driven instead of model-driven. Experiments demonstrate that GADMM-Net significantly improves on the basic ADMM-Net and achieves higher spectral resolution with faster computation speed.

Separation of Multicomponent Chirp Signals Using Morphological Component Analysis and Fractional Fourier Transform

A chirp signal is a large-bandwidth signal which is widely used in engineering. In many applications, it is necessary to decompose a mixed chirp signal into its components. However, the traditional Fourier transform method cannot process a mixed chirp signal when its components intersect in the joint time–frequency domain. Combining the advantages of the morphological component analysis (MCA) with multicomponent signal processing and the fractional Fourier transform (FrFT) in chirp signal processing, this letter proposes the MCA-FrFT method to decompose a multicomponent chirp signal. First, the cost function is defined using the FrFT and optimized by the split augmented Lagrangian shrinkage algorithm (SALSA), and then, all the morphological components are obtained. The proposed method is verified by simulations, and simulation results show that the proposed method has good performance in separating the multicomponent chirp signals into components. Besides, the proposed method is evaluated experimentally in the sea target detection, and the experimental results confirm that the proposed method can not only extract the low observable targets from a heavy sea-clutter environment but also separate them from each other.

Adaptive importance sampling for estimating multi-component chirp signal parameters in colored noise

The problem of estimating the center frequency and the chirp rate of multi-component chirp signals from data corrupted with colored noise often occurs in many signal processing applications. In the Bayesian framework, an algorithm based on adaptive importance sampling (AIS) and modified discrete chirp Fourier transform (MDCFT) was introduced in the present paper in order to calculate the center frequency and the chirp rate of chirp signals from observations corrupted by additive autoregressive (AR) random noise. First, importance functions (IFs) were constructed to approximate the marginal posterior distributions of interested parameters with observed data, and AIS was then employed to evaluate the posterior distributions. MDCFT was adopted to detect the spectral peaks of chirp signals, and the obtained results were applied to construct IFs with multivariate student-t distribution. It was found that the quality of the samples generated from multivariate student-t distribution was gradually improved. Finally, computer simulations validated the results obtained from the proposed algorithm. In comparison with the Markov chain-based method, the proposed method had better SNR adaptability and excellent convergence rate and required fewer samples. Furthermore, the proposed algorithm can be considered as a further expansion of previous works related to AIS method for estimating multi-component chirp signal parameters in white noise.

Multicomponent Chirp Signal Detection Based on Discrete Chirp-Fourier Transform

This paper investigates the signal detection of multiple chirps based on the discrete chirp-Fourier transform (DCFT). The detection method based on signal energy is proposed and the detection performance is analyzed. Firstly, the relationship of signal energy in both the time and DCFT domain is analyzed. An important property is presented, that is, the total energy of the signal in the time domain is equal to the sum of energy along the direction of constant frequency in the DCFT domain. The detection decision threshold of the multicomponent chirp signal is derived in ideal noiseless environment. Secondly, by analyzing the characters of the additive independent identical distribution Gaussian white noise in the DCFT domain, the modified detection decision threshold of the multicomponent chirp signal is determined in noisy environment. Finally, the simulation results show the effectiveness of the proposed method.

Intrinsic chirp component decomposition by using Fourier Series representation

In this paper, we consider the decomposition problem for multi-component chirp signals (MCCSs). We develop a general model to characterize MCCSs, where instantaneous frequencies (IFs) and instantaneous amplitudes (IAs) of the intrinsic chirp components (ICCs) are modeled as Fourier series. The decomposition problem thus boils down to identifying the developed model. The IF estimation is addressed using the framework of the general parameterized time-frequency transform and then the signal can be easily reconstructed by solving a linear system. For the practical implementation of our method, we present a two-step algorithm, which is initiated by an iterative scheme to achieve preliminary separation of the ICCs, followed by a joint-refinement step to get high-resolution ICC reconstructions. Our method acts as a time-varying band-pass filter and can even separate ICCs that cross in the time-frequency domain. The method is applied to analyze several simulated and real signals, which indicates its usefulness in various applications.

Joint Estimation of Time-Frequency Signature and DOA Based on STFD for Multicomponent Chirp Signals.

In the study of the joint estimation of time-frequency signature and direction of arrival (DOA) for multicomponent chirp signals, an estimation method based on spatial time-frequency distributions (STFDs) is proposed in this paper. Firstly, array signal model for multicomponent chirp signals is presented and then array processing is applied in time-frequency analysis to mitigate cross-terms. According to the results of the array processing, Hough transform is performed and the estimation of time-frequency signature is obtained. Subsequently, subspace method for DOA estimation based on STFD matrix is achieved. Simulation results demonstrate the validity of the proposed method.

A New Method of Multi-Component Chirp Signal Array Detection

This paper presents a multi-component chirp signal detection with new methods of parameter estimation. The method using spatial characteristics of the antenna array. By array average fractional Fourier domain weighting function is introduced to reduce noise and suppress mutual interference between the signals from different sources. And compared to a single array element method. The proposed method greatly improves the multi-component chirp signal detection and parameter estimation performance. Simulation results show the effectiveness of the method.

Parameter estimation of multi-component chirp signals based on discrete chirp Fourier transform and population Monte Carlo

In this paper, a parameter estimation method for multi-component chirp signals with white Gaussian noise is proposed based on the modified discrete chirp Fourier transform (MDCFT) and the population Monte Carlo (PMC) methodology, in which the model order is unknown. By utilizing the integrability of linear parameters in the Bayesian model, this paper considers the posterior distribution of nonlinear parameters. MDCFT was adopted to calculate the chirpogram of the observed data, and clear peaks can be detected in the discrete chirp Fourier transform domain. The importance function (IF) was constructed according to the peaks, and the PMC algorithm was employed to evaluate the posterior distribution. The proposed method cannot only use the selected IF to generate the sample fitting target function in the parameter region of interest, but can also utilize samples and importance weights to update the IF adaptively. The simulation results indicated that the proposed method can realize joint Bayesian model selection and parameter estimation of multi-component chirp signals. Compared with the two existing methods based on Monte Carlo methodology, the proposed method exhibits improved performance.

Direction-of-arrival Estimation of Multicomponent Chirp Signals Based on the Fractional Fourier Transform

Direction-of-arrival(DOA)estimationof multicomponent chirp signals is difficult by use of the conventional DOA estimation algorithms. Since the fractional Fourier transform (FRFT) is appropriate for processing chirp-like signals, a novel method, based on the FRFT, is proposed to deal with the problem mentioned above. Firstly, the new model of chirp signals received by a planar array is constructed in the fractional Fourier domain (FRFD). Secondly, the relevant steering vector is defined. Finally, a novel estimation algorithm of DOA is proposed based on the FRFT. The simulation results illustrate the good performance of the proposed algorithm for DOA estimation of multicomponent chirp signals. Keywords-Direction-of-arrival estimation; fractional Fourier transform; chirp signal; , multicomponent

Parameter Estimation of Multicomponent Chirp Signals via Sparse Representation

A novel algorithm for parameter estimation of multicomponent chirp signals in complicated noise environment is proposed. By the matching pursuit (MP) algorithm, the signal is decomposed into Gabor atoms which provide sparse information that represents the signal time-frequency signature. The Hough transform (HT) is then directly used to estimate the parameter of chirp components without computing the time-frequency distribution. Simulation results show that this algorithm is capable of estimating parameters of multicomponent chirp signals even in the presence of strong intended interference and colored noise.

Instantaneous frequency estimation of multi-component Chirp signals in noisy environments

A classical time-varying signal, the multi-component Chirp signal has been widely used and the ability to estimate its instantaneous frequency (IF) is very useful. But in noisy environments, it is hard to estimate the IF of a multi-component Chirp signal accurately. Wigner distribution maxima (WDM) are usually utilized for this estimation. But in practice, estimation bias increases when some points deviate from the true IF in high noise environments. This paper presents a new method of multi-component Chirp signal IF estimation named Wigner Viterbi fit (WVF), based on Wigner-Ville distribution (WVD) and the Viterbi algorithm. First, we transform the WVD of the Chirp signal into digital image, and apply the Viterbi algorithm to separate the components and estimate their IF. At last, we establish a linear model to fit the estimation results. Theoretical analysis and simulation results prove that this new method has high precision and better performance than WDM in high noise environments, and better suppression of interference and the edge effect. Compared with WDM, WVF can reduce the mean square error (MSE) by 50% when the signal to noise ration (SNR) is in the range of −15dB to −11dB. WVF is an effective and promising IF estimation method.

Multicomponent chirp signals analysis using product cubic phase function

This paper presents an algorithm for estimating the parameters of multicomponent chirp signals. The estimator is based on the cubic phase function (CPF), which is efficient to estimate the parameters of monocomponent first-, second-, and third-order polynomial phase signal. When the CPF is dealing with multicomponent chirp signals, the spurious peaks arise and hence the identifiability problem exists. A new approach based on the product cubic phase function (PCPF) is proposed to remove the identifiability problem. The occurrence probability of spurious peak, and the effect of noise to the estimator are statistically studied. The simulation examples are provided for validating the theoretical analysis.

On the multiangle centered discrete fractional Fourier transform

Existing versions of the discrete fractional Fourier transform (DFRFT) are based on the discrete Fourier transform (DFT). These approaches need a full basis of DFT eigenvectors that serve as discrete versions of Hermite-Gauss functions. In this letter, we define a DFRFT based on a centered version of the DFT (CDFRFT) using eigenvectors derived from the Gru/spl uml/nbaum tridiagonal commutor that serve as excellent discrete approximations to the Hermite-Gauss functions. We develop a fast and efficient way to compute the multiangle version of the CDFRFT for a discrete set of angles using the FFT algorithm. We then show that the associated chirp-frequency representation is a useful analysis tool for multicomponent chirp signals.

Tracking and separating non-stationary multi-component chirp signals

In this paper we are concerned with the problems of (1) tracking or estimating the unknown, time-varying instantaneous frequency (IF) of a chirp signal from a multi-component signal (we assume our multi-component signal to be formed of additive chirp signals, disjoint in the time–frequency domain, and Gaussian noise) and (2) reconstructing a specific chirp signal based on the estimate of its IF found at (1). The algorithm we developed is based on a previously proposed method adapted now for the case of multi-component signals. It combines an adaptive smoothing procedure with a noise resistant Fourier filter to generate an algorithm with an extremely fine frequency resolution. The method is non-parametric, that is, we assume no prior knowledge about the form of the time-varying IF of the chirp or about the chirp itself. We demonstrate how the method works on simulated data and compare its performance to other presently used procedures.