Quadratic Frequency Modulation Research Articles

Quantitative SNR analysis of QFM signals in the LPFT domain with Gaussian windows

The purpose of this paper is to present a quantitative SNR analysis of quadratic frequency modulated (QFM) signals. This analysis is located in the continuous-time local polynomial Fourier transform (LPFT) domain using a Gaussian window function based on the definition of 3 dB signal-to-noise ratio (SNR). First, the maximum value of the local polynomial periodogram (LPP), and the 3 dB bandwidth in the LPFT domain for a QFM signal is derived, respectively. Then, based on these results, the 3 dB SNR of a QFM signal with Gaussian window function is given in the LPFT domain with one novel idea highlighted: the relationship among standard SNR, parameters of QFM signals and Gaussian window function is clear, and the potential application is demonstrated in the parameter estimation of a QFM signal using the LPFT. Moreover, the 3 dB SNR in the LPFT domain is compared with that in the linear canonical transform (LCT) domain. The validity of theoretical derivations is confirmed via simulation results. It is shown that, in terms of SNR, QFM signals in the LPFT domain can achieve a significantly better performance than those in the LCT domain.

ISAR imaging of target with complex motion associated with the fractional Fourier transform

High-resolution inverse synthetic aperture radar (ISAR) imaging based on parameter estimation of polynomial phase signal is a quite significant research hotspot, in which the azimuth echo can be modeled as multi-component quadratic frequency modulation (QFM) signal after preprocessing, which leads to the time-varying Doppler frequency. In this paper, an effective parameter estimation method called the product form of symmetric correlation function based on the fractional Fourier transform (PFrSCF) is proposed. In proposed method, a novel symmetric correlation function is used to reduce phase order of QFM signal firstly. Then, the PFrSCF can estimate two parameters of QFM signal simultaneously by the fractional Fourier transform and suppress cross term by the product in fractional Fourier transform domain. Compared with other methods, the PFrSCF is capable of suppressing cross term effectively and ensuring the good accuracy of parameters. Moreover, the PFrSCF is robust in noisy environment. Finally, associated with range-instantaneous-Doppler imaging technology, a novel ISAR imaging algorithm is presented based on PFrSCF method. The performances of PFrSCF method and the corresponding ISAR imaging algorithm of target are verified by simulated and real data.

An Efficient ISAR Imaging of Targets with Complex Motions Based on a Quasi-Time-Frequency Analysis Bilinear Coherent Algorithm.

The inverse synthetic aperture radar (ISAR) imaging for targets with complex motions has always been a challenging task due to the time-varying Doppler parameter, especially at the low signal-to-noise ratio (SNR) condition. In this paper, an efficient ISAR imaging algorithm for maneuvering targets based on a noise-resistance bilinear coherent integration is developed without the parameter estimation. First, the received signals of the ISAR in a range bin are modelled as a multicomponent quadratic frequency-modulated (QFM) signal after the translational motion compensation. Second, a novel quasi-time-frequency representation noise-resistance bilinear Radon-cubic phase function (CPF)-Fourier transform (RCFT) is proposed, which is based on the coherent integration of the energy of auto-terms along the slope line trajectory. In doing so, the RCFT also effectively suppresses the cross-terms and spurious peaks interference at no expense of the time-frequency resolution loss. Third, the cross-range positions of target’s scatters in ISAR image are obtained via a simple maximization projection from the RCFT result to the Doppler centroid axis, and the final high-resolution ISAR image is thus produced by regrouping all the range-Doppler frequency centroids. Compared with the existing time-frequency analysis-based and parameter estimation-based ISAR imaging algorithms, the proposed method presents the following features: (1) Better cross-term interference suppression at no time-frequency resolution loss; (2) computationally efficient without estimating the parameters of each scatters; (3) higher signal processing gain because of 2-D coherent integration realization and its bilinear function feature. The simulation results are provided to demonstrate the performance of the proposed method.

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv’s distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

Ground Moving Target Refocusing in SAR Imagery Using Scaled GHAF

In this paper, a new method is proposed to refocus a ground moving target in synthetic aperture radar imagery. In this method, range migration is compensated in the 2-D frequency domain, which can easily be implemented by using the complex multiplications, the fast Fourier transform (FFT), and the inverse FFT operations. Then, the received target signal in a range gate is characterized as a quadratic frequency-modulated (QFM) signal. Finally, a novel parameter estimation method, i.e., scaled generalized high-order ambiguity function (HAF), is proposed to transform the target signal into a signal on 2-D time–frequency plane and realize the 2-D coherent integration, where the peak position accurately determines the second- and third-order parameters of a QFM signal. Compared with our previously proposed generalized Hough-HAF method, the proposed method can obtain a better target focusing performance, since it can eliminate the incoherent operations in both range and azimuth directions. In addition, the proposed method is computationally efficient, since it is free of searching in the whole target focusing procedure. Both simulated and real data processing results are provided to validate the effectiveness of the proposed algorithm.

Parameter estimation of QFM signal based on MPKF

In order to reconstruct the quadratic frequency modulated (QFM) signal, such as radar signal due to the complexity. A novel method for the parameter estimation of multi-component QFM signal based on a modified product kernel function (MPKF) is proposed in this paper. The method has fewer external cross-terms and light computational burden because of non-iterative operations. Moreover, it is robust against additive noise. Finally, simulated and real data results confirm the proposed method.

Analysis of Maneuvering Targets with Complex Motions by Two-Dimensional Product Modified Lv's Distribution for Quadratic Frequency Modulation Signals.

For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM) signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR) and the quadratic chirp rate (QCR) are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF) and modified scaled Fourier transform (mSFT), an effective parameter estimation algorithm is proposed—referred to as the Two-Dimensional product modified Lv’s distribution (2D-PMLVD)—for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT) and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified.

An ISAR Imaging Algorithm for Maneuvering Targets With Low SNR Based on Parameter Estimation of Multicomponent Quadratic FM Signals and Nonuniform FFT

The inverse synthetic aperture radar (ISAR) imaging for maneuvering targets has always been a challenging task due to the time-varying Doppler parameter, especially in the low signal-to-noise ratio (SNR) environment. In this paper, a novel ISAR imaging algorithm for maneuvering targets in the low SNR environment based on the parameter estimation approach is presented. First, the received signals of the ISAR in a range bin are modeled as a multicomponent quadratic frequency-modulated (QFM) signal after the migration compensation. Then, to estimate the parameters of the QFM signal, two cubic phase functions (CPFs), namely coherently integrated generalized CPF (CIGCPF) and coherently integrated CPF (CICPF), are developed. The CIGCPF and CICPF are simple and only require the fast Fourier transform (FFT) and the nonuniform FFT (NUFFT). Due to the usage of the NUFFT, the computational cost is reduced, and the searching procedure is unnecessary for the nonuniformly spaced signal. Thanks to the coherent integrations and NUFFT, the CIGCPF and CICPF, which demonstrate the excellent noise-tolerant performance and reduce the error propagation effect, are efficient and suitable for the multicomponent QFM signals in the low SNR environment. Finally, several simulation examples, analyses of the noise-tolerant performance of the proposed method, and ISAR imaging results of the simulated data demonstrate the effectiveness of the proposed method.

Imaging of high‐speed manoeuvering target via improved version of product high‐order ambiguity function

This study presents a novel algorithm for radar imaging of high-speed manoeuvering target. It is based on the fact that the azimuth part of the echo is modelled as the superposition of multiple quadratic frequency modulated (QFM) signals, and the range-Doppler algorithm is inappropriate to generate a focused radar image in this case. In this study, the improved version of product high-order ambiguity function (IPHAF) is proposed to estimate the parameters of multiple QFM signals. This estimator requires only one-dimensional (1D) maximisations without the scaling operation compared with the traditional product high-order ambiguity function. The radar image quality can be improved by the IPHAF technique, and the experimental results validate the effectiveness of the method presented in this study.

Algorithm based on the linear canonical transform for QFM signal parameters estimation

In this study, a novel algorithm based on the linear canonical transform (LCT) is proposed for parameters estimation of a quadratic frequency modulated (QFM) signal. First, a new kind of generalised LCT (GLCT) is defined and the GLCT of the QFM signal will generate an impulse. The third-order phase coefficient of the QFM signal can be estimated in accordance to the position information of such impulse. After compensating off the third-order phase coefficient, the QFM signal can be approximated to linear frequency modulated (LFM) signal and the second-order, first-order phase coefficient and the amplitude can be estimated by algorithms for estimating the LFM signal. The proposed algorithm does not suffer a heavy computational burden because it only requires one dimensionality maximisation and the LCT has fast numerical algorithm as well. Moreover, the proposed algorithm has accurate estimation and low signal to noise ratio (SNR) threshold. Meanwhile, high-output SNR of the proposed algorithm can be gotten with a small number of sampling points. Comparisons with existing algorithms verify that the proposed algorithm has a good performance in the aspects of computational complexity, accuracy and output SNR in some cases.

Parameter estimation method for multiple quadratic frequency‐modulated signals

Generalised cubic phase function (GCPF)-based estimator is efficient in estimating the third-order coefficient for mono-component quadratic frequency-modulated (QFM) signal. However, it suffers from cross-terms and spurious peaks when dealing with multi-component QFM signals. To efficiently estimate the third-order coefficients of multi-component QFM, a novel coherently integrated GCPF (CIGCPF) algorithm is proposed to enhance the auto-terms and suppress the cross-terms and spurious peaks. Comparisons with state-of-the-art algorithms indicate that CIGCPF not only solves the identification problem for multi-component QFM signals, but also can acquire higher anti-noise performance.

Inverse Synthetic Aperture Radar Imaging of Nonuniformly Rotating Target Based on the Parameters Estimation of Multicomponent Quadratic Frequency-Modulated Signals

Inverse synthetic aperture radar (ISAR) is very useful in radar signature applications. In ISAR imaging of nonuniformly rotating target, the radar echo signal in a range cell can be modeled as multicomponent quadratic frequency-modulated (QFM) signals. The high-quality radar images can be obtained by the parameters estimation of QFM signals combined with the range-instantaneous-Doppler technique. In this paper, a novel algorithm for the parameters estimation of QFM signal via the modified cubic phase function (MCPF) is presented. This algorithm estimates the quadratic phase coefficient at first, and the other parameters can be estimated by the traditional CPF and the fast Fourier transform. The implementation of MCPF algorithm requires only 1-D maximizations, and the comparison with some existing algorithms is discussed. The ISAR imaging results of simulated and raw data validate the effectiveness of the novel algorithm proposed in this paper.

Diffraction management and soliton dynamics in frequency-chirped ℙT symmetric lattices.

We address two closely related problems: diffraction management and soliton dynamics in parity-time ( ℙT) symmetric lattices with a quadratic frequency modulation. The normal, anomalous, or zero diffraction is possible for narrow beams with a broad band of spatial frequencies. The frequency band of nondiffraction beams can be enlarged by increasing the chirp rate of lattices. Counter-intuitively, the gain-loss component plays the same role as the real part of lattice on the suppression of diffraction, which leads to an effective reduction of critical lattice depth for nondiffraction beams. Additionally, we reveal the existence of a novel type of "bright" solitons in defocusing Kerr media modulated by chirped ℙT lattices. We also demonstrate that lattice chirp can be utilized to suppress the instability of solitons. Our results expand the concept of ℙT symmetry in both linear and nonlinear regimes, and may find interesting optical applications.

ISAR Imaging of a Ship Target Based on Parameter Estimation of Multicomponent Quadratic Frequency-Modulated Signals

High-resolution inverse synthetic aperture radar (ISAR) imaging of a ship target is a challenging task because of fluctuation with the ocean waves. The images obtained with a standard range-Doppler algorithm are usually blurred. Consequently, the range-instantaneous-Doppler (RID) technique should be used to improve the image quality. In this paper, the received signal in a range cell is modeled as a multicomponent quadratic frequency-modulated (QFM) signal after range compression and motion compensation, and then a new RID ISAR imaging algorithm is proposed that introduces a new method for estimating parameters of the QFM signal. By defining a new function and using the scaled Fourier transform (SCFT) with respect to the time axis, the coherent integration of auto-terms can be realized via the subsequent Fourier transformation with respect to the lag-time axis, and a peak can be obtained in the 2-D frequency plane, which is appropriate for parameter estimation of the QFM signal to reconstruct RID images. The proposed algorithm is accurate and fast since the defined function has moderate order nonlinearity and the SCFT can be performed via chirp z-transform. Experiments demonstrate the performance of the new algorithm. Comparisons with existing algorithms are also given, which show that the proposed algorithm can efficiently produce a focused image with less fake scatterers.

Diffraction management of focused light beams in optical lattices with a quadratic frequency modulation

We reveal that the effective diffraction experienced by light beams launched along the central guiding channel of optical lattice with a quadratic frequency modulation can be tuned in strength and sign. Complete suppression of the linear diffraction in the broad band of spatial frequencies is shown to be possible, thus profoundly affecting properties of nonlinear self-sustained beams as well. In particular, we report on the properties of a new class of stable solitons supported by such lattices in defocusing media.

Formation and analysis of the interference field of a bifocal lens when a laser beam is transmitted off-axis

This paper proposes a device that operates on the basis of a polarization interferometer and makes it possible to use laser radiation to form two-dimensional interferograms and interference signals that satisfy the quadratic frequency modulation (QFM) law. QFM signals with smoothly varying informational parameters are investigated, and it is shown that they can be used to monitor small linear and angular displacements. © 2004 Optical Society of America

The Radar Measurement of Range, Velocity and Acceleration

This paper is a study of the ultimate attainable accuracy in the radar measurement of range, range rate, and range acceleration. It is assumed that these quantities are to be measured by a coherent radar with a large output signal-to-noise ratio. The approach is entirely theoretical, and the accuracy evaluated is the accuracy that would be attained with an ideal receiver which performs maximum-likelihood estimates of the unknown parameters. The transmitted waveformn is fixed and arbitrary, and the error variances and covariances are evaluated in detail in termns of the amplitude and frequency modulation of the transmitted wave. Specific results are also given for constant amplitude pulses carrying arbitrary combinations of linear and quadratic frequency modulation.