Linear Frequency Modulation Research Articles

ISAR Imaging for a Composite Target-Layered Rough Surface Scene Based on the Accelerated Time-Domain Scattering Algorithm

Most existing imaging studies are mainly used for a single target or a composite scene consisting of a target and a rough surface (TRS) below it, such as the target-ocean scene. This article focuses on inverse synthetic aperture radar (ISAR) imaging of a special composite scene consisting of a target and layered rough surfaces (TLRS) below it, such as a target and a snow-soil layered scene. Differently from previous imaging algorithms based on the frequency-domain (FD) method, this article combines the time-domain ray bouncing (TDRB) method with imaging algorithms to develop an accurate ISAR imaging framework to obtain composite images of the TLRS scene. To improve the simulation efficiency of the time-domain (TD) echo matrix for ISAR imaging, the multi-thread parallel is used to accelerate the TD scattering algorithm, then, the ISAR imaging formulas based on scattering field expressions in the TLRS scene are derived. Since the linear frequency modulation pulse used in traditional radar imaging has longer pulsewidth than the Gaussian, the matched filter is modified to realize pulse compression under modulating Gaussian pulse excitations to enhance the imaging efficiency. Simulation results show that the proposed ISAR imaging framework ensures the image quality and improves the simulation efficiency significantly. Finally, the ISAR images of the target-snow-soil scene with different parameters are simulated. This article addresses the correlation between the scattering mechanism and image features for ISAR images based on different scattering components, a topic that the literatures do lack.

Optimization of laser stabilization via self-injection locking to a whispering-gallery-mode microresonator: experimental study.

Self-injection locking of a diode laser to a high-quality-factor microresonator is widely used for frequency stabilization and linewidth narrowing. We constructed several microresonator-based laser sources with measured instantaneous linewidths of 1 Hz and used them for investigation and implementation of the self-injection locking effect. We studied analytically and experimentally the dependence of the stabilization coefficient on tunable parameters such as locking phase and coupling rate. It was shown that precise control of the locking phase allows fine-tuning of the generated frequency from the stabilized laser diode. We also showed that it is possible for such laser sources to realize fast continuous and linear frequency modulation by injection current tuning inside the self-injection locking regime. We conceptually demonstrate coherent frequency-modulated continuous wave LIDAR over a distance of 10 km using such a microresonator-stabilized laser diode in the frequency-chirping regime and measure velocities as low as sub-micrometer per second in the unmodulated case. These results could be of interest to cutting-edge technology applications such as space debris monitoring and long-range object classification, high-resolution spectroscopy, and others.

Photonic-Assisted Generation of Flexible and Switchable Multi-Band Linearly Frequency Modulated Microwave Waveforms

A novel photonic scheme based on parallel dual-drive Mach-Zehnder modulator (DDMZM) to generate flexible and switchable multi-band linearly frequency modulated (LFM) microwave waveforms is proposed. In the scheme, a radio frequency (RF) local oscillator is applied to one arm of DDMZM1 and DDMZM2 with a relative phase of 90°, respectively; while a single-chirp signal to the other arms of the two DDMZMs with a tunable relative phase shift. The generated two independently lightwaves are detected by a balanced photodetector (BPD) and the switchable multi-band LFM signals are generated flexibly. By appropriately adjusting the phase difference <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ</i> , dual-band complementary LFM signals and multi-band LFM signals can be easily switched. Based on simulations, the dual-band complementary LFM waveforms centered at 10 GHz and 30 GHz are generated with a doubled bandwidth (3.2 GHz) as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ =</i> 0, the multi-band LFM microwave waveforms with center frequency-bandwidth of 10 GHz-1.6 GHz, 20 GHz-6.4 GHz and 30 GHz-1.6 GHz, covering X, K and Ka bands, are simultaneously obtained with flatness of 1.9 dB as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ</i> = π/2 or 3π/2. Their autocorrelation results manifest high peak-to-sidelobe ratio (PSR) about 14 dB, and good pulse compression capabilities. The presented scheme features its compact structure, easiness in switching control, as well as larger bandwidth, and has potential applications in multifunctional radars.

Single channel convolutive blind source separation for LFM radar signals

Abstract We propose a single channel blind source separation algorithm for convolutively mixed linear frequency modulation (LFM) signals based on smoothed Wigner-Ville distribution (SWVD) time-frequency analysis, Canny edge detection, and Hough transform detection. First, the SWVD time-frequency analysis diagram is obtained as an image based on the LFM time-frequency characteristics. Second, Canny edge detection is performed on the image. Then, Hough transform is used to detect the characteristic parameters of the linear signal. Finally, the source signal is recovered. The simulation results show that the algorithm is effective for single channel detection and extraction of convolutively mixed LFM signals.

Mainlobe Deceptive Jammer Suppression in SF-RDA Radar: Joint Transmit-Receive Processing

The problem of mainlobe deceptive jammer suppression with a novel stepped frequency (SF)-receive delay array (RDA) radar is addressed in this paper. In our system design, the linear frequency modulation (LFM) waveform with a SF across the antenna elements is transmitted in a uniform linear array, and the received echo is delayed with a time shift between adjacent antenna elements, introducing extra range-dependent degrees-of-freedom (DOFs) in both transmit and receive domains. Consider a typical form of mainlobe jammers, where multiple false targets are generated in the same transmit pulse or same range bin behind the true target after short time modulation. In this respect, the jammers are discriminated from the true target in the joint transmit-receive spatial frequency domain, and suppressed via a data-dependent beamformer based on the minimum variance distortionless response (MVDR) criterion. To further solve the problem of sample selection due to the pseudo-random distribution of the false targets, two kinds of robust beamformers based on the enhanced Capon power spectrum (ECPS) and the eigen-projection elimination (EPE), are developed to reconstruct the jammer-plus-noise covariance matrix and estimate the steering vector of the true target. The performance of the proposed methods in suppression of mainlobe deceptive jammers is evaluated via numerical simulations and compared with the existing systems and robust beamforming methods.

МЕТОД ГЕНЕРАЦИИ СВЕРХШИРОКОПОЛОСНЫХ СВЧ-СИГНАЛОВ С ЛИНЕЙНО-ЧАСТОТНОЙ МОДУЛЯЦИЕЙ НА ОСНОВЕ САМОГЕТЕРОДИНИРОВАНИЯ ИЗЛУЧЕНИЯ ЛАЗЕРНОГО ДИОДА

In this paper, microwave photonic technique of ultrawideband linearly frequency modulated signals generation is proposed. The proposed method based on direct modulation of the laser diode current, which provides a periodic change in the emission frequency. The Michelson interferometer summarizes laser signal and its replica with time delay exceeding 10 ms, which, in turn, is defined by time difference between arms. Optoelectronic conversion is performed in high-speed high-power photodiode. The proposed approach makes it possible to generate microwave signals with linear frequency modulation in the frequency range up to several tens of gigahertz by means of laser pump current modulation in the frequency range less than 100 MHz. The method of ultra-wideband microwave signals generation is implemented using a Michelson fiber-optic interferometer with Faraday mirrors. Such interferometer topology provides a doubling of the path length, and reduced gyroscopic effects due to a counter-propagating double pass. Changing the parameters of the generated microwave ultrawideband signals with frequency modulation is achieved by pump current shape and amplitude control. It is also proposed to use real-time oscilloscope without need of changing of the internal structure of such generator to pre-tune it. Time-frequency analysis is used to extract frequency versus time dependence. By so doing, direct impulse response estimation is performed. This method allows to characterize laser diode frequency response for arbitrary microwave waveform generation by means of pump current waveform calculation from experimental data.

Simultaneous Polarization Measurement and High-Resolution Imaging Algorithm Inspired by Bat Sound Waveform

The acquisition and utilization of polarization information is an open topic because polarization plays a significant role in many fields, such as radar target detection, classification, recognition, synthetic aperture radar (SAR) imaging, anti-jamming, etc. Inspired by the bat sound waveform and combined with the properties of the stepped linear frequency modulation (SLFM) signal, in this article, a novel polarization waveform, namely, simultaneous SLFM (SSLFM), which can be used for small airborne and spaceborne polarimetric SAR (PolSAR) platform, is proposed. Moreover, a method based on the SSLFM signal is proposed to realize simultaneous polarization measurement and double high-resolution imaging. It is demonstrated that the method can better make use of the polarization information of echoes and obtain a better imaging effect. The feasibility of the proposed method is verified by simulation experiments.

Dual-loop diode-tuned Fourier domain harmonically mode-locked opto-electronic oscillator with over 50 dB side-mode spur reduction.

We propose and demonstrate a dual-loop harmonic Fourier domain mode-locked optoelectronic oscillator (FDML-OEO) for drastically reducing the side-mode spurs. The frequency domain mode-locking is achieved by synchronizing the scanning period of the filter to an integer fraction of the round trip times of the two loops with a self-made low cost diode-tuned RF filter. We found, for the first time to the best of authors' knowledge, that the frequency scanning bandwidth (FSBW) of the mode-locked output is strongly affected by the length mismatch between the two fiber loops. By using the phase noise of FDML OEO's delayed self-heterodyne signal as a performance indicator, we found experimentally that both the locking bandwidth and the FSBW of the device are inversely proportional to the length mis-match of the two loops. Finally, with dual-loop fiber lengths of 2041m and 2449.2m, including 2039m common fiber loop, we successfully obtained linearly chirped microwave signals around 9GHz with a phase noise of -127dBc/Hz at 10kHz offset from the 9GHz carrier, a FSBW of 0.4GHz, and a chirp rate of 200THz/s at 500.38 kHz repetition rate. More impressively, the side-mode spur ratio of the linear frequency modulated (LFM) signal is reduced to less than -83dB, the lowest ever achieved for a FDML OEO to the best of authors' knowledge, which is more than 50dB improvement over that achieved with a single loop FDML OEO reported previously.

Multiband dual- and cross-LFM waveform generation using a dual-drive Mach–Zehnder​ modulator

Linear frequency modulation (LFM) signals are widely used in modern radar systems owing to their intrinsic pulse compression capability but are restricted due to a limited range-Doppler resolution. On the other hand, dual- or cross-LFM signals have complementary LFM waveforms at the same time instant that reduces the range-Doppler coupling and thus improving range-Doppler resolution. We propose a simple microwave-photonic-based approach to generate multiband dual- and cross-LFM waveforms using only a single dual-drive Mach–Zehnder modulator (DDMZM). A theoretical analysis is carried out, which is modeled and verified through experiments. Dual- and cross-LFM waveforms at a carrier frequency of 6 GHz and 18 GHz with a bandwidth of 2 GHz is generated by controlling the DC and RF bias of the DDMZM. The tunability of the carrier frequency from 3 GHz to 9 GHz is also verified. A range resolution of 6.3 cm for dual- and cross-LFM waveforms, is obtained with a time-bandwidth-product (TBWP) of 20,000. The proposed technique is a promising solution for dual- and cross-LFM waveform generation in two-band multipurpose radar systems.

Azimuth Estimation of Multi-LFM Signals Based on Improved Complex Acoustic Intensity Method

The complex acoustic intensity method is one of the common methods used for the azimuth estimation of single-vector sensors. However, this method establishes a relationship between frequency and azimuth, which limits its practical applicability for multiple linear frequency modulation (LFM) signals with overlapping frequency domains. In this paper, the time–frequency distribution information of the LFM signal is combined with the complex acoustic intensity method, and more signal parameter information is used to expand the application scenario of the single-vector sensor. The proposed method first processes the time–frequency graph of the signal to obtain a stable and clear time–frequency distribution, and then obtains the acoustic intensity distribution of the signal using the time integration of the energy on the ridge of the signal to estimate the target orientation more stably. The simulation results show that the root mean square error of azimuth estimation is less than 1° when the SNR is greater than 0 dB. Furthermore, a pool experiment was carried out to verify the effectiveness of the proposed method.

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 frequency-aligned 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.

Airborne Radar Anti-Jamming Waveform Design Based on Deep Reinforcement Learning.

Airborne radars are susceptible to a large number of clutter, noise and variable jamming signals in the real environment, especially when faced with active main lobe jamming, as the waveform shortcut technology in the traditional regime can no longer meet the actual battlefield radar anti-jamming requirements. Therefore, it is necessary to study anti-main-lobe jamming techniques for airborne radars in complex environments to improve their battlefield survivability. In this paper, we propose an airborne radar waveform design method based on a deep reinforcement learning (DRL) algorithm under clutter and jamming conditions, after previous research on reinforcement-learning (RL)-based airborne radar anti-jamming waveform design methods that have improved the anti-jamming performance of airborne radars. The method uses a Markov decision process (MDP) to describe the complex operating environment of airborne radars, calculates the value of the radar anti-jamming waveform strategy under various jamming states using deep neural networks and designs the optimal anti-jamming waveform strategy for airborne radars based on the duelling double deep Q network (D3QN) algorithm. In addition, the method uses an iterative transformation method (ITM) to generate the time domain signals of the optimal waveform strategy. Simulation results show that the airborne radar waveform designed based on the deep reinforcement learning algorithm proposed in this paper improves the signal-to-jamming plus noise ratio (SJNR) by 2.08 dB and 3.03 dB, and target detection probability by 26.79% and 44.25%, respectively, compared with the waveform designed based on the reinforcement learning algorithm and the conventional linear frequency modulation (LFM) signal at a radar transmit power of 5 W. The airborne radar waveform design method proposed in this paper helps airborne radars to enhance anti-jamming performance in complex environments while further improving target detection performance.

Direction of arrival estimation based on slope fitting of wideband array signal in fractional Fourier transform domain

AbstractTraditional direction of arrival (DOA) estimation methods of wideband linear frequency modulated (LFM) signal based on the fractional Fourier transform (FRFT) highly depend on the peak value of LFM signal in the FRFT domain. However, the peak value can be affected by various factors, such as a low signal‐to‐noise ratio (SNR), a small number of snapshots, or the large incident angle of signals, which can lead to a decrease in DOA estimation accuracy. To tackle this problem, based on the energy‐concentrated property of LFM signal in the FRFT domain, the DOA estimation is accomplished by adopting the approach of slope fitting for the wideband array signal in the FRFT domain in this study. The method uses the correspondence between the peak position in the FRFT domain and the delay of the received signal on different uniform linear array elements. The least square method based on threshold outlier detection is used for slope fitting. Compared to conventional methods, the method of this study has high accuracy and relatively low complexity in the case of low SNR or large incident angle of the signal without relying on the peak value. The effectiveness of this method is verified by theoretical analysis and Monte‐Carlo simulations. The proposed method provides a new path for DOA estimation of LFM signal.

Broadband Signal Digitization Based on Low-Speed Non-Uniform Photonic Sampling

A new non-uniform photonic sampling (NPS) strategy and its special signal reconstruction algorithm are proposed to achieve digital acquisition of broadband periodic signals at a low sampling rate. Compared with the existing schemes, the NPS strategy can largely reduce the sampling number to acquire identical signal information as that obtained by using its equivalent high-speed uniform photonic sampling, which is beneficial for reducing the sampling time and the data volume of the NPS-based analog-to-digital converter (ADC). In addition, the calculation time of the proposed algorithm is millions of times lower than that of the digital alias-free signal processing (DASP) algorithm used before, which benefits from the fast Fourier transform calculation of a one-dimensional data array instead of a two-dimensional data array calculation in the DASP algorithm. A simulation is performed to validate the feasibility of the proposed scheme. In the simulation, a single-channel NPS-based ADC with an average sampling rate of 1 GSa/s is demonstrated by using the proposed NPS strategy and signal reconstruction algorithm. The results indicate the reconstructed signal information for a single-tone microwave signal at 9.9 GHz and a linear frequency modulation signal in the frequency range of 1 GHz to 9 GHz are identical to those obtained by using its equivalent high-speed uniform photonic sampling-based ADC with a sampling rate of 20 GSa/s.

Non-linear Frequency Estimation Based Upon Convolution Neural Network

A frequency estimator is to find the frequency of the received signal distorted by noise, and it has been found in systems such as radar, sonar, etc. In this research, the linear frequency modulation signal(LFM)of the radar system, the detection of the moving target and its frequency estimation were highlighted. The pre-trained convolutional neural network algorithm was used, which proved highly accurate in detecting the target and estimating its frequency, despite the lower level of the signal to the noise ratio(SNR) where it was dealt with. On the basis of the signals received as a two-dimensional image and taking into account the Doppler effect, as the target moves at different speeds and accelerations, the signals have been classified into single-frequency signals and LFM signals

Vortex-electromagnetic-wave-based ISAR imaging for high-speed maneuvering targets

Vortex electromagnetic wave (VEMW) carrying orbital angular momentum (OAM), which is expected to introduce additional degrees of freedom in inverse synthetic aperture radar(ISAR) imaging. However, the current research about maneuvering targets is based on the "stop go" hypothesis, which does not apply to high-speed motion scenarios due to the intrapulse movement of the target. To improve the imaging quality, this letter proposes a VEMW-based high-speed maneuvering targets imaging method. Firstly, the ISAR imaging scenario of high-speed target is established. According to the spatial geometric relationship between radar and maneuvering target, the vortex echo is deduced and its characteristics are analyzed. Subsequently, a frequency modulation rate estimation method considering both calculation efficiency and high precision is proposed to realize the accurate estimation of target speed. Then, an adaptive azimuth image compensation method based on minimum entropy is proposed. Through the setting of threshold, the number of component signals in linear frequency modulation (LFM) signal is determined and compensated successively. Finally, the range profile and azimuth profile are combined to reconstruct the three-dimensional information. The simulation results demonstrate that this work can effectively eliminate the influence of high-speed motion on range and azimuth profile, also benefit the development of ISAR imaging technique of high-speed maneuvering targets.

A Novel Interrupted-Sampling Repeater Jamming Suppression Method Based on Time-Frequency Analysis and Target Sparse Reconstruction

Interrupted-sampling repeater jamming (ISRJ) is a new kind of coherent jamming for linear frequency modulation (LFM) signals. Based on digital radio frequency memory (DRFM), ISRJ can generate multiple false target groups by intercepting, storing, and retransmitting radar signal fragments, which significantly affects the postprocessing results of radar systems. Furthermore, due to the fragment interception of ISRJ, ISRJ false targets present a regular and discontinuous time-frequency (TF) distribution in contrast with real targets. Considering this intrinsic property and the coherent nature of ISRJ, this study proposes a new method based on TF analysis and target sparse reconstruction to address the ISRJ suppression issue. In this method, the echo signal is first sparsely represented to obtain both the real and false target positions. Then, according to the acquired target positions, information entropy features of targets are extracted in TF data for subsequent target identification. Finally, guided by the identification result, the real targets can be retained and reconstructed by adaptive filtering in the sparse domain to realize ISRJ suppression. Simulations have validated the effectiveness of the proposed method under various situations.

A Novel Jamming Method against SAR Using Nonlinear Frequency Modulation Waveform with Very High Sidelobes

Synthetic aperture radar (SAR) systems have the capacity for day-and-night and all-weather surveillance, which has become increasingly indispensable for military surveillance and global comprehensive environmental monitoring. With the development of the high-resolution SAR imaging technique, studies on SAR jamming have also received much interest. Traditional jamming methods are based on linear-frequency-modulated (LFM) signals, and this method can achieve high main-lobe jamming gain. However, its sidelobe jamming energy is very low. To solve this issue, a novel nonlinear frequency modulation (NLFM) waveform design method for SAR jamming is proposed in this paper. Compared with LFM waveforms, the designed waveforms have the same main-lobe jamming gain and very high sidelobes, which can significantly improve jamming performance. Moreover, detailed simulation experiments were carried out to verify the effectiveness of the newly proposed jamming scheme.

Nonlinear Frequency-Modulated Waveforms Modeling and Optimization for Radar Applications

Conventional radars commonly use a linear frequency-modulated (LFM) waveform as the transmitted signal. The LFM radar is a simple system, but its impulse-response function produces a −13.25 dB sidelobe, which in turn can make the detection of weak targets difficult by drowning out adjacent weak target information with the sidelobe of a strong target. To overcome this challenge, this paper presents a modeling and optimization method for non-linear frequency-modulated (NLFM) waveforms. Firstly, the time-frequency relationship model of the NLFM signal was combined by using the Legendre polynomial. Next, the signal was optimized by using a bio-inspired method, known as the Firefly algorithm. Finally, the numerical results show that the advantages of the proposed NLFM waveform include high resolution and high sensitivity, as well as ultra-low sidelobes without the loss of the signal-to-noise ratio (SNR). To the authors’ knowledge, this is the first study to use NLFM signals for target-velocity improvement measurements. Importantly, the results show that mitigating the sidelobe of the radar waveform can significantly improve the accuracy of the velocity measurements.

Estimation and Classification of NLFM Signals Based on the Time-Chirp Representation.

A new approach to the estimation and classification of nonlinear frequency modulated (NLFM) signals is presented in the paper. These problems are crucial in electronic reconnaissance systems whose role is to indicate what signals are being received and recognized by the intercepting receiver. NLFM signals offer a variety of useful properties not available for signals with linear frequency modulation (LFM). In particular, NLFM signals can ensure the desired reduction of sidelobes of an autocorrelation (AC) function and desired power spectral density (PSD); therefore, such signals are more frequently used in modern radar and echolocation systems. Due to their nonlinear properties, the discussed signals are difficult to recognize and therefore require sophisticated methods of analysis, estimation and classification. NLFM signals with frequency content varying with time are mainly analyzed by time-frequency algorithms. However, the methods presented in the paper belong to time-chirp domain, which is relatively rarely cited in the literature. It is proposed to use polynomial approximations of nonlinear frequency and phase functions describing signals. This allows for applying the cubic phase function (CPF) as an estimator of phase polynomial coefficients. Originally, the CPF involved only third-order nonlinearities of the phase function. The extension of the CPF using nonuniform sampling is used to analyse the higher order polynomial phase. In this paper, a sixth order polynomial is considered. It is proposed to estimate the instantaneous frequency using a polynomial with coefficients calculated from the coefficients of the phase polynomial obtained by CPF. The determined coefficients also constitute the set of distinctive features for a classification task. The proposed CPF-based classification method was examined for three common NLFM signals and one LFM signal. Two types of neural network classifiers: learning vector quantization (LVQ) and multilayer perceptron (MLP) are considered for such defined classification problem. The performance of both the estimation and classification processes was analyzed using Monte Carlo simulation studies for different SNRs. The results of the simulation research revealed good estimation performance and error-free classification for the SNR range encountered in practical applications.