Linear Frequency Modulation Research Articles

Simultaneous Generation of Two Negatively Correlated Linearly Frequency-Modulated Pulses Based on an Integrated Anti-Reflection Spectral Shaper

Grating-based spectral shaping (SS) combined with wavelength-to-time (WTT) mapping has proved to be an essential approach to the photonic generation of linearly frequency-modulated (LFM) pulses due to its potential to yield the large time-bandwidth product (TBWP) and to be fully integrated. One of the most challenging issues of chip-level integration is the grating-induced reflection which may significantly impact the laser source. Since the on-chip nonreciprocal devices such as optical isolators and circulators remain difficult to realize, a silicon-integrated anti-reflection spectral shaper based on a Mach–Zehnder interferometer (MZI) comprising two linearly chirped grating-assisted contra-directional couplers (LCGA-CDCs) has been proposed and demonstrated. Thanks to the isolation between the input and output ports of the contra-directional couplers, the reported shaper presents an effective suppression of the reflecting power returned to its input port with a measured rejection ratio of around −10 dB covering the entire C-band. To predict the instantaneous frequency responses of the generated microwave pulses, an equivalent asymmetric MZI configuration with wavelength-dependent length difference has also been introduced to explain the mechanism of SS. Two negatively correlated LFM waveforms with up-chirped profiles and large TBWPs of 45.60 and 53.52 are simultaneously generated using a fabricated sample. Our work paves the way for an all-optical integration of the photonic-assisted isolator-free LFM pulse generation, presenting great potential for multiple application scenarios in pulsed radar systems.

A method for LFM signal parameter estimation based on MWC system and STFT-DPT

A method of estimating linear frequency modulation (LFM) signal parameters using compressed sampling (CS) data of a Modulated Wideband Converter (MWC) system is proposed. The short-time Fourier transform algorithm is used to analyze the CS signal of the MWC system, and the obtained CS signal frequency will present a form of multi-segment distribution. By intercepting the CS signal corresponding to the first segment frequency and analyzing the intercepted segment signal with discrete polynomial transform and Rife algorithm, the chirp rate and initial frequency estimation of the segment CS signal can be preliminarily estimated. According to the random sequence with cyclic displacement, the spectrum shift relationship between the input signal and the output signal can be calculated. Therefore, the parameter of the original signal can be estimated by using single channel CS data. Then, all channels are analyzed with the same method, and a more stable parameter estimation result can be obtained than the single channel output. Finally, combined with the simulation experiment, the proposed method can be used to estimate the initial frequency and chirp rate of the LFM signal using CS data effectively.

Instantaneous Frequency Measurement Using Photonics-Assisted Broadband Signal Generation and Processing

A photonics-based instantaneous microwave frequency measurement with broadband signal generation and processing is proposed and demonstrated. In this scheme, a broadband triangular linear frequency-modulated (LFM) signal is first optically generated, and photonic mixing of the LFM signal with a signal under test (SUT) is implemented before extracting the frequency information in the oscilloscope. In the experiment, both accurate single-frequency and multifrequency measurements are successfully realized using low-speed electronic devices. The experimental results confirm a measurement accuracy of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&lt;$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 50 MHz within a frequency range from 1 to 39 GHz.

Beampattern Synthesis Based on Novel Receive Delay Array for Mainlobe Interference Mitigation

This paper investigates beampattern synthesis methods based on a novel Receive Delay Array (RDA) to mitigate interferences located in the mainlobe of the beampattern. In our system design, the RDA is developed by transmitting a stepped frequency linear frequency modulation waveform and delaying the received echo with a small time offset between adjacent receive antenna elements. In doing so, a range-angle-dependent beampattern is obtained in the joint transmit-receive spatial domain. A two-stage beamforming scheme, including the equivalent data-independent transmit beamforming and dimension-reduced data-dependent receive beamforming, is then proposed to mitigate mainlobe interferences. Furthermore, according to the adaptive array theory, by designing a transmit weight vector dependent of the interference steering vector, two beampattern synthesis algorithms are developed respectively based on the maximum gain and minimum deviation to adjust multiple responses of the transmit beampattern precisely. The mainlobe of the receive beampattern is also broadened with the use of the derivative constraint. By combining the devised transmit and receive weight vectors, a two-dimensional joint transmit-receive beampattern with a flat-top mainlobe and broadened nulls can be formed, where the interferences are mitigated against the direction-of-arrival (DOA) mismatch. Theoretical and practical analysis as well as parametric studies are provided to demonstrate the effectiveness of the proposed beampattern synthesis methods in mitigating mainlobe interferences.

An improved signal-dependent QTFD based on iterative regional RGK optimization for multi-component LFM signals

It is quite challenging for the quadratic time-frequency distribution (QTFD) to analyze the multi-component linear frequency modulation (MC-LFM) signals due to its inevitable cross-term issue, particularly in the case of simultaneous strong components and weak components involved in the MC-LFM signals. This paper proposes a novel signal-dependent QTFD based on regional radially Gaussian kernel (RRGK) to improve the time-frequency representations (TFR) of the MC-LFM signals with distinguishing component amplitudes. The model of MC-LFM signals is firstly introduced, and the detrended Radon transform of ambiguity domain (RTA) technique is combined with energy distribution feature in the ambiguity domain analysis for the detection of potential auto-terms concentrated along lines passing through the origin of the Doppler-lag plane. The combined two-step signal detection method can be easily extended to other signal-dependent QTFDs. Then the Doppler-lag distribution area of each detected auto-term is automatically selected with stronger components peeled to restrict the searching area of RGK. Afterwards, a novel iterative regional RGK-based TFD (IRRGD) is developed to resolve strong and weak components under a proper trade-off between auto-term resolution and cross-term suppression in the TFD. Finally, filtering is performed in (t, f) domain to further improve the TFD results. Also, a quantitative indicator is proposed to measure weak signal preservation. Both simulation and experimental results have verified the superiorities of the proposed method over other existing state-of-the-art algorithms.

GNSS-Over-Fiber Sensing System for High Precision 3D Nodal Displacement and Vibration Detection

Aiming at realizing comprehensive structural health monitoring, a GNSS (Global Navigation Satellite System) over fiber sensing approach is presented and experimentally demonstrated to achieve 3D nodal displacement and vibration detection simultaneously. GNSS signals from multi-antennas are transferred to a receiver based on an optical fiber link, also used as distributed sensing fiber. Broadband linear frequency-modulated (LFM) probe light with high linearity is generated based on electro-optic modulation to probe distributed vibrations and monitor the transmission time delay along the whole fiber with high precision. The spectral components generated by vibrations are detected using the cross-correlation method to achieve distributed vibration sensing. In addition, with the assistance of high-precision hardware-delay measurement, the variation of transmission time delay can be obtained, improving the precision of 3D displacement measurement in the GNSS-over-fiber architecture. In the proof-of-concept experiment, a 3D baseline can be obtained with the precision of 2.8, 3.6, and 2.0 mm, while vibrations with frequencies of 40 kHz, 80 kHz, and 100 kHz along 250 m fiber are successfully detected with a spatial resolution of 1 m.

Phase-Derived Ranging Based Fiber Transfer Delay Measurement Using a Composite Signal for Distributed Radars with Fiber Networks

Fiber transfer delay (FTD) variations influence the coherence of distributed radars with fiber networks, resulting in a performance degradation in target detecting and imaging. To measure and compensate for the variation, a phase-derived ranging based FTD measurement using a composite signal is proposed. The composite signal comprises a sinusoidal component and a linear frequency modulation (LFM) component. As the composite signal passes through a fiber under test (FUT), the sinusoidal component generates a phase shift that corresponds to the FTD. The phase shift can be represented by two parameters: the number of complete periods of 2π that can be estimated by using the LFM component, and a phase shift less than 2π that be measured employing the sinusoidal component. When using the proposed measurement system to measure FTD variations in a distributed radar, only an additional sinusoidal component is needed, which minimizes interference with radar signals. Moreover, the proposed measurement system can share core function modules such as signal generation and process modules with distributed radars, which enhances the compatibility and reduces the overall complexity. Experiments are carried out to measure a variable optical delay line and a long optical fiber. The experiment results verify the feasibility of the measurement system and show that a measurement range of more than 15 km, an accuracy of ±0.1 ps and a measurement time of 105 ms can be achieved.

A fine acquisition algorithm based on fast three-time FRFT for dynamic and weak GNSS signals

As high-dynamics and weak-signal are of two primary concerns of navigation using Global Navigation Satellite System (GNSS) signals, an acquisition algorithm based on three-time fractional Fourier transform (FRFT) is presented to simplify the calculation effectively. Firstly, the correlation results similar to linear frequency modulated (LFM) signals are derived on the basis of the high dynamic GNSS signal model. Then, the principle of obtaining the optimum rotation angle is analyzed, which is measured by FRFT projection lengths with two selected rotation angles. Finally, Doppler shift, Doppler rate, and code phase are accurately estimated in a real-time and low signal to noise ratio (SNR) wireless communication system. The theoretical analysis and simulation results show that the fast FRFT algorithm can accurately estimate the high dynamic parameters by converting the traditional two-dimensional search process to only three times FRFT. While the acquisition performance is basically the same, the computational complexity and running time are greatly reduced, which is more conductive to practical application.

Wireless Picosecond Time Synchronization for Distributed Antenna Arrays

Distributed antenna arrays have been proposed for many applications ranging from space-based observatories to automated vehicles. Achieving good performance in distributed antenna systems requires stringent synchronization at the wavelength and information levels to ensure that the transmitted signals arrive coherently at the target, or scattered and received signals can be appropriately processed via distributed algorithms. In this article, we address the challenge of high-precision time synchronization to align the operations of elements in a distributed antenna array and overcome time-varying bias between platforms primarily due to oscillator drift. We use a spectrally sparse two-tone waveform, which obtains approximately optimal time estimation accuracy, in a two-way time transfer process. We also describe a technique for determining the true time delay using the ambiguous two-tone matched filter output, and we compare the time synchronization precision of the two-tone waveform with the more common linear frequency modulation (LFM) waveform. We experimentally demonstrate wireless time synchronization using a single-pulse 40-MHz two-tone waveform over a 90-cm 5.8-GHz wireless link in a laboratory setting, obtaining a timing precision of 2.26 ps.

Reduced-Complexity Estimation of FM Instantaneous Parameters via Deep-Learning

Signal frequency estimation is a fundamental problem in signal processing. Deep learning is a fundamental method to solve this problem. This paper used five deep learning methods and three datasets including different singles Single Tone (ST), Linear- Frequency-Modulated (LFM), and Quadratic-Frequency-Modulated (QFM). This signal is affected by Additive White Gaussian (AWG) noise and Additive Symmetric alpha Stable (SαS) noise. Geometric SNR (GSNR) is used to determine the impulsiveness of noise in a Gaussian and SαS noise mixture. Deep learning methods are Gated Recurrent Unit (GRU), Long Short-Term Memory (LSTM), Bi-Direction Long Short-Term Memory (BiLSTM), and Convolution Neural Network (1D-CNN &amp; 2D-CNN). When compared to a deep learning classifier with few layers to get on high accuracy and complexity reduces for Instantaneous Frequency (IF) estimation, Linear Chirp Rate (LCR) estimation, and Quadratic Chirp Rate (QCR) estimation. IF estimation of ST signals, IF and LCR estimation of LFM signals, and IF, LCR, and QCR estimation of QFM signals. The accuracy of the ST dataset in GRU is 58.09, LSTM is 46.61, BiLSTM is 45.95, 1D-CNN is 51.48, and 2D-CNN is 54.13. The accuracy of the LFM dataset in GRU is 82.89, LSTM is 66.28, BiLSTM is 20%, 1D-CNN is 74.79, and 2D-CNN is 98.26. The accuracy of the QFM dataset in GRU is 78.76, LSTM is 67.8, BiLSTM is 69.91, 1D-CNN is 75.8, and 2D-CNN is 98.2. The results show that 2D-CNN is better than other methods for parameter estimation in LFM signals and QFM signals, and the GRU is better for parameter estimation in ST signals.

High resolution acoustic tomography based on backpropagation of waves

A method of high-resolution acoustic tomography of scattering inhomogeneities based on the method of reverse time migration is proposed. An inhomogeneous background medium with a known distribution of refractive inhomogeneities is considered, where it is necessary to detect scattering inhomogeneities. Probing is carried out by broadband arbitrary waveforms. The method of reverse time migration is supplemented with linear filtering of the direct propagation field, which makes it possible to increase the resolution of reconstructed images. The results of numerical modeling and experiment are presented. Sounding was carried out in water at frequencies from 20 to 350 kHz using a signal with linear frequency modulation. The source of the ultrasonic signal was fixed and irradiated the objects under study in the water. The scattered signal was measured in a plane near the surface in water on a rectangular area with a step of less than 2 mm. Signal processing by the proposed method made it possible to reconstruct a three-dimensional image of scattering inhomogeneities with a resolution of about 7 mm. Comparison of the proposed method and the reverse time migration method showed that the proposed method allows obtaining a higher resolution.

K-Ambiguity function in the framework of offset linear canonical transform

A new version of ambiguity function (AF) associated with the offset linear canonical transform (OLCT) is considered in this paper. This new version of AF coined as the [Formula: see text]-AF associated with the OLCT ([Formula: see text]-AFOL) is defined based on the OLCT and the fractional instantaneous auto-correlation. A natural magnification effect characterized by the extra degrees of freedom of the OLCT and by a factor [Formula: see text] on the frequency axis enables the [Formula: see text]-AFOL to have flexibility to be used in cross-term reduction. Firstly, we defined the [Formula: see text]-AF associated with the OLCT ([Formula: see text]-AFOL), and establish its relationship with the [Formula: see text]-Wigner distribution in OLCT domain. Later on, we define the basic properties including the scaling, conjugate-symmetry, shifting, marginal and Moyal’s formulae of [Formula: see text]-AFOL in depth. The results show that [Formula: see text]-AFOL can be viewed as one of the generalizations of the classical AF which has elegance, simplicity and flexibility in the frequency marginal property. The novelty of our paper lies in applications part, where we have shown how the proposed transform is used for the detection of single-component and bi-component linear frequency-modulated (LFM) signals.

Deconvolved Fractional Fourier Domain Beamforming for Linear Frequency Modulation Signals

To estimate the direction of arrival (DOA) of a linear frequency modulation (LFM) signal in a low signal-to-noise ratio (SNR) hydroacoustic environment by a small aperture array, a novel deconvolved beamforming method based on fractional Fourier domain delay-and-sum beamforming (FrFB) was proposed. Fractional Fourier transform (FrFT) was used to convert the received signal into the fractional Fourier domain, and delay-and-sum beamforming was subsequently performed. Noise resistance was acquired by focusing the energy of the LFM signal distributed in the time-frequency domain. Then, according to the convolution structure of the FrFB complex output, the influence of the fractional Fourier domain complex beam pattern was removed by deconvolution, and the target spatial distribution was restored. Therefore, an improved spatial resolution of DOA estimation was obtained without increasing the array aperture. The simulation and experimental results show that, with a small aperture array at low SNR, the proposed method possesses higher spatial resolution than FrFB and frequency-domain deconvolved conventional beamforming.

A Comparison of the Performance of Four Acoustic Modulation Techniques for Robot Communication in Pipes

Autonomous robotics is an emerging technology for the inspection of a vast network of underground pipes. Communication between autonomous robots is essential to optimise their efficiency and network coverage. However, sending a message acoustically is not a well-researched topic because most of the existing literature is devoted to the study of the acoustic properties of the pipe for the purpose of sensing rather than communication. In particular, the influence of multi-modal propagation and background noise on the quality of acoustic communication in pipes has not been well understood. This paper studies the performance of four standard acoustic communication techniques in a dry drainage pipe to fill this knowledge gap. The noise resistance, communication range and data rate of these techniques are estimated through numerical simulations and laboratory experiments. It has been found that the techniques based on shift keying requires at least 5--10 dB signal to noise ratio (SNR) to function properly while the chirp linear frequency modulation technique can operate reliably with SNR = 0 dB or event lower SNR. The results also suggest that the multi-modal propagation in the pipe has significant effects on the package error rate. The frequency dependent sound attenuation in the pipe also affects the communication range and data rate. In particular, for a 150 mm diameter dry pipe the maximum robot operation distance is likely to be limited to 50--100 m with the highest carrier frequency of around 10 kHz and data rates below 6300 bps. The results of this work pave the way to the development of acoustic communication modules to be deployed on tetheless robots designed to inspect a buried pipe network autonomously and collaboratively.

Passive Location for 5G OFDM Radiation Sources Based on Virtual Synthetic Aperture

Passive location technology has been greatly developed because of its low power consumption, long detection distance, good concealment, and strong anti-interference ability. Orthogonal frequency-division multiplexing (OFDM) is an efficient multi-carrier transmission technology, which is an important signal form of 5G communication. Researching passive locations for OFDM signals can realize the location of base stations, which is of great significance in the military. Space-borne passive location technology has a contradiction between wide coverage and high precision. Therefore, a single-satellite passive location algorithm for OFDM radiation sources based on the virtual synthetic aperture is proposed. The algorithm introduces virtual synthetic aperture technology, using antenna movement to accumulate data coherently over a long time period and synthesizing a long azimuth virtual aperture. In addition, it utilizes fast Fourier transform (FFT) to extract phase information at a specific frequency based on the multi-carrier modulation technology of the OFDM signal. Pilot technology of the communication system is used for phase compensation and noise reduction. Thus, the azimuth linear frequency modulation (LFM) signal containing the location information of the radiation source is obtained. The radiation source location can be obtained by range searching and azimuth focusing. Simulation results verify the effectiveness of the algorithm and show that the algorithm can realize high-precision and wide-coverage location for the OFDM radiation sources using a single antenna, turning the hardware structure into software to reduce the cost and complexity of the system.

A method of underwater sound source range estimation without prior knowledge based on single sensor in shallow water

Introduction: The lack of prior knowledge of the marine environment increases the difficulty of passive ranging of underwater sound sources by using a single hydrophone. The dispersion curve of the normal mode contains extensive marine environmental information, which can be extracted without prior knowledge, but the characteristics of dispersion curves of different modes vary, and the mode order cannot be determined from the received data.Methods: Herein, a method based on a single hydrophone that can jointly identify the mode order and estimate the propagation range in unknown marine environment is proposed. The method uses Bayesian theory as the main methodology and is applicable to broadband pulse sound sources in shallow seas with long-range propagation. The dispersion curves extracted from the data and those calculated by the dispersion formula are the input signal and the replica of the methods, respectively. Accurate identification of the normal mode order and estimation of the propagation range can be achieved by establishing the joint cost function.Results: In the case of unknown a priori knowledge of the marine environment, the method enables rapid inversion, is tolerant to environmental parameter mismatch, and is low cost and practical.Discussion: The simulation and measured data analysis results demonstrate the accuracy and validity of the method. The measured data contains linear frequency modulation impulse source signal and explosion sound source signals, and the mean relative error of range estimation is less than 5%.

Research on Interrupted Sampling Repeater Jamming Performance Based on Joint Frequency Shift/Phase Modulation.

Interrupted sampling repeater jamming (ISRJ) is a classic active coherent jamming. Due to its structural limitations, it has inherent defects such as a discontinuous time-frequency (TF) distribution, strong distribution regularity of pulse compression results, limited jamming amplitude, and strong false targets lagging behind the real target. These defects have not been fully resolved yet due to the limitation of the theoretical analysis system. Based on the analysis of the influence factors of ISRJ on the interference performance for linear-frequency-modulated (LFM) and phase-coded signals, this paper proposes an improved ISRJ method based on the joint subsection frequency shift and two-phase modulation. The coherent superposition of jamming signals at different positions for LFM signals is achieved by controlling the frequency shift matrix and the phase modulation parameters to form a strong pre-lead false target or multiple positions and ranges of blanket jamming areas. For the phase-coded signal, the pre-lead false targets are generated through code prediction and the two-phase modulation of the code sequence, resulting in similar noise interference. The simulation results show that this method can overcome the inherent defects of ISRJ.

W-band super-resolution ground imaging radar based on collimated vortex waves

W-band electromagnetic vortex-waves generated by a uniform circular array are tightly collimated by a paraboloidal reflector into a radiation cone with a small vertex angle and beam width. A low height drone-borne super-resolution conceptual imaging radar is designed and analyzed comprehensively yielding novel results. Range resolution is obtained by a wideband linear frequency modulation waveform. Angular resolutions are based on the antenna beam widths and the orthogonality of vortex wave modes. Novel algorithms for angular localizations of multiple targets are given. The spatial resolutions associated with the geometry of a down looking radar and the ground are given. Though, no platform motion is needed for vortex imaging, Doppler beam sharpening is also implemented for a slowly moving drone-borne radar for an additional resolution capability.

A New Subsample Time Delay Estimation Algorithm for LFM-Based Detection

This paper investigated a Subsample Time delay Estimation (STE) algorithm based on the amplitude of cross-correlation function to improve the estimation accuracy. In this paper, a rough time delay estimation is applied based on traditional cross correlator, and a fine estimation is achieved by approximating the sampled cross-correlation sequence to the amplitude of the theoretical cross-correlation function for linear frequency modulation (LFM) signal. Simulation results show that the proposed algorithm outperforms existing methods and can effectively improve time delay estimation accuracy with the complexity comparable to the traditional cross-correlation method. The theoretical Cramér-Rao Bound (CRB) is derived, and simulations demonstrate that the performance of STE can approach the boundary. Eventually, four important parameters discussed in the simulation to explore the impact on Mean Squared Error (MSE).

High Resolution Backscattering Acoustic Tomography Method Based on Reverse Time Migration for Arbitrary Wideband Sounding Signal

Backscattered wave acoustic tomography using wideband probing signals makes it possible to obtain three-dimensional (3D) images of scattering inhomogeneities. Signal processing based on the reverse time migration (RTM) method allows one to take into account the influence of background refractive obstacles of the medium to minimize distortions of reconstructed tomographic images. We propose a noniterative method of acoustic tomography in an immersion medium based on RTM approach supplemented with linear signal preprocessing to enhance resolution of reconstructing tomography images. The visualization of scattering objects is based on wave inversion from the measurement area considering the probing wave field specially distorted to perform regularized back convolution. The applicability of the proposed method for visualizing scattering objects in water is shown analytically, numerically and experimentally. The proposed method is resistant to noise according to regularization. The results obtained show the agreement between the numerical and analytical solution. Using the example of sounding with linear frequency modulation signals, it is demonstrated that the proposed method allows increasing the resolution of tomographic images in comparison with conventional RTM. The novelty of the proposed method is the preliminary filtration of the forward propagation wave in the course of solving the inverse problem. This approach improves the resolution of tomographic images and allows considering the influence of obstacles.