Nonlinear Frequency Modulation Research Articles

Dynamic mode decomposition-based technique for cross-term suppression in the Wigner-Ville distribution

This paper presents a new method for time-frequency representation (TFR) using dynamic mode decomposition (DMD) and Wigner-Ville distribution (WVD), which is termed as DMD-WVD. The proposed method helps in removing cross-term in WVD-based TFR. In the suggested method, the DMD decomposes the multi-component signal into a set of modes where each mode is considered as mono-component signal. The analytic modes of these obtained mono-component signals are computed using the Hilbert transform. The WVD is computed for each analytic mode and added together to obtain cross-term free TFR based on the WVD. The effectiveness of the proposed method for TFR is evaluated using Rényi entropy (RE). Experimental results for synthetic signals namely, multi-component amplitude modulated signal, multi-component linear frequency modulated (LFM) signal, multi-component nonlinear frequency modulated (NLFM) signal, multi-component signal consisting of LFM and NLFM mono-component signal, multi-component signal consisting of sinusoidal and quadratic frequency modulated mono-component signals, and synthetic mechanical bearing fault signal and natural signals namely, electroencephalogram (EEG) and bat echolocation signals are presented in order to show the effectiveness of the proposed method for TFR. It is clear from the results that the proposed method suppresses cross-term effectively as compared to the other existing methods namely, smoothed pseudo WVD (SPWVD), empirical mode decomposition (EMD)-WVD, EMD-SPWVD, variational mode decomposition (VMD)-WVD, VMD-SPWVD, and DMD-SPWVD.

High-Resolution Dipole Remote Detection Logging Based on Optimal Nonlinear Frequency Modulation Excitation.

In order to improve the detection range and imaging resolution of dipole remote detection logging, an optimal nonlinear frequency modulation (ONLFM) excitation method is proposed in this paper. In this method, the optimal waveform model of the sound source is designed with objective functions of SNR and resolution to obtain the highest resolution under the condition of the required SNR. This optimal model is a multi-constraint optimization problem, and the simulated annealing method has been used to solve it. Solving the optimal model can obtain the optimal spectrum, and the ONLFM waveform can be designed by using the stationary phase principle. Compared with the electric pulse sound source used in traditional technology, this ONLFM sound source can improve the energy and extend the frequency band range of the reflected wave, which can provide the higher resolution and SNR. The simulation results show that the ONLFM sound source can effectively improve the SNR and resolution of the reflected wave, and the detection range and imaging resolution of dipole shear wave remote detection will be improved.

Fourier transform with matched non-linear frequency modulation in femtosecond laser ranging with imbalanced dispersion.

We propose a new algorithm based on the Fourier transform with matched non-linear frequency modulation for processing femtosecond laser ranging data. The algorithm allows us to compensate for both the influence of the third-order dispersion in the fiber-based dispersive Fourier spectrometer and the influence of imbalanced second- and third-order dispersions in the interferometer. Computer simulations and experimental results show that the proposed algorithm significantly increases the accuracy of measuring the position of an object at larger displacements than the well-established non-linear time stretching.

Separation of signal and harmonics in non-explosive seismic prospecting with amplitude and nonlinear frequency-modulated signals

When vibroseis oscillations are excited, along with the main signal, harmonics are generated. They travel into the Earth and, like the main signal, interact with the target reflectors. Harmonics have a wider than that of the main signal frequency band, so they can be used to increase the resolution of the seismic data. To do this, the signal-related data should be separated from the harmonic-related data. This problem can be successfully solved by the previously proposed optimization recursive filtering algorithm, which, however, was developed only for linearly frequency-modulated signals. In this work, the algorithm is generalized to the case of amplitude modulation and nonlinear frequency modulation. Examples of application of the technique to increase the resolution of real vibroseis data are given.

Modeling of harmonics of amplitude and nonlinear frequency-modulated signals

In vibroseismic data, nonlinear signal distortions called harmonics are usually present. The previously proposed method of separating the signal and its harmonics makes it possible to improve the quality of the initial data, as well as to obtain additional information about the geological structure of the earth interior. One of the limitations of the proposed methodology is its initial development for linear frequency-modulated signals. A new method of prediction of harmonics that allows non-linear frequency modulation as well as amplitude variation is proposed.

Non-linear frequency modulated thermal wave imaging for subsurface analysis

Thermographic analysis for subsurface non-destructive evaluation often encounters challenges in achieving better depth scanning and enhanced depth resolution. Usually, deeper depth analysis will be facilitated by the strength of the low-frequency components and the depth resolution on the frequency sweep of the stimulation, along with material properties in this active thermographic modality. Non-linear frequency modulation became prominent for subsurface analysis due to its ability to provide a band of frequencies with increased energy at low frequencies. This manuscript introduced novel Logarithmic frequency modulated stimulation for subsurface analysis and compared it with its well-established linear frequency counterpart. A quantitative analysis was performed using detectability and sizing of the defects. Experimental results demonstrate that the proposed modality offered an edge over the state of the art, as shown by the experimentation carried out over a carbon fibre-reinforced plastic specimen with embedded flat bottom holes.

Nonlinear frequency modulation for Fourier transform ion mobility mass spectrometry improves experimental efficiency

Through optimization of terminal frequencies and effective sampling rates, we have developed nonlinear sawtooth-shaped frequency sweeps for efficient Fourier transform ion mobility mass spectrometry (FT-IM-MS) experiments. This is in contrast to conventional FT-IM-MS experiments where ion gates are modulated according to a linear frequency sweep. Linear frequency sweeps are effective but can be hindered by the amount of useful signal obtained using a single sweep over a large frequency range imposed by ion gating inefficiencies, particularly small ion packets, and gate depletion. These negative factors are direct consequences of the inherently low gate pulse widths of high-frequency ion gating events, placing an upper bound on FT-IM-MS performance. Here, we report alternative ion modulation strategies. Sawtooth frequency sweeps may be constructed for the purpose of either extending high-SNR transients or conducting efficient signal-averaging experiments for low-SNR transients. The data obtained using this approach show high-SNR signals for a set of low-mass tetraalkylammonium salts (<1000 m/z) where resolving powers in excess of 500 are achieved. Data for low-SNR obtained for multimeric protein complexes streptavidin (53 kDa) and GroEL (800 kDa) also reveal large increases in the signal-to-noise ratio for reconstructed arrival time distributions.

METHOD OF MINIMIZATION SIDELOBES LEVEL AUTOCORRELATION FUNCTIONS OF SIGNALS WITH NON-LINEAR FREQUENCY MODULATION

Context. At present, when creating new and upgrading existing radar systems, solid-state generator devices are widely used, which imposes certain restrictions on the peak power of probing signals. To overcome this limitation, longer duration signals with internal pulse modulation are used. The main efforts of the researchers are focused on reducing the maximum level of the side lobes of the autocorrelation function of such signals, which, without taking additional measures, has a significant level, which complicates the work of systems for detecting and stabilizing the level of false alarms. Attention is paid to signals with non-linear frequency modulation, which consist of two and three linearly frequency-modulated fragments. The maximum level of the side lobes of such signals depends significantly on the frequency-time parameters of the fragments, and therefore it is very difficult to obtain its stable value. Searching for signals with minimal side lobe level values by optimizing their time-frequency parameters is a difficult task, because changing the parameters of previous signal fragments leads to changes in the parameters of subsequent fragments&#x0D; Objective. The aim of the work is to develop a method for simplifying the search for local minima of the level of side lobes of two- and three-fragment signals with nonlinear frequency modulation by using a modified mathematical model with a whole number of periods of radio oscillations of linear-frequency modulated fragments.&#x0D; Method. The developed method is based on the proposed modification of the mathematical model, which corrects the frequencytime parameters of two- and three-fragment signals with non-linear frequency modulation by modifying the values of the frequency modulation speed while providing an integer number of complete periods of radio frequency oscillations for each of the fragments, which simplifies the process of finding local minima of the level of side lobes.&#x0D; Results. Modification of the initial mathematical model leads to the expansion of the possible range of values of frequency-time parameters, ratios of durations and frequency deviations of linearly-frequency modulated fragments and ensures stability of the mathematical model with a decrease in the maximum level of side lobes of the autocorrelation function.&#x0D; Conclusions. It has been experimentally confirmed that the use of the proposed method of modifying the input frequency-time parameters of signals with non-linear frequency modulation in the vast majority of cases reduces the maximum level of side lobes and simpli-fies the process of finding its local minima. The optimal ratios of durations and deviations of the frequency of the signal frag-ments are determined, subject to these, stable operation of the models is ensured and, in most cases, - less than the value of the maximum level of the side lobes.

Effective reduction of sidelobes in pulse compression radars using NLFM signal processing approaches

Pulse compression techniques are widely used in modern radar systems to enhance range resolution and detection capability. As signal design is one of the basic factors of an efficient radar system, the problem of designing a radar signal with good characteristics using pulse compression is addressed in this paper. A linear frequency modulated (LFM) waveform has been widely used for conventional radars. However, it has a higher sidelobe level which makes the detection of weak targets very difficult in presence of strong targets returns and as a result the problem of masking occurs. In order to get suppressed sidelobes of radar matched filter output as well as preserve the main lobe resolution and level to overcome the problem of masking, nonlinear frequency modulated (NLFM) signals are used in modern radars. In this paper, we will introduce two different approaches to design an optimized NLFM signal which is characterized by optimized sidelobe level (SLL). The first is the exponential piecewise linear function (EPWL) which is the modification of piecewise linear (PWL) functions relying on an exponential predistortioning function. The second is the odd-term polynomial approximation (OTPA) in which the generation of NLFM signal depends only on odd-powered terms of the polynomial function. Furthermore, the simulation results of autocorrelation functions (ACF) of the proposed signals show its superiority over the traditional LFM signals and significantly enhancement compared to the recent background work. The Doppler sensitivity of the designed signals has been evaluated, revealing that the first approach offers Doppler tolerance and is suitable for surveillance radar systems, while the second approach with a lower sidelobe level is used in applications such as Synthetic Aperture Radar (SAR). Finally, the ambiguity function of the designed signals has been measured to illustrate the effect of the Doppler effect relative to different velocities.

A Phase-Sensitive Optical Time Domain Reflectometry with Non-Uniform Frequency Multiplexed NLFM Pulse.

In the domain of optical fiber distributed acoustic sensing, the persistent challenge of extending sensing distances while concurrently improving spatial resolution and frequency response range has been a complex endeavor. The amalgamation of pulse compression and frequency division multiplexing methodologies has provided certain advantages. Nevertheless, this approach is accompanied by the drawback of significant bandwidth utilization and amplified hardware investments. This study introduces an innovative distributed optical fiber acoustic sensing system aimed at optimizing the efficient utilization of spectral resources by combining compressed pulses and frequency division multiplexing. The system continuously injects non-linear frequency modulation detection pulses spanning various frequency ranges. The incorporation of non-uniform frequency division multiplexing augments the vibration frequency response spectrum. Additionally, nonlinear frequency modulation adeptly reduces crosstalk and enhances sidelobe suppression, all while maintaining a favorable signal-to-noise ratio. Consequently, this methodology substantially advances the spatial resolution of the sensing system. Experimental validation encompassed the multiplexing of eight frequencies within a 120 MHz bandwidth. The results illustrate a spatial resolution of approximately 5 m and an expanded frequency response range extending from 1 to 20 kHz across a 16.3 km optical fiber. This achievement not only enhances spectral resource utilization but also reduces hardware costs, making the system even more suitable for practical engineering applications.

Automatic high depth-resolvability inspection of TBC debonding defects using nonlinear frequency modulation photothermal radar

In this article, a novel nonlinear frequency modulation (NLFM) photothermal radar whose instantaneous frequency curve is a concave quadratic function is proposed and further combines K-means clustering image segmentation algorithm to achieve automatic high depth-resolvability inspection of debonding defects in thermal barrier coating (TBC) structure. Firstly, a 3-dimensional (3D) photothermal finite element (FE) model of TBC structure is established, where the extrapolated Beer-Lambert model is introduced to describe the spatially volumetric heat source within the ceramic coating. Afterwards, the superior depth resolvability of the proposed NLFM photothermal radar is demonstrated compared to conventional waveforms using the established FE model. Meanwhile, its depth resolvability dependence on the thickness and thermal diffusivity of the ceramic coating is also investigated. Finally, the photothermal experiments of the TBC structure containing artificial debonding defects are conducted, and the influence of the coating thickness and metal substrate on the non-destructive testing (NDT) detection of TBC structure by NLFM photothermal radar combining K-means clustering is also experimentally studied. The results reveal that NLFM photothermal radar combining K-means clustering can achieve automatic high depth-resolvability inspection of debonding defects in TBC structure and the coating thickness and metal substrate have also a great influence on the photothermal NDT of the debonding defects of TBC structure.

Waveform Adaptation for Target Classification Using HRRP in a Cognitive Framework

Waveform adaptation is a key-feature for modern radar systems and essential for cognitive radar. In this work we present a concept for the enhancement of the classification performance by using optimised transmit waveforms and a Gaussian template matching high range resolution profile (HRRP)classifier. A straight forward approach is presented, aiming to improve specific parts of the confusion matrix which will be exploited within a cognitive framework. The optimisation includes different types of uncertainties and is designed during a training process to be accessed by a library. Taking different uncertainties into account, the calculation of the expected performance, the optimisation, the range side lobe constraint and the time-domain realisation is explained. A non-linear frequency modulation (NLFM) waveform is used since it provides a compression gain with range resolution and a constant envelope. Based on an electromagnetic simulation the concept is validated for different ground targets and aspect angle uncertainties. The adaptation is compared to a commonly used linear frequency modulation (LFM). The results of the mean performance improvement reached an enhancement between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${8.8}{\%}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${20.9}{\%}$</tex-math></inline-formula> .

Smart Jamming Against SAR Based on Nonlinear Frequency-Modulated Signal

The traditional methods of jamming against synthetic aperture radar (SAR), which are implemented based on linear frequency-modulated (LFM) signals, are currently unable to meet the needs of electronic countermeasures. Compared with the LFM signal, the frequency of the nonlinear frequency-modulated (NLFM) signal varies nonlinearly with time. Because of this time-frequency structure, the NLFM signal is naturally mismatched with the linear matched filter of SAR; thus, a stronger and more flexible jamming effect is produced. In this paper, the NLFM signal is used in the SAR jamming field for the first time, and a smart jamming method against SAR based on the NLFM signal is proposed, which can produce the following two jamming effects: barrage and deceptive. First, the shaping factor is defined to generate the expected NLFM signal. The shaping factor controls the jamming range in the fast time direction for barrage jamming. For deceptive jamming, a jamming method involving piecewise weighting is proposed. The shaping factor is used to control the defocusing degree of false targets. Subsequently, the pulse compression results of the jamming signal are deduced, and the influence of different parameters on the jamming effect is theoretically analyzed. Experimental results based on simulation show that the method can control the jamming range and effect in the fast time direction while achieving a flexible deceptive jamming effect.

Lamb wave based damage imaging under nonlinear chirp excitation

Considering a trade-off between temporal-spatial resolution and multi-mode nature of Lamb waves, tone bursts with short durations are usually used as excitations in Lamb wave based damage detection. A short-duration excitation usually requires a large amplitude to carry sufficient energy so as to obtain response signals with enough signal-to-noise ratio and cover a large inspection area. In this paper, an alternative Lamb wave damage imaging method using nonlinear chirp (nonlinear frequency modulation, NLFM) excitation with a long duration and a small amplitude is proposed. The signal processing techniques of pulse compression and dispersion compensation are adopted to compress the long-duration wave packets of response signals into short ones. Compared with conventional tone burst excitations with short durations and small amplitudes, due to the long duration of the nonlinear chirp excitation and the use of pulse compression, sufficient energy can be applied to transducers under small amplitude excitations so the image contrast in imaging will not degrade. Furthermore, as large amplitude excitations are no longer required, high voltage amplifiers are not necessary so the hardware of the Lamb wave testing system is simplified. Experiments on a carbon steel plate with an artificial crack are carried out and Lamb wave signals are collected using a linear array consisting of nine PZTs. Experimental results under the NLFM signal and conventional tone bursts are provided. Experimental results show that under the condition of the same excitation amplitude, the proposed method under the NLFM excitation can achieve better imaging quality compared with methods under conventional tone bursts.

A novel transmission loss compensation method for radome based on non‐linear frequency modulation waveform design

AbstractThe radome can protect the enclosed antenna from harsh weather and environmental conditions; however, it will cause a non‐negligible effect particularly transmission loss on the wideband signal which has been widely used in electronic systems. For this, a novel transmission loss compensation method for radome based on non‐linear frequency modulation (NLFM) waveform design is proposed. First, the transmission coefficient calculation process is given, Then, the detailed NLFM waveform design method is described in detail. Finally, the simulation experiments are demonstrated to verify the effectiveness of the proposed compensation method. Based on the designed NLFM waveform, the transmission loss can be compensated and a flat frequency response can be obtained, which can achieve excellent performance of pulse compression in the range direction. The proposed NLFM design method has great potential application value in the electronic system.

Research the Nonlinear Frequency Modulation of Tunable Light Source to Improve the Spatial Resolution of OFDR

The main factor affecting the optical fiber spatial resolution of OFDR system is the non-linearity of laser frequency tuning.We demonstrated a M-Z interferometry and performed nonlinear measurements at different frequencies. The main and auxiliary interferometers with tunable laser source(TLS) were built, and the auxiliary interferometer was used to correct the nonlinearity modulation of the frequecny of the main laser.The interpolation compensation scheme was proposed.The research results of the nonlinear frequency modulation of TLS to improve the spatial resolution of optical fiber vibration sensing was demonstrated,the spatial resolution is 0.17m.

Constrained radar waveform optimization for a cooperative radar-communication system

The coexistence of radar-sensing and communication systems research has received a surge of interest in recent times to tackle the issue of spectrum inadequacy. Designing an optimized radar waveform for a coexistence scenario has been a challenging task for accomplishing the convergence of radar-sensing and communication functionalities, without degrading the performance at either end. This paper proposes a novel global optimization-based Spatial Branch and Bound (SBnB) approach to optimize the phase coefficients of a Non-Linear Frequency Modulated (NLFM) waveform in a CRCS framework. In addition, the Modified-Power Ratio Constraint-Cramér–Rao Lower Bound (M-PRC-CRLB), a local optimization-based approach is proposed to optimize the phase coefficients of an NLFM waveform. The spectral energy distribution and auto-correlation characteristics of an NLFM waveform are comprehensively investigated for various values of polynomial order (N) and at different threshold Signal-to-Noise-Ratio (SNR) values. To compare the proposed waveform design approaches (M-PRC-CRLB, SBnB) with the existing waveform design approaches namely, Minimum Estimation Error Variance (MEEV) and PRC- CRLB, a Peak-to-Side-Lobe-Ratio (PSLR), and Integrated-Side-Lobe-Ratio (ISLR) are evaluated at various polynomial orders and threshold SNR values. Furthermore, the performance of a CRCS is assessed using the radar estimation rate and communication data rate. The simulation results reveal that the proposed optimized radar waveform design approaches provide improved performance compared to the existing radar waveform design approaches in terms of radar estimation rate. Further, the proposed global optimization-based SBnB approach achieves a comparable performance of the communication data rate. In addition, the proposed approaches accomplish enhanced spectral utilization, controlled side-lobe energy levels, reduced range-domain ambiguities, and a higher information rate in a CRCS.

A 2-D Method Based on Nonlinear Frequency Modulation Waveform and Phase Coding for Range Ambiguity Suppression

Range ambiguity suppression is a key technical challenge for synthetic aperture radar (SAR) systems. Waveform diversity technology is a potential solution due to its low system complexity. In this letter, a 2-D method based on orthogonal nonlinear frequency modulation (NLFM) waveform and azimuth phase coding (APC) for range ambiguity suppression is proposed. This approach not only suppresses range ambiguity energies instead of dispersing them, but also works for multiple consecutive orders of range ambiguity energies. The imaging processing and range ambiguity suppression performance are described in detail. In addition, the range-ambiguity-to-signal radio (RASR) is analyzed, and the simulation results for the point target and distribution scenarios are given to verify the effectiveness and practicality of the proposed scheme.

A Novel MIMO-SAR Echo Separation Solution for Reducing the System Complexity: Spectrum Preprocessing and Segment Synthesis

The problem of echo separation using digital beamforming (DBF) on receive for multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) is of notable importance to allow for practical systems. Regrettably, current DBF-MIMO-SAR schemes, such as the short-term shift-orthogonal (STSO) scheme, are computationally cumbersome, increasing the required hardware complexity. To alleviate this problem, we here propose an improved echo separation solution for realizing a low-cost MIMO-SAR system. We detail a generic waveform design scheme as well as optimized monostatic radar waveforms (e.g., nonlinear frequency modulation (NLFM) signal) showing how these can be directly adopted in the proposed scheme to improve the imaging performance. The proposed scheme enables the number of the interference segments generated by unmatched waveforms to be halved by the use of the fast time spectrum preprocessing and segment synthesis, dramatically simplifying the array configuration and reduces the system complexity. By exploiting inter-pulse phase coding techniques, the proposed method can provide a reconfigurable waveform transmitting scheme, allowing the system resources in range frequency, elevation space, and Doppler domains to be jointly exploited for the separation of aliased signal returns. The proposed scheme is evaluated using extensive numerical and measured data sets, demonstrating the feasibility and potential of the proposed method for resource-limited spaceborne/airborne MIMO-SAR systems.

Infrared thermal wave detection of interfacial debonding defects of thermal barrier coatings based on non-linear frequency modulation

In order to improve the reliability of detecting the debonding defects at the interface of thermal barrier coatings (TBC), a non-linear frequency modulated (NLFM) infrared thermal wave detection method is proposed. A NLFM infrared thermal wave detection system is built, and zirconia TBC specimens are prepared and tested. The effects of defect diameter, excitation power, initial frequency and termination frequency on the defect detection effect are analyzed. Three algorithms such as principal component analysis (PCA) are used to process the image sequence, and the signal-to-noise ratio (SNR) of each sequence processing algorithm is calculated and compared. The results show that the larger the diameter of the defect, the easier it is to be detected, and the appropriate adjustment of the excitation power or the reduction of the initial and termination frequencies is beneficial to the detection of defects. Compared with the other two algorithms, the PCA method is more effective for image sequence processing. It offers a reference for detecting debonding flaws at the TBC interface.