Frequency Modulation Waveform Research Articles

High-spatial-resolution transcranial focused ultrasound neuromodulation using frequency-modulated pattern interference radiation force

Stimulating the brain in a precise location is crucial in ultrasound neuromodulation. However, improving the resolution proves a challenge owing to the characteristics of transcranial focused ultrasound. In this paper, we present a new neuromodulation system that overcomes the existing limitations based on an acoustic radiation force with a frequency-modulated waveform and standing waves. By using the frequency-modulated pattern interference radiation force (FM-PIRF), the axial spatial resolution can be reduced to a single wavelength level and the target location can be controlled in axial direction electronically. A linear frequency-modulated chirp waveform used in the experiment was designed based on the simulation results. The displacement of the polydimethylsiloxane (PDMS) cantilever was measured at intervals of 0.1 mm to visualize the distribution of radiation force. These results and methods experimentally show that FM-PIRF has improved spatial resolution and capability of electrical movement.

Low in-band spurious arbitrary waveform generator based on a 1-bit time-wavelength interleaved photonic digital-to-analog conversion.

We proposed an arbitrary waveform generator based on a 1-bit photonic digital-to-analog conversion (PDAC). The system is based on the principle of photonic pulse sampling and time interleaving. High-speed optical pulses are generated and modulated by digital signals and then synthesized in one path. The analog signals are obtained by an optical-to-electrical conversion of the time-interleaved pulses. Due to the 1-bit structure, there are no spurious components in principle. In the experiment, a 1-bit PDAC of 50 GSa/s is realized, and the X-band linear frequency-modulated (LFM) waveform with a bandwidth of 4 GHz is generated, the signal-to-spur-rejection ratio is as high as 50 dB, and the millimeter-wave 64QAM signal is generated, with an EVM of 4.27%.

SAM-SFM: High-Efficiency and High-Resolution Tandem Mass Spectrometry Enabled by Sinusoidal Amplitude Modulation of Multiple Sinusoidal Frequency-Modulated Waveforms.

In miniature ion trap mass spectrometry, achieving a balance between isolation resolution and efficiency is a formidable challenge. The presence of absorption curves causes target ions to inadvertently absorb energy from AC signal components near their resonant frequencies. To mitigate this issue, SAM-SFM waveforms introduce a parameter known as the decreasing factor. Unlike SWIFT waveforms, SAM-SFM's spectral profile intentionally departs from a rectangular window, adopting an arch-shaped excitation window to minimize the impact on target ions and improve ion isolation efficiency. SAM-SFM waveforms have the advantage of low computational complexity, enabling real-time computation using an embedded FPGA technology. Regardless of any parameter changes, the FPGA can consistently guarantee waveform output within 1 μs. This not only enhances throughput but also eliminates the need for a PC in miniature mass spectrometry devices. The performance of SAM-SFM has been validated on an improved "Brick" miniature ion trap mass spectrometer. Comparative experiments with SWIFT waveforms confirm the lossless unit-mass isolation capabilities of SAM-SFM. This waveform has the capability to simultaneously isolate multiple target ions, even allowing for the lossless isolation of ions with lower abundance within isotopic clusters, albeit at the cost of requiring extended isolation durations.

A Novel DCSK-Based Linear Frequency Modulation Waveform Design for Joint Radar and Communication Systems

A Novel DCSK-Based Linear Frequency Modulation Waveform Design for Joint Radar and Communication Systems

Photonic generation of Barker encoded dual-nonlinear frequency modulated RADAR waveforms

Photonics enables the development of versatile waveform generators with carrier frequency tunability and broad bandwidths, allowing for high-range resolution for modern radar systems. Linear frequency-modulated waveforms are widely employed in various radar applications due to their large time-bandwidth products but are limited in functionality due to high sidelobe levels, resulting in a poor signal-to-noise ratio (SNR). On the other hand, non-linear frequency-modulated waveforms (NLFM) have a faster sweep rate at the edges than at the center, resulting in high SNRs, which can be boosted further through encoding techniques. A photonic approach for generating Barker-encoded dual-NLFM waveforms through a dual-drive Mach Zehnder modulator is proposed with improved range resolution, pulse compression ratio, and peak-to-sidelobe ratio. A theoretical analysis is performed, which is then modeled, and experimentally confirmed. Barker-encoded dual-NLFM waveforms are generated at 6 GHz with 500 MHz chirp bandwidth showing a maximum range resolution of 19.89 cm with PCR of 9803.

Photonic generation of a tunable multi-band linearly frequency-modulated waveform

A photonic-assisted tunable multi-band linearly frequency-modulated (LFM) waveform generator based on optical heterodyne detection is proposed and experimentally demonstrated. The multi-band LFM waveform is generated from a photodetector (PD), where a broadband LFM optical pulse and a multi-wavelength optical signal with the same magnitude at different wavelengths are heterodyne-detected. The LFM optical pulse is generated from a three-electrode distributed Bragg reflector laser diode (DBR-LD). The multi-wavelength optical signal is produced through a Mach-Zehnder modulator (MZM), in which a light wave from an optical fiber laser (OFL) is nonlinearly intensity-modulated by a radio frequency (RF) signal. By tuning the wavelength of the LFM optical pulse lower than that of the multi-wavelength optical signal, a multi-band LFM waveform is generated at the PD. The center frequency of the generated LFM waveform can be adjusted by manipulating the wavelength of the OFL. The versatility in the bandwidth and temporal duration of the LFM waveform is attained through the precise tuning of the LFM optical pulse. The tuning of the center frequency difference between frequency bands is performed by altering the frequency of the RF signal. Experimental results have corroborated the realization of a tunable multi-band LFM waveform generator. The bandwidth and temporal duration of each band and the center frequency difference between frequency bands have tuning ranges from 0.7 to 6.7 GHz, 1 to 50 μs, and 2 to 6.7 GHz, respectively. The demonstration shows new avenues to implement high-performance multi-band LFM waveform generators for applications in multi-functional modern radar systems.

Radar-Centric Photonic Terahertz Integrated Sensing and Communication System Based on LFM-PSK Waveform

The radar-centric terahertz integrated sensing and communication (THz-ISAC) is identified as a significant application in future wireless access networks. Up to date, previously reported demonstrations regarding radar sensing performance lack sufficient support in a complex environment with a strong target masking effect. This work tacks this problem by proposing a radar-centric waveform combining linear frequency modulation (LFM) waveform and phase shift keying (PSK). We first derive sensing metrics of the LFM-PSK waveform through theoretical analysis, including range resolution, peak sidelobe ratio (PSLR), and Cramér-Rao lower bound (CRLB). Then a proof-of-concept experiment on a photonics-assisted integrated sensing and communication (ISAC) system operating at 330 with 18 GHz bandwidth is conducted to verify the performance of the proposed LFM-PSK waveform. In the experiment, the proposed waveform can reach a PSLR of up to 20.9 dB and a range resolution of 1.3 cm, simultaneously accommodating a data transmission of 6 Gbit/s. In addition, the effect of embedding symbols on sensing metrics is also discussed, and by comparing the range solution and PSLR with various data rates, around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim$</tex-math> </inline-formula> 6 dB gain in the PSLR without any deterioration of range resolution is observed.

Cognitive Radar Waveform Design Method under the Joint Constraints of Transmit Energy and Spectrum Bandwidth

The water-filling (WF) algorithm is a widely used design strategy in the radar waveform design field to maximize the signal-to-interference-plus-noise ratio (SINR). To address the problem of the poor resolution performance of the waveform caused by the inability to effectively control the bandwidth, a novel waveform-related optimization model is established in this paper. Specifically, a corrected SINR expression is first derived to construct the objective function in our optimization model. Then, equivalent bandwidth and energy constraints are imposed on the waveform to formulate the waveform-related non-convex optimization model. Next, the optimal frequency spectrum is obtained using the Karush–Kuhn–Tucker condition of our non-convex model. Finally, the transmit waveform in the time domain is synthesized under the constant modulus constraint. Different experiments based on simulated and real-measured data are constructed to demonstrate the superior performance of the designed waveform on the SINR and equivalent bandwidth compared to the linear frequency modulated signal and waveform designed by the WF algorithm. In addition, to further evaluate the effectiveness of the proposed algorithm in the application of cognitive radar (CR), a closed-loop radar system design strategy is introduced based on our waveform design method. The experiments under real-measured data confirm the advantages of CR compared to the traditional open-loop radar structure.

Photonic joint radar and communication system using a chirp-polarity coded LFM waveform

A photonic joint radar and communication system using a frequency improved, bandwidth doubled, chirp-polarity coded linear frequency modulation (LFM) waveform is proposed and demonstrated. In the scheme, a dual-polarization modulator is driven by a repetitive LFM waveform and an RF signal to generate different optical sidebands in two orthogonal polarization directions. Then, the orthogonally polarized optical sidebands are filtered and polarization modulated to achieve chirp-polarity coding. The generated signal is employed to simultaneously perform dual functions. Both the radar echo and the communication reception are processed based on optical de-chirping. The approach is demonstrated by simulation. A chirp-polarity coded LFM waveform with central frequency of 24 GHz, bandwidth of 8 GHz, bit rate of 10 Mbit/s is generated and processed for dual functions. The radar range resolution, unambiguous range, and range-Doppler resolution are investigated. The optical demodulation of the communication is verified, and the speed improvement of communication is discussed.

Instantaneous bandwidth expansion of photonic sampling analog-to-digital conversion for linear frequency modulation waveforms based on up-sampling and fractional Fourier transform signal processing.

An approach to expanding the instantaneous bandwidth of a photonic sampling analog-to-digital converter (ADC) for receiving linear frequency modulation waveforms (LFMWs) is proposed and experimentally demonstrated based on up-sampling and filtering in the fractional Fourier domain. Through twice zero interpolation, the equivalent sampling rate is quadrupled, which also quadruples the nominal instantaneous bandwidth of the photonic sampling ADC. In addition, with the assistance of bandpass filtering in the fraction Fourier domain, the image signals and the harmonic distortions generated in the interpolation process are filtered out. As a result, the effective instantaneous bandwidth of the photonic sampling ADC is doubled. In the experiment, the instantaneous bandwidth of a photonic sampling ADC with a sampling rate of 5 GSa/s for receiving LFMWs is increased from 2.5 GHz to 5 GHz by using the proposed method. Input LFMWs within the frequency range of 24-27 GHz and 30-33 GHz, i.e., with an instantaneous bandwidth of 3 GHz, are digitized without frequency-domain aliasing. Besides, the ability of the proposed method to enhance the ranging accuracy in a broadband radar system is demonstrated. This method reduces the hardware complexity of the photonic sampling ADC for receiving broadband LFMWs in radar systems.

Mechanism and Characteristic of Nonlinear Clutter in Harmonic Radar With Frequency-Modulated Waveform

Harmonic radar is a special radar system that has been widely used in insect tracking, search and rescue, and electronic equipment detection in recent years due to its excellent anti-clutter capability. However, in complex close-range scenarios, harmonic radar still suffers from nonlinear clutter interferences, which will cause a large number of clutter false alarms and seriously affect the performance of target detection. This paper analyzes the mechanism and the characteristic of nonlinear clutter through experimental results in complex close-range scenarios. It is found that the nonlinear clutter is generated by the harmonics and intermodulation components of the multipath signals. More importantly, it is the first time for the multipath intermodulation phenomenon to be revealed in harmonic radar with frequency-modulated waveform. A nonlinear clutter signal model is developed to explain this special phenomenon in this paper. The proposed theory is verified by the simulation and measurement results. The work in this paper lays a theoretical foundation for the subsequent work on nonlinear clutter suppression.

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> .

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.

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.

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.

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.

Waveform Design Using Coprime Frequency-Modulated Pulse Trains for Reverberation Suppression of Active Sonar

Over the last two decades, low-frequency active sonar has become an attractive tool for underwater target detection. The reverberation to signal ratio (RSR) of transmitted waveforms is an important factor affecting the detection capability of low-frequency active sonar. Therefore, reasonable waveform design for reverberation suppression of active sonar is an important topic. Pulse trains of linear frequency-modulated (PTFM) waveforms have been proposed and manifested their good performance in suppressing reverberation. The number of sub-pulses is positively related to the reverberation to signal ratio; the lower the number of sub-pulses, the lower the reverberation to signal ratio. However, to avoid ambiguity in a Doppler measurement, the PTFM waveforms have a requirement for the number of sub-pulses to be satisfied, which prevents its reverberation suppression performance from being further improved. In this paper, we propose a coprime pulse train of linear frequency-modulated (CPTFM) waveform, which reduces the number of sub-pulses to some extent. Therefore, the ability of reverberation suppression of the CPTFM waveform can be improved. The RSR was chosen as the metric to evaluate the waveform’s ability to suppress reverberation, and the theoretical formula for the RSR of the CPTFM waveform was derived in zone A and B. With the overlap of zones A and B brought about by the decrease in the number of sub-pulses, the average RSR of zones A and B is used in this paper to evaluate the reverberation suppression ability of the waveform. The simulation experiment shows that the proposed CPTFM waveform decreases the average RSR by 7 dB and 20 dB in comparison to the reference PTFM waveform and continuous waveform (CW), which is consistent with the theoretical results by the derived formulas.

Research on Ultra-Wideband NLFM Waveform Synthesis and Grating Lobe Suppression.

Ultra-wideband (UWB) nonlinear frequency modulation (NLFM) waveforms have the advantages of low sidelobes and high resolution. By extending the frequency domain wideband synthesis method to the NLFM waveform, the synthetic bandwidth will be limited, and the grating lobe will grow as the number of subpulses increases at a fixed synthetic bandwidth. Aiming for the highly periodic grating lobes caused by equally spaced splicing and small subpulse time-bandwidth products (TxBW), a multisubpulse UWB NLFM waveform synthesis method is proposed in this paper. Random frequency hopping and spectral correction are utilized to disperse the energy of periodic grating lobes and optimize the matched filter of the subpulse, thereby reducing notches and Fresnel ripples in the synthesized spectrum. The results of the hardware-in-the-loop simulation experiment show that the peak sidelobe ratio (PSLR) and the integral sidelobe ratio (ISLR) of the NLFM synthetic wideband waveform (SWW) obtained by 50 subpulses with a bandwidth of 36 MHz are improved by 4.8 dBs and 4.5 dBs, respectively, when compared to the frequency domain wideband synthesis method, and that the grating lobe is suppressed by an average of 10.6 dBs. It also performs well in terms of point target resolution, and it has potential for 2D radar super-resolution imaging.

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.

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.