Linear Chirp Research Articles

A Novel Ultra−High Resolution Imaging Algorithm Based on the Accurate High−Order 2−D Spectrum for Space−Borne SAR

Ultra−high spatial resolution, which can bring more detail to ground observation, is a constant pursuit of the modern space−borne synthetic aperture radar. However, the exact imaging in this case has always been a complex technical problem due to its complicated imaging geometry and signal structure. To achieve those applications’ strict requirements, a novel ultra−high resolution imaging algorithm based on an accurate high−order 2−D spectrum is presented in this paper. The only first two Doppler parameters needed as range models in the defective spectrum are replaced by a polynomial range model, which can derive coefficients from the relative motion between the radar and the targets. Then, the new spectrum is calculated through the Lagrange inversion formula. Based on this, the novel imaging algorithm is elaborated in detail as follows: The range high−order term of the spectrum is compensated completely, and the range chirp rate space variance is eliminated by the cubic phase term. Two steps of range cell migration correct are applied in this algorithm before and after the range compression; one is the traditional linear chirp scaling method, and another is the interpolation to correct the quadratic range cell migration introduced by the range chirp rate equalization. The simulation results illustrate that the proposed algorithm can handle the exact imaging processing with a 0.25 m resolution around the azimuth and range in 2 km × 6 km, which validates the feasibility of the proposed algorithm.

Comparison of Linear and Quadratic Chirp in Beat Wave Acceleration in Vacuum

Electron acceleration due to beating of two slightly different frequency LP (Linearly polarised) laser pulses with finite spot size in a vacuum has been studied. In this scheme, two lasers are incident at a point with some angle, due to beating of LP lasers constructive interference occurs. The resultant electric and magnetic field of this constructive interference helps in acceleration of pre-accelerated electron which is injected and trapped by the field. In this paper, we have seen the effect of linear and quadratic chirp on laser beat wave acceleration in vacuum and a comparison between the two is made for effective energy gain.

Fourier Deconvolution Ion Mobility Spectrometry.

Multiplexing the ion packet injection with advanced signal processing is an effective method to improve both the ion throughput and signal-to-noise ratio for ion mobility spectrometry. Generally used multiplexing methods include Hadamard transform ion mobility spectrometry (HT-IMS), Fourier transform ion mobility spectrometry (FT-IMS), and correlation ion mobility spectrometry (C-IMS). However, HT-IMS sometimes suffer from false peaks and further processing is needed, FT-IMS generally requires longer spectra acquisition time than the traditional signal averaging method, and C-IMS also demonstrated drawbacks such as spectra baseline distortions when using traditional on-off binary gating switches. To improve the performance of multiplexing ion mobility spectrometry, this study investigates the Fourier deconvolution to increase the resolving power and signal-to-noise ratio at the same time. This approach modulates the ion gate with a linear square wave chirp sequence and synchronizes the data acquisition and ion gate modulation and then reconstructs the ion mobility spectra based on convolution theorems. The equivalent ion injection period is decreased to microseconds scale with the signal-to-noise ratio improved by up to 13 times on average, and the resolving power is improved by up to 50% compared with traditional signal averaging methods without hardware modifications.

A fully integrated 2TX–4RX 60-GHz FMCW radar transceiver for short-range applications

ABSTRACT A fully integrated 2-transmitter–4-receiver (2TX–4RX) multiple-input multiple-output (MIMO) radar front-end in the 57–64-GHz band for short-range applications is presented in this paper. The proposed architecture with 8 elements within a one-dimensional virtual array enables theoretical angular resolution down to . The TX chains operate in time-division multiplexing (TDM) mode, and each delivers 12 dBm of saturated output power with output-referred 1-dB compression point (OP1dB) larger than 5 dBm over 7-GHz bandwidth. The millimeter-wave (mm-wave) part of the RX chains has a noise figure lower than 13 dB, and a conversion gain of 17 dB in the 60-GHz unlicensed band. The receiver chain shows a maximum conversion gain of 77 dB, while achieving an input-referred 1-dB compression point (IP1dB) greater than – 12.5 dBm, including baseband circuitry. The programmable baseband processing chain with 60-dB gain allows beat frequency selection in the frequency range from 100 kHz up to 1.3 MHz. Linear chirps are synthesized using a fractional-N phase-locked loop (PLL) with a fundamental voltage-controlled oscillator (VCO). The integrated system includes a programmable multiplying delay-locked loop (MDLL) which scales-up external high purity 40-MHz frequency reference to a referent 240-MHz clock used in the frequency-modulated continuous-wave (FMCW) synthesizer. The front-end is implemented in a 130-nm SiGe:C BiCMOS process. The chip occupies an area of 12 mm2 including pads and consumes 930 mW, combined from 1.2-V and 3.3-V supplies.

Focused Lunar Imaging Experiment Using the Back Projection Algorithm Based on Sanya Incoherent Scatter Radar

Previous ground-based, radar lunar imaging experiments have usually employed the Range-Doppler (RD) algorithm. This algorithm performs in the frequency domain and has high computational efficiency. However, in the case of a long coherent integration time, the defocus phenomenon will appear, and the image will be smeared. This study proposes the use of the back projection (BP) algorithm to obtain focused lunar images to solve this problem. The BP algorithm is a time-domain algorithm which is frequently employed in synthetic aperture radar (SAR) imaging and can theoretically achieve the focused imaging of each pixel in an arbitrarily long coherent integration time. However, the largest drawback of this algorithm is its high computational complexity. Therefore, this study only applies this method to map local regions of the moon. We select Sanya incoherent scatter radar (SYISR) as the transmitting and receiving device and utilize the linear frequency modulation chirp pulse to transmit right-hand, circularly polarized electromagnetic waves and to receive left-hand, circularly polarized echoes. RD and BP algorithms are simultaneously adopted to image the Pythagoras crater region, and a contrastive analysis is performed. The results show that the BP algorithm can be well applied to a ground-based, radar lunar imaging experiment and that it has a better focusing performance, but the effect is not as obvious as expected. Thus, the processing method needs to be further improved. In addition, the computational efficiency of BP is very low, and certain fast algorithms need to be applied to improve it.

Adaptable Pulse Compression in ϕ-OTDR With Direct Digital Synthesis of Probe Waveforms and Rigorously Defined Nonlinear Chirping

Recent research in Phase-Sensitive Optical Time Doman Reflectometry (ϕ-OTDR) has been focused, among others, on performing spatially resolved measurements with various methods including the use of frequency modulated probes. However, conventional schemes either rely on phase-coded sequences, involve inflexible generation of the probe frequency modulation or mostly employ simple linear frequency modulated (LFM) pulses which suffer from elevated sidelobes introducing degradation in range resolution. In this contribution, we propose and experimentally demonstrate a novel ϕ-OTDR scheme which employs a readily adaptable Direct Digital Synthesis (DDS) of pulses with custom frequency modulation formats and demonstrate advanced optical pulse compression with a nonlinear frequency modulated (NLFM) waveform containing a complex, rigorously defined modulation law optimized for bandwidth-limited synthesis and sidelobe suppression. The proposed method offers high fidelity chirped waveforms, and when employed in resolving a 50-cm event at ∼1.13 km using a 1.2-µs probe pulse, matched filtering with the DDS-generated NLFM waveform results in a significant reduction in range ambiguity owing to autocorrelation sidelobe suppression of ∼20 dB with no averages and windowing functions, for an improvement of ∼16 dB compared to conventional linear chirping. Experimental results also show that the contribution of autocorrelation sidelobes to the power in the compressed backscattering responses around localized events is suppressed by up to ∼18 dB when advanced pulse compression with an optical NLFM pulse is employed.

Picosecond pulse-shaping for strong three-dimensional field-free alignment of generic asymmetric-top molecules

Fixing molecules in space is a crucial step for the imaging of molecular structure and dynamics. Here, we demonstrate three-dimensional (3D) field-free alignment of the prototypical asymmetric top molecule indole using elliptically polarized, shaped, off-resonant laser pulses. A truncated laser pulse is produced using a combination of extreme linear chirping and controlled phase and amplitude shaping using a spatial-light-modulator (SLM) based pulse shaper of a broadband laser pulse. The angular confinement is detected through velocity-map imaging of H+ and C2+ fragments resulting from strong-field ionization and Coulomb explosion of the aligned molecules by intense femtosecond laser pulses. The achieved three-dimensional alignment is characterized by comparing the result of ion-velocity-map measurements for different alignment directions and for different times during and after the alignment laser pulse to accurate computational results. The achieved strong three-dimensional field-free alignment of < {cos }^{2}delta > =0.89 demonstrates the feasibility of both, strong three-dimensional alignment of generic complex molecules and its quantitative characterization.

A Linear Chirp Wireless Transmission Method utilizing Doppler Effect

The Chirp Spread Spectrum(CSS) based wireless communication has been widely used in Wireless Sensor Network(WSN). These sensors generally have slow speed, and is becoming more demand for higher data rate. However, due to the low transmission rate of CSS, there are still many problems to be studied. A new modulation method based on the linear chirps is introduced in this paper. Unlike the BOK(Binary Orthogonal Keying) and DM(Direct Modulation) methods, this modulation technique is to implant Doppler frequency shift into the linear chirps. M-ary modulation is realized in a single pulse by this proposed modulation technique. Demodulation is accomplished by calculating the position of the compress pulse peak within the pulse duration, or by using different reference chirp signals in the matching filter.

Shape anisotropy effect on magnetization reversal induced by linear down chirp pulse

We investigate the shape anisotropy effect on the magnetization reversal of a nanoparticle driven by a down-chirp microwave field pulse (DCMP). Based on the Landau–Lifshitz–Gilbert equation, numerical results reveal that the microwave amplitude, initial frequency, and chirp rate of DCMP decrease with the increase of shape anisotropy. For a certain shape of the nanoparticle, the reversal time is significantly reduced. These findings can be attributed as the shape anisotropy opposes the magnetocrystalline anisotropy, and thus the energy barrier decreases. The result of damping dependence of reversal indicates that there exists an optimal damping situation at which magnetization is fastest. Moreover, the required microwave field amplitude can be lowered by applying the spin-polarized current simultaneously. The usage of an optimum combination of DCMP and current is suggested to achieve cost-effective and faster switching. So these findings might be useful to realize the fast and power-efficient data storage device.

Temporal-filtering dissipative soliton in an optical parametric oscillator

Abstract Dissipative solitons have been realized in mode-locked fiber lasers in the theoretical framework of the Ginzburg–Landau equation and have significantly improved the pulse energy and peak power levels of such lasers. It is interesting to explore whether dissipative solitons exist in optical parametric oscillators in the framework of three-wave coupling equations in order to substantially increase the performance of optical parametric oscillators. Here, we demonstrate a temporal-filtering dissipative soliton in a synchronously pumped optical parametric oscillator. The temporal-gain filtering of the pump pulse combined with strong cascading nonlinearity and dispersion in the optical parametric oscillator enables the generation of a broad spectrum with a nearly linear chirp; consequently, a significantly compressed pulse and high peak power can be realized after dechirping outside the cavity. Furthermore, we realized, for the first time, dissipative solitons in an optical system with a negative nonlinear phase shift and anomalous dispersion, extending the parameter region of dissipative solitons. The findings may open a new research block for dissipative solitons and provide new opportunities for mid-infrared ultrafast science.

Direct Signal Separation via Extraction of Local Frequencies With Adaptive Time-Varying Parameters

Real-world phenomena that can be formulated as signals are often affected by a number of factors and appear as multi-component modes. To understand and process such phenomena, “divide-and-conquer” is probably the most common strategy to address the problem. In other words, the captured signal is decomposed into signal components for each individual component to be processed. Unfortunately, for signals that are superimposition of non-stationary amplitude-frequency modulated (AM-FM) components, the “divide-and-conquer” strategy is bound to fail, since there is no way to be sure that the decomposed components take on the AM-FM formulations which are necessary for the extraction of their instantaneous frequencies (IFs) and amplitudes (IAs). In this paper, we propose an adaptive signal separation operation (ASSO) for effective and accurate separation of a single-channel blind-source multi-component signal, via introducing a time-varying parameter that adapts locally to IFs and using linear chirp (linear frequency modulation) signals to approximate components at each time instant. We derive more accurate component recovery formulae based on the linear chirp signal local approximation. In addition, a recovery scheme, together with a ridge detection method, is also proposed to extract the signal components one by one, and the time-varying parameter is updated for each component. The proposed method is suitable for engineering implementation, being capable of separating complicated signals into their components or sub-signals and reconstructing the signal trend directly. Numerical experiments on synthetic and real-world signals are presented to demonstrate our improvement over the previous attempts.

Spaceborne High-Squint High-Resolution SAR Imaging Based on Two-Dimensional Spatial-Variant Range Cell Migration Correction

High-squint imaging is an effective means to enhance the flexibility and coverage ability of spaceborne synthetic aperture radar (SAR). Although existing imaging algorithms based on linear range cell migration correction (LRCMC) and nonlinear chirp scaling (NCS) can reduce the range-azimuth coupling of the spectrum and the spatial-variant of the Doppler parameter to some extent, they become invalid as the resolution increases. On one hand, the beam rotation of sliding spotlight SAR results in nonlinear azimuth-variant of the Doppler centre, and the traditional deramping operation, which removes the linear variation, will cause spectrum aliasing. On the other hand, these algorithms assume the azimuth-variants of range cell migration (RCM) are consistent in the total swath. However, the azimuth-variants of RCM are different in different range cells, which cannot be neglected in high-resolution imaging. To solve these problems, a novel imaging algorithm based on two-dimensional spatial-variant range cell migration correction is proposed in this paper. First, LRCMC is utilized, and the nonlinear azimuth deramping operation is conducted to obtain aliasing-free spectrum. Then, the azimuth-variant of RCM is corrected by azimuth interpolation and polynomial compensation. Noting that the interpolation coefficient varies linearly with slant range, this can weaken the azimuth-variant differences of RCM in different range cells. Meanwhile, azimuth polynomial compensation can correct the consistent azimuth-variant of RCM, and hence the azimuth-variant of RCM can be totally corrected. Finally, the compression is performed via the range chirp scaling and azimuth NCS. The effectiveness of the proposed algorithm is verified by computer simulations.

Amplification of pulsed light with arbitrary frequency chirps on nanosecond timescales.

We have developed a system for producing amplified pulses of frequency-chirped light at 780nm on nanosecond timescales. The system starts with tunable cw laser light and employs a pair of fiber-based phase modulators, a semiconductor optical amplifier, and a tapered amplifier to achieve chirp rates exceeding 3 GHz/10ns and peak powers greater than 1W. Driving the modulators with an arbitrary waveform generator enables arbitrary chirp shapes, such as two-frequency linear chirps. We overcome the optical power limitations of the modulators by duty cycling and avoid unseeded operation of the tapered amplifier by multiplexing the chirped pulses with "dummy" light from a separate diode laser.

3Pb6-2 A characteristic evaluation of signals generated by combining multiple linear chirp signals and M-sequence

3Pb6-2 A characteristic evaluation of signals generated by combining multiple linear chirp signals and M-sequence

One or Two Ridges? An Exact Mode Separation Condition for the Gabor Transform

In this paper, we investigate the conditions for the separation of two pure tones from the spectrogram computed with a Gaussian window. For this purpose, we put forward necessary and sufficient conditions for the existence of spectrogram ridges associated with each signal. We then show how this condition easily extends to the case of parallel linear chirps, i.e., signals with constant amplitude, linear instantaneous frequency, and same chirp rate.

Second-Order Horizontal Multi-Synchrosqueezing Transform for Hydrocarbon Reservoir Identification

Time-frequency (TF) analysis has received considerable attention in seismic spectral anomaly detection for its superiority in significantly revealing the frequency content of seismic signals changing with time variation. In this letter, a novel method termed second-order horizontal multi-synchrosqueezing transform (SHMSST) is proposed for hydrocarbon reservoir identification. First, a Gaussian-modulated linear chirp model is constructed in the frequency domain for describing the signals with slowly or rapidly linear-varying group delay. Then, the second-order local group delay estimation of the model is deduced in the TF domain through an approach similar to the instantaneous frequency estimation in the synchrosqueezing transform (SST). Finally, the rearrangement procedure is executed iteratively to concentrate the blurry TF energy into the estimated group delay, which provides an energy-concentrated TF representation for the signals with distinct nonlinear and nonstationary features. Synthetic signal and field seismic data illustrate the effectiveness of the proposed SHMSST in time localization and direct hydrocarbon detection.

Terahertz wave amplification by a laser-modulated relativistic electron beam

Generation of tunable terahertz radiation based on the interaction of a frequency-chirped low power terahertz wave with a relativistic electron beam is proposed. The electron beam is first modulated temporally due to the ponderomotive force induced by the beat wave of two copropagating intense laser beams of slightly different frequencies. Then the electron beam interacts with a low-amplitude driver wave at terahertz frequency with a linear frequency chirping. A nonlinear transverse current density is driven that emits terahertz radiation at an up-shifted frequency with a relatively enhanced amplitude. The modulation process is analyzed theoretically by a complete set of fluid equations and considering the effects of both the electrons space-charge potential and the beat wave ponderomotive force. The initial density and energy of the electron beam are both optimized in order to improve the terahertz amplification process. The effect of the driver's frequency chirping, as well as the effects of the initial electron beam density and energy on the emitted terahertz radiation are investigated numerically. It is shown that the frequency chirping of the driver wave plays a key role in terahertz amplification. It is shown that there is an optimum chirp value for which the terahertz radiation is amplified significantly compared with the case without chirping. Moreover, transverse effects of the laser beams and the driver wave on the emitted terahertz radiation are also investigated.

Logarithmic Frequency Waveforms

This article introduces a new class of Doppler-tolerant and estimation-capable radar waveforms called logarithmic frequency waveforms (LFWs). These waveforms are created by mapping the magnitudes, phases, and spacing of good digital radar codes onto a set of carriers defined over a logarithmically warped frequency axis. This mapping preserves the digital code's desirable autocorrelation mainlobe-to-sidelobe ratio when matched filtering is done over the warped frequency variable. The logarithm converts the multiplicative Doppler shift into an additive translation of the code's autocorrelation; thus, the location of the matched filter output's maximum is used to estimate the waveform's Doppler shift. This applies even if the code is neither inherently Doppler tolerant nor Doppler detection capable. We introduce two major classes of LFWs, logarithmic frequency codes, and logarithmic frequency rulers. We numerically illustrate their ambiguity functions and compare their Doppler estimation performance in additive white Gaussian noise against the linear chirp (linear frequency modulated) outfitted with the extended matched filter and the hyperbolic-frequency-modulated waveform.

FM-CW compact reflectometer using DDS signal generation

A prototype of a compact coherent fast frequency sweeping RF back-end is being developed at IPFN-IST using commercial Monolithic Microwave Integrated Circuits (MMIC). On this work we present the usability of this concept of compact reflectometry associated with a Direct Digital Synthesis (DDS) source. Flexibility is one of the design goals for the back-end prototype, so that it can easily match the required frequency range. The backend alone covers the NATO J-band (10 GHz to 20 GHz) and is designed to drive external full band frequency multipliers, resulting in an ultra-wideband coverage of up to 140 GHz. FM-CW radar precision is strongly dependent on the probing source linearity. DDS nowadays plays an important role in signal generation in many fields of applications for communication systems as well as in radar technology. Modern DDSs are fully integrated, low-cost, single chip solutions that only need an external clock source for generating sinusoidal output signals up to several gigahertz. The DDS benefits from the totally digital generation of the output signal, which allows full control of the signal’s frequency and phase, both with very high precision and resolution. Recent implementations feature automatic sweeping capability, thus allowing the DDS to generate very linear and agile frequency chirps, assuming a high quality and constant frequency reference clock source. We propose to implement a DDS signal generation solution with the capability of a full band sweep in 1 μs. On the receiver side the IF and reference signals will be digitised allowing the use of high flexible data processing techniques. Input/output signals will allow the synchronisation of several systems.

Ultrawide-band silicon microring avalanche photodiode with linear photocurrent-wavelength response

We report a CMOS-compatible silicon microring-enhanced avalanche photodiode based on linear defect-state absorption in a p + p n + junction, with high responsivities exceeding 1 A/W at telecommunication wavelengths. The large photogenerated currents give rise to giant thermo-optic nonlinearity in the microring resonator, resulting in a linear photocurrent-wavelength response spanning the full free spectral range of the microring. This unique photocurrent spectrum could enable novel applications in wavelength-resolved photodetection, such as compact on-chip spectrometers, linear chirp frequency laser source characterization, and low-cost refractometric sensors without requiring precise wavelength-tunable lasers.