Showing papers on "Chirp published in 2018"

Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement.

Abstract: Brillouin optical time-domain analysis (BOTDA) requires frequency mapping of the Brillouin spectrum to obtain environmental information (e.g., temperature or strain) over the length of the sensing fiber, with the finite frequency-sweeping time-limiting applications to only static or slowly varying strain or temperature environments. To solve this problem, we propose the use of an optical chirp chain probe wave to remove the requirement of frequency sweeping for the Brillouin spectrum, which enables distributed ultrafast strain measurement with a single pump pulse. The optical chirp chain is generated using a frequency-agile technique via a fast-frequency-changing microwave, which covers a larger frequency range around the Stokes frequency relative to the pump wave, so that a distributed Brillouin gain spectrum along the fiber is realized. Dynamic strain measurements for periodic mechanical vibration, mechanical shock, and a switch event are demonstrated at sampling rates of 25 kHz, 2.5 MHz and 6.25 MHz, respectively. To the best of our knowledge, this is the first demonstration of distributed Brillouin strain sensing with a wide-dynamic range at a sampling rate of up to the MHz level.

Attosecond time–energy structure of X-ray free-electron laser pulses

Abstract: The time–energy information of ultrashort X-ray free-electron laser pulses generated by the Linac Coherent Light Source is measured with attosecond resolution via angular streaking of neon 1s photoelectrons. The X-ray pulses promote electrons from the neon core level into an ionization continuum, where they are dressed with the electric field of a circularly polarized infrared laser. This induces characteristic modulations of the resulting photoelectron energy and angular distribution. From these modulations we recover the single-shot attosecond intensity structure and chirp of arbitrary X-ray pulses based on self-amplified spontaneous emission, which have eluded direct measurement so far. We characterize individual attosecond pulses, including their instantaneous frequency, and identify double pulses with well-defined delays and spectral properties, thus paving the way for X-ray pump/X-ray probe attosecond free-electron laser science.

Evidence of linear chirp in mid-infrared quantum cascade lasers

Abstract: Since the first demonstration of the quantum cascade laser (QCL) frequency comb in 2012, there have been open questions concerning the reproducibility of comb states, and, critically for metrological applications, the phase stability. To address these important issues, we measure the intermodal phase relation of a QCL comb operating at 8 μm using a coherent beatnote spectroscopy. We find these intermodal phase differences to be constant within experimental uncertainty over several repeat measurements, and the comb states reproducible to an average of 21 mrad after cycling the power of the device. These phases describe a comb state exhibiting a simple, linear chirp, which in fact corresponds to the lowest state of chirp to minimize the amplitude modulation, as required for combs driven by four-wave mixing in a gain medium with a short gain recovery lifetime. All together, these findings could pave the way for pulse shaping in the QCL platform.

Highly efficient generation of 0.2 mJ terahertz pulses in lithium niobate at room temperature with sub-50 fs chirped Ti:sapphire laser pulses.

Abstract: We demonstrate generation of 0.2 mJ terahertz (THz) pulses in lithium niobate driven by Ti:sapphire laser pulses at room temperature. Employing tilted pulse front technique, the 800 nm-to-THz energy conversion efficiency has been optimized to 0.3% through chirping the sub-50 fs pump laser pulses to overcome multi-photon absorption and to extend effective interaction length for phase matching. Our approach paves the way for mJ-level THz generation via optical rectification using existing Ti:sapphire laser systems which can deliver Joule-level pulse energy with sub-50 fs pulse duration.

100 GBd Intensity Modulation and Direct Detection With an InP-Based Monolithic DFB Laser Mach–Zehnder Modulator

Abstract: We demonstrate 100 GBd operation of an optical transmitter module including a distributed feedback laser monolithically integrated with a Mach–Zehnder modulator (DFB-MZM), to the best of our knowledge for the first time. Combining high-speed optics and electronics with digital signal processing (DSP), different schemes for intensity modulation and direct detection at 100, 200, and 300 Gbit/s are analyzed, using electrical signals from a 100 GSa/s BiCMOS DAC. Due to close-to-zero transmitter chirp, 100 Gbit/s NRZ transmission over 1.8 km and 200 Gbit/s PAM4 transmission over 1.2 km at 1550 nm with a bit error rate (BER) below the 7% overhead forward error correction (FEC) threshold (3.8 × 10−3) is achieved. At 200 Gbit/s PAM4, the DFB-MZM module consumes only 0.85 pJ/bit, making it a promising device for attractive dual-lane 400 Gbit/s systems. We also achieve 300 Gbit/s PAM8 transmission over 1.2 km with a BER below the 20% overhead FEC threshold (1.9 × 10−2) by implementing advanced DSP based on a pattern-dependent lookup table to mitigate the electrical and optical device bandwidth limitations.

Performance comparison of DML, EML and MZM in dispersion-unmanaged short reach transmissions with digital signal processing.

Abstract: In this paper, transmission performances of directly modulated laser (DML), electro-absorption modulated laser (EML) and Mach-Zehnder modulator (MZM) are experimentally compared in dispersion-unmanaged high-speed transmission systems with digital signal processing (DSP). We show that, although the DML based transmitter is often believed to be less favorable in C-band high-speed transmissions, it exhibits superior performance over the other two transmitters when either linear or nonlinear digital signal processing is adopted. By theoretical and experimental analysis, we reveal that the superiority of DML can be attributed to the compensation of fiber power fading by its inherent adiabatic chirp as well as the mitigation of chirp induced distortions by the linear or nonlinear equalization. Experimental results of 56Gb/s 4-level pulse amplitude modulation (PAM4) signals under various equalization schemes including linear feedforward equalization, simplified nonlinear Volterra equalization and partial response signaling are presented. Particularly, we show that for DML a 40km transmission distance can be achieved to satisfy the extended range-4 (ER4) Ethernet interconnect using a simplified Volterra equalizer, and a 20km transmission distance can be supported using a linear equalizer. In contrast, for MZM and EML, the achievable transmission distances are respectively 20km and 15km using the Volterra equalizer, respectively, and 15km and 10km using linear equalizer, respectively. Moreover, we show that even using the combination of the Volterra equalizer and partial response signaling, the transmission distances of MZM and EML based systems are limited to 30km and 20km.

A Peer-to-Peer Interference Analysis for Automotive Chirp Sequence Radars

Abstract: Mutual interference between automotive radar sensors is becoming a major concern due to the rapid increase of vehicles equipped with such systems. While there has been a plenty of studies on the interference of frequency modulated continuous wave (FMCW) radars, no work on chirp sequence (CS) radars has been reported in the literature in spite of their growing popularity in the automotive field. In this regard, this work presents an investigation of mutual interference for automotive CS radars. We analytically derive formulas describing the probability of ghost target appearance, and the signal-to-interference mitigation gain for interference of different waveforms, including continuous wave, FMCW, and CS waveforms, with comparison to an equivalent FMCW radar model. The derived formulas on the signal-to-interference mitigation gain are also verified by simulation results.

Evidence of Linear Chirp in Mid-Infrared Quantum Cascade Lasers

Abstract: We measure the inter-modal phase relation of a quantum cascade laser frequency comb operating at 8 um using a coherent beatnote spectroscopy. We find these phases to be reproducible after cycling the power of the device, and to be smoothly varying with driving current. Moreover, these phases describe a comb state exhibiting a simple, linear chirp, which in fact corresponds to the lowest state of chirp to minimise the amplitude modulation, as required for combs driven by four wave mixing in a gain medium with a short gain recovery lifetime.

Laser Phase-Noise Cancellation in Chirped-Pulse Distributed Acoustic Sensors

Abstract: Distributed acoustic sensors based on chirped-pulse phase sensitive-optical time-domain reflectometry (chirped-pulse ΦOTDR) have proven capable of performing fully distributed, single shot measurements of true strain or temperature perturbations, with no need for frequency scanning or phase detection methods. The corresponding refractive index variations in the fiber are revealed in the chirped-pulse ΦOTDR trace through a local temporal shift, which is evaluated using trace-to-trace correlations. The accuracy in the detection of this perturbation depends upon the correlation noise and the coherence of the laser source. In this paper, we theoretically and experimentally analyze the impact of the laser phase noise in chirped-pulse ΦOTDR. In particular, it is shown that the noise in the readings of strain/temperature variations scales directly with the frequency noise power spectral density of the laser. To validate the developed model, an experimental study has been performed using three lasers with different static linewidths (5 MHz, 50 kHz, and 25 kHz), i.e., with different phase noise. Besides, we present a simple technique to mitigate the effect of the laser phase noise in chirped-pulse ΦOTDR measurements. The proposed procedure enables to detect perturbations with high signal-to-noise ratio even when using relatively broad linewidth (i.e., comparatively high phase noise) lasers. Up to 17 dB increase in signal-to-noise ratio has been experimentally achieved by applying the proposed noise cancellation technique.

Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics

Abstract: Broadband radio-frequency chirped waveforms (RFCWs) with dynamically tunable parameters are of fundamental interest to many practical applications. Recently, photonic-assisted solutions have been demonstrated to overcome the bandwidth and flexibility constraints of electronic RFCW generation techniques. However, state-of-the-art photonic techniques involve broadband mode-locked lasers, complex dual laser systems, or fast electronics, increasing significantly the complexity and cost of the resulting platforms. Here we demonstrate a novel concept for photonic generation of broadband RFCWs using a simple architecture, involving a single CW laser, a recirculating frequency-shifting loop, and standard low-frequency electronics. All the chirp waveform parameters, namely sign and value of the chirp rate, central frequency and bandwidth, duration and repetition rate, are easily reconfigurable. We report the generation of mutually coherent RF chirps, with bandwidth above 28 GHz, and time-bandwidth product exceeding 1000, limited by the available detection bandwidth. The capabilities of this simple platform fulfill the stringent requirements for real-world applications.

Ultraflat, broadband, and highly coherent supercontinuum generation in all-solid microstructured optical fibers with all-normal dispersion

Abstract: High flatness, wide bandwidth, and high-coherence properties of supercontinuum (SC) generation in fibers are crucial in many applications. It is challenging to achieve SC spectra in a combination of the properties, since special dispersion profiles are required, especially when pump pulses with duration over 100 fs are employed. We propose an all-solid microstructured fiber composed only of hexagonal glass elements. The optimized fiber possesses an ultraflat all-normal dispersion profile, covering a wide wavelength interval of approximately 1.55 μm. An SC spectrum spanning from approximately 1030 to 2030 nm (corresponding to nearly one octave) with flatness <3 dB is numerically generated in the fiber with 200 fs pump pulses at 1.55 μm. The results indicate that the broadband ultraflat SC sources can be all-fiber and miniaturized due to commercially achievable 200-fs fiber lasers. Moreover, the SC pulses feature high coherence and a single pulse in the time domain, which can be compressed to 13.9-fs pulses with high quality even for simple linear chirp compensation. The Fourier-limited pulse duration of the spectrum is 3.19 fs, corresponding to only 0.62 optical cycles.

Threshold-Free Interference Cancellation Method for Automotive FMCW Radar Systems

Abstract: Radar systems are key components for today's advanced driver assistance systems such as adaptive cruise control or emergency brake assistants. Along with the rising utilization of radars in modern cars, the issue of interference amongst themselves arises. It has been shown in previous work that interference between different frequency modulated continuous wave (FMCW) radar systems leads to an increased noise floor. This may severely impact the detectability of objects, especially those with a small radar cross section like pedestrians. In this work we propose a novel concept to mitigate interference in FMCW radar transceivers using digital signal processing. The actual interference cancellation is carried out in frequency domain taking into account a sequence of FMCW chirps. Therewith noise suppression is performed, the interference is cancelled, and the object information is retained in the radar image. In contrast to existing interference cancellation concepts, no threshold needs to be chosen in advance. We prove our method with simulation results, and compare it to existing work.

A 23-GHz Low-Phase-Noise Digital Bang–Bang PLL for Fast Triangular and Sawtooth Chirp Modulation

Abstract: Frequency-modulated continuous-wave (FMCW) radars with high resolution require the generation of low-phase-noise, low-spurs, and highly linear chirp signals with large peak-to-peak value (chirp bandwidth) and a short period of the modulation signal [1]. In radar systems, the spot phase noise of the chirp generator is converted to the intermediate frequency of the receiver making it difficult to detect two close targets, while spurs cause the detection of false targets. For those reasons, medium-range radar applications in the 77-to-81GHz band typically specify spot phase noise lower than −90dBc/Hz at 1MHz offset and spur level below −50dBc. Unlike triangular chirps, saw-tooth chirps allow for a reduced dead time for range detection. However, any practical modulator needs a finite time (idle time) to make a large frequency jump at the end of the saw-tooth, and this limits the duty cycle of the saw-tooth. For instance, a fast saw-tooth chirp with 200kHz rate and 95% duty cycle leaves the idle time of only 250ns. Fractional-N PLLs can be used as chirp modulators. Unfortunately, low phase noise and spur levels require a narrow PLL bandwidth, while short idle time demands for a wide one. The two-point injection of the modulation signal, both from the modulus control of the divider and the tuning input of the voltage-controlled oscillator (VCO), is a known method to simultaneously achieve a narrow PLL bandwidth and fast modulation. However, even in that scheme, a frequency modulation error is mainly limited by gain mismatch between the two injection paths and by the linearity of the VCO [2]. In this work, a 20-to-24GHz digital bang-bang PLL, which uses the two-point modulation scheme to generate triangular and saw-tooth chirp signals, is presented. Unlike previous works [1-4], this architecture is able to generate fast saw-tooth chirps with the slope up to 173MHz/js, the idle time below 200ns, and the rms frequency error of better than 0.06%. The gain mismatch between the two modulation paths are automatically calibrated by a digital algorithm [5], and the input of the digitally controlled oscillator (DCO) is pre-distorted via an automatic background correction scheme, which compensates for the DCO nonlinearity.

On the Estimation of LFM Signal Parameters: Analytical Formulation

Abstract: We propose analytical formulations, approximations, upper and lower bounds for the angle sweep of maximum magnitude of fractional Fourier transform of mono- and multicomponent linear frequency modulated (LFM) signals. We employ a successive coarse-to-fine grid-search algorithm to estimate the chirp rates of multicomponent nonseparable LFM signals. Extensive numerical simulations show the validity of analytical formulations and performance of the proposed estimator. Obtained analytical results may also find themselves other application areas, where nonstationary signals are of interest.

150 km fast BOTDA based on the optical chirp chain probe wave and Brillouin loss scheme.

Abstract: Distributed long-range Brillouin optical time domain analysis (BOTDA) is an extremely time-consuming sensing scheme, which requires frequency mapping of the Brillouin spectrum and a large number of average times Here, we propose a fast long-range BOTDA based on the optical chirp chain (OCC) probe wave and Brillouin loss scheme The OCC-modulated probe wave is enabled by cascading fast-frequency-changing microwave chirp segments head-to-tail, which covers a large frequency range around the anti-Stokes frequency relative to the pump wave The combination of the OCC technique and Brillouin loss scheme provides several advantages, ie, fast measurement, a high Brillouin threshold, no additional amplification scheme, and freedom from the nonlocal effect In the experiment, 6 m spatial resolution, 32 s measurement time, and 3 MHz measurement precision were achieved over a 150 km single-mode fiber

Energy-Chirp Compensation in a Laser Wakefield Accelerator.

Abstract: The energy spread in laser wakefield accelerators is primarily limited by the energy chirp introduced during the injection and acceleration processes. Here, we propose the use of longitudinal density tailoring to reduce the beam chirp at the end of the accelerator. Experimental data sustained by quasi-3D particle-in-cell simulations show that broadband electron beams can be converted to quasimonoenergetic beams of ≤10% energy spread while maintaining a high charge of more than 120 pC. In the linear and quasilinear regimes of wakefield acceleration, the method could provide even lower, subpercent level, energy spread.

Transmission of dual-chirp microwave waveform over fiber with compensation of dispersion-induced power fading.

Abstract: We propose a microwave photonic link to transmit a dual-chirp microwave waveform over fiber with compensation of dispersion-induced power fading. In a center office (CO), we use a polarization-dependent dual-parallel Mach-Zehnder modulator (DPMZM) which is driven by a radio frequency (RF) carrier and a baseband single-chirped waveform to realize carrier-suppressed dual-sideband (CS-DSB) modulation at two orthogonal polarization states. When the CS-DSB optical signal is detected by a photodetector (PD) at a base station (BS), the dual-chirp waveform is generated. However, along with the transmission to different BSs before emission, the chromatic dispersion of fiber will cause power fading. In our link, we can simply adjust the polarization controller (PC) in each BS to compensate for the dispersion-induced power fading for different transmission distances and RF carrier frequencies. Besides, the link can realize one to multitransmission with shared dual-chirp microwave source in CO for radars. The proposed scheme is theoretically analyzed and experimentally verified.

Recent Progress in Fast Distributed Brillouin Optical Fiber Sensing

Abstract: Brillouin-based optical fiber sensing has been regarded as a good distributed measurement tool for the modern large geometrical structure and the industrial facilities because it can demodulate the distributed environment information (e.g., temperature and strain) along the sensing fiber. Brillouin optical time domain analysis (BOTDA), which is an excellent and attractive scheme, has been widely developed thanks to its high performance in a signal-to-noise ratio, a spatial resolution, and sensing distance. However, the sampling rate of the classical BOTDA is severely limited by several factors (especially the serially frequency-sweeping process) so that it cannot be suitable for the quickly distributed measurement. In this work, we summarize some promising breakthroughs about the fast BOTDA, which can be named as an optical frequency comb technique, an optical frequency-agile technique, a slope-assisted technique, and an optical chirp chain technique.

Comparative study between linear and non-linear frequency-modulated pulse-compression thermography

Abstract: Pulse-compression thermography is an emerging non-destructive technique whose effectiveness strictly depends on the choice of the coded excitations used to modulate the heating stimulus. In this paper, the features of frequency-modulated coded signals, i.e., chirps, have been tested for imaging thin Teflon defects embedded within a carbon fiber composite specimen. With the aim of maximizing the heat transferred within the sample, the use of several optimized non-linear chirp signals has been also investigated and their defect detection capability compared in terms of the maximum achievable signal-to-noise ratio.

Ionization waves of arbitrary velocity driven by a flying focus

Abstract: A chirped laser pulse focused by a chromatic lens exhibits a dynamic, or flying, focus in which the trajectory of the peak intensity decouples from the group velocity. In a medium, the flying focus can trigger an ionization front that follows this trajectory. By adjusting the chirp, the ionization front can be made to travel at an arbitrary velocity along the optical axis. We present analytical calculations and simulations describing the propagation of the flying focus pulse, the self-similar form of its intensity profile, and ionization wave formation. The ability to control the speed of the ionization wave and, in conjunction, mitigate plasma refraction has the potential to advance several laser-based applications, including Raman amplification, photon acceleration, high-order-harmonic generation, and THz generation.

Linearly chirped mid-infrared supercontinuum in all-normal-dispersion chalcogenide photonic crystal fibers

Abstract: We demonstrate all-normal dispersion supercontinuum generation in chalcogenide photonic crystal fibers pumped at 2070-2080 nm with a femtosecond fiber laser. At 2.9 kW peak power, the generated supercontinuum has a 3 dB bandwidth of 27.6 THz and −20 dB bandwidth of 75.5 THz. We experimentally investigated the supercontinuum evolution inside our sample fiber at various peak powers and fiber lengths and study the impact of fiber water absorption on the generated supercontinuum spectrum. Multiple tests with fiber length— ranging from 0.34 to 10 cm—provide insight on pulse evolution along fiber length. Our simulations, which utilizes the generalized nonlinear Schrodinger equation model, match perfectly the experiments for all tested pump powers and fiber lengths, and confirm that the output pulse has a linear chirp, allowing linear pulse compression.

Three-Dimensional Imaging of Space Debris With Space-Based Terahertz Radar

Abstract: The increasing natural or man-made space debris could pose a serious threat to orbital space-based systems and their operators. Consequently, their detection, reorganization, and tracking are of considerable significance. However, the traditional solutions, including ground-based radar and optical telescope, cannot exactly observe the debris with small diameter. Imaging with space-based terahertz (THz) radar in combination with inverse synthetic aperture radar (ISAR) technique enables us to obtain high-resolution 3-D image. In this paper, we have developed a high-resolution THz radar that operates at 340 GHz with a bandwidth of 28.8 GHz and the output peak power of 5 mW for proof-of-concept. In addition, using the characteristic that space debris rotates about its main axis, we have established a 3-D ISAR imaging geometry as well as its corresponding signal model. Then, a 3-D wavenumber-domain image formation algorithm is presented and has been validated by point target simulation. The experimental results have confirmed that the THz radar can effectively achieve high-resolution 3-D imaging of the spinning space debris.

Efficient swept sine chirp excitation in the non-linear vibro-acoustic wave modulation technique used for damage detection:

Abstract: In this article, the non-linear vibro-acoustic modulation technique is used for structural damage detection. A new experimental configuration and data processing strategy are proposed to improve the damage detection capability of the technique. The swept sine chirp excitation is used for both low-frequency vibration/modal and high-frequency ultrasonic excitations. The adaptive resampling procedure is then applied to extract information about modulation intensity that relates to damage. The proposed method is illustrated using numerical simulations and experimental tests. The latter involves crack detection in an aluminium beam. The results of the proposed method are compared with the classical approach based on single harmonic excitation, demonstrating that similar damage detection information can be extracted. However, the major advantage of the proposed method is simplicity and robustness since no a priori selection of excitation frequencies is needed. As a result, crack detection is more reliable and u...

Enhancement of Doppler Unambiguity for Chirp-Sequence Modulated TDM-MIMO Radars

Abstract: Current automotive radar sensors enhance the angular resolution using a multiple-input multiple-output approach. The often applied time-division multiplexing scheme has the drawback of a reduced unambiguous Doppler velocity proportional to the number of transmitters. In this paper, a signal processing scheme is proposed to regain the same unambiguous Doppler as in the single-input multiple-output case with only one transmit antenna. Simulation and measurement results are shown to prove that the signal processing leads to an enhanced unambiguous Doppler velocity estimation.

Dynamics of Gaussian beam modeled by fractional Schrödinger equation with a variable coefficient.

Abstract: In the paper, we investigate the propagation dynamics of the Gaussian beam modeled by the fractional Schrodinger equation (FSE) with a variable coefficient. In the absence of the beam's chirp, for smaller Levy index, the Gaussian beam firstly splits into two beams, however under the action of the longitudinal periodic modulation, they exhibit a periodically oscillating behaviour. And with the increasing of the Levy index, the splitting behaviour gradually diminishes. Until the Levy index equals to 2, the splitting behaviour is completely replaced by a periodic diffraction behaviour. In the presence of the beam's chirp, one of the splitting beams is gradually suppressed with the increasing of the chirp, while another beam on the opposite direction becomes stronger and exhibits a periodically oscillating behaviour. Also, the oscillating amplitude and period are investigated and the results show that the former is dependent on the modulation frequency, the Levy index and the beam's chirp, the latter depends only on the modulation frequency. Thus, the evolution of the Gaussian beam can be well manipulated to achieve the beam management in the framework of the FSE by controlling the system parameters and the chirp parameter.

Design of Chirp Waveforms for Multiple-Access Ultrasonic Indoor Positioning

Abstract: In ultrasonic positioning systems (UPSs) chirp waveforms have attracted much attention due to its high range resolution. However, the multiple-access schemes for the chirp-based UPS are limited. In its application to multiple-access ultrasonic positioning, effective waveform diversity design is a prerequisite. In a multiple-access UPS, each transmitter should transmit a unique waveform with impulse-like auto-correlation and relatively flat cross-correlations to the waveforms transmitted by other transmitters. Proposed in this paper is a methodology whereby multiple transmitters can transmit chirp signals simultaneously. The chirp waveforms are constructed by concatenating a number of linear sub-chirps of the same durations and bandwidths but different starting and stopping frequencies. This process is optimized by selecting sequences with impulse-like auto-correlations and relatively flat cross-correlations. First, the efficiency of the proposed methodology is evaluated by several metrics and, then, in an indoor environment, through simulations and experiments for ultrasonic positioning.

Refocusing and Motion Parameter Estimation for Ground Moving Targets Based on Improved Axis Rotation-Time Reversal Transform

Abstract: In this paper, a new algorithm is presented to image ground moving targets and estimate their motion parameters in a synthetic aperture radar system based on improved axis rotation-time reversal transform (IAR-TRT). In this algorithm, the second-order Keystone transform) is applied to correct the range curvature, where the Doppler ambiguity caused by a fast-moving target is considered. Then, residual linear range migration and Doppler frequency migration are eliminated by IAR-TRT, which performs an improved axis rotation transform to correct the range walk and subsequently realizes the coherent integration based on time reversal transform. Finally, a ground moving target is well focused. Additionally, the proposed method has a relatively low computational complexity since the exhaustive searching for Doppler chirp rate estimation is avoided. The effectiveness of the proposed algorithm is validated by both simulated and real data.