Showing papers on "Chirp published in 2015"

Chirp signal-based aerial acoustic communication for smart devices

Abstract: Smart devices such as smartphones and tablet/wearable PCs are equipped with voice user interface, ie, speaker and microphone Accordingly, various aerial acoustic communication techniques have been introduced to utilize the voice user interface as a communication interface In this paper, we propose an aerial acoustic communication system using inaudible audio signal for low-rate communication in indoor environments By adopting chirp signal, which is widely used for radar applications due to its capability of resolving multi-path propagation, the proposed acoustic modem supports long-range communication independent of device characteristics over severely frequency-selective acoustic channel We also design a backend server architecture to compensate for the low data rate of chirp signal-based acoustic modem Via extensive experiments, we evaluate various characteristics of the proposed modem including multi-path resolution and multiple chirp signal detection We also verify that the proposed chirp signal can deliver data at 16 bps in typical indoor environments, where its maximum transmission range is drastically extended up to 25 m compared to the few meters of the previous research

Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential.

Abstract: We study periodic inversion and phase transition of normal, displaced, and chirped finite energy Airy beams propagating in a parabolic potential. This propagation leads to an unusual oscillation: for half of the oscillation period the Airy beam accelerates in one transverse direction, with the main Airy beam lobe leading the train of pulses, whereas in the other half of the period it accelerates in the opposite direction, with the main lobe still leading – but now the whole beam is inverted. The inversion happens at a critical point, at which the beam profile changes from an Airy profile to a Gaussian one. Thus, there are two distinct phases in the propagation of an Airy beam in the parabolic potential – the normal Airy and the single-peak Gaussian phase. The length of the single-peak phase is determined by the size of the decay parameter: the smaller the decay, the smaller the length. A linear chirp introduces a transverse displacement of the beam at the phase transition point, but does not change the location of the point. A quadratic chirp moves the phase transition point, but does not affect the beam profile. The two-dimensional case is discussed briefly, being equivalent to a product of two one-dimensional cases.

MIMO SAR OFDM Chirp Waveform Diversity Design With Random Matrix Modulation

Abstract: Multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) has received much attention due to its interesting application potentials, but effective waveform diversity design is still a technical challenge. In a MIMO SAR, each antenna should transmit a unique waveform, orthogonal to the waveforms transmitted by other antennas. The waveforms should have a large time-bandwidth product, low cross-correlation interferences, and a low peak-average ratio. To reach these aims, this paper proposes an orthogonal frequency division multiplexing (OFDM) chirp waveform with random matrix modulation. The designed waveforms are time-delay and frequency-shift decorrelated. Referring to MIMO SAR high-resolution imaging, the proposed OFDM chirp waveform parameters are optimally designed, and their performances are analyzed through the ambiguity function and range-Doppler-based MIMO SAR imaging algorithm. Extensive and comparative simulation results show that the waveforms have the superiorities of high range resolution, constant time domain and almost constant frequency-domain modulus, large time-bandwidth product, low peak-average ratio, and low time-delay and frequency-shift correlation peaks. More importantly, this scheme can easily generate over three orthogonal waveforms with a large time-bandwidth product.

Molecular harmonic extension and enhancement from H 2 + ions in the presence of spatially inhomogeneous fields

Abstract: Molecular high-order harmonic generation from the ${{\mathrm{H}}_{2}}^{+}$ ion driven by spatial inhomogeneous fields consisting of the chirped pulse and a terahertz pulse has been theoretically investigated by numerically solving the non--Born-Oppenheimer time-dependent Schr\"odinger equation. It shows that with the introduction of the chirp as well as the spatial inhomogeneity of the pulse, not only the harmonic cutoff is remarkably extended, but also the single short quantum path is selected to contribute to the harmonic spectra. Moreover, through investigation the effects of the laser and the molecular parameters on the inhomogeneous harmonic generation, we found 1.92- and 3.3-dB enhanced fields for the chirp-free and chirped inhomogeneous pulses, respectively. Isotopic effect shows that intense harmonics can be generated from the lighter molecule. Furthermore, with the enhancement of the initial vibrational state and by properly adding a terahertz controlling pulse, the harmonic yield is enhanced by almost five orders of magnitude compared with the initial single chirped case. As a result, a 362-eV supercontinuum (which corresponds to a 4.0-dB laser field enhancement) with five orders of magnitude improvement is obtained. Finally, by properly superposing the harmonics, a series of intense extreme ultraviolet pulses with durations from 22 to 52 as can be produced.

Nonlinear Imaging Method Using Second Order Phase Symmetry Analysis and Inverse Filtering

Abstract: This paper presents a nonlinear imaging method based on nonlinear elastic guided waves, for the damage detection and localisation in a composite laminate. The proposed technique relies on the study of the structural nonlinear responses by means of a combination of second order phase symmetry analysis (PSA) with chirp excitation and inverse filtering (IF) method. PSA was used to exploit the invariant properties of the propagating elastic waves with the phase angle of the pulse compressed chirp signals, in order to characterise the second order nonlinear behaviour of the medium. Then, the IF approach was applied to a library of second order nonlinear responses to obtain a two-dimensional image of the damage. The experimental tests carried out on an impact damage composite sample were compared to standard C-scan. The results showed that the present technique allowed achieving the optimal focalisation of the nonlinear source in the spatial and time domain, by taking advantage of multiple scattering and a small number of receiver sensors.

Dual-Chirp Microwave Waveform Generation Using a Dual-Parallel Mach-Zehnder Modulator

Abstract: A photonic approach to generating a dual-chirp microwave waveform using a single dual-parallel Mach-Zehnder modulator (DPMZM) is proposed and experimentally demonstrated. A dual-chirp microwave waveform can be used in a radar system to improve its range-Doppler resolution. In the proposed approach, a baseband single-chirp waveform is applied to one sub-Mach-Zehnder modulator (sub-MZM) in the DPMZM and a microwave carrier is applied to the other sub-MZM. By biasing the two sub-MZMs at the minimum transmission point to suppress the optical carrier, a dual-chirp microwave waveform with a central frequency upconverted to the frequency of the microwave carrier is generated. A theoretical analysis is performed, which is then verified by a proof-of-concept experiment. A dual-chirp microwave waveform at 6 GHz with a tunable bandwidth at 200 MHz and 2 GHz is generated.

An Efficient Frequency and Phase Estimation Algorithm With CRB Performance for FMCW Radar Applications

Abstract: In this paper, a chirp $z$ -transform (CZT)-based algorithm for frequency-modulated continuous wave (FMCW) radar applications is presented. The proposed algorithm is optimized for real-time implementation in field-programmable gate arrays. To achieve a very high accuracy, the FMCW radar uses an additional phase evaluation. Therefore, a phase calculation based on the CZT algorithm is derived and compared with a correlation based algorithm. For a better classification of the algorithm, the respective Cramer–Rao bounds are calculated. The performance of the algorithm is shown by the evaluation of different radar measurements with a K-band radar. In the measurements, an accuracy of $5~\mu $ m with a mean standard deviation of 774 nm is achieved, which nearly matches the theoretically predicted mean standard deviation of 160 nm.

Pre-chirp managed nonlinear amplification in fibers delivering 100 W, 60 fs pulses

Abstract: We demonstrate a pre-chirp managed Yb-doped fiber laser system that outputs 75 MHz, 130 W spectrally broadened pulses, which are compressed by a diffraction-grating pair to 60 fs with average powers as high as 100 W. Fine tuning the pulse chirp prior to amplification leads to high-quality compressed pulses. Detailed experiments and numerical simulation reveal that the optimum pre-chirp group-delay dispersion increases from negative to positive with increasing output power for rod-type high-power fiber amplifiers. The resulting laser parameters are suitable for extreme nonlinear optics applications such as frequency conversion in femtosecond enhancement cavities.

ISAR Imaging of Nonuniformly Rotating Target Based on a Fast Parameter Estimation Algorithm of Cubic Phase Signal

Abstract: In inverse synthetic aperture radar (ISAR) imaging of nonuniformly rotating targets, such as highly maneuvering airplanes and ships fluctuating with oceanic waves, azimuth echoes have to be modeled as cubic phase signals (CPSs) after the range migration compensation and the translational-induced phase error correction. For the CPS model, the chirp rate and the quadratic chirp rate, which deteriorate the azimuth focusing quality due to the Doppler frequency shift, need to be estimated with a parameter estimation algorithm. In this paper, by employing the proposed generalized scaled Fourier transform (GSCFT) and the nonuniform fast Fourier transform (NUFFT), a fast parameter estimation algorithm is presented and utilized in the ISAR imaging of the nonuniformly rotating target. Compared to the scaled Fourier transform-based algorithm, advantages of the fast parameter estimation algorithm include the following: 1) the computational cost is lower due to the utilization of the NUFFT, and 2) the GSCFT has a wider applicability in ISAR imaging applications. The CPS model and the algorithm implementation are verified with the real radar data of a ship target. In addition, the cross-term, which plays an important role in correlation algorithms, is analyzed for the fast parameter estimation algorithm. Through simulations of the synthetic data and the real radar data, we verify the effectiveness of the fast parameter estimation algorithm and the corresponding ISAR imaging algorithm.

76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar

Abstract: This paper presents the design of a linear frequency-modulated continuous-wave (FMCW) radar transmitter (TX) for automotive radar applications. The TX has a wide operating range from 76 to 81 GHz by employing a frequency-doubling architecture using an LC voltage-controlled oscillator operating at 38–40.5 GHz and a differential frequency doubler using a single transformer. A chirp generator is integrated into the TX, which provides various frequency chirp profiles with programmable chirp slope and sweep duration. The proposed CMOS FMCW TX can be applied to various modulation algorithms for multiple target detection and the avoidance of ghost targets. The TX is implemented using 65-nm CMOS technology. The chip size is 1.48 $\,\times\,$ 1.85 mm $^{2}$ . The measurement results shows a 76–81-GHz frequency range and 3-dBm output power while dissipating 320 mW. The phase-noise density of the TX is ${-}{\hbox{83.33}}$ dBm/Hz at an offset frequency of 1 MHz when the output frequency is 77 GHz.

Effect of initial frequency chirp on Airy pulse propagation in an optical fiber

Abstract: We study both analytically and numerically the propagation dynamics of an initially chirped Airy pulse in an optical fiber. It is found that the linear propagation of an initially chirped Airy pulse depends considerably on whether the second-order dispersion parameter β(2) and chirp C have the same or opposite signs. For β(2)C 0. The impact of truncation coefficient and Kerr nonlinearity on the chirped Airy pulse propagation is also disclosed separately.

Spectrotemporal Shaping of Seeded Free-Electron Laser Pulses

Abstract: We demonstrate the ability to control and shape the spectrotemporal content of extreme-ultraviolet (XUV) pulses produced by a seeded free-electron laser (FEL). The control over the spectrotemporal properties of XUV light was achieved by precisely manipulating the linear frequency chirp of the seed laser. Our results agree with existing theory, which allows us to retrieve the temporal properties (amplitude and phase) of the FEL pulse from measurements of the spectra as a function of the FEL operating parameters. Furthermore, we show the first direct evidence of the full temporal coherence of FEL light and generate Fourier limited pulses by fine-tuning the FEL temporal phase. The possibility of tailoring the spectrotemporal content of intense short-wavelength pulses represents the first step towards efficient nonlinear optics in the XUV to x-ray spectral region and will enable precise manipulation of core-electron excitations using the methods of coherent quantum control.

Diffraction-free beams in fractional Schr\"odinger equation

Abstract: We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schr\"odinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories $z=\pm2(x-x_0)$, which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone $z=2\sqrt{x^2+y^2}$ and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE.

Component Extraction for Non-Stationary Multi-Component Signal Using Parameterized De-chirping and Band-Pass Filter

Abstract: In most applications, component extraction is important when components of non-stationary multi-component signal are key features to be monitored and analyzed. Existing methods are either sensitive to noise or forced to select a proper time-frequency representation for the considered signal. In this paper, we present a novel component extraction method for non-stationary multi-component signal. The proposed method combines parameterized de-chirping and band-pass filter to obtain components of multi-component signal, which avoids dealing with time-frequency representation of the signal and works well under heavy noise. In addition, it is able to analyze the multi-component signal whose components have intersected instantaneous frequency trajectories. Simulation results show that the proposed method is promising in analyzing complicated multi-component signals. Moreover, it works effective in a high noise environment in terms of improving the output signal-to-noise rate for the interested component.

High-speed flow microscopy using compressed sensing with ultrafast laser pulses.

Abstract: We demonstrate an imaging system employing continuous high-rate photonically-enabled compressed sensing (CHiRP-CS) to enable efficient microscopic imaging of rapidly moving objects with only a few percent of the samples traditionally required for Nyquist sampling. Ultrahigh-rate spectral shaping is achieved through chirp processing of broadband laser pulses and permits ultrafast structured illumination of the object flow. Image reconstructions of high-speed microscopic flows are demonstrated at effective rates up to 39.6 Gigapixel/sec from a 720-MHz sampling rate.

All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator

Abstract: Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Differential equations model and govern fundamental physical phenomena and engineering systems in virtually any field of science and engineering, such as temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, and the response of different resistor-capacitor circuits, etc. In this study, we experimentally demonstrate a feasible integrated scheme to solve first-order linear ordinary differential equation with constant-coefficient tunable based on a single silicon microring resonator. Besides, we analyze the impact of the chirp and pulse-width of input signals on the computing deviation. This device can be compatible with the electronic technology (typically complementary metal-oxide semiconductor technology), which may motivate the development of integrated photonic circuits for optical computing.

Generalized Frequency Scaling and Backprojection for LFM-CW SAR Processing

Abstract: This paper presents a generalized treatment of image formation for a linear-frequency-modulated continuous wave (LFM-CW) synthetic aperture radar (SAR) signal, which is a key technology in making very small SAR systems viable. The signal model is derived, which includes the continuous platform motion. The effect of this motion on the SAR signal is discussed, and an efficient compensation method is developed. Processing algorithms are developed including precise and approximate backprojection methods and a generalized frequency scaling algorithm that accounts for an arbitrary number of terms of a Taylor expansion approximation of the SAR signal in the Doppler frequency domain. Together, these algorithms allow for the processing of LFM-CW SAR data for a wide variety of system parameters, even in scenarios where traditional algorithms and signal approximations break down.

Electron beam energy chirp control with a rectangular corrugated structure at the Linac Coherent Light Source

Abstract: Electron beam energy chirp is an important parameter that affects the bandwidth and performance of a linac-based, free-electron laser. In this paper we study the wakefields generated by a beam passing between flat metallic plates with small corrugations, and then apply such a device as a passive dechirper for the Linac Coherent Light Source (LCLS) energy chirp control with a multi-GeV and femtosecond electron beam. Similar devices have been tested in several places at relatively low energies ($\ensuremath{\sim}100\text{ }\mathrm{MeV}$) and with relatively long bunches ($g1\text{ }\text{ }\mathrm{ps}$). In the parameter regime of the LCLS dechirper, with the corrugation size similar to the gap between the plates, the analytical solutions of the wakefields are no longer applicable, and we resort to a field matching program to obtain the wakes. Based on the numerical calculations, we fit the short-range, longitudinal wakes to simple formulas, valid over a large, useful parameter range. Finally, since the transverse wakefields---both dipole and quadrupole---are strong, we compute and include them in beam dynamics simulations to investigate the error tolerances when this device is introduced in the LCLS.

Implementation of the OFDM Chirp Waveform on MIMO SAR Systems

Abstract: Attention has been devoted to multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) systems in recent years. The applications of MIMO SAR systems, which involve high-resolution wide-swath remote sensing, 3-D imaging, and multibaseline interferometry, are seriously limited by the available sets of orthogonal waveforms. Although orthogonal frequency-division multiplexing (OFDM) chirp waveforms are proposed to avoid intrapulse interferences, this waveform scheme has not been investigated for practical implementation. In this paper, challenges in implementing the OFDM chirp waveforms on practical systems are analyzed and solved. First, the small extra carrier frequency between the mutually orthogonal waveforms, which renders the OFDM chirp waveforms not strictly on common spectral support, is avoided by improving the modulation of the OFDM chirp waveform. Second, the tedious demodulation, which is realized by circular-shift addition in the time domain and subcarrier extraction in the frequency domain, is improved. Third, the radar systematic error and the Doppler shift, which introduce bandwidth leakage and degrade the waveform orthogonality significantly, are compensated. Finally, taking all these challenges into consideration, a novel signal processing algorithm along with a MIMO SAR system model is proposed. Theoretical analysis is validated by simulations and systematic calibration measurements based on a C-band system.

FPGA-Based Implementation of Multiple Modes in Near Field Inductive Communication Using Frequency Splitting and MIMO Configuration

Abstract: Conventional near field inductive wireless power transfer theory shows that systems suffer from splitting frequency behaviors when strong coupling condition exists between the transmitter and the receiver. However, this characteristic has not been explored for communication. Our analysis demonstrates that the splitting behaviour of frequency creates multiple frequencies that support inductive communication in MIMO configuration. As a result, we implement a binary chirp modulation on an FPGA and validate two channel communication using splitting. This paper introduces the use of chirp signals to spread data and excite inductive MIMO systems. The simulation and experiment show that the splitting frequency depends on a quality factor and the flux coupling condition between the data source and receiver. In other words, the degree of mutual coupling defines the splitting mode. This paper proves that multi-channel communication using splitting can be used for data transmission. The results show that data rates of 50 Mbps or 69 Kbps can be achieved for each channel between the transmitters and receivers when the transmitter and receiver operate at the original resonant frequency of 13.56 MHz or 28 KHz, respectively and the distance between them varies from about 1 cm to 10 cm.

On the Pulse Extension Loss in Digital Beamforming SAR

Abstract: One of the benefits of synthetic aperture radar (SAR) systems utilizing digital beamforming is the ability to increase the receive power. The relevant SAR technique is known as SCan-On-REceive (SCORE), which steers the receive antenna beam such that it follows the radar pulse echo traversing the ground. This allows the use of a narrow receive beam in elevation, and therefore, the height of the receive antenna can be increased, resulting in a higher gain, which explains the higher receive power. Although advantageous, this technique has some pitfalls, which impose an upper limit on the antenna size and constrain the selection of SAR operation parameters. These limitations (which are often neglected in the system conception) are caused by the pulse extent on the ground and the way it is modulated by the receive antenna pattern. This letter addresses and quantifies the effects caused by the transmit pulse length (here denoted as pulse extension loss) through a rigorous analysis, with the purpose of introducing an important SAR performance figure. Closed expressions are derived for the simplified case of a uniform linear antenna array.

Large Time-Bandwidth Product MIMO Radar Waveform Design Based on Chirp Rate Diversity

Abstract: Multiple-input multiple-output (MIMO) radar waveform diversity design has received much attention, but most of the existing waveforms lack a large time-bandwidth product and are difficult to be implemented by real-life hardwares. In this paper, we propose a large time-bandwidth product waveform diversity design scheme based on chirp rate diversity for MIMO radar. The proposed scheme can generate a large number of pseudo-orthogonal waveforms that have large time-bandwidth product, constant modulus, no range-Doppler coupling target response, good orthogonality, and Doppler tolerance. In addition, the waveforms are orthogonal on both transmit and receive. The waveform performance is in-depth analyzed with the correlation and ambiguity functions. Furthermore, the corresponding frequency demodulation in the receiver is also discussed. Numerical results validate the superiorities of the designed waveforms in MIMO radar applications.

Swept optical SSB-SC modulation technique for high-resolution large-dynamic-range static strain measurement using FBG-FP sensors.

Abstract: This Letter presents a static strain demodulation technique for FBG-FP sensors using a suppressed carrier LiNbO3 (LN) optical single sideband (SSB-SC) modulator. A narrow-linewidth tunable laser source is generated by driving the modulator using a linear chirp signal. Then this tunable single-frequency laser is used to interrogate the FBG-FP sensors with the Pound–Drever–Hall (PDH) technique, which is beneficial to eliminate the influence of light intensity fluctuation of the modulator at different tuning frequencies. The static strain is demodulated by calculating the wavelength difference of the PDH signals between the sensing FBG-FP sensor and the reference FBG-FP sensor. As an experimental result using the modulator, the linearity (R2) of the time-frequency response increases from 0.989 to 0.997, and the frequency-swept range (dynamic range) increases from hundreds of MHz to several GHz compared with commercial PZT-tunable lasers. The high-linearity time-wavelength relationship of the modulator is beneficial for improving the strain measurement resolution, as it can solve the problem of the frequency-swept nonlinearity effectively. In the laboratory test, a 0.67 nanostrain static strain resolution, with a 6 GHz dynamic range, is demonstrated.

A Novel SAR Imaging Algorithm Based on Compressed Sensing

Abstract: To reduce the amount of measurements, compressed sensing (CS) has been introduced to synthetic aperture radar (SAR). In this letter, a novel CS-SAR imaging algorithm is proposed, which consists of 2-D undersampling, range reconstruction, range–azimuth decoupling, and azimuth reconstruction. In the proposed algorithm, the range profile is reconstructed in the fractional Fourier domain, and range–azimuth decoupling in the case of azimuth undersampling is realized by using the reference function multiplication and chirp- $z$ transform. Comparisons with the existing 2-D undersampling CS-SAR imaging algorithms are also presented. Experimental results from both simulated and real data demonstrate that the proposed algorithm can efficiently realize high-quality imaging with limited measurements.

Electron acceleration to GeV energy by a chirped laser pulse in vacuum in the presence of azimuthal magnetic field

Abstract: Electron acceleration by a frequency-chirped circularly polarized (CP) laser pulse in vacuum in the presence of azimuthal magnetic field has been studied. A laser pulse propagating along +z-axis interacts with a pre-accelerated electron injected at a small angle in the direction of propagation of laser pulse in vacuum. The electron is accelerated with high energy in the presence of azimuthal magnetic field till the saturation of betatron resonance. A linear frequency chirp increases the duration of interaction of laser pulse with electron and hence enforces the resonance for longer duration. The presence of azimuthal magnetic field further improves the electron acceleration by keeping the electron motion parallel to the direction of propagation for longer distances. Thus, resonant enhancement appears due to the combined effect of chirped CP laser pulse and azimuthal magnetic field. An electron with few MeV of initial energy gains high energy of the order of GeV. Higher energy gain is obtained with intense chirped laser pulse in the presence of azimuthal magnetic field.

Optimization of free electron laser performance by dispersion-based beam-tilt correction

Abstract: Free electron lasers in the X-ray regime require a good slice alignment along the electron bunch to achieve their best performance. A transverse beam slice shift reduces this alignment and spoils projected emittance and optics. Coherent synchrotron radiation specifically for over-compression and transverse wakefields are major contributors to this. In the case of the large-bandwidth operation, based on a strictly monotonic energy chirp of the bunch, the here introduced correction additionally enhances the spectral bandwidth of the FEL pulse. Well-defined leaking of dispersion at places with a strictly monotonic longitudinal phase space can compensate a beam tilt. This work presents a way to characterize the beam tilt as well as a method to correct for it within a linear accelerator with at least one high dispersive section with corrector magnets.

ISAR Imaging of Targets With Complex Motions Based on Modified Lv’s Distribution for Cubic Phase Signal

Abstract: For targets with complex motions, such as highly maneuvering airplanes and ships fluctuating with oceanic waves, the Doppler frequencies of scatterers are actually time-varying and azimuth echoes of a range cell have to be modeled as multicomponent cubic phase signals (CPSs) after the range alignment and the phase adjustment. In inverse synthetic aperture radar (ISAR) imaging based on the CPS model, the chirp rate and the quadratic chirp rate are identified as causes of the image defocus. In this paper, by employing a novel parametric symmetric self-correlation function and the keystone transform, an effective estimation algorithm, known as the modified Lv’s distribution (MLVD), is presented for the CPS and applied to ISAR imaging of targets with complex motions. The MLVD is simple and can be easily implemented using the complex multiplication, the fast-Fourier transform (FFT), and the inverse FFT (IFFT). The implementation, the cross-term, the antinoise performance, and the computational cost are analyzed for the MLVD. Compared to three representative estimation algorithms for the CPS, the MLVD can acquire a higher antinoise performance and eliminate the brute-force searching without the interpolation. Through simulations and analyses for synthetic models and the real radar data, we verify the effectiveness of the MLVD and the corresponding ISAR imaging algorithm.