Stepped-frequency Chirp Signal Research Articles

Coherent stepped-frequency waveform generation based on recirculating microwave photonic frequency conversion.

We propose a novel method for generating coherent and wideband stepped-frequency waveforms using recirculating microwave photonic frequency conversion (MWP-FC). By injecting a narrowband signal into an MWP-FC loop utilizing a dual-parallel Mach-Zehnder modulator (DPMZM), the signal frequency is continuously converted to produce a stepped-frequency waveform with a wide bandwidth. Within the MWP-FC loop, photo-electric conversion is achieved based on self-mixing detection, where the optical phase noise can be suppressed, guaranteeing stability and coherence of the generated signal. In a proof-of-concept experiment, a stepped-frequency signal with a frequency interval of 2 GHz and a bandwidth of about 16 GHz and a stepped-frequency chirp signal with a frequency interval of 3 GHz and a bandwidth of about 15 GHz are generated. In addition, coherence of the generated signals is verified by coherent integration and de-chirping.

Distributed Microwave Photonic MIMO Radar With Accurate Target Position Estimation

A distributed microwave photonic multiple-input multiple-output (MIMO) radar is presented to accurately estimate the two-dimensional (2-D) position of targets. With wavelength-division-multiplexing-based recirculating frequency shifting, mutually orthogonal broadband stepped-frequency chirp (SFC) signals can be produced simultaneously, avoiding the complex implementation of a distributed MIMO radar. Microwave photonic dechirping is also performed to process broadband echoes, while a bandwidth synthesis is carried out to fast and accurately estimate the time of arrival (TOA). Thus, 2-D localization can be obtained by a back-projection (BP) algorithm. In a proof-of-concept experiment, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times2$ </tex-math></inline-formula> MIMO radar with a bandwidth of 18 GHz is conducted, providing a 1-D ranging error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&lt; \pm 1$ </tex-math></inline-formula> mm and a 2-D positioning error of < 1 cm.

Enhanced compressed sensing autofocus for high-resolution airborne synthetic aperture radar

The limited accuracy of the navigation system leads to deviations between the real and measured trajectories in airborne synthetic aperture radar (SAR) which results in residual motion (phase) errors and seriously degrades the image quality. The residual errors are usually corrected by using autofocus methods. In this paper, we investigate the autofocus for a high-resolution airborne SAR system which employs stepped-frequency chirp (SFC) signal to achieve high range resolution. As a promising waveform to improve radar range resolution, the SFC signal is widely realized in practical systems. We characterize the backscattering from the scene, phase errors, and receiver noise with a linear matrix-based formulation. In addition, we propose a compressed sampling method that is directly applied to the scene and received signal to provide a sparse raw dataset. We describe the autofocus problem as a constrained optimization problem and propose a new compressed sensing (CS)-based autofocus method to solve it. This method iteratively estimates the phase error and reconstructs the high-resolution SAR image. The image reconstruction is based on the proximity algorithm which applies the shrinkage proximal operator to solve the problem in a computationally efficient manner. We validate the effectiveness of the proposed method using both simulated and real SAR images. Based on visual results and a variety of metrics, the proposed method outperforms the classical autofocus approaches. Also, it provides better or comparable results, with much lower computational complexity, in comparison to that of the recent CS-based autofocus methods.

High-Resolution Microwave Photonic Radar With Sparse Stepped Frequency Chirp Signals

High-Resolution Microwave Photonic Radar With Sparse Stepped Frequency Chirp Signals

High-Resolution ISAR Imaging Under Low SNR With Sparse Stepped-Frequency Chirp Signals

To obtain high-resolution imaging while reducing the radar operating bandwidth under a low signal-to-noise ratio (SNR), this article proposes a genetic method for accurate residual radial motion estimation and well-focused imaging of the sparse stepped-frequency chirp signal (SSFCS). First, the signal model is constructed by incorporating the residual radial motion parameters into the dictionary. Then, high-quality high-resolution range profiles (HRRPs) are synthesized by Beta process regression (BPR), which has enhanced flexibility in data description and superior performance in parameter estimation. In addition, the genetic method updates the population, i.e., the candidates for the residual radial motion parameters, iteratively according to the image entropy to meet the required precision for well-focused imaging. Experimental results of Monte Carlo simulations and imaging results of simulated and measured data have demonstrated that the proposed method achieves more accurate estimation in residual radial motion parameters and better-focused imaging than the available methods.

A High-Accuracy Phase-Derived Velocity Measurement Method for High-Speed Spatial Targets Based on Stepped-Frequency Chirp Signals

In this article, we propose a phase-derived velocity measurement (PDVM) method for high-speed spatial targets based on the stepped-frequency chirp signal (SFCS). This method is capable of accurately measuring the velocity of high-speed targets and yields root-mean-squared error values at the level of centimeters per second; therefore, it has great potential for measuring the micromotion of targets and is of significant importance for target recognition. The traditional phase-derived measurement method is not applicable for high-speed targets. The main challenge that we have solved is how to extract the echo phase from the high-resolution range profile, which is corrupted by range migration, intrapulse motion, and range straddling under high-speed target conditions. To guide the implementation of the proposed method in radar systems, constraint conditions for the compensation accuracy are thoroughly derived and systematically justified under different radar parameter settings. The simulation results are presented to validate the high accuracy of the method under various circumstances. In addition, the small-amplitude micromotion measurement capability of the proposed method is verified, and reconstruction of the target micromotion trajectory is demonstrated.

Microwave Photonic Imaging Radar With a Sub-Centimeter-Level Resolution

Microwave photonic radars enable fast or even real-time high-resolution imaging thanks to its broad bandwidth. Nevertheless, the frequency range of the radars usually overlaps with other existed radio-frequency (RF) applications, and only a centimeter-level imaging resolution has been reported, making them insufficient for civilian applications. Here, we propose a microwave photonic imaging radar with a sub-centimeter-level resolution by introducing a frequency-stepped chirp signal based on an optical frequency shifting loop. As compared with the conventional linear-frequency modulated (LFM) signal, the frequency-stepped chirp signal can bring the system excellent capability of anti-interference. In an experiment, a frequency-stepped chirp signal with a total bandwidth of 18.2 GHz (16.9 to 35.1 GHz) is generated. Postprocessing the radar echo, radar imaging with a two-dimensional imaging resolution of ∼8.5 mm × ∼8.3 mm is achieved. An auto-regressive algorithm is used to reconstruct the disturbed signal when a frequency interference exists, and the high-resolution imaging is sustained.

Very High Resolution SAR Imaging With DGPS-Supported Airborne X-Band Data

High spatial resolution imaging in synthetic-aperture radar (SAR) can provide accurate monitoring capacity and has been gaining great attention recently in the fields of military and civilian. Apparently, the slant range resolution of the SAR system depends on the radar operating bandwidth. Currently, the large bandwidth signal synthesizing technology of the stepped frequency chirp signal waveform is highly practical for achieving high spatial resolution. However, the system structure and the corresponding signal processing technology become more complex. In order to verify the feasibility and operability of the large full-bandwidth system, a 3.6-GHz full-bandwidth airborne experimental SAR system operating at X-band, featured by full-bandwidth transmitting and receiving, has been designed by the Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences, as a test bed for the development and implementation of the future spaceborne realizations. For this large full-bandwidth SAR system, in addition to the hardware resource, the motion compensation (MOCO) is an urgent problem. The improvement of spatial resolution will aggravate the effect of motion errors. In order to focus the SAR images accurately, this article presents a technical approach by utilizing the differential global positioning system (DGPS) technology to improve the position accuracy of the inertial measurement unit device. Meanwhile, considering the significant deviation of range cell migration correction (RCMC) due to the residual range-variant errors, this article proposes an accurate MOCO strategy with DGPS-supported to implement the second-order MOCO, space-variant residual range envelope, and space-variant residual phase error in azimuth before RCMC. Finally, this article presents the outfield experiment and reports the corresponding analysis and processing results of an outfield flight experiment successfully conducted in March 2019.

Adaptive optimal waveform design algorithm based on frequency‐stepped chirp signal

In this study, the authors propose an adaptive optimal waveform design algorithm, based on a frequency-stepped chirp signal with arbitrary sub-pulse bandwidths and chirp slopes. The waveform is designed to maximise the signal-to-interference-plus-noise ratio at the receiver. The integral sidelobe level of an autocorrelation function is constrained at a low level, thereby increasing the detection probability of the weak echoes reflected from dim targets. An energy constraint and a low peak-to-average power ratio constraint are also taken into account owing to the flexible power allocation for interference suppression. By doing so, the radar system improves the efficiency of the transmitter power resources and avoids the non-linear effects of the power amplifier. What is more, a cyclic iterative algorithm is employed to solve the optimisation problem. At last, numerical simulation results evaluate the effectiveness of the designed waveform compared with a linear frequency modulation signal, resulting in a great improvement in the target detection performance.

A Novel Echo-Based Error Estimation and Ripple Elimination Method for Stepped Frequency Chirp SAR Signal

Stepped frequency chirp signals are widely used in synthetic aperture radar (SAR) systems to obtain high range resolution images. In practice, however, unavoidable sub-band errors caused by system and propagation errors degrade the performance of the synthetic signals. In this paper, a novel method is proposed to estimate the sub-band errors based on the overlapped spectra between adjacent sub-band signals, while most of the other methods are relied on some additional information. Besides, a filter for eliminating the ripples caused by the overlapped spectra is presented. Finally, the simulation and ground-based real data validate the method.

Time‐varying three‐dimensional interferometric imaging for space rotating targets with stepped‐frequency chirp signal

Three-dimensional (3D) radar imaging can provide abundant information about space targets, thus playing a significant role in space target recognition, measurement and cataloguing. In this study, a time-varying interferometric 3D imaging method for space rotating targets is proposed based on stepped-frequency chirp signal. In this study, with L-shaped three-antenna configuration, the interferometric signal model is first set up and high-resolution range profile (HRRP) series of the three antennas are obtained. Then through interferometric processing of HRRP series on different interferometric planes, the instantaneous spatial positions in the azimuth and pitching directions of each target scatterer are reconstructed. Combining with the instantaneous positions in range direction extracted from HRRP series, the time-varying 3D image of target can be reconstructed accordingly. Compared to existing 3D imaging method for space rotating targets, the proposed method can obtain real time-varying 3D image of target with one multi-antenna set radar. Simulation results verify the validity and robustness of the proposed method.

Precise Calibration of Channel Imbalance for Very High Resolution SAR With Stepped Frequency

Synthetic aperture radar (SAR) images require a high-resolution system for accurate interpretations. This high range resolution can be achieved by stepped frequency chirp signals. To reconstruct a wideband waveform from each subband signal, amplitude/phase/delay imbalance between the channels should be precisely compensated. In this paper, the system configuration is first presented. Further, a calibration strategy was proposed based on three calibration loops: the reference calibration, transmitting calibration, and receiving calibration loops for coarsely compensating the channel imbalance. Then, two different methods based on the cost functions were proposed to remove the residual channel imbalance. The proposed methods were validated using stepped frequency SAR data acquired by an X-band airborne SAR system with a total bandwidth of 3.6 GHz, yielding (unweighted) a 3-dB range resolution of 4 cm.

Imaging approach for airborne stepped-frequency synthetic aperture radar in the squinted mode

University of Chinese Academy of Sciences, Haidian, Beijing, ChinaAbstract. For synthetic aperture radar (SAR) imaging, a stepped-frequency chirp signal iswidely used to obtain ultrahigh range resolution. There are mainly two challenges in thestepped-frequency SAR imaging. One is the subbands synthesis, and the other is the estimationand compensation of amplitude andphase errors of the subbandscaused by the radar system andthe propagation. An imaging approach for the airborne squinted sliding-spotlight SAR withstepped-frequency chirps is proposed to achieve ultrahigh two-dimensional (2-D) resolution.Due to the squint angle, a Doppler centroid shift is introduced and then a modified space-variantcompensationmethodfortherangedifferencebetweenthesubbandsisrealizedviamultiplyingaphaserampinthe2-Dfrequencydomain.Moreover,arange-dependentphasegradientautofocusalgorithm based on raw data is proposed to estimate and compensate the residual phase errorafter the internal calibration. Afterward, the frequency-domain synthetic bandwidth method isused to complete the bandwidth synthesis. Finally, the extended Omega-K algorithm is appliedto focus the synthesized data. The simulation results and the real data processing results provethe validity of the proposed approach.

Moving target detection method for bistatic radar using random stepped-frequency chirp signal

As random stepped-frequency chirp (RSFC) signal is used in wide-band radar applications such as synthetic aperture radar (SAR) and inverse SAR. RSFC has advantages over the linear stepped-frequency chirp, including suppressing the range ambiguity, decoupling the range-Doppler coupling, and reducing the signal interference. RSFC is usually descrambled and then fed to the inverse fast Fourier transform (IFFT) to achieve a coherent integration as well as a high-resolution range. However, this method needs frequency descrambling and accurate velocity pre-estimation for moving target detection. We propose a coherent integration method based on time-dechirping for bistatic radar. This method can detect moving targets without frequency descrambling or accurate velocity pre-estimation. This paper first models the target echo mathematically and outlines the difficulties associated with the processing of IFFT for RSFC. Then the detailed principles of the proposed method are introduced and the flowchart is given. Finally, numerical simulations are conducted to verify the effectiveness of the proposed method and show its detecting ability in the presence of noise.

Moving Target's HRRP Synthesis With Sparse Frequency-Stepped Chirp Signal via Atomic Norm Minimization

Compressive sensing (CS) has been introduced into inverse synthetic aperture radar (ISAR) imaging with partial measurements. However, in the case of transmitting sparse frequency-stepped chirp signal (FSCS), the CS-based method will produce an irregular range cell migration (IRCM) problem in the recovered high-resolution range profiles (HRRPs). The IRCM is induced by the basis mismatch problem in CS, and it will degrade the ISAR image. To obviate the IRCM, an atomic norm minimization (ANM) method is proposed in this letter. By reformulating the ANM as a semidefinite program (SDP), the echo with full FSCS can be recovered using off-the-shelf SDP solvers. Thus, HRRPs without IRCM can be achieved via the conventional inverse fast Fourier transform. As a result, an improved ISAR image will be obtained. Real data results demonstrate the advantages of the proposed method over the CS-based and matrix completion-based methods.

High resolution range profile of compressive sensing radar with low computational complexity

On the basis of compressive sensing radar, this study presents a new method of reconstructing the moving target's high-resolution range profile (HRRP) with low computational complexity. With regard to the spatial sparsity of the radar scene, only a few sub-pulses of frequency-stepped chirp signal (FSCS) are used to sample the target's frequency responses. To reduce the computational complexity of traditional compressive sensing (CS) algorithm which uses FSCS to reconstruct moving target's HRRP, a dynamically deduced sensing matrix is established based on target's velocity estimation. Besides, the orthogonality of the deduced sensing matrix is analysed from the perspective of FSCS frequency encoding types to enhance the HRRP construction accuracy using CS algorithms. Numerical simulations demonstrate that the proposed method performs better than traditional algorithm with smaller estimation error and better robustness against noise.

Compressive Sensing of Stepped-Frequency Radar Based on Transfer Learning

It usually suffers from long observing time and interference sensitivity when a radar transmits the high-range-resolution stepped-frequency chirp signal. Motivated by this, only partial pulses of the stepped-frequency chirp are utilized. For the obtained incomplete frequency data, a Bayesian model based on transfer learning is proposed to reconstruct the corresponding full-band frequency data. In the training phase, a complex beta process factor analysis (CBPFA) model is utilized to statistically model each aspect-frame from a set of given full-band frequency data, whose probability density function (pdf) can be learned from this CBPFA model. It is important to note that the numbers of factors and dictionaries are automatically learned from the data. The inference of CBPFA can be performed via the variational Bayesian (VB) method. In the reconstruction phase for the incomplete frequency data that “related” to the training samples, its corresponding full-band frequency data can be analytically reconstructed via the compressive sensing (CS) method and Bayesian criterion based on the transfer knowledge of the previous pdfs learned from the training phase. About the “relatedness” between each training frame and the incomplete test frequency data, we utilize the frame condition distribution of incomplete test frequency data to represent. The proposed method is validated on the measured high range resolution (HRR) data.

Correction of Channel Imbalance for MIMO SAR Using Stepped-Frequency Chirps

To simultaneously achieve two-dimensional high resolution and wide swath in synthetic aperture radar (SAR), azimuth MIMO structure combined with stepped-frequency chirp signals was developed via splitting the antenna intoNsubapertures. During transmitting each subaperture transmits a chirp pulse at a different carrier frequency, while during receiving every subaperture receives theNscattered pulses at the same time. Separating theNscattered pulses received by each subaperture and downlinking them to the ground yieldN2different signal paths. Due to the dedicated network in the SAR system, the channel imbalance is inevitable. To correct the channel imbalance, this paper presents an external calibration method, where the channel characteristics are estimated from the peak value of a strong point target for each channel. Simulation and real raw data experiments are performed to validate the proposed method.

光学线性调频步进信号合成与高分辨测距演示

光学线性调频步进信号合成与高分辨测距演示

A novel cognitive ISAR imaging method with random stepped frequency chirp signal

The random stepped frequency chirp signal (RSFCS) has better performance in anti-jamming than that of conventional stepped frequency chirp signal (SFCS). In combination with the theory of compressing sensing (CS), a novel ISAR imaging method is proposed based on RSFCS, in which the high resolution range profile (HRRP) is reconstructed by using the conventional OMP algorithm, whereas the cognitive approach is introduced to further reduce the number of sub-pulse in RSFCS. In the proposed method, via cognizing the characteristics of moving targets, the number of sub-pulse in each burst can be adjusted adaptively. Finally, in the cross-range direction, the accurate reconstruction of ISAR image by using CS theory is implemented, which can effectively accomplish unwrapping. With the proposed method, high quality HRRP and ISAR image can be achieved with fewer sub-pulses of RSFCS and lower burst repetition frequency (BRF). Some simulation results are given to validate the effectiveness and robustness of the proposed algorithm.