Range Frequency Domain Research Articles

A Novel Chirp-Z Transform Algorithm for Multi-Receiver Synthetic Aperture Sonar Based on Range Frequency Division

When a synthetic aperture sonar (SAS) system operates under low-frequency broadband conditions, the azimuth range coupling of the point target reference spectrum (PTRS) is severe, and the high-resolution imaging range is limited. To solve the above issue, we first convert multi-receivers’ signal into the equivalent monostatic signal and then divide the equivalent monostatic signal into range subblocks and the range frequency subbands within each range subblock in order. The azimuth range coupling terms are converted into linear terms based on piece-wise linear approximation (PLA), and the phase error of the PTRS within each subband is less than π/4. Then, we use the chirp-z transform (CZT) to correct range cell migration (RCM) to obtain low-resolution results for different subbands. After RCM correction, the subbands’ signals are coherently summed in the range frequency domain to obtain a high-resolution image. Finally, different subblocks are concatenated in the range time domain to obtain the final result of the whole swath. The processing of different subblocks and different subbands can be implemented in parallel. Computer simulation experiments and field data have verified the superiority of the proposed method over existing methods.

High-resolution wide-swath SAR imaging with multifrequency pulse diversity mode in azimuth multichannel system

ABSTRACT High-resolution wide-swath (HRWS) imaging has emerged as a focal point in synthetic aperture radar (SAR) research. However, conventional SAR systems face challenges in achieving both high azimuth resolution and wide swath simultaneously due to the minimum antenna area constraint. In this paper, we propose a HRWS imaging method based on multifrequency pulse diversity (MFPD) and azimuth multichannel (AMC) technique, capable of resolving range and Doppler ambiguities concurrently. In MFPD mode, range ambiguous echoes can be separated by matched filters in the range frequency domain, as multifrequency pulses are transmitted by a single channel in the transmitter. To further enhance the ambiguity resolution ability of the system and address azimuth incoherence, a novel scheme applying the MFPD to AMC system is proposed, categorized into two distinct scenarios. 1) Uniform Sampling: This scenario satisfies the displaced phase centre antenna condition. Under this condition, high range resolution imaging can be achieved through spectrum splicing in range frequency domain, simultaneously resolving Doppler ambiguity. 2) Non-uniform Sampling: In this scenario, the ambiguous echoes are processed by spatial digital beamforming and spectrum splicing in two-dimensional frequency domain. Finally, the HRWS imaging can be obtained by performing the traditional SAR algorithm. Furthermore, the proposed method can synthesize a wideband signal from multifrequency signals, thereby enhancing the feasibility of super-high-resolution imaging. Simulation results demonstrate the effectiveness of the proposed method.

Simultaneous Measurement of Thermal Conductivity and Volumetric Heat Capacity of Thermal Interface Materials Using Thermoreflectance.

Thermal interface materials are crucial to minimize the thermal resistance between a semiconductor device and a heat sink, especially for high-power electronic devices, which are susceptible to self-heating-induced failures. The effectiveness of these interface materials depends on their low thermal contact resistance coupled with high thermal conductivity. Various characterization techniques are used to determine the thermal properties of the thermal interface materials. However, their bulk or free-standing thermal properties are typically assessed rather than their thermal performance when applied as a thin layer in real application. In this study, we introduce a low-frequency range frequency domain thermoreflectance method that can measure the effective thermal conductivity and volumetric heat capacity of thermal interface materials simultaneously in situ, illustrated on silver-filled thermal interface material samples, offering a distinct advantage over traditional techniques such as ASTM D5470. Monte Carlo fitting is used to quantify the thermal conductivities and heat capacities and their uncertainties, which are compared to a more efficient least-squares method.

Seismo-acoustic anomalous interference pattern in shallow water

In shallow water layered leaky waveguide, the sound energy below the cut-off frequency is coupled to the seismic sound field. Very low frequency (VLF) sound is propagated in both water-borne and bottom-trapped modes. Under these circumstances, the interference characteristics of sound field and its application are different from those of medium and high frequency, which is the subject of this study. In a multi-channel seismic exploration experiment in the South Yellow Sea, an anomalous interference pattern for the VLF band, e.g., the waveguide invariant of interference striations changes from positive to negative with increase of frequency, was observed in the range-frequency domain. Numerical simulations and modal analyses show that the anomalous interference pattern corresponds to the interference between waterborne modes and bottom-trapped modes, because the group velocity for these two types normal modes change differently in the VLF band.

Range-Frequency Domain Iterative Notch Filtering Method for RFI Mitigation in SAR

Range-Frequency Domain Iterative Notch Filtering Method for RFI Mitigation in SAR

Understanding and applications of striation-based beamforming in underwater acoustics

Utilizing the shallow water acoustic interference phenomenon in the range-frequency domain, striation-based beamforming (SBF) was proposed to estimate waveguide invariant and enhance active sonar output. In the past decade, SBF has also been applied to enhance LOFARgrams to improve tracking performance. In this paper, the correlation theory is used to understand SBF, and some further applications of SBF in underwater acoustic problems are also discussed. It shows that SBF essentially selects the optimal signal components with the best correlation. During the process, the correlation of array signals is improved and the ability to converge signals arriving via different paths is achieved to ensure array gain. The level of gain improvement is related to the direction of striation-based processing. Hence, a cost function can be constructed to facilitate the implementations of SBF in tasks such as striation slope estimation and source range estimation. Additionally, the SBF technique can be further applied to estimate the Green's function by introducing the cross-correlation preprocessing. Utilizing the mathematical connection between SBF and CBF, SBF can also be naturally extended to other beamforming algorithms and improve their performance, such as the subspace algorithms. The above is explained using simulation and experimental results.

A Modified Range Doppler Algorithm for High-Squint SAR Data Imaging

The high-squint airborne Synthetic Aperture Radar (SAR) has the ability to detect the target area flexibly, and the detection swath is significantly increased compared with the side-looking SAR system. Therefore, it is of great significance to carry out research on high-precision imaging methods for high-squint airborne SAR. However, the high-squint SAR echoes have large Range Cell Migration (RCM), resulting in severe range–azimuth coupling and strong spatial variation. In this paper, a Modified Range Doppler Algorithm (MRDA) is proposed to cope with these effects introduced by the significant RCM in high-squint airborne SAR imaging. The bulk compensation preprocessing is first adopted to remove the considerable RCM and severe cross-coupling in a two-dimensional frequency domain. Then, Non-Linear Chirp Scaling (NLCS) in the range direction is utilized to equalize the range-variant chirp rate caused by the residual RCM and coupling and, therefore, the consistent range phase compensation can be fulfilled in range frequency domain. The modified correlation processing is executed to compensate the residual Doppler phase modulation, the residual RCM and the range-variant cubic phase modulation, which guarantees the characteristics of high efficiency and high precision. The simulations have demonstrated that the MRDA can focus the SAR echoes with large squint angles more effectively than the algorithms based on the Linear Range Walk Correction (LRWC) method.

High-Resolution Azimuth Missing Data SAR Imaging Based on Sparse Representation Autofocusing

Due to significant electromagnetic interference, radar interruptions, and other factors, Azimuth Missing Data (AMD) may occur in Synthetic Aperture Radar (SAR) echo, resulting in severe defocusing and even false targets. An important approach to solving this problem is to utilize Compressed Sensing (CS) methods on AMD echo to reconstruct complete echo, which can be abbreviated as the AMD Imaging Algorithm (AMDIA). However, the State-of-the-Art AMDIA (SOA-AMDIA) do not consider the influence of motion phase errors, resulting in an unacceptable estimation error of the complete echo reconstruction. Therefore, in order to enhance the practical applicability of AMDIA, this article proposes an improved AMDIA using Sparse Representation Autofocusing (SRA-AMDIA). The proposed SRA-AMDIA aims to accurately focus the imaging result, even in the Phase Error AMD (PE-AMD) echo case. Firstly, a Phase-Compensation Function (PCF) based on the phase history of the scene centroid is designed. When the PCF is multiplied with the PE-AMD echo in the range-frequency domain, a coarse-focused sparse representation signal can be obtained in the range-Doppler domain. However, due to the influence of unknown PE, the sparsity of this sparse representation signal is unsatisfying, breaking the sparse constraints requirement of the CS method. Therefore, we introduced a minimum entropy autofocusing algorithm to autofocus this sparse representation signal. Next, the estimated PE is compensated for this sparse representation signal, and a more sparse representation signal is obtained. Hence, the non-PE complete echo can be reconstructed. Finally, the estimated complete echo can be used with classic imaging algorithms to obtain high-resolution imaging results under the PE-AMD condition. Simulation and real measured data have verified the effectiveness of the proposed SRA-AMDIA.

Use of Interference Patterns to Control Sound Field Focusing in Shallow Water

The possibility of controlling localized fields in multimode shallow water waveguides based on the principle of interference invariance was studied. Within the framework of the numerical experiments in a wide frequency range of 100–350 Hz and range intervals of 10–100 km, the possibilities of focusing the sound field by wavefront reversal and controlling of the focusing of the focal spot by frequency tuning in shallow water waveguides was analyzed. The focal spot scanning was carried out by frequency tuning with a fixed distribution of the sound field at receiving and transmitting vertical antenna apertures. A comparative analysis of the features of focusing and focal spot control for summer and winter stratification of the water layer was carried out. It is shown that the parameters of the focal spot during frequency tuning were more stable in the winter waveguide. It is demonstrated that the sound frequency tuning had a piecewise continuous character and was carried out on a domain of one continuous track and jump-passing on the other track in accordance with the waveguide interference fringes in the range–frequency domain.

A Modified Keystone-Based Forward-Looking Arc Array Synthetic Aperture Radar 3D Imaging Method

An arc array synthetic aperture radar (AA-SAR) is a new type of omnidirectional observation and imaging system. Based on linear array 3D imaging, this paper introduces a keystone algorithm combined with the arc array SAR 2D imaging method and proposes a modified 3D imaging algorithm based on keystone transformation. The first step is to discuss the target azimuth angle, retain the far-field approximation method of the first-order term, analyze the influence of the forward motion of the platform on the along-track position, and realize the two-dimensional focusing of the target slant range-azimuth direction. The second step is to redefine a new azimuth angle variable in the slant-range along-track imaging and use the keystone-based processing algorithm in the range frequency domain to eliminate the coupling term generated by the array angle and the slant-range time. The corrected data are used to perform along-track pulse compression to obtain the focused image of the target and realize the three-dimensional imaging of the target. Finally, in this article, the spatial resolution of the AA-SAR system in the forward-looking state is analyzed in detail, and the change in the spatial resolution of the system and the effectiveness of the algorithm are verified through simulation.

High-Resolution and Wide-Swath SAR Imaging With Sub-Band Frequency Diverse Array

High-resolution and wide-swath imaging serves as an important task for synthetic aperture radar (SAR). However, the tradeoff between high azimuth resolution and wide unambiguous swath coverage has not been well optimized in traditional SAR system. Meanwhile, the ultrawideband signal is required to obtain ultrahigh range resolution imaging. It is not easy to increase the bandwidth directly due to the difficulty of system design. To this end, this article makes notable contribution on a sub-band frequency diverse array framework to realize range ambiguous echoes separation and wideband signal synthesis from narrowband signals. By introducing a small frequency increment across the elements within each subarray, the transmit steering vector within each subarray is range-angle-dependent, making it feasible to resolve range ambiguity in the spatial frequency. In addition, the transmitted waveforms of different subarrays occupy different frequency bands in range frequency domain, which play a pivotal role in achieving high-resolution imaging. With phase compensation and sub-band frequency spectrum splicing technique, the wideband signal can be obtained. Simulation results have verified the effectiveness of the proposed approach.

An Extended Frequency Scaling Algorithm for Bistatic SAR With High Squint Angle

Bistatic synthetic aperture radar (BiSAR) is an extended and complementary observation method to conventional monostatic SAR remote sensing. When high range and azimuth resolution are required in BiSAR, the transmitting platform, i.e., the LEO satellite, should work in the spotlight or sliding spotlight mode, which means a wide bandwidth Chirp signal is transmitted, and the targets are illuminated for a long enough time as well. In order to reduce the sampling frequency in the receiving system and improve the efficiency of the focusing procedure for this BiSAR configuration, the echoes should be dechirp received. A bistatic extended frequency scaling algorithm (Bi-EFSA) is proposed in this paper to deal with the dechirp received bistatic SAR echoes. The first step of Bi-EFSA is the range walk correction in the 2-D time domain, which reduces the space variance of the range curvatures and removals the serious coupling between range and azimuth caused by the high squint angle. After that, the range compression is achieved by secondary range compression (SRC) and bulk shift. Then, the space variance of the azimuth frequency modulation rate, introduced by the range walk correction step, is corrected by implementing the azimuth nonlinear chirp scaling (ANCS) operation. Following this, the focused results in the range frequency and azimuth time domain are obtained by the azimuth compression. The point targets and extended-scene simulations validate the effectiveness of the proposed algorithm.

Airborne Elevation DBF-TOPS SAR/InSAR Method Based on LOS Motion Compensation and Channel Error Equalization

Digital beamforming (DBF) TOPS SAR in elevation is a new synthetic aperture radar (SAR) system, which has the advantage of wide swath coverage and a high signal-to-noise ratio (SNR). In this paper, considering the phase preservation demand for interferometric SAR (InSAR) processing, the complete processing chain for DBF-TOPS SAR/InSAR in elevation is proposed with a wide beam angle and channels’ amplitude and phase errors. Firstly, we analyze the airborne motion compensation method along the line-of-sight direction for TOPS SAR with squint angle. Furthermore, for the large-range beam angle of DBF, the sub-swaths division process is presented for the range-dependent radar look angle, and the sub-swaths division criterion is also given in the analytic expression. Then, the relative amplitude and phase errors’ estimation and compensation method between channels is provided in the range frequency domain based on the pivoting filter with coherence weighting, which is convenient for DBF processing and SNR improvement. Finally, the DEMs are generated under different conditions to compare the phase preservation performance. The effectiveness of the proposed processing chain is verified with both simulated data and airborne real DBF-TOPS SAR/InSAR data.

Maneuvering Target Coherent Integration and Detection in PRI-Staggered Radar Systems

As for a new-style radar, the random pulse repetition interval (PRI) pulse waveform may be transmitted, and then the target Doppler parameter estimation precision and detection ability by using the conventional techniques may be invalid due to the irregular signal sampling. To solve these problems, this letter proposes a simple, yet effective and quasi-optimal coherent integration method with random pulse resampling. The proposed method first reconstructs the nonuniformly sampled signal into a uniform grid in the range frequency domain based on the modified sinc interpolation theory. Then, a matched filtering function related to the target chirp parameter is constructed in order to eliminate the residual coupling between range and azimuth. Finally, a moving target can be well imaged after performing the target motion compensation.

Abnormal interference of very low frequency sound field in shallow water

In a multi-channel seismic exploration experiment in the South Yellow Sea, a tuned air gun array with a shooting interval of 37.5m was used as broadband pulse source, and a horizontal line array with 336 elements is used to receive transmitted signals. The received single shot records in the range-time domain are transformed into an interference pattern in the range-frequency domain using Fourier transform. It is found that there is an abnormal interference pattern of the very low frequency (VLF) sound field in the stratified shallow water environment. It is a complex nonlinear structure, no longer regular striations in the range-frequency domain. The mechanism of this particular interference pattern is interpreted according to normal mode theory. In shallow water stratified leaky waveguide, VLF sound propagates as waterborne modes and bottom-trapped modes. These two kinds of normal mode interfere with each other and form the particular stable interference pattern. In the experimental environment, the group speeds for these two type normal modes change differently with frequency. And it causes slope of interference striations change from positive to negative with increase of frequency. The theoretical simulation results are in good agreement with the experimental data. It is shown that the structure of interference pattern is sensitive to bottom structure and geoacoustic parameters.

A Fast Two-Dimensional Velocity Estimation Method for Multi-Channel UWB SAR

Moving target detection in ultra-wideband synthetic aperture radar (UWB SAR) has to accumulate target energy with long integration time to improve the probability of target detection. The traditional detection and parameters estimation algorithms usually rely on parameter searching, leading to a heavy computing burden. In this paper, a fast two-dimensional velocity estimation method of moving target for multi-channel UWB SAR is proposed. The method processes the multi-channel data separately to realize the target's coherent accumulation and one-dimensional velocity estimation. Then the multi-channel signals are processed jointly to realize the two-dimensional velocity estimation. Specifically, for each channel, the second-order keystone transform is used to correct the range curvature. The symmetric autocorrelation function in the range-frequency domain is used to accumulate the moving-target energy, achieving the target detection and target's azimuth signal extraction. Next, considering the long integration time, the azimuth signal is processed by the non-uniform cubic phase function (NUCPF) based on the fourth-order phase signal to estimate the relative velocity. The azimuth signal is transformed into the Doppler domain for multi-channel data, and the interferometric signal is calculated. The phase generated by the interferometric signal is related to the radial velocity of the target. Thus, the two-dimensional velocity of the target is obtained. Finally, the effectiveness of the algorithm is verified by simulation experiments.

Performance Metrics for Striation-based Beamforming and Application Requirements with the Horizontal Line Array in Shallow Water

Due to the dispersion of normal modes in shallow water, there exist regular striations on the interference spectrogram in space-frequency domain. Based on the range-frequency domain striations, waveguide invariant can be estimated with the prior knowledge of source range. Utilizing striations along the array, Rouseff and Zurk [J. Acoust. Soc. Amer. 130 (2011) EL76–EL81] proposed the striation-based beamforming (SBF), which shows a theoretical possibility to estimate waveguide invariant that is independent of source range. To make this beamforming technique more practical, its application requirements and performance limitation should be defined. These two issues are researched with the phase and amplitude relationships deduced by the frequency-shift compensation theory. It shows the source whose spectrum varies slowly and received signals that contain the complete information of transmission time are keys for applying SBF to real work. The azimuth limitation can lead to the degradation of array gain and distortion of interference structure. Matching parameters of waveguide invariant and source range, respectively, two modified striation-based beamformers are developed to eliminate the azimuth limitation. Simulation and experimental results are presented.

FDBP-InSAR: An Efficient Algorithm for InSAR Imaging via Frequency Domain Back Projection

High-quality focusing with accurate phase-preserving is a significant and challenging step in interferometric synthetic aperture radar (InSAR) imaging. Compared with conventional frequency-based imaging algorithms, the time-domain back-projection algorithm (TDBPA) can greatly ensure the accuracy of imaging and phase-preserving by point-to-point coherent integration but suffers from huge computational complexity. In this paper, we propose an efficient InSAR imaging method, called a frequency-domain back-projection algorithm (FDBPA), to achieve high-resolution focusing and accurate phase-preserving of InSAR imaging. More specifically, FDBPA is utilized to replace the traditional point-to-point coherent integration of TDBPA with frequency-domain transform. It divides the echo spectrum into uniform grids and transforms the range compression data into the range frequency domain. Phase compensation and non-uniform Fourier transform of the underlying scene are implemented to achieve image focusing in the wavenumber domain. Then, the interferometric phase of the target scene can be preserved by accurate phase compensation of the target’s distance. FDBPA avoids the repetitive calculation of index values and point-to-point coherent integration which reduces the time complexity compared with TDBPA. The characteristics of focusing and phase-preserving of our method are analyzed via simulations and experiments. The results demonstrate the efficiency and high-quality imaging of the FDBPA method. It can improve the imaging efficiency by more than three times, while keeping similar imaging accuracy compared with TDBPA.

Signal Modeling and Analysis for Elevation Frequency Scanning HRWS SAR

Elevation frequency scanning synthetic aperture radar (EF-SCAN SAR) can isolate range ambiguities in the range-frequency domain. Therefore, range ambiguity suppression can be accomplished through range-frequency bandpass filtering, which can outperform spatial filtering-based ambiguity suppression. In this article, the analytic space–time signal model of an intrapulse frequency scanning array is derived. Based on the analysis of the characteristics of this signal model, waveform design criteria for EF-SCAN SAR are developed to effectively separate the range ambiguities in the range frequency domain. The ground echo model of EF-SCAN SAR is also developed based on this space–time signal model. The impact of intrapulse frequency scanning on the performance of high-resolution and wide-swath (HRWS) imaging is analyzed based on the derivation and analysis of the echo spectrum. Finally, an imaging algorithm for EF-SCAN SAR is developed based on this analysis. Numerical simulations verify the effectiveness of the proposed waveform design criteria and imaging algorithm.

Multi-Channel SAR System Design for HRWS and GMTI in Low PRF

High-resolution and wide-swath (HRWS) is an important challenge in synthetic aperture radar (SAR). Combined SAR with array, the azimuth dual-channel SAR configuration achieves high azimuth resolution and HRWS in low Pulse repetition frequency (PRF) by doppler band synthesizing technology. However, low PRF introduces ambiguity to ground moving target indication (GMTI). Interferometry is performed between two look data in the range frequency domain to resolve the ambiguity by decreasing the interferometry phase. As a result, the phase becomes insensitive to the radial velocity of moving targets. This condition brings difficultly in moving target detection. Two channels together with two equivalent channels are exploited fully to solve these problems. The four-channel interferometry is also conducted to improve the GMTI performance. Parameters, including system and motion parameters, are estimated unambiguously to complete HRWS imaging and GMTI. System parameter design is also considered to satisfy the requirements of HRWS and GMTI simultaneously. Simulations demonstrate the validity of the proposed methods.