Bandwidth Extrapolation Research Articles

PyBWE: Python tools for Bandwidth Extrapolation of planetary radar signals

PyBWE: Python tools for Bandwidth Extrapolation of planetary radar signals

Range resolution enhancement of SHAllow RADar (SHARAD) data via bandwidth extrapolation technique: Enabling new features detection and improving geophysical investigation

The SHAllow RADar (SHARAD) is a subsurface sounding radar provided by the Italian Space Agency (ASI) as a facility instrument for NASA's Mars Reconnaissance Orbiter (MRO) mission, the second longest-lived mission to orbit Mars after Mars Odyssey. Developed by an Italian-US Team, SHARAD was designed to investigate to depth of up to one kilometer in the Martian subsurface and to map dielectric discontinuities associated with compositional and/or structural changes. The radar mapping began in November 2006 and, after 16 years of operations, SHARAD has mapped most of the planet's surface (∼55%), contributing a data volume for the entire MRO mission that exceeds that of all the past Mars missions combined.Designed to complement the lower-frequency, relatively narrower bandwidth capability of the MARSIS sounding radar, SHARAD emits an 85μs, frequency-modulated (10 MHz) chirp at a central frequency of 20 MHz to increase the signal-to-noise ratio (SNR) and achieve a finer resolution compared to MARSIS. On the ground, echoes recorded by the radar are range compressed using conventional pulse compression techniques yielding a nominal range resolution of 15 m (vacuum, 5–8 m in typical Martian materials). Additionally, synthetic aperture processing is performed in along-track to increase the resolution up to 300–500 m.Throughout the entire mission duration, SHARAD provided a diverse and extensive range of imaging data. It was able to observe the internal structures of Planum Boreum and Planum Australe, two icy deposits that contain the North and South Polar Layered Deposits (NPLD-SPLD), thought to contain valuable information about the planet's past climate. The radar unveiled the massive deposits of buried CO2 ice below the southern residual ice cap (SRIC), which confirmed the influence of the planet obliquity and insolation in the accumulation of dry ice. Furthermore, it revealed the intricate lava flows structures in the Tharsis Volcanic region, suggesting that the planet experienced deposition by multiple volcanic episodes.However, radar resolution often poses a limitation for subsurface investigations in many regions. Only recently, processing techniques have focused on enhancing SHARAD radargrams vertical resolution by implementing the Bandwidth Extrapolation (BWE) technique. This approach has demonstrated an improvement of the vertical resolution while preserving the time-of-arrival (TOA) and amplitude of the detected echoes. The resulting super-resolved data products exhibit better separation between radar returns, thus improving the overall understanding of the investigated terrains. The obtained results demonstrate the value of implementing the BWE techniques in the data processing pipeline whenever radar sounders are involved.

Multi-Task Learning for Low-Frequency Extrapolation and Elastic Model Building From Seismic Data

Low-frequency signal content in seismic data as well as a realistic initial model are key ingredients for robust and efficient full-waveform inversions. However, acquiring low-frequency data is challenging in practice for active seismic surveys. Data-driven solutions show promise to extrapolate low-frequency data given a high-frequency counterpart. While being established for synthetic acoustic examples, the application of bandwidth extrapolation to field datasets remains non-trivial. Rather than aiming to reach superior accuracy in bandwidth extrapolation, we propose to jointly reconstruct low-frequency data and a smooth background subsurface model within a multi-task deep learning framework. We automatically balance data, model and trace-wise correlation loss terms in the objective functional and show that this approach improves the extrapolation capability of the network. We also design a pipeline for generating synthetic data suitable for field data applications. Finally, we apply the same trained network to synthetic and real marine streamer datasets and run an elastic full-waveform inversion from the extrapolated dataset.

Reduced-Complexity Decimeter-Level Bluetooth Ranging in Multipath Environments

In this paper, we investigate enhanced super-resolution range estimators with decimeter-level accuracy for multi-antenna and multipath Bluetooth systems. To enhance the traditional MUSIC range estimator for a two-way frequency-hopping Bluetooth channel model, we apply forward-backward averaging and bandwidth extrapolation using Burg’s algorithm to improve ranging accuracy, which is limited by the used Bluetooth bandwidth and the quality of the estimated sample covariance matrix. For the multi-antenna case, we compare the Summed Antenna Processing and Individual Antenna Processing methods to process multiple-antenna Bluetooth channel measurements and enhance the range estimation accuracy compared to the single-antenna case. In addition, we investigate a sparsity-aware range estimator which exploits the sparsity of Bluetooth channel impulse response and achieves comparable ranging accuracy to the enhanced MUSIC estimator but at a much lower computational complexity. We apply the greedy Orthogonal Matching Pursuit algorithm to heuristically solve the sparsity-constrained optimization problem for Bluetooth ranging. Furthermore, we evaluate the computational complexity of our investigated Bluetooth range estimators with two complexity-reduction techniques to further reduce the complexity of MUSIC range estimator. Moreover, we analyze the Cramer-Rao Lower Bound (CRLB) on unbiased range estimation using the frequency-hopping Bluetooth channel model and derive a new insightful CRLB expression for a two-path channel model. Finally, we evaluate the Root-Mean-Square Error and Empirical Cumulative Distribution Function performance of our investigated range estimators both on simulated and real-world Bluetooth data that we collected in line-of-sight (LOS) and non-line-of-sight (NLOS) multipath scenarios. Our proposed enhancements on the range estimators improved the ranging accuracy by 58% for our collected Bluetooth data.

Range resolution enhancement of WISDOM/ExoMars radar soundings by the Bandwidth Extrapolation technique: Validation and application to field campaign measurements

The ExoMars 2022 rover mission has been designed to search for traces of life, past or present, on Mars and more specifically below its hostile surface. This will be the first mission able to collect samples down to 2 ​m in the Martian subsurface, where organic molecules and bio-signatures may be preserved. The images of the subsurface (or radargrams) provided by the ground penetrating radar WISDOM onboard the ExoMars rover will be key to select the safest and scientifically most relevant locations for drilling. However, the vertical resolution of WISDOM radargrams is limited (to ~5.5 ​cm in a typical soil of dielectric constant 4) by the bandwidth of the instrument when applying classical processing techniques. Here we propose to enhance WISDOM radargrams vertical resolution by implementing the Bandwidth Extrapolation (BWE) technique. We demonstrate that this technique yields an improvement of WISDOM vertical resolution by a factor of 3 while well preserving the time of arrival and amplitude of the detected echoes. We validate the BWE technique on synthetic data before applying it to experimental observations acquired both in controlled and natural environments. The resulting super-resolved radargrams greatly improve our understanding of the investigated terrains with a better separation of echoes from underground reflectors, and demonstrate the value of implementing the BWE technique in the WISDOM data processing pipeline which will ultimately provide images of the Martian subsurface down to a few meters depth with a vertical resolution of ~2 ​cm in typical soils.

High-Resolution Range-Doppler Maps by Coherent Extension of Narrowband Pulses

The range resolution of radar is inversely proportional to the swept bandwidth. However, this bandwidth may not be available due to a variety of reasons, including spectrum congestion and lack of instantaneous bandwidth despite access to a larger tunable bandwidth. Existing approaches to achieving high-range resolution include bandwidth extrapolation, ultrawideband coherent processing, and spectral splicing of narrowband stepped-frequency pulses. In this article, we achieve high-range resolution of a wideband chirp from a sequence of narrowband pulses using coherent-phase extension of the beat tones of an FMCW dechirper. By phase matching the beat tones across pulse boundaries, the algorithm trades a longer observation interval for a smaller swept bandwidth. Phase matching of the short beat tones is applied in two steps to first obtain the coarse estimate of the beat frequencies which are then used as the starting point in the formation of the range-Doppler map that now enjoys the two-dimensional fast-Fourier transform (2-D-FFT) gain. With this approach, a fraction of the total bandwidth to obtain a range resolution of a wideband chirp is used. Using both simulations and experimental data, the proposed high-resolution algorithm is applied to a narrowband chirp sequence with bandwidth B to generate range-Doppler maps with range resolution corresponding to a wideband chirp sequence of bandwidth NB.

Boundary absorption approximation in the spatial high-frequency extrapolation method for parametric room impulse response synthesis.

The spatial high-frequency extrapolation method extrapolates low-frequency band-limited spatial room impulse responses (SRIRs) to higher frequencies based on a frame-by-frame time/frequency analysis that determines directional reflected components within the SRIR. Such extrapolation can be used to extend finite-difference time domain (FDTD) wave propagation simulations, limited to only relatively low frequencies, to the full audio band. For this bandwidth extrapolation, a boundary absorption weighting function is proposed based on a parametric approximation of the energy decay relief of the SRIR used as the input to the algorithm. Results using examples of both measured and FDTD simulated impulse responses demonstrate that this approach can be applied successfully to a range of acoustic spaces. Objective measures show a close approximation to reverberation time and acceptable early decay time values. Results are verified through accompanying auralizations that demonstrate the plausibility of this approach when compared to the original reference case.

Resolution enhancement for ISAR imaging via improved statistical compressive sensing

Developing compressed sensing (CS) theory reveals that optimal reconstruction of an unknown signal can be achieved from very limited observations by utilizing signal sparsity. For inverse synthetic aperture radar (ISAR), the image of an interesting target is generally constructed by limited strong scattering centers, representing strong spatial sparsity. Such prior sparsity intrinsically paves a way to improved ISAR imaging performance. In this paper, we develop a super-resolution algorithm for forming ISAR images from limited observations. When the amplitude of the target scattered field follows an identical Laplace probability distribution, the approach converts super-resolution imaging into sparsity-driven optimization in the Bayesian statistics sense. We show that improved performance is achievable by taking advantage of the meaningful spatial structure of the scattered field. Further, we use the nonidentical Laplace distribution with small scale on strong signal components and large scale on noise to discriminate strong scattering centers from noise. A maximum likelihood estimator combined with a bandwidth extrapolation technique is also developed to estimate the scale parameters. Real measured data processing indicates the proposal can reconstruct the high-resolution image though only limited pulses even with low SNR, which shows advantages over current super-resolution imaging methods.

Bandwidth extrapolation of LFM signals for narrowband radar systems

Existing bandwidth extrapolation (BWE) techniques developed for wideband radar systems use stretch processing. A major drawback of these BWE techniques is that the range depth of interest (RDOI) can only be a small fraction of the radar unambiguous distance. This drawback restricts existing BWE techniques from being applied to narrowband radar systems where the RDOI can extend to a significant fraction of the radar unambiguous distance. To address this problem, we formulate a new BWE technique based on matched filtering (MF) and show that the proposed approach allows the RDOI to be as large as the radar unambiguous distance. We demonstrate the capability of the proposed method using both simulated data and real data collected from an over-the-horizon (OTH) radar system. We show that the proposed technique successfully resolves closely spaced targets where conventional range-Doppler (RD) processing technique has failed and is capable of improving the range resolution in the presence of stationary clutter that is 20–50 dB stronger than the targets. In addition to range resolution improvement, we observe that the proposed technique also improves the signal-to-noise ratio (SNR) of the targets.

Analysis on the Resolution of Polarimetric Radar and Performance Evaluation of the Polarimetric Bandwidth Extrapolation Method

Polarimetric radar provides useful information on scattering mechanisms, and advances in polarimetric synthetic aperture radar (POLSAR) technology have shown the effect of polarization information on various applications. The disadvantage of POLSAR is low azimuth resolution capability. Since the effective pulse repetition frequency (PRF) in each polarimetric channel of POLSAR is half the total PRF, the resolution is twice as low as the single-polarization SAR. This drawback may be mitigated by employing a superresolution method designed for polarimetric radar such as polarimetric bandwidth extrapolation (PBWE), previously proposed by the authors. Thus far, the authors only empirically showed that polarization information helps in improving resolution via numerical simulations. In this paper, theoretical analysis on the resolution of a polarimetric radar is provided. Along with the resolution, estimation accuracy of the polarization property of the target is studied. In the analysis, we employ the recently proposed metric called the statistical resolution limit (SRL) that provides the highest resolution achievable by any unbiased parametric spectral estimator. The SRL of polarimetric radar is derived and compared with that of single-polarization radar. The Cramér–Rao bound (CRB) of the polarization estimation error of the polarimetric radar is also derived. The complexified full Fisher information matrix and the CRBs of signal parameters are derived first for the general multichannel signal in nonwhite Gaussian noise. Then, the SRL and the polarization estimation error are derived using the CRBs of signal parameters for the cases where two point targets are closely located. It is shown analytically and numerically that the polarization information helps in improving the SRL. It is also shown that the polarimetric processing significantly improves the accuracy of the polarization estimation when two targets are located closer than the Fourier resolution cell. Finally, the performance of the PBWE is evaluated via simulations and is compared to the SRL and the CRB for the polarization estimation.

Generating dense and super-resolution ISAR image by combining bandwidth extrapolation and compressive sensing

Recent developing compressive sensing (CS) theory indicates that it is possible to obtain precise recovery of a sparse signal from very limited measurements, which provides a new way for data acquisition and signal processing as nature signals usually involve some degree of sparsity. In this paper, we present an algorithm for inversed synthetic aperture radar (ISAR) imaging with super resolution by combining CS and bandwidth extrapolation (BWE) technique. For ISAR imaging, the backscattering field of target is usually contributed by a few strong scattering centers, whose number is much less than that of image pixels. Thus, CS is intuitively suitable for constructing super resolution ISAR image. According to CS theory, the number of extracted dominating scatterers relies on the signal length, which indicates that if only limited data is available, it is difficult to generate dense ISAR image robustly by CS, and some signal components tend to lose. To soften this constraint, BWE is combined with CS imaging to increase the degree of freedom of signal while preserving its coherence. A refined CS-based formation for ISAR image-resolution enhancement is then developed. Both real and simulated data experiments are performed to evaluate the proposed approach, and an example of using this technique demonstrates the enhanced image resolution in application of maneuvering target imaging.

A super-resolution algorithm for synthetic aperture radar based on modified spatially variant apodization

The existing spatially variant apodizations (SVAs) either cannot depress the sidelobes effectively or reduce the energy of the mainlobe. To improve this, a modified SVA (MSVA) is put forward in this paper, which expands the traditional filter from 3-taps to 5-taps and sets relevant parameters according to different sampling rates to get the excellent result that satisfies constrained optimization theory. A modified super-SVA is also presented, which compares the result after the iteration with the original signal and makes the one whose amplitude is smaller as the initial value of the next iteration. This method can eliminate the sidelobes produced by the intermediate operation, so that the following bandwidth extrapolation is more available. Super-MSVA is presented based on the modified SVA and modified super-SVA, which is suitable for any Nyquist sampling rate, can extrapolate the signal bandwidth many times through iteration with a commensurate improvement in resolution, as demonstrated by the result of the experiment.

A Two-Dimensional Bandwidth Extrapolation Technique for Polarimetric Synthetic Aperture Radar Images

The resolution of a synthetic aperture radar (SAR) image, in range and azimuth, is determined by the transmitted bandwidth and the synthetic aperture length, respectively. Various superresolution techniques for improving resolution have been proposed, and we have proposed an algorithm that we call polarimetric bandwidth extrapolation (PBWE). To apply PBWE to a radar image, one needs to first apply PBWE in the range direction and then in the azimuth direction, or <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vice versa </i> . In this paper, PBWE is further extended to the 2-D case. This extended case (2D-PBWE) utilizes a 2-D polarimetric linear prediction model and expands the spatial frequency bandwidth in range and azimuth directions simultaneously. The performance of the 2D-PBWE is shown through a simulated radar image and a real polarimetric SAR image

Advances in non-linear apodization

Selected new methods and applications of non-linear apodization for irre gula rly-shaped and parse coherent apertures and arrays are presented. The benefits include unproved impulse response performance, i.e., reduced peak sidelobes and integrated sidelobe power, along with impr oved mainlobe res olution, compared to classic windowing techniques. Non-linear apodization (NLA) techniques can also strve as powerful engines for effective superresolution and bandwidth extrapolation of coherent data for filling spars e apertures. The sparse aperture filling property of superresolution algorithms for radar data forms the basis for a new concept which is introd uced here: Synthetic Multiple Aperture Radar Technology (SMART). Increased swath and/or reduced antenna size are some of the benefits postu lated for SMART applied to synthetic aperture radar (SAR) systems. The benefits of the se new methods and applications for non-linear apodization are then demonstrated for two specific applications: 1) sidelobe control for Y -type synthetic aperture radiometers, such as the European Soil Moisture and Ocean Salinity (SMOS) system [12] and JPL's propos ed GeoSTAR [13] concept; and, 2) ftlling of spa rse synthetic apertur e radar data by exploiting the band width extrapolation properties of non-linear apodization based superresolution techniques. The methods that have been developed and demonstrated herein have potential application to a wide range of passive and active microwave remote sensing and radar systems.

Analysis of the limit to superresolution in incoherent imaging

Superresolution algorithms have demonstrated impressive image-restoration results in the space domain. We consider the limits on superresolution performance in terms of usable bandwidth of the restored frequency spectrum. On the basis of a characterization of the spectral extrapolation errors (viz., null objects), we derive an expression for an approximate bound on accurate bandwidth extension for the general class of superresolution algorithms that incorporate a priori assumptions of a nonnegative, space-limited object. It is shown that accurate bandwidth extension is inversely related to the spatial extent of the object and the noise level in the image. For superresolution of sampled data, we present preliminary results relating bandwidth extrapolation to the difference between sampling rate and the discrete optical cutoff frequency. Simulation results are presented that substantiate the derived bandwidth extrapolation bounds.