Nonlinearity Correction Algorithm for Wideband FMCW Radars

International audienceThis paper presents a novel nonlinearity correction algorithm for wideband frequency modulated continuous wave (FMCW) radars based on high-order ambiguity functions (HAF) and time resampling. By emphasizing the polynomial phase nature of the FMCW signal, it is shown that the HAF is an excellent tool for estimating the sweep nonlinearity polynomial coefficients. The estimated coefficients are used to build a correction function which is applied to the beat signal by time resampling . The nonlinearity correction algorithm is tested by simulation and validated on real data sets acquired with an X-band FMCW radar

FMCW Transceiver Wideband Sweep Nonlinearity Software Correction

International audienceThis paper presents a novel sideband sweep nonlinearity software correction method for a frequency modulated continuous wave (FMCW) transceiver based on the high-order ambiguity function (HAF) and time resampling. By emphasizing the polynomial-phase nature of the FMCW signal, it is shown that the HAF processing algorithm is well suited for estimating the sweep nonlinearity coefficients. The estimated coefficients are used to build a correction function which is applied by resampling the beat signal on each sweep interval. The sweep nonlinearity correction procedure is validated on real data acquired with a low-cost X-band T/R module

A LINEARIZATION METHOD FOR A UWB VCO-BASED CHIRP GENERATOR USING DUAL COMPENSATION

Ultra-Wideband (UWB) chirp generators are used on Frequency Modulated Continuous Wave (FMCW) radar systems for high-resolution and high-accuracy range measurements. At the Center for Remote Sensing of Ice Sheets (CReSIS), we have developed two UWB radar sensors for high resolution measurements of surface elevation and snow cover over Greenland and Antarctica. These radar systems are routinely operated from both surface and airborne platforms. Low cost implementations of UWB chirp generators are possible using an UWB Voltage Controlled Oscillator (VCO). VCOs possess several advantages over other competing technologies, but their frequency-voltage tuning characteristics are inherently non-linear. This nonlinear relationship between the tuning voltage and the output frequency should be corrected with a linearization system to implement a linear frequency modulated (LFM) waveform, also known as a chirp. If the waveform is not properly linearized, undesired additional frequency modulation is found in the waveform. This additional frequency modulation results in undesired sidebands at the frequency spectrum of the Intermediate Frequency (IF) stage of the FMCW radar. Since the spectrum of the filtered IF stage represents the measured range, the uncorrected nonlinear behavior of the VCO will cause a degradation of the range sensing performance of a FMCW radar. This issue is intensified as the chirp rate and nominal range of the target increase. A linearization method has been developed to linearize the output of a VCO-based chirp generator with 6 GHz of bandwidth. The linearization system is composed of a Phase Lock Loop (PLL) and an external compensation added to the loop. The nonlinear behavior of the VCO was treated as added disturbances to the loop, and a wide loop bandwidth PLL was designed for wideband compensation of these disturbances. Moreover, the PLL requires a loop filter able to attenuate the reference spurs. The PLL has been designed with a loop bandwidth as wide as possible while maintaining the reference spur level below 35 dBc. Several design considerations were made for the large loop bandwidth design. Furthermore, the large variations in the tuning sensitivity of the oscillator forced a design with a large phase margin at the average tuning sensitivity. This design constraint degraded the tracking performance of the PLL. A second compensation signal, externally generated, was added to the compensation signal of the PLL. By adding a compensation signal, which was not affected by the frequency response effects of the loop compensation, the loop tracking error is reduced. This technique enabled us to produce an output chirp signal that is a much closer replica of the scaled version of the reference signal. Furthermore, a type 1 PLL was chosen for improved transient response, compared to that of the type 2 PLL. This type of PLL requires an external compensation to obtain a finite steady state error when applying a frequency ramp to the input. The external compensation signal required to solve this issue was included in the second compensation signal mentioned above. Measurements for the PLL performance and the chirp generator performance were performed in the laboratory using a radar demonstrator. The experimental results show that the designed loop bandwidth was successfully achieved without significantly increasing the spurious signal level. The chirp generator measurements show a direct relationship between the bandwidth of the external compensation and the range resolution performance

Analyse temps-frequence et traitement des signaux RSO à haute résolution spatiale pour la surveillance des grands ouvrages d'art

The thesis is composed of two research axis. The first one consists in proposing time-frequency signal processing tools for frequency modulated continuous wave (FMCW) radars used for displacements measurements, while the second one consists in designing a spaceborne synthetic aperture radar (SAR) signal processing methodology for infrastructure monitoring when an external point cloud of the envisaged structure is available. In the first part of the thesis, we propose our solutions to the nonlinearity problem of an X-band FMCW radar designed for millimetric displacement measurements of short-range targets. The nonlinear tuning curve of the voltage controlled oscillator from the transceiver can cause a dramatic resolution degradation for wideband sweeps. To mitigate this shortcoming, we have developed two time warping-based methods adapted to wideband nonlinearities: one estimates the nonlinear terms using the high order ambiguity function, while the other is an autofocus approach which exploits the spectral concentration of the beat signal. Onwards, as the core of the thesis, we propose a novel method for scattering centers detection and tracking in spaceborne SAR images adapted to infrastructure monitoring applications. The method is based on refocusing each SAR image on a provided 3D point cloud of the envisaged infrastructure and identifying the reliable scatterers to be monitored by means of four dimensional (4D) tomography. The refocusing algorithm is compatible with stripmap, spotlight and sliding spotlight SAR images and consists of an azimuth defocusing followed by a modified back-projection algorithm on the given set of points which exploits the time-frequency structure of the defocused azimuth signal. The scattering centers of the refocused image are detected in the 4D tomography framework by testing if the main response is at zero elevation in the local elevation-velocity spectral distribution. The mean displacement velocity is estimated from the peak response on the zero elevation axis, while the displacements time series for detected single scatterers is computed as double phase difference of complex amplitudes.Finally, we present the measurement campaigns carried out on the Puylaurent water-dam and the Chastel landslide using GPS measurements, topographic surveys and laser scans to generate the point clouds of the two structures. The comparison between in-situ data and the results obtained by combining TerraSAR-X data with the generated point clouds validate the developed SAR signal processing chain.Cette thèse s'articule autour de deux axes de recherche. Le premier axe aborde les aspects méthodologiques liés au traitement temps-fréquence des signaux issus d'un radar FMCW (à onde continue modulée en fréquence) dans le contexte de la mesure des déplacements fins. Le second axe est dédié à la conception et à la validation d'une chaîne de traitement des images RSO (radar à synthèse d'ouverture) satellitaire. Lorsqu'un maillage 3D de la structure envisagée est disponible, les traitements proposés sont validés par l'intercomparaison avec les techniques conventionnelles d'auscultation des grands ouvrages d'art.D'une part, nous étudions la correction de la non-linéarité d'un radar FMCW en bande X, à courte portée, conçu pour la mesure des déplacements millimétriques. La caractéristique de commande non linéaire de l'oscillateur à large bande, entraine une perte de résolution à la réception. Afin de pallier cet inconvénient, nous avons développé deux méthodes basées sur le ré-échantillonnage temporel (time warping) dans le cas des signaux à large bande non-stationnaires. La première approche estime la loi de fréquence instantanée non linéaire à l'aide de la fonction d'ambiguïté d'ordre supérieur, tandis que la deuxième approche exploite la mesure de concentration spectrale du signal de battement dans un algorithme d'autofocus radial.D'autre part, nous proposons un cadre méthodologique général pour la détection et le pistage des centres de diffusion dans les images RSO pour la surveillance des grands ouvrages d'art. La méthode est basée sur la ré-focalisation de chaque image radar sur le maillage 3D de l'infrastructure étudiée afin d'identifier les diffuseurs pertinents par tomographie 4D (distance – azimut – élévation – vitesse de déformation). L'algorithme de ré-focalisation est parfaitement compatible avec les images RSO acquises dans les différents modes (« stripmap », « spotlight » et « sliding spotlight ») : dé-focalisation en azimut suivie par rétroprojection modifiée (conditionnée par la structure temps-fréquence du signal) sur l'ensemble donné des points. Dans la pile d'images ré-focalisées, les centres de diffusion sont détectés par tomographie 4D : test de conformité à l'hypothèse d'élévation zéro dans le plan élévation – vitesse de déformation. La vitesse moyenne correspond au maximum à l'élévation zéro, tandis que la série temporelle des déplacements est obtenue par double différence de phase des amplitudes complexes pour chaque diffuseur pertinent.Nous présentons également les campagnes in situ effectuées au barrage de Puylaurent (et glissement de Chastel) : les relevés GPS, topographiques et LIDAR sol employées au calcul des maillages 3D. La comparaison entre les déplacements mesurés in situ et les résultats obtenus par l'exploitation conjointe de la télédétection RSO satellitaires et les maillages 3D valident la chaîne de traitement proposée.Teza cuprinde două axe principale de cercetare. Prima axă abordează aspecte metodologice de prelucraretimp-frecvenţă a semnalelor furnizate de radare cu emisie continuă şi modulaţie de frecvenţă (FMCW)în contextul măsurării deplasărilor milimetrice. În cadrul celei de-a doua axe, este proiectată şi validatăo metodă de prelucrare a imaginilor satelitare SAR (radar cu apertură sintetică) ce este destinatămonitorizării infrastructurii critice şi care se bazează pe existenţa unui model 3D al structurii respective.În prima parte a tezei, sunt investigate soluţii de corecţie a neliniarităţii unui radar FMCW în bandaX destinat măsurării deplasărilor milimetrice. Caracteristica de comandă neliniară a oscilatorului debandă largă determină o degradare a rezoluţiei în distanţă. Pentru a rezolva acest inconvenient, au fostelaborate două metode de corecţie a neliniarităţii, adaptate pentru semnale de bandă largă, ce se bazeazăpe conceptul de reeşantionare neuniformă sau deformare a axei temporare. Prima abordare estimeazăparametrii neliniarităţii utilizând funcţii de ambiguitate de ordin superior, iar cea de-a doua exploateazăo măsură de concentraţie spectrală a semnalului de bătăi într-un algoritm de autofocalizare în distanţă.În a doua parte a lucrării, este propusă o metodologie generală de detecţie şi monitorizare a centrilorde împrăştiere în imagini SAR în scopul monitorizării elementelor de infrastructură critică. Metoda sebazează pe refocalizarea fiecărei imagini radar pe un model 3D al structurii investigate în scopul identificăriicentrilor de împrăştiere pertinenţi (ţinte fiabile ce pot fi monitorizate în timp) cu ajutorul tomografiei SAR4D (distanţă-azimut-elevaţie-viteză de deplasare). Algoritmul de refocalizare este compatibil cu imaginiSAR achiziţionate în moduri diferite (« stripmap », « spotlight » şi « sliding spotlight ») şi constă într-odefocalizare în azimut urmată de o retroproiecţie modificată (condiţionată de structura timp-frecvenţă asemnalului) pe modelul 3D al structurii. Ţintele sunt identificate în stiva de imagini refocalizate cu ajutorultomografiei 4D prin efectuarea unui test de conformitate cu ipoteza că centrii de împrăştiere pertinenţivor avea elevaţie zero în planul local elevaţie-viteză. Viteza medie de deformare corespunde maximuluide pe axa de elevaţie nulă, iar seria temporară a deplasărilor se obţine printr-o dublă diferenţă de fază aamplitudinilor complexe corespunzătoare ţintelor identificate.În final sunt prezentate campaniile de măsurători pe teren efectuate la un baraj şi o alunecare de terendin regiunea Puylaurent (Franţa) destinate obţinerii modelului 3D al celor două elemente de infrastructurăprin măsurători GPS, topografice şi LIDAR. Comparaţia între deformările măsurate pe teren şi rezultateleobţinute prin combinarea imaginilor SAR cu modelele 3D au permis validarea metodologiei propuse

Long-Range Imaging Radar for Autonomous Navigation

This thesis describes the theoretical and practical implementation of a long-range high-resolution millimetre wave imaging radar system to aid with the navigation and guidance of both airborne and ground-based autonomous vehicles. To achieve true autonomy, a vehicle must be able to sense its environment, comprehensively, over a broad range of scales. Objects in the immediate vicinity of the vehicle must be classified at high resolution to ensure that the vehicle can traverse the terrain. At slightly longer ranges, individual features such as trees and low branches must be resolved to allow for short-range path planning. At long range, general terrain characteristics must be known so that the vehicle can plan around difficult or impassable obstructions. Finally, at the largest scale, the vehicle must be aware of the direction to its objective. In the past, short-range sensors based on radar and laser technology have been capable of producing high-resolution maps in the immediate vicinity of the vehicle extending out to a few hundred metres at most. For path planning, and navigation applications where a vehicle must traverse many kilometres of unstructured terrain, a sensor capable of imaging out to at least 3km is required to permit mid and long-range motion planning. This thesis addresses this need by describing the development a high-resolution interrupted frequency modulated continuous wave (FMICW) radar operating at 94GHz. The contributions of this thesis include a comprehensive analysis of both FMCW and FMICW processes leading to an effective implementation of a radar prototype which is capable of producing high-resolution reflectivity images of the ground at low grazing angles. A number of techniques are described that use these images and some a priori knowledge of the area, for both feature and image based navigation. It is shown that sub-pixel registration accuracies can be achieved to achieve navigation accuracies from a single image that are superior to those available from GPS. For a ground vehicle to traverse unknown terrain effectively, it must select an appropriate path from as long a range as possible. This thesis describes a technique to use the reflectivity maps generated by the radar to plan a path up to 3km long over rough terrain. It makes the assumption that any change in the reflectivity characteristics of the terrain being traversed should be avoided if possible, and so, uses a modified form of the gradient-descent algorithm to plan a path to achieve this. The millimetre wave radar described here will improve the performance of autonomous vehicles by extending the range of their high-resolution sensing capability by an order of magnitude to 3km. This will in turn enable significantly enhanced capability and wider future application for these systems

Investigation of Non-coherent Discrete Target Range Estimation Techniques for High-precision Location

Ranging is an essential and crucial task for radar systems. How to solve the range-detection problem effectively and precisely is massively important. Meanwhile, unambiguity and high resolution are the points of interest as well. Coherent and non-coherent techniques can be applied to achieve range estimation, and both of them have advantages and disadvantages. Coherent estimates offer higher precision but are more vulnerable to noise and clutter and phase wrap errors, particularly in a complex or harsh environment, while the non-coherent approaches are simpler but provide lower precision. With the purpose of mitigating inaccuracy and perturbation in range estimation, miscellaneous techniques are employed to achieve optimally precise detection. Numerous elegant processing solutions stemming from non-coherent estimate are now introduced into the coherent realm, and vice versa. This thesis describes two non-coherent ranging estimate techniques with novel algorithms to mitigate the instinct deficit of non-coherent ranging approaches. One technique is based on peak detection and realised by Kth-order Polynomial Interpolation, while another is based on Z-transform and realised by Most-likelihood Chirp Z-transform. A two-stage approach for the fine ranging estimate is applied to the Discrete Fourier transform domain of both algorithms. An N-point Discrete Fourier transform is implemented to attain a coarse estimation; an accurate process around the point of interest determined in the first stage is conducted. For KPI technique, it interpolates around the peak of Discrete Fourier transform profiles of the chirp signal to achieve accurate interpolation and optimum precision. For Most-likelihood Chirp Z-transform technique, the Chirp Z-transform accurately implements the periodogram where only a narrow band spectrum is processed. Furthermore, the concept of most-likelihood estimator is introduced to combine with Chirp Z-transform to acquire better ranging performance. Cramer-Rao lower bound is presented to evaluate the performance of these two techniques from the perspective of statistical signal processing. Mathematical derivation, simulation modelling, theoretical analysis and experimental validation are conducted to assess technique performance. Further research will be pushed forward to algorithm optimisation and system development of a location system using non-coherent techniques and make a comparison to a coherent approach

A Compact, Reconfigurable, Multi-UWB Radar for Snow Thickness Evaluation and Altimetry: Development and Field Trials

We developed a portable ultra-wideband radar system capable of reconfigurable operation in multiple frequency bands (separate or simultaneous) spanning from microwaves through millimeter waves. The instrument provides a compact solution for fine-resolution measurements of elevation changes and superficial snow/firn thickness from low-altitude, mid-sized airborne platforms. In this article, we provide an overview of the radar system design and its performance during laboratory testing. We demonstrate its application in aerial surveys of snow layer thickness at S/C bands, dual-band airborne altimetry at Ku-/Ka-bands, and present first-order comparisons with coincident airborne lidar data

Optimized Synthetic Aperture Radar (SAR) processing for Airborne UWB FMCW Radar

Remote Sensing of snow covered sea ice in melting Polar Regions has become crucial in estimating the results of increased global warming and to overcome the Earth’s energy imbalance. And to accurately map the snow models over sea ice, it has become essential to build radar systems that has increased sensitivity and to use post processing techniques that enhance the performance. The Center for Remote Sensing of Ice Sheets (CReSIS) at KU has developed ultra-wideband snow radar system that operates over 2-18 GHz frequency range to effectively measure the snow thickness including very thin snow cover and map the snow-ice and snow-ice interfaces precisely. Synthetic Aperture Radar (SAR) processing is one of the post processing technique employed to further increase the sensitivity of the radar in terms of resolution and SNR. In this thesis, a time domain correlation SAR technique which is essentially a matched filter application is described and implemented. It is verified initially with an ideal simulated point target data and then with point target data collected by the snow radar system over sea-ice. Both gave the results as expected with the theoretical values. It is also shown how noise is multiplied with increasing synthetic aperture length. The effect of aircraft motion non-linearities on SAR processing are also studied at different altitudes. To overcome the effect of non-linearities and multiplicative noise, a multilooking SAR processing is proposed and explained. This is then applied to the field data collected by the snow radar in 2014 to 2017 over sea ice and observed that the azimuth resolution is improved by 4 m approximately. The optimum parameters like SAR aperture length and the number of looks are extracted based on the results of SAR processing on various data sets. Finally, a comparison of SAR application to low and high altitude data sets collected in 2016 over the same region is also provided to show that longer apertures are required for high altitude to achieve same amount of improvement in SNR and azimuth resolution

Remote vital signs monitoring using a mm-wave FMCW radar

A vision on the migration from contact standard health monitoring measurement devices to non-contact measurement technologies has gained a tremendous attention in literature and in industry. A promising method for realizing the remote measurement of vital signs is using electromagnetic radars such as frequency modulated continuous wave (FMCW) radars. However, using these radars has challenges to precisely acquire the respiration and heart rates. A solution for higher accurate measurement of the vital signs can be the use of mm-wave frequencies, which gives a high-resolution sensing of displacements in an environment in the order of sub-mm changes. On the other hand, being in mm-wave bands increases both hardware and signal processing designs and implementations. In this work, a mm-wave radar is used to monitor the breathing and the heart rates as well as their waveforms for further clinical diagnostics. To that end, we established a complete analysis of the FMCW radars principles by considering hardware impairments. The analysis considers the effect of antenna coupling, RF cross-talk, stationary clutters, phase noise, IQ imbalances, and the thermal noise. Also, the effect of the individual hardware imperfections on the phase quality is shown by simulations and experiments. The simulations are carried out with a Matlab Simulink model. For the experiments, Texas Instruments (TI) mm-wave FMCW radars have been used. To earn insight into vital signs monitoring, different experiments are designed. In the experiments, the effect of the thermal instability of the RF parts on the phase is shown. In addition, to mimic the behaviour of the chest vibration due to respiration and the heartbeats, a two-pendulum system is designed and tested. Particularly, the pendulum system performance in terms of vibration frequency estimations of the two pendulums versus distance is then measured. In the simulations, the system performance is obtained for different signal to noise ratios (SNR) and different phase noise levels, as well as different stationary clutters. Finally, to test the TI sensors for different directions to the subjects, Hexoskin smart garment is used as a reference sensor, which is a reliable commercial product. Our results show great system improvement in terms of accuracy of the vital signs detection in comparison to other similar research. For different sleep positions, the accuracy of HR and BR are greater than 94\% and 96\%, respectively. In addition to detecting the vital rates, we have shown that their waveforms can also be reconstructed by using an adaptive optimum filter