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

Short-Range FMCW Radar Platform for Millimetric Displacements Measurement

International audienceA frequency modulated continuous wave (FMCW) radar platform for millimetric displacement measurements of short-range targets is presented in this paper. The platform's transceiver is based on a heterodyne architecture because the beat frequency is relatively small for short-range targets and it can be placed in the frequency range influenced by the specific homodyne architecture problems: DC offset, self-mixing and 1/f noise. The platform's displacement measurement capability was tested on range profiles and SAR images acquired for various targets. The displacements were computed from the interferometric phase. The displacements errors were situated below 0.1 mm for metallic bar targets placed at a few meters from the radar

Short-range wideband FMCW radar for millimetric displacement measurements

International audienceThe frequency modulated continuous wave (FMCW) radar is an alternative to the pulse radar when the distance to the target is short. Typical FMCW radar implementations have a homodyne architecture transceiver which limits the performances for short-range applications: the beat frequency can be relatively small and placed in the frequency range affected by the specific homodyne issues (DC offset, self-mixing and 1/f noise). Additionally, one classical problem of a FMCW radar is that the voltage controlled oscillator adds a certain degree of nonlinearity which can cause a dramatic resolution degradation for wideband sweeps. This paper proposes a short-range X-band FMCW radar platform which solves these two problems by using a heterodyne transceiver and a wideband nonlinearity correction algorithm based on high-order ambiguity functions and time resampling. The platform's displacement measurement capability was tested on range profiles and synthetic aperture radar (SAR) images acquired for various targets. The displacements were computed from the interferometric phase and the measurement errors were situated below 0.1 mm for metal bar targets placed at a few meters from the 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

Deconvolution Method for Eliminating Reference Signal Coupling/Reflections in Bistatic SAR

Bistatic radar receivers that use an opportunistic transmitter require a reference channel to capture the original transmitted signal, which is then used as a reference signal for constructing the matched-filter during the range compression step. Because the reference signal is received from line-of-sight, it is orders in magnitude larger than the reflections captured by the receive channel. It is generally difficult to construct the system such that the reference signal is not leaked into the received signal, either via coupling in the circuitry or via reflections off objects in the vicinity of the receiver. Due to its much larger amplitude, the reference signal can easily mask smaller targets with its side-lobes. In this paper we propose a novel deconvolution method for bistatic SAR images as a means of eliminating leakage of the reference signal

SAR Images Refocusing and Scattering Center Detection for Infrastructure Monitoring

International audienceInfrastructure monitoring applications can require the tracking of slowly moving points of a certain structure. Given a certain point from a structure to be monitored, in the context of available SAR products where the image is already focused in a slant range - azimuth grid, it is not obvious if this point is the scattering center, if it is in layover or if it is visible from the respective orbit. This paper proposes a refocusing procedure of SAR images on a set of measured points among with a 4D tomography based scattering center detection. The refocusing procedure consists of an azimuth de-focusing followed by a modified back-projection on the given set of points. The presence of a scattering center at the given positions is detected by computing the local elevation-velocity plane for each point and testing if the main response is at zero elevation. The refocusing and scattering center detection algorithm is validated on real data acquired with the TerraSAR-X satellite during March-June 2012. The mean displacement velocities of the detected scatterers show good agreement with the in-situ measurements

Estimation d'un signal complexe à partir d'un modèle parcimonieux perturbé

International audienceDans ce travail nous abordons le problème de l'estimation, en présence de bruit, d'un signal à valeurs complexes admettant une représentation parcimonieuse dans une famille paramétrique de vecteurs dont les paramètres sont connus de manière imprécise. Nous formulons ce problème d'estimation comme celui de la minimisation d'une fonction de coût non convexe sous contraintes non convexes. Un algorithme de type explicite-implicite (forward-backward) permet d'apporter une solution numérique à ce problème d'optimisation. La mise en oeuvre de cet algorithme nécessite le calcul d'un opérateur proximal dont nous donnons la forme exacte. Nous montrons que la méthode proposée peut être vue comme une généralisation d'une technique de seuillage dur itératif. En utilisant des résultats récents d'analyse non lisse, nous étudions la convergence de l'algorithme d'optimisation employé. Par ailleurs, nous illustrons le bon comportement numérique de l'approche proposée sur des exemples d'analyse spectrale parcimonieuse

A CONSTRAINED OPTIMIZATION APPROACH FOR COMPLEX SPARSE PERTURBED MODELS

In this paper, we consider the problem of estimating a complex-valued signal having a sparse representation in an uncountable family of vectors. The available observations are corrupted with an additive noise and the elements of the dictionary are parameterized by a scalar real variable. By a linearization technique, the original model is recast as a constrained sparse perturbed model. An optimization approach is then proposed to estimate the parameters involved in this model. The cost function includes an arbitrary Lipschitz differentiable data fidelity term accounting for the noise statistics, and an ℓ0 penalty. A forward-backward algorithm is employed to solve the resulting nonconvex and non-smooth minimization problem. This algorithm can be viewed as a generalization of an iterative hard thresholding method and its local convergence can be established. Simulation results illustrate the good practical performance of the proposed approach when applied to spectrum estimation

Range Autofocusing for FMCW Radars Using Time Warping and a Spectral Concentration Measure

International audienceThis paper proposes a novel range autofocusing algorithm for linear frequency modulated continuous wave radars based on time warping and a spectral concentration measure. The algorithm deals with the estimation and correction of nonlinearities caused by the voltage controlled oscillator's nonlinear tuning curve and assumes that this curve is described by an a priori known model and depends only on a few unknown parameters. The procedure is based on time warping the beat signal in turn with every function resulted from different model parameters combinations and evaluating the concentration of the warped signal's spectrum. The estimated nonlinearity parameters of the model are the ones which provide the best spectral concentration. The algorithm is tested with simulations and real data provided by an X-band radar

Cramer-Rao Bound for a Sparse Complex Model

4pComplex-valued data play a prominent role in a number of signal and image processing applications. The aim of this paper is to establish some theoretical results concerning the Cramer-Rao bound for estimating a spars complex-valued vector. Instead of considering a countable dictionary of vectors, we address the more challenging case of an uncountable set of vectors parameterized by a real variable. We also present a proximal forward-backward algorithm to minimize an l0 penalized cost, which allows us to approach the derived bounds. These results are illustrated on a spectrum analysis problem in the case of irregularly sampled observations