Résumé: The scattering of an electromagnetic wave by agricultural tilled soils is studied by using the first-order small-slope approximation. The rough surface is the superposition of two levels of roughness.A two-dimensional Gaussian random process describes the small-scale roughness, and a two-dimensional narrow-band Gaussian random process defined around a certain spatial frequency describes the largescale component. The incoherent intensity obtained by the small-slope approximation is expressed as a combination of three terms. The first term is the intensity of small-scale roughness multiplied by an attenuation factor, the second is that of large-scale roughness multiplied by an attenuation factor and the third is the coupling intensity between the two roughness levels. When the surface is illuminated perpendicularly to the furrows and the conditions are right, the Floquet modes can be observed in the signature of the largescale roughness. These effects are not observable for an impingingwave parallel to the furrows. Knowing that the correlation lengths of the large-scale roughness are much larger than those of the small-scale component, we derive an approximate expression for the coupling intensity which then depends only on the small-scale roughness spectrum and the root-mean-square height of the large-scale spectrum. Resulting expressions are studied for a cloddy sowing soil and a ploughed soil in monostatic configurations, in L- and C-bands.We also analyze the influence of the anisotropy of the large-scale roughness component autocorrelation function on the electromagnetic signature.

Résumé: The polarization state of electromagnetic (EM) waves scattered from a random medium is given within the Poincaré space by the three normalized Stokes parameters. Polarimetric radar data are frequently multilook processed to reduce signal fluctuations by spatially averaging the scattered signals. In this article, a universal probability law is established, applicable to each of the three normalized Stokes parameters for multilook configurations and valid for a multivariate Gaussian model. As an application case, we consider the scattering of a polarized monochromatic plane wave from a stratified ground with an arbitrary number of slightly rough interfaces. Resulting expressions are studied for a snowy ground in L-band and are validated by comparison with Monte Carlo simulations.

Résumé: ithin the framework of the rst-order small perturbation method, we derive the statistics of the layered rough surface index and the normalized difference polarization index for three-dimensional layered structures with slightly rough interfaces illuminated by a monochromatic plane wave and for multilook returns. We establish closed-form expressions for the probability density function and cumulative distribution function. The rst- and second-order moments are given by relation recurrences. We validate from Monte Carlo simulations the obtained theoretical formulas.

Résumé: The polarization state of waves scattered from multilayered structures with randomly rough boundaries is given by the Stokes vector and its four components. Polarimetric radars use multilook processing to reduce statistical fluctuations by spatially averaging the scattered signals. In this article, we obtain and express the probability density function, the cumulative density function, the expected value, and the variance for each Stokes parameter in the multilook case in closed form. The slightly rough boundaries are the realizations of second-order stationary centered Gaussian bidimensional spatial random processes, and the layered structure is illuminated by a monochromatic plane wave. The zenithal and azimuthal components of the far scattered electric field are obtained from the first-order small perturbation method. The theory leads to a multivariate Gaussian model. Finally, we obtain a universal function for the probability distribution for the last three Stokes parameters. Numerical simulations are performed and coincide with the theoretical derivations. For a ground snow system represented by three interfaces air/snow cover/frozen soil/unfrozen soil, we obtain the marginal probabilities and compare the theoretical results with Monte Carlo simulations. We show that the marginal probability distributions for multilook data are very different from those for single-look returns. Some features of coherent phenomena are observed since multilook processing reduced statistical fluctuations.

Résumé: Horizontally stratified structures are commonly used to represent naturally occurring structures, such as soils. The electromagnetic signature of such a medium illuminated by radar and the polarization state of the scattered wave are fully determined by the knowledge of the four Stokes parameters. In this article, we determine the statistics of the four Stokes parameters for the signal scattered by layered structures with an arbitrary number of slightly rough interfaces. The rough interfaces are realizations of second-order stationary centered Gaussian stochastic processes and the layered structure is illuminated by an elliptically polarized monochromatic wave. The zenithal and azimuthal components of the far scattered electric field are derived from the first-order small perturbation method. The derivation leads to a multivariate Gaussian model for the underlying complex scattered amplitudes, and we establish the closed-form expressions of the probability density function, the cumulative density function, and the first- and second-order moments for the four Stokes parameters. For an observation direction outside the incidence plane, we establish the condition on the incidence wave parameters for which the zenithal and azimuthal components are uncorrelated. For an air/snow cover/frozen soil/unfrozen soil structure, we analyze the marginal probabilities and validate the theory by comparison with Monte Carlo simulations. More generally, when the two complex components of the field scattered by the illuminated zone are Gaussian random variables, these statistics offer possibilities for in-depth investigating the polarization of scattering processes from random media.

Résumé: We study the scattering of a linearly polarized electromagnetic plane wave by a two-dimensional random slightly rough surface separating the vacuum from a chiral medium. We implement the first-order small perturbation method (SPM) and the first-order small slope approximation (SSA) and determine the analytical expressions of the coherent and incoherent intensities. The effects of chirality on the polarization of the wave scattered within the vacuum are analyzed. The coherent intensity has a cross-polarized component as well as the incoherent intensity in the incidence plane. We show that there are configurations for which a total polarization coupling occurs with the co-polarized incoherent intensity equal to zero.

Résumé: The authors derive the distribution of the phase difference between two multilook scattering signals for a multilayer stack with randomly rough surfaces under a plane wave excitation. First, for infinite slightly rough surfaces described by Gaussian centred stochastic processes, the authors show that the underlying complex scattering signals follow a Gaussian joint distribution. Also, it is demonstrated that this property is within the scope of the first‐order perturbation theory. Secondly, the authors use this joint probability law to derive the closed‐form expression for the probability density function of the phase difference. The theoretical formula is verified by comparison with Monte‐Carlo simulations.

Résumé: The goal of the present paper is on retrieving the electrical and geometrical parameters of a stratified medium with two rough interfaces. The inversion problem is formulated as a cost function optimization problem, and it is solved using the simulated annealing algorithm. The cost function consists in the integrated squared deviation between the co-polarized incoherent intensities obtained from the Small Slope Approximation and those obtained from the Small Perturbation Method. The inversion scheme is applied to the electrical and geometrical parameters involved into the analytical expressions of the incoherent intensities given by the SPM. We study the influence of the shape of the autocorrelation function and the isotropy factor upon the estimation of parameters. We test the sensitivity of the inversion scheme to noisy synthetic data. The study is applied to snow-covered soils in L-band. For the configurations under study, we show that the inverse method is efficient for eightparameter or ten-parameter predicting problems.

Résumé: We derive the statistics for the multilook intensity ratio for a multilayered medium bounded by randomly rough surfaces. Calculations are carried out in the context of the first-order small perturbation method and assume slightly rough surfaces of infinite extent and centered Gaussian height distributions. We show that the probability distributions for the co- and cross-polarized intensity ratios for -look data are functions of three parameters and that the mean exists for n>1 and the variance for n>2. The obtained theoretical expressions are verified by comparison with the Monte Carlo results.

Résumé: We determine the probability distribution of the normalized difference polarization index (NDPI) for a stack of slightly rough interfaces illuminated by a plane wave. For infinite surface areas and Gaussian-centered height distributions, we show within the framework of the first-order small perturbation method that the co- and cross-polarized NDPIs are random variables, the probability laws of which depend only on two parameters. Contrary to the intensity ratio which follows a heavy-tailed distribution, the NDPI has finite mean and variance. For a sand layer covering a granite surface and Gaussian correlation functions, we analyze the combined influence of the anisotropy and cross correlation upon the probability laws.

Résumé: In this paper we determine the statistical distributions of the co-and cross-polarized Layered Rough Surface Index (LRSI) for three-dimensional layered structures with an arbitrary number of slightly rough interfaces illuminated by an electromagnetic plane wave. For infinite surface areas and Gaussian centered height distributions, we show within the framework of the first-order small perturbation method that the LRSI under a given observation direction is a random variable, whose statistical distribution is only function of two parameters. Contrary to the intensity ratio which follows a heavy-tailed distribution, the LRSI has finite mean and variance. For a structure air/clayey soil/rock, we analyze the influence of a snow layer upon the probability laws in the cases of Gaussian or exponential correlation functions.

Résumé: We determine the statistical distributions for the co- and cross-polarized scattered intensity ratios characterizing three-dimensional layered structures with an arbitrary number of rough interfaces illuminated by a plane wave. Within the framework of the first-order small perturbation method, we show for slightly rough interfaces with infinite surface areas and Gaussian height distributions that the intensity ratio is a random variable, the probability law of which is a function of two parameters. For air/clayey soil/rock structures, we analyze the influence of a snow layer upon the probability laws and we validate the closed-form formulae by comparison with Monte-Carlo simulations.

Résumé: Orthogonal Frequency Division Multiplexing (OFDM) is of great interest for the development of the fifth-generation technology. It is the cornerstone of Multiple-input multiple-output (MIMO) systems. Even though inter carrier interference (ICI) and inter symbol interference (ISI) have been processed for the fourth-generation standards, they still present a huge problem for the fifth-generation standards. This paper explores the tradeoff between the length of the cyclic prefix and the performances of the OFDM system. It also studies the effect of carrier frequency offset (CFO) on OFDM systems. A blind frequency offset estimator that uses the correlations between the remodulated sequence in the receiver side and the conventional received symbol is presented and a closed form solution is derived. The proposed estimator is derived under short interval when the correlation is high, so it has low computational complexity. Lin and Beek’s estimators are used for comparison. Simulations demonstrate the effectiveness of the proposed estimator under Rayleigh fading channel.

Résumé: In this paper, we study the level crossing rate (LCR) and the average fade distance (AFD) of signal scattering from layered rough surfaces. First, we implement the first-order perturbation method, and we establish the analytical expression of the joint probability density function (PDF) of the modulus of the field filtered by a sensor and its spatial derivative. We also consider the case of the field intensity. Then, we derive from the joint PDF the closed-form formulas for the LCR and the AFD as functions of the statistical parameters of rough interfaces. Numerical simulations are conducted to validate the theoretical results and show that the second-order descriptors are very sensitive to the values of cross-correlation parameters of rough interfaces.

Résumé: This paper explores common speech signal representations along with a brief description of their corresponding analysis–synthesis stages. The main focus is on adaptive sinusoidal representations where a refined model of speech is suggested. This model is referred to as Refined adaptive Sinusoidal Representation (R_aSR). Based on the performance of the recently suggested adaptive Sinusoidal Models of speech, significant refinements are proposed at both the analysis and adaptive stages. First, a quasi-harmonic representation of speech is used in the analysis stage in order to obtain an initial estimation of the instantaneous model parameters. Next, in the adaptive stage, an adaptive scheme combined with an iterative frequency correction mechanism is used to allow a robust estimation of model parameters (amplitudes, frequencies, and phases). Finally, the speech signal is reconstructed as a sum of its estimated time-varying instantaneous components after an interpolation scheme. Objective evaluation tests prove that the suggested R_aSR achieves high quality reconstruction when applied in modeling voiced speech signals compared to state-of-the-art models. Moreover, transparent perceived quality was attained using the R_aSR according to results obtained from listening evaluation tests.

Résumé: We study the scattering of electromagnetic wave from a 2-D random rough surface that separates the vacuum from a perfect electromagnetic conductor (PEMC). We implement the first-order perturbation method and the first-order small-slope approximation and we establish the analytical expressions of the coherent and incoherent intensities. In contrast with the two special cases, the perfect electric conductor and the perfect magnetic conductor, the coherent intensity reflected by the PEMC has a cross-component. We also show that there is a depolarization in the incidence plane and that there are configurations, where the wave depolarization is complete and the incoherent intensity is reduced to its cross-component.

Résumé: Within the framework of the first-order small perturbation method (SPM), we establish some statistical and spatial properties of signal scattering by 2-D slightly rough random surfaces. The work concerns the total field within the intermediate field-zone for an ergodic and stationary Gaussian surface under illumination by a monochromatic plane wave. For infinite extension surfaces, we obtain the probability density functions (pdfs) for the modulus and phase of the total field components. The modulus pdf is expressed as an infinite sum of modified Bessel functions while the phase pdf is expressed in terms of the error function. Under oblique illumination, the total field is not wide-sense stationary. From a spatial point of view, for a given elevation and under all incidences, we show that the total field is ergodic to the second order. Under oblique incidence, the spatial distribution of the total field modulus is a Rayleigh law and the phase is uniform. Under normal incidence, we establish that the spatial and statistical distributions are interchangeable.

Résumé: The sea-ice thickness, a key parameter in Arctic studies, is derived from radar altimeter height measurements of the freeboard, taking into account not only snow load, but also the penetration depth of the electromagnetic waves inside the snow—this is the not generally the case. Within the framework of the small slope approximation method, we study in Ku-band (f=13GHz, λ =2.31cmin the air) the electromagnetic signature of an air/snow/sea ice rough layered medium. The snow is inhomogeneous and is represented as a stack of several layers with different relative permittivities. We show that the electromagnetic response is very sensitive to the isotropy factor of the air/snow interface and to the cross-correlation parameters of interfaces.

Résumé: We determine the statistical distributions of the copolarized and cross-polarized phase differences of fields scattered from a stack of two 2-D rough interfaces in any observation plane. This communication is carried within the framework of the first-order small perturbation method. The probability laws are established for Gaussian distributions of heights and for infinite extension interfaces. We show that, outside the incidence plane, the cross-polarized phase difference is not uniformly distributed and contains information about the stratified medium.

Résumé: For Speech Synthesis, the understanding of the physical and mathematical models of speech is essential. Hence, Speech Modeling is a large field, and is well documented in literature. The aim in this paper is to provide a background review of several speech models used in speech synthesis, specifically the Source Filter Model, Linear Prediction Model, Sinusoidal Model, and Harmonic/Noise Model. The most important models of speech signals will be described starting from the earlier ones up until the last ones, in order to highlight major improvements over these models. It would be desirable a parametric model of speech, that is relatively simple, flexible, high quality, and robust in re-synthesis. Emphasis will be given in Harmonic / Noise Model, since it seems to be more promising and robust model of speech.

Résumé: We propose a theoretical study on the electromagnetic wave scattering from three-dimensional layered structures with an arbitrary number of rough interfaces by using the small perturbation method and the small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not, isotropic or not. The electromagnetic field in each medium is represented by a continuum of plane waves and a perturbation theory is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitudes under the first-order small slope approximation are deduced from results derived from the first-order small perturbation method. We analyze with the small slope approximation model the combined influence of the anisotropy and cross-correlation upon the electromagnetic signature of a natural stratified structure.

Résumé: We propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using the small perturbation method and the small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not. The electromagnetic field in each medium is represented by a Rayleigh expansion and a perturbation method is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitude under the first-order small slope approximation are deduced from results derived from the first-order small perturbation method. Comparison between these two analytical models and a numerical method based on the combination of scattering matrices is presented.

Résumé: We present statistical properties of signal scattering by two-dimensional slightly rough random surface. The work concerns the intermediate-field zone. Calculations are carried out within the framework of the first-order small perturbation method. The surface is assumed to be ergodic and stationary and the height distribution to be Gaussian. Under an oblique incidence, we demonstrate that the first-order scattered field is not wide-sense stationary. For a given altitude, under the normal incidence,the scattered field is a strictly stationary random process. By using the stationary phase method, we show that the scattered field becomes asymptotically a strictly stationary random process when increasing the altitude of the observation point.We also define the condition that must be satisfied by an antenna transfer function so that the measured scattered field becomes stationary and ergodic.

Résumé: We determine the probability law of the ratio between the co-polarized intensities scattered from a stack of two two-dimensional rough interfaces in the incidence plane. Calculations are carried out within the framework of the first-order small perturbation method. For slightly rough interfaces with infinite length and Gaussian height distributions, we show that the probability density function is only a function of two parameters and has an infinite average and an infinite variance. For a sand layer on a granite surface in backscattering configurations, we study the influence of the incidence angle and the cross-spectral density upon this probability law.

Résumé: We propose a statistical study of the scattering of an incident plane wave by a stack of two two-dimensional rough interfaces. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. The electromagnetic fields are represented by Rayleigh expansions, and a perturbation method is used for solving the boundary value problem and determining the first-order scattering amplitudes. For slightly rough interfaces with a finite extension, we show that the modulus of the co- and cross-polarized scattering amplitudes follows a Hoyt law and that the phase is not uniformly distributed. For interfaces with an infinite extension, the modulus follows a Rayleigh law and the phase is uniformly distributed. We show that these results are true for correlated or uncorrelated interfaces and for isotropic or anisotropic interfaces.

Résumé: We determine the statistical distribution of the co-polarized phase difference of fields scattered from a stack of two two-dimensional rough interfaces in the incidence plane. The electromagnetic fields are represented by Rayleigh expansions and a perturbation method is used to solve the boundary value problem and to determine the first-order scattering amplitudes. For slightly rough interfaces with infinite length and Gaussian height distributions, we show that the probability density function is only a function of two parameters. For a sand layer on a granite surface in backscattering configurations, we study the influence of the incidence angle, the layer thickness, the cross-spectral density and the wave frequency upon both parameters of the probability law.

Résumé: We present a statistical study of electromagnetic wave scattering by a stack of two random rough interfaces that are characterised by Gaussian distributed heights and by exponential correlation functions. These interfaces can be correlated or not. The coherent and incoherent intensities and the statistical distribution of the scattered field in modulus and phase are obtained using the Rayleigh expansion and the small perturbation method. For a structure of finite extension, we show that the modulus follows a Hoyt law and the phase is not uniform. For a structure of infinite extension, whether the interfaces are correlated or not, the modulus of the field follows a Rayleigh law while the phase is uniform.

Résumé: In the framework of the small perturbation method, we present a new theoretical derivation of the statistical and spatial properties of a field scattered by a one-dimensional slightly rough random surface. The work concerns the intermediate field zone where the scattered field is reduced to the contribution of the progressive plane waves. The surface is assumed to be stationary, ergodic and Gaussian. First, from a statistical point of view, we demonstrate that under oblique incidence the scattered field is not stationary while it is strictly stationary under normal incidence. For an infinite surface, the scattered field modulus obeys to Hoyt law and the phase is not uniform. Second, from a spatial point of view, for a given altitude and under all incidences, we show that the scattered field is ergodic. Under oblique incidence, the phase is spatially uniform and the modulus is given by a Rayleigh law. Under normal incidence, the phase is not uniform and the modulus is given by a Hoyt law. Third, from a practical point of view, we show that the field measured by a directional antenna is ergodic and stationary if the angular transfer function of the antenna does not contain the specular direction.

Résumé: This article presents an original method for the theoretical analysis of the intensity radiated by a dielectric waveguide with rough walls. The method is based on Maxwell's equations under their covariant form written in nonorthogonal coordinate systems adapted to the geometry of the waveguide. The solutions are found by using a perturbation method starting from a guide with smooth walls. The statistical characteristics of the radiant intensity, the mean value, and the probability density function are analytically determined.

Résumé: This paper presents an original method of analyzing radiation loss from dielectric slab with random wall imperfections. The method is based on Maxwell's equations under their covariant form written in a nonorthogonal coordinate system. The solution is found by using a perturbation method applied to the smooth surface problem. The statistical characteristics of the radiation intensity, the average value and the probability density function, are analytically determined.

Résumé: In order to study the problems of scattering by rough metallic surfaces, we have used Maxwell's equations in covariant form within the framework of a non-orthogonal coordinates system adapted to the geometry of the problem. Electromagnetic fields are written in Fourier's integral form. The solution is found by using a perturbation method applied to the smooth surface problem; this is fully justified when the defects are of small magnitude. For the direct problem, the mean value of diffraction intensity is obtained for random rough surfaces of finite conductivity by computer simulation. In the case of the inverse problem, the reconstruction of the profile of the metal surface from values of the diffraction intensity, obtained by simulation, is found using an iterative algorithm.

Résumé: This study presents the characterization of rough surfaces, based on the small perturbation method (SPM) and the small slopes approximation model (SSA). The inversion problem is then formulated as a cost function optimization problem and is solved using a global optimization algorithm known as simulated annealing (SA). The examples of analysis and inversion show that the small perturbation method (SPM) is more efficient compared to the small slopes approximation model (SSA) to recover the electrical and geometric parameters, and also shows that this inverse method is feasible and efficient using the algorithm of simulated annealing.

Résumé: This study presents the characterization of rough surfaces, based on the small perturbation method (SPM) and the small slopes approximation model (SSA). The inversion problem is then formulated as a cost function optimization problem and is solved using a global optimization algorithm known as simulated annealing (SA). The examples of analysis and inversion show that the small perturbation method (SPM) is more efficient compared to the small slopes approximation model (SSA) to recover the electrical and geometric parameters, and also shows that this inverse method is feasible and efficient using the algorithm of simulated annealing.

Résumé: The aim of this work is to find the electrical parameters and the thickness of the central layer of a stratified medium with two rough interfaces. The inversion problem is formulated as a cost function optimization problem, and it is solved using the Particle Swarm Optimization (PSO) algorithm. The cost function is based on the ratio of intensities. The inversion scheme is applied to the electrical parameters of the two layers and the thickness of the central layer involved in the analytical expressions of the incoherent intensities given by the Small Perturbation Method (SPM). We study the influence of the correlation function on the estimation of the parameters. The study is applied to the layers of an L-band subsoil. For the studied configurations, we show that the algorithm used in the inverse method to recover the requested parameters is efficient and gives excellent results.

Résumé: Nous déterminons l’expression analytique de la loi de probabilité du rapport des intensités diffusées par un milieu stratifié présentant deux interfaces faiblement rugueuse éclairée par une onde plane électromagnétique. Les formules obtenues sont valides pour des intensités en polarisations directes et croisées et en approche simple visée et multivisées. Les calculs sont menés dans le cadre de la méthode des petites perturbations à l’ordre 1 et suppose que les scènes éclairées sont d’extensions infinies et que les interfaces présentent des distributions des hauteurs gaussiennes. Nous montrons que pour les signatures électromagnétiques basées sur plus de deux visées, la loi de probabilité a une moyenne finie et une variance finie. Les lois de probabilité théoriques sont validées par comparaison avec des histrogrammes issus de tirages de Monte-Carlo.

Résumé: We study the scattering of electromagnetic wave from a two-dimensional random rough surface that separates the vacuum from a perfect electromagnetic conductor (PEMC). We implement the first-order perturbation method and we establish the analytical expressions of the coherent and incoherent intensities. In contrast with the two special cases, the perfect electric conductor and the perfect magnetic conductor, the coherent intensity reflected by the PEMC has a cross-component. We also show that there is a depolarization in the incidence plane and that there are configurations where the wave depolarization is complete and the incoherent intensity is reduced to its crosscomponent.

Résumé: In order to study the problems of scattering by rough dielectric surfaces, we have used Maxwell’s equations within the framework of the small perturbation method. For the direct problem, the mean value of scattering intensities ratio is obtained for random rough surfaces separates the vacuum from a dielectric with a complex permittivity e by computer simulation. In the case of the inverse problem, the reconstruction of the complex permittivity epsilon from values of the scattering intensities ratio, obtained by simulation, is found using an iterative algorithm.

Résumé: In the framework of the small perturbations model, a theoretical investigation of the electromagnetic signature of layered with air / snow / clay soil / rock, rough interfaces in the Ku band is presented. We show in this paper that the electromagnetic response can be influenced by the incident wave, the isotropy factors, the cross-correlation parameters and the layers thickness of snow.

Résumé: The Co- and Cross-Polarized Scattered Intensity ratio of 3D Layered Structures with Randomly Rough Interfaces - Archive ouverte HAL Arrêt de service programmé du vendredi 10 juin 16h jusqu’au lundi 13 juin 9h. Pour en savoir plus Accéder directement au contenu Accéder directement à la navigation Toggle navigation HAL HAL - Archives Ouvertes La connaissance libre et partagée Accueil Dépôt Consultation Les derniers dépôts Par type de publication Par discipline Par année de publication Par structure de recherche Les portails de l'archive Recherche Documentation insu-01720554, version 1 Communication dans un congrès The Co- and Cross-Polarized Scattered Intensity ratio of 3D Layered Structures with Randomly Rough Interfaces

Résumé: This paper studied the effect of carrier frequency offset on orthogonal frequency division multiplexing (OFDM) systems. An optimal frequency offset estimator based on Maximum Likelihood ML, is developed. The correlation between remodulated sequence in the receiver side and the conventional OFDM symbol is used . Although, the proposed estimator is derived under additive white Gaussian noise (AWGN) channel, it has good results under multipath fading channel. Beek’s estimator is used for the sake comparison. Simulations demonstrate the effectiveness of the proposed estimator under AWGN channel and multipath fading channel.

Résumé: In this paper, we propose an analysis of P band radar signal potential to retrieve soil moisture root profile. Our analysis is based on two electromagnetic models, the small perturbation method and the small slope approximation. There models consider electromagnetic scattering from threedimensional layered structures with an arbitrary number of rough surfaces. Simulations are proposed for different types of moisture profiles, for different hydrological conditions.

Résumé: In this paper, we propose an analysis of P band radar signal potential to retrieve soil moisture root profile. Our analysis is based on two electromagnetic models, the small perturbation method and the small slope approximation. There models consider electromagnetic scattering from threedimensional layered structures with an arbitrary number of rough surfaces. Simulations are proposed for different types of moisture profiles, for different hydrological conditions.

Résumé: In the framework of the small slope approximation, we study in Ku band the electromagnetic signature of layered Air/Snow/Sea-Ice rough interfaces. The snow is inhomogeneous and represented as a stack of several layers with different relative permittivities. We show that the electromagnetic response is sensitive to the values of isotropy factors and cross-correlation parameters.

Résumé: Remote sensing of the sea-ice thickness is one of the main objectives of the Ku-band radar altimeter SIRAL - CRYOSAT II mission. On the one hand, sea-ice thickness is derived from the measurement of the height of the freeboard of the floes, and based on isostasy, assuming that the density of the water, the ice, as well as the snow, are known. On the other hand even if the snow load is known, the penetration of the electromagnetic waves into the snow strongly depends on the electrical and geophysical characteristics of the snow layer (density, temperature, permittivity, roughness). The remote sensing of the snow layer thickness (SLT) remains a real challenge and will be useful to correct the snow load for converting freeboard measurements from satellite altimetry into sea-ice thickness. If the dual frequency radar altimetry data show a good potential for remote sensing of snow and more generally of penetrating media [1], providing the SLT from Ku band data alone is highly motivated by the orbit of CRYOSAT designed to cover the entire Arctic.

Résumé: Remote sensing of the sea-ice thickness is one of the main objectives of the CRYOSAT II mission. The sea-ice thickness is derived from the height measurement of the freeboard, assuming not only that the snow load, but also the penetration depth of the electromagnetic waves inside the snow are known, which is not generally the case. A theoretical study, based on a 2D modelling of the reflection and scattering of electromagnetic waves by a stratified medium at normal incidence has been performed. In a first step, the interfaces between the layers are assumed plane, in a second step, a small roughness is taken into account and the small perturbation method (SPM) is used to solve the scattering problem. The main conclusion is that the backscattered signal from the stratified medium is strongly related to the dielectric characteristics. It can vary significantly even if the variations of the stratified medium are small. This is an important result to be kept in mind when attempting the signal inversion.