Discontinuities at origin have been used to better approximate measured curves in recent papers but generally not explicitly and their physical validity has not always been demonstrated. In this communication, we show that these discontinuities can be explained by physically acceptable discontinuities in the real physical device. We propose simple criteria to accept or reject these discontinuities, in either passive or active devices, depending on the order of the discontinuity. In addition, we show that models having such discontinuities behave differently from classical models. In particular, these discontinuities explain non-integer dB/dB slopes of harmonic power and intermodulation power as a function of input power. Recent and older measurements of intermodulation products in passive devices, telephony base-station and RF transistors show such a behavior so that supposed lack of measurement cannot be used as a reason to reject discontinuities as non-physical.

Broadcasting systems have to deal with channel variability in order to offer the best spectrum efficiency to the receivers. However, the transmission parameters that optimize the spectrum efficiency generally leads to a large link unavailability. In this paper, we study the performance of hierarchical and non-hierarchical modulations in terms of spectrum efficiency and link unavailability for DVB-S2 systems. Our first contribution is the design of the hierarchical 16-APSK for the DVB-S2 standard. Then we introduce the link unavailability to compare the per- formance of hierarchical and non-hierarchical modulations in terms of spectrum efficiency and link unavailability. The results show that hierarchical modulation is a good alternative to non-hierarchical modulation for the DVB-S2 standard.

Content distribution over ad-hoc networks has been widely studied and numerous solutions can be adapted to VANETs (vehicular networks). VANETs, however, can also benefit from an infrastructure in order to improve the efficiency of any content dissemination technique, while allowing more transmissions resources to be available for safety applications. Unfortunately, so far, no such solution has been proposed. In this paper, we introduce the use of an 802.11p infrastructure based on Road Side Units (RSU) for downloading data (eg a map) to vehicles on a highway. At the application level, the main challenge is then how to deliver data to a large number of moving receivers with limited connectivity. While broadcasting data through each RSU should efficiently provide the cars with most of the data, one could believe that some specific transmissions based on vehicles needs could help to reach full downloads. Using simulations, we observed however that the best performances are achieved by a pure broadcasting system.

The kernel least-mean-square (KLMS) algorithm is a popular algorithm in nonlinear adaptive filtering due to its simplicity and robustness. In kernel adaptive filters, the statistics of the input to the linear filter depends on the parameters of the kernel employed. Moreover, practical implementations require a finite nonlinearity model order. A Gaussian KLMS has two design parameters, the step size and the Gaussian kernel bandwidth. Thus, its design requires analytical models for the algorithm behavior as a function of these two parameters. This paper studies the steady-state behavior and the transient behavior of the Gaussian KLMS algorithm for Gaussian inputs and a finite order nonlinearity model. In particular, we derive recursive expressions for the mean-weight-error vector and the mean-square-error. The model predictions show excellent agreement with Monte Carlo simulations in transient and steady state. This allows the explicit analytical determination of stability limits, and gives opportunity to choose the algorithm parameters a priori in order to achieve prescribed convergence speed and quality of the estimate. Design examples are presented which validate the theoretical analysis and illustrates its application.

This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reßectances result froma nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The Þrst step of the proposedmethod estimates the abundance vectors for all the image pixels using a Bayesian approach an aGaussian process latent variable model for the nonlinear function (relating the abundance vectors to the observations). The endmembers are subsequently estimated using Gaussian process regression. The performance of the unmixing strategy is Þrst evaluated on synthetic data. The proposed method provides accurate abundance and endmember estimations when compared to other linear and nonlinear unmixing strategies. An interesting property is its robustness to the absence of pure pixels in the image. The analysis of a real hyperspectral image shows results that are in good agreement with state of the art unmixing strategies and with a recent classiÞcation method.

Periodic nonuniform sampling of order three (PNS3) is a sampling scheme composed of three periodic sequences with the same period. It is well-known that this sampling scheme can be useful to remove aliasing. Previous studies have provided conditions on the spectrum support for exact reconstruction in the case of functions. This paper deals more generally with the best mean-square interpolation for stationary processes with any known power spectrum, from PNS3 and possibly aliasing. We show that the best estimation is based upon particular linear filters, which depend on the gap between the sampling sequences. The mean-time error also depends on this gap. The errorless interpolation is a particular case. It requires the knowledge of the spectral support rather than the spectral true values.

Multifractal analysis has matured into a widely used signal and image processing tool. Due to the statistical nature of multifractal processes (strongly non-Gaussian and intricate dependence) the accurate estimation of multifractal parameters is very challenging in situations where the sample size is small (notably including a range of biomedical applications) and currently available estimators need to be improved. To overcome such limitations, the present contribution proposes a Bayesian estimation procedure for the multifractality (or intermittence) parameter. Its originality is threefold : First, the use of wavelet leaders, a recently introduced multiresolution quantity that has been shown to yield significant benefits for multifractal analysis ; Second, the construction of a simple yet generic semi-parametric model for the marginals and covariance structure of wavelet leaders for the large class of multiplicative cascade based multifractal processes ; Third, the construction of original Bayesian estimators associated with the model and the constraints imposed by multifractal theory. Performance are numerically assessed and illustrated for synthetic multifractal processes for a range of multifractal parameter values. The proposed procedure yields significantly improved estimation performance for small sample sizes.

In recent years, wake vortex monitoring in real time has emerged as one of the key challenges in air trac control at landing or taking-o. In clear air, several experimental tests have demonstrated that Lidar is an eective sensor for wake vortex monitoring. In rainy weather, Lidar becomes blind and Radar is a candidate sensor to detect the motion of raindrops in wake vortices. Thus, investigation on radar monitoring of wake vortices in rainy weather is of both scientic and practical interests. This topic has been tackled through three successive steps during thisthesis. Firstly, the motion of raindrops in wake vortices has been modeled and simulated. The equation of the motion has been derived and the methodology to compute the raindrops' trajectory and distribution in the flow induced by the wake vortices has been proposed. Secondly, two simulators have been developed for evaluating the radar signatures of raindrops in wake vortices. One simulator is based on the simulation of radar signal time series, by superimposing the radar backscattered signal from each raindrop in the wake vortex region. The other one is based on the raindrops' number concentration and velocity distribution in wake vortices, enabling the computation of radar signatures much more eciently. Those simulators have been used to reproduce experimental configurations and the comparison between measured and simulated signature has shown an interesting agreement at X and W band. Lastly, the interpretation of radar signatures of raindrops in wake vortices has been presented. Based on the computation of three spectral moments, the dependence of radar signatures on rain rate, vortex circulation and radar parameters has been studied for vortices generated by different aircraft types. A wake vortex detection method based on the analysis of Doppler spectrum width of raindrops has been proposed. Considering radar scanning under flight path, a methodology to estimate the wake vortex characteristics has been proposed. Preliminary simulation results have shown its effectiveness. The radar signatures of wake vortices in rainy weather have been modeled and analyzed in this thesis. The simulation results have demonstrated the capability of radar to detect wake vortex in rainy weather. The methodologies developed in this thesis can be further exploited for designing new wake vortex radar systems.

In recent years, wake vortex monitoring in real time has emerged as one of the key challenges in air trac control at landing or taking-o. In clear air, several experimental tests have demonstrated that Lidar is an eective sensor for wake vortex monitoring. In rainy weather, Lidar becomes blind and Radar is a candidate sensor to detect the motion of raindrops in wake vortices. Thus, investigation on radar monitoring of wake vortices in rainy weather is of both scientic and practical interests. This topic has been tackled through three successive steps during thisthesis. Firstly, the motion of raindrops in wake vortices has been modeled and simulated. The equation of the motion has been derived and the methodology to compute the raindrops' trajectory and distribution in the flow induced by the wake vortices has been proposed. Secondly, two simulators have been developed for evaluating the radar signatures of raindrops in wake vortices. One simulator is based on the simulation of radar signal time series, by superimposing the radar backscattered signal from each raindrop in the wake vortex region. The other one is based on the raindrops' number concentration and velocity distribution in wake vortices, enabling the computation of radar signatures much more eciently. Those simulators have been used to reproduce experimental configurations and the comparison between measured and simulated signature has shown an interesting agreement at X and W band. Lastly, the interpretation of radar signatures of raindrops in wake vortices has been presented. Based on the computation of three spectral moments, the dependence of radar signatures on rain rate, vortex circulation and radar parameters has been studied for vortices generated by different aircraft types. A wake vortex detection method based on the analysis of Doppler spectrum width of raindrops has been proposed. Considering radar scanning under flight path, a methodology to estimate the wake vortex characteristics has been proposed. Preliminary simulation results have shown its effectiveness. The radar signatures of wake vortices in rainy weather have been modeled and analyzed in this thesis. The simulation results have demonstrated the capability of radar to detect wake vortex in rainy weather. The methodologies developed in this thesis can be further exploited for designing new wake vortex radar systems.

Les dispositifs passifs ne sont pas parfaitement linéaires aux très fortes puissances. Ils créent des harmoniques et des produits d’intermodulation pairs et impairs. Ces produits peuvent perturber fortement les performances des récepteurs utilisant les mêmes équipements passifs ou simplement installés sur le même site que les émetteurs. Ces produits n’obéissent pas à la loi classique de croissance en fonction de la puissance d’entrée avec une pente en dB/dB égale à l’ordre du produit. Ceci a interdit, jusqu’à présent, de modéliser correctement ces dispositifs. On propose une modélisation par des fonctions non analytiques qui permet de mieux reproduire cette caractéristique avec un nombre minimal de coefficients et à partir d’un nombre minimal de mesures.