The theory of uniform sampling, developed among others by C. Shannon, is the foundation of today digital signal processing. Since then, numerous works have been dedicated to non uniform sampling schemes. On the one hand, these schemes model uniform sampling device imperfections. On the other hand, sampling can be intentionally performed in a non uniform way to benefit from specific properties, in particular simplifications concerning the choice of the mean sampling frequency. Most of these works have focused on theoretical approaches, adopting simplified models for signals and sampling devices. However, in many application domains, such as satellite communications, analog-to-digital conversion is submitted to strong constraints over the involved bandwidth due to the very high frequencies used. These operational conditions enhance the imperfections of the involved electronic devices and require the choice of particular signal models and sampling schemes. This thesis aims at proposing sampling models suitable for this context. These models apply to random band-pass signals, which are the classical models for telecommunication signals. They must take into account technological, economical factors and on-board complexity constraints and allow to integrate particular functionalities useful for telecommunication applications. This thesis first contribution is to develop non uniform sampling formulas that can digitally integrate functionalities that appear to be tricky in the analog domain at the considered frequencies. The thesis second contribution consists in applying non uniform sampling theory to the estimation and compensation of synchronization errors encountered in particular sampling devices, the time-interleaved analog-to-digital converters. This estimation will be performed through supervised or blind methods.

The theory of uniform sampling, developed among others by C. Shannon, is the foundation of today digital signal processing. Since then, numerous works have been dedicated to non uniform sampling schemes. On the one hand, these schemes model uniform sampling device imperfections. On the other hand, sampling can be intentionally performed in a non uniform way to benefit from specific properties, in particular simplifications concerning the choice of the mean sampling frequency. Most of these works have focused on theoretical approaches, adopting simplified models for signals and sampling devices. However, in many application domains, such as satellite communications, analog-to-digital conversion is submitted to strong constraints over the involved bandwidth due to the very high frequencies used. These operational conditions enhance the imperfections of the involved electronic devices and require the choice of particular signal models and sampling schemes. This thesis aims at proposing sampling models suitable for this context. These models apply to random band-pass signals, which are the classical models for telecommunication signals. They must take into account technological, economical factors and on-board complexity constraints and allow to integrate particular functionalities useful for telecommunication applications. This thesis first contribution is to develop non uniform sampling formulas that can digitally integrate functionalities that appear to be tricky in the analog domain at the considered frequencies. The thesis second contribution consists in applying non uniform sampling theory to the estimation and compensation of synchronization errors encountered in particular sampling devices, the time-interleaved analog-to-digital converters. This estimation will be performed through supervised or blind methods.

Random propagation times are able to model waves attenuation and velocity. It is true for electromagnetic waves (light, radar, guided propagation) and also for acoustics and ultrasounds (acoustics for high frequencies). About the latter, it can be shown that stable probability laws are well-fitted for frequencies up to dozens of megahertz in numerous cases. Nowadays, medical applications are performed using propagation through perfluorocarbon (PFC). Experiments were done to measure attenuations and phase changes. Using these results, this paper addresses the question to know if stable probability laws can be used to characterize the propagation of ultrasounds through PFC liquids.

This paper studies a fast multi-band image fusion algorithm for highspatial low-spectral resolution and low-spatial high-spectral resolution images. The popular forward model and the conventional Gaussian prior are used to form the posterior of the target image. Maximizing the posterior leads to solving a matrix Sylvester equation. By exploiting the properties of the circulant and decimation matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained, avoiding any iterative update step. Simulation results show that the proposed algorithm achieves the same performance as existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.

We develop a novel high-resolution method for the estimation of the direction of incidence of energy emitted by sources in 3D space from wideband measurements collected by a planar array of sensors. We make use of recent generalizations of Kronecker’s theorem and formulate the direction of arrival estimation problem as an optimization problem in the space of sequences generating so called “general domain Hankel matrices” of fixed rank. The unequal sampling at different wavelengths is handled by using appropriate interpolation operators. The algorithm is operational for general array geometries (i.e., not restricted to, e.g., rectangular arrays) and for equidistantly as well as unequally spaced receivers. Numerical simulations for different sensor arrays and various signal-to-noise ratios are provided and demonstrate its excellent performance.

In this paper, we propose a hierarchical Bayesian model approximating the l20 mixed-norm regularization by a multivariate Bernoulli Laplace prior to solve the EEG inverse problem by promoting spatial structured sparsity. The posterior distribution of this model is too complex to derive closed-form expressions of the standard Bayesian estimators. However, this posterior can be sampled using an MCMC method and the generated samples can be used to compute Bayesian estimators of the unknown model parameters. The proposed MCMC algorithm is based on a partially collapsed Gibbs sampler and a dual dipole random shift proposal for the non-zero positions. Note that the proposed method estimates the brain activity and all other model parameters jointly in a completely unsupervised framework. The results obtained on synthetic data with controlled ground truth show the good performance of the proposed method when compared to the l21 approach in different scenarios, and its capacity to estimate point-like source activity.

The use of the continuous phase modulation (CPM) is interesting when the channel represents a strong non-linearity and in the case of limited spectral support ; particularly for the uplink, where the satellite holds an amplifier per carrier, and for downlinks where the terminal equipment works very close to the saturation region. Numerous studies have been conducted on this issue but the proposed solutions use iterative CPM demodulation/decoding concatenated with convolutional or block error correcting codes. The use of LDPC codes has not yet been introduced. Particularly, no works, to our knowledge, have been done on the optimization of sparse graph-based codes adapted for the context described here. In this study, we propose to perform the asymptotic analysis and the design of turbo-CPM systems based on the optimization of sparse graph-based codes. Moreover, an analysis on the corresponding receiver will be done.

The use of the continuous phase modulation (CPM) is interesting when the channel represents a strong non-linearity and in the case of limited spectral support; particularly for the uplink, where the satellite holds an amplifier per carrier, and for downlinks where the terminal equipment works very close to the saturation region. Numerous studies have been conducted on this issue but the proposed solutions use iterative CPM demodulation/decoding concatenated with convolutional or block error correcting codes. The use of LDPC codes has not yet been introduced. Particularly, no works, to our knowledge, have been done on the optimization of sparse graph-based codes adapted for the context described here. In this study, we propose to perform the asymptotic analysis and the design of turbo-CPM systems based on the optimization of sparse graph-based codes. Moreover, an analysis on the corresponding receiver will be done.

In this thesis, we look at the possibility to deploy a Lower-than-Best-Effort (LBE) service over long delay links such as satellite links. The objective is to provide a second priority class dedicated to background or signaling traffic. In the context of long delay links, an LBE service might also help to optimize the use of the link capacity. In addition, an LBE service can enable a low-cost or even free Internet access to remote communities via satellite communication. Two possible deployment levels of an LBE approach exists : either at the MAC layer or at the transport layer. In this thesis, we are interested in an end-to-end approach and thus specifically focus on transport layer solutions. We first propose to study LEDBAT (Low Extra Delay Background Transport) because of its potential. Indeed, LEDBAT has been standardized by the IETF and is widely deployed within the official BitTorrent client. Unfortunately, the tuning of LEDBAT parameters is revealed to highly depend on network conditions. In the worst case scenario, LEDBAT flows can starve other traffic such as commercial traffic performing over a satellite link. LEDBAT also suffers from an intra-unfairness issue, called the latecomer advantage. These reasons often prevent operators from using LBE protocols over wireless and long-delay links as a misconfiguration can overload link capacity. Therefore, we design FLOWER, a new delay-based transport protocol, as an alternative to LEDBAT. By using a fuzzy controller to modulate the sending rate, FLOWER aims to solve LEDBAT issues while fulfilling the role of an LBE protocol. Our simulation results show that FLOWER can carry LBE traffic not only in the long delay context, but in a wide range of network conditions where LEDBAT usually fails.

In this thesis, we look at the possibility to deploy a Lower-than-Best-Effort (LBE) service over long delay links such as satellite links. The objective is to provide a second priority class dedicated to background or signaling traffic. In the context of long delay links, an LBE service might also help to optimize the use of the link capacity. In addition, an LBE service can enable a low-cost or even free Internet access to remote communities via satellite communication. Two possible deployment levels of an LBE approach exists : either at the MAC layer or at the transport layer. In this thesis, we are interested in an end-to-end approach and thus specifically focus on transport layer solutions. We first propose to study LEDBAT (Low Extra Delay Background Transport) because of its potential. Indeed, LEDBAT has been standardized by the IETF and is widely deployed within the official BitTorrent client. Unfortunately, the tuning of LEDBAT parameters is revealed to highly depend on network conditions. In the worst case scenario, LEDBAT flows can starve other traffic such as commercial traffic performing over a satellite link. LEDBAT also suffers from an intra-unfairness issue, called the latecomer advantage. These reasons often prevent operators from using LBE protocols over wireless and long-delay links as a misconfiguration can overload link capacity. Therefore, we design FLOWER, a new delay-based transport protocol, as an alternative to LEDBAT. By using a fuzzy controller to modulate the sending rate, FLOWER aims to solve LEDBAT issues while fulfilling the role of an LBE protocol. Our simulation results show that FLOWER can carry LBE traffic not only in the long delay context, but in a wide range of network conditions where LEDBAT usually fails.