The k-distribution method for treating the spectral properties of and absorbing-emitting medium represents an alternative to line-by-line calculations which reduces the number of evaluations of the radiative transport equation from the order of a million to the order of ten without any significant loss of accuracy. For problems where an appropriate reference temperature can be defined, the k-distribution method is formally exact and consists only of a change of variables in the spectral domain. However, when no appropriate reference temperature can be defined such as for strongly non-isothermal media, the method results in errors. These errors are difficult to quantify. There have been several attempts to implement corrections to the k-distribution method to extend its application to inhomogeneous media by modeling the effects of temperature, pressure, and concentration gradient. The Multi-Source Full Spectrum K-Distribution Method (MSFSK) introduced here extends the k-distribution method to non-isothermal media without variations in pressure or concentration. The MSFSK method manages to attain this goal by applying the superposition principle to the original RTE before applying the k-distribution transformation to decompose the problem into a set of sub-problems each of which is able to be solved effectively via the ordinary or modified full spectrum k-distribution method. The concept behind this new Multi-Source Full Spectrum K-Distribution Method is to break up the problem domain into isothermal or nearly isothermal emission zones. For each zone, the heat flux and flux divergence are calculated considering only emission from that zone. The RTE is solved using the full spectrum k-distribution method. The k-distribution for each gas volume is generated using the temperature of the current emission zone as the reference temperature. This process is repeated for each emission zone and the heat flux and flux divergence are summed. This method is applied to a variety of one dimensional slab geometry problems are results are presented. It is shown that the MSFSK method provides very accurate results for the radiative heat flux and flux divergence in these geometries. The effect of different quadrature schemes for performing the spectral integration on solution accuracy. / text

Dans le contexte de la caractérisation des tissus mammaires, on peut se demander ce que l’examen d’un attribut en échographie quantitative (« quantitative ultrasound » - QUS) d’un milieu diffusant (tel un tissu biologique mou) pendant la propagation d’une onde de cisaillement ajoute à son pouvoir discriminant. Ce travail présente une étude du comportement variable temporel de trois paramètres statistiques (l’intensité moyenne, le paramètre de structure et le paramètre de regroupement des diffuseurs) d’un modèle général pour l’enveloppe écho de l’onde ultrasonore rétrodiffusée (c.-à-d., la K-distribution homodyne) sous la propagation des ondes de cisaillement. Des ondes de cisaillement transitoires ont été générés en utilisant la mèthode d’ imagerie de cisaillement supersonique ( «supersonic shear imaging » - SSI) dans trois fantômes in-vitro macroscopiquement homogènes imitant le sein avec des propriétés mécaniques différentes, et deux fantômes ex-vivo hétérogénes avec tumeurs de souris incluses dans un milieu environnant d’agargélatine. Une comparaison de l’étendue des trois paramètres de la K-distribution homodyne avec et sans propagation d’ondes de cisaillement a montré que les paramètres étaient significativement (p < 0,001) affectès par la propagation d’ondes de cisaillement dans les expériences in-vitro et ex-vivo. Les résultats ont également démontré que la plage dynamique des paramétres statistiques au cours de la propagation des ondes de cisaillement peut aider à discriminer (avec p < 0,001) les trois fantômes homogènes in-vitro les uns des autres, ainsi que les tumeurs de souris de leur milieu environnant dans les fantômes hétérogénes ex-vivo. De plus, un modéle de régression linéaire a été appliqué pour corréler la plage de l’intensité moyenne sous la propagation des ondes de cisaillement avec l’amplitude maximale de déplacement du « speckle » ultrasonore. La régression linéaire obtenue a été significative : fantômes in vitro : R2 = 0.98, p < 0,001 ; tumeurs ex-vivo : R2 = 0,56, p = 0,013 ; milieu environnant ex-vivo : R2 = 0,59, p = 0,009. En revanche, la régression linéaire n’a pas été aussi significative entre l’intensité moyenne sans propagation d’ondes de cisaillement et les propriétés mécaniques du milieu : fantômes in vitro : R2 = 0,07, p = 0,328, tumeurs ex-vivo : R2 = 0,55, p = 0,022 ; milieu environnant ex-vivo : R2 = 0,45, p = 0,047. Cette nouvelle approche peut fournir des informations supplémentaires à l’échographie quantitative statistique traditionnellement réalisée dans un cadre statique (c.-à-d., sans propagation d’ondes de cisaillement), par exemple, dans le contexte de l’imagerie ultrasonore en vue de la classification du cancer du sein. / In the context of breast tissue characterization, one may wonder what the consideration of a quantitative ultrasound (QUS) feature of a scattering medium (such as a soft biological tissue) under propagation of a shear wave adds to its discriminant power. This work presents a study of the time varying behavior of three statistical parameters (the mean intensity, the structure parameter and the clustering parameter of scatterers) of a general model for the ultrasound backscattering echo envelope (i.e., the homodyned K-distribution) under shear wave propagation. Transient shear waves were generated using the supersonic shear imaging (SSI) method in three in-vitro macroscopically homogenous breast mimicking phantoms with different mechanical properties, and two ex-vivo heterogeneous phantoms with mice tumors included in an agar gelatin surrounding medium. A comparison of the range of the three homodyned K-distribution parameters with and without shear wave propagation showed that the parameters were significantly (p < 0.001) affected by shear wave propagation in the in-vitro and ex-vivo experiments. The results also demonstrated that the dynamic range of the statistical parameters during shear wave propagation may help discriminate (with p < 0.001) the three in-vitro homogenous phantoms from each other, and also the mice tumors from their surrounding medium in the ex-vivo heterogeneous phantoms. Furthermore, a linear regression model was applied to relate the range of the mean intensity under shear wave propagation with the maximum displacement amplitude of speckle. The linear regression was found to be significant : in-vitro phantoms : R2 = 0.98, p < 0.001 ; ex-vivo tumors : R2 = 0.56, p = 0.013 ; ex-vivo surrounding medium : R2 = 0.59, p = 0.009. In contrast, the linear regression was not as significant between the mean intensity without shear wave propagation and mechanical properties of the medium : in-vitro phantoms : R2 = 0.07, p = 0.328, ex-vivo tumors : R2 =0.55, p = 0.022 ; ex-vivo surrounding medium : R2 = 0.45, p = 0.047. This novel approach may provide additional information to statistical QUS traditionally performed in a static framework (i.e., without shear wave propagation), for instance, in the context of ultrasound imaging for breast cancer classification.

abstract: A critical problem for airborne, ship board, and land based radars operating in maritime or littoral environments is the detection, identification and tracking of targets against backscattering caused by the roughness of the sea surface. Statistical models, such as the compound K-distribution (CKD), were shown to accurately describe two separate structures of the sea clutter intensity fluctuations. The first structure is the texture that is associated with long sea waves and exhibits long temporal decorrelation period. The second structure is the speckle that accounts for reflections from multiple scatters and exhibits a short temporal decorrelation period from pulse to pulse. Existing methods for estimating the CKD model parameters do not include the thermal noise power, which is critical for real sea clutter processing. Estimation methods that include the noise power are either computationally intensive or require very large data records. This work proposes two new approaches for accurately estimating all three CKD model parameters, including noise power. The first method integrates, in an iterative fashion, the noise power estimation, using one-dimensional nonlinear curve fitting, with the estimation of the shape and scale parameters, using closed-form solutions in terms of the CKD intensity moments. The second method is similar to the first except it replaces integer-based intensity moments with fractional moments which have been shown to achieve more accurate estimates of the shape parameter. These new methods can be implemented in real time without requiring large data records. They can also achieve accurate estimation performance as demonstrated with simulated and real sea clutter observation datasets. The work also investigates the numerically computed Cram\'er-Rao lower bound (CRLB) of the variance of the shape parameter estimate using intensity observations in thermal noise with unknown power. Using the CRLB, the asymptotic estimation performance behavior of the new estimators is studied and compared to that of other estimators. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2019

Conventional fixed threshold detectors set a fixed threshold based on the overall statistical characteristics of the spatially uniform clutter over all ranges to give a specific probability of false alarm and detection. However, in radar applications clutter statistics are not known a priori. Constant False Alarm Rate (CFAR) techniques provide an adaptive threshold to estimate the clutter statistics and to distinguish targets from clutter. In Cell Averaging CFAR (CA-CFAR) the threshold is controlled by averaging the fixed size CFAR cells surrounding the cell under test. In this thesis, radar detection of targets in sea clutter modelled by compound Kdistribution is examined from a statistical detection viewpoint by Monte Carlo simulations. The performance of CA-CFAR processors is analysed under varying conditions of sea clutter spatial correlation and spikiness for several cases of false alarm probability, the length of cell size used in the CFAR processor and the number of pulses integrated prior to CA-CFAR processor. v The detection performance of CA-CFAR is compared with the performance of fixed threshold detection. The performance evaluations are quantified by CFAR loss. CFAR loss is defined as the increase in average signal to clutter ratio compared to that of fixed threshold, required to achieve a given probability of detection and probability of false alarm. Curves for CFAR loss to the spikiness and spatial correlation of clutter, number of pulses integrated and the length of cell size are presented.

Radar signal processing techniques aim to suppress clutter to enable target detection. Many clutter suppression techniques have been developed to improve the detection performance in literature. Among these methods, the most widely known is MTI plus coherent integrator, which gives sufficient radar performance in various scenarios. However, when the correlation coefficient of clutter is small or the spectral separation between the target and clutter is small, classical approaches to clutter suppression fall short. In this study, we consider the ARMA spectral estimation performance in sea clutter modelled by compound K-distribution through Monte Carlo simulations. The method is applied for varying conditions of clutter spikiness and auto correlation sequences (ACS) depending on the radar operation. The performance of clutter suppression using ARMA spectral estimator, which will be called ARMA-CS in this work, is analyzed under varying ARMA model orders. To compare the clutter suppression of ARMA-CS with that of conventional methods, we use improvement factor (IF) which is the ratio between the output Signal to Interference Ratio (SIR) and input SIR as performance measure. In all cases, the performance of ARMA-CS method is better than conventional clutter suppression methods when the correlation among clutter samples is small or the spectral separation between target and clutter is small.

The K-distribution method is a fast approximative method used for calculating thermal infrared radiative transfer in the atmosphere, as opposed to the traditional Line-by-line method, which is precise, but very time-costly. Here we consider the atmosphere to consist of homogeneous and plane-parallel layers in local thermal equilibrium. This lets us use efficient upwards recursion for calculating the thermal infrared radiative transfer and ultimately the outgoing irradiance at the top of the atmosphere. Our specific implementation of the K-distribution method revolves around changing the integration space from the wavenumber domain to the g domain by employing Gauss-Legendre quadrature in two steps. The method is implemented in MATLAB and is shown to be several thousand times faster than the traditional Line-by-line method, with the relative error being only 3 % for the outgoing irradiance at the top of the atmosphere.

Cette thèse traite du traitement adaptatif spatio-temporel dans le domaine radar. Pour augmenter les performances en détection, cette approche consiste à maximiser le rapport entre la puissance de la cible et celle des interférences, à savoir le bruit thermique et le fouillis. De nombreuses variantes de cet algorithme existent, une d’entre elles est fondée sur une modélisation autorégressive vectorielle des interférences. Sa principale difficulté réside dans l’estimation des matrices autorégressives à partir des données d’entrainement ; ce point constitue l’axe de notre travail de recherche. En particulier, notre contribution porte sur deux aspects. D’une part, dans le cas où l’on suppose que le bruit thermique est négligeable devant le fouillis non gaussien, les matrices autorégressives sont estimées en utilisant la méthode du point fixe. Ainsi, l’algorithme est robuste à la distribution non gaussienne du fouillis.D’autre part, nous proposons une nouvelle modélisation des interférences différenciant le bruit thermique et le fouillis : le fouillis est considéré comme un processus autorégressif vectoriel, gaussien et perturbé par le bruit blanc thermique. Ainsi, de nouvelles techniques d'estimation des matrices autorégressives sont proposées. La première est une estimation aveugle par bloc reposant sur la technique à erreurs dans les variables. Ainsi, l’estimation des matrices autorégressives reste robuste pour un rapport faible entre la puissance de la cible et celle du fouillis (< 5 dB). Ensuite, des méthodes récursives ont été développées. Elles sont fondées sur des approches du type Kalman : filtrage de Kalman étendu et filtrage par sigma point (UKF et CDKF), ainsi que sur le filtre H∞.Une étude comparative sur des données synthétiques et réelles, avec un fouillis gaussien ou non gaussien, est menée pour révéler la pertinence des différents estimateurs en terme de probabilité de détection. / This dissertation deals with space-time adaptive processing in the radar’s field. To improve the detection’s performances, this approach consists in maximizing the ratio between the target’s power and the interference’s one, i.e. the thermal noise and the clutter. Several variants of its algorithm exist, one of them is based on multichannel autoregressive modelling of interferences. Its main problem lies in the estimation of autoregressive matrices with training data and guides our research’s work. Especially, our contribution is twofold.On the one hand, when thermal noise is considered negligible, autoregressive matrices are estimated with fixed point method. Thus, the algorithm is robust against non-gaussian clutter.On the other hand, a new modelling of interferences is proposed. The clutter and thermal noise are separated : the clutter is considered as a multichannel autoregressive process which is Gaussian and disturbed by the white thermal noise. Thus, new estimation’s algorithms are developed. The first one is a blind estimation based on errors in variable methods. Then, recursive approaches are proposed and used extension of Kalman filter : the extended Kalman filter and the Sigma Point Kalman filter (UKF and CDKF), and the H∞ filter. A comparative study on synthetic and real data with Gausian and non Gaussian clutter is carried out to show the relevance of the different algorithms about detection’s probability.

Les réseaux de capteurs sans fil (RCSF) sont des réseaux ad hoc généralement constitués d’entités autonomes miniaturisées appelés noeuds capteurs pouvant communiquer entre eux par liaison radio. Les RCSF ont suscité beaucoup d’engouement dans la recherche scientifique en raison notamment des nouveaux problèmes de routage sous forte contrainte de durée de vie du réseau et de faibles capacités des noeuds.Ce type de réseau diffère des réseaux filaires par ses caractéristiques et limitations qui ont motivé le développement d’une nouvelle approche de conception cross-layer ignorant certains paradigmes de l’approche classique permettant l’échange mutuel d’informations même entre couches non adjacentes. Cette approche qui n’est pas encore standardisée, a démontré son intérêt à travers plusieurs travaux visant un meilleur compromis entre consommation d’énergie et une certaine qualité de service.Nos contributions peuvent être classées en deux catégories suivant la stratégie de routage à savoir le routage ad-hoc et le routage suivant la technique de clustering.Dans la première partie, nous proposons une architecture cross-layer, modulaire, adaptable et extensible nommée XL-AODV (cross layer AODV) basée sur l'échange du SNR (Signal-to-Noise-Ratio) entre la couche réseau et la couche physique qui a été modélisée par la distribution K. Nous évaluons sous le simulateur NS2 les performances de notre approche XL-AODV. Une analyse comparative avec AODV, a montré pour différentes configurations de réseaux, l’efficacité de notre proposition en termes de gains énergétiques et de latence de bout en bout.Pour la deuxième partie, nous proposons une première approche XL-LEACH qui constitue une amélioration de la version originale de LEACH, en l'adaptant aux réseaux de capteurs denses et à grande échelle tout en tenant compte des caractéristiques de la couche physique modélisée par la distribution K. Dans une troisième partie, nous introduisons une amélioration de XL-LEACH par l'approche dite, XL-CLEACH (XL Cooperative LEACH) en intégrant la communication coopérative au niveau MAC. Nous avons prouvé par une étude analytique qui a été validée par les simulations, le gain apporté en termes de consommation d’énergie, de la durée de vie du réseau et du TES (Taux d'Erreur Symbol). Les architectures XL-LEACH et XL-CLEACH ont été implémentées sous MATLAB. / Wireless sensor networks (WSN) can be defined as an ad hoc network consisting of miniaturized autonomous entities, called sensor nodes which communicate with each other over a radio link. WSNs is a research topic which has gained a lot of interest due, in particular, to new routing problems under low node capacity and high network lifetime constraints.WSNs differ from wired networks in their characteristics and limitations which have motivated the development of a new cross-layer design that ignores certain paradigms of the classical approach allowing the mutual exchange of information even between non-adjacent layers. This approach, which is not yet standardized, has gained a lot of attention through several works aiming to energy consumption minimization under a required QoS (Quality of Service).In this thesis, our contributions can be classified are twofold according to the considered routing strategy namely the ad-hoc routing and clustering based routing.In the first part, we propose a new adaptable and extensible cross-layer design called XL-AODV (Cross Layer AODV) based on the exchange of the SNR (Signal-to-Noise-Ratio) between the network and the physical layer which has been modelled by the K distribution.We evaluate under the NS2 simulator, the performance of XL-AODV. A comparative analysis with AODV, showed for different network configurations, the efficiency of our proposition in terms of energy saving and end-to-end latency.In the second part, we propose an XL-LEACH approach which is an improvement of the original version of LEACH by its adapting to dense and large scale sensor networks. We have also taken into account the characteristics of the physical layer modelled by the K distribution.In a third part, XL-CLEACH (XL Cooperative LEACH) approach is introduced to improve XL-LEACH by integrating the cooperative communication at the MAC layer.We have proved through an analytical study and validated by simulations, the gain in terms of energy consumption, network lifetime and SER (Symbol Error Rate). The XL-LEACH and XL-CLEACH architecture were implemented under MATLAB.