Les premières recherches en détection, localisation et séparation de signaux remontent au début du 20ème siècle. Ces recherches sont d’actualité encore aujourd’hui, notamment du fait de la croissance rapide des systèmes de communications constatée ces deux dernières décennies. Par ailleurs, la littérature du domaine consacre très peu d’études relatives à certains contextes jugés difficiles dont certains sont traités dans cette thèse. Ce travail porte sur la localisation de signaux par détection des temps d’arrivée ou estimation des directions d’arrivée et sur la séparation de sources dépendantes ou à module constant. L’idée principale est de tirer profit de certaines informations a priori disponibles sur les signaux sources telles que la parcimonie, la cyclostationarité, la non-circularité, le module constant, la structure autoregressive et les séquences pilote dans un contexte coopératif. Une première partie détaille trois contributions : (i) un nouveau détecteur pour l’estimation des temps d’arrivée basé sur la minimisation de la probabilité d’erreur ; (ii) une estimation améliorée de la puissance du bruit, basée sur les statistiques d’ordre ; (iii) une quantification de la précision et de la résolution de l’estimation des directions d’arrivée au regard de certains a priori considérés sur les sources. Une deuxième partie est consacrée à la séparation de sources exploitant différentes informations sur celles-ci : (i) la séparation de signaux de communication à module constant ; (ii) la séparation de sources dépendantes connaissant la nature de la dépendance et (iii) la séparation de sources autorégressives dépendantes connaissant la structure autorégressive. / Signal detection, localization, and separation problems date back to the beginning of the twentieth century. Nowadays, this subject is still a hot topic receiving more and more attention, notably with the rapid growth of wireless communication systems that arose in the last two decades and it turns out that many challenging aspects remain poorly addressed by the available literature relative to this subject. This thesis deals with signal detection, localization using temporal or directional measurements, and separation of dependent source signals. The main objective is to make use of some available priors about the source signals such as sparsity, cyclo-stationarity, non-circularity, constant modulus, autoregressive structure or training sequences in a cooperative framework. The first part is devoted to the analysis of (i) signal’s time-of-arrival estimation using a new minimum error rate based detector, (ii) noise power estimation using an improved order-statistics estimator and (iii) side information impact on direction-of-arrival estimation accuracy and resolution. In the second part, the source separation problem is investigated at the light of different priors about the original sources. Three kinds of prior have been considered : (i) separation of constant modulus communication signals, (ii) separation of dependent source signals knowing their dependency structure and (iii) separation of dependent autoregressive sources knowing their autoregressive structure.

Traditionally, source coding (data compression) and channel coding (error protection) are performed separately and sequentially, resulting in what we call a tandem (separate) coding system. In practical implementations, however, tandem coding might involve a large delay and a high coding/decoding complexity, since one needs to remove the redundancy in the source coding part and then insert certain redundancy in the channel coding part. On the other hand, joint source-channel coding (JSCC), which coordinates source and channel coding or combines them into a single step, may offer substantial improvements over the tandem coding approach. This thesis deals with the fundamental Shannon-theoretic limits for a variety of communication systems via JSCC. More specifically, we investigate the reliability function (which is the largest rate at which the coding probability of error vanishes exponentially with increasing blocklength) for JSCC for the following discrete-time communication systems: (i) discrete memoryless systems; (ii) discrete memoryless systems with perfect channel feedback; (iii) discrete memoryless systems with source side information; (iv) discrete systems with Markovian memory; (v) continuous-valued (particularly Gaussian) memoryless systems; (vi) discrete asymmetric 2-user source-channel systems. For the above systems, we establish upper and lower bounds for the JSCC reliability function and we analytically compute these bounds. The conditions for which the upper and lower bounds coincide are also provided. We show that the conditions are satisfied for a large class of source-channel systems, and hence exactly determine the reliability function. We next provide a systematic comparison between the JSCC reliability function and the tandem coding reliability function (the reliability function resulting from separate source and channel coding). We show that the JSCC reliability function is substantially larger than the tandem coding reliability function for most cases. In particular, the JSCC reliability function is close to twice as large as the tandem coding reliability function for many source-channel pairs. This exponent gain provides a theoretical underpinning and justification for JSCC design as opposed to the widely used tandem coding method, since JSCC will yield a faster exponential rate of decay for the system error probability and thus provides substantial reductions in complexity and coding/decoding delay for real-world communication systems. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-05-13 22:31:56.425