Peixoto, A. A. T. Detecção multiusuário baseada em tensores para sistemas de comunicação sem fio cooperativos. 2017. 115 f. Dissertação (Mestrado em Engenharia Elétrica e da Computação) - Campus de Sobral, Universidade Federal do Ceará, Sobral, 2017. / Submitted by Programa de Pós-Graduação Engenharia Elétrica e de Computação (secretaria_ppgeec@sobral.ufc.br) on 2017-08-14T13:53:24Z No. of bitstreams: 1 2017_dis_aatpeixoto.pdf: 1646922 bytes, checksum: a562da60d08daac64247b2013ca22436 (MD5) / Approved for entry into archive by Djeanne Costa (djeannecosta@gmail.com) on 2017-08-17T11:50:56Z (GMT) No. of bitstreams: 1 2017_dis_aatpeixoto.pdf: 1646922 bytes, checksum: a562da60d08daac64247b2013ca22436 (MD5) / Made available in DSpace on 2017-08-17T11:50:56Z (GMT). No. of bitstreams: 1 2017_dis_aatpeixoto.pdf: 1646922 bytes, checksum: a562da60d08daac64247b2013ca22436 (MD5) Previous issue date: 2017-07 / Signal processing applications in wireless communications may sometimes take advantage of multilinear algebra concepts. This can be done by modeling the signals as high order tensors. From this context, tensor decompositions such as the Parallel Factor analysis (PARAFAC), may be found useful. On the other hand, cooperative communications and Multiple-Input Multiple-Output (MIMO) systems are ways for granting better data rates, capacity, fading mitigation and coverage. Joining the signal processing capabilities of tensor algebra, MIMO and cooperative communications can bring great benefits in wireless communications systems. In this dissertation, two receivers are proposed for two system models that are a multiuser DS-CDMA (Direct-Sequence Code-Division Multiple-Access) uplink based on multirelay cooperative communications. The two system models are almost the same, except that in one of them, multiuser interference is considered at the relays. The Amplify-and-Forward (AF) protocol is used on all the relays, thus exploiting cooperative diversity. For the received signal of the first system model, a quadrilinear PARAFAC decomposition will be adopted and by doing so, the proposed tensor-based semi-blind receiver can jointly estimate the transmitted symbols, channel gains and spatial signatures of all users by assuming previous knowledge of the users spreading codes and a few transmitted symbols. For the second system model, multiuser interference is considered at the relays, then, a receiver based on a trilinear PARAFAC decomposition is proposed. The estimation of the second receiver is done in two phases with the first phase being a supervised stage where non-orthogonal training sequences are sent by all users. During the second phase, the users' data symbols are then estimated. Both receivers use the Alternating Least Squares (ALS) algorithm to fit the tensor models, assuming no channel state information (CSI) at the base station neither at the relays. With computational simulations, we will also provide performance evaluation of the proposed receivers for various cases and system variations. / As aplicações de processamento de sinal em sistemas de comunicações sem fio às vezes podem tirar proveito de conceitos de álgebra multilinear. Isso pode ser feito modelando os sinais como tensores de ordem elevada. Neste contexto, as decomposições tensoriais, tais como a análise de fatores paralelos (Parallel Facor - PARAFAC), podem ser úteis. Por outro lado, as comunicações cooperativas e a área de sistemas de múltiplas-entradas e múltiplas-saídas (Multiple-Input Multiple-Ouput - MIMO) são uma maneira de se alcançar melhores taxas de dados, capacidade, qualidade de transmissão e cobertura. Juntando-se as capacidades de processamento de sinal da álgebra tensorial, dos sistemas MIMO e das comunicações cooperativas, podemos obter grandes benefícios nos sistemas de comunicações sem fio. Nesta dissertação, dois receptores são propostos para dois modelos de sistema, que são o enlace reverso de um sistema DS-CDMA multiusuário baseado em comunicações cooperativas auxiliadas por múltiplos retransmissores. Os dois modelos de sistema são quase iguais, exceto que em um deles, a interferência de múltiplos usuários é considerada nos retransmissores. O protocolo Amplify-and-Forward (AF) é aplicado em cada retransmissor, explorando a diversidade cooperativa. Para o sinal recebido no primeiro modelo de sistema, uma decomposição tensorial PARAFAC quadrilinear será adotada e, ao fazê-lo, o receptor semi-cego proposto pode estimar conjuntamente os símbolos transmitidos, ganhos de canais e assinaturas espaciais de todos os usuários, assumindo o conhecimento prévio dos códigos de espalhamento dos usuários e alguns símbolos transmitidos. Para o segundo modelo de sistema, interferência multiusuário é considerada nos retransmissores dos usuários, então, um receptor baseado em uma decomposição PARAFAC trilinear é proposto. O segundo receptor realiza as estimações em duas fases, sendo a primeira fase um estágio supervisionado em que todos os usuários enviam sequências de treinamento não ortogonais. Durante a segunda fase, os símbolos de dados dos usuários são então estimados. Ambos os receptores usam o algoritmo ALS (Alternating Least Squares) para ajustar os modelos tensoriais, assumindo nenhuma informação de estado do canal (CSI - Channel State Information) na estação base nem nos retransmissores. Com simulações computacionais, também forneceremos avaliação de desempenho dos receptores propostos para vários casos e variações do sistema.

FERNANDES, C. E. R. High-order statistical methods for blind channel identification and source detection with applications to wireless communications. 2008. 151 f. Tese (Doutorado em Engenharia de Teleinformática) – Centro de Tecnologia, Universidade Federal do Ceará, Fortaleza, 2008. / Submitted by Marlene Sousa (mmarlene@ufc.br) on 2016-04-01T18:38:00Z No. of bitstreams: 1 2008_tese_cerfernandes.pdf: 1821153 bytes, checksum: 5c0a056817e62e60afcf7d7944ef2a4b (MD5) / Approved for entry into archive by Marlene Sousa(mmarlene@ufc.br) on 2016-04-06T18:37:37Z (GMT) No. of bitstreams: 1 2008_tese_cerfernandes.pdf: 1821153 bytes, checksum: 5c0a056817e62e60afcf7d7944ef2a4b (MD5) / Made available in DSpace on 2016-04-06T18:37:37Z (GMT). No. of bitstreams: 1 2008_tese_cerfernandes.pdf: 1821153 bytes, checksum: 5c0a056817e62e60afcf7d7944ef2a4b (MD5) Previous issue date: 2008-05-30 / Current telecommunications systems offer services that require very high transmission rates. The channel identification problem arises in this context with a major issue. The use of blind techniques have been of great interest in the search for a better balance between an appropriate binary rates and the quality of the retrieved information. Relying on special properties of cumulants of 4th order of the signals to the channel output, this thesis introduces new signal processing tools with applications in mobile radio communication systems. Exploring the symmetrical structure of the output cumulants, the problem of blind channel identification is approached from a multilinear model tensor 4th order cumulant based on a decomposition into parallel factors (PARAFAC). If SISO, the components of the new model have a tensor Hankel structure. In the case of MIMO channels without memory, the redundancy of tensor factors is explored in the estimation of the coefficients of the channel. In this context, new blind channel identification algorithms developed in this thesis are based on a least squares optimization problem single step (SS-LS). The proposed methods fully exploit the multilinear structure of the cumulant tensor and their symmetries and redundancies, thus avoiding any form of preprocessing. Indeed, the SS-LS approach induces a solution based on a single minimization procedure without intermediate steps, contrary to what happens in most of the existing literature methods. Using only the cumulants of order 4 and exploring the concept of Virtual Arrangement, this is also the problem of location of sources, in a multiuser environment. An original Contribution is to increase the number of virtual sensors based on a particular decomposition of cumulants tensioner, thereby improving the resolution of the arrangement whose structure is typically obtained when using order statistics 6. It is considered also the estimation physical of a MIMO channel of communication with muti-routes. Via a fully blind approach, the multipath channel is first treated as a convolutional model and a new technique is proposed to estimate its coefficients. This non-parametric technique generalizes the methods previously proposed for SISO and MIMO cases (out of memory). Making use of a tensor formalism to represent the multipath MIMO channel, its physical parameters may be obtained using a combined technique of ALS-MUSIC type, based on a subspace algorithm. Finally, it will be considered the problem of determining the order of FIR channels, particularly in the case of MISO systems. A complete procedure is introduced to the detection and estimation of selective MISO communication channels in frequency. The new algorithm, based on a deflation approach successively detects each signal source, determines the order of their individual broadcast channel and estimates the associated coefficients. / Os sistemas de telecomunicações atuais oferecem servios que demandam taxas de transmissão muito elevadas. O problema da identificação de canal aparece nesse contexto com um problema da maior importância. O uso de técnicas cegas tem sido de grande interesse na busca por um melhor compromisso entre uma taxas binária adequada e a qualidade da informação recuperada. Apoiando-se em propriedades especiais dos cumulantes de 4a ordem dos sinais à saída do canal, esta tese introduz novas ferramentas de processamento de sinais com aplicações em sistemas de comunicação rádio-móveis. Explorando a estrutura simétrica dos cumulantes de saída, o problema da identificação cega de canais é abordado a partir de um modelo multilinear do tensor de cumulantes 4a ordem, baseado em uma decomposição em fatores paralelos (Parafac). No caso SISO, os componentes do novo modelo tensorial apresentam uma estrutura Hankel. No caso de canais MIMO sem memória, a redundância dos fatores tensoriais é explorada na estimação dos coeficientes dos canal. Neste contexto, novos algoritmos de identificação cega de canais são desenvolvidos nesta tese com base em um problema de otimização de mínimos quadrados de passo único (SS-LS). Os métodos propostos exploram plenamente a estrutura multilinear do tensor de cumulantes bem como suas simetrias e redundâncias, evitando assim qualquer forma de pré-processamento. Com efeito, a abordagem SS-LS induz uma solução baseada em um único procedimento de minimização, sem etapas intermediárias, contrariamente ao que ocorre na maior parte dos métodos existentes na literatura. Utilizando apenas os cumulantes de ordem 4 e explorando o conceito de Arranjo Virtual, trata-se também o problema da localização de fontes, num contexto multiusuário. Uma contribução original consiste em aumentar o número de sensores virtuais com base em uma decomposição particular do tensor de cumulantes, melhorando assim a resolução do arranjo, cuja estrutura é tipicamente obtida quando se usa estatísticas de ordem 6. Considera-se ainda a estimação dos parâmetros físicos de um canal de comunicação MIMO com muti-percursos. Através de uma abordagem completamente cega, o canal multi-percurso é primeiramente tratado como um modelo convolutivo e uma nova técnica é proposta para estimar seus coeficientes. Esta técnica não-paramétrica generaliza os métodos previamente propostos para os casos SISO e MIMO (sem memória). Fazendo uso de um formalismo tensorial para representar o canal de multi-percursos MIMO, seus parâmetros físicos podem ser obtidos através de uma técnica combinada de tipo ALS-MUSIC, baseada em um algoritmo de subespaço. Por fim, será considerado o problema da determinação de ordem de canais FIR, particularmente no caso de sistemas MISO. Um procedimento completo é introduzido para a detecção e estimação de canais de comunicação MISO seletivos em freqüência. O novo algoritmo, baseado em uma abordagem de deflação, detecta sucessivamente cada fonte de sinal, determina a ordem de seu canal de transmissão individual e estima os coeficientes associados. / Les systémes de télécommunications modernes exigent des débits de transmission trés élevés. Dans ce cadre, le probléme d’identification de canaux est un enjeu majeur. L’utilisation de techniques aveugles est d’un grand intérét pour avoir le meilleur compromis entre un taux binaire adéquat et la qualité de l’information récupérée. En utilisant les propriétés des cumulants d’ordre 4 des signaux de sortie du canal, cette thése introduit de nouvelles méthodes de traitement du signal tensoriel avec des applications pour les systémes de communication radio-mobiles. En utilisant la structure symétrique des cumulants de sortie, nous traitons le probléme de l’identification aveugle de canaux en introduisant un mod`ele multilinéaire pour le tenseur des cumulants d’ordre 4, basé sur une décomposition de type Parafac. Dans le cas SISO, les composantes du modéle tensoriel ont une structure de Hankel. Dans le cas de canaux MIMO instantanés, la redondance des facteurs tensoriels est exploitée pour l’estimation des coefficients du canal. Dans ce contexte, nous développons des algorithmes d’identification aveugle basés sur une minimisation de type moindres carrés à pas unique (SS-LS). Les méthodes proposées exploitent la structure multilinéaire du tenseur de cumulants aussi bien que les relations de symétrie et de redondance, ce qui permet d’éviter toute sorte de traitement au préalable. En effet, l’approche SS-LS induit une solution basée sur une seule et unique procédure d’optimisation, sans les étapes intermédiaires requises par la majorité des méthodes existant dans la littérature. En exploitant seulement les cumulants d’ordre 4 et le concept de réseau virtuel, nous abordons aussi le probléme de la localisation de sources dans le cadre d’un réseau d’antennes multiutilisateur. Une contribution originale consiste à augmenter le nombre de capteurs virtuels en exploitant un arrangement particulier du tenseur de cumulants, de maniére à améliorer la résolution du réseau, dont la structure équivaut à celle qui est typiquement issue de l’utilisation des statistiques d’ordre 6. Nous traitons par ailleurs le probléme de l’estimation des paramétres physiques d’un canal de communication de type MIMO à trajets multiples. Dans un premier temps, nous consid´erons le canal à trajets multiples comme un modèle MIMO convolutif et proposons une nouvelle technique d’estimation des coefficients. Cette technique non-paramétrique généralise les mèthodes proposées dans les chapitres précédents pour les cas SISO et MIMO instantané. En représentant le canal multi-trajet à l’aide d’un formalisme tensoriel, les paramètres physiques sont obtenus en utilisant une technique combinée de type ALS-MUSIC, basée sur un algorithme de sous-espaces. Enfin, nous considérons le problème de la d´etermination d’ordre de canaux de type RIF, dans le contexte des systèmes MISO. Nous introduisons une procédure complète qui combine la détection des signaux avec l’estimation des canaux de communication MISO sélectifs en fréquence. Ce nouvel algorithme, basé sur une technique de déflation, est capable de détecter successivement les sources, de déterminer l’ordre de chaque canal de transmission et d’estimer les coefficients associ´es.

nÃo hà / The results of academic performance in the discipline of Mathematics in Basic Education in Brazil, according to the benchmarking cycles of the Basic Education Assessment System (SAEB), point to a scenario that is not motivating. The negative results of Cearà revealed by SAEB, together with the national and international trend of large-scale evaluations, culminated, in 1992, when the first cycle of large-scale educational assessment of Cearà was carried out, with the aim of providing more accurate and timely information on local education and to monitor policies aimed at advancing the quality, equity, and efficiency of the state education system. However, several factors contribute to the fact that learning does not consolidate as expected. In this sense, the present thesis proposal has as general objective the accomplishment of a study that addresses two techniques of analysis, one bilinear and another trilinear, with the purpose of identifying socioeconomic factors and of institutional school climate, in conventional and professional schools, which are associated to the academic performance, especially in the Mathematics discipline, of high school students, in the city of Fortaleza-CE. The quantitative paradigm is used to measure and establish correlations, trying to identify patterns. Multivariate Analysis, in particular the Principal Component Analysis (PCA) and Multilinear Algebra technique, will be used through the tensor analysis focusing on the Decomposition in Parallel Factors (PARAFAC). The results show that: (i) that the Analysis of Variance (ANOVA) test pointed to a significant difference between students in conventional and professional schools for mathematics; (ii) the efficiency of multilinear algebra for data processing in the field of educational evaluation, since the findings in PARAFAC are directed toward the PCA, a tool readily validated by the academic community for this type of analysis. / Os resultados de desempenho acadÃmico na disciplina de MatemÃtica na EducaÃÃo BÃsica, no Brasil, segundo os ciclos de aferiÃÃo do Sistema de AvaliaÃÃo da EducaÃÃo BÃsica (SAEB), apontam para um cenÃrio nada motivador. Os resultados negativos do CearÃ, revelados pelo SAEB, em conjunto com a tendÃncia nacional e internacional de avaliaÃÃes em larga escala, culminam para que, em 1992, fosse realizado o primeiro ciclo de aferiÃÃo educacional em larga escala do CearÃ, com o intuito de dar respostas mais precisas e rÃpidas sobre a educaÃÃo local e, ainda, monitorar as polÃticas direcionadas para o avanÃo da qualidade, da equidade e da eficiÃncia do sistema educacional estadual. Contudo, diversos sÃo os fatores que contribuem para que a aprendizagem nÃo se consolide conforme o esperado. Nesse sentido, a presente proposta de tese traz como objetivo geral a realizaÃÃo de um estudo que aborde duas tÃcnicas de anÃlise, sendo uma bilinear e outra trilinear, com o intuito de identificar fatores socioeconÃmicos e de clima institucional escolar, em escolas convencionais e profissionais, que estejam associados ao desempenho acadÃmico, em especial, na disciplina de MatemÃtica, dos alunos do ensino mÃdio, no municÃpio de Fortaleza-CE. O paradigma quantitativo à utilizado de modo a realizar medidas e estabelecer correlaÃÃes, procurando identificar padrÃes. Far-se-à uso da AnÃlise Multivariada, em especial a tÃcnica de AnÃlise de Componentes Principais (PCA) e da Ãlgebra Multilinear, por meio da anÃlise tensorial focando-se na decomposiÃÃo em Fatores Paralelos (PARAFAC). Os resultados mostram: i) que o teste de AnÃlise de VariÃncia (ANOVA) apontou, para a disciplina de MatemÃtica, diferenÃa significativa entre os alunos das escolas convencionais e profissionais; ii) a eficiÃncia da Ãlgebra multilinear para tratamento de dados no campo da avaliaÃÃo educacional, uma vez que os achados no PARAFAC se encaminham na direÃÃo da PCA, ferramenta prontamente validada pela comunidade acadÃmica para esse tipo de anÃlise.

Dissolved organic matter (DOM) is a complex mixture of organic compounds and represents the largest reservoirs of carbon (C) on earth. Particulate organic matter (POM) is another important carbon component in C cycling and controls a variety of biogeochemical processes. Estuaries, as important interfaces between land and ocean, play important roles in retaining and transforming such organic matter (OM) and serve as both sources and sinks of DOM and POM. There is a diverse array of both autochthonous and allochthonous OM sources in wetland/estuarine ecosystems. A comprehensive study on the sources, transformation and fate of OM in such ecosystems is essential in advancing our understanding of C cycling and better constraining the global C budget. In this work, DOM characteristics were investigated in different estuaries. Dissolved organic matter source strengths and dynamics were assessed in a seagrass-dominated subtropical estuarine lagoon. DOM dynamics controlled by hydrology and seagrass primary productivity were confirmed, and the primary source of DOM was quantified using the combination of excitation emission matrix fluorescence with parallel factor analysis (EEM-PARAFAC) and stable C isotope analysis. Seagrass can contribute up to 72% of the DOM in the study area. The spatial and temporal variation of DOM dynamics was also studied in a freshwated dominated estuary fringed with extensive salt marshes. The data showed that DOM was primarily derived from freshwater marshes and controlled by hydrology while salt marsh plants play a significant role in structuring the distribution patterns of DOM quality and quantity. The OM dynamics was also investigated in a mangrove-dominate estuary and a comparative study was conducted between the DOM and POM pools. The results revealed both similarity and dissimilarity in DOM and POM composition. The dynamics of both OM pools are largely uncoupled as a result of source differences. Fringe mangrove swamps are suggested to export similar amounts of DOM and POM and should be considered as an important source in coastal C budgets. Lastly, chemical characterizations were conducted on the featured fluorescence component in OM in an attempt to better understand the composition and origins of the specific PARAFAC component. The traditionally defined ‘protein-like’ fluorescence was found to contain both proteinaceous and phenolic compounds, suggesting that the application of this parameter as a proxy for amino acid content and bioavailability may be limited.

Spatial and temporal patterns of dissolved organic matter (DOM) were characterized using a combination of spectroluorometric measurements and multivariate analysis techniques. The study was conducted over a four-year (2012-2016) period in multiple watersheds located in the Gulf-Atlantic Coastal Plain Physiographic region of the southeast USA as well as in the Indo-Gangetic Plain of India. Surface water samples were collected from five major lakes in the Mississippi, an estuarine region in the southeastern Louisiana, and from the coastal region in the eastern Mississippi Sound in the USA, and a large river (Ganges River) in India. Absorption and fluorescence measurements were performed to generate absorption spectra and excitation-emission matrices (EEMs). Using parallel factor analyses (PARAFAC), EEM models were developed to characterize the biogeochemistry of DOM in three studies in this project. Principal component analysis and regression analyses of DOM data indicated that the northern Mississippi lakes were majorly influenced by agricultural land use, estuarine region was affected by natural DOM export from forests and wetlands, while the coastal waters were affected by a mix of anthropogenic and natural inputs of DOM. Spatial analyses indicated that DOM derived from watershed with increased wetland coverage was humic and aromatic while the DOM derived from agricultural watersheds was bioavailable. Temporal patterns of DOM in the estuary indicated the influence of hydrologic conditions and summer temperatures, and revealed strong seasonality in DOM evolution in the watershed. During high discharge periods (spring), aromatic and humic DOM was exported from the watershed while strong photochemical degradation during summer resulted bioavailable DOM. Comparison between two river systems, a highly urbanized large river and a small pristine river, indicated the influence of anthropogenic inputs of DOM in the large river system. DOM was bioavailable during summer due to anthropogenic activities in the large river system while it varied with hydrological connectivity in a small river system during summer and winter. In conclusion, this study has improved my understandings of the DOM properties, which are critical for a comprehensive assessment of biogeochemical processes undergoing in important water bodies on which our society is heavily dependent upon.

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La disponibilité et la persistance à l'échelle locale des métaux lourds pourraient être critiques notamment pour l'usage futur des zones agricoles ou urbaines, au droit desquelles de nombreux sites industriels se sont installés dans le passé. La gestion de ces situations environnementales complexes nécessitent le développement de nouvelles méthodes d'analyse peu invasives (capteurs environnementaux), comme celles utilisant des biosenseurs bactériens, afin d'identifier et d'évaluer directement l'effet biologique et la disponibilité chimique des métaux. Ainsi dans ce travail de thèse, nous avons cherché à identifier, à l'aide d'outils mathématiques de l'algèbre multilinéaire, les réponses de senseurs bactériens fluorescents dans des conditions environnementales variées, qu'il s'agisse d'un stress engendré par la présence à forte dose d'un métal ou d'une carence nutritive engendrée par son absence. Cette identification est fondée sur l'analyse quantitative à l'échelle d'une population bactérienne de signaux multidimensionnels. Elle repose en particulier sur (i) l'acquisition de données spectrales (fluorescence) multi-variées sur des suspensions de biosenseurs multicolores interagissant avec des métaux et sur (ii) le développement d'algorithme de décomposition tensoriels. Les méthodes proposées, développées et utilisées dans ce travail s'efforcent d'identifier « sans a priori» a minima, la réponse fonctionnelle de biosenseurs sous différentes conditions environnementales, par des méthodes de décomposition de tenseurs sous contraintes des signaux spectraux observables. Elles tirent parti de la variabilité des réponses systémiques et permettent de déterminer les sources élémentaires identifiant le système et leur comportement en fonction des paramètres extérieurs. Elles sont inspirées des méthodes CP et PARALIND . L'avantage de ce type d'approche, par rapport aux approches classiques, est l'identification unique des réponses des biosenseurs sous de faibles contraintes. Le travail a consisté à développer des algorithmes efficaces de séparations de sources pour les signaux fluorescents émis par des senseurs bactériens, garantissant la séparabilité des sources fluorescentes et l'unicité de la décomposition. Le point original de la thèse est la prise en compte des contraintes liées à la physique des phénomènes analysés telles que (i) la parcimonie des coefficients de mélange ou la positivité des signaux source, afin de réduire au maximum l'usage d'a priori ou (ii) la détermination non empirique de l'ordre de la décomposition (nombre de sources). Cette posture a permis aussi d'améliorer l'identification en optimisant les mesures physiques par l'utilisation de spectres synchrones ou en apportant une diversité suffisante aux plans d'expériences. L'usage des spectres synchrones s'est avéré déterminant à la fois pour améliorer la séparation des sources de fluorescence, mais aussi pour augmenter le rapport signal sur bruit des biosenseurs les plus faibles. Cette méthode d'analyse spectrale originale permet d'élargir fortement la gamme chromatique des biosenseurs fluorescents multicolores utilisables simultanément. Enfin, une nouvelle méthode d'estimation de la concentration de polluants métalliques présents dans un échantillon à partir de la réponse spectrale d'un mélange de biosenseurs non-spécifiques a été développée / Availability and persistence of heavy metals could be critical for future use of agricultural or urban areas, on which many industrial sites have installed in the past. The management of these complex environmental situations requiring the development of new analytical methods minimally invasive, such as bacterial biosensors, to identify and directly assess the biological effects and the chemical availability of metals. The aims of this thesis was to identify the responses of fluorescent bacterial sensors various environmental conditions, using mathematical tools of algebra multi-linear, whether stress caused by the presence of high dose of a metal or a nutrient deficiency caused by his absence. This identification is based on quantitative analysis of multidimensional signals at the bacterial population-scale. It is based in particular on (i) the acquisition of multivariate spectral data on suspensions of multicolored biosensors interacting with metals and (ii) the development of algorithms for tensor decomposition. The proposed methods, developed and used in this study attempt to identify functional response of biosensors without \textsl{a priori} by decomposition of tensor containing the spectral signals. These methods take advantage of the variability of systemic responses and allow to determine the basic sources identifying the system and their behavior to external factors. They are inspired by the CP and PARALIND methods. The advantage of this approach, compared to conventional approaches, is the unique identification of the responses of biosensors at low constraints. The work was to develop efficient algorithms for the source separation of fluorescent signals emitted by bacterial sensors, ensuring the sources separability and the uniqueness of the decomposition. The original point of this thesis is the consideration of the physical constraints of analyzed phenomena such as (i) the sparsity of mixing coefficients or positivity of sources signals in order to minimize the use of a priori or (ii) the non-empirical determination of the order of decomposition (number of sources).This posture has also improved the identification optimizing physical measurements by the use of synchronous spectra or providing sufficient diversity in design of experiments. The use of synchronous spectra proved crucial both to improve the separation of fluorescent sources, but also to increase the signal to noise ratio of the lowest biosensors. This original method of spectral analysis can greatly expand the color range of multicolored fluorescent biosensors used simultaneously. Finally, a new method of estimating the concentration of metal pollutants present in a sample from the spectral response of a mixture of non-specific biosensor was developed