Minimal state-space realizations of 2D convolutional codes

In this thesis we consider two-dimensional (2D) convolutional codes. As happens in the one-dimensional (1D) case one of the major issues is obtaining minimal state-space realizations for these codes. It turns out that the problem of minimal realization of codes is not equivalent to the minimal realization of encoders. This is due to the fact that the same code may admit different encoders with different McMillan degrees. Here we focus on the study of minimality of the realizations of 2D convolutional codes by means of separable Roesser models. Such models can be regarded as a series connection between two 1D systems. As a first step we provide an algorithm to obtain a minimal realization of a 1D convolutional code starting from a minimal realization of an encoder of the code. Then, we restrict our study to two particular classes of 2D convolutional codes. The first class to be considered is the one of codes which admit encoders of type n 1. For these codes, minimal encoders (i.e., encoders for which a minimal realization is also minimal as a code realization) are characterized enabling the construction of minimal code realizations starting from such encoders. The second class of codes to be considered is the one constituted by what we have called composition codes. For a subclass of these codes, we propose a method to obtain minimal realizations by means of separable Roesser models.

A Periodic State Space Model to Monthly Long-term Temperature Data

This work presents a periodic state space model to model monthly temperature data. Additionally, some issues are discussed, as the parameter estimation or the Kalman filter recursions adapted to a periodic model. This framework is applied to monthly long-term temperature time series of Lisbon.

Structural Time Series Modeling: an Application to Environmental Variables

A structural time series model is one which is set up in terms of components which have a direct interpretation. In this paper, the discussion focuses on the dynamic modeling procedure based on the state space approach (associated to the Kalman filter), in the context of surface water quality monitoring, in order to analyze and evaluate the temporal evolution of the environmental variables, and thus identify trends or possible changes in water quality (change point detection). The approach is applied to environmental time series: time series of surface water quality variables in a river basin. The statistical modeling procedure is applied to monthly values of physico- chemical variables measured in a network of 8 water monitoring sites over a 15-year period (1999-2014) in the River Ave hydrological basin located in the Northwest region of Portugal.

Numerical modelling of radionuclide migration in near-surface systems

Em todo o mundo são usados, hoje em dia, modelos numéricos hidrogeoquímicos para simular fenómenos naturais e fenómenos decorrentes de actividades antrópicas. Estes modelos ajudam-nos a compreender o ambiente envolvente, a sua variabilidade espacial e evolução temporal. No presente trabalho apresenta-se o desenvolvimento de modelos numéricos hidrogeoquímicos aplicados no contexto do repositório geológico profundo para resíduos nucleares de elevada actividade. A avaliação da performance de um repositório geológico profundo inclui o estudo da evolução geoquímica do repositório, bem como a análise dos cenários de mau funcionamento do repositório, e respectivas consequências ambientais. Se se escaparem acidentalmente radionuclídeos de um repositório, estes poderão atravessar as barreiras de engenharia e barreiras naturais que constituem o repositório, atingindo eventualmente, os ecosistemas superficiais. Neste caso, os sedimentos subsuperficiais constituem a última barreira natural antes dos ecosistemas superficiais. No presente trabalho foram desenvolvidos modelos numéricos que integram processos biogeoquímicos, geoquímicos, hidrodinâmicos e de transporte de solutos, para entender e quantificar a influência destes processos na mobilidade de radionuclídeos em sistemas subsuperficiais. Os resultados alcançados reflectem a robustez dos instrumentos numéricos utilizados para desenvolver simulações descritivas e predictivas de processos hidrogeoquímicos que influenciam a mobilidade de radionuclídeos. A simulação (descritiva) de uma experiência laboratorial revela que a actividade microbiana induz a diminuição do potencial redox da água subterrânea que, por sua vez, favorece a retenção de radionuclídeos sensíveis ao potencial redox, como o urânio. As simulações predictivas indicam que processos de co-precipitação com minerais de elementos maioritários, precipitação de fases puras, intercâmbio catiónico e adsorção à superfície de minerais favorecem a retenção de U, Cs, Sr e Ra na fase sólida de uma argila glaciar e uma moreia rica em calcite. A etiquetagem dos radionuclídeos nas simulações numéricas permitiu concluir que a diluição isotópica joga um papel importante no potencial impacte dos radionuclídeos nos sistemas subsuperficiais. A partir dos resultados das simulações numéricas é possivel calcular coeficientes de distribuição efectivos. Esta metodologia proporciona a simulação de ensaios de traçadores de longa duração que não seriam exequíveis à escala da vida humana. A partir destas simulações podem ser obtidos coeficientes de retardamento que são úteis no contexto da avaliação da performance de repositórios geológicos profundos.

Channel modelling for MIMO systems

Systems equipped with multiple antennas at the transmitter and at the receiver, known as MIMO (Multiple Input Multiple Output) systems, offer higher capacities, allowing an efficient exploitation of the available spectrum and/or the employment of more demanding applications. It is well known that the radio channel is characterized by multipath propagation, a phenomenon deemed problematic and whose mitigation has been achieved through techniques such as diversity, beamforming or adaptive antennas. By exploring conveniently the spatial domain MIMO systems turn the characteristics of the multipath channel into an advantage and allow creating multiple parallel and independent virtual channels. However, the achievable benefits are constrained by the propagation channel’s characteristics, which may not always be ideal. This work focuses on the characterization of the MIMO radio channel. It begins with the presentation of the fundamental results from information theory that triggered the interest on these systems, including the discussion of some of their potential benefits and a review of the existing channel models for MIMO systems. The characterization of the MIMO channel developed in this work is based on experimental measurements of the double-directional channel. The measurement system is based on a vector network analyzer and a two-dimensional positioning platform, both controlled by a computer, allowing the measurement of the channel’s frequency response at the locations of a synthetic array. Data is then processed using the SAGE (Space-Alternating Expectation-Maximization) algorithm to obtain the parameters (delay, direction of arrival and complex amplitude) of the channel’s most relevant multipath components. Afterwards, using a clustering algorithm these data are grouped into clusters. Finally, statistical information is extracted allowing the characterization of the channel’s multipath components. The information about the multipath characteristics of the channel, induced by existing scatterers in the propagation scenario, enables the characterization of MIMO channel and thus to evaluate its performance. The method was finally validated using MIMO measurements.