Distributed coding for systems with cooperative diversity

O presente trabalho propõe-se a divulgar as mais significativas técnicas de esquemas cooperativos, de forma a ultrapassar alguns dos problemas dos sistemas móveis sem fios da próxima geração, estendendo a área de cobertura destes sistemas, assim como a sua capacidade e fiabilidade. O estudo de diversos esquemas cooperativos é efetuado em termos de capacidade e de taxa de erros, fazendo variar o número de relays e de antenas em cada elemento do sistema. Diversos algoritmos com aplicação em sistemas cooperativos são desenvolvidos e propostos ao longo desta tese, como códigos espaço-frequência aplicados de forma distribuída nos relays, para sistemas baseados na tecnologia OFDM e sob diversos cenários próximos da realidade. Os sistemas cooperativos são particularmente úteis em situações em que o caminho direto entre dois terminais não está acessível ou tem uma fraca qualidade de transmissão. Tendo este aspeto em consideração, e pretendendo ter a máxima eficiência espetral e máxima diversidade, um algoritmo com precodificação é também proposto para múltiplos relays, cada um equipado com uma ou duas antenas. A formulação matemática associada aos algoritmos propostos é apresentada, assim como a derivação da probabilidade de erro teórica. O desempenho dos sistemas assistidos por relays usando os algoritmos propostos é comparado em relação a outros esquemas cooperativos equivalentes e a esquemas não-cooperativos, considerando cenários com diferentes qualidades de canal, daí advindo importantes conclusões em relação a estes sistemas.

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

Quasilinear elliptic systems with measure data

We study the existence of solutions of quasilinear elliptic systems involving $N$ equations and a measure on the right hand side, with the form $$\left\{\begin{array}{ll} -\sum_{i=1}^n \frac{\partial}{\partial x_i}\left(\sum\limits_{\beta=1}^{N}\sum\limits_{j=1}^{n}% a_{i,j}^{\alpha,\beta}\left( x,u\right)\frac{\partial}{\partial x_j}u^\beta\right)=\mu^\alpha& \mbox{ in }\Omega ,\\ u=0 & \mbox{ on }\partial\Omega, \end{array}\right.$$ where $\alpha\in\{1,\dots,N\}$ is the equation index, $\Omega$ is an open bounded subset of $\mathbb{R}^{n}$, $u:\Omega\rightarrow\mathbb{R}^{N}$ and $\mu$ is a finite Randon measure on $\mathbb{R}^{n}$ with values into $\mathbb{R}^{N}$. Existence of a solution is proved for two different sets of assumptions on $A$. Examples are provided that satisfy our conditions, but do not satisfy conditions required on previous works on this matter.

Critical magnetic elds in superconducting systems with semi-metallic bands

In this work, we study the Zeeman splitting effects in the parallel magnetic field versus temperature phase diagram of two-dimensional superconductors with one graphene-like band and the orbital effects of perpendicular magnetic fields in isotropic two-dimensional semi-metallic superconductors. We show that when parallel magnetic fields are applied to graphene and as the intraband interaction decreases to a critical value, the width of the metastability region present in the phase diagram decreases, vanishing completely at that critical value. In the case of two-band superconductors with one graphene-like band, a new critical interaction, associated primarily with the graphene-like band, is required in order for a second metastability region to be present in the phase diagram. For intermediate values of this interaction, a low-temperature first-order transition line bifurcates at an intermediate temperature into a first-order transition between superconducting phases and a second-order transition line between the normal and the superconducting states. In our study on the upper critical fields in generic semi-metallic superconductors, we find that the pair propagator decays faster than that of a superconductor with a metallic band. As result, the zero field band gap equation does not have solution for weak intraband interactions, meaning that there is a critical intraband interaction value in order for a superconducting phase to be present in semi-metallic superconductors. Finally, we show that the out-of-plane critical magnetic field versus temperature phase diagram displays a positive curvature, contrasting with the parabolic-like behaviour typical of metallic superconductors.