Digital predistortion for compensation of nonlinearities in Radio over Fiber Links

In order to cope up with the ever increasing demand for larger transmission bandwidth, Radio over Fiber technology is a very beneficial solution. These systems are expected to play a major role within future fifth generation wireless networks due to their inherent capillary distribution properties. Nonlinear compensation techniques are becoming increasingly important to improve the performance of telecommunication channels by compensating for channel nonlinearities. Indeed, significant bounds on the technology usability and performance degradation occur due to nonlinear characteristics of optical transmitter, nonlinear generation of spurious frequencies, which, in the case of RoF links exploiting Directly Modulated Lasers , has the combined effect of laser chirp and optical fiber dispersion among its prevailing causes. The purpose of the research is to analyze some of the main causes of harmonic and intermodulation distortion present in Radio over Fiber (RoF) links, and to suggest a solution to reduce their effects, through a digital predistortion technique. Predistortion is an effective and interesting solution to linearize and this allows to demonstrate that the laser’s chirp and the optical fiber’s dispersion are the main causes which generate harmonic distortion. The improvements illustrated are only theoretical, based on a feasibility point of view. The simulations performed lead to significant improvements for short and long distances of radio over fiber link lengths. The algorithm utilized for simulation has been implemented on MATLAB. The effects of chirp and fiber nonlinearity in a directly modulated fiber transmission system are investigated by simulation, and a cost effective and rather simple technique for compensating these effects is discussed. A detailed description of its functional model is given, and its attractive features both in terms of quality improvement of the received signal, and cost effectiveness of the system are illustrated.

Differential forms on Carnot groups

The main goal of this thesis is to understand and link together some of the early works by Michel Rumin and Pierre Julg. The work is centered around the so-called Rumin complex, which is a construction in subRiemannian geometry. A Carnot manifold is a manifold endowed with a horizontal distribution. If further a metric is given, one gets a subRiemannian manifold. Such data arise in different contexts, such as: - formulation of the second principle of thermodynamics; - optimal control; - propagation of singularities for sums of squares of vector fields; - real hypersurfaces in complex manifolds; - ideal boundaries of rank one symmetric spaces; - asymptotic geometry of nilpotent groups; - modelization of human vision. Differential forms on a Carnot manifold have weights, which produces a filtered complex. In view of applications to nilpotent groups, Rumin has defined a substitute for the de Rham complex, adapted to this filtration. The presence of a filtered complex also suggests the use of the formal machinery of spectral sequences in the study of cohomology. The goal was indeed to understand the link between Rumin's operator and the differentials which appear in the various spectral sequences we have worked with: - the weight spectral sequence; - a special spectral sequence introduced by Julg and called by him Forman's spectral sequence; - Forman's spectral sequence (which turns out to be unrelated to the previous one). We will see that in general Rumin's operator depends on choices. However, in some special cases, it does not because it has an alternative interpretation as a differential in a natural spectral sequence. After defining Carnot groups and analysing their main properties, we will introduce the concept of weights of forms which will produce a splitting on the exterior differential operator d. We shall see how the Rumin complex arises from this splitting and proceed to carry out the complete computations in some key examples. From the third chapter onwards we will focus on Julg's paper, describing his new filtration and its relationship with the weight spectral sequence. We will study the connection between the spectral sequences and Rumin's complex in the n-dimensional Heisenberg group and the 7-dimensional quaternionic Heisenberg group and then generalize the result to Carnot groups using the weight filtration. Finally, we shall explain why Julg required the independence of choices in some special Rumin operators, introducing the Szego map and describing its main properties.

Fibered knots and links in lens spaces

La tesi propone alcuni esempi di link fibrati in spazi lenticolari. Sfruttando la compatibilità fra le mosse di chirurgia intera e la nozione di open book decomposition, si ricava un esempio di link fibrato prima in L(p,1), per poi generalizzarlo a L(p,q). Si conclude determinando una struttura di contatto equivalente alla open book relativa agli spazi del tipo L(p,1).