Synchronization and Detection Techniques for Navigation and Communication Systems

Synchronization is a key issue in any communication system, but it becomes fundamental in the navigation systems, which are entirely based on the estimation of the time delay of the signals coming from the satellites. Thus, even if synchronization has been a well known topic for many years, the introduction of new modulations and new physical layer techniques in the modern standards makes the traditional synchronization strategies completely ineffective. For this reason, the design of advanced and innovative techniques for synchronization in modern communication systems, like DVB-SH, DVB-T2, DVB-RCS, WiMAX, LTE, and in the modern navigation system, like Galileo, has been the topic of the activity. Recent years have seen the consolidation of two different trends: the introduction of Orthogonal Frequency Division Multiplexing (OFDM) in the communication systems, and of the Binary Offset Carrier (BOC) modulation in the modern Global Navigation Satellite Systems (GNSS). Thus, a particular attention has been given to the investigation of the synchronization algorithms in these areas.

Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

Static analysis of functionally graded cylindrical and conical shells or panels using the generalized unconstrained third order theory coupled with the stress recovery

A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded conical and cylindrical shells subjected to mechanical loadings. Several types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the conical or cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally conical and cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Code synchronization and interference management techniques for satellite navigation and communications

This thesis collects the outcomes of a Ph.D. course in Telecommunications engineering and it is focused on enabling techniques for Spread Spectrum (SS) navigation and communication satellite systems. It provides innovations for both interference management and code synchronization techniques. These two aspects are critical for modern navigation and communication systems and constitute the common denominator of the work. The thesis is organized in two parts: the former deals with interference management. We have proposed a novel technique for the enhancement of the sensitivity level of an advanced interference detection and localization system operating in the Global Navigation Satellite System (GNSS) bands, which allows the identification of interfering signals received with power even lower than the GNSS signals. Moreover, we have introduced an effective cancellation technique for signals transmitted by jammers, exploiting their repetitive characteristics, which strongly reduces the interference level at the receiver. The second part, deals with code synchronization. More in detail, we have designed the code synchronization circuit for a Telemetry, Tracking and Control system operating during the Launch and Early Orbit Phase; the proposed solution allows to cope with the very large frequency uncertainty and dynamics characterizing this scenario, and performs the estimation of the code epoch, of the carrier frequency and of the carrier frequency variation rate. Furthermore, considering a generic pair of circuits performing code acquisition, we have proposed a comprehensive framework for the design and the analysis of the optimal cooperation procedure, which minimizes the time required to accomplish synchronization. The study results particularly interesting since it enables the reduction of the code acquisition time without increasing the computational complexity. Finally, considering a network of collaborating navigation receivers, we have proposed an innovative cooperative code acquisition scheme, which allows exploit the shared code epoch information between neighbor nodes, according to the Peer-to-Peer paradigm.

Modelling and analysis of thin-walled beams in the context of the Generalized Beam Theory

In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After an introduction to the subject and a quick review of some of the most well-known approaches to describe the behaviour of thin-walled beams, a novel formulation of the GBT is presented. This formulation contains the classic shear-deformable GBT available in the literature and contributes an additional description of cross-section warping that is variable along the wall thickness besides along the wall midline. Shear deformation is introduced in such a way that the classical shear strain components of the Timoshenko beam theory are recovered exactly. According to the new kinematics proposed, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition. Later, a procedure for a posteriori reconstruction of all the three-dimensional stress components in the finite element analysis of thin-walled beams using the GBT is presented. The reconstruction is simple and based on the use of three-dimensional equilibrium equations and of the RCP procedure. Finally, once the stress reconstruction procedure is presented, a study of several existing issues on the constitutive relations in the GBT is carried out. Specifically, a constitutive law based on mirroring the kinematic constraints of the GBT model into a specific stress field assumption is proposed. It is shown that this method is equally valid for isotropic and orthotropic beams and coincides with the conventional GBT approach available in the literature. Later on, an analogous procedure is presented for the case of laminated beams. Lastly, as a way to improve an inherently poor description of shear deformability in the GBT, the introduction of shear correction factors is proposed. Throughout this work, numerous examples are provided to determine the validity of all the proposed contributions to the field.