A Study of Synchronization Techniques for Optical Communication Systems

The study of synchronization techniques and related topics in the design of high data rate, deep space, optical communication systems was reported. Data cover: (1) effects of timing errors in narrow pulsed digital optical systems, (2) accuracy of microwave timing systems operating in low powered optical systems, (3) development of improved tracking systems for the optical channel and determination of their tracking performance, (4) development of usable photodetector mathematical models for application to analysis and performance design in communication receivers, and (5) study application of multi-level block encoding to optical transmission of digital data

Pricing financial and insurance products in the multivariate setting

In finance and insurance there is often the need to construct multivariate distributions to take into account more than one source of risk, where such risks cannot be assumed to be independent. In the course of this thesis we are going to explore three models, namely the copula models, the trivariate reduction scheme and mixtures as candidate models for capturing the dependence between multiple sources of risk. This thesis contains results of three different projects. The first one is in financial mathematics, more precisely on the pricing of financial derivatives (multi-asset options) which depend on multiple underlying assets, where we construct the dependence between such assets using copula models and the trivariate reduction scheme. The second and the third projects are in actuarial mathematics, more specifically on the pricing of the premia that need to be paid by policyholders in the automobile insurance when more than one type of claim is considered. We do the pricing including all the information available about the characteristics of the policyholders and their cars (i.e. a priori ratemaking) and about the numbers of claims per type in which the policyholders have been involved (i.e. a posteriori ratemaking). In both projects we model the dependence between the multiple types of claims using mixture distributions/regression models: we consider the different types of claims to be modelled in terms of their own distribution/regression model but with a common heterogeneity factor which follows a mixing distribution/regression model that is responsible for the dependence between the multiple types of claims. In the second project we present a new model (i.e. the bivariate Negative Binomial-Inverse Gaussian regression model) and in the third one we present a new family of models (i.e. the bivariate mixed Poisson regression models with varying dispersion), both as suitable alternatives to the classically used bivariate mixed Poisson regression models

Adaptive OFDM Radar for Target Detection and Tracking

We develop algorithms to detect and track targets by employing a wideband orthogonal frequency division multiplexing: OFDM) radar signal. The frequency diversity of the OFDM signal improves the sensing performance since the scattering centers of a target resonate variably at different frequencies. In addition, being a wideband signal, OFDM improves the range resolution and provides spectral efficiency. We first design the spectrum of the OFDM signal to improve the radar\u27s wideband ambiguity function. Our designed waveform enhances the range resolution and motivates us to use adaptive OFDM waveform in specific problems, such as the detection and tracking of targets. We develop methods for detecting a moving target in the presence of multipath, which exist, for example, in urban environments. We exploit the multipath reflections by utilizing different Doppler shifts. We analytically evaluate the asymptotic performance of the detector and adaptively design the OFDM waveform, by maximizing the noncentrality-parameter expression, to further improve the detection performance. Next, we transform the detection problem into the task of a sparse-signal estimation by making use of the sparsity of multiple paths. We propose an efficient sparse-recovery algorithm by employing a collection of multiple small Dantzig selectors, and analytically compute the reconstruction performance in terms of the $ell_1$-constrained minimal singular value. We solve a constrained multi-objective optimization algorithm to design the OFDM waveform and infer that the resultant signal-energy distribution is in proportion to the distribution of the target energy across different subcarriers. Then, we develop tracking methods for both a single and multiple targets. We propose an tracking method for a low-grazing angle target by realistically modeling different physical and statistical effects, such as the meteorological conditions in the troposphere, curved surface of the earth, and roughness of the sea-surface. To further enhance the tracking performance, we integrate a maximum mutual information based waveform design technique into the tracker. To track multiple targets, we exploit the inherent sparsity on the delay-Doppler plane to develop an computationally efficient procedure. For computational efficiency, we use more prior information to dynamically partition a small portion of the delay-Doppler plane. We utilize the block-sparsity property to propose a block version of the CoSaMP algorithm in the tracking filter