Analysing energy detector diversity receivers for spectrum sensing

The analysis of energy detector systems is a well studied topic in the literature: numerous models have been derived describing the behaviour of single and multiple antenna architectures operating in a variety of radio environments. However, in many cases of interest, these models are not in a closed form and so their evaluation requires the use of numerical methods. In general, these are computationally expensive, which can cause difficulties in certain scenarios, such as in the optimisation of device parameters on low cost hardware. The problem becomes acute in situations where the signal to noise ratio is small and reliable detection is to be ensured or where the number of samples of the received signal is large. Furthermore, due to the analytic complexity of the models, further insight into the behaviour of various system parameters of interest is not readily apparent. In this thesis, an approximation based approach is taken towards the analysis of such systems. By focusing on the situations where exact analyses become complicated, and making a small number of astute simplifications to the underlying mathematical models, it is possible to derive novel, accurate and compact descriptions of system behaviour. Approximations are derived for the analysis of energy detectors with single and multiple antennae operating on additive white Gaussian noise (AWGN) and independent and identically distributed Rayleigh, Nakagami-m and Rice channels; in the multiple antenna case, approximations are derived for systems with maximal ratio combiner (MRC), equal gain combiner (EGC) and square law combiner (SLC) diversity. In each case, error bounds are derived describing the maximum error resulting from the use of the approximations. In addition, it is demonstrated that the derived approximations require fewer computations of simple functions than any of the exact models available in the literature. Consequently, the regions of applicability of the approximations directly complement the regions of applicability of the available exact models. Further novel approximations for other system parameters of interest, such as sample complexity, minimum detectable signal to noise ratio and diversity gain, are also derived. In the course of the analysis, a novel theorem describing the convergence of the chi square, noncentral chi square and gamma distributions towards the normal distribution is derived. The theorem describes a tight upper bound on the error resulting from the application of the central limit theorem to random variables of the aforementioned distributions and gives a much better description of the resulting error than existing Berry-Esseen type bounds. A second novel theorem, providing an upper bound on the maximum error resulting from the use of the central limit theorem to approximate the noncentral chi square distribution where the noncentrality parameter is a multiple of the number of degrees of freedom, is also derived.

Access to modified geiparvarins using Pd(0)-mediated C-C bond forming reactions

Geiparvarin is a natural product which contains both a 3(2H)-furanone and a coumarin moiety in its structure. The aim of this project was to investigate the use of Pd(0)-mediated C–C bondforming reactions to produce structurally modified geiparvarins. Chapter 1 consists of a review of the relevant literature, including that pertaining to the syntheses of selected naturally occurring 3(2H)-furanones. The known syntheses of geiparvarin and closely related analogues are examined, along with the documented biological activity of these compounds. The synthetic routes which allow access to 4-substituted-3(2H)-furanones are also described. Chapter 2 describes in detail the synthesis of a variety of novel structurally modified geiparvarins by two complementary routes, both approaches utilising Pd(0)-mediated crosscoupling reactions, and discusses the characterisation of these compounds. The preparation of 5-ethyl-3(2H)-furanones is described, as is their incorporation into geiparvarin and the corresponding 5″-alkylgeiparvarin analogues via formation and dehydration of intermediate alcohols. Halogenation of 5-ethyl-3(2H)-furanones and the corresponding geiparvarin derivatives is discussed, along with further reactions of the resulting halides. Preparation of 3″-arylgeiparvarins involving both Suzuki–Miyura and Stille reactions, using the appropriate intermediate iodides and bromides, is described. The application of Stille and Heck conditions to give 3″-ethenylgeiparvarin analogues and Sonogashira conditions to produce 3″-ethynylgeiparvarin analogues, using the relevant intermediate iodides, is also extensively outlined. Chapter 3 contains all of the experimental data and details of the synthetic methods employed for the compounds prepared during the course of this research. All novel compounds prepared were fully characterised using NMR spectroscopy, IR spectroscopy, mass spectrometry and elemental analysis; the details of which are included.

Preserving patent policy space and securing access to medicines in developing countries: the role of states and pharmaceutical corporations

This thesis examines the tension between patent rights and the right to health and it recognizes patent rights on pharmaceutical products as one of the factors responsible for the problem of lack of access to affordable medicines in developing countries. The thesis contends that, in order to preserve their patent policy space and secure access to affordable medicines for their citizens, developing countries should incorporate a model of human rights into the design, implementation, interpretation, and enforcement of their national patent laws. The thesis provides a systematic analysis of court decisions from four key developing countries (Brazil, India, Kenya, and South Africa) and it assesses how the national courts in these countries resolve the tension between patent rights and the right to health. Essentially, this thesis demonstrates how a model of human rights can be incorporated into the adjudication of disputes involving patent rights in national courts. Focusing specifically on Brazil, the thesis equally demonstrates how policy makers and law makers at the national level can incorporate a model of human rights into the design or amendment of their national patent law. This thesis also contributes to the ongoing debate in the field of business and human rights with regard to the mechanisms that can be used to hold corporate actors accountable for their human rights responsibilities. This thesis recognizes that, while states bear the primary responsibility to respect, protect, and fulfil the right to health, corporate actors such as pharmaceutical companies also have a baseline responsibility to respect the right to health. This thesis therefore contends that pharmaceutical companies that own patent rights on pharmaceutical products can be held accountable for their right to health responsibilities at the national level through the incorporation of a model of civic participation into a country’s patent law system.