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.

Chamber investigations of atmospheric mercury oxidation chemistry

Mercury is a potent neurotoxin even at low concentrations. The unoxidised metal has a high vapour pressure and can circulate through the atmosphere, but when oxidised can deposit and be accumulated through the food chain. This work aims to investigate the oxidation processes of atmospheric Hg0(g). The first part describes efforts to make a portable Hg sensor based on Cavity Enhanced Absorption Spectroscopy (CEAS). The detection limit achieved was 66 ngm−3 for a 10 second averaging time. The second part of this work describes experiments carried out in a temperature controlled atmospheric simulation chamber in the Desert Research Institute, Reno, Nevada, USA. The chamber was built around an existing Hg CRDS system that could measure Hg concentrations in the chamber of<100 ngm−3 at 1 Hz enabling reactions to be followed. The main oxidant studied was bromine, which was quantified with a LED based CEAS system across the chamber. Hg oxidation in the chamber was found to be mostly too slow for current models to explain. A seven reaction model was developed and tested to find which parameters were capable of explaining the deviation. The model was overdetermined and no unique solution could be found. The most likely possibility was that the first oxidation step Hg + Br →HgBr was slower than the preferred literature value by a factor of two. However, if the more uncertain data at low [Br2] was included then the only parameter that could explain the experiments was a fast, temperature independent dissociation of HgBr some hundreds of times faster than predicted thermolysis or photolysis rates. Overall this work concluded that to quantitatively understand the reaction of Hg with Br2, the intermediates HgBr and Br must be measured. This conclusion will help to guide the planning of future studies of atmospheric Hg chemistry.