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.

A craniometric study of population dynamics and social organisation in the European upper Palaeolithic and Mesolithic

The purpose of this study is to explore aspects of social organisation during the Upper Palaeolithic and Mesolithic periods using craniometric data. Different hypotheses were tested using geometric morphometrics, alongside traditional craniometric data. The clustering of individuals from the same site, as well as a correspondence to an isolation-by-distance model—particular in the Mesolithic samples—points to population structure within these groups. Moreover, discontinuities in cranial traits between the early Upper Palaeolithic and later periods could suggest that the Last Glacial Maximum had a disruptive effect on populations in Europe. Differences in social organisation can often result from cultural norms regarding post-marital residence. Such differences can be tested by comparing cranial data to that of geographic information. Greater variation in male cranial traits relative to females, after controlling for location, suggests that the overall pattern of residence during the Upper Palaeolithic and Mesolithic was one of matrilocality. It has been suggested that coastal occupation was density dependent and these populations show a greater degree of sedentism than their inland counterparts. Moreover, it has been proposed that coastal areas were not continuously occupied until the Late Pleistocene due to spatial restrictions that would adversely affect reproductive opportunities. This study corroborates the pattern seen in cranial traits corresponded with that of a more sedentary population. The results are consistent with the hypothesis that coastal populations are more sedentary than inland populations during these periods. This study adds new information regarding the social dynamics of prehistoric populations in Europe and sheds light on some of the conditions that may have paved the way for the transition to agriculture