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.

The exploration of potato-associated bacteria in the Central Andean Highlands and their application in integrated crop management systems

Potato is the most important food crop after wheat and rice. A changing climate, coupled with a heightened consumer awareness of how food is produced and legislative changes governing the usage of agrochemicals, means that alternative more integrated and sustainable approaches are needed for crop management practices. Bioprospecting in the Central Andean Highlands resulted in the isolation and in vitro screening of 600 bacterial isolates. The best performing isolates, under in vitro conditions, were field trialled in their home countries. Six of the isolates, Pseudomonas sp. R41805 (Bolivia), Pseudomonas palleroniana R43631 (Peru), Bacillus sp. R47065, R47131, Paenibacillus sp. B3a R49541, and Bacillus simplex M3-4 R49538 (Ecuador), showed significant increase in the yield of potato. Using – omic technologies (i.e. volatilomic, transcriptomic, proteomic and metabolomic), the influence of microbial isolates on plant defence responses was determined. Volatile organic compounds of bacterial isolates were identified using GC/MS. RT-qPCR analysis revealed the significant expression of Ethylene Response Factor 3 (ERF3) and the results of this study suggest that the dual inoculation of potato with Pseudomonas sp. R41805 and Rhizophagus irregularis MUCL 41833 may play a part in the activation of plant defence system via ERF3. The proteomic analysis by 2-DE study has shown that priming by Pseudomonas sp. R41805 can induce the expression of proteins related to photosynthesis and protein folding in in vitro potato plantlets. The metabolomics study has shown that the total glycoalkaloid (TGA) content of greenhouse-grown potato tubers following inoculation with Pseudomonas sp. R41805 did not exceed the acceptable safety limit (200 mg kg-1 FW). As a result of this study, a number of bacteria have been identified with commercial potential that may offer sustainable alternatives in both Andean and European agricultural settings.

The inverse limit of GIT quotients of Grassmannians by the maximal torus

There are finitely many GIT quotients of