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.

New phosphorescence based probes and techniques for the analysis of cellular oxygen and respiration

Real time monitoring of oxygenation and respiration is on the cutting edge of bioanalysis, including studies of cell metabolism, bioenergetics, mitochondrial function and drug toxicity. This thesis presents the development and evaluation of new luminescent probes and techniques for intracellular O2 sensing and imaging. A new oxygen consumption rate (OCR) platform based on the commercial microfluidic perfusion channel μ-slides compatible with extra- and intracellular O2 sensitive probes, different cell lines and measurement conditions was developed. The design of semi-closed channels allowed cell treatments, multiplexing with other assays and two-fold higher sensitivity to compare with microtiter plate. We compared three common OCR platforms: hermetically sealed quartz cuvettes for absolute OCRs, partially sealed with mineral oil 96-WPs for relative OCRs, and open 96-WPs for local cell oxygenation. Both 96-WP platforms were calibrated against absolute OCR platform with MEF cell line, phosphorescent O2 probe MitoXpress-Intra and time-resolved fluorescence reader. Found correlations allow tracing of cell respiration over time in a high throughput format with the possibility of cell stimulation and of changing measurement conditions. A new multimodal intracellular O2 probe, based on the phosphorescent reporter dye PtTFPP, fluorescent FRET donor and two-photon antennae PFO and cationic nanoparticles RL-100 was described. This probe, called MM2, possesses high brightness, photo- and chemical stability, low toxicity, efficient cell staining and high-resolution intracellular O2 imaging with 2D and 3D cell cultures in intensity, ratiometric and lifetime-based modalities with luminescence readers and FLIM microscopes. Extended range of O2 sensitive probes was designed and studied in order to optimize their spectral characteristics and intracellular targeting, using different NPs materials, delivery vectors, ratiometric pairs and IR dyes. The presented improvements provide useful tool for high sensitive monitoring and imaging of intracellular O2 in different measurement formats with wide range of physiological applications.