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.

Reasoning with imprecise trade-offs in decision making under certainty and uncertainty

In many real world situations, we make decisions in the presence of multiple, often conflicting and non-commensurate objectives. The process of optimizing systematically and simultaneously over a set of objective functions is known as multi-objective optimization. In multi-objective optimization, we have a (possibly exponentially large) set of decisions and each decision has a set of alternatives. Each alternative depends on the state of the world, and is evaluated with respect to a number of criteria. In this thesis, we consider the decision making problems in two scenarios. In the first scenario, the current state of the world, under which the decisions are to be made, is known in advance. In the second scenario, the current state of the world is unknown at the time of making decisions. For decision making under certainty, we consider the framework of multiobjective constraint optimization and focus on extending the algorithms to solve these models to the case where there are additional trade-offs. We focus especially on branch-and-bound algorithms that use a mini-buckets algorithm for generating the upper bound at each node of the search tree (in the context of maximizing values of objectives). Since the size of the guiding upper bound sets can become very large during the search, we introduce efficient methods for reducing these sets, yet still maintaining the upper bound property. We define a formalism for imprecise trade-offs, which allows the decision maker during the elicitation stage, to specify a preference for one multi-objective utility vector over another, and use such preferences to infer other preferences. The induced preference relation then is used to eliminate the dominated utility vectors during the computation. For testing the dominance between multi-objective utility vectors, we present three different approaches. The first is based on a linear programming approach, the second is by use of distance-based algorithm (which uses a measure of the distance between a point and a convex cone); the third approach makes use of a matrix multiplication, which results in much faster dominance checks with respect to the preference relation induced by the trade-offs. Furthermore, we show that our trade-offs approach, which is based on a preference inference technique, can also be given an alternative semantics based on the well known Multi-Attribute Utility Theory. Our comprehensive experimental results on common multi-objective constraint optimization benchmarks demonstrate that the proposed enhancements allow the algorithms to scale up to much larger problems than before. For decision making problems under uncertainty, we describe multi-objective influence diagrams, based on a set of p objectives, where utility values are vectors in Rp, and are typically only partially ordered. These can be solved by a variable elimination algorithm, leading to a set of maximal values of expected utility. If the Pareto ordering is used this set can often be prohibitively large. We consider approximate representations of the Pareto set based on ϵ-coverings, allowing much larger problems to be solved. In addition, we define a method for incorporating user trade-offs, which also greatly improves the efficiency.

Lower extremity amputation in people with diabetes: Trends and determinants

Introduction: The prevalence of diabetes is rising rapidly. Assessing quality of diabetes care is difficult. Lower Extremity Amputation (LEA) is recognised as a marker of the quality of diabetes care. The focus of this thesis was first to describe the trends in LEA rates in people with and without diabetes in the Republic of Ireland (RoI) in recent years and then, to explore the determinants of LEA in people with diabetes. While clinical and socio-demographic determinants have been well-established, the role of service-related factors has been less well-explored. Methods: Using hospital discharge data, trends in LEA rates in people with and without diabetes were described and compared to other countries. Background work included concordance studies exploring the reliability of hospital discharge data for recording LEA and diabetes and estimation of diabetes prevalence rates in the RoI from a nationally representative study (SLAN 2007). To explore determinants, a systematic review and meta-analysis assessed the effect of contact with a podiatrist on the outcome of LEA in people with diabetes. Finally, a case-control study using hospital discharge data explored determinants of LEA in people with diabetes with a particular focus on the timing of access to secondary healthcare services as a risk factor. Results: There are high levels of agreement between hospital discharge data and medical records for LEA and diabetes. Thus, hospital discharge data was deemed sufficiently reliable for use in this PhD thesis. A decrease in major diabetes-related LEA rates in people with diabetes was observed in the RoI from 2005-2012. In 2012, the relative risk of a person with diabetes undergoing a major LEA was 6.2 times (95% CI 4.8-8.1) that of a person without diabetes. Based on the systematic review and meta-analysis, contact with a podiatrist did not significantly affect the relative risk (RR) of LEA in people with diabetes. Results from the case-control study identified being single, documented CKD and documented hypertension as significant risk factors for LEA in people with diabetes whilst documented retinopathy was protective. Within the seven year time window included in the study, no association was detected between LEA in patients with diabetes and timing of patient access to secondary healthcare for diabetes management. Discussion: Many countries have reported reduced major LEA rates in people with diabetes coinciding with improved organisation of healthcare systems. Reassuringly, these first national estimates in people with diabetes in the RoI from 2005 to 2012 demonstrated reducing trends in major LEA rates. This may be attributable to changes in diabetes care and also, secular trends in smoking, dyslipidaemia and hypertension. Consistent with international practice, LEA trends data in Ireland can be used to monitor quality of care. Quantifying this improvement precisely, though, is problematic without robust denominator data on the prevalence of diabetes. However, a reduction in major diabetes-related LEA rates suggests improved quality of diabetes care. Much controversy exists around the reliability of hospital discharge data in the RoI. This thesis includes the first multi-site study to explore this issue and found hospital discharge data reliable for the reporting of the procedure of LEA and diagnosis of diabetes. This project did not detect protective effects of access to services including podiatry and secondary healthcare for LEA in people with diabetes. A major limitation of the systematic review and meta-analysis was the design and quality of the included studies. The data available in the area of effect of contact with a podiatrist on LEA risk are too sparse to say anything definitive about the efficacy of podiatry on LEA. Limitations of the case-control study include lack of a diabetes register in Ireland, restricted information from secondary healthcare and lack of data available from primary healthcare. Due to these issues, duration of disease could not be accounted for in the study which limits the conclusions that can be drawn from the results. The model of diabetes care in the RoI is currently undergoing a re-configuration with plans to introduce integrated care. In the future, trends in LEA rates should be continuously monitored to evaluate the effectiveness of changes to the healthcare system. Efforts are already underway to improve the availability of routine data from primary healthcare with the recent development of the iPCRN (Irish Primary Care Research Network). Linkage of primary and secondary healthcare records with a unique patient identifier should be the goal for the future.