Goodness-of-fit and detection problems in impulsive interference.

Abstract

After defining the structure to a signal detection scheme, this dissertation describes and addresses some of the unresolved issues associated with its use when the interference encountered is impulsive. The alpha-stable (alpha-S) family of distributions is used as a model of this interference due to its physical interpretation and its general form. Despite its attractive features, difficulties arise in using this distribution due to, amongst other things, the lack of a general closed form expression for its probability density function. Relevant to the detection scheme used, this affects parameter estimation, signal detector design and goodness-of-fit tests. Significant contributions are made in the latter through the introduction of characteristic function based test that uses the parametric bootstrap. A modification of this test is then made to define a test of the level of impulsive behaviour - again the parametric bootstrap is employed to maintain levels of significance for this and another test based on testing the alpha-S parameter values. The performance of these tests is examined under simulated and two sources of real, impulsive data, namely human heart rate variability and fluctuations in stock prices. Once the appropriateness of the model assumption has been verified, the final, signal detection process may take place. Detectors based on the locally optimum criterion and approximations to it are described and compared to their rank-based counterparts. Results are presented that suggest compelling arguments based on performance and computational complexity for the consideration of rank-based techniques.Keywords: Impulsive behaviour, alpha-stable distribution, stable laws, Gaussianity testing, parameter estimation, goodness-of-fit, parametric bootstrap, signal detection, locally optimum detectors, rank-based detectors.