The importance of extending the statistical signal processing methodology to the alpha-stable framework is apparent. First, scientists and engineers have started to appreciate alpha-spectra and the elegant scaling and self-similarity properties of stable distributions. Additionally, real life applications exist in which impulsive channels tend to produce large-amplitude, short-duration interferences more frequently than Gaussian channels do. The stable law has been shown to successfully model noise over certain impulsive channels. In this dissertation, we propose new robust techniques for source detection and localization in the presence of signals and/or noise modeled as complex isotropic stable processes.

First, we present optimal, maximum likelihood-based approaches to the direction-of-arrival estimation problem and we introduce the Cauchy Beamformer. We show that the Cauchy Beamformer provides better bearing estimates than the Gaussian Beamformer in a wide range of impulsive noise environments and for very low signal-to-noise ratios. In addition, we calculate the Cramer-Rao bound on the estimation error covariance for the case of deterministic incoming signals retrieved in the presence of additive complex Cauchy noise.

In the second part of the dissertation, we develop subspace methods based on fractional lower-order statistics, for applications where reduced computational cost is a crucial design parameter. We define the spatial covariation matrix of the observation vector process and employ subspace-based bearing estimation techniques to the sample covariation matrix resulting in improved direction-of-arrival estimates in impulsive noise environments. We name the introduced technique Robust Covariation-Based Multiple Signal Classification or ROC-MUSIC. In addition, we present consistent estimators for the marginals of the covariation matrix and we study their asymptotic performance through both theory and simulations.

Finally, in the last part of the dissertation, we investigate the problem of localizing wideband sources in the presence of noise modeled as a complex isotropic stable process. We consider the frequency-domain representation of the sensor outputs and show that the spectral density of complex stable processes plays a role in array processing problems analogous to that played by the power spectral density of second-order processes.

Chapter 0: Title, Dedication, Acknowledgments, Contents, Abstract

Chapter 1: Introduction

Chapter 2: Array Signal Processing Fundamentals and Current Approaches

Chapter 3: Alpha-Stable Random Variables and Processes

Chapter 4: Maximum Likelihood DOA Estimation in Alpha-Stable Noise

Chapter 5: Subspace Techniques with Alpha-Stable Distributions

Chapter 6: Wide-Band Source Localization in the Alpha-Stable Framework

Chapter 7: Future Work

Appendix A: Derivation of CRB for Complex Isotropic Cauchy Noise

Appendix B: Fractional Lower Order Moments of Products of SaS Random Variables

Appendix C: Asymptotic Performance of the MFLOM Estimator

Bibliography

P.T.'s Publications