Title

Non-Gaussian clutter simulation and distribution approximation using spherically invariant random vectors

Date of Award

2004

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical Engineering and Computer Science

Advisor(s)

Donald D. Weiner

Keywords

Non-Gaussian clutter, Spherically invariant random vectors

Subject Categories

Electrical and Computer Engineering | Engineering

Abstract

Conventional radar receivers are based on the assumption of Gaussian distributed clutter. In a non-homogeneous environment and as the resolution capabilities of radar systems improve, the validity of this assumption becomes questionable and the clutter is often observed to be non-Gaussian. For example, the Weibull and K-distributions have been shown to approximate some experimentally measured non-Gaussian clutter data. In this environment the detection performance of the Gaussian receiver may be significantly below that of the optimum non-Gaussian receiver.

In order to obtain improved detection performance, it is necessary to characterize the correlated non-Gaussian clutter samples. This characterization by means of spherically invariant random vectors (SIRVs) is the primary focus of this dissertation. Although SIRVs have been previously investigated and appear to be an appropriate model for the non-Gaussian clutter, many questions remain. Can the library of known SIRVs be expanded? Can efficient techniques be developed for computer generation? Given random data suitably modeled by an SIRV, how effectively can the unknown distribution be approximated? The answers to these and related questions are addressed in this dissertation. In particular, an enlarged library of distributions that conform to the SIRV model is presented, as well as efficient techniques for their computer generation. A technique for approximating an unknown univariate distribution from a small sample of experimental data, the Öztürk algorithm, is extended to the multivariate case for SIRVs. In this approach the envelope of the SIRV is used to reduce the multivariate distribution approximation problem to an equivalent univariate approximation problem. Problems are encountered, however, in the need to normalize the SIRV distributions with respect to their covariance matrix. It is difficult to estimate the covariance matrix when the type of SIRV distribution is unknown. Therefore, the sample covariance matrix is used. A key result of the dissertation is that the resulting error can be incorporated into the approximation process, thereby reducing its impact. Once the clutter distribution has been approximated, the covariance matrix can then be re-estimated using the approximated distribution. Finally, techniques for approximating an SIRV with multivariate Gaussian mixtures are proposed.

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