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THIRD ANNUAL
ASAP '95 WORKSHOP

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Direction Finding with
Fractional Lower-Order
Statistics

Panagiotis Tsakalides and Chrysostomos L. Nikias
University of Southern California
Signal and Image Processing Institute
Department of Electrical Engineering, Systems
Los Angeles, CA 90089-2564
email: tsakalid@sipi.usc.edu

Abstract
Statistical array processing based on the linear theory of random processes with finite second-order moments has been the focus of considerable research. Specifically, critical problems, such as high-resolution direction finding, null- and beam-steering, and detection of the number of sources illuminating an array of sensors, have been studied under the assumption of a Gaussian noise model.

Looking toward real-world applications, we are interested in developing array processing methods for a larger class of random processes that include the Gaussian processes as special cases. The availability of such methods would make it possible to operate in environments that significantly deviate from Gaussianity.

In particular, radar systems operate in environments where the dominant source of interference (clutter) contains a significant noise component, termed "impulsive," to indicate the probability of large interference levels. The effects of impulsive noise in the operation of conventional radar systems are drastic, significantly degrading their overall performance and giving rise to the need for designing new robust signal processing algorithms.

At ASAP '94 we introduced optimal, maximum likelihood-based (ML) approaches to the source localization problem in the presence of noise modeled as a complex isotropic stable process. Due to the high computational load of optimal ML techniques, suboptimal methods need to be developed for the solution of the direction-of-arrival (DOA) estimation problem in the presence of impulsive noise.

This presentation introduces a new class of subspace methods for bearing estimation based on properties of fractional lower-order moments and covariations. We define the covariation matrix of the array sensor outputs and show that eigendecomposition-based methods, such as the MUSIC algorithm, can be applied to the sample covariation matrix to extract bearing information from the measurements. We present consistent estimators for the covariation matrix and study their asymptotic performance. The improved performance of the new methods is demonstrated with real radar signals made available by DoD.

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