The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-245

“Cumulants and Array Processing”

by Mithat C. Dogan

September 1993

Signal processing using an array of antennas is an attractive solution to problems of source detection and parameter estimation. Array processing algorithms are originally designed to extract important phase information about the propagating source wavefronts by cross-correlating sensor measurements. If source processes are non-Gaussian, then higher-order statistics (cumulants) of received signals provide additional information about the parameters of interest and are insensitive to additive Gaussian observation noise. Our motivation of using cumulants in array processing applications is to recover more phase information than is possible by using only second-order statistics. We start the dissertation by a compact introduction to array processing models, spatial spectrum estimation techniques and properties of cumulants. Then, we show how fourth-order cumulants increase the phase information that can be extracted from the sensor measurements. We introduce the concept of virtual sensors, and explain how cumulants can be used to compute cross-correlations among actual and virtual sensors to increase the effective aperture of the array. Using the interpretation of cumulants, we address the joint array calibration and direction-finding problem using an arbitrary antenna array. We prove that using a single doublet, it is possible to estimate the directions, steering vectors, and the waveforms of the non-Gaussian sources using cumulants. We determine bounds on effective aperture extension (without knowing sensor locations) by using cumulants. The upper bound on existing cumulant-based methods can be exceeded when we use minimum-redundancy array design concepts together with cumulants. We propose designs for both linear and two-dimensional arrays. Cumulants have long been promoted in signal processing applications for their ability to suppress additive Gaussian observation noise. We show that it may be possible to suppress additive non-Gaussian noise if we place a sensor far-enough from the main array, whose noise component can be non-Gaussian but independent from the noise components in the main array sensors. Finally, we address the problem of single sensor detection and classification of multiple linear non-Gaussian processes. This problem is solved by exploiting the fact that polyspectra possess an array of arguments, unlike spectrum. The dissertation concludes with future research directions and an extensive bibliography.

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