University Events

Description: Topic: Variance Reduction Techniques For Power Spectral Density Estimation With Coprime Sensor Arrays

Location: Lester W. Cory Conference Room, Science & Engineering Building (SENG), Room 213A

ABSTRACT:
A coprime sensor array (CSA) is a sparse array geometry that interleaves two spatially undersampled uniform linear arrays (ULAs) with coprime undersampling factors. The CSA spans the same aperture and has equivalent resolution as a fully populated ULA, but uses fewer sensors. Previous works have introduced three CSA processors as spatial power spectral density (PSD) estimators: the Product, Min, and Blend processors. However, two of these processors display increased PSD estimate variance over the ULA PSD estimate. This dissertation focuses on reducing the variance of the CSA PSD estimators. PSD estimation traditionally relies on averaging uncorrelated coherent measurements (snapshots) to reduce variance. However, non-stationary underwater sonar environments often preclude increasing the number of snapshots required to achieve a desirable PSD variance. In the traditional signal processing literature, there are two alternative methods to reduce variance without additional snapshot cost. The multitaper (MT) method and Welch's overlapping segment averaging (WOSA) method improve PSD variance by O(K) at the expense of an O(K) resolution decrease by averaging K uncorrelated PSD estimates. Multitaper obtains these uncorrelated estimates by windowing the array with K orthogonal tapers that span the entire array aperture. In contrast, WOSA obtains the uncorrelated estimates by subdividing the array into K possibly overlapping segments.

This dissertation extends these two existing ULA variance reduction techniques to the CSA processors, making four main contributions. The first proposes the multitapered Product processor (MT-Product) that estimates the spatial PSD with reduced variance with respect to the traditional CSA Product processor but still uses fewer sensors than a fully populated ULA. The second proposes the multitapered Min processor (MT-Min) that reduces the PSD estimate variance further than either MT-Product or Product. The MT-Min estimator has variance comparable to a multitapered ULA. The third proposes the multitapered Blend processor (MT-Blend) that blends MT-Product's attenuation of multiple source cross-terms with MT-Min's low variance while still achieving an O(K) variance reduction over the traditional Blend processor. The final contribution proposes the Welch overlapping segment averaging Product processor (WOSA-Product) that estimates the spatial PSD with reduced variance with respect to the traditional CSA Product processor but still uses fewer sensors than a fully populated ULA. WOSA-Product is generally able to form a larger number of uncorrelated PSD estimates than MT-Product. Closed-form statistics for spatially white Gaussian processes are derived for MT-Product, MT-Min, and WOSA-Product. Simulations verify the variance reduction predicted by the analytical derivations each processor, and the effects of WOSA-Product segment length on resolution, variance reduction, and peak sidelobe levels are discussed.

NOTE: All ECE Graduate Students are ENCOURAGED to attend. All interested parties are invited to attend. Open to the public.

Advisor: Dr. John R. Buck
Committee Members: Dr. Dayalan Kasilingam and Paul J. Gendron, Department of Electrical & Computer Engineering; Dr. Kathleen E. Wage, Department of Electrical and Computer Engineering, George Mason University.

*For further information, please contact Dr. John Buck at 508.999.9237, or via email at jbuck@umassd.edu.