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Date of Award

11-1987

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical and Computer Engineering

Supervisor

Professor S. Haykin

Abstract

The impact of the array geometry for linear arrays on the estimation of the direction of arrival of incident plane waves is examined in this thesis. The fundamental result is the establishment of the conditions under which array structures, different from uniformly spaced, may provide improved accuracy or reliability in these estimates. We are primarily concerned with the use of high accuracy estimators, attempting to obtain accuracies well within the classical beamwidth of the array.

Several different criteria for designing thinned array structures are described, with the principal emphasis on redundancy based designs. For a single plane wave incident on the array, the Weiss-Weinstein bound, which is an estimator independent bound, is applied to a variety of array structures and indicates that the thinned arrays will yield greater accuracy, provided the SNR is sufficiently large. The bound allows us to investigate the effects of a priori information on the estimation performance of the different structures considered.

Maximum likelihood estimation is applied to the identical problem and similar tradeoffs are observed. We propose the concept of outlier probability as a measure for discriminating between array structures and provide models for characterization. Certain algorithms in the literature for the design of nonuniform arrays are shown to be poor under these measures.

The impact of array structure in a multipath environment consisting a target with a strong specular reflection is illustrated using exact maximum likelihood estimation. It is shown that the most significant gains to be made for thinned arrays occur when the multipath is such that target and image are well within a beamwidth of the array. Under these conditions, it is found that the nonuniform arrays often outperform uniform arrays consisting of many more elements for all values of SNR and phase differences between the two plane waves.

An experimental, 32-element array was constructed and brought into the field in order to gather multipath data over water, in a real world environment. For the very closely spaced target and image of this experiment, the nonuniform arrays outperform uniform arrays consisting of even twice as many elements.

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