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“A Source Representation Space Approach to Digital Array Processing”
by Kevin M. Buckley
July 1986
This dissertation describes the development and application of a model for sources, as observed by a sensor array processing structure, which accounts for variation in source propagation and observation parameters.
The source observation is a KL-dimensional vector which contains L delayed samples of the output of the elements of a generally configured array of K sensors. The model, termed a Source Representation Space, is an efficient 2nd order characterization of source observations. It is the subspace of the KL -dimensional observation vector space which, for the selected dimension and range of source parameter variation, contains the maximum observed source energy of any equal dimension subspace. It is defined as the span of the significant eigenvectors of a properly constructed Hermitian source sample covariance matrix. The model is generally formulated to represent sources over ranges of propagation and observation parameters. The principle application addressed in this dissertation is the representation of sources over ranges of location and frequency.
The source representation space is used as a source model for spatial/spectral filtering. For this application, where beamformer response is naturally considered in terms of 2nd order characteristics, this representation is employed very effectively. The new representation is used in the control of portions of the response of a broadband linearly-constrained minimum variance beamformer. A class of eigenvector constraints are derived which, compared to existing response point and derivative constraints, is illustrated to provide better response control. Also, a deterministic beamformer design procedure is formulated based on the developed eigenvector constraints. With the procedure, beamformers for broadband and arbitrarily configured arrays can be effectively designed. To date, a general design procedure for broadband and arbitrarily configured array beamformers has not been presented.
For application to broadband Source Location Estimation (SLE), several new broadband spatial spectra estimation algorithms are developed. For power spatial spectra estimation, deterministic and minimum variance beamformers are employed which are designed using eigenvector linear constraints. For eigenvector based high resolution methods, the source representation space is used: 1) to provide valuable insight for algorithm development; 2) as a model of sources for direct broadband data processing algorithms; and 3) to derive transformations which provide source focusing.