Pajovic
Milutin
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The development and application of random matrix theory in adaptive signal processing in the sample deficient regime
Pajovic
Milutin
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Thesis
This thesis studies the problems associated with adaptive signal processing in the
sample deficient regime using random matrix theory. The scenarios in which the
sample deficient regime arises include, among others, the cases where the number of
observations available in a period over which the channel can be approximated as timeinvariant
is limited (wireless communications), the number of available observations is
limited by the measurement process (medical applications), or the number of unknown
coefficients is large compared to the number of observations (modern sonar and radar
systems). Random matrix theory, which studies how different encodings of eigenvalues
and eigenvectors of a random matrix behave, provides suitable tools for analyzing how
the statistics estimated from a limited data set behave with respect to their ensemble
counterparts.
The applications of adaptive signal processing considered in the thesis are (1)
adaptive beamforming for spatial spectrum estimation, (2) tracking of time-varying
channels and (3) equalization of time-varying communication channels. The thesis
analyzes the performance of the considered adaptive processors when operating in
the deficient sample support regime. In addition, it gains insights into behavior
of different estimators based on the estimated second order statistics of the data
originating from time-varying environment. Finally, it studies how to optimize the
adaptive processors and algorithms so as to account for deficient sample support and
improve the performance.
In particular, random matrix quantities needed for the analysis are characterized
in the first part. In the second part, the thesis studies the problem of regularization
in the form of diagonal loading for two conventionally used spatial power spectrum
estimators based on adaptive beamforming, and shows the asymptotic properties of
the estimators, studies how the optimal diagonal loading behaves and compares the
estimators on the grounds of performance and sensitivity to optimal diagonal loading. In the third part, the performance of the least squares based channel tracking
algorithm is analyzed, and several practical insights are obtained. Finally, the performance
of multi-channel decision feedback equalizers in time-varying channels is
characterized, and insights concerning the optimal selection of the number of sensors,
their separation and constituent filter lengths are presented.