Abstract:
The problem of parameters estimation of plane wave signals using an array of sen-
sors has received a considerable attention from researchers and engineers during
the last few decades. In general, the parameters of interest are the frequencies
and direction-of-arrivals of incoming signals. Although, a number of methods have
been proposed in literature, the subspace-based methods including MUSIC and
ESPRIT are widely used to estimate the required parameters because of their
relatively less computational cost and high resolution. In the presence of coher-
ent signals, these covariance-based methods require an additional step of spatial
smoothing. Another subspace based method is Matrix Pencil method that is a
direct data domain method and analyzes the data on snapshot by snapshot bases;
consequently, a non-stationary environment can be handled, easily. Moreover, Ma-
trix Pencil method is directly applicable in scenarios where the input signals are
fully correlated or coherent since it implicitly performs spatial smoothing while
constructing the data matrix. The main focus in this thesis is on several improve-
ments to the existing Matrix Pencil methods (especially related to reduction in
computational complexity with comparable estimation accuracy).
First of all, in Matrix Pencil method it is commonly assumed that noise is
spatially uncorrelated. In the presence of correlated noise, matrix pencil method
often fails to yield unbiased estimates of required parameters since the signal sub-
space estimated through singular value decomposition of the (noisy) data matrix
is biased. To combat with spatially correlated noise, we proposed a Generalized
Matrix Pencil method which utilizes a generalized singular value decomposition to
obtain unbiased estimates of the required parameters.
Since, parameters estimation of plane wave signals is a real-time problem, it is
vital to maintain the computational burden of parameters estimation algorithms
as low as possible. Many efforts have already been made to minimize the com-
putational burden of exiting methods. In the context of Matrix Pencil method
algorithms, the (existing) Unitary Matrix Pencil method reduces the computa-
tional complexity to about one-fourth by converting the complex data matrix in
Matrix Pencil method into a real matrix using a unitary matrix transformation.
If some a priori information about direction-of-arrival or frequency of incoming
signals is available, as in radar and sonar applications, then a reduced dimensional
processing of covariance/data matrix is possible. For such scenarios, a number
of researchers have proposed the beamspace approach, which first projects the
original data into a subspace of lower dimensions (using DFT) and then processes
the beamspace data by using well known algorithms such as MUSIC and ESPRIT.
In order to reduce the computational complexity of Matrix Pencil based algorithms,
we propose Beamspace Matrix Pencil methods that transform the complex data
matrix into a real and reduced dimensional matrix using selected rows of a DFT
matrix. Depending upon the number of selected rows, the computational burden
is reduced several times with comparable estimation accuracy to that of existing
methods. Moreover, if there is no a priori information available then Beamspace
technique can be applied via parallel processing with overlapped sectors as can be
done in the case of Beamspace MUSIC and ESPRIT. In addition to this, we also
propose a Multiple Invariance Beamspace Matrix Pencil method, which exploits the
multiple invariance structure inherent in the DFT transformed manifold matrix to
improve the estimation accuracy without any significant increase in computational
burden.
In order to enhance the estimation accuracy, multiple snapshots are often
used in Matrix Pencil methods. However, a straight forward implementation of
Beamspace technique on multiple snapshot cases may decrease its computational
advantage. Therefore, we propose a Multiple Snapshot Beamspace Matrix Pencil
method, which not only utilizes a priori information about direction-of-arrival but
also uses the frequency information of incoming signals so as to further reduce the
computational burden of Beamspace Matrix Pencil method.
In the thesis, we also address the grouping problem of estimated parameters
in already existing multi-dimensional Matrix Pencil and Unitary Matrix Pencil
methods. In particular, we extend the (existing) two-dimensional Modified Matrix
Pencil method for three-dimensional scenarios in which the required parameters
are always estimated in an automatically grouped form. Moreover, it is shown
that the matrices whose Eigenvalues yield the required parameters (in Unitary
Matrix Pencil methods) bear the same Eigenstructure. By exploiting this same
Eigenstructure property, we propose a Modified Unitary Matrix Pencil method in
which the required parameters are obtained in a grouped form thereby eliminating
the need of an extra grouping algorithm. This, not only reduces the computational
burden but also alleviates the problem of wrong grouping.
Finally, in this project we developed a direction-of-arrival estimation system
consisting of a uniform linear array of six sensors. The hardware details of the
developed system are reported in this thesis. This system is subsequently used to
compare the performance of various Matrix Pencil methods for real-world data.
Key words: Sensor array, array signal processing, direction-of-arrival estimation,
parameters estimation, plane wave signals, coherent signals, spatially correlated
noise, subspace based method, computational complexity, unitary matrix pencil,
beamspace matrix pencil, DFT transformation, multiple invariance, multiple snap-
shot matrix pencil, automatic grouping, comparison analysis, real-world data.