Efficient direction of arrival estimation and the three-dimensional matrix pencil method to find DOA of the signals along with their wavelengths

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Tapan K. Sarkar


Direction of arrival, Matrix pencil, Wavelengths, Unitary matrix

Subject Categories

Electrical and Computer Engineering


This dissertation deals with problems in the area of adaptive array processing for smart antenna and radar systems. The direction of arrival (DOA) problem has been studied extensively by many researchers, and several methods are proposed in this thesis in order to increase the accuracy of the estimated direction of arrival angles of the signals impinging on the antenna arrays. Increasing the accuracy is important as well as reducing the computational complexity of the system especially under real time applications. In this dissertation, unitary transformations have been successfully applied to the Matrix Pencil (MP) method, which is a very popular DOA estimation method to reduce computational complexity. The computations done in the MP method to find the DOA are complex valued operations. So, converting these complex valued operations into real valued ones will reduce the computational complexity greatly. This reduction is done by taking advantage of the centro-hermitian property of the matrix and applying the unitary transform to the data matrix.

In the second part of the dissertation, the 1-dimensional (1-D) unitary matrix pencil method has been extended for the 2-dimensional (2-D) case to find the azimuth and the elevation angles of the signals arriving at the planar antenna arrays, where all the computations are done with real valued computations. In the 2-D MP method, the computational complexity is due to the Singular Value Decomposition (SVD) computation, MP computations, and the pole pairing computations which are all done with complex valued operations as opposed to the newly proposed 2-D Unitary MP method. Hence, the computational complexity is reduced by this method.

Finally, in a DOA problem, it is usually assumed that the carrier wavelength of the signals is known. However, in practice seldom do all of the signals arrive at the antenna array at a single pre-specified frequency, but at different frequencies. The question then is what to do when there are signals at multiple frequencies, which are unknown. The newly proposed method can be used to find the wavelength of these incoming signals. We extended the MP method to the 3-dimensional (3-D) case to find the angle of the arrival as well as the wavelength of the signals. In the 3-D MP method, three separate poles are found in the x, y, and z directions in Cartesian coordinates, and then they are paired to find the right pair that corresponds to the angle of arrivals and the wavelengths. The problem is successfully formulated and numerical examples are provided to determine the efficiency of the new method.


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