الفهرس 
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Abstract
This thesis introduces a sparse array representation, a novel nested arc array to generate virtual non-uniform arcs arrays, and circulars arrays that have been presented and investigated. The virtual increase of the array aperture has been developed using higher-order statistics, namely, the Forth-order Cumulants (FOC) ended array contains a combination of physical as well as virtual sensors. The proposed arrays were developed to be direct distributed, that distribution takes the shape of a butterfly. The increased Degrees of Freedom (DOFs) in the resultant virtual array make it suitable for over-and under-determined direction of arrival (DOA) estimation. That relaxes the condition to detect more sources than the available sensors. The Cramer-Rao bound (CRB), the number of nested arc arrays, consequently, the structure and the configuration of the double nested arc and the super nested arc, and the overlap between sensors for such arrays are developed and investigated for various arrays. The proposed array and its upgraded performance are superior to that of the uniform arc array, and uniform circular array. Further, the proposed array and its upgrades are suitable for two-dimensional (2D) DOA estimation problems.
The proposed array got two sequential upgrades for the nested arc array:
Double nested arc array.
Super Nested arc array.
Numerical results show good statistical behavior of those arrays.