الفهرس 
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Abstract
This thesis demonstrates different structures and configurations of the nested arc array to select the highest-performance structure. Using higher-order statistics, namely, the Forth-order Cumulants (FOC) to virtually increase the array aperture, accordingly, increases virtually the number of arcs and circulars arrays that have been presented and investigated. develop a direct way to distribute the generated virtual sensors which have been presented and investigated. For reaching the least optimal number of physical sensors, with the highest virtual increase of the array aperture, and low overlapped between the sensors. Two sequential upgrades were made to the nested arc array to be the double nested arc array, and the super nested arc array that gives superior performance compared to the uniform arc array, uniform circular array, and other different nested arc array configurations.
Chapter 1: It begins with an introduction to the relevance of research to the direction of arrival estimation, and the use of many DOAE methods using array signal processing. That is because array signal processing is a method for estimating an accurate parameter. DOAE techniques were applied for different types of array structures. The motivation to work with this problem, main goals, and contributions of the research were presented as well. The chapter also represents the objective and the outline of the research.
Chapter 2: A literature was reviewed for the DOA estimation methods and sparse array characteristics given with their advantages and disadvantages.
Chapter 3: The nested arc array is applied for different configurations and structures, the use of the FOC to extend virtually the array aperture, the generated virtual sensors distributions (locations) are formulated and apply the Cramer-Rao bound investigation on different configurations of the nested arc array.
Chapter 4: Direct formulation for distributing the virtual extension of the nested arc array location. Calculating the magnitude and the direction of its related vectors measured from the main origin (central) physical sensor. Calculation of the separation angles between the generated virtual sensors, and the radius. determination of the number of vectors, the number of the total aperture, the number of arcs, and then the number of virtual circles.
Chapter 5: Upgrade the nested arc to the double nested arc array configuration forming the virtual extended butterfly antenna. Calculating the number of virtual sensors and their location, number of virtual arcs, number of virtual circles, and the number of wasted overlapped generated virtual sensors for different structures. Compared the CRB results for all cases.
Chapter 6: Super nested arc array configuration results from merging the double nested arc array. Apply the same calculation as the previous chapter. The proposed array performance is superior to that of the uniform one. Further, the nested arc array is appropriate for two-dimensional (2D) DOA estimation problems.
Chapter 7: Multiple signals direction of arrival estimation, applying the Music DOAE on nested arc array. comparing the performance of RMSE vs SNR, and RMSE vs number of snapshots.
Chapter 8: This chapter explains conclusions and states future work that might be done based on this work.