Cramer-Rao Bound Investigation of the Double-Nested Arc Array Virtual Extension and Butterfly Antenna Configuration

This paper exploits a sparse array representation, a novel double-nested arc array to generate a multiple virtual nested arc array that forms the virtual non-uniform circular array which has been presented and investigated. The nested arc array has been developed using higher-order statistics, namely using the fourth-order cumulants (FOC), to increase the array aperture. The extended array contains a hybrid of physical and virtual sensors which is distributed in a butterfly shape. The enhanced degrees of freedom (DOFs) in the resultant virtual array make it appropriate for over-and under-determined direction-of-arrival (DOA) estimation. The Cramer-Rao bound (CRB), the number of nested arc arrays, the structure of the double-nested arc related to each other, and the overlap between sensors for such an array are developed and investigated for various arrays. The proposed array performance is superior to that of the uniform one. Further, the proposed array is appropriate for two-dimensional (2D) DOA estimation problems.