Cramer-Rao bound investigation of a novel virtually extended nested arc array for 2D DOA estimation

This paper exploits a sparse array representation, a novel nested arc array, to generate a virtual non-uniform circular arrays that have been presented and investigated. To increase the array aperture, the virtual array has been developed using higher-order statistics, namely, the Forth-Order Cumulants (FOC). The extended array contains a combination of physical as well as virtual sensors. The increased degrees of freedom (DOFs) in the resultant virtual array make it suitable for over-and under-determined direction of arrival (DOA) estimation. The Cramer-Rao bound (CRB) and the (DOA) estimation 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 offered array is suitable for two-dimensional (2D) DOA estimation problems.