An Optimum Volumetric Array Design Approach for Both Azimuth and Elevation Isotropic DOA Estimation

In this study, a new volumetric array design approach is presented for both azimuth and elevation isotropic direction of arrival (DOA) estimation. The presented method uses a minimum number of additional sensors to extend the given arrays to a volumetric array which has equal values for the Cramér-Rao lower bound (CRLB) for the entire azimuth and elevation angles. This approach can be applied to all arbitrary linear and planar arrays. Moreover, the design approach also takes into account the electromagnetic mutual coupling (MC) effect between the array elements and both the azimuth and elevation angular ambiguity uncertainties in an optimum manner while extending the array. It has been verified both analytically and with simulations that the designed volumetric arrays satisfy the two dimensional (2-D) isotropic DOA estimation conditions. The proposed approach is applied to Uniform Linear Arrays (ULA), Uniform Circular Arrays (UCA), V-shaped Arrays, and an arbitrary planar array to extend to optimum volumetric arrays with considerable results.