Sparse 3D Array made from Nested Linear Array Branches for Underdetermined Source Localization

Non-uniform sparse arrays like nested arrays have the ability to estimate the direction-of-arrival (DOA) of more sources than the number of sensors. These arrays are designed in such a manner such that their difference coarray is hole free. Then, the increased degrees-of-freedom (DOF) of the coarray is utilized to perform underdetermined DOA estimation. In this paper, we extend the nested array configuration to three-dimensional geometry to cover the entire azimuth and elevation range. The proposed 3D sparse array is made from three orthogonal nested array branches and the final structure is composed of a direct sum of these three branches. We study the structure and geometry of the difference coarray of the proposed array and extend the coarray based DOA estimation algorithm to 3D arrays. We propose a computationally efficient way to construct the full rank coarray covariance matrix for 3D sparse arrays. We also derive the unconditional Cramer-Rao Bound (CRB) for 3D sparse array signal model. Simulation results show the effectiveness and advantages of the proposed 3D structure.