Cramér-Rao Bound of Direction-Finding using uniform Hexagonal Array

Direction-of-arrival (DOA) estimation is an important branch in the field of array signal processing. It can be applied in such fields as wireless communication, sonar, radar, biomedicine, and radio detection. This fact together with the development of the geometries used in the past years is the principal motivation of this research project. Although various studies have focused on the uniform hexagonal array for direction finding, there is scanty use of the uniform hexagonal array in conjunction with Cram´er-Rao bound for direction finding. In this research project, the direction-of-arrival estimation of Cram´er-Rao bound based on the uniform hexagonal array was studied. The proposed approach concentrated on deriving the array manifold vector for the uniform hexagonal array and Cram´er-Rao bound of the uniform hexagonal array. The Cram´er-Rao bound based on the uniform hexagonal array were compared with Cram´er-Rao bound based on the uniform circular array. The array manifold vector and Cram´er-Rao bound for the uniform hexagonal array were derived. The Cram´er-Rao bound based on the uniform hexagonal array was compared with Cram´er-Rao bound of uniform circular array. The conclusions are as follows, the Cram´er-Rao bound of uniform hexagonal array decreases with an increase in the number of sensors, whereas that of circular array reduces with increase in the number of sensors. The comparison between the uniform hexagonal array and uniform circular array shows that the Cram´er-Rao bound of the uniform hexagonal array was slightly higher as compared to the Cram´er-Rao bound of the uniform circular array. Thus, uniform circular array is a better approximator as compared to uniform hexagonal array. Graphical representation validated the analytical result.