Cramér-Rao Bound of Direction Finding Using a Uniform Hexagonal Array

Abstract

Direction-of-arrival (DOA) estimation is a key area of sensor array processing which is encountered  in many important engineering applications. Although various studies have focused on the uniform hexagonal array for direction finding, there is a scanty use of the uniform hexagonal array in conjunction with Cramer-Rao bound for direction finding estimation. The advantage of Cramér- Rao bound based on the uniform hexagonal array: overcome the problem of unwanted radiation in undesired directions. In this paper, the direction-of-arrival estimation of Cramér-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 Cramer-Rao bound of the uniform hexagonal array. The Cramér-Rao bound based on the uniform hexagonal array was compared with Cramer-Rao bound based on the uniform circular array. The conclusions are as follows. The Cramer-Rao bound of uniform hexagonal array decreases with an increase in the number of sensors. The comparison between the uniform hexagonal array and uniform circular array shows that the Cramér-Rao bound of the uniform hexagonal array was slightly higher as compared to the Cramér-Rao bound of the uniform circular array. The analytical results are supported by graphical representation.