Cramér-Rao Bound of Direction Finding Using a Uniform Hexagonal Array
Grace Wakarima Ndiritu *
Department of Mathematics, Computing and Information Technology, University of Embu, Embu, Kenya.
Dominic Makaa Kitavi
Department of Mathematics, Computing and Information Technology, University of Embu, Embu, Kenya.
Cyrus Gitonga Ngari
Department of Mathematics, Computing and Information Technology, University of Embu, Embu, Kenya.
*Author to whom correspondence should be addressed.
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.
Keywords: Direction-of-arrival estimation, Array manifold vector, Cramér-Rao bound, Uniform hexagonal array.