Obtaining the Optimal Shape of Planar Antenna Arrays for Direction-of-Arrival Joint Estimation of One and Two Coordinates of Signal Sources on Azimuth

Abstract

In this paper, an approach for obtaining optimal planar antenna arrays consisting of omnidirectional sensors for the direction-of-arrival estimation is proposed. Exact expressions of the Cramer-Rao lower bound are used. The obtained formulas describe the influence of the location of antenna elements on the accuracy of the direction-of-arrival non-joint estimation for one arriving signal and joint estimation with two signal sources. It has been shown that the accuracy of the direction-of-arrival non-joint estimation is determined as the sum of the squares of the differences between all the coordinates of omnidirectional elements along x- and y-axis if one signal arrives. If two signals arrive, the accuracy of the direction-of-arrival joint estimation depends on the sum of cosines having the argument with the difference between sensor coordinates and signals radius-vectors. The optimal locations of the antenna elements using the obtained expressions can be calculated very easily in order to reduce the direction-finding errors near particular sectors. In order to confirm the proposed methodology the optimal antenna arrays constructed after minimization of the new formulas are researched. It is found out that the new shapes of antenna arrays based on the analytical expressions have better direction-of-arrival accuracy in comparison with the circular ones.