Cramér-Rao Bound of Direction Finding Using Uniform Arc Arrays
Veronicah Nyokabi *
Department of Mathematics, Computing and Information Technology, University of Embu, Kenya.
Dominic Makaa Kitavi
Department of Mathematics, Computing and Information Technology, University of Embu, Kenya.
Cyrus Gitonga Ngari
Department of Mathematics, Computing and Information Technology, University of Embu, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Direction-of-Arrival estimation accuracy using arc array geometry is considered in this paper.
There is a scanty use of Uniform Arc Array (UAA) in conjunction with Cramer-Rao bound (CRB)
for Direction-of-Arrival estimation. This paper proposed to use Uniform Arc Array formed from a considered Uniform Circular Array (UCA) in conjunction with CRB for Direction-of-Arrival estimation. This Uniform Arc Array is obtained by squeezing all sensors on the Uniform Circular Array circumference uniformly onto the Arc Array. Cramer-Rao bounds for the Uniform Arc Array and that of the Uniform Circular Array are derived. Comparison of performance of the Uniform Circular Array and Uniform Arc Array is done. It was observed that Uniform Arc Array has better estimation accuracy as compared to Uniform Circular Array when number of sensors equals four and ve and azimuth angle ranging between $$\frac{\pi}{9}~ and ~\frac{7}{18}\pi~ and~ also ~\frac{10}{9}\pi ~and ~\frac{25}{18}\pi$$. However, UCA and UAA have equal performance when the number of sensors equals three and the azimuth angle ranging between 0 and 2π. UCA has better estimation accuracy as compared to UAA when the number of sensors equals four and ve and the azimuth angle ranging between
$$\frac{\pi}{2} ~and~ \pi ~and ~also~ \frac{3}{2}\pi ~and~ 2\pi$$
Keywords: Array signal processing, direction-of-arrival estimation, direction finding, Cramér-Rao bound, uniform arc array