# Cramér-Rao Bound of Direction Finding Using Uniform Arc Arrays

## Main Article Content

## 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

$$\frac{\pi}{2} ~and~ \pi ~and ~also~ \frac{3}{2}\pi ~and~ 2\pi$$

## Article Details

*Journal of Advances in Mathematics and Computer Science*,

*33*(1), 1-15. https://doi.org/10.9734/jamcs/2019/v33i130168

## References

Xiaofei Z, Jianfeng L, Lingyun X, Novel two-dimensional DOA estimation with L-shaped array. EURASIP Journal on Advances in Signal Processing. 2011;1-50.

Tuncer TE, Friedlander B. editors. Classical and modern direction-of-arrival estimation. Academic Press; 2009.

Stoica P, Nehorai A. MUSIC, maximum likelihood, and cramer-rao bound: Further results and comparisons. IEEE Transactions on Acoustics, Speech, and Signal Processing. 1990;38(12)- 2140-2150.

Tam PK, Wong KT. Cramer-Rao bounds for direction nding by an acoustic vector sensor under nonideal gain-phase responses, noncollocation, or nonorthogonal orientation. IEEE Sensors Journal. 2009;9(8):969-982.

Kitavi DM, Thomas KW, Chun-Chiu H. An L-shaped array with nonorthogonal axes-its cramer-rao bound for direction nding 2 3 ifa. IEEE Transactions on Aerospace and Electronic Systems. 2017;1-8.

Ciavarrini GM, Greco S, Vecchio A. Geolocation of internet hosts: Accuracy limits through cramer-rao lower bound. Computer Networks; 2018.

Ioannides P, Balanis CA. Uniform circular and rectangular arrays for adaptive beamforming applications. IEEE Antennas and Wireless Propagation Letters. 2005;4(1):351-354.

Tuncer TE, Yasar TK, Friedlander B. Narrowband and wideband doa estimation for uniform and nonuniform linear arrays. 1st ed. Elsevier; 2009.

Tan CM, Fletcher P, Beach M, a R. Nix, Landmann M, Thom RS. On the application of circular arrays in direction nding part I: Investigation into the estimation algorithms. 1st Annual COST 273 Workshop, Espoo, Finland; 2002;29-30.

Shirvani-Moghaddam S, Akbari F. A novel ULA-based geometry for improving AOA estimation. EURASIP Journal on Advances in Signal Processing. 2011;(1)-39.

Wu Y, So HC. Simple and accurate two-dimensional angle estimation for a single source with uniform circular array. IEEE Antennas and Wireless Propagation Letters. 2008;7:78-80.

Kummer WH. Basic array theory. Proceedings of the IEEE. 1992;80(1):127-140.

Lee S, Lo Y. On the pattern function of circular arc arrays. IEEE Transactions on Antennas and Propagaton. 1965;13(4):649-650.

Lim KB, Xin K, Hong GS. Detection and estimation of circular arc segments. Pattern Recognition Letters. 1995;16(6):627-636.

Van HL, Trees. Optimum array processing part IV detection, estimation, and modulation theory. John Wiley and Sons; 2004.