Yu. B. Nechaev – Honored Scientist of RF, Dr.Sc. (Phys.-Math.), Professor,

Professor of Information Systems Department, Voronezh State University

E-mail: nechaev_ub@mail.ru

I. V. Peshkov – Ph.D. (Phys.-Math.), Associate Professor,

Associate Professor of Department of Physics, Radio Engineering and Electronics,

Bunin Yelets State University

E-mail: ilvpeshkov@gmail.com

Evaluation of the angular coordinates of radio emission sources is of serious research interest in such tasks as radiolocation, sonar and wireless telecommunication systems and is mainly used for separation of goals. The configurations of the used antenna arrays, which were investigated, are mainly concerned uniform linear, uniform rectangular, as well as uniform annular arrays. The main advantage of linear arrays for radio direction finding tasks is the narrow main lobe of the radiation pattern, however, scanning is possible only in the azimuth plane. In the tasks requiring both azimuth and elevation direction finding, planar arrays were used. To date, works devoted to a comparative study of the characteristics of radio direction finding with superresolution for different configurations of the AR often only concern one or two types of arrays, and therefore obtaining an array with the best characteristics is very important.

In this article, a method has been proposed for constructing antenna arrays of optimal shape from the point of view of reducing radio direction finding errors in azimuth or elevation. The proposed method consists in minimizing the generalized expression of the Cramer–Rao lower boundary, which shows that the accuracy of radio direction finding is inversely proportional to the sum of the squares of the differences between the coordinates of all omnidirectional elements along the axes of the abscissas, ordinates, and applicates. Thus, knowing the intended area of the source of the signal, the arrangement of the elements of the antenna array is optimized in accordance with the maximum likelihood function. Study of the MUSIC method is being conducted, showing that new forms of antenna arrays have better accuracy than circular ones.

1. Chetan D., Jadhav A.N. Simulation study on DOA estimation using MUSIC algorithm. Intl. J. Tech. Eng. Sys. 2011. V. 2. № 1.
2. Liu Z., He J., Liu Z. Computationally efficient DOA and polarization estimation of coherent sources with linear electromagnetic vectorsensor array. EURASIP Journal on Advances in Signal Processing. 2011. Article ID 490289. DOI: 10.1155/2011/490289
3. Hosseini S.M., Sadeghzadeh R.A., Virdee B.S. DOA estimation using multiple measurement vector model with sparse solutions in linear array scenarios.EURASIP Journal onWireless Communications and Networking. 2017. 2017:58.
4. Abu-Al-Nadi D.I., Ismail T.H., Al-Tous H. et al. Design of linear phased array for interference suppression using array polynomial method and particle swarm optimization. Wireless Personal Communications. 2012. V. 63. № 2. P. 501–513.
5. Friedlander B., Tuncer T. Classical and modern direction-of-arrival estimation. Academic Press. 2009.
6. Abouda A., El-Sallabi H.M., Haggman S.G. Impact of antenna array geometry on MIMO channel eigenvalues. Proc. IEEE Intl. Symp. on Personal, Indoor and Mobile Radio Comm. 2005. V. 1. P. 568–572.
7. Kiani Sh., Pezeshk A.M. A comparative study of several array geometries for 2D DOA estimation. Procedia Computer Science. 2015. V. 58. P. 18–25.
8. Nechaev Yu., Peshkov I.V. Evaluating Cramer–Rao bound for 2D direction-finding via planar antenna arrays. Visnyk NTUU KPI. Ser. Radiotekhnika radioaparatobuduvannia. 2016. № 67. P. 12–17.
9. Nechaev Yu.B., Algazinov E., Peshkov I. Estimation of the Cramer–Rao bound for radio direction-finding on the azimuth and elevation of the cylindical antenna arrays. 41st International Conference on Telecommunications and Signal Processing (TSP). 2018. DOI: 10.1109/ TSP.2018.8441419
10. Wu B. Realization and simulation of DOA estimation using MUSIC algorithm with uniform circular arrays. 4th Asia-Pacific Conf. on Environmental Electromagnetics. 2006. P. 908–912.
11. Shi H., Li Z., Cao J. et al. Two-dimensional DOA estimation of coherent sources using two parallel uniform linear arrays. EURASIP Journal on Wireless Communications and Networking. 2017. 2017:60.
12. Poormohammad S., Farzaneh F. Precision of direction of arrival (DOA) estimation using novel three dimensional array geometries. International Journal of Electronics and Communications. 2017. V. 75. P. 35–45.
13. Lange O., Yang B. Antenna geometry optimization for 2D direction-of-arrival estimation for radar imaging. International ITG Workshop on Smart Antennas. 2011. DOI: 10.1109/WSA.2011.5741909
14. Ghani A., Keyvani F., Sedighy S.H. Antenna array placement on limited bound for isotropic and optimal direction-of-arrival estimation. IET Signal Processing. 2018. V. 12. № 3. P. 277–283.
15. Birinci T., Tanık Y. Optimization of nonuniform array geometry for DOA estimation with the constraint on gross error probability. Signal Processing. 2007. V. 87. № 10. P. 2360–2369.
16. Zhang L.C. et al. L-shaped array structure optimization via Cramer–Rao bound. Applied Mechanics and Materials. 2014. V. 556–562. P. 3365–3368.
17. Thang Vu D., Renaux A., Boyer R., Marcos S. A Cramér Rao bounds based analysis of 3D antenna array geometries made from ULA branches. Multidimensional Systems and Signal Processing. 2013. V. 24. № 1. P. 121–155.
18. Nechaev Y., Peshkov I., Fortunova N. Evaluation and minimization of Cramer–Rao bound for conformal antenna arrays with directional emitters for DOA-estimation. Progress In Electromagnetics Research C. 2019. V. 90. P. 139–154.
19. Gazzah H., Marcos S. Cramer-Rao bounds for antenna array design. IEEE Transactions on Signal Processing. 2006. V. 54. P. 336–345.
20. Delmas J.P., El Korso M.N., Gazzah H., Castella M. CRB analysis of planar antenna arrays for optimizing near-field source localization. Signal Processing. 2016. V. 127. P. 117–134.
21. Schmidt R.O. Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propagat. 1986. V. 34. P. 276–280.
22. Moriya H. etc. Novel 3-D array configuration based on CRLB formulation for high-resolution DOA estimation. Proceedings of ISAP 2012. Nagoya, Japan. P. 1140–1143.