Open Access Open Access  Restricted Access Subscription or Fee Access

Shape Optimization of Low-Element Antenna Arrays Based on the Minimization of the Azimuthal or Elevation Angles According to the Lower Cramer-Rao Bound

Ilya Peshkov(1*)

(1) Bunin Yelets State University, Russian Federation
(*) Corresponding author



This study proposes a method for designing optimally shaped antenna arrays from the perspective of error reduction of azimuthal or elevation angles for the identification of the direction of detected radio signals. The accuracy is determined by the lower Cramer–Rao bound, which is a statistical estimate of the error dispersion. It is the level below which it is impossible to access the signal regardless of the direction identification algorithm used. Thus, the purpose of this study is to build an antenna array in which the locations of the elements allow the minimization of the dispersion errors pertaining to the directionality of the detected radio signals. The proposed method minimizes the generalized expression of the lower Cramer–Rao bound. It shows that the accuracy of the identification of the radio direction is inversely proportional to the sum-of-the-squared differences between the coordinates of all omnidirectional elements along the x–, y–, and z–axes. Based on the estimated location area of the signal source, the arrangement of the antenna array elements is optimized in accordance with the maximum likelihood function that constitutes the basis of the lower Cramer–Rao bound. The optimization is based on the maximization of the probability of estimation. Accordingly, a study on the Multiple Signal Classification method is conducted and it shows that the accuracy of the direction identification can be increased up to 10-fold in comparison with similar, conventional (uniform), circular arrays.
Copyright © 2019 Praise Worthy Prize - All rights reserved.


Radio Direction Detection; Optimization; Lower Cramer-Rao Bound; Antenna; Super-Resolution

Full Text:



B. Friedlander, T. Tuncer, Classical and modern direction-of-arrival estimation (Academic Press, 2009).

H. Qayyum, M. Ashraf, Performance comparison of direction-of-arrival estimation algorithms for towed array sonar system, Digital Information Processing and Communications ICDIPC, 2011, Volume 189.

G. Bartoli, R. Fantacci, D. Marabissi, LTE-A femto-cell interference mitigation with MuSiC DOA estimation and null steering in an actual indoor environment, IEEE International Conference on Communications, Budapest, Hungary, 2013, pages 2707–2711.

Slimani, A., Bennani, S., El Alami, A., Harkat, H., Conception and Optimization of Patch Array Antenna for WiMAX Applications Using Stubs and Slots Techniques Matching, (2015) International Journal on Communications Antenna and Propagation (IRECAP), 5 (1), pp. 39-45.

Elkamchouchi, H., Mohamed, D., Mohamed, O., Ali, W., Multiuser Detection Using Blind Robust Beamforming in Multipath Environment for LTE System, (2016) International Journal on Communications Antenna and Propagation (IRECAP), 6 (5), pp. 291-298.

D. I. Abu-Al-Nadi, T. H. Ismail, H. Al-Tous, M.J. Mismar, Design of linear phased array for interference suppression using array polynomial method and particle swarm optimization, Wirel Pers Commun, Volume 63, 2012, pages 501.

F. Harrou, Y. Sun, Statistical monitoring of linear AAs, Eng Sci Technol, Volume 19, (Issue 4), 2016, pages 1781–1787.

S. M. Hosseini, R. A. Sadeghzadeh, B. S. Virdee, DOA estimation using multiple measurement vector model with sparse solutions in linear array scenarios, Wirel Commun Netw, Volume 2017, 2017, pages 58.

Z. Liu, J. He, Z. Liu, Computationally efficient DOA and polarization estimation of coherent sources with linear electromagnetic vector-sensor array, EURASIP J Adv Signal Process, Volume 2011, 2011, pages 490289.

R. O. Schmidt, Multiple emitter location and signal parameter estimation, IEEE Trans Antennas Propagat, Volume 34, 1986, pages 276–280.

A. Abouda, H. M. El-Sallabi, S. G. Haggman, Impact of AA geometry on MIMO channel eigenvalues, Proceedings of the IEEE International Symposium on Personal, Indoor and Mobile Radio Comm., Volume 1, 2005, pages 568–572.

Y. Nechaev, I. Peshkov, Evaluating Cramer–Rao bound for 2D direction-finding via planar AAs, Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, Volume 67, 2016, pages 12–17.

Y. Nechaev, I. Peshkov, N. Fortunova, Evaluation and minimization of Cramer–Rao bound for conformal AAs with directional emitters for DOA-estimation, Progr Electromagn Res C, Volume 90, 2019, pages 139–154.

H. Shi, Z. Li, J. Cao, H. Chen, Two-dimensional DOA estimation of coherent sources using two parallel uniform linear arrays, Wirel Com Netw, Volume 2017, 2017, pages 60.

B. Wu, Realization and simulation of DOA estimation using MUSIC algorithm with uniform circular arrays, The 4th Asia-Pacific Conference on Environmental Electromagnetics, 2006, pages 908–912.

J. Xie, Z. He, H. Li, 2D DOA estimation with sparse uniform circular arrays in the presence of mutual coupling, EURASIP Adv Signal Process, Volume 2011, 2011, pages 127.

Z. Xiaofei, Z. Ming, C. Han, Two-dimensional DOA estimation for acoustic vector-sensor array using a successive MUSIC, Multidim Syst Signal Process, Volume 25, 2014, pages 583–600.

O. Lange, Y. Bin, Antenna geometry optimization for 2D direction-of-arrival estimation for radar imaging, International ITG Workshop on Smart Antennas, Aachen, 2011, pages 1–8.

A. Ghani, F. Keyvani, S. H. Sedighy, AA placement on limited bound for isotropic and optimal direction-of-arrival estimation, IET Signal Processing, Volume 12, (Issue 3), 2018, pages 277–283.

T. Birinci, Y. Tanık, Optimization of nonuniform array geometry for DOA estimation with the constraint on gross error probability, Signal Process, Volume 87, (Issue 10), 2007, pages 2360–2369.

L. C. Zhang, X. F. Zhang, C. Jiang, L-shaped array structure optimization via Cramer–Rao bound, Appl Mech Mater, Volume 556-562, 2014, pages 3365-3368.

Ü. Baysal, R. Moses, On the geometry of isotropic arrays, IEEE Trans Signal Proc, Volume 51, 2013, pages 1469–1478.

J. P. Delmas, M. N. El Korso, H. Gazzah, M. Castella, CRB analysis of planar AAs for optimizing near-field source localization, Signal Process, Volume 127, 2016, pages 117–134.

H. Gazzah H, S. Marcos, Cramer–Rao bounds for AA design, IEEE Trans Signal Processing, Volume 54, 2006, pages 336–345.

H. Gazzah, K. Abed-Meraim, Optimum ambiguity-free directional and omnidirectional planar AAs for DOA estimation, IEEE Trans Signal Process, Volume 57, 2009, pages 3942–3953.

H. Moriya, K. Ichige, H. Arai, Novel 3-D array configuration based on CRLB formulation for high-resolution DOA estimation (Nagoya, Japan, 2012, pp. 1140–1143).

Ouamri, A., Ouamri, A., Keche, M., Low Complexity Method for DOA Estimation Based on Nystrom Method, (2017) International Journal on Communications Antenna and Propagation (IRECAP), 7 (3), pp. 239-245.

G. Liu, H. Chen, X. Sun, R. C. Qiu, Modified MUSIC Algorithm for DOA estimation With Nystrom Approximation, IEEE Sensors Journal, Volume 16(12), 2016, pages 4673 – 4674.

Altamirano, C., de Almeida, C., Inter-User Interference Reduction in Massive MIMO for Linear and Planar Arrays, (2019) International Journal on Communications Antenna and Propagation (IRECAP), 9 (1), pp. 30-35.

R. C. D. Dongarsane, A. N. Jadhav, Simulation study on DOA estimation using MUSIC algorithm, Intl J Tech Eng Sys, Volume 2, (Issue 1), 2011, pages 54–57.

Y. Hua, T. K. Sarkar, D. D. Weiner, An L-shaped array for estimating 2-D directions of wave arrival, IEEE Trans Antennas Propag, Volume 44, 1996, pages 889–895.

Y. Nechaev, E. Algazinov, I. Peshkov, Estimation of the Cramer–Rao bound for radio direction-finding on the azimuth and elevation of the cylindrical AAs 2018 41st International Conference on Telecommunications and Signal Processing (TSP), Athens, Greece, 2018, pp. 1–4.

Nechaev, Y., Peshkov, I., Obtaining the Optimal Shape of Planar Antenna Arrays for Direction-of-Arrival Joint Estimation of One and Two Coordinates of Signal Sources on Azimuth, (2019) International Journal on Communications Antenna and Propagation (IRECAP), 9 (2), pp. 126-136.

P. Sarah, F. Forouhar, Precision of direction of arrival (DOA) estimation using novel three dimensional array geometries, AEU Int J Electron Commun, Volume 75, 2017, pages 35–45.

S. Kiani, A. M. Pezeshk, A comparative study of several array geometries for 2D DOA estimation, Procedia Comput Sci, Volume 58, 2015, pages 18–25.

V. D. Thang, A. Renaux, R. Boyer, A Cramér Rao bounds based analysis of 3D AA geometries made from ULA branches, Multidimensional Sys Signal Process, Volume 24, 2011, pages 1–35.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2020 Praise Worthy Prize