Evaluating Cramer-Rao Bound for Conformal Antenna Arrays with Directional Emitters for Doa-Estimation


  • Yu. B. Nechaev Voronezh State University, Russian Federation
  • I. V. Peshkov Elets State University, Russian Federation
  • N. A. Fortunova Bunin Yelets State University, Russian Federation




radio remote control, super-resolution, digital antenna array, circular antenna arrays, directional emitters, directivity


Introduction. The direction-of-arrival estimation of signal sources is of serious research interest in various fields. As an example, the coordinate information in three-dimensional space can be used for spatial diversity and filtering to increase concurrent users. The influence of the directivity coefficient of a separate antenna element on the accuracy of determining the angular coordinates of radio sources of circular, cubic and spherical antenna arrays consisting of directional radiating elements that have found the widest application in modern wireless communication technologies is investigated. Theoretical results. For the correct functioning of advanced radio direction-finding algorithms along with the antenna arrays under consideration the accurate expressions describing the amplitude-phase distribution of the electromagnetic field of the arrays have been derived, so-called steering vectors. The Cramer-Rao lower bound for estimating errors and accuracy of direction-of-arrival estimation is discussed for a number planar waves arriving on an antenna array consisting of directional elements. Experimental results. A theoretical study of the operation of these antenna arrays using the Cramer-Rao lower bound was carried out, as well as computer simulations with the implementation of the MUSIC superresolution method. The influence of the directivity factor of the individual antenna element on the accuracy of the direction-of-arrival estimation of the radio emission sources by using the circular (cylindrical), cubic and spherical antenna arrays consisting of the directional antenna elements was investigated. The limits of the change of the coefficient of directional action of a separate element, at which the maximum accuracy of an estimation of angular coordinates is achieved, is determined. It is shown that further increasing the directivity factor of each antenna element makes the mean square error in the determination of the coordinates of the signals increase as well. The estimation of the resolution of conformal antenna arrays is carried out depending on the directional factor of each antenna coefficient. It is found that the best configuration is spherical. Conclusions. Thus, a comprehensive statistical analysis of radio direction finding with the azimuth and elevation for the conformal antennas depending on the directivity of the antenna elements constituting them was implemented. With an increase in the gain of individual antennas, the accuracy of direction finding can vary significantly depending on the azimuthal position of the signal and an acceptable choice of directional coefficient is four to six.

Author Biographies

Yu. B. Nechaev, Voronezh State University

Nechaev Yu. B.

I. V. Peshkov, Elets State University

Peshkov I. W.

N. A. Fortunova, Bunin Yelets State University

Fortunova N. A., Cand. of Sci (Techn), Assoc. Prof.


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Electrodynamics. Microwave devices. Antennas