V. A. Sergeev1
1 National Research Lobachevsky State University of Nizhny Novgorod (Nizhny Novgorod, Russia)

Uniform circular array (UCA) antennas are widely used in radar and sonar systems to determine the angle-of-arrival (AoA) of a useful signal from an arbitrary direction. A fairly large number of papers have been devoted to the study of the characteristics of UCA antennas. In these papers, among other things, the maximum achievable accuracy of the signal AoA estimates has been obtained for the signal-to-noise ratios (SNR) values exceeding certain thresholds. At the same time, the relationship between these SNR threshold values and the maximum achievable accuracy of the signal AoA estimates, as well as the dependence of these two key metrics on the number of UCA elements, antenna diameter and signal wavelength has not been studied in known works. However, these characteristics of the UCA antenna are very important for optimal selection of the antenna geometry.

In this paper, we carefully study the problem of optimizing the parameters of the uniform circular antenna arrays taking into account two main metrics that define the system performance: the theoretical boundary for the accuracy of the useful signal AoA estimates and the threshold values of the signal-to-noise ratio at which this boundary is achieved.

We have developed a three-step algorithm for finding the maximum likelihood (ML) estimates of the angle-of-arrival of a useful signal coming from a source located in the far-field zone of the UCA antenna. Based on the detailed numerical simulations of the signal processing in the UCA antenna with different numbers of elements and the ratio of the antenna aperture to the signal wavelength, the dependences of the root mean-square errors (MSE) of ML estimates in a wide range of values of the signal-to-noise ratio have been obtained. Threshold signal-to-noise ratios values have been found. When SNR values exceed these thresholds, the accuracy of the maximum likelihood AoA estimates reaches the theoretical lower Cramer–Rao bounds (CRB) and does not depend on the signal radiation source direction.

Recommendations on the choice of optimal sizes of circular antenna arrays for specific practical problems have been given. Detailed study of the characteristics of the UCA with a different number of elements and different apertures allows to make practical recommendations for choosing the geometry of the UCA antenna systems.

Sergeev V.A. Optimization of the size of the circular antenna array in the problem of determining the direction to the radiation source in the far-field zone. Antennas. 2023. № 5. P. 13–22. DOI: https://doi.org/10.18127/j03209601-202305-02 (in Russian)

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