Mathematical model of phased array antenna aperture in the presence of errors in the position of antenna elements
Authors: Gabrielyan D. D. , Zanin K. M. , Fedorov D. S. 
Published: October 2023

The analysis of the directional characteristics of a phased array antenna is one of the main problems in the development of an antenna. The key issue in carrying out this analysis is an adequate representation of the directional characteristics of the phased array antenna with known directional patterns and the set-up as part of the aperture of antenna elements. There are many works considering the directional characteristics of the antenna, taking into account the mutual connection between the antenna elements. A number of works are devoted to the study of the directional characteristics of a phased array antenna in the presence of random errors of the amplitude-phase distribution in the radiating aperture. However, the issues related to the influence of the antenna elements installation error in the radiating aperture on the directional characteristics of the phased array antenna practically did not receive their consideration. With this in mind, this article discusses a mathematical model of the radiating aperture of a phased array antenna in the presence of errors in the antenna elements installation. At the same time, the installation error means not only the displacement of the antenna elements, but also its rotation relative to three axes, due to a violation of the shape of the radiating aperture. The objective of the article is to investigate the influence of the antenna element installation errors, including the displacement and reversal of the antenna elements in the radiating aperture, on the directional characteristics of the phased array antenna, based on strict consideration of the relationship between the directional characteristics of the phased array antenna and the parameters of the antenna elements installation in the radiating aperture. The main results obtained in the article are as follows. 1. A mathematical model of the radiating aperture of the phased array antenna, taking into account the errors of installation of the antenna elements in the aperture, including displacement of the phase center of the antenna elements and rotation of the antenna elements relative to the plane of the radiating aperture at three angles. 2. Investigation of the main patterns of changes in the directional characteristics of the phased array antenna due to the presence of errors in the antenna elements installation in the radiating aperture of the phased array antenna. In particular, errors in the installation of antenna elements practically do not lead to a change in the main beam either in width or in level. The most significant changes in the directional characteristics are manifested as follows: the structure and level of the side lobes of the directional patterns of the phased array antenna change; there is a cross-polarized component in the directional pattern, which, unlike the main component, is weakly directional. The developed mathematical model and the obtained simulation results allow us to determine the relationship between the parameters of the antenna elements installation errors as part of the phased array antenna aperture with a change in the amplitude, phase and polarization directional pattern, on the basis of which requirements for the accuracy of the parameters of the radiating aperture and the accuracy of the antenna elements installation can be formulated. These results are most significant for communication and radar systems that use orthogonal polarization signals when receiving and radiating.