Afanasiev O.V.1, M.P. Slichenko2, O.N. Zavalishina3

1-3 JSC «Concern «Sozvezdie» (Voronezh, Russia)

During the development of multichannel detector-direction finder, it is necessary to analyze the achievable performance indicators, the most important of which are the operating frequency range, direction finding accuracy and ultimate sensitivity. To calculate the potential accuracy of direction finding of radio emission sources, the expression for the lower bound of the Cramer-Rao inequality is widely used. With regard to the direction finding problem, the authors' studies have shown that this expression is valid only if the origin of the coordinate system in which the vector complex radiation pattern of the antenna system is specified is located in the "energy" center of the array. This is clearly indicated in the works, where an antenna array with displaced geometric and "energy" centers is considered. However, the presence of mutual influences of the reflecting elements, the carrier body and arbitrary spatial placement of the detector-direction finder lead to a change in the ratio of the levels of the received signal. The resulting electromagnetic field in the area where the elements of the antenna system are located has a complex structure. As a result, the spatial position of the "energy" center of the antenna system does not coincide with the geometric center and is frequency dependent. Therefore, to use the well-known expression for the lower bound of the Cramer-Rao inequality, this dependence must be taken into account, otherwise, such an estimate of the potential direction finding accuracy will contain an additional error.

The proof of the theorem on the amount of Fisher information in the case of azimuth direction finding by a multichannel direction finder with an antenna system of arbitrary structure is obtained in the work. A theorem on the amount of Fisher’s information in the case of azimuthal direction finding by a multichannel detector-direction finder with an antenna system of an arbitrary structure with a vector complex radiation pattern given in an arbitrary coordinate system is formulated and proved. In the general case of direction finding by a multichannel direction finder with a vector complex radiation pattern of an arbitrary type and defined in an arbitrary coordinate system, when assessing the potential accuracy of direction finding in a complex electromagnetic environment, the expression obtained in this work should be used. The use of the well-known expression for the lower bound of the Cramer-Rao inequality is permissible only in the particular case when the origin of the coordinate system by the vector complex radiation pattern is determined at the "energy" center of the antenna array.

The use of the obtained expressions in practice will improve the accuracy and reliability of calculations of potentially achievable indicators of the efficiency of direction finding depending on the structure and characteristics of the direction finder antenna system, the number of antennas and the characteristics of the radio receiving path. The generalized expression for the lower bound of the Cramer-Rao inequality acts as the main calculated ratio.

Afanasiev O.V., Slichenko M.P., Zavalishina O.N. The Theorem on the amount of Fisher’s information in the case of azimuth direction finding by a multichannel detector-direction finder with an antenna system of arbitrary structure. Radiotekhnika. 2023. V. 87. № 5.
P. 143−156. DOI: https://doi.org/10.18127/j00338486-202305-15 (In Russian)

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