Potential accuracy of direction finding by non-monopulse detector-direction finder with ring antenna array for various switching options
Authors: Dmitriev I.S. , Zavalishina O.N. , Slichenko M.P. 
Published: February 2025

In the general case, the law of distribution of direction finding errors of radio emission sources (RES) against the background of radio interference and internal noise is polymodal and is not described by a Gaussian density. The distribution of these errors depends on the true bearing, the distribution of interference and noise, the structure of the detector-direction finder and its antenna system (AS), the algorithm for processing the mixture of the direction-finding signal and interference. For practice, a more acceptable measure of direction finding efficiency is direction finding sensitivity – the minimum value of the energy signal-to-noise ratio at the input of the direction finding receiver, which ensures that the specified threshold correct detection probability, the values of the normal root-mean-square error (RMSE) and the probability of an anomalous direction finding error on background of white Gaussian noise. In practice, radio direction finders with ring antenna arrays based on a switched two-channel interferometer are widely used, which determine the direction of arrival of a radio wave based on the results of a sequential pairwise "interrogation" of antenna elements (AE). This article considers the direction finding sensitivity of various structures of azimuth direction finders using ring antenna arrays, according to the criterion of normal RMSE of direction finding based on the generalized Cramer–Rao inequality under the assumption of direction finding by the maximum likelihood method. This makes it possible to obtain a generalized expression for the lower bound of the dispersion of the direction finding error of the mentioned set of two-channel interferometers through expressions of their likelihood functions.

The purpose of the paper is to analyze the direction-finding sensitivity according to the criterion of normal RMSE direction-finding of radio direction-finders in the case of using a switched two-channel interferometer with ring antenna arrays for various switching options in comparison with the sensitivity of a multi-channel monopulse direction finder.

In this paper, generalized expressions for the lower bound of the dispersion of the Cramer–Rao inequality are obtained, which allow one to perform an analytical calculation of the RMSE of direction finding, or to determine the direction finding sensitivity for a given RMSE using a two-channel switched interferometer. Statistical modeling was performed, confirming the reliability of the obtained analytical expressions. Comparison of the potentially achievable direction finding characteristics of a direction finder with a ring antenna arrays of different structure, having different switching options, showed that direction finding by a monopulse direction finder will allow achieving a significant energy gain. The anisotropy of the direction-finding sensitivity of a two-channel switched interferometer with a constant reference element, which is one of the ring elements, is confirmed. Comparison of the results of this work with similar results that the expressions for the lower bound of the dispersion of the direction finding error for various structures of radio direction finders with an annular antenna array are identical to the corresponding expressions obtained by the method of linearization of the phase direction finding algorithm.

The practical application of the obtained expressions will reduce the resource intensity of calculations of achievable indicators of the RES direction finding efficiency for the considered options for switching the direction finder with the ring antenna arrays, which will allow not to carry out statistical modeling, but to analyze the functioning of the direction finder depending on the options for switching the direction finder, the characteristics of the AS of the direction finder, number of antennas and characteristics of the radio receiving path.