Mathematical model a two-channel amplitude-based direction finder for assessing the influence of antenna beamwidth and antenna axis offset angle on direction-finding accuracy

Abstract

The paper presents a mathematical model of a two-channel amplitude-based direction finder for assessing the influence of antenna beamwidth and antenna axis offset angle on the direction-finding accuracy of frequency-hopping spread-spectrum signals in the sub-GHz range. The relevance of the study is determined by the need for simple and practically implementable solutions for estimating the azimuth direction to FHSS signal sources in airborne and ground-based radio monitoring and guidance systems. The introduction establishes the relationship between the present work and the authors' previous studies devoted to FHSS signal detection and amplitude estimation. The problem statement defines the main assumptions of the study, including one-dimensional azimuth estimation, far-field source conditions, a source distance range of 500-5000 m, line-of-sight propagation, and the use of two calibrated receiver channels. The review of recent publications shows that, for amplitude-comparison systems in the sub-GHz range, the quantitative influence of antenna parameters on direction-finding accuracy remains insufficiently studied. In the results section, the cosine-power approximation of the antenna main lobe is justified and compared with Gaussian and parabolic models. The model parameter is linked to the datasheet beamwidths of the commercially available antennas HG909Y and PE51YA1013, resulting in n approx. 6 and n approx. 20, respectively. Analytical expressions are derived for the normalized difference signal, the sensitivity coefficient, and the root-mean-square azimuth estimation error. Numerical simulations demonstrate that a narrower radiation pattern provides higher angular accuracy but reduces the operating sector. For both considered antenna configurations, the most balanced antenna axis offset angle is found to be 20 degrees. The conclusions state that the HG909Y-based configuration is more suitable for the airborne case, whereas the PE51YA1013-based configuration is preferable for a higher-accuracy ground-based implementation.

Keywords: FHSS, direction finding, DF, DoA, amplitude-based method, SDR, UAV.