Article
Alternative Formulation of Antenna Arrays for DF Systems
Considering Active-Element Patterns and Scattering Matrices
Bernardo Fabiani, Eduardo Sakomura, Eduardo Silveira, Daniel Nascimento * , Daniel Ferreira
and Marcelo Pinho
Citation: Fabiani, B.; Sakomura, E.;
Silveira, E.; Nascimento, D.; Ferreira,
D.; Pinho, M. Alternative Formulation
of Antenna Arrays for DF Systems
Considering Active-Element Patterns
and Scattering Matrices. Sensors 2021,
21, 5048. https://doi.org/10.3390/
s21155048
Academic Editor: Ángela María
Coves Soler
Received: 3 July 2021
Accepted: 22 July 2021
Published: 26 July 2021
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4.0/).
Laboratory of Antennas and Propagation, Aeronautics Institute of Technology,
Sao Jose dos Campos 12228-900, Brazil; bernardomoscardinifabiani@gmail.com (B.F.);
eduardosakomura@gmail.com (E.S.); eduardosilveiranes@gmail.com (E.S.); danielbf@ita.br (D.F.);
mpinho@ieee.org (M.P.)
* Correspondence: danielcn@ita.br
Abstract:
Direction finding (DF) systems are used to determine the direction-of-arrival (DoA) of
electromagnetic waves, thus allowing for the tracking of RF sources. In this paper, we present an
alternative formulation of antenna arrays for modeling DF systems. To improve the accuracy of the
data provided by the DF systems, the effects of mutual coupling in the array, polarization of the
received waves, and impedance mismatches in the RF front-end receiver are all taken into account
in the steering vectors of the DoA algorithms. A closed-form expression, which uses scattering
parameter data and active-element patterns, is derived to compute the receiver output voltages.
Special attention is given to the analysis of wave polarization relative to the DF system orientation.
Applying the formulation introduced here, a complete characterization of the received waves is
accomplished without the need for system calibration techniques. The validation of the proposed
model is carried out by measurements of a 2.2 GHz DF system running a MUSIC algorithm. Tests
are performed with a linear array of printed monopoles and with a planar microstrip antenna array
having polarization diversity. The experimental results show DoA estimation errors below 6
◦
and
correct classification of the polarization of incoming waves, confirming the good performance of the
developed formulation.
Keywords:
direction finding; direction-of-arrival; microstrip antenna array; multiple signal classifi-
cation MUSIC; mutual coupling; polarization diversity; printed monopole array
1. Introduction
Direction finding (DF) systems are employed to estimate the direction-of-arrival (DoA)
of electromagnetic waves, thus allowing for the tracking of radiofrequency sources in
both military and civilian scenarios, such as surveillance, security, navigation, or even
rescue [1–3]
. Among the countless applications of DF systems, we can point out the lo-
calization of pirate radios in the vicinity of airports [
4
], jamming attack detection [
5
,
6
],
surveillance of borders and restricted areas [
7
], and security of events [
8
]. More recently,
the use of drones by terrorist organizations has been a concern of the international commu-
nity [
9
], and DF systems capable of localizing drone controllers could help police to catch
criminals.
Typically, a DF system is composed of an antenna array, a circuit for conditioning
the received signals, and a processor running an algorithm that estimates the DoA of the
incoming waves. Many antenna array configurations are presented in the literature as
solutions for DF systems, as well as a variety of algorithms for DoA estimation [
1
,
2
,
10
–
16
].
However, due to formulation complexity, some algorithms for DoA estimation do not often
consider the inherent properties of antenna arrays [
17
], i.e., the radiation patterns, mutual
coupling, and polarization are not taken into account in the calculations [
15
,
18
,
19
]. To
compensate for this simplification, some calibration techniques have been proposed [
20
–
22
],
Sensors 2021, 21, 5048. https://doi.org/10.3390/s21155048 https://www.mdpi.com/journal/sensors
