Research Article
Thermos Array: Two-Dimensional Sparse Array with Reduced
Mutual Coupling
Lei Sun, Minglei Yang , and Baixiao Chen
National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China
Correspondence should be addressed to Minglei Yang; mlyang@xidian.edu.cn
Received 24 October 2017; Revised 6 February 2018; Accepted 11 March 2018; Published 29 April 2018
Academic Editor:
Shiwen Yang
Copyright © 2018 Lei Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Sparse planar arrays, such as the billboard array, the open box array, and the two-dimensional nested array, have drawn lots of
interest owing to their ability of two-dimensional angle estimation. Unfortunately, these arrays often suffer from mutual-
coupling problems due to the large number of sensor pairs with small spacing d (usually equal to a half wavelength), which will
degrade the performance of direction of arrival (DOA) estimation. Recently, the two-dimensional half-open box array and the
hourglass array are proposed to reduce the mutual coupling. But both of them still have many sensor pairs with small spacing d,
which implies that the reduction of mutual coupling is still limited. In this paper, we propose a new sparse planar array which
has fewer number of sensor pairs with small spacing d. It is named as the thermos array because its shape seems like a thermos.
Although the resulting difference coarray (DCA) of the thermos array is not hole-free, a large filled rectangular part in the DCA
can be facilitated to perform spatial-smoothing-based DOA estimation. Moreover, it enjoys closed-form expressions for the
sensor locations and the number of available degrees of freedom. Simulations show that the thermos array can achieve better
DOA estimation performance than the hourglass array in the presence of mutual coupling, which indicates that our thermos
array is more robust to the mutual-coupling array.
1. Introduction
Many planar arrays, such as the billboard array [1], open box
array [2], and the two-dimensional nested array [3], can
estimate the azimuth and elevation angles of sources simulta-
neously. And these arrays have been demonstrated to be able
to resolve more sources than number of sensors by exploiting
the second-order statistic information of data received by
sensors. However, in real-word application, the mutual
coupling among the adjacent sensors [4] with small spacing
cannot be ignored. And the angle estimation performance
of these aforementioned arrays often degrade significantly
due to the mutual coupling.
In order to solve the problem of mutual coupling, two
different approaches have been studied. The fi rst one is devel-
oping some estimation methodologies based on mutual-
coupling models [5–7]. Unfortunately, as mentioned in [8],
these estimation methodologies often fail when there is
model mismatch. Based on the principle that large interele-
ment spacing can reduce the effect of mutual coupling, the
second approach is to design new arrays in which the number
of sensor pairs with small spacing d (usually equal to a half
wavelength) is greatly reduced. The coprime array [9, 10]
and the super nested array [8] belong to this type for linear
array design. However, these linear arrays can only estimate
the azimuth angles or the elevation angles of the sources,
that is, they cannot estimate the two-dimensional angles
simultaneously. Recently, the two-dimensional half-open
box array and hourglass array were proposed [11], which
are capable of reducing mutual coupling by placing the
sensors properly. In the meantime, the difference coarrays
(DCAs) of these arrays can also be kept as filled rectangu-
lar arrays. Among the planar arrays mentioned above, the
hourglass arrays show the best performance when mutual
coupling exists.
Figure 1(a) shows an example of the hourglass array.
We can observe that the four corners in the hourglass
array are dense parts with three or four sensors with
small spacing, which will bring in the mutual-coupling
problem among these sensors. As reported in [11], the
Hindawi
International Journal of Antennas and Propagation
Volume 2018, Article ID 3624514, 8 pages
https://doi.org/10.1155/2018/3624514