4884 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 9, SEPTEMBER 2014
An Efficient Integral Equation/Modified Surface
Integration Method for Analysis of Antenna-Radome
Structures in Receiving Mode
Binbin Wang, Mang He, Jinbo Liu, Hongwei Chen,
Guoqiang Zhao, and Chuanfang Zhang
Abstract—An efficient approach that combines the coupled volume sur-
face integral equation (VSIE) accelerated by multilevel fast multipole algo-
rithm (MLFMA) and the modified surface integration (MSI) method is pro-
posed to analyze the antenna-radome structures (ARS) in receiving mode.
The hybrid method not only reduces the computational time and memory
requirement as compared to the purely full-wave solutions, but also more
importantly overcomes the difficulties in conventional high-frequency ap-
proximate methods for analyzing the properties of the radome-enclosed re-
ceiving anten nas or arrays. Numerica l results are shown to illustrate the
validity, efficien cy, and accuracy of the proposed method.
Index Terms—Fast algorithm, integral equation, radome, receiving a n-
tenna, surface integration.
I. INTRODUCTION
It is well known that the presence of radome has pronounced effects
on the performance of the enclosed antennas or arrays [1]. In practice
engineering, the designs of antenna and radome are usually treated as
two detached processes. A direct consequence of such situation is that
the performance of antennas may be severely degraded when working
together with a radome, even if both the antenna and radome are well
designed in the two separated procedures. Therefore, when we need to
evaluate the electromagnetic (EM) properties of the ARS, it is highly
desired that the antenna and radome can be considered as a w hole rather
than two independent parts.
A number of m ethods, including full-wave solutions [2]–[15],
high-frequency approximate methods [16]–[18], and hybrid ap-
proaches [19], [20], have been reported to deal with the ARS
problems. Among these methods, the full-wave types can evaluate
the radome effects on antennas accurately, but they are only suited to
analyze small/moderate-sized ARS since a large amount of computa-
tional time and core memory are required if the size of radome is large
in terms of wavelength, even when fast algorithms are utilized [13].
In contrast, the high-frequency methods, such as the aperture-integra-
tion surface-integration (AI-SI) [16] and physical optics (PO) [17],
[18] methods, seek approximate but efficient solutions for large-size
radome with s mooth shape. The hybrid approaches, which combine
the advantages of both the full-wave and approximate methods, solve
complicated interactions between antennas and radome by using
domain-decomposition concept and choosing suitable solutions within
different domains while preserving acceptable accuracy [19], [20].
However, in almost all the above-mentioned methods, only the ef-
fects of radome on antennas’ radiation patterns have been considered,
i.e. the properties of the ARS in transmitting mode are extensively
Manuscript received F ebruary 13, 2014; revised June 27, 2014; accepted June
29, 2014. Date of publication July 02, 2014; date of current version September
01, 2014. This work was supported by the National Natural Science Foundation
of China under Grant 61471040. (Corresponding author: M. He).
B. Wang, M. He, J. Liu, G. Zhao, and C. Zhang are with the School of Infor-
mation and Electronics, Beijing Institute of Technology, Beijing 100081, China
(e-mail: hemang@bit.edu.cn).
H. Chen is with the Beijing Electro-mechanical Engineering Institu te, Beijing
100074, China.
Color versions of one or more of the figures in this communication are avail-
able online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TAP.2014.2334707
studied, while how radomes alter the performance of receiving an-
tennas is seldom taken into account. For full-wave solutions, from the-
oretical point of view, there is no difference in analyzing the A RS
working in transmitting or receiving modes although in both cases
heavy computational burdens will be faced when the electrical size of
the structure becomes large. But on the other hand, for high-frequency
approximate or hybrid methods, analyses of the ARS in two different
working situations are fundamentally distinct. In transmitting mode, ra-
diation from antennas that incidents on the i nner surface of the r
adome
is directly computed (in PO method) or by using the equivalent aper-
ture distribution (in AI-SI method), then far-field radiation of the en-
tire structure is obtained via the equivalence theorem. Whil
eforARS
in receiving mode, which is commonly e ncountered in the telemetry,
direction finding, and passive guidance applications, the unique exci-
tation of the ARS is the incident plane wave that in th
eory can only be
generated by sources distributed on an infinitely large plane. Since the
finite-sized radome cannot encompass the sources of infinite extent en-
tirely, the equivalence theorem, which is the ba
sis of the PO and AI-SI
methods, cannot be used to compute the transmitted fields within the
space enclosed by radome as the excitation of the receiving antennas.
Therefore, it is difficult to investigate
the properties of the ARS in re-
ceiving mode by using existing methods, especially in the analysis of
large-size structure, since in this case full-wave methods are not effi-
cient whereas the use of approximate or
hybrid methods is problematic.
In this communication, an efficient approach that combines the fast
algorithm accelerated VSIE solution and the MSI method is proposed
for the analysis of ARS in receiving mo
de. In Section II, a new MSI
method is devised for determination of the transmitted fields through
the radom e, and then the MLFMA accelerated VSIE solver to calcu-
late the induced currents on ant
ennasisbriefly described as well. In
Section III, numerical examples are shown to demonstrate the effi-
ciency and accuracy of the proposed method. Finally, conclusions are
presented in Section IV.
II. F
ORMULATION
The confi guration of the A RS working in receiving mode is shown
in Fig. 1, where the radome consists of -layered dielectrics
indexed by
, , and the outermost and in-
nermost layers are free space. The thickness, volume, relative permit-
tivity, and loss tangent of the
th layer are denoted by , , ,and
, respectively. As shown in Fig. 1, the region of the radome is
with its boundary given by ,where
, ,and represent the outer, inner, and bottom surfaces of the
radome, respectively. The direction of the incident plane wave is dic-
tated by the vector
.
As discussed in the last section, for analysis of the receiving-mode
ARS, there are two problems to be solved: one is the calculation of the
transmitted fields
in the space enclosed by an arbitrarily-shaped
dielectric radome after the incident plane wave goes through it; and
the other one is the computation of the induced currents on receiving
antennas under the excitation fields obtained in the previous step.
A. Computation of the Transmitted Fields Within the Space Enclosed
by Radome
The conventional AI-SI method [16] is usually used for the anal-
ysis of the radome effects on radiation patterns of aperture antennas, in
which the presumed aperture distribution of the antenna is integrated to
obtain the equivalent excitation fields of the radome. However, when
we investigate the properties of the ARS in receiving mode, the SI
process in the conventional AI-SI method is not applicable, because in
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