迭代混合方法：精确分析雷达天线罩接收模式的高效算法

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本文档深入探讨了一种新颖的基于迭代的混合积分方程方法，用于快速高效地分析被雷达天线罩包围的天线在接收模式下的性能。该方法结合了体积-表面积分方程（Volume-Surface Integral Equation, VSIE）与修正的表面积分（Modified Surface Integration, MSI）技术，旨在提高计算精度。以往的研究中，混合方法可能忽略了雷达天线罩阴影墙的影响以及天线与罩之间相互作用的处理，而本文提出的创新之处在于将这些因素纳入考虑，通过迭代方式解决VSIE。为了进一步加速计算，作者们将天线-罩结构（Antenna-Radome Structure, ARS）的不同部分嵌入到三维八叉树（Octree）中，这样可以有效地利用多级fast multipole algorithm (MLFMA)。这种方法在VSIE求解阶段和MSI阶段都能实现并行计算，从而提升效率。 MLFMA是一种在电磁场计算中常用的近似算法，它通过分解问题为不同尺度的子问题来减少计算量。在本文的应用中，它使得处理大型ARS时的复杂性显著降低，同时保持了足够的计算精度。通过与原始混合方法进行对比，新的迭代混合方法显示出更高的准确性和计算效率，这对于雷达设计工程师来说，意味着更短的仿真时间，而得到的结果更为精确，有助于优化天线罩的设计，提高雷达系统的整体性能。这项研究提供了一个强大的工具箱，不仅改进了传统的分析方法，而且在处理复杂几何结构和电磁交互时展现出了优越的性能。对于那些关注雷达系统设计和电磁兼容性的研究人员和工程师来说，这篇文章提供了有价值的新思路和技术手段，值得深入学习和应用。

2436 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 65, NO. 5, MAY 2017

Fast and Efﬁcient Analysis of Radome-Enclosed

Antennas in Receiving Mode by an Iterative-Based

Hybrid Integral Equation/Modiﬁed Surface

Integration Method

Binbin Wang, Mang He, Senior Member, IEEE, Jinbo Liu, Chuanfang Zhang, and Houjun Sun

Abstract—An iterative-based hybrid method, which combines

the volume-surface integral equation (VSIE) and the modiﬁed

surface integration (MSI) method, is presented to analyze the

radome-enclosed antennas in receiving mode. Compared with the

previously published hybrid approaches, this method improves

computational accuracy by including the effects of shaded wall

of the radome and the mutual interactions between antennas and

radome during the numerical solution of the VSIE in an iterative

manner. By embedding different parts of the antenna-radome

structure (ARS) into three distinct oct-trees, the multilevel fast

multipole algorithm (MLFMA) is used to accelerate both the

VSIE solution and the surface/volume integrations in the MSI

stage. The new method obtains more accurate results than its

original version within less CPU time, and keeps good accuracy

with much less memory usage and computational time when

compared with the MLFMA-accelerated full-wave VSIE solution

for the entire ARS.

Index Terms—Integral equation, iterative method, multilevel

fast multipole algorithm (MLFMA), radome, receiving antenna,

surface integration (SI).

I. INTRODUCTION

ADOME has widespread applications in protecting

antennas from adverse environmental effects, but the per-

formance of the enclosed antenna or array will be much or less

altered due to the presence of the radome. Hence, accurate

evaluation of the radome’s effects is essential to the design of

radome-enclosed antennas in practice engineering. A number

of effective solutions have been reported to handle this prob-

lem [1]–[9], including the full-wave solutions [2]–[4], [8], [9],

the high-frequency approximate methods [2], [5], [6], and

the hybrid approaches [1], [2], [7]. However, it is found

that almost all of the existing methods are only proposed

to study the radome effects on antennas in transmitting

mode [2]–[9]. Although in many application scenarios, such

as in telemetry, direction ﬁnding, passive guidance, and ﬁre-

control radars [1], [2], antennas usually operate in receiving

Manuscript received September 26, 2015; revised August 26, 2016; accepted

January 28, 2017. Date of publication March 1, 2017; date of current

version May 3, 2017. This work was supported by the National Natural

Science Foundation of China under Grant 61471040. (Corresponding author:

Mang He).

The authors are with the School of Information and Electronics, Beijing

Institute of Technology, Beijing 100081, China (e-mail: hemang@bit.edu.cn).

Color versions of one or more of the ﬁgures in this paper are available

online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TAP.2017.2676718

mode, the development of analysis method for the antenna-

radome structure (ARS) in this commonly used working mode

has received much less attention. In the authors’ viewpoint,

there are two main possible reasons for such delayed research

situation: 1) when full-wave methods are used to analyze ARS

with electrically large size in receiving mode, the computa-

tional burden is still formidable as for the transmitting case,

although the utilization of fast solvers can alleviate the prob-

lem to some extent [14] and 2) on the other hand, existing high

frequency or hybrid methods, which are accurate enough for

the analysis of ARS in transmitting mode, cannot be used for

the receiving mode directly, and the reason can be explained

as follows. In transmitting mode, the equivalent source on the

outer wall of the radome is obtained by direct computations

(the physical optics (PO) method [2]) or by the equivalent

aperture (the aperture integration-surface integration (AI-SI)

method [5]) of radiation ﬁelds from the transmit antennas,

and then, far-ﬁeld pattern of ARS is easily achieved via the

equivalence theorem. Whereas for the analysis of ARS in

receiving mode, the excitation ﬁeld of the receiving antennas,

which is exactly the transmitted ﬁeld within the space enclosed

by the radome, should be obtained ﬁrst. But in this case,

the unique excitation of the ARS is the incident plane wave

and in theory the extent of plane-wave source is inﬁnite.

Since the radome of ﬁnite size cannot entirely encompass this

“inﬁnitely sized” source, the equivalence theorem, which is

the basis of the PO and AI-SI methods, cannot be directly

used to achieve the excitation ﬁelds. Therefore, it is difﬁcult

to apply existing methods to study the ARS properties in

receiving mode, especially for the large-size problems, since,

in this case, full-wave analyses are inefﬁcient, while the use

of approximate or hybrid methods is problematic.

Recently, Wang et al. [1] proposed a hybrid integral

equation/ modiﬁed SI (MSI) method (called original IE/MSI

method hereafter in this paper) to analyze the performance

of ARS in receiving mode. This approach not only obviates

the previously stated deﬁciency of existing high frequency and

hybrid methods for ARS in receiving mode, but also reduces

memory requirement massively as compared to the purely

fast solvers accelerated full-wave solutions. However, as was

pointed out in [1], this method still has two drawbacks. The

ﬁrst one is that it will become less accurate when the incidence

angle of plane wave with respect to the radome’s axis increases

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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