MASTER THESIS PROJECT IN ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS
STOCKHOLM, SWEDEN 2020
Investigation of
Hybrid Simulation
Methods for
Evaluation of EMF
Exposure in Close
Proximity of 5G
Millimeter-Wave Base
Stations
David Anguiano Sanjurjo
Investigation of Hybrid Simulation
Methods for Evaluation of EMF
Exposure in Close Proximity of 5G
Millimeter-Wave Base Stations
David Anguiano Sanjurjo
Examiner
Oscar Quevedo Teruel (KTH Royal Institute of Technology)
Supervisors
Qingbi Liao (KTH Royal Institute of Technology) Bo Xu (Ericsson AB)
Abstract
With the emergence of Fifth Generation (5G) mobile networks, the employment of higher frequencies in the millimeter-wave (mmWave) range and the realization of a great number of beams in 5G radio base stations (RBS) make the electromagnetic (EM) simulation of RBS products very costly in terms of hardware and time requirements. In order to compute the electromagnetic field (EMF) exposure in close proximity of the RBS, more efficient simulation methods are required.
The move to mmWave frequencies enables the use of the so-called high frequency methods for EM simulation with RBS antennas. In this thesis, conventional full-wave simulation solvers and different implementations of hybridization of high frequency methods with conventional methods are used with different commercial EM simulation tools, and their performance is evaluated for the purpose of EMF exposure assessment in close proximity of 5G mmWave RBS.
Among all the investigated methods, the hybrid scheme with Finite Integration Technique (FIT) and Shooting and Bouncing Rays (SBR) methods, e.g., that implemented in CST Studio Suite 2020, outperforms in terms of hardware requirements and time costs, although the accuracy is compromised on the side and behind the mmWave RBS. The Multilevel Fast Multipole Method (MLFMM), e.g., that implemented in Altair FEKO 2019, though not a hybrid method, also has good performance but requires very large Random Access Memory (RAM), and it cannot handle very exquisite details of RBS. The Finite Difference Time Domain (FDTD) method implemented in EMPIRE XPU can also handle the investigated problems effciently, but for extremely large problems, its requirements on RAM may become the bottleneck. In the thesis, many other hybrid implementations are also investigated, but it is found that they are not suitable for the EMF exposure assessment in close proximity of the mmWave RBS with evaluation on a planar area of 0.42 m× 1 m at 28
GHz due to various reasons.
Keywords
Sammanfattning
För den femte generationens (5G) mobilnät kommer användningen av millimetervågor och det stora antalet lober som en radiobasstation (RBS) kan hantera att betyda ett kraftigt ökat behov av hårdvara och större tidsåtgång för att göra beräkningar av exponeringen för elektromagnetiska fält nära utrustningen. Därför behövs mer effektiva simuleringsmetoder.
Eftersom systemen opererar på millimetervåg-frekvenser kan högfrekvensmetoder användas i simuleringen av simuleringen av en RBS. I den här avhandlingen utvärderas konventionella metoder, samt olika hybridmetoder för beräkningen av EMF-exponeringen av millimetervågor i närheten av en RBS. De utvärderade hybridmetoderna är implementerade i olika mjukvaror och blandar användandet av högfrekvensmetoder och konventionella metoder.
Av alla utvärderade metoder fungerar hybridmetoden implementerad med finita integralmetoden (FIT) och ”Shooting and Bouncing Rays”-metoden (SBR) i CST bäst i termer av vilken hårdvara som behövs för beräkningarna och för tidsåtgången. Dock är noggrannheten i beräkningarna på sidan av och bakom RBSen mindre bra. Multilevel Fast Multipole Method (MLFMM)”-lösaren i Feko i FEKO använder ingen hybridmetod men presterar bra, men den kräver mycket RAM-minne och kan inte ta hänsyn till små detaljer i RBSen. Finita differensmetoden i tidsdomänen (FDTD) i EMPIRE kan också användas men dess RAM-krav blir en flaskhals för stora simuleringar. Ytterligare hybridmetoder är undersökta i avhandlingen men med slutsatsen att de inte är användbara (av olika anledningar) för beräkningen av EMF-exponeringen från en RBS opererandes på frekvensen 28 GHz och över en yta som är 0.42 x 1 m.
Acknowledgements
First, I would like to thank all the people from KTH and Ericcson who helped and assisted me in this project. Specially, I want to thank my supervisor in Ericsson, Bo Xu, for his continuous assistance and guidance.
Finally, I would like to thank Ericsson for letting me carry out my master thesis with them. It has been a very pleasant and didactic experience.
Acronyms
5G Fifth Generation
AS Asymptotic Solver
CPU Central Processing Unit
DDM Domain Decomposition Method
EIRP Effective Isotropic Radiated Power
EM Electromagnetic
EMF Electromagnetic Field
FDTD Finite Difference Time Domain
FEM Finite Element Method
FIT Finite Integration Technique
GB GigaByte
GHz GigaHertz
GO Geometrical Optics
GPU Graphics Processing Unit
GTD Geometrical Theory of Diffraction
ICNIRP International Commission on Non-Ionizing Radiation Protection LE-PO Large Element Physical Optics
MoM Method of Moments
mmWave Millimeter Wave
MLFMM Multilevel Fast Multipole Method MIMO Multiple Input Multiple Output
PEC Perfect Electric Conductor
PO Physical Optics
PTD Physical Theory of Diffraction
RAM Random Access Memory
rms root-mean-square
SBR Shooting and Bouncing Rays
SP Simulation Project
SAR Specific Absorption Rate
TS Time Domain Solver
Contents
1 Introduction
1
1.1 Background . . . 1
1.2 Problem . . . 1
1.3 Purpose and Goal . . . 2
1.4 Methodology . . . 2
1.5 Delimitations . . . 2
1.6 Structure of the thesis . . . 2
2 Background
4
2.1 EMF Exposure . . . 42.2 Numerical Computational Methods . . . 7
2.2.1 Full-wave methods . . . 7
2.2.2 High Frequency Methods . . . 9
2.3 Hybridization of numerical methods . . . 11
3 Methodology
13
3.1 Simulation Models . . . 143.1.1 Phase 1: PEC Box Model . . . 14
3.1.2 Phase 2: RBS Product Model . . . 17
3.2 Simulation Methods . . . 18
3.3 Data Collection and Analysis . . . 21
3.3.1 Data Collection . . . 21
3.3.2 Post-Processing and Data Analysis . . . 24
3.4 Hardware . . . 26
4 Results
27
4.1 Phase 1: PEC Box Model . . . 27CONTENTS
4.2 Phase 2: RBS Product Model. . . 34
5 Conclusion and Future Work
40
5.1 Conclusion . . . 40 5.2 Future Work . . . 41
References
42
List of Figures
2.1.1 Iso-surface compliance boundary (exclusion zone) of an Radio Base Station (RBS) employing massive Multiple Input Multiple OutputMultiple Input Multiple Output (MIMO). (copyright©Ericsson AB) 6 2.1.2 An illustration of box-shaped compliance boundary. . . 6 3.1.1 PEC box model used in phase 1. . . 15 3.1.2 Perspective view of the RBS product model used in phase 2. . . 15 3.1.3 Requested area for evaluation of electric and magnetic field strength on
the xy plane in phase 2 - RBS product model. . . . 16 3.1.4 Simplified RBS product model for FEKO MLFMM. . . 16 3.2.1 Implementation of hybrid scheme for LE-PO in FEKO. Yellow-colored
surfaces are solved with MLFMM while orange-colored surfaces are solved with LE-PO. . . 20 3.3.1 Flow chart of hybrid CST AS simulation and data collection process for
multiple beams. . . 22 3.3.2 Flow chart of EMPIRE simulation and data collection process for
multiple beams. . . 23 3.3.3 Flow chart of FEKO MLFMM simulation and data collection process for
multiple beams. . . 23 4.1.1 Far field results for the 0° beam for CST TS vs EMPIRE vs FEKO
MLFMM, CST TS vs CST AS, CST TS vs FEKO LE-PO and CST TS vs FEKO RL-GO, respectively. . . 29 4.1.2 Near field results for the 0° beam from CST TS, EMPIRE, FEKO
LIST OF FIGURES
4.1.3 Far field results for the 30° beam for CST TS vs EMPIRE vs FEKO MLFMM, CST TS vs CST AS, CST TS vs FEKO LE-PO and CST TS vs FEKO RL-GO, respectively. . . 31 4.1.4 Near field results for the 30° beam from CST TS, EMPIRE, FEKO
MLFMM, CST AS, FEKO LE-PO and FEKO RL-GO, respectively. . . 32 4.2.1 Far field results of the product model from CST AS, EMPIRE and FEKO
MLFMM . . . 37 4.2.2 Near field results of 0°, 10°, and 20° beams from EMPIRE, CST AS and
FEKO MLFMM. . . 38 4.2.3 Near field results of 30°, 40°, and 60° beams from EMPIRE, CST AS and
FEKO MLFMM . . . 39 5.0.1 Electric field results of 0°, 10°, and 20° beams from EMPIRE, CST AS and
FEKO MLFMM. . . 45 5.0.2 Electric field results of 30°, 40°, and 60° beams from EMPIRE, CST AS
and FEKO MLFMM. . . 46 5.0.3 Magnetic field results of 0°, 10°, and 20° beams from EMPIRE, CST AS
and FEKO MLFMM . . . 47 5.0.4 Magnetic field results of 30°, 40°, and 60° beams from EMPIRE, CST AS
List of Tables
2.1.1 Incident power density limits in ICNIRP 1998 (above 10 GHz) and ICNIRP 2020 (above 6 GHz) guidelines. (f corresponds to frequency in
GHz) . . . 5
3.1.1 Progressive phase shift angles for adjacent element in the y-direction for different beams scanning in the xy-plane. . . . 17
3.3.1 Normalized EIRP levels for the different beams for phase 1 (only the 0° and 30° beams) and phase 2. . . 25
3.4.1 Hardware specifications of the different simulation platforms. . . 26
4.1.1 Simulation time for PEC box model. . . 28
4.1.2 U (dB) values for the 0° and 30° beams. . . 28
4.2.1 U (dB) values for the different beams. (EMPIRE near field results are reference.) . . . 35
4.2.2 Simulation time and RAM requirement for the RBS product model simulation in EMPIRE, FEKO MLFMM and CST AS . . . 35
Chapter 1
Introduction
This chapter gives a brief description of this master thesis by stating its main characteristics, like the goal and the problem statement. It also provides an outline of how the remaining chapters are organized.
1.1
Background
The new Fifth Generation (5G) mobile networks have introduced higher frequencies in the range of GigaHertz (GHz), also known as the Millimeter Wave (mmWave) bands. At these frequencies, the physical dimension of antennas is very small. When the antennas are integrated in the RBS, it becomes an electrically large problem, which usually requires huge amount of resources in terms of hardware requirements and computational time. In contrary, it is possible to use numerical computational methods that treat the Electromagnetic (EM) waves as rays in order to evaluate the performance of the antennas. This type of simulation methods is called the high frequency or asymptotic method, and they can be very efficient for solving large-scale EM problems.
1.2
Problem
Due to the fact that the mmWave antennas have become very small, the integration environment, for example, the radio unit structure, in the 5G RBS is usually electrically very large. Therefore, the simulation of antennas together with the radio unit structure becomes very demanding for conventional full-wave simulation methods.
CHAPTER 1. INTRODUCTION
The hybrid methods implemented in the commercial software tools are intended to calculate the radiation characteristics in the far-field region. Therefore, for evaluation of EMF exposure in close proximity of mmWave RBS, the performance of the hybrid methods should be investigated in contrast to the conventional full-wave simulations.
1.3
Purpose and Goal
The purpose of this master thesis is to evaluate whether the so-called asymptotic methods, or high frequency methods, are efficient and accurate compared to the conventional full-wave simulation methods when evaluating EMF exposure in close proximity of the mmWave RBS.
Therefore, the main goal is to implement hybrid schemes in different commercial simulation software tools and to analyze their performance compared to conventional methods.
1.4
Methodology
The project is divided in two phases, for each of which two different models are used. The goal of the first phase is to implement the investigated hybrid methods and evaluate their accuracy and efficiency compared to the conventional methods, while, in the second phase, the selected methods from the first phase are tested for evaluating EMF exposure using a realistic RBS model.
1.5
Delimitations
The main limitation comes from the fact that different hardware platforms are used for running the different simulation methods, which compromises the comparison of simulation speeds.
1.6
Structure of the thesis
CHAPTER 1. INTRODUCTION
• Chapter 1 presents a brief introduction of relevant background information, research problem, methodology, delimitations, and the structure of the thesis. • Chapter 2 mainly introduces the relevant background for understanding of this
report.
• Chapter 3 covers the methodology used in this study. It describes the entire research process including planned measurements, test environment, and evaluation framework.
• Chapter 4 summarizes the results and provides the analysis and discussion about this thesis.
• Chapter 5 concludes the research and defines the final conclusions of this study as well as directions for future work.
Chapter 2
Background
This chapter aims to present the relevant background for the understanding of this thesis. It contains a brief description of EMF exposure requirements for RBS, the mainstream numerical computational methods involved in this project, and hybridization of these methods.
2.1
EMF Exposure
Before a product emitting electromagnetic fields is placed on the market and put into service, it has to comply with relevant regulations and standards related to human exposure to EMFs. The most widely adopted EMF exposure guidelines are those developed by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) [1] in 1998. Very recently in 2020, the ICNIRP published the updated Electromagnetic Field (EMF) exposure guidelines [2]. These guidelines establish certain EMF exposure limits for two groups of human beings: one for the general public and the other for occupational workers. General public exposure limits are applicable for people not aware of EMF exposure, while occupational exposure limits are relevant for people who are aware of the potential risks of EMF exposure and what precautions should be taken.
In the ICNIRP guidelines [1, 2], the EMF exposure limits termed reference levels are usually used to demonstrate compliance in practice. In this thesis, the relevant reference level quantity is incident power density. For local exposure, the power density should be averaged over 20 cm2for the ICNIRP 1998 guidelines and over 4 cm2
CHAPTER 2. BACKGROUND
Table 2.1.1: Incident power density limits in ICNIRP 1998 (above 10 GHz) and ICNIRP 2020 (above 6 GHz) guidelines. (f corresponds to frequency in GHz)
ICNIRP 1998 [1] ICNIRP 2020 [2]
General public Occupational General public Occupational 10W/m2 50W/m2 55/f0.177W/m2
275/f0.177W/m2
for the ICNIRP 2020 guidelines. Above 30 GHz, the ICNIRP 2020 guidelines also require to ensure the power density averaged over 1 cm2 not exceeding twice of the limits averaged over 4 cm2. In table 2.1.1, the reference levels from the ICNIRP 1998 [1] and ICNIRP 2020 [2] for frequencies above 10 GHz are stated in terms of incident power density.
Incident power density is defined as the power flow through the unit area, i.e., the spatially-averaged Poynting vector, which can be expressed as
Sinc = Z
A
Re (E× H∗)· ˆn dA (2.1)
where E is the root-mean-square (rms) complex electric field, H is the rms complex magnetic field, the superscript∗ denotes the conjugate, ˆn is the the unit vector normal to the projected body surface, and A is the averaging area. Taking A → 0, the point incident power density can be expressed as
Sincp =Re (E× H∗)· ˆn (2.2)
However, when taking ˆninto consideration for the Perfect Electric Conductor (PEC) box model and the RBS product model in the following chapters, it is cumbersome to define the direction of ˆnfor the averaging area A. Moreover, the focus of the thesis is on the simulation methods rather than EMF exposure compliance. Thus in this thesis, the module of the point Poynting vector, i.e.,
|S| = |Re (E × H∗)| , (2.3)
is considered for incident power density when comparing different methods and plotting results.
The so-called compliance boundary (i.e., exclusion zone) of the RBS is defined outside which the EMF exposure is below the relevant EMF exposure limits. The compliance
CHAPTER 2. BACKGROUND
Figure 2.1.1: Iso-surface compliance boundary (exclusion zone) of an RBS employing massive Multiple Input Multiple OutputMIMO. (copyright©Ericsson AB)
CHAPTER 2. BACKGROUND
boundary can be an iso-surface (see e.g., Figure 2.1.1), or a simplified shape, such as box-shaped (see e.g., Figure 2.1.2). For the distance of the compliance boundary locating in the far-field region of the RBS antenna, the compliance boundary can be well characterized through the antenna radiation pattern, see Figure 2.1.1 for a 5G massive MIMO RBS. However, when the transmitted power of the RBS is relatively low or the evaluation direction is outside the range of the main lobe, the compliance boundary can be located in the near field region. In such case, the antenna radiation pattern usually gives a conservative estimate of EMF exposure. Therefore, an accurate evaluation of EMF exposure is needed when the compliance boundary is close to RBS.
2.2
Numerical Computational Methods
Over time, new advances have been made in finding physical and mathematical solutions to EM problems. These advances go through finding numerical solutions to either the differential or integral form of the Maxwell’s equations. The numerical methods and algorithms created to solve these equations with no approximations are known as full-wave methods.
In the last years, the emergence of the new generation of mobile networks has provoked a move to higher frequencies where mathematical techniques based on ray optics can be applied to reduce the computational requirements of these calculations. However, these high frequency methods are not approximation-free since they treat the high frequency waves as rays. They use fundamental approximations of the Maxwell’s equations, which gain validity when going up in frequency.
In this section, the main full-wave and high frequency methods, also called asymptotic methods, evaluated in this project are briefly described.
2.2.1
Full-wave methods
Full-wave methods are particularly distinguished by performing a complete EM analysis of the Maxwell’s equations and, as mentioned before, they are divided in two types depending on how they approach the Maxwell’s equations: integral methods and differential methods. Some of the best-known full-wave numerical methods are the Finite Difference Time Domain (FDTD) and its relative the Finite
CHAPTER 2. BACKGROUND
Integration Technique (FIT), the Method of Moments (MoM), and the Finite Element Method (FEM). All of them, except for FEM, are used in this project with the purpose of obtaining an accurate solution of our EM problem. These methods can also be classified by whether they are applied in the frequency domain or the time domain.
In differential equation solvers, such as FDTD and FEM, the field values inside the simulation region are the unknowns and they usually have an efficiency of O(N ) [3], where N is the number of unknowns. The simulation region where the differential solver is applied must present an absorbing boundary. In differential solvers, the complexity of the EM problem can increase the unknowns count a lot, for which the Random Access Memory (RAM) and simulation time requirements are increased dramatically . Due to this fact, the integral solvers, such as MoM, are more popular when dealing with large EM problems since the unknowns count can be smaller. However, there is a drawback related to the memory requirements of this kind of methods, which can need O(N2)memory usage [3].
• FDTD:
The FDTD is a powerful differential equation solver invented by Yee [4] in 1966, which gives a direct solution to Maxwell’s time-dependent differential equations. It approximates the partial differential equations by replacing the space and time derivatives with finite differences, converting a continuous system to a discrete system. It is proclaimed to be very robust and accurate while being able to deal with a large variety of EM problems, making this solver very appropriate for real practical problems. Moreover, it is quite simple and easy to implement so that it has become a very popular method.
Some of the FDTD’s advantages are the following:
– It can solve broadband problems usually centered in the resonance
frequency.
– It is capable of dealing with EM problems containing complex and
arbitrary-shaped structures in an efficient way.
– It is compatible with almost all types of medium and materials.
CHAPTER 2. BACKGROUND
performing computing .
The main drawback of this method would be the large computational resources needed for solving electrically large problems. In these cases, the bottleneck is usually the long simulation time.
• FIT:
FIT was introduced by Weiland in 1977 [5]. It discretizes the problem in a similar way to FDTD, however, Maxwell’s equations are solved in their integral form. This method is supposed to be able to deal with more complex structures than FDTD in an accurate manner. The advantages of FIT are quite similar to FDTD’s, it is easy and simple to implement, it can be parallelized for high performance computing, and it supports quite complex structures.
• MoM:
MoM was first published by Harrington in 1968 [6]. It is an integral solver applied in the frequency domain that converts the Maxwell’s integral equations to a matrix equation. For MoM, only the scattered structure is discretized, and thus it has smaller number of unknowns compared to FDTD and FIT. However, since the memory usage is about O(N2), the memory requirements are usually much larger than in FDTD and FIT. Moreover, the number of unknowns in MoM is dependent on the frequency, so the hardware requirements increase exponentially with frequency. For the cases with electrically large structures, the Multilevel Fast Multipole Method (MLFMM) [7] is a more convenient choice.
– MLFMM: MLFMM is a numerical method derived from MoM. It provides
a fast numerical way to compute the matrix calculations by decreasing the memory usage from O(N2)to O(N ). This makes MLFMM the fastest full-wave method and the most convenient for electrically large problems.
2.2.2
High Frequency Methods
High frequency solvers are supposed to be more efficient than full-wave methods when calculating the scattered field from electrically large structures. By making use of ray physics, different high frequency methods have been developed. Some of these methods are Geometrical Optics (GO) [8] and Physical Optics (PO) [9], which are used to calculated the reflected and transmitted electromagnetic waves. In order to calculate
CHAPTER 2. BACKGROUND
the diffracted fields, other methods, such as Geometrical Theory of Diffraction (GTD) [10], Uniform Theory of Diffraction (UTD) and Physical Theory of Diffraction (PTD) [11], were developed. These methods can be combined in order to calculate both reflected and diffracted fields.
• GO:
GO is based on the Fermat’s principle, that a ray going from one point to another point takes the path that minimizes the optical distance between both points, according to equation (2.1), where n(s) is the refraction index and δ is the variation operator.
δ Z p2
p1
n(s)ds = 0 (2.4)
Thanks to Fermat’s principle, the reflected fields can be calculated from the incident fields. To calculate the scattered fields at a certain distance from the reflection point, the ray tube theory and conservation of energy flux for light intensity is used.
• GTD:
In order to overcome the problem faced by GO when calculating the fields around wedges and in the shadow boundary, GTD was developed. The diffracted ray fields are calculated according to equation (2.2):
Ed(r) = Ei(pd)· ⃗D »
(ρdpd)eiks/(s(ρdpd+ s)) (2.5)
where ⃗Dis the dyadic diffraction coefficient, and ρdpdis the radius of the curved wedge at the point pdof reflection. At the transition regions (close to the wedge), the diffraction coefficient of GTD becomes infinite so that the field in this region become singular, invalidating GTD solution in these regions.
• PO:
PO calculates the scattered field by approximating the induced surface-currents from the incident field in the scatterer surface with the PO approximation:
JPO(r) = 2 ˆn(r)× H(i)(r) , (2.6)
CHAPTER 2. BACKGROUND
is the magnetic incident field. This approximation is applied over an electrically small surface, which is assumed to be flat and smooth at high frequencies. However, the resulting surface currents, also called PO currents, are not correct in the shadow boundary.
• PTD:
With PTD, the edge current was introduced to correct the diffraction problem faced by PO. The PTD current is formulated in equation (2.4):
JPTD(r) = JPO(r) + JU(r) (2.7)
where JUis the edge wave current, which is used to correct the limited accuracy of JPO. In theory, PTD is a more accurate way to calculate the diffracted field compared to GTD and UTD.
2.3
Hybridization of numerical methods
For the purpose of analyzing complex electromagnetic problems, many numerical methods have been developed. However, there are multi-scale problems that are very difficult to address with the available methods. For this kind of problems, the hybridization of different methods is very useful in order to solve them in an efficient way. These multi-scale problems are usually found in the radar framework and, nowadays, in the 5G technology, too, due to the high frequencies used. To solve these problems, the Domain Decomposition Method (DDM) was developed.
DDM is one of the most effective methodologies to address large multi-scale problems. The DDM is dividing the simulation domain into smaller sub-domains, which can be treated independently. In order to solve the entire domain, certain boundary conditions between sub-domains are applied. This allows to use the most convenient method for each sub-domain, as well as a more efficient mesh.
If we look at the topic of this project, DDM is very useful to hybridize high frequency and full-wave solvers. The sub-domain involving the source and the surfaces close to it could be solved with a full-wave method, while the rest of the domain, whose size is electrically large, could be solved with a high frequency method.
CHAPTER 2. BACKGROUND
approaches, such as different boundary conditions. The Equivalence Principle [12] is one of the methods used for this purpose. The interaction between sub-domains can be modelled by calculating the induced magnetic and electric currents on the equivalence surface, i.e., Huygens box source. These currents can be induced by others sub-domains or by sources inside the own sub-domain.
Regarding the hybridization of full-wave and high frequency solvers, we usually have an equivalence surface surrounding the source region where the antenna is located. In this region, a full-wave method is used to get the induced currents in the equivalence surface. The rest of the simulation domain is treated as other sub-domain, in which a high frequency method is used. As a first step, the induced currents on the equivalence surface are calculated in order to calculate the interaction of the source sub-domain with the rest of the simulation domain. With these equivalent currents is possible to determine how the outgoing fields from the source sub-domain interact with the rest of the simulation domain. In this project, this interaction is calculated through high frequency solvers. The scattered fields from the surfaces outside the source domain can induced currents back to the equivalence surface of the source sub-domain. This interaction can be considered if it is expected to be relevant, otherwise, it could be ignore to accelerate simulation.
Chapter 3
Methodology
The purpose of this chapter is to provide an overview of the methodology used in this project. It gives detailed introduction of the different simulation methods and models used and also describes the methods adopted for data processing and analysis.
The first section, 3.1, details the models used in the simulations and their purposes.
The second section, 3.2, describes the simulation methods evaluated in this project and explains how they are implemented in the different software tools.
The third section, 3.3, describes how the simulation results were collected, post-processed and analyzed.
The forth section, 3.4, describes the hardware platforms used for running the different simulation methods.
To begin with the research project, the relevant literature about the selected simulation methods is collected and reviewed. Then, the proposed simulation methods are investigated in order to understand the advantages and disadvantages of each method and to find the optimal setup for each software tool.
The data collection process, in which the required simulations are performed, is divided in two phases that will be referred to as phase 1 and phase 2 from now on. Phase 1 uses a simplified model to implement the investigated hybrid methods and compare them to conventional methods, while in phase 2, the best performing methods are used to evaluate the EMF exposure from a realistic mmWave RBS product model. The simplified model is used to understand the limitations of each simulation method.
CHAPTER 3. METHODOLOGY
In this phase, we focus on discovering the degree of simplicity or complexity of setting up each method, the simulation time, and computational accuracy. Phase 2 aims to test the best performing simulation methods in a real case in order to check that the conclusions from the first phase are applicable to a more complex structure.
3.1
Simulation Models
As described above, the investigation of proper simulation methods for mmWave RBS is divided in two phases. The simplified model used in phase 1 is formed by a 2×2 patch antenna array placed in the center of the front face of an electrically large PEC box, which mimics a 5G antenna-integrated RBS. Phase 2 uses an mmWave RBS model based on the physical measurement of a real product. In phase 2, the full-wave and hybrid methods selected through phase 1 are used to perform a more detailed analysis for realistic scenarios.
Either of these phases is also carried out in two steps. The first step is to simulate the model through full-wave methods. Various full-wave methods implemented in different simulation software are compared to check their agreement. If the full-wave solvers show good agreement, we can take these results as the benchmark solutions for comparison with the hybrid methods in the second step. In comparison, the accuracy, the simulation speed, and the complexity of implementation of the hybrid methods are compared to the full-wave methods.
3.1.1
Phase 1: PEC Box Model
The goal of this first model is to facilitate the implementation and comparison of the different simulation methods. In order to minimize the effort, a simplified model is required, for which the advantages and disadvantages of each method can be easily spotted. Also, the simulation time of the simplified model is relatively short, which can facilitate finding the optimal simulation settings of each method.
In this model, the antenna is a 2× 2 array working at 28 GHz, of which the element is a rectangular patch with a width and length of 0.42λ and an element spacing of 0.7λ, where λ is the wavelength at 28 GHz. The antenna array is placed in the center of one of the faces of an electrically large PEC box. The PEC box has a width of 23λ and a height of 14λ. There is a small cavity right below the antenna array to facilitate some
CHAPTER 3. METHODOLOGY
Figure 3.1.1: PEC box model used in phase 1.
CHAPTER 3. METHODOLOGY
Figure 3.1.3: Requested area for evaluation of electric and magnetic field strength on the xy plane in phase 2 - RBS product model.
CHAPTER 3. METHODOLOGY
of the evaluated hybrid methods. Some of the investigated hybrid methods require a minimum distance between the sub-domain with the antennas and the sub-domain with other structures (in some literature it is called ’antenna platform’).
Two beams are simulated in phase 1: the broadside beam corresponding to a phase shift between array elements of 0°, and the 30° beam corresponding to a phase shift of 180°. In phase 1, the size of the area, where the electromagnetic field is calculated, is 0.45m in the y-direction and 0.45 m in the x-direction. Figure 3.1.1 shows the model used in phase 1.
3.1.2
Phase 2: RBS Product Model
Once the suitable simulation methods are identified in phase 1, a realistic RBS product model is adopted to test the selected methods under practical circumstances. This model presents a rectangular patch antenna array formed by 192 elements (24 columns and 8 rows). The RBS product model has a total width (in the y-axis in Figure 3.1.2) of 19λ, a total height (in the z-axis in Figure 3.1.2) of 26λ, and a depth of 11λ. Figure 3.1.2 shows the RBS product model used in phase 2.
In phase 2, the performance of the selected methods are evaluated when determining power density distribution in close proximity of the RBS product model for different beams. As mentioned in Section 2.1, the incident power density is evaluated but taken the module of the Poynting vector without spatial averaging for convenience. Also, the electric and magnetic field results can be found in the Appendix. This procedure is performed for different beams to evaluate|S| in close proximity to the RBS product in the xy-plane. In this case, the simulated beams correspond to the progressive phase shift angles between adjacent elements in the y-direction changing from 0° to 150°, as shown in Table 3.1.1.
Table 3.1.1: Progressive phase shift angles for adjacent element in the y-direction for different beams scanning in the xy-plane.
Progressive phase shift 0° 30° 60° 90° 120° 150° Beam direction (ϕ) 0° 10° 20° 30° 40° 60°
In this phase, the size of the plane where the electromagnetic field is calculated is much larger than in the phase 1 in order to investigate the applicability of different methods in a scenario close to the assessment of a real product. The size of the plane is 1 m in
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the y-direction and 0.42 m in the x-direction (see figure 3.1.3).
Regarding the MLFMM solver in FEKO, the iterative process used in MLFMM could not converge due to some energy trapped in the cavities formed by the heat sinks (see Figure 3.1.2). For this reason, the RBS product model had to be simplified for FEKO MLFMM. In the simplified model, the heat sinks are substituted by a PEC block (see Figure 3.1.4).
3.2
Simulation Methods
In this section, the software tools and solvers implemented in these tools used for the simulations are described, as well as the way they are used in this project. Four simulation software tools are considered: ANSYS HFSS (2020R1) [13], CST Studio Suite 2020 [14], Altair FEKO 2019 [15] and EMPIRE XPU V8.0 [16]. HFSS, CST, and FEKO have various full-wave and high-frequency solvers and support high-degree of hybridization between different solvers. However, HFSS was later excluded from the project, after we had found out that it does not have the required features for plotting the near field with its high frequency solver yet.
• CST Studio Suite 2020 Microwave Studio:
– Time Domain Solver (TS):
This solver uses the FIT, which is a time domain method for approximation-free solutions. This method is considered as the most accurate one of the investigated methods but is also the most computationally demanding. This method is referred to as CST TS.
– TS + Asymptotic Solver (AS):
AS uses Shooting and Bouncing Rays (SBR), which is a high frequency method that uses both GO and PO. SBR can be parallelized and run on the Graphics Processing Unit (GPU) for a more efficient simulation. It also supports PTD for diffraction calculation. This method is suitable for electrically large PEC objects, which would be very costly simulated using full-wave methods like FIT.
The way to implement the hybrid method (TS + AS) in CST is by using the hybrid task feature, in which it is possible to connect two different
CHAPTER 3. METHODOLOGY
Simulation Projects (SPs), which are referred to as the Source SP and the Platform SP, with different solvers. The Source SP contains the antenna array, and it is solved firstly by the full-wave solver, TS. Then, the resulting equivalent near-field source is imported to the Platform SP, which contains the rest of the model (i.e., the PEC box in Phase 1 and the RBS model behind the antenna array in Phase 2). The Platform SP is finally solved by the high frequency solver, AS, with the imported equivalent field source. In the following, this hybrid scheme is referred to as CST AS.
• EMPIRE XPU v8.0:
– Finite Difference Time Domain (FDTD):
EMPIRE XPU is full-wave simulation software developed by IMST based on the FDTD method. This software promises to give very efficient simulation so it is used for benchmarking together with other full-wave solver like CST TS.
• Altair FEKO 2019:
FEKO supports a variety of simulation methods including MoM, MLFMM, PO, and GO.
– MLFMM:
We use FEKO MLFMM as another full-wave solver for benchmarking and to be hybridized with the different high frequency solvers. As its name shows, it uses the Multilevel Fast Multipole Method, which is more efficient MoM-based solver for electrically large problems. MLFMM is an acceleration method for MoM that subdivides the simulation region into different regions and computes the interaction between regions and hence provides a faster solution path.
– MLFMM + LE-PO:
FEKO has a PO solver and a so-called Large Element Physical Optics (LE-PO) solver, which is an approximation of PO for electrically very large objects. In this project, the LE-PO solver is investigated by being hybridized with MLFMM.
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Figure 3.2.1: Implementation of hybrid scheme for LE-PO in FEKO. Yellow-colored surfaces are solved with MLFMM while orange-colored surfaces are solved with LE-PO.
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FEKO. Each face of the model can be configured to be solved by MLFMM or LE/PO. In this case, the faces belonging to the antenna and the surfaces close to it are solved with MLFMM while the rest of the model is solved with LE-PO. In Figure 3.2.1, the implementation of hybridization of MLFMM and LE-PO is illustrated. One important aspect of the implementation of LE-PO in FEKO is that it will only solved the faces that are directly illuminated by the source. In the following, this hybrid scheme is referred to as FEKO LE-PO.
– Huygens box + RL-GO:
RL-GO stands for ray launching geometrical optics, which is also based on the SBR method. It also can be parallelized and run on the GPU. FEKO 2019 version added diffraction calculation to the RL-GO solver so this solver seems suitable to be hybridized with the Huygens box sources. We can divide the model in two different SPs, in a similar way to CST, Platform SP and Source SP. We created the Source SP where the antennas are simulated with MoM/MLFMM. In this case, the use of MLFMM is not recommended, since the source problem is very small to take advantage of the MLFMM efficiency. Therefore, MoM is used to solve the Source SP. Then, the resulting Huygens box sources are imported to the Platform SP, in which RL-GO is used. In the following, this hybrid scheme is referred to as FEKO RL-GO.
3.3
Data Collection and Analysis
3.3.1
Data Collection
The data collection consists of obtaining the far field and near field for different scanning beams from the different simulation software tools. This process is done in a mostly automated way, which needs to be implemented differently in each software. The far field and near field results from the different software tools are post-processed in MATLAB to have the same format for all results.
• CST Studio:
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Figure 3.3.1: Flow chart of hybrid CST AS simulation and data collection process for multiple beams.
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Figure 3.3.2: Flow chart of EMPIRE simulation and data collection process for multiple beams.
Figure 3.3.3: Flow chart of FEKO MLFMM simulation and data collection process for multiple beams.
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automatic sequential simulations for different beams, phase shift is to be assigned to each port. For each run of parameter sweeping, the phase shift needs to be modified for each beam realization. To automatize this process, a CST Macro, which is an internal VBA-based script tool to control the software, is created. Finally, the far field and near field results can be exported at the end of each beam simulation by configuring a CST post-processing result template. Figure 3.3.1 shows the entire process for simulation and data collection for CST AS.
• EMPIRE:
EMPIRE also provides a feature to perform parameter sweeping, and the ports phase shift can be easily introduced and parameterized in the Port Setup Wizard. Once the simulation finishes, the far field and near field results needs to be exported manually (this may be automatized through the Python script). Figure 3.3.2 shows the entire process for simulation and data collection for EMPIRE.
• FEKO:
FEKO provides an interface called EDITFEKO, in which the script can be used to build and configure simulation projects. We use this interface to configure the phase shift of the ports. However, there is no feature to do a parameter sweep, so we need to run the parameter sweeping controlled from MATLAB. The far field and near field results can be easily configured to be automatically exported. Figure 3.3.3 shows the entire process for simulation and data collection for FEKO MLFMM.
3.3.2
Post-Processing and Data Analysis
The data analysis consists of basically a series of comparisons of results from different simulation methods. The parameters considered in these comparisons are the following:
• Far field: We compare the far-field results as a first check. For a hybrid method to be acceptably accurate, it should give a similar far field to the full-wave methods. A very different far field would suggest an inaccurate near-field result. For comparison, the far-field results for each simulation method are post-processed
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in MATLAB in order to have a standard plot of the 2D far field, specifically the θ = 90polar cut.
• Near field: As only beams steered in the xy plane are investigated in this thesis, the near-field distribution in the same plane are computed, and the resultant power density distribution is assessed with different methods. Figure 3.1.3 shows the near-field cut that is calculated in the phase 2 - RBS product model.
The near-field results are post-processed in MATLAB, in which they are normalized to a certain Effective Isotropic Radiated Power (EIRP) level for each beam, since each software tool uses different input power and may present different efficiency values. The EIRP levels used for the normalization are similar to the ones of realistic RBS products and are stated in Table 3.3.1.
Table 3.3.1: Normalized EIRP levels for the different beams for phase 1 (only the 0° and 30°beams) and phase 2.
Beam direction (ϕ) 0° 10° 20° 30° 40° 60° EIRP (dBm) 59 58.8 58.8 58.8 56.6 56.1
Similar to the evaluation of uncertainty between different methods in the numerical Specific Absorption Rate (SAR) calculation [17], the uncertainty of the numerical method investigated in this thesis can be expressed as
U (dB) = 10 log10 1 + max r |Scmp(r)| − Sref(r) max r |S ref(r)| (3.1)
Here, Sref(r) is the module of power density of the benchmark solution at a point r, while|Scmp(r)| is the module of power density of the compared method at the same point r.
• Simulation time: We obviously pursue a faster simulation method with good accuracy in order to simulate the large number of beams in a more efficient way. Therefore, the simulation time of different methods is one of the key parameters for the result analysis. The best method would be the one with a better trade-off between simulation speed and accuracy.
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Table 3.4.1: Hardware specifications of the different simulation platforms.
CST and FEKO MLFMM EMPIRE
FEKO RL-GO and FEKO LE-PO
CPU Intel Xeon Intel Xeon Intel i7-8650U 1.9GHz E5-2609 2.4GHz E5-2697 2.6GHz
GPU NVIDIA Tesla M2075 Not used Not used
(only used by RL-GO)
RAM 96 GB 128 GB 32 GB
3.4
Hardware
Different hardware platforms have been used to run the selected simulation methods in order to accelerate the data collection process by running different methods simultaneously. This fact should be considered when evaluating the performance of the simulation methods. Table 3.4.1 shows the relevant hardware used for each method.
Chapter 4
Results
As it is described in section 3.1, the project is divided in two phases. The results of the phase 1 are presented in section 4.1, while the results of the phase 2 are presented in section 4.2.
4.1
Phase 1: PEC Box Model
For each simulation method, two beams of the PEC box model are simulated, the broadside beam and the 30° beam, corresponding to a phase shift between array elements of 0° and 180° respectively. In Table 4.1.1, the simulation times for each method are displayed. Table 4.1.2 presents the values of uncertainty U for the investigated simulation methods.
The far-field and near-field results of the broadside beam for the different simulation methods are shown in Figures 4.1.1 and 4.1.2, respectively. The far field and near field results of the 30 degrees beam from the different simulation methods are shown in figures 4.1.3 and 4.1.4, respectively.
From the broadside beam results of the full-wave solvers (see Figure 4.1.2), a good agreement is observed between CST TS and EMPIRE. However, FEKO MLFMM does not agree with CST TS and EMPIRE in the back of the PEC box, where the electric field is very weak, but they have very good agreement in the front and sides. Regarding the 30° beam (see Figure 4.1.4), we observe the same thing as in the broadside case. CST TS and EMPIRE give very similar results, and FEKO MLFMM differs with them in the back of the PEC box. The reason why MLFMM provides different results in the
CHAPTER 4. RESULTS
Table 4.1.1: Simulation time for PEC box model. Simulation method Simulation time
CST TS 2h 30min
EMPIRE 1h 20min
FEKO MLFMM 40 min
CST AS (run on CPU) 50 min
FEKO LEPO 1h 10 min
FEKO RL-GO 2h
Table 4.1.2: U (dB) values for the 0° and 30° beams. U (0° beam) U (30° beam) CST TS NA(reference) NA(reference) EMPIRE 0.496 0.766 FEKO MLFMM 0.507 1.258 CST AS 2.7 2.685 FEKO LEPO 0.465 1.007 FEKO RL-GO 2.368 2.933
back of the PEC box could be attributed to the low intensity of the electromagnetic field there and the limited dynamic range in the MLFMM solver. However, this issue should be further investigated. Among the investigated full-wave methods, though simulations are run on different hardware, FEKO MLFMM is the fastest, see Table 4.1.1, but it suffers a lack of accuracy in the back of the model. EMPIRE demonstrates to be considerably faster than CST TS and similarly accurate, even with a less powerful hardware. Therefore, we take the CST TS results as the benchmark solution for the comparisons in phase 1.
For both the 0° and the 30° beams in Figures 4.1.2 and 4.1.4, the CST AS results are partly similar to the benchmark solution (CST TS). The CST AS near-field results give similar values to those from CST TS in the front of the PEC box. However, the sides and back parts are not very similar, as the electric field values from CST AS are quite higher than the ones from CST TS. The lack of accuracy of CST AS in these regions can be explained by a possible deficient calculation of the diffraction of the EM waves on the wedges of the PEC box. With regard to the simulation speed, CST AS is similar to EMPIRE and FEKO MLFMM while more efficient than CST TS. However, CST AS is based on the SBR method, of which the ray-launching stage can be parallelized and run by GPU. This would decrease the simulation time considerably. In this case, the simulations were run in the Central Processing Unit (CPU), and this factor should be considered when comparing the simulation speed. Since CST AS gives similar results
CHAPTER 4. RESULTS
Figure 4.1.1: Far field results for the 0° beam for CST TS vs EMPIRE vs FEKO MLFMM, CST TS vs CST AS, CST TS vs FEKO LE-PO and CST TS vs FEKO RL-GO, respectively.
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Figure 4.1.2: Near field results for the 0° beam from CST TS, EMPIRE, FEKO MLFMM, CST AS, FEKO LE-PO and FEKO RL-GO, respectively.
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Figure 4.1.3: Far field results for the 30° beam for CST TS vs EMPIRE vs FEKO MLFMM, CST TS vs CST AS, CST TS vs FEKO LE-PO and CST TS vs FEKO RL-GO, respectively.
CHAPTER 4. RESULTS
Figure 4.1.4: Near field results for the 30° beam from CST TS, EMPIRE, FEKO MLFMM, CST AS, FEKO LE-PO and FEKO RL-GO, respectively.
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in the front of the model, where the maximum EMF exposure is found, this method is selected to be implemented in phase 2 for the RBS product model.
As is explained in section 3.2, FEKO provides different high frequency solvers, which can be hybridized with MoM/MLFMM. In FEKO, the hybridization of different solvers is quite flexible, as different methods can be applied to to different objects, faces, etc. The results obtained with these methods are compared to the benchmark solution.
The first hybrid scheme that is evaluated from FEKO is FEKO LE-PO. A very important consideration for this method is that PO/LE-PO only considers the directly illuminated surfaces. This means that only the front face of the PEC box is solved by PO/LE-PO solver, ignoring the rest of the faces of the PEC box. Therefore, before analyzing the results, good accuracy only in the front of the PEC box is expected. From the FEKO LE-PO results, (see Figures 4.1.2 and 4.1.4), we get similar conclusion as for CST AS. As it was expected, the near-field and far-field results in the front of the PEC box are similar to the benchmark solution, but the sides and back values, where considering the not illuminated faces and the diffraction calculation are essential for an accurate result, are not good as they are quite higher than the benchmark results. FEKO LE-PO has similar simulation time to EMPIRE and CST AS. Furthermore, it is supposed to be more efficient compared to EMPIRE and CST TS when the complexity of the EM problem increases. Due to the poor results and the fact that PO/LE-PO does not consider the not-illuminated faces, this method is not considered in phase 2.
The next hybrid scheme investigated in FEKO is FEKO RL-GO. In order to get decent results, the size of the cavity, where the antenna is placed, had to be increased with respect to previous simulation methods. The cavity size used with other methods causes a very long simulation and bad accuracy with FEKO RL-GO. Also in FEKO, the Huygens box source will be automatically transformed to spherical wave modes. If the distance between the Huygens box source and the cavity is too small, the software will truncate the higher order modes. Therefore, the cavity size used with FEKO RL-GO is around three times larger than the original. Even with the larger cavity, the FEKO RL-GO results are quite poor, both in the front, sides and back of the PEC box. Moreover, FEKO RL-GO is slower than the other hybrid methods, EMPIRE and FEKO MLFMM, and only faster than CST TS, even though FEKO RL-GO is run on GPU. Therefore, this method is not considered in phase 2.
CHAPTER 4. RESULTS
In phase 1, we found that the EMF in the back and sides of the PEC box model was very low due to the large size of the PEC box. We also observed that the hybrid schemes and MLFMM do not give enough accurate results in the back, but they do give good results in the front and part of the sides. Since the relatively high EMF exposure levels that determine the compliance boundary are expected to be found in the front of the antenna or slightly in the sides, depending on the beam, in phase 2, we apply the full-wave solvers (CST TS, EMPIRE and FEKO MLFMM) and the best performing hybrid scheme, CST AS, to investigate the EMF exposure in close proximity of the RBS product model and to investigate the applicability of different methods.
4.2
Phase 2: RBS Product Model
In the previous phase, the following methods were selected to be tested and compared in phase 2: CST TS and EMPIRE (as the benchmark solution), FEKO MLFMM and CST AS. In phase 2, the selected methods are implemented for determining the EMF exposure compliance distance in a realistic model, and the results obtained with these simulation methods are compared and analyzed. Among the selected simulation methods, CST TS could not perform the simulation for phase 2 due to the increase of the RAM requirements originated from the larger size of the problem. However, EMPIRE, which gives very similar results to CST TS in phase 1, is capable of this simulation. Therefore, EMPIRE is used as the benchmark solution in phase 2.
We already know that the evaluated hybrid schemes do not give accurate results in the back and sides of the RBS structure, but they give good results in the front and part of the sides where the diffraction effects are not very important. In phase 2, the aim of the comparisons is to find out if the hybrid schemes are capable of evaluating EMF exposure in close proximity of the RBS product model.
In the first step, we compare the far-field results from three different simulation methods for the beams steered in the azimuthal plane. These results are presented in Figure 4.2.1. It can be noticed that the far-field results for three methods are very similar for the ϕ range from−90° to 90°, but considerably different in the rest of the range, as suggested in phase 1. In Figures 4.2.2 and 4.2.3, the power density results for different beams from three solvers are presented. The figures are plotted in contour form, in which 14.8 dBW/m2 is equal to 55fG−0.177W/m2 (fG = 28 for this model), and 10 dBW/m2 is equal to 10 W/m2. Remind that such power density distribution
CHAPTER 4. RESULTS
Table 4.2.1: U (dB) values for the different beams. (EMPIRE near field results are reference.)
U (0° beam) U (10° beam) U (20° beam)
CST AS 2.019 1.577 1.504
FEKO MLFMM 0.82 2.685 2.918
U (30° beam) U (40° beam) U (60° beam)
CST AS 1.489 1.351 1.058
FEKO MLFMM 3.08 3.09 3.12
Table 4.2.2: Simulation time and RAM requirement for the RBS product model simulation in EMPIRE, FEKO MLFMM and CST AS
EMPIRE FEKO MLFMM CST AS (run on CPU) Average simulation time 5h 15min 25min 6h 40min
Required RAM 18GB 40GB 1.15GB
corresponds to|Re (E × H∗)| without considering spatial averaging. Table 4.2.1 shows the value of U for CST AS and FEKO MLFMM using EMPIRE near field results as the benchmark solution. It can be seen that the power density distribution are similar where the values are high for the three solvers. Three solvers present good agreement for locating the EMF reference levels, however, as in phase 1, they do not agree in the back and sides of the model.
In Table 4.2.2, the average simulation time of the different beam simulations and the RAM requirements, which usually are the bottleneck for some of the investigated methods, are shown. FEKO MLFMM proves to be the fastest method with a large difference with the others but not in the exact same conditions, since it could only handle the RBS simplified model. Moreover, as it was expected, the required RAM is quite high, and it might be a problem if a larger near-field monitor is requested or a finer mesh is needed. On the other hand, CST AS is very efficient in terms of required RAM but the simulation time is even higher than EMPIRE’s. As it was mentioned, CST AS could make use of parallelization on GPU, what would decrease the simulation time considerably. Finally, EMPIRE presents quite decent simulation time and RAM requirements. However, these are supposed to increase exponentially if a larger near-field monitor is requested. This is due to the need of a radiation boundary to enclose the simulation domain in the differential solvers like FDTD. If the near-field monitor size is increased, the volume of the simulation domain will increase, too, which eventually needs considerably amount of RAM and time.
CHAPTER 4. RESULTS
monitor so as to find what method holds better when the problem size increases. The size of the requested near-field plane is 1 m in the y-direction and 1.32 m in the x-direction (i.e., 1 m in front of the antenna array). The required time in FEKO MLFMM barely increases compared to previous field monitor size. However, the required RAM increases considerably. On the other hand, the required time in the EMPIRE simulation increases dramatically, which leads to the failure of the simulation. CST AS manages to finish the simulation, and the required RAM remains very low around 2 GigaByte (GB). However, the simulation time is greatly increased.
CHAPTER 4. RESULTS
Figure 4.2.1: Far field results of the product model from CST AS, EMPIRE and FEKO MLFMM
CHAPTER 4. RESULTS
Figure 4.2.2: Near field results of 0°, 10°, and 20° beams from EMPIRE, CST AS and FEKO MLFMM.
CHAPTER 4. RESULTS
Figure 4.2.3: Near field results of 30°, 40°, and 60° beams from EMPIRE, CST AS and FEKO MLFMM
Chapter 5
Conclusion and Future Work
5.1
Conclusion
When applied to the power density evaluation in close proximity of mmWave RBS, the hybridization of full-wave methods and high frequency methods showed promising results in terms of RAM requirements and simulation time. Although the accuracy in the shadow region of both phase 1 and phase 2 models is comprised, the results obtained using CST AS, comparing with the full-wave simulation results using FEKO MLFMM solver and EMPIRE FDTD solver, may still be considered acceptable in general. The reduced accuracy of the hybrid methods can be attributed to a deficient calculation of the diffracted fields in the wedges, and this diffraction problem could be more severe when the source is close to surfaces where the high frequency solver is applied.
The hybridization of SBR and FIT, such as that implemented in CST AS, is capable of evaluating the EMF exposure in the front of the antenna with good performance, although the accuracy in the shadow region is reduced. In phase 1, its simulation speed is better than most of the full-wave methods, and it showed very low RAM requirements. In phase 2, its simulation time was not as efficient as expected. However, this should be further investigated since we only use CPU for this solver due to the limitation of hardware, and the use of GPU could greatly improve its performance.
On the other hand, the hybridization of MoM/MLFMM and PO/LE-PO is another good candidate when the region of interest for the evaluation of the EMF exposure is the
CHAPTER 5. CONCLUSION AND FUTURE WORK
front of the model. This hybrid method in FEKO using MLFMM and LE-PO showed good performance in terms of simulation speed and accuracy in phase 1. However, since it only considers the illuminated surfaces, it is not a suitable if the evaluation region also includes those behind the back plane of the antennas.
The hybridization of SBR and the Huygens box expanded to the spherical wave modes seems to be a less efficient method when the Huygens box is close to the SBR region. It gives poor results in the far-field and near-field calculations, and also shows slow simulation speed for the problem of interest. Also, in phase 1, the model required some additional changes in order to be solved properly.
With regard to the full-wave methods, FDTD (for example that implemented in EMPIRE showing a fast simulation speed) and FIT (for example that implemented in CST) show very good agreement. MLFMM (for example that implemented in FEKO) proves to be a fast method, however, it could not deal with very sophisticated details of the model in phase 2, and its RAM requirements are very high.
5.2
Future Work
In order to improve the work done in this project, the selected methods were not run on the same hardware conditions due to the realistic limitations. Therefore, the performance comparison in simulation time should be considered as a constructive insight of the use of the hybrid methods.
The near field assessment for the EMF exposure purposes are based on the module of Poynting vector, while for more thorough EMF exposure assessment above 6 GHz, a more detailed study on the uncertainty of the peak spatial-average incident power density shall be carried out.
References
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[2] Health Physics. ”Guidelines for limiting exposure to electromagnetic fields (100 KHz to 300 GHz)”. International Commission on Non-Ionizing Radiation Protection (ICNIRP), 2020.
[3] David B. Davison. ”Computational electromagnetics for RF and microwave engineering”. 2005.
[4] Kane Yee. ”Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media”. 1966.
[5] T. Weiland. ”A discretization method for the solution ofMaxwell’s equations for six-component fields”. 1977.
[6] R. F. Harrington. ”Field Computation by Moment of Method”. 1968, 1993. [7] P. Havé E. Darve. ”A fast multipole method for Maxwell equations stable at all
frequencies”. 2004.
[8] Lee SW Ling H, Chou RC. ”Shooting and bouncing rays: calculating the RCS of an arbitrarily shaped cavity”. 1989.
[9] Macdonald HM. ”The effect produced by an obstacle on a train of electric waves”. 1913.
[10] Keller JB. ”Geometrical theory of diffraction”. 1962. [11] Ufimtsev PY. ”Backscatter”. 2005.
REFERENCES
[12] Lu CC Chew WC. ”The use of Huygens equivalence principle for solving the volume integral equation of scattering”. 1993.
[13] “ANSYS HFSS: High Frequency Electromagnetic Field Simulation Software”. [14] “CST Studio Suite 3D EM simulation and analisys software”.
[15] “Electromagnetic Simulation Software | Altair Feko”.
[16] “EMPIRE XPU: High performance 3D time domain EM modelling tool”.
[17] Determining the peak spatial-average specific absorption rate (sar) in the human body from wireless communications devices, 30 mhz to 6 ghz – part 1: General requirements for using the finite-difference time-domain (fdtd) method for sar calculations. October 2017.
Appendix
The electric field results for the three simulation methods used in phase 2 (RBS product model) are presented in Figures 5.0.1 and 5.0.2 while the magnetic field results are presented in Figures 5.0.3 and 5.0.4.
REFERENCES
Figure 5.0.1: Electric field results of 0°, 10°, and 20° beams from EMPIRE, CST AS and FEKO MLFMM.
REFERENCES
Figure 5.0.2: Electric field results of 30°, 40°, and 60° beams from EMPIRE, CST AS and FEKO MLFMM.
REFERENCES
Figure 5.0.3: Magnetic field results of 0°, 10°, and 20° beams from EMPIRE, CST AS and FEKO MLFMM
REFERENCES
Figure 5.0.4: Magnetic field results of 30°, 40°, and 60° beams from EMPIRE, CST AS and FEKO MLFMM
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