Radio Frequency Exposure From 5G Small Cells Utilizing

UPTEC E 20016

Examensarbete 30 hpJuni 2020

Radio Frequency Exposure From 5G Small Cells Utilizing Massive MIMO

Mattias Dahlstedt

Popularvetenskaplig sammanfattningBehovet for snabb dataoverforing blir bara storre och storre. I dagens lageanvands mobila natverk som 3G och 4G (3:e och 4:e generationen) for att forsokauppfylla dessa behov. Inom en snart framtid raknas det med att datatrafikenar sa stor att dessa system inte ar goda nog. Darfor planeras ett nytt systemkallat 5G (5:e generationen) att implementeras. I och med detta kommer manganya antenner installeras som anvander sig av hogre frekvenser och som tackermindre befolkningsytor. Dessa sa kallade massive MIMO antenner kommer varauppbyggda av manga sma antenn-element. De arbetar tillsammans for att skapaen fokuserad elektromagnetisk strale av energi som sen en mobiltelefon kommeratt ta emot och lasa som mottagen data.

Samtidigt finns det krav pa hur hoga effekter en antenn far skicka ut sastralningen inte blir skadlig for allmanheten. En antenn maste placeras sa attallmanhenten inte har chans att befinna sig nara nog for att stralningsdosenska bli for hog. Riktlinjerna for accepterad stralningsdos ar noga utvarderadeefter hur den elektromagnetiska stralningen varmer upp kroppsvavnad. Lokaluppvarmning av kroppsvavnad ar det enda som ar vetenskapligt bevisat varaskadligt for en manniska och riktlinjerna ar utifran detta skapade med storasakerhetsmarginaler. For att kunna placera ut antenner pa befolkningsrikaplatser maste man utvardera hur den elektromagnetiska stralningen utbredersig nara en antenn.

I detta projekt utvarderas hur mycket effekt en massive MIMO antenn sanderut pa tva olika satt. Forst antas all effekt skickas ut konstant i en riktningvinkelrat mot antennens yta. Den totala mottagna effekten kan da ses som ettvarsta tankbara fall. I verkligheten kommer antennen inte skicka ut sin stralningi en riktning konstant. Istallet kommer antennens stralning riktas at mangaolika anvandare i olika positioner runt antennen. Antennen kommer aven underdelar av tiden anvandas till att ta emot signaler fran mobiltelefonen som harkontakt med antennen, aven kallad anvandaren. Dessutom kommer antennensta sysslolos stora delar av tiden da det inte finns tillrackligt manga anvandare.En statistisk analys gjordes dar dessa faktorer anvandes. Denna utrakning gaven bild av hur mycket den mottagna effekten kan forvantas minska i jamforelsemed det varsta tankbara fallet nar all effekt skickas rakt fram. Slutsaten blevatt den forvantade mottagna effekten fran antennen kommer minska atminstonemed en faktor 5 i jamforelse med den maximala effekten.

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Abstract

The radio frequency (RF) electromagnetic field (EMF) exposure of a 5G small cell radiobase station (RBS) using massive MIMO antenna is assessed. The compliance distance for auniform antenna excitation is determined for a 4x4- and an 8x8 planar array antenna at fourdifferent carrier frequencies, 10, 15, 28 and 60 GHz. Three different exposure standards areused to find the compliance distance, the ICNIRP-, the FCC- and a draft IEEE standard.Simulations using the method of moments (MoM) was used to analyze the antennas and cal-culate the power density. The compliance distance converges to Fries far field formula in thefar field region, where said formula is valid. Each standard use different averaging areas andthe convergence is slower for a larger averaging area. This can be explained by the act ofaveraging working as a low pass filter. A lower frequency also leads to a slower convergence,as the far field is located further away.

A statistical model is developed to assess the time-averaged realistic maximum power level,based on a 8x8 planar array antenna using a carrier frequency of 28 GHz. Parameters such asTDD, user position and utilization are considered and the model is valid in both the near fieldand the far field regions. The user positions are determined to obtain a realistic conservativeRF EMF exposure with a confidence level of 95%. The antenna can transmit the signal in adefined set of 47 different beam directions spanning -60 to 60 degrees in azimuth and -15 to15 degrees in elevation. The set of 47 beams are simulated using the method of moments tocalculate the electromagnetic fields in the vicinity of the RBS antenna. For the user distribu-tions investigated and at a distance of 20 cm, the power reduction factor is below 0.22. Asthe distance becomes larger the power reduction factor converges toward around 0.17 usinga weighted user distribution and toward 0.10 using a uniform user distribution. This impliesthat the compliance distance can be reduced significantly compared with the results using thetheoretical maximum power.

A four panel model is created with the same input parameters as in the one panel case. Themodel is based on a small cell radio base station product produced by Ericsson. A statisticalmodel is created to assess the RF exposure which are made to converge towards the one panelcase far away from the antenna. The users are distributed uniformly and separately over the4 panels with priority given to the panels with highest exposure. The power reduction factoris one forth of the single panel case close to the antenna and converges toward the single panelresults. In general, a four panel product will also have a significant reduction in compliancedistance compared to the results obtained by using constant maximum power.

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Contents1 Acknowledgement 3

2 Introduction 52.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Literature study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Project setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Theory 73.1 Electromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Antenna theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Computational electromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 RF exposure limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Simulations of broadside beam exposure from planar array antennas 124.1 Creating a MoM simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2 Exposure and compliance distance computations . . . . . . . . . . . . . . . . . . . 134.3 Power density and compliance distance results . . . . . . . . . . . . . . . . . . . . . 134.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5 Statistical analysis of the realistic time averaged power 225.1 Single panel model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2 The normalized exposure and the expected PRF for the one panel model . . . . . . 265.3 Creating the four panel model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.4 The normalized exposure and the expected PRF for the four panel model . . . . . 315.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

6 Conclusion 37

Bibliography 42

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1 Acknowledgement

I would like to thank Uppsala University for four and a half great years to prepare me for thisproject.

I would like to thank the department of signals and systems and all the people working therefor inspiring me to pursue this field. Especially, I want to thank Mikael Sternad for being mysubject reviewer during this project.

I would like to thank Björn Thors for helping me with the mathematical derivations, simula-tions and in general having great insight about the subject.

I would like to thank Christer Törnevik for great input and support. Also a big thank you forbeing a calming influence at stressful times.

I would like to thank all colleagues in the research group at Ericsson for using up their time,space and for using the code constructed by you. Much of the project was a continuation of theirwork together with Björn and Christer and would not be possible without them.

Finally, I would like to thank Ericsson for the opportunity to work on this project during theselast 5 months.

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Abbreviations

EIRP - Effective Isotropic Radiated Power

EMF - Electromagnetic Field

ER - Exposure Ratio

FCC - Federal Communications Commission

HPBW - Half-Power Beam-Width

ICNIRP - International Commission on Non-Ionizing Radiation Protection

IEEE - Institute of Electrical and Electronic Engineers

IoT - Internet of Things

LTE - Long Term Evolution

MIMO - Multiple Input Multiple Output

MoM - Method of Moments

PRF - Power Reduction Factor

RBS - Radio Base Station

RF - Radio Frequency

SAR - Specific Absorption Rate

TDD - Time Division Duplexing

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2 Introduction

2.1 Background

Historically the wireless data traffic from mobile-phones has increased. The demand for contin-uous wireless video streaming and other applications requiring high data transfer speed will onlyincrease. When watching the trends, the data traffic in mobile networks grew by 65% from 2016 to2017 worldwide, while the number of mobile phone users grew as well [1]. As this trend is expectedto continue and with the implementation of Internet of Things (IoT), the need for a high capacitysystem is required, which the current systems of LTE (4G) and WCDMA (3G) alone does not fulfill.

One way to increase the capacity substantially is to use massive MIMO antennas with up tohundreds of elements situated in a NxM matrix formation. By exciting the elements in differentphases, a narrow beam is created, by which the electromagnetic field is transmitted towards theusers. The capacity can be increased from using spacial multiplexing and higher bandwidth due toa large chunk of spectra being unused at higher frequencies. The multiuser antenna configurationcan serve the users within the same time frame while using the same frequency. Time divisionduplexing (TDD) is used to separate the uplink and the downlink signals in time, which unlikewhen using FDD is scalable with unlimited number of antennas independent of the number ofusers [2]. Because the antenna elements are about size of half a wavelength, the antennas becomessmaller as the frequency is increased, which facilitates antenna installation.

The directivity of a Massive MIMO (Multiple Input Multiple Output) antenna also creates lessinterference for other users. The system can then rely on spatial multiplexing by sending a signalto a specific user without disturbing nearby users. With a more isotropic antenna, the energyis spread over a wider angular range which results in interference. Using an antenna with highdirectivity, the interference becomes less of a problem.

A massive MIMO antenna is more energy efficient. Most of the energy is directed to the user,with less leakage in other directions compared to an antenna with less directivity [3]. Therefor lesstransmitted power is needed to create a signal that is readable by the user.

The requirement of lower latency will be necessary when implementing the 5G network. Cur-rently, most applications do not need a very low latency. As applications such as two-way gamingand virtual reality will be created, a much lower latency is needed [4]. The biggest factor con-tributing to latency is fading. A fading-dip will make the terminal wait until the received signalis clearer. The fading in a massive MIMO system will not limit the latency as the fading dips willlargely be avoided with beam-forming and the law of large numbers [3].

Historically the sizes of the cells have decreased, from the beginning of wireless communicationssystems having cells with a area of 100s of km2 to currently where some cells can be less than 1km2 in urban areas. By using small cells in high populated areas, the information transfer capacitywill be increased. In 5G systems, picocells with a very small cellsize will be implemented. With alow power output of up to 30 dBm and a range of 100 m, will be a cost effective way of increasingthe capacity. A small cell has several benefits such as reuse of valuable spectra and the low usercount at each base station [5], [6].

The frequencies used today spans from 100s of MHz to 3 GHz. Part of the 5G network is theuse of higher frequencies up to the mmwave band [7]. For frequencies smaller than 10 GHz, thefundamental exposure limit (basic restriction) is given in terms of specific absorption rate (SAR),specified by the International Commission on Non-Ionizing Radiation Protection which is mea-sured in W/kg. The ICNIRP exposure limits are used in most countries worldwide. Above 10GHz, the basic restrictions change to power density in free space measured in W/m2. When thefrequencies are this high, almost all energy is absorbed in the skin with very little penetrationto deeper tissue layers. The guidelines set by ICNIRP are specified to protect with wide safetymargins, from established adverse health effects related to whole-body heat stress and excessivelocalized tissue heating as these are the only effects scientifically proved to have health effects. [8].The RF exposure shall according to the guidelines be averaged in time over several minutes.

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2.2 Literature study

Exposure to RF EMF radiation has long been a subject of study. In [9], the power absorbed interms of SAR and the induced electric field are assessed. The human body is modeled as a cylin-drical shape and a numerical method was used to determine the absorbed power and the SAR. In[8], a literature review of the potential biological effects of non-ionizing radiation in the frequencyband from 30-300 GHz is presented. The focus lies on what is needed to ensure safety from theupcoming 5G networks that is about to be implemented.

Several studies on the whole-body SAR and peak spatial SAR for lower frequencies in the rangeof 100s of MHz to a few GHz has been published. An example of this is [10], where an heuristicestimation is created by using different observed properties of antennas at different distances. In[11], statistically valid models of three humans are used to estimate both whole body and peakspatial SAR. In [12], measurements of SAR and the EMF are used to find the compliance distanceclose to the antenna in a 900 MHz base station. In [13], the compliance distance is assessed forfrequencies between 800 MHz to 2.6 GHz using numerical simulations to compute the electromag-netic fields. These studies are made for antennas in a lower frequency band.

Some articles have considered RF EMF exposure for frequencies above 10 GHz. In [14], a studyon EMF exposure from a frequency band from 10 to 60 GHz, was presented. The article focuseson low-powered base station antennas and array antennas in mobile devices. In [15], a statisticalmodel of the power reduction factor is created for a one-panel massive MIMO antenna. This isdone using approximations and assumptions of the far field exposure, TDD and the number ofusers within a 6 minute averaging time. In [16] a statistical model is created where the compliancedistance is assessed. The model is based on a specific system with assumptions made on usersdistributions based on specific sites. The compliance distance is found for a 8x8-antenna with acarrier frequency of 2 GHz, where the power output is high enough to reach the far field.

In this project the RF EMF exposure is assessed for a small cell 5G RBS employing massiveMIMO. The model in [15] is generalized to work also in the near field. For lower power levels, anear field exposure assessment is necessary as far-field conditions do not necessarily apply. Histori-cally, the compliance distance has been assessed by computing the maximum power density outputand comparing that to the relevant exposure limits. In the case of a massive MIMO system, this isa very conservative approach as the directivity of the antenna and the spatial multiplexing makesit improbable that the radiated power is constantly transmitted in one specific direction whenaveraged over a period of several minutes [16]. A more realistic estimation of the exposure usinga statistical model taking factors such as TDD, utilization and time-averaging into account. Theinternational standard IEC 62232:2017 [17], specifies that an actual maximum power can be usedby finding the 95th percentile case of all possible exposure scenarios.

2.3 Project setup

This project can be divided into two parts. The first part in section 4, presents simulations of a4x4 and a 8x8 antenna using four different frequencies. The beam is transmitting in the broadsidedirection. Using standards from ICNIRP, FCC and a recent draft standard proposed by IEEE, thecompliance distance was calculated for an output power that spans from 2 mW to 1000 mW. Thismodel assumed constant maximum power, which is a very conservative estimation, disregardingfactors such as TDD, utilization and time-averaging. This was done, partly as a learning experi-ence and also get some results to compare with theoretical estimations. There is also an analysisof how the use of different averaging areas effects the exposure.

In the second part, a statistical model is created based on the model in [15], including param-eters such as TDD, utilization and time-averaging. The model was based on existing productsworking in the 28 GHz frequency band. The objective was to find how the power reduction factor(PRF) changes with distance. The model creates a view of how the exposure from a single-paneland four-panel antenna is reduced, when taken into account parameters such as TDD, utilizationand time-averaging.

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3 Theory

3.1 Electromagnetism

Maxwell’s equations are used to describe and solve problems involving electromagnetism. Theyare central in our understanding of electromagnetic waves, as the waves were first discovered inthe equations and was later proved to exist by Heinrich Hertz. Maxwell’s equation can be usedto find the electric or magnetic fields induced by charges and currents. They also describe howthe electric and magnetic fields are linked to each other, where changes in one of the fields willcreate the other and vice versa. This fact can be used to derive the electromagnetic wave-equation.Maxwell’s equations are give by:

∇ · ~E =ρ

ε0(1)

∇ · ~B = 0 (2)

∇× ~E = −∂~B

∂t(3)

∇× ~B = µ0~J + µ0ε0

∂ ~E

∂t(4)

where ~E is the electric field, ~B is the magnetic field, ρ is the charge density and ~J is the currentdensity. The constants µ0 = 4π ∗ 10−7 is the vacuum permeability, ε0 = 8.85 ∗ 10−12 is the vacuumpermittivity. From this, η =

√µ0

ε0is defined as the intrinsic impedance. Maxwell’s equations

are hard to solve for many problems, and are only in very idealized cases possible to solve inclosed form. Instead, simplified models are often used to create a reasonable description of theelectromagnetic fields [18]. Formulas for the electric and magnetic fields from a infinitesimallysmall dipole antenna, with the current oriented in the z-direction, can be found using Maxwell’sequations by assuming the fields are calculated in the far field [19].

~E(r, φ, θ) = jηkI0l

8πre−jkr sin θθ (5)

~H(r, φ, θ) = jkI0l

8πre−jkr sin θφ (6)

where k = ω/c, the electric field is radiating in θ while the magnetic field is radiating in φ. Bothfields are complex, which is denoted by the imaginary number j, k is the wavenumber, I0 is thepeak current and l is the length of the antenna. This is a relatively simple formula, but is reallyonly useful as an approximation of the fields. The equations only applies in the far-field region fora single frequency component of the radiation field where absorptions or reflections are neglected.In this project, numerical methods are used to calculate electric and magnetic fields in the nearfield region.

The power flux of an electromagnetic field can be found with the Poynting vector, which is mea-sured in unit W/m2:

~S = ~E × ~H (7)

As the electric and magnetic field can be represented as complex vectors, the Poynting vector willbe both active and reactive. The active power, the real part of the Poynting vector, is the powerof interest in this project. The time averaged active power density can be calculated using

~S = Re ~E × ~H∗

2

(8)

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The wave impedance is defined as

Z =E

H⇐⇒ H =

E

Z(9)

In the far field, by inserting equations (5) and (6) in equation (9), the impedance can be approxi-mated with a constant:

Z = η ≈ 377 Ω (10)

From this an approximation of the time averaged power density can be calculated without using themagnetic field which can be hard to measure. The power density can be calculated with S = EH.Inserting (9) into this, using the wave impedance at the far field:

S =E2

rms

η=E2

peak

2η(11)

3.2 Antenna theory

An antenna is used to transmit and receive electromagnetic waves for wireless communication.Anything that can induce a current can be used as an antenna. As most metals are conductive,an antenna is usually built of these materials. One of the most common antennas is the dipoleantenna where a wire is connected to a voltage source in the middle, which induces a oscillatingcurrent. The current will create electromagnetic waves radiating from the antenna. When thelength of the dipole is half a wavelength, it is called a half-wave dipole. In this project, half-wavedipoles are used in a massive MIMO array antenna configuration.

Antennas have some important properties that have to be defined. As an antenna generally doesnot radiate the power uniformly in every direction, a term for directivity is defined. The directivityof an antenna is written as

D =U(θ, φ)

Uisotropic(12)

where U is the radiation intensity. Often the maximum value is used as the general directivity ofthe antenna. Similarly the gain of an antenna is the directivity multiplied with electrical efficiency.The maximum gain G of an array antenna can be approximated by

G =4πA

λ2(13)

where the parameter A is the array area and λ is the wavelength. In many cases, the area isdependent on the wavelength with antenna element spacing being a function of λ. With an MxM-antenna and a spacing of half a wavelength, the area becomes A = M2λ2/4. The wavelength cancelsand this makes the gain independent from the frequency and only dependent on the number ofelements used. The formula can also be written in logarithmic form:

GdBi = 10 log10(4πA

λ2) (14)

The half power beam width (HPBW) is defined as the angular range found between where thegain is half of the maximum gain of a given beam. Usually, the HPBW angle is given horizontallyand vertically, ΘH and ΘV and can be approximated by [15]

ΘV/H =0.866λ

WV/H(15)

where WV/H is the dimension of the antenna vertically or horizontally. The beam solid angle isthe solid angle where G(θ, φ) ≥ Gmax/2. It can be approximated using [15]

Ωi,j =ΘVΘH

sin θ0

√sin2 φ0 +

Θ2H

Θ2V

cos2 φ0

√sin2 φ0 +

Θ2V

Θ2H

cos2 φ0

(16)

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where ΘV and ΘH are the HPBW obtained from equation (15), φ0 and θ0 are the correspondingspherical coordinates of the beam angle.

The array factor is a function which when multiplied with the antenna element pattern may beused to approximate the pattern of an array antenna. This can be used to find how a large arrayof antenna elements can be used to direct a beam in a specific direction

Darray(θ, φ) = Delement(θ, φ)AF(θ, φ) (17)

In free space conditions, the power density decays with the inverse distance squared and the meanpower density can be calculated

S =PTG

4πr2(18)

where PT is the transmitted power, G is the gain and r is the distance from the antenna.

There are three field regions defined around an antenna. The reactive near field region lies nearestto the antenna and is commonly defined to extend to region

R < 0.62

√D3

λ(19)

The radiating near field region, also called the Fresnel region, is the region located between thenear field region and the far field region. The fields are not predominantly reactive fields and theangular field distribution depends on the distance from the antenna

0.62

√D3

λ< R <

2D2

λ(20)

The far field, also called the Fraunhofer region, is where the radiation pattern is the same inde-pendent of distance. As long as R >> D and R >> λ, the Fraunhofer region is defined as

R >2D2

λ(21)

where D is the dimension of the antenna. For a 8x8 planar array antenna with a distance ofλ/2 between elements the antenna dimension D = 8λ/2 = 4λ, which is equal to a side-length ofthe antenna. The limit where the far-field begins is also known as the Fraunhofer distance. Thefar-field is important as many formulas used are only valid there.

An approximate formula for the progressive phase shift is needed to create the different beamconfigurations, and the one used in the statistical model is given by (see Appendix 1)

β = −k0(dyny sinφ0 sin θ0 + dznz cos θ0) (22)

where k0, dy and dz are the wavenumber and the distance between the elements in y- and z-direction. The integers ny and nz are the indices corresponding to the antenna element position.The angles θ0 and φ0 correspond to the desired beam direction.

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3.3 Computational electromagnetism

When studying the behavior of an antenna, you usually go back to analyzing Maxwell’s field equa-tions. These equations are in general hard to solve analytically. Instead, numerical methods areoften used to find the electric and magnetic fields radiating from an antenna. In this project,a software called FEKO created by Altair was used. FEKO primarily makes use of the methodof moments (MoM) to compute the electric- and the magnetic fields radiating from the antennamodel created in the software.

FEKO is an analytic tool which analyzes the electromagnetic fields from any type of antenna.Although the method of moments is used in this project, FEKO can use other numerical methodssuch as the finite element method, to compute the electromagnetic fields. The advantage of MoM isthat only the antenna has to be discretized [20]. However, the points for where the electromagneticfields are calculated, has to be defined.

There are two ways to create a model in FEKO. A model can be drawn, using CADFEKO. Itcan also be created in EDITFEKO, where the antenna is created by coding. A model created bythe team at Ericsson Research in EDITFEKO was used and expanded upon in this project.

3.4 RF exposure limits

ICNIRP is an international independent organization, which main goal is to provide scientificadvice and guidance on the health and environmental effects of non-ionizing radiation. The orga-nization is formally recognized by the World Health Organization (WHO) and the limits definedby ICNIRP are used in a large part of the world, including the European Union. Depending onfrequency, the limits are different. Between 10 GHz and 300 GHz, the ICNIRP limits are definedusing the power density averaged over an area of 20 cm2. The maximum exposure is set to 10W/m2 averaged over 6 minutes. To include peak power, the standard also includes a maximumexposure of 200 W/m2 averaged over a smaller area of 1 cm2 [21].

In the USA, the standard is specified by the governmental agency FCC, which is responsibleof regulating wireless communication. The FCC standard is more conservative than the ICNIRPguidelines for higher frequencies. Above 1500 MHz, the power density limit is 10 W/m2 averagedover a 1 cm2 area. Although having the same power density limit, the averaging area is smallerthan the one specified by ICNIRP [22].

IEEE is in the process of revising its standard C.95.1 [23]. The averaging time is 6 minutes andit is defined between 6 GHz and 300 GHz. However, the averaging area is set to be 4 cm2 whichis smaller than the 20 cm2 specified by ICNIRP. The new power density limit is also frequencydependent. The formula for the power density limit is written as

Slimit = 55f−0.1770 (23)

where f0 is measured in GHz. It is set up so that the limit is very close to 40 W/m2 at f0 = 6

GHz and 20 W/m2 at f0 = 300 GHz. The three different power density limits can be viewed inTable 1.

Table 1: The power density limits for each averaging area as defined by ICNIRP, IEEE and FCC.

ICNIRP IEEE FCC1 cm2 200 W/m2 - 10 W/m2

4 cm2 - 55f−0.1770 W/m2 -

20 cm2 10 W/m2 - -

The RF EMF exposure is often presented in terms of the exposure ratio, which is the relevantexposure level divided by the corresponding limit. For power density, the exposure ratio is givenby

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ER(r) = max

˜A~S(r) · ndASlimit(f)

(24)

where the power density vector, ~S(r), can be calculated with equations (8) or (11). The vectorn is the normal vector to the averaging area and the function Slimit(f) is the used power densitylimit. The compliance distance is easily found as the distance, rCD, for which the exposure ratio(ER) is one.

A theoretical value for the expected compliance distance in the far field can be found form thefar-field formula (18). By setting the power density as Slimit and solving for r, the compliancedistance can be computed as

rCD =

√PTG

4πSlimit(25)

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4 Simulations of broadside beam exposure from planar arrayantennas

4.1 Creating a MoM simulation model

A very conservative study of the front compliance distance was made, where parameters suchas TDD, utilization and time-averaging were disregarded. An existing FEKO model was usedand modified in EDITFEKO. In total, eight different models were created with four different fre-quencies and two different antenna dimensions. The antennas were placed with their back-planecentered in the yz-plane. The elements were created as half-wave dipoles using a thin wire witha polarization angle of 45 degrees with respect to the z-axis. A voltage source was placed at themiddle of each dipole element. A uniform excitation in amplitude and phase was used to createa beam directed straight forward. The distance between the antennas elements were spaced withhalf a wave-length. The distance between the ground and the antenna elements was set to λ/4.Each model was meshed with small triangles with edge-length of λ/8 and a wire segment lengthof λ/10. The electric and magnetic fields were calculated at a uniform grid, creating a volume inthe shape of a box. The dimensions of the box was created so the maximum power density at adistance can be found using any of the three averaging areas defined in the different standards.The biggest side length on the averaging area was around 4.5 cm. As the averaging areas wereplaced parallel to the antenna, the length of the computation volume in y- and z-direction weredefined to be 16 cm wide, centered around the origin. The length of the volume in the x-directionwas created so the compliance distance can be found for the maximum output power of 1 W.Using equation (25), and the smallest limit slimit = 10 W/m2, PT = 1 W and the gain calculatedfrom (13) for an 8x8-antenna, the compliance distance was found to be approximately 1.3 m. Thecalculation volume in the x-direction was defined to be from zero to 1.5 m which should contain thecompliance distance for any transmitted power up to 1 W. The total power output from the an-tenna was normalized to 1 W, which allowed re-scaling to any power level in a post-processing step.

Two different antenna models were created, a 4x4- and a 8x8-model. The progressive phase shiftbetween the currents in the different elements were set to zero degrees. This creates a beamwhich has its maximum gain in the broadside beam direction. The carrier frequencies were chosento be 10 GHz, 15 GHz, 28 GHz and 60 GHz to span a possible frequency range for 5G applications.

The simulation models are shown in Fig 1 and 2. The gain was calculated using the tools withinthe built in post-processor POSTFEKO.

Figure 1: The FEKO model of the 4x4-antenna with a 28 GHz carrier frequency to the left. Thecorresponding gain is displayed to the right.

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Figure 2: The FEKO model of the 8x8-antenna with a 28 GHz carrier frequency 28 GHz to theleft. The corresponding gain is displayed to the right.

4.2 Exposure and compliance distance computations

The used transmitted powers were chosen to span from 2 mW to 1000 mW. As the output powerincreases, the compliance distance will increase beyond the Fraunhofer distance. The upper limit1 W should theoretically create a compliance distance a fair bit away from the far field limit. Thelower limit was chosen as the output power of 2 mW. A power output lower than 10.7 mW impliesinherent compliance with the IEEE standard at 60 GHz.

The data from the simulations was read and saved in vectors at each point x,y,z that was de-fined in the model volume. Using (8), the time averaged, active power density was computed ateach point. The power density in the direction of the normal vector of the averaging area wascomputed using the dot product, which in this case was in the direction of the x-axis. The time av-eraged power density was also computed using the wave impedance and the electric field using (11).

The purpose was to find the compliance distance, defined as the smallest distance beyond whichthe power density does not exceeded the limit value. As there are several limit standards used indifferent parts of the world, the average power density has to be calculated using three differentaveraging areas, 1 cm2, 4 cm2 and 20 cm2. Within the 20 cm2 averaging area, the number ofsamples is not necessarily distributed symmetrically around the point chosen because the squareroot 20 cm2 is irrational. To create a better estimation of the power density around each point,the S-matrix was interpolated over each x with a finer mesh. The power density was averaged ateach point with the interpolated S-matrix using the number of samples corresponding to the sizeof the averaging area. The maximum power density at each distance x0 was saved in a vector.The exposure ratio was calculated with dividing by the corresponding power limit, as described in(24).

The exposure ratio was used to find the compliance distance. The distance rDC was calculated byfinding where the exposure ratio was less or equal to 1. The maximum exposure ratio for eachvalue x was interpolated to find a distance where the exposure ratio is very close to 1.

4.3 Power density and compliance distance results

The maximum gain using a 8x8-antenna using equation (14) and the results obtained in FEKOare given in Table 2. The simulated result are close to identical to the theoretical results obtainedfrom (14). The power density was calculated using (8) and (11) as shown in Fig. 3 - 6. Thepower density is displayed in logarithmic scale. Even though (11) is only valid in the far field,

13

Table 2: A table over the gain.

4x4 8x8Gain Formula (14) 17.0 dBi 23.0 dBiFEKO calculations 17.1 dBi 23.1 dBi

it was a good way to check convergence and validate the simulations. The convergence of thesimulation data toward said formula was a good indication that the simulations were reliable. Thelargest difference between the graphs were found in the near field, which was expected as the waveimpedance can not be seen as a constant in that region.

Figure 3: Simulated power density as a function of distance, using a 4x4-antenna. The powerdensity was calculated using the Poynting vector.

Figure 4: Simulated power density as a function of distance, using a 4x4-antenna. The powerdensity was calculated using the electric field and the wave impedance,S = E2

377 .

14

Figure 5: Simulated power density as a function of distance, using a 8x8-antenna. The powerdensity was calculated using the Poynting vector.

Figure 6: Simulated power density as a function of distance, using a 8x8-antenna. The powerdensity was calculated using the electric field and the wave impedance, S = E2

377 .

An assessment of the front compliance distance was conducted for the different standards. Usingthe ICNIRP 20 cm2 averaging area, the data converges toward the far field formula. With themaximum transmitted power of 1 W, the compliance distance is found to be around 0.63 m for a4x4-antenna and 1.26 m for the 8x8-antenna.

15

Figure 7: Compliance distance of the investigated 4x4 array antenna, using the ICNIRP standardwith a 20 cm2 averaging area.


A calculation of the compliance distance, using an averaging area of 1 cm2, was made. The powerdensity limit used was 200 W/m2. This measurement is also part of the ICNIRP standard andis only relevant if the compliance distance is higher at any point than previous case. As seen infigures 9 and 10, the compliance distance is significantly shorter, which makes the data irrelevantin this case.

16



The compliance distance was computed, using the frequency dependent IEEE-limit as shown inFig. 11 and 12. The averaging area used was a square with an averaging area of 4 cm2. Comparedwith the ICNIRP limit, the averaging area is smaller, which obviously will use fewer samples toaverage. With smaller averaging areas, the power density calculated will be close to the peakvalues. As predicted, the compliance distance is found to be zero when the output power is 2 mW.The lowest power of 10 mW gives a distance to be slightly above zero using the 8x8-antenna at 60GHz. When the transmitted power is 1 W, the compliance distance spans from 0.33 m to 0.39 mfor the 4x4-antenna and from 0.64 m to 0.78 m for the 8x8 antenna.

17

Figure 11: Compliance distance of the investigated 4x4 array antenna, using the IEEE standardwith a 4 cm2 averaging area.

Figure 12: Compliance distance of the investigated 8x8 array antenna, using the IEEE standardwith a 4 cm2 averaging area.

The FCC averaging area of 1 cm2 is more conservative as the averaged power density will behavecloser to the peak value as seen in Fig. 6. The compliance distance converges quite fast towardthe far field formula as shown in Fig. 13 and 14.

18

Figure 13: Compliance distance of the investigated 4x4 array antenna, using the FCC standardwith a 1 cm2 averaging area.

Figure 14: Compliance distance of the investigated 8x8 array antenna, using the FCC standardwith a 1 cm2 averaging area.

19

4.4 Discussion

When the averaging area is larger than the antenna, it will for small distances enclose much of thepower transmitted. As the antenna array size is reduced with increasing frequency, the spatiallyaveraged power density increases as shown in Fig. 3 and 5. The antenna size is also dependent onthe number of elements. The side-length of the two antenna models is shown in Table 3.

Table 3: Side length of the different antennas. The side lengths of the three different averagingareas are 1 cm, 2 cm and 4.5 cm.

Frequency 10 GHz 15 GHz 28 GHz 60 GHz4x4 6.0 cm 4.0 cm 2.1 cm 1.0 cm8x8 12.0 cm 8.0 cm 4.3 cm 2.0 cm

The minor difference between the far field formula and the simulation results can be explained bythe gain used in the far field formula. The gain is not constant over the span of the averaging areaand not applicable very close to the antenna. This can be seen when watching the compliancedistance being slightly below the value from the far field equation, using an averaging area of 20cm2.

The act of averaging can be seen as a low-pass filter which will reduce spatial variations of thefield. When using a small area, only a few samples were averaged and the effects of the low-passfilter will not be as prominent. However, when the area is big, the field is averaged over manysamples and the effects can be seen when looking at the power density close to the antenna.

An interesting comparison can be made between the regulations created by FCC and ICNIRPas they have the same power density limit, while they make use of different averaging areas. Asshown in Fig. 15 and 16, in the far field region the difference is very small, but at lower powerlevels, the compliance distance is larger when using a small averaging area. This can be attributedto the effect described above, where the act of averaging works as a low pass filter.

0.05 0.1 0.15 0.2 0.25

Transmitted Power [W]

0

0.1

0.2

0.3

0.4

0.5

0.6

Co

mp

lian

ce

Dis

tan

ce

[m

]

ICNIRP: The averaging area: 20 cm2, S

limit = 10 W/m

2, Gain = 23 dBi, using an 8x8 antenna.

Figure 15: The compliance distance in the near field, using an averaging area of 20 cm2 and apower density limit of 10 W/m2.

20

0.05 0.1 0.15 0.2 0.25


0

0.1

0.2

0.3

0.4

0.5

0.6

Co

mp

lian

ce

Dis

tan

ce

[m

]

FCC: The averaging area: 1 cm2, S

limit = 10 W/m


Figure 16: The compliance distance in the near field, using an averaging area of 1 cm2 and a powerdensity limit of 10 W/m2.

The IEEE standard was used with an averaging areas of 4 cm2. Again, the power density convergestoward the far field formula. When looking at the specific carrier frequency of 60 GHz the powerthreshold of where the compliance distance is always zero can be computed. An averaging area of4 cm2 gives a power threshold of 10.7 mW. As seen in Fig. 17 the compliance distance is zero foran transmitted power lower than this value.

0.05 0.1 0.15 0.2 0.25 0.3


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Co

mp

lian

ce

Dis

tan

ce

[m

]

IEEE: The averaging area: 4 cm2, S

limit = 55f

0

-0.177 W/m


Figure 17: The compliance distance in the near field, using an averaging area of 4 cm2 and a powerdensity limit of 55f−0.177

0 W/m2.

21

5 Statistical analysis of the realistic time averaged power

5.1 Single panel model

Using the theoretical maximum power as in section 4 is very conservative. By including compo-nents like TDD, utilization and time-averaging, a more realistic model can be created. In this part,a statistical model was created which includes these parameters.

An 8x8-antenna model was used, as it reflects the size of a realistic array antenna for 5G RBSproducts employing massive MIMO. The carrier frequency is set to 28 GHz and the averaging areawas chosen to be the area of 20 cm2. This is the area used by the ICNIRP standard which ismostly widely adopted standard world-wide. The simulated 3D-volume was chosen to be larger inthe y- and z-direction, so the model could be reused in later simulations, for the four panel case.The volume in the x-direction was chosen to reach 1 m away from the antenna. The far-field canbe calculated using (21) to be 0.34 m, which was far less than the chosen distance. In figure 8, itcan be seen that the compliance distance using a 28 GHz antenna and the ICNIRP standard, thecompliance distance converges toward the theoretical value of the far field formula (25). As thedistance increases beyond the far-field region limit, the exposure changes very predictably whichmakes simulations far away unnecessary.

yz

x

1cm

4cm

5cm

Figure 18: The blue averaging areas are used to calculate the mean power density over a 20 cm2

surface for different distances and different beam directions.

The antenna has a predefined scan range in azimuth (-60 to 60 degrees) and elevation (-15 to 15degrees). A grid of beams system with 47 different fixed beams covering the scanning area of theantenna was assumed. A schematic view of the directions of the different beams can be seen in Fig.21. A set of 47 different simulations was created, corresponding to these defined beam directions.As seen in equation (22), the input on the phase was in polar coordinates θ and φ. As the outputangles are defined in azimuth and elevation, these need to be converted into polar coordinates.The angle φ is equivalent to the azimuth angle η, when the antenna lies in the yz-plane. However,the angle θ is not the same as the elevation angle ξ. The angle θ is the angle from the z-axis to thebeam direction vector, whereas the elevation angle is the angle from the x-axis to the projection~ζ in the xz-plane as seen in Fig. 19. A derivation of the conversion from φ and θ to azimuth andelevation can be found in the appendix. The equations used for the conversion was

φ = η (26)

cosθ =cos(η) sin(ξ)√

cos2(η) sin2(ξ) + cos2(ξ)(27)

22

x

y

z

Beam direction, ~r

~ζ

~ρ

θ

φ = η

ξ

Figure 19: A picture of the difference between the azimuth and elevation angles to φ and θ. Theangle between the red plane and the xz-plane is the azimuth angle. The angle between the blueplane and the xy-plane is the elevation angle.

When setting up the simulations, equation (22) was used to approximately calculate the excitationphase for the different dipoles.1 The beam angles are given in azimuth and elevation angles. Thecorresponding φ and θ were computed using equations (26) and (27). The gain of the antennawas checked in POSTFEKO. The maximum gain should be directed in the corresponding polarcoordinates. If they were not, the phase was adjusted manually until a beam was created inthe correct direction. An examples of this can be seen in figure 20. Inserting the azimuth andelevation angles in equations (26) and (27), the polar angles was calculated to be φ = −41 andθ = 94.5.

Figure 20: The simulation model of the 8x8-antenna with a beam directed in −41 azimuth and−6 elevation. The maximum gain is displayed to the right.

MATLAB was again used to compute the exposure ratio. The averaging area used was 20 cm2,with its midpoint at (y, z) = (0, 0). A representation of the averaging area above the antenna canbe seen in 18. The point chosen is straight in front of the antenna, as it is realistic to assume thatit will correspond to maximum exposure. The power density over the area is computed with (8)and the exposure ratio is calculated using the same method as in section 4. For each distance, theexposure ratios from each of the 47 beams were calculated. The exposure ratio was then sorted ina list where the beam with the highest exposure was put first and the rest following in a descendingorder. The exposure was then normalized to the maximum exposure, see Table 4.

1The approximation is that effects of mutual coupling is neglected.

23

-60 -40 -20 0 20 40 60

azimuth,

-15

-10

-5

0

5

10

15

ele

va

tio

n,

Schematic view of the set of beams used, ( °, °)

(-51°,-13°) (-36°,-13°) (-24°,-13°) (-12°,-13°) (0°,-13°) (12°,-13°) (24°,-13°) (36°,-13°) (51°,-13°)

(-55°,-6°) (-41°,-6°) (-29°,-6°) (-17°,-6°) (-5°,-6°) (5°,-6°) (17°,-6°) (29°,-6°) (41°,-6°) (55°,-6°)

(-51°,0°) (-36°,0°) (-24°,0°) (-12°,0°) (0°,0°) (12°,0°) (24°,0°) (36°,0°) (51°,0°)

(-55°,6°) (-41°,6°) (-29°,6°) (-17°,6°) (-5°,6°) (5°,6°) (17°,6°) (29°,6°) (41°,6°) (55°,6°)

(-51°,13°) (-36°,13°) (-24°,13°) (-12°,13°) (0°,13°) (12°,13°) (24°,13°) (36°,13°) (51°,13°)

Figure 21: A schematic view of the set of beams used.

Table 4: A sorted list of the normalized exposure ratios from the 8x8 antenna. The highest exposureis first, the second highest second and so on.

ER1(r)ER1(r)ER2(r)ER1(r)

.

.

.ER47(r)ER1(r)

The statistical model created, is based on the model described in [15]. The number of users isdenoted n and there are provided service by the antenna N times during the 6 minute period. Thetotal number of independent users as seen by the antenna is therefor nN. This number has beendistributed over the scanning area of the antenna. The value of N is chosen to be 10 which is arguedfor in [15]. The user distribution W1(ξ, η) is based on two user distribution scenarios described in[15]. The two user distributions, a uniform distribution and a cosine-based distribution which ismore biased toward the broadside beam, are shown in Fig. 22. The uniform distribution of thescanning area is a constant and described by

-15-10

-50

510

15

(degrees)-50

0

50

(degrees)

0

0.5

1

1.5

2

2.5

3

W(

,)

0

0.5

50

1

15

1.5

W(

,)

10

2

(degrees)

0 5

2.5

(degrees)

3

0-5

-10-50-15

Figure 22: A uniform user distribution and a cosine based user distribution weighted toward thebroadside beam.

Wi(ξ, η) =9

π2(28)

24

The cosine-based weighting function can be written as

Wi(ξ, η) =9

πcos2(6ξ)cos(

3

2η) (29)

where η is the azimuth angle and spans from −60 to 60. ξ is the angle in elevation and spansfrom −15 to 15. First, the probability of a user existing at the highest possible exposure area iscalculated by

P1 =Ω1W1(ξ, η)∑47i=1 ΩiWi(ξ, η)

(30)

where Ω1 corresponds to the solid beam angle with the highest exposure and can be calculatedwith equation (16). The probability for each beam is thereafter calculated as

Pi =ΩiWi(ξ, η)∑47j=i ΩjWj(ξ, η)

(31)

The probability of ki users existing at the highest exposure direction can be written as an cumula-tive binomial distribution. The user-coefficient in the direction of highest exposure can be obtainedwith a 95-percentile confidence level from k1

P (X ≤ k1) =

k1∑j=0

(Ntot

j

)(1− P1)jPNtot−j

1 ≥ 0.95 (32)

where Ntot = nN is the total number of users that will be distributed. The following k-values arecalculated with the same formula but taking account for the users already distributed.

P (X ≤ ki) =

ki∑j=0

(Nij

)(1− Pi)jPNi−j

i ≥ 0.95 (33)

The term Ni is the number of users not yet distributed. The number of users is then calculatedfrom the highest exposure until all users are distributed, i.e. until

∑47i=1 ki = Ntot.

The power reduction factor is the reduction of power compared with sending a beam straightforward constantly, while taking into account TDD, utilization of the antennas and user distribu-tion. The expectation of the power reduction factor as a function of utilization can be found in[15]. The equation is modified by using the simulated values of the RF exposure and can now beused also in the near field region.

E[P (ρ, n, r)] = TDD

nconv∑n=1

ρ

nN

(k1(r, n)ER1(r) + k2(r, n)ER2(r) + ...+ k47(r, n)ER47(r)

ER1(r)

)(1−ρ)ρn−1

(34)

where ρ is the utilization. A theoretical maximum can be found by assuming all users are directedin the direction of the highest exposure. This would mean the user-coefficient k1 = nN and allother coefficients are zero. As the exposure is normalized with the highest value, the factor ER1

is equal to one. From this the theoretical maximum is obtained in 35.


nconv∑n=1

ρ(1− ρ)ρn−1 (35)

This can be simplified to E[P (ρ, n, r)] = TDDρ as can be seen in Appendix 3. The PRF is thuslinear with utilization when all the users are placed straight in front of the antenna.

25

5.2 The normalized exposure and the expected PRF for the one panelmodel

A schematic plot of the normalized exposure is created when the averaging area is placed straight infront of the antenna. The normalized exposure of each beam is displayed as a function of the beamsazimuth and elevation angles for different distances as shown in Fig. 23-27. Close to the antenna,the power density is high for any of the beams selected. At the far field region the schematic plotslooks very similar, independent of distance. The normalized exposure of the broadside beam is oneas it also works as the normalizing factor. The four beams closest to the broadside beam has anexposure reduction of around 0.4. Beams outside of these five has an reduction of around 0.1 orlower.

-60 -40 -20 0 20 40 60

azimuth, in degrees

-15

-10

-5

0

5

10

15

ele

vation,

in d

egre

es

The normalized exposure, averaged over an area centered around the middle of the panel. Distance: 0.01 m

0.599 0.875 0.947 0.977 0.989 0.983 0.962 0.902 0.603

0.503 0.829 0.927 0.979 0.995 0.997 0.986 0.937 0.837 0.48

0.606 0.898 0.961 0.99 1 0.99 0.961 0.898 0.606

0.48 0.837 0.937 0.986 0.997 0.995 0.979 0.927 0.829 0.503

0.603 0.902 0.962 0.983 0.989 0.977 0.947 0.875 0.599

0

0.2

0.4

0.6

0.8

1

No

rma

lize

d E

xp

osu

re

Figure 23: A schematic view over the normalized exposure using an averaging area around thex-axis at a distance of 0.01 m.

-60 -40 -20 0 20 40 60

azimuth, in degrees

-15

-10

-5

0

5

10

15

ele

vation,

in d

egre

es


0.06 0.142 0.428 0.805 0.891 0.817 0.445 0.145 0.063

0.065 0.105 0.254 0.767 0.936 0.935 0.774 0.257 0.106 0.067

0.063 0.153 0.475 0.905 1 0.905 0.475 0.153 0.063

0.067 0.106 0.257 0.774 0.935 0.936 0.767 0.254 0.105 0.065

0.063 0.145 0.445 0.817 0.891 0.805 0.428 0.142 0.06

0

0.2

0.4

0.6

0.8

1

No

rma

lize

d E

xp

osu

re


26

-60 -40 -20 0 20 40 60

azimuth, in degrees

-15

-10

-5

0

5

10

15

ele

vatio

n,

in d

egre

es


0.023 0.025 0.055 0.304 0.518 0.311 0.055 0.026 0.026

0.027 0.029 0.065 0.25 0.85 0.852 0.254 0.064 0.029 0.028

0.03 0.036 0.096 0.585 1 0.585 0.096 0.036 0.03

0.028 0.029 0.064 0.253 0.852 0.85 0.25 0.065 0.029 0.027

0.026 0.026 0.055 0.311 0.518 0.304 0.055 0.025 0.023

0

0.2

0.4

0.6

0.8

1

No

rma

lize

d E

xp

osu

re


-60 -40 -20 0 20 40 60

azimuth, in degrees

-15

-10

-5

0

5

10

15

ele

vation,

in d

egre

es


0.005 0.003 0.004 0.009 0.073 0.01 0.004 0.003 0.005

0.019 0.011 0.008 0.023 0.427 0.421 0.023 0.008 0.012 0.02

0.015 0.02 0.039 0.108 1 0.108 0.039 0.02 0.015

0.02 0.012 0.008 0.022 0.421 0.427 0.023 0.008 0.011 0.019

0.005 0.003 0.004 0.01 0.073 0.009 0.004 0.003 0.005

0

0.2

0.4

0.6

0.8

1

No

rma

lize

d E

xp

osu

re


-60 -40 -20 0 20 40 60

azimuth, in degrees

-15

-10

-5

0

5

10

15

ele

vation,

in d

egre

es

The normalized exposure, averaged over an area centered around the middle of the panel. Distance: 1 m

0.003 0.002 0.002 0.001 0.019 0.001 0.002 0.002 0.003

0.021 0.01 0.001 0.013 0.369 0.363 0.013 0.001 0.01 0.022

0.015 0.022 0.036 0.045 1 0.045 0.036 0.022 0.015

0.022 0.01 0.001 0.012 0.362 0.369 0.013 0.001 0.01 0.021

0.003 0.002 0.002 0.001 0.019 0.001 0.002 0.002 0.004

0

0.2

0.4

0.6

0.8

1

No

rma

lize

d E

xp

osu

re

Figure 27: A schematic view over the normalized exposure using an averaging area around thex-axis at a distance of 1 m.

27

The power reduction factor was calculated using (34) and the computed normalized exposures fromthe simulations as shown in Fig. 28 and 29. The user coefficients ki,j were calculated from equations(32) and (33) with a 95-percentile confidence level. The results are compared to the theoreticalmax, where every user is assumed to be placed in the direction of the broadside beam. Very close tothe antenna, the power reduction factor is very close to the theoretical max, depending on chosenTDD and utilization. As the distance increases toward 20 cm, the PRF decreases rapidly and at adistance above 20 cm, the PRF has a maximum value of around 22% using the cosine-based userdistribution. Using the uniform user distribution, the maximum PRF is around 14%.

0 10 20 30 40 50 60 70 80 90 100

Utilization, (%)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Distance: 0.01 m

Distance: 0.05 m

Distance: 0.1 m

Distance: 0.15 m

Distance: 0.2 m

Distance: 0.25 m

Distance: 0.3 m

Distance: 0.35 m

Distance: 0.4 m

Distance: 0.45 m

Distance: 0.5 m

Distance: 0.55 m

Distance: 0.6 m

Distance: 0.65 m

Distance: 0.7 m

Distance: 0.75 m

Distance: 0.8 m

Distance: 0.85 m

Distance: 0.9 m

Distance: 0.95 m

Distance: 1 m

Theoretical Max

Figure 28: The expected power reduction factor as a function of utilization for different distances.The user distribution is uniform.

0 10 20 30 40 50 60 70 80 90 100

Utilization, (%)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8Distance: 0.01 m

Distance: 0.05 m

Distance: 0.1 m

Distance: 0.15 m

Distance: 0.2 m

Distance: 0.25 m

Distance: 0.3 m

Distance: 0.35 m

Distance: 0.4 m

Distance: 0.45 m

Distance: 0.5 m

Distance: 0.55 m

Distance: 0.6 m

Distance: 0.65 m

Distance: 0.7 m

Distance: 0.75 m

Distance: 0.8 m

Distance: 0.85 m

Distance: 0.9 m

Distance: 0.95 m

Distance: 1 m

Theoretical Max

Figure 29: The expected power reduction factor as a function of utilization for different distances.The user distribution is cosine based.

A graph of the maximum PRF as a function of the distance is provided in Fig. 30. The resultsare also compared with the far-field results of the maximum PRF in [15]. The maximum PRF wasalso calculated using the averaging area of 4 cm2. As seen in Fig. 31, the conversion toward aconstant value is significantly faster using a smaller averaging area.

28

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Distance [m]

0

0.5

Maximum Power Reduction Factor at each distance, using one panel model and a uniform user distribution

Simulated results

Far Field Results

Far field limit

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Distance [m]

0

0.5

Maximum Power Reduction Factor at each distance, using one panel model and a cos-based user distribution

Simulated results

Far Field Results

Far field limit

Figure 30: The maximum PRF as a function of distance from the results in Fig. 28 and 29. Thefar-field limit result corresponds to the maximum PRF gotten from [15].

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Distance [m]

0

0.2

0.4

0.6

Maximum Power Reduction Factor at each distance, using one panel model and a uniform user distribution

Simulated results

Far Field Results

Far field limit

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Distance [m]

0

0.2

0.4

0.6

Maximum Power Reduction Factor at each distance, using one panel model and a cos-based user distribution

Simulated results

Far Field Results

Far field limit

Figure 31: The maximum PRF as a function of distance with an averaging area of 4 cm2. Thefar-field limit result corresponds to the maximum PRF gotten from [15].

5.3 Creating the four panel model

A statistical model, simulating a four panel antenna was created. This model was based on thegeometry of a real Ericsson RBS product. The intention of the model was to see how the exposurechanges, when four panels are shared among the users. Similarly to what was done when creatingthe one panel model, a statistical model was created using the same inputs. A realistic assumptionof the exposure close to and far away from the antenna was made. Far away, the distance betweenthe panels will be very small compared to the distance from the antenna to the measurement-point. The number of users was assumed to be the same as in the one panel model. The four panelmodel should therefore converge to the results from the one panel model far away from the antenna.

Close to the antenna, the maximum exposure was harder to find. A choice was made to analyzethe exposure along two lines around which the averaging area was centered. For small distances,a fair assumption is that the maximum exposure lies right in front of one of the panels. As thepanel only takes care of one forth of the total number of users and the other three panels hasminimal contribution, the total exposure should be one forth of the exposure measured from theone panel case. An other interesting line is in the middle of the antenna configuration. The smallercontributions from all four panels should at some distance exceed the exposure right in front ofone of the panels.

A four panel model, each with a defined set of 47 beams, would in a simulation have 474 combi-nations of beams. This is not possible to simulate, so instead 47 large area simulations with onepanel was made. Results for the four different panels are then obtained by using different positions

29

of the averaging area corresponding to a case where the array position is shifted, see Fig. 32. Thetotal exposure can then be calculated by using the principle of superposition. This can be doneby assuming that the mutual coupling between the panels is negligible. As the distance betweenthe elements are far smaller than the distance between the nearest panel and the panels are placedaway from the radiation direction, this is a fair assumption.

y

z

x

y

z

Figure 32: To the left, a visual representation of the two averaging areas over a four panel model. Tothe right, the corresponding areas used when having one panel simulating four panels by changingthe averaging area. The red area is the averaging area above the mid-point of the antenna. Thegreen area is the averaging area above one of the panels.

The exposure from all four panels were sorted in four different descending lists. Each exposurevalue was normalized with the highest possible exposure from one panel, which was assumed tobe the exposure obtained when the averaging area is situated straight in front of the antenna. InTable 5, a representation of the list is written for each panel.

Table 5: A sorted list of the exposures from the 4 panels having 47 different beams. The normalizingfactor ERnorm, is the exposure from the broadside beam when the averaging area is straight infront of the antenna.

Panel 1 Panel 2 Panel 3 Panel 4ER1,1(r)ERnorm(r)

ER1,2(r)ERnorm(r)

ER1,3(r)ERnorm(r)

ER1,4(r)ERnorm(r)

ER2,1(r)ERnorm(r)

ER2,2(r)ERnorm(r)

ER2,3(r)ERnorm(r)

ER2,4(r)ERnorm(r)

. . . .

. . . .

. . . .ER47,1(r)ERnorm(r)

ER47,2(r)ERnorm(r)

ER47,3(r)ERnorm(r)

ER47,4(r)ERnorm(r)

Each user is distributed uniformly and separately over the 4 panels. Because the averaged numberof users over the exposure time is a multiple of ten, sometimes the number of users are one fewerfor two of the panels. An example of how many users are distributed to each panel can be seen inTable 6. To make the estimation conservative, the panel with the highest exposure contribution isalways chosen, as long as the panel has not filled the quota of users already. If the panels with thehighest exposure quota is full, the next highest is chosen, and so on.

30

Table 6: Number of users to each of the four panels, for n = 1,2,..., nconv

nN = 10 nN = 20 nN = nconvN

N1 = 3 N1 = 5 ... N1 = dnconvN4 e

N2 = 3 N2 = 5 ... N2 = dnconvN4 e

N3 = 2 N3 = 5 ... N3 = bnconvN4 c

N4 = 2 N4 = 5 ... N4 = bnconvN4 c

Far away from the antenna, the user positions should be equal to those using one panel. The usercoefficients ki,j were found by taking the mean of the probabilities of each beam at each step inthe list. The probability of a user being placed at max exposure for each panel is

P1 =

∑4j=1 Ω1,jW1,j(ξ, η)∑47

i=1

∑4j=1 Ωi,jWi,j(ξ, η)

(36)

where Ω1,1, Ω1,2, Ω1,3 and Ω1,4 are the beam width angles of the beam with maximum exposurefor each panel. The probability of a user at all the other positions are then found

Pm =

∑4j=1 Ωi,jWi,j(ξ, η)∑47

i=m

∑4j=1 Ωi,jWi,j(ξ, η)

(37)

The number of users at each position is created in the same way as in the previous model usingequations (32) and (33). The users ki,j,n(r) will now be distributed to a specific panel and the sumof the coefficients to a specific panel will be equal to the total number of users to that panel

47∑i=1

ki,j(r, n) = Nj (38)

E[Ptot(ρ, n, r)] = TDD

nconv∑n=1

ρ

nN

(47∑i=1

panels∑j=1

ki,j(r, n)ERi,j(r)

ERnorm(r)

)(1− ρ)ρn−1 (39)

As the distance gets large, the exposure from all four panels tend to be equal and the values ofthe user coefficients should converge toward the one panel case. Inserting the converging exposureinto (39), shows that it converges toward the one panel case.

5.4 The normalized exposure and the expected PRF for the four panelmodel

The superposition of the maximum exposure from all panels was calculated using an averagingarea in the middle and above panel four, as shown in Fig. 33. As the distance to the antennagrows, the exposure converges.

31

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Distance [m]

0

5

10

15

20

25

30

Ex

po

sure

rat

io

Sum of the maximum exposure from four panels, with the averaging area in the middle and over panel 4

Over panel 4

In the middle

Figure 33: The super-positioned maximum exposure for both cases of the position of the averagingarea.

The evolution of the normalized exposure was measured and expressed in a schematic view as afunction of azimuth and elevation, see Fig. 37-41. Two averaging area was used, one centeredaround the x-axis and one right above one of the panels. Most of the power will radiate outside ofthe area when the averaging area is close to the panel. This makes the exposure very small fromeither panel. At a distance of 0.35 m, power from the main beam from all four panels are radiatingthrough the averaging area. As the distance grows, the highest exposure moves toward the mainbeam of the broadside beam.

Figure 34: A schematic view over the normalized exposure using an averaging area around thex-axis. The distance to the averaging area is 0.05 m.

32



Figure 37: A schematic view over the normalized exposure using an averaging area around thex-axis. The distance to the averaging area is 1 m.

33

A similar schematic view is created, with the averaging area centered straight above panel 4. Thenormalized exposure is identical from panel 4 to the one panel case. This behavior is expected asthe averaging area is placed straight in front of that panel in the same way as in the one panel caseand the normalizing factor is equal. The angles from the averaging area to the other three panelsare very steep close to the antenna. The power radiating in that direction is therefor minimal.Still, as the distance grows, the highest exposure comes from the broadside beam.

Figure 38: A schematic view over the normalized exposure using an averaging area above panel 4.The distance to the averaging area is 0.05 m.


34


Figure 41: A schematic view over the normalized exposure using an averaging area above panel 4.The distance to the averaging area is 1 m.

The maximum PRF compared with the maximum of the one panel case for the one panel case, isshown in figure 42. As expected, the one-panel case results in a larger exposure for small distanceswhereas the results converge in the far field region.

Figure 42: The maximum PRF as a function of distance, using the method of distributing eachuser to the panel with highest exposure.

35

5.5 Discussion

If all users are distributed straight in front of the antenna in the one panel model, i.e. k1 = Ntot,all the power is directed toward the broadside direction. This is the theoretical max which willconverge toward the TDD value when utilization reaches 100%. If TDD is 1 the PRF will convergetoward 1.

What the TDD value will eventually be in the 5G network is unclear, but a reasonable value0.75 [15]. If another value of TDD is preferable it is easy to scale with the results in this paper.The TDD value scales the power reduction factor linearly and therefor can the results be changedeasily depending on what TDD is used.

The directions of the beams in the simulations have a precision of ±0.5 degrees, as the phasesare manually inserted after the calculated phases are used to roughly find the right phase configu-ration with equation 22. The accuracy in the far field of the angles φ and θ in the simulations wasset to one degree. This was done to minimize the computational load, which was already very heavy.

The power reduction factor converges slowly for large values of the utilization ρ. In theory,the sum should have an infinite number of terms, but in practice that is not possible. Whenimplemented in MATLAB, the number of terms is set to a large number. The problem is, the al-gorithm has to distribute a large number of users when n is large. Therefore, the program becomescomputationally heavy. Very high utilization levels are not realistic, so this is of minor importance.

The beams closest to the broadside beam are not regarded in [15]. In this model, the normal-ized exposure is calculated for these beams and contribute to the results. Therefore the PRFconverges to a higher value compared with the far field results.

Using a smaller averaging area, the PRF converges faster toward a constant value. The beamsadjacent to the broadside beam will give a greater contribution to the exposure. As the area isbigger, some of the adjacent beams will radiate some of the power through the bigger averagingarea. When the area is smaller, the contributions from the adjacent beams will be smaller atsmaller distances.

For the four panel case, the normalized exposure for each panel moves toward the center, asthe distance grows. In figure 33, the sum of the maximum exposure also displays convergencetowards a specific value. This is expected, and also shows that the schematic of the exposure willconverge toward the one panel case. A larger simulation volume, recording field strength valuesfurther away from the panel, would show the maximum exposure from the center beam with avalue very close to one. A simulation with larger distances would therefore show the convergenceof the PRF to the one panel case.

The maximum PRF curve shown in Fig. 42, is not very smooth. This can be attributed tohow each user is distributed to a panel and due to the resolution of the distances where the PRFare calculated, which was 5 cm. The beam which will give the highest exposure contribution willchange with such a large distance between calculated points. Both the highest exposure beam andthe beams adjacent to that beam will have a different value because when the distances increase,the maximum PRF can change quite fast. The big changes will create a somewhat choppy curve.

The total PRF of the four panel model is a combination of using both areas. When close tothe antenna, the PRF is higher above one of the panels. As the distance grows, the PRF will behigher when the total exposure gets contributions from all four panels. The PRF from both resultsconverges to the one panel results.

The user distribution weighted toward the direction of the broadside beam has in general a largerPRF compared to the PRF from the uniform user distribution case. To create an efficient basestation, the antenna configuration should be aimed toward an area where users likely to be found.Therefore, the PRF calculated from using the cosine-based distribution is probably more realis-tic.

36

6 Conclusion

The RF EMF exposure of a 5G small cell RBS using massive MIMO antenna was assessed. Thecompliance distance for a uniform antenna excitation was determined for a 4x4 and an 8x8 planararray antenna using frequencies between 10 and 60 GHz. The power density was averaged overthree different areas, 1 cm2, 4 cm2 and 20 cm2. A statistical model was also created, based on a 28GHz small cell RBS, single 8x8 planar array antenna, including factors such as TDD, utilizationand time-averaging. A similar model, using a four panel antenna was also created. From theproject, three main points can be deduced:

• A larger averaging area makes the convergence of the compliance distance toward the resultsfrom the far-field formula slower. In the near field, the compliance distance will be smallerwhen a small averaging area is used.

• The RF exposure from a single panel RBS is reduced significantly in the near field regioncompared to the theoretical maximum. The PRF very close to the antenna is close to thetheoretical maximum, but as the distance increases to 20 cm and beyond, the PRF convergestoward 17% or 10% depending on which user distribution is used. These results assume aTDD value of 75% and a very high utilization.

• Using a four panel model of a 5G small cell RBS, the PRF is around one forth of theresults from the one panel model at small distances. When increasing the distance, the PRFconverges toward the the one panel model results.

37

Appendix

1

The AF and progressive phase shift is derived for an NxM phased array antenna. A NxM dipole-antenna matrix is placed in the yz-plane, where x = 0. The indices of the midpoint of each elementis defined as (ny, nz), where ny, nz ∈ N. The electric field in the far field from one element can bedescribed with equation (5). The radiation in direction ~r1 from element in (ny, nz) far away fromthe antenna, can be approximated by assuming the vector as ~r1 is parallel with ~r.

~r1 ≈ ~r − ~r0 (40)

The vector ~r0 is the directional vector in the yz-plane as seen in figure 43. The vector ~r0 is projectedonto the y- and z-axis.

~r0 = y0y + z0z (41)

The coefficients y0 and z0 is the distance from the antenna element to origo in y- and z-direction.This can also be written as the distance between two adjacent antenna elements times the indexnumber ny and nz, y0 = dyny and z0 = dznz. The projection of ~k in terms of the basis vector indirection of the x-, y- and z-axis.

~k = k0(cosφ sin θx+ sinφ sin θy + cos θz) (42)

Inserting the vectors from equations (40), (41) and (42) in the exponential part of equation (5)with a phase β.

e−j(~r1·~k+β) = e−j~r·

~kej(k0y0 sin θ sinφ+k0z0 cos θ+β) (43)

The electric field from one element of the planar array antenna can then be written as

Eny,nz= jη

kI0l

8πrej(nydyk0 sin θ sinφ+dznz cos θ+β) sin θ (44)

The phase is divided into two phases, in y- and z-direction, β = βy + βz. The array-factor, AF,defined as the factor multiplied with the electric field of the single element to get the electric fieldof the entire antenna. As the electric field from the single element is chosen arbitrarily, it candescribe the electric field from any of the elements. The electric field of the entire antenna is thesuperposition of the field from every element.

~Etot = jηkI0l

8πr

N∑ny=1

M∑nz=1

ej(k0nydy sin θ sinφ+βy)ej(k0nzdz cos θ+βz) (45)

from which the AF can be found

AF =

N∑ny=1

ej(nydyk0 sin θ sinφ+βy)M∑

nz=1

ej(nzdzk0 cos θ+βz) (46)

For simplicity, a variable change of the exponents makes

Ψy = k0dy sin θ sinφ+ βy/ny (47)

Ψz = k0dz cos θ + βz/nz (48)

The AF then becomes

38

x

y

z

~r

~r0

~r1

~rproj

θ

φ

Figure 43: An 8x8 antenna, with the corresponding vectors used to derive the direction of radiation.

AF =

N∑ny=1

ejnyΨy

M∑nz=1

ejnzΨz (49)

Using Euler’s formula and some algebra, the AF can then be written as, with the condition of theantenna is centered around origo [19]

AF =1

N

sin(NΨy

2 )

sin(Ψy

2 )

1

M

sin(MΨz

2 )

sin(Ψz

2 )(50)

A local maximum lies at Ψy = 0 and Ψz = 0, which from [19] corresponds to the main beam. Fromequations (47) and (48)

βy = −k0nydy sin θ0 sinφ0 (51)

βz = −k0nzdz cos θ0 (52)

The phase β of the current that directs the beam in direction φ0 and θ0.

β = −k0(nydy sin θ0 sinφ0 + nzdz cos θ0) (53)

39

2

The conversion from azimuth and elevation to φ and θ are derived. First, a vector ~r has an elevationangle, η, and an azimuth angle, ξ. They do not correspond to the angles φ and θ, which are usedto calculate the phase. Therefor, a formula is found to convert between the angles.

The vector ~ρ is the projection of ~r in the xy-plane and ~η is the projection of ~r in the xz-plane.From this, the vector ~r can be written in terms of x,y,z. The x,y,z components of ~r are

x = |ρ| cos(η) = |ζ| cos(ξ)

y = |ρ| sin(η)

z = |ζ| sin(ξ)

where the parameters ρ, ζ, η and ξ can be seen in Fig 19. From the value of x, |ζ| can bedetermined.

|ζ| = |ρ|cos(η)

cos(ξ)

From this, the amplitude of ~r can be calculated.

|~r| =√x2 + y2 + z2 =

√ρ2 cos2(η) + ρ2 sin2(η) + ρ2

cos2(η)

cos2(ξ)sin2(ξ) (54)

which can be simplified to

|~r| = |ρ|cos(ξ)

√cos2(ξ) + cos2(η) sin2(ξ) (55)

The vector ~r can be described as

~r =< |ρ| cos(η), |ρ| sin(η), |ρ|cos(η) sin(ξ)

cos(ξ)> (56)

The angle θ can be found by computing cos θ = r · z.

cosθ =~r

|~r|· z =

cos(η) sin(ξ)√cos2(η) sin2(ξ) + cos2(ξ)

(57)

The angle φ is the same as the azimuth angle, η.

φ = η (58)

40

3

The expected PRF is simplified when all users are assumed to be placed straight in front of theantenna.


nconv∑n=1

ρ(1− ρ)ρn−1 (59)

All factors not depending on n is removed outside of the sum:

E[P (ρ, n, r)] = TDDρ(1− ρ)

nconv∑n=1

ρn−1 (60)

Substitute m = n− 1:

E[P (ρ, n, r)] = TDDρ(1− ρ)

nconv−1∑m=0

ρm (61)

If nconv is assumed to approach infinity and because |ρ| < 1, the sum can be seen as

∞∑m=0

ρm =1

1− ρ(62)

Inserting 62 into 61

E[P (ρ, n, r)] = TDDρ(1− ρ)1

1− ρ= TDDρ (63)

41

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