IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 4, AUGUST 2012 747

Experimental Assessment of Specific AbsorptionRate Using Room Electromagnetics

Aliou Bamba, Wout Joseph, Member, IEEE, Jørgen Bach Andersen, Life Fellow, IEEE, Emmeric Tanghe,Gunter Vermeeren, David Plets, Jesper Ødum Nielsen, and Luc Martens, Member, IEEE

Abstract—A closed room environment is viewed as a lossy cav-ity, characterized by possibly a line-of-sight component and diffusescattering parts from walls and internal obstacles. A theory usedin acoustics and reverberation chambers is applied for the electro-magnetic case, and main issues related to measurement systems,antennas characteristics, diffuse energy properties, and human ex-posure are investigated. The goal of this paper aims first towardvalidation of the assessment of the reverberation time in an en-vironment using a virtual multiple-input-multiple-output channelsystem. Second, the reverberation time in an adjacent room is in-vestigated, and hence, a measurement-based method is readily de-veloped to assess the absorption cross section and the whole-bodyspecific absorption rate of humans at 2.3 GHz in a realistic closedenvironment.

Index Terms—Absorption cross section (ACS), diffuse scatter-ing, power density, reverberation time, room electromagnetics, spe-cific absorption rate (SAR) .

I. INTRODUCTION

INDOOR microwave propagation has been investigated indetail for a long time. More recently, room electromagnetics

has become appealing because it does not require full knowl-edge of all details of the propagation environment [1], whichmakes it less tricky. Currently, propagation models are com-plex [2]–[5]. A very simple propagation model with only fewparameters is obtained by considering the indoor environment asa lossy cavity where all the effective losses can be described witha single parameter. The theory of wideband propagation in anenvironment is applied, similar to studies in acoustics and rever-beration chambers. The acoustics community has been applyingthe method [6] since the 1920s (Sabine’s equation), but the fun-damental difference to the radio case is the polarization [7]. Thebasic model is very simple and considers a first arriving line-of-

Manuscript received June 6, 2011; revised October 20, 2011; acceptedFebruary 13, 2012. Date of publication March 23, 2012; date of current versionAugust 17, 2012. This work was supported in part by the European Union’sSeventh Framework Program (FP7/2007-2013) under Grant 244149 and inpart by the Fund for Scientific Research-Flanders (FWO-V, Belgium) projectG.0325.11N.

A. Bamba, W. Joseph, E. Tanghe, G. Vermeeren, D. Plets, and L.Martens are with the Department of Information Technology, GhentUniversity/IBBT, Ghent B-9050, Belgium (e-mail: aliou.bamba@intec.ugent.be; wout.joseph@intec.ugent.be; emmeric.tanghe@intec.ugent.be;gunter.vermeeren@intec.ugent.be; David.Plets@UGent.be; luc.martens@intec.ugent.be).

J. B. Andersen and J. Ø. Nielsen are with the APNet, Department ofElectronic Systems, Faculty of Engineering and Science, Aalborg University,Aalborg DK-9220, Denmark (e-mail: jba@es.aau.dk; jni@es.aau.dk).

Digital Object Identifier 10.1109/TEMC.2012.2189572

sight) (LOS) signal if present and after that multiple reflectionsand scatterings giving rise to a tail with exponential decay anda time constant noted as the reverberation time, similar to theacoustics case. Room electromagnetics basic theory is discussedin [7].

Here, the theory of room electromagnetics is applied fortransceivers in the same room and for the first time is extendedfor adjacent rooms.

Electromagnetic measurements near the body are importantfor electromagnetic compatibility studies, for the characteriza-tion of antennas near dielectric media, and for potential healtheffects of electromagnetic radiation.

The reverberation time assessment using a channel sounder isinvestigated in [1] and [7]. In this paper, the reverberation timeassessment is compared for two different measurement sys-tems, namely the channel sounder and the virtual multipleinput-multiple-output (MIMO) channel sounder. The use of the vir-tual MIMO has several benefits, i.e., it is much cheaper thanthe channel sounder, there is no coupling between antennas, etc.However, the cost of using a virtual MIMO channel sounder isthe increased measurement time, but the measurement of thereverberation time takes only a few minutes. The reverberationtime assessment is of main importance because it is a functionof the absorption area in the room, the total surface absorbingelectromagnetic radiation, and hence linked to the absorptioncross section (ACS), i.e., the body surface area (BSA) beingexposed to radiation, for humans in realistic environments andother lossy objects.

The International Commission on Non-Ionizing RadiationProtection (ICNIRP) [8] defines guidelines for specific absorp-tion rate (SAR) as a basic restriction for human exposure in theradio-frequency (RF) band. A statistical exposure tool to deter-mine the distribution of the whole-body averaged SAR in a re-alistic indoor-picocell environment is proposed in [9]. The SARis a difficult quantity to measure in an actual human. Therefor,the studies of the SAR in realistic human body models and re-alistic environments are based on numerical computations suchas the finite-difference time-domain (FDTD) technique, suchas in [10] and [11]. These computations are dependent on theaccuracy of the phantom modeling and on the used numericalcode, are time consuming, etc. Rather than using such numericalcomputational methods, a measurement-based approach basedon theACS is a suitable alternative for the assessment of thewhole-body averaged SAR (SARwb ), and is readily developedin this paper.

From the ACS, and given an incident power density, it ishence easy to derive the whole-body SAR [12].

0018-9375/$31.00 © 2012 IEEE

748 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 4, AUGUST 2012

Fig. 1. Virtual channel sounder setup.

The outline of this paper is as follows: the two measure-ment system configuration and the environments are describedin Section II. Section III describes the methodology to extractthe reverberation time τ , and in Section IV we present the bench-marking results of both measurement systems and other featuresof the reverberation time. Section V is devoted to the ACS as-sessment and the experimental whole-body SAR calculation.Conclusions are presented in Section VI.

II. CONFIGURATION AND ENVIRONMENT

A. Virtual MIMO Channel Sounder Setup

The virtual channel sounder setup for the multiple-input-single-output (MISO) measurements is shown in Fig. 1.

A network analyzer (Rohde & Schwarz ZVR) is used to mea-sure the complex channel frequency response for a set of trans-mitting and receiving antenna positions. The channel is probedin a 500-MHz measurement bandwidth with a frequency resolu-tion of 1.25 MHz (401 frequency points) and a central frequencyof 2.3 GHz. As transmitting (Tx) and receiving (Rx) antennas,broadband omnidirectional biconical antennas of type Electro-Metrics EM-6116 are used. To be able to perform measurementsfor large Tx–Rx separations, one port of the network analyzer isconnected to the Tx through an RF/optical link with an opticalfiber of length 500 m. A Dirac pulse signal (in the frequencydomain) generated by the network analyzer is sent into the Txvia an optical fiber. The RF signal sent into the Tx and the RFsignal coming from the Rx are both amplified using an amplifierof type Nextec-RF NB00453 with an average gain of 37 dB.

The amplifiers assure that the signal-to-noise ratio at the re-ceiving port of the network analyzer is at least 20 dB for eachmeasured location of the Tx and Rx. The calibration of thenetwork analyzer is done at the connectors of the Tx and Rxantennas, and as such includes both the RF/optical link and theamplifiers.

The Rx is fixed and the Tx is positioned at 51 different loca-tions forming a virtual uniform linear array (ULA). Both anten-nas are polarized vertically and positioned at a height of 1.8 mduring measurements. The separation between two adjacent

positions in the array is 0.8 cm. One measurement (all 51 vir-tual antenna positions of the array) last about 5 min. At eachTx position in the array, the network analyzer measures theS21 scattering parameter ten times (i.e., ten time observations),which we average to obtain one power delay profile (PDP) perTx–Rx combination. Since we have 51 Tx and 1 Rx, we have510 PDPs for the whole ULA which is averaged to obtain theaverage PDP in dB, labeled as APDP, and given by

APDP(t)|dB = 10 log(|Sav21 (t)|2)

where Sav21 (t) is the average PDP in a linear domain over the

number of Tx positions. The spatial averaging is necessary toavoid the effect of fading; it is performed by the stepper motormoving the antennas around. The PDP is plotted within a delayof 800 ns, which is enough to observe the decay of the power.The scattering parameter S21 is translated into the time domainby using an IFFT operation with a UNIFORM window (seeSection III-A for motivations).

B. Channel Sounder Setup

The measurements were also carried out using an MIMOchannel sounder, based on the correlation principle. The systemallows truly simultaneous measurement of all up to 8 Rx and 16Tx branches. Details of the measurement system can be foundin [13]. The main characteristics of the setup used in this set ofmeasurements are as follows.

1) Measurements time-triggered at 60 Hz. This ensuresproper sampling of the channel, which is changing dueto both movements of the Rx and other external changes.

2) Bandwidth: 100 MHz.3) Carrier frequency: 2.3 GHz.4) Measurement duration: 10 s (600 measurements).5) Rx channels: four mockup laptop arrays are measured

simultaneously, each with four antennas (measured viaswitch). The laptop arrays have two top-mounted and twoside-mounted dipole-like antennas.

6) Tx channels: four dual-band branches, four element lineararray with vertically polarized elements. Each of the fourlaptops is placed on a table in front of a person. Duringeach measurement, the persons are moving the laptops ran-domly on the table with displacements of approximatelyplus/minus 10 cm. For the current work, the PDPs are ob-tained as an average over all the measurements made withthe four antennas on the laptop.

C. Description of the Environment

1) Environment in Aalborg, Denmark: The measurementswere performed in a seminar room of Aalborg University(AAU), shown in Fig. 2, where only the right part is used.The room is equipped with tables, chairs, and ordinary meetingroom facilities.

The locations for Rx in this room are summarized in Table I.The Tx had a fixed position whereas the Rx occupies positions

Rx1, Rx7, Rx12, and Rx18 as shown in Fig. 2.The measurements with the channel sounder occurred in May,

2010.

BAMBA et al.: EXPERIMENTAL ASSESSMENT OF SPECIFIC ABSORPTION RATE USING ROOM ELECTROMAGNETICS 749

Fig. 2. Seminar room: Tx and Rx measurement positions.

TABLE ILOCATIONS FOR RX IN THE SEMINAR ROOM IN AALBORG

2) Environment in Ghent, Belgium: The measurements wereperformed in rooms C3/3-3 and C3/3-4 at the third floor of anoffice building in Ghent, Belgium. The ground plan is shownin Fig. 3. This floor is comprised of different rooms indexedby C3/3 − iwhere i is the ith room. We are only interested inrooms C3/3-3 and C3/3-4. A description of these rooms is asfollows: room C3/3-3 contains desks (with chairs, computers,etc.), people, dressers, and other furniture such as cardboards,books, etc. and room C3/3-4 contains about the same things.

The receiver is always located in room C3/3-3 whereas thetransmitter is either located in room C3/3-3 (Room-Room, in-dexed by RR) or in room C3/3-4 (Adjacent-Room, indexed byAR). The measurements with the virtual channel sounder wereperformed from September 20th to September 24th, 2010.

III. METHODOLOGY

A. Extraction of the Reverberation Time (τ )

In indoor propagation, multiple reflections and scattering giverise to a tail with an exponential decay in the PDP curve anda time constant noted as the reverberation time [7]. In a logscale, this is equivalent to a tail of the impulse response whichis linear, and its slope leads to the reverberation time according

to the following formula:

τ = −10 log(e)slope

where e = 2.718. . . is Euler’s number and “slope” is the slopeof the linear tail in the impulse response.

For the assessment of τ , the amplitudes of the average PDPat different delays do not have to be accurate (because we areinterested in the slope), instead the frequency resolution, i.e.,the temporal resolution has to be as accurate as possible. Thisis the reason why the UNIFORM window has been used in theIFFT computation, since it has a noise-power-bandwidth factorof 1.

Actually, the experimental APDP (in dB) does not have aperfect linear tail because of the noise level of the network ana-lyzer, the measurement uncertainties, etc. We need to derive thereverberation time over a certain delay range (or a certain rangeof power) for which the APDP tail is approximated by linearregression. This choice should be done automatically becausethe manual detection would suffer from judgment subjectivity(see the next section). The methodology is shown in the flowgraph of Fig. 4.

B. Automatic Detection Algorithm

In this section, we introduce the algorithm (in Fig. 5) usedfor the automatic reverberation time detection. One may de-tect automatically the reverberation time using a fixed delayrange (or a fixed power range). Such kind of algorithm wouldbe good for a certain room and propagation environment. Butwhen changing the room (mainly the volume), the Tx–Rx sepa-ration for the same room, or when the propagation environmentchanges, the received power may be different. Then, the PDP tailvaries and neither the delay range nor the power range will bevalid.

We define here different quantities using the APDP curve (asin Fig. 5) to explain the algorithm.

1) τfirst: the arrival time of the first component.2) Tmean : the mean arrival time.3) Pmin : the minimum APDP value.4) ΔPn : the difference between Pmin and the value of the

first peak before Pmin .5) ΔPp : the difference between Pmin and the value of the

first peak after Pmin .The following threshold is then defined:

Threshold = Pmin + min(ΔPn ,ΔPp)

where min(a, b) is the minimum value of a and b; we introduceΔPn and ΔPp to ensure that the Threshold will be in the noisezone (see Fig. 5).

All APDP values lower than Threshold are gathered in anarray, called “NoiseArray.” We finally define the noise floor by

Pnoise = mean(NoiseArray) + 3 dB

where 3 dB is added to be two times above the noise mean value.It should be noted that the algorithm described in this section

is only used for the ULA measurements.

750 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 4, AUGUST 2012

Fig. 3. Third floor of an office building in Ghent.

Fig. 4. Flowchart of methodology for the virtual channel sounder method.

Fig. 5. PDF (transceiver in an adjacent room) and explanation of automaticdetection algorithm.

Let us denote by τnoise the delay corresponding to Pnoise . Thereverberation time is derived by performing a linear regressionfit between Tmean and τnoise as shown in Fig. 5, with

Tmean =∫

τP (τ)dτ∫

P (τ)dτ

where we replace APDP(τ ) by P(τ ) for notation convenience.

C. Absorption Area and ACS

When electromagnetic fields propagate in a room, rays im-pinge walls, objects, ceiling, possibly human(s), etc. and thisresults in an absorption area, i.e., the total surface absorbed byradiation. Considering all objects fixed (except people), the ab-sorption area will only vary according to the number of peoplein the room. The total effective absorption area is given by

A′n = A′

0 + n × ACS

where A′n is the total effective absorbing area, A0 is the effective

absorbing area without people, n ∈ N is the number of people inthe room, and ACS is the absorption cross section (we assumethat all present persons have the same ACS), i.e., the humanbody surface absorbing electromagnetic radiation.

The methodology is based on room electromagnetics theory[7], which states that all losses in a closed room can be describedwith a single parameter, called the reverberation time and isdetermined from the PDP (see Section III-A).

From the reverberation time [7] it is possible to assess theeffective absorption area A′

n :

A′n =

4V

cτn

where V , c = 3×108 m/s, and τn are the room volume, thelight velocity, and the reverberation time when n person(s) arepresent in the room, respectively.

By varying the room occupation with people, the effectiveabsorbing areas as a function of the number of people (n = 0, 2,3, 7, 10, etc.) are obtained from the reverberation times values.The ACS is then the slope of the linear regression of the pointsrelated to the different absorbing areas for the different numberof people (see Section V-A).

D. Calculation of SAR From ACS and Vice Versa

As stated in Section I, the SAR is the physical quantityused for defining the basic restrictions [8]. Basically, SARwb is

BAMBA et al.: EXPERIMENTAL ASSESSMENT OF SPECIFIC ABSORPTION RATE USING ROOM ELECTROMAGNETICS 751

defined as the amount of power absorbed by an individual permass unity, and is given by

SARwb =Pabs,pers

m

=Pabs,pers,dif + Pabs,pers,los

m(1)

where Pabs,pers , Pabs,pers,dif , and Pabs,pers,los are the totalpower absorbed, the diffuse power absorbed, and the powerabsorbed due to LOS component, respectively, by a person inW and m is his/her weight in kg.

In room electromagnetics analysis, a person is exposed totwo sources of power, i.e., the diffuse scattered field from thereverberation phenomenon and the coherent power from theLOS component.

First, the power absorbed due to the diffuse multipath com-ponents (DMC) is determined. The power density in the diffusefield has been investigated in [1], and expressed as follows:

Idif =1

πA′ e− d 0

c τ ∗ ηpol

where d0 , λ, and ηpol are the shortest distance (separation) be-tween the transceivers, the wavelength, and the polarizationfactor of the DMC, respectively. Assume that the DMC is com-pletely diffuse (the polarization is then completely random), apolarization factor of 0.5 is considered.

The power absorbed by a person in a diffuse field is definedas

Pabs,pers,dif =∫ 2π

0

∫ π

0I ′dif (θ, φ)A(θ, φ) cos θ sin θdθdφ

(2)where I ′dif (θ, φ) is the receiving radiance in W.sr−1 .m−2 . Be-cause in completely diffuse field the intensity is independent ofthe direction (azimuth-elevation), (2) is now expressed as

Pabs,pers,dif = I ′dif

∫ 2π

0

∫ π

0A(θ, φ) cos θ sin θdθdφ

= Idif × Aaverage

≡ Idif × ACS (3)

where Idif and A(θ, φ) are the incoming irradiance in W.m−2

and the ACS from an incident plane wave, respectively.In general, A(θ, φ) is not known excepted from numerical

calculations. From the measurements, we know the averagewhole-body ACS (Aaverage), which is equivalent to the ACS.

Second, the power absorbed by a person due to the LOScomponent is

Pabs,pers,los = Ilos × A(θ0 , φ0)

= Ilos × Alos (4)

where Ilos is the LOS component power density, which is di-rection independent because an antenna with isotropic radiationpattern (fields coming from all directions with the same magni-tude) is used.

The power density for the LOS component (Ilos) is computedfrom the received LOS component and the receiving area of theRx antenna and will be investigated in Section V-B.

TABLE IIPARAMETERS FROM CHANNEL SOUNDER MEASUREMENT

TABLE IIIPARAMETERS FROM VIRTUAL CHANNEL SOUNDER MEASUREMENT

A(θ0 , φ0) is still unknown, but let us assume the following:the LOS component only sees one side of the body, and the frontand back of a body are identical in terms of surface. So we cansay that Alos = A av e r a g e

2 = ACS2 ; hence, (4) becomes

Pabs,pers,los = Ilos ×ACS

2. (5)

Using (1), (3), and (5), the whole-body SAR is defined as

SARwb =ACS(Itotal + Idif )

2m

where Itotal = Ilos + Idif is the total incident power density.

IV. BENCHMARKING

A. Channel Sounder Versus Virtual Channel Sounder

In order to validate the measurement system, we compare theresults of the channel sounder with those of the virtual channelsounder. The measurements campaign has been performed inthe same room in Aalborg with both measurement systems. Theroom volume is about 118 m3 . The measurements have beendone at different dates and the Tx and Rx locations were thesame (as best as possible) for the two measurement campaigns(see Section II).

Tables II and III summarize the results for the reverberationtime obtained for both measurement systems. D, Pers., Tmean ,and A′ represent the Tx–Rx separation, the number of personsin the room, the mean-delay arrival time of the rays, and theabsorption area, respectively.

As we are mainly interested in the reverberation time τ , wefocus the comparison on this parameter as illustrated in thediagram chart in Fig. 6. For the channel sounder, we obtaina mean value of τ (τmean ) equal to 24.5 ns with a standarddeviation στ equal to 1.7 ns which is 6.9% of τmean . We obtain

752 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 4, AUGUST 2012

Fig. 6. Channel sounder and the virtual channel sounder.

τmean = 25.8 ns and στ = 1.6 ns (6.2% of τmean ) for the virtualchannel sounder.

The deviation between reverberation time obtained with thetwo measurement systems is only about 1.3 ns (5.2% of theirmean value).

The observed small discrepancies between the results of thetwo measurement systems may be due to the following reasons.

1) Differences between the measurement system setups.2) Variations in Tx–Rx positions: for a certain position, the

Tx–Rx separation may not be exactly the same for thetwo measurement campaigns (second column of TablesII and III). The theory actually says that the reverberationtime should be independent of the location, assuming onlydiffuse scattering.

3) Furniture, tables, people, etc. were not exactly in the samepositions for both measurement campaigns.

4) Different number of people in the room as illustrated inthe diagram chart (see Fig. 6)

Given the small deviations between the reverberation timeobtained for each measurement system at different locations,we can say that the reverberation time is independent of thetransceiver location, as suggested by the room electromagneticstheory [7], regardless of the measurement system. However, weobserve that the results obtained with the channel sounder aresystematically lower than the ones obtained with the virtualchannel sounder; this might be due to different polarizations ofthe used antennas.

B. Different Antennas

Using the virtual channel setup, we investigated the rever-beration time variation using different antennas. We first use abroadband omnidirectional biconical antenna of type Electro-Metrics EM-6116 denoted “ibbt” and the “laptop antennas”mentioned in Section II-B denoted here as “aau.”

For the biconical antenna (ibbt), we obtain a mean value ofτ (τmean ) about 25.9 ns whereas we obtain τmean = 24.1 ns forthe laptop antenna, which gives a difference of 1.8 ns (7.2% oftheir mean value). Table IV summarizes the results for differentantennas. Few variations between the results are observed, butthis was expected due the reasons mentioned in Section IV-Aexcept that we used here the same measurement system. Again,we find almost the same values of the reverberation time usingone measurement system with different antennas, indicating that

TABLE IVPARAMETERS FOR DIFFERENT ANTENNAS USING THE VIRTUAL CHANNEL

SOUNDER, IBBT = BICONICAL ANTENNA, AND AAU = LAPTOP ANTENNA

the reverberation time is independent of the antennas althoughit should be noted that the polarization might have a slightinfluence if a special algorithm is not used to extract only thediffuse part.

C. Reverberation Time in an Adjacent Room

Up to now, reverberation times were investigated for Tx–Rxlocated in the same room (see Section IV-A).

The reverberation time when the transmitter (Tx) is locatedin a room adjacent to the receiver (Rx) room is investigatedhere. The transmitter is located in room C3/3-4 and the receiveris located in room C3/3-3 (see Fig. 3). The basic theory is thesame as the case where the transmitter is located in the sameroom, unless that there is an energy exchange between the tworooms for the coupling elements case [6]. Let the transmitterbe located in room RTx (C3/3-4) and the receiver in room RRx(C3/3-3). Both rooms are closed and separated by a wall withsurface S.P(t) is the power transmitted in room RTx ; α is thewall transmission factor.

In the following, we assume complete diffuse field in bothrooms, and then the power density is direction independent, i.e.,I(θ, ϕ) = I .

The room RRx is fed by two sources.1) α2P (t), which is the transmitted LOS power scaled by the

wall transmission factor.2) Pexch , which is due to the exchanged energy from RTx to

RRx through surface S by the diffuse field.These received input powers in room RRx are balanced by

the increase in energy per second and the losses through wallsas follows [6]:

α2P (t) + Pexch = VdWRx

dt+

cηA

4WRx (6)

where V is the volume of the room where Rx is located, η is thewall absorption factor, and A is the total absorbed area.

The energy W and the power density I in the two roomsare related as follows: WRx = α2 × WTx and IRx = α2 × ITx .Assuming that the radiance ITx(θ, ϕ) is in the diffuse field andimpinges uniformly on wall S (with α being its transmissionfactor), then the transmitted power via the surface S to the roomRRx is

Pexch = S

∫ 2π

0

∫ π2

0α2ITx(θ, ϕ) sin(θ) cos(θ)dθdϕ,

= πα2ITxS

= πIRxS.

BAMBA et al.: EXPERIMENTAL ASSESSMENT OF SPECIFIC ABSORPTION RATE USING ROOM ELECTROMAGNETICS 753

Fig. 7. Reverberation time investigation.

Using WRx = 4π IR xc [7] (c is the velocity of light in the vac-

uum), Pexch is expressed as a function of WRx as follows:

Pexch =cS

4WRx . (7)

If the source is turned OFF, i.e., P (t) = 0 and using (7), (6)becomes

VdWRx

dt+

c

4(ηA − S)WRx = 0

which is a homogeneous equation with the solution

WRx = W0e− t

τ

with

τ =τ0

1 − SηA

. (8)

Here, τ0 = 4VcηA is the reverberation time when both Tx and Rx

are located in the same room RRx , i.e., room C3/3-3, ηA = A′

is the effective area of the total absorbing surface in room RRx ,and V is the volume of the room RRx . The volume V is roughlyabout 360 m3 .

From (8), it is easy to check that τ > τ0 for S < A′. Physi-cally, τ > τ0 could be explained by the exchanged energy be-tween both rooms, making the reverberation time more longer.The measurement results are shown in Fig. 7. The mean val-ues of the reverberation time when the transceivers are locatedin the same room and adjacent room are τ0 = 45.32 ns andτ = 58.90 ns, respectively. It is clear from Fig. 7 that τ0 (Tx andRx in the same room) is lower than τ (Tx and Rx in adjacentroom) as shown in (8). The variation of the reverberation timein both cases is related to the number of people in the room,given that this influences the total absorbing area and hence thereverberation time.

From the measurements in Fig. 7, we obtain τ0τ |meas =

45.3258.90 = 0.769. From (8), we deduce τ0

τ |calc = 1 − SA ′ . The sur-

face S being about 28 m2 and the effective area A′ = 105.7 m2

(derived from τ0 measurement), we obtain τ0τ |calc = 1 −

28105.7 = 0.735. This shows that the measurement results are in

Fig. 8. Absorption area as a function of room occupation.

TABLE VACS FROM MEASUREMENT DATA

good agreement with the calculation of the theory as both ratiosagree excellently.

V. EXPERIMENTAL DETERMINATION OF SARwb

A. Absorption Cross Section

The measurements were performed in an office environ-ment (room C3/3-3, volume ≈ 360 m3) in Ghent, Belgium (seeFig. 3). Three spatial locations for the Tx and one location forthe Rx are selected. Data of both frequencies 2.30 and 3 GHzwere used. An illustration of the absorption area as a function ofroom occupation is shown in Fig. 8. The measurement results interms of ACS for the different locations and the two frequenciesare summarized in Table V. The average ACS at 2.3 GHz isabout 0.34 and 0.36 m2 at 3 GHz. We notice that the ACS variesslightly as a function of the frequency.

Assuming that the mean weight and height of people undertest are 70 kg and 175 cm, respectively, we obtain from Fuji-moto’s formula [14] a mean BSA of about 1.79 m2 . From thecorrelation between the BSA and the ACS at 2 GHz [12], wederive an ACS of about 0.49 m2 . Recently, the authors [15] haveinvestigated the surface of the visual human (VH) illuminatedby a plane wave at 2.1 GHz for three orientations (front, rightside, and oblique). An illuminated surface of about 0.44, 0.23,and 0.39 m2 has been found for the front, right side, and obliqueorientation, respectively.

It should be acknowledged that the persons may not be ex-posed identically, leading to the observed small differences.

754 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 4, AUGUST 2012

B. Power Density

As already stated in Section III-D, power illuminating a per-son is absorbed in two ways in a closed environment, namelyby the LOS component and by the diffuse part. There may bealso a power absorption due to the specular components (causedby specular reflections), but we do not take this into account inthis paper because of the room electromagnetics theory sim-plification. In this section, we investigate the power density ofthese two components for the transceivers located in the sameroom. The LOS component power density is calculated fromthe experimental received power at a certain position and the Rxreceiving area. The LOS component power density is [16]

Pd =Pr

Aeff(9)

where Pd , Pr , and Aeff are the power density, the received power,and the effective area of the receiving antenna, respectively.

The use of the hypothetical isotropic antenna allows us to

write that Aeff = Aisotr. = λ2

4π [16]. Since we measure the re-ceived power and the wavelength is known, it is then easy toderive the power density from (9). Its expression is as follows:

Pd = 4πPr

λ2 .

This is the experimental way to measure the power density of theLOS component. Since the power density of the LOS componentis determined from the PDP, the LOS component amplitude isof main importance whereas its arrival time is nonrelevant. TheFLAT TOP window has the best amplitude accuracy because ofits largest wide-main-lobe. The FLAT TOP window has beenused in the IFFT computation leading to the determination ofthe LOS component power density.

Theoretically from a distance d of the transmitter, it is ex-pressed as

Pd =Pt

4πd2

where Pt is the radiated power by the transmitting antenna.The diffuse power density is derived at a certain position

using (2) once the reverberation time and the absorption areaare known. Fig. 9 shows the power densities (LOS, diffuse) fordifferent distances in the same room (room C3/3-3 in Fig. 3) foran input power of 1 W. The experimental LOS power densityagrees with the theoretical LOS power density.

The LOS power absorption is important in the vicinity ofthe transmitting antennas, i.e., in a radius smaller than 4 m.As we move away from the transmitter, the LOS power den-sity decreases dramatically, making the power absorption lesssignificant for higher distances. Experimental and theoreticalresults for the diffuse power density agree very well, althoughit should be admitted that the theoretical results use the experi-mental reverberation time and absorption area (only the distanceis actually theoretical); see (2).

The diffuse power also decreases with increasing separation.As shown in Fig. 9, the LOS field dominates the diffuse field inthe vicinity of the transmitter, whereas the diffuse field is dom-inating for long Tx–Rx separation. This leads to the so-called

Fig. 9. Power density for 1 W input as a function of separation between Txand Rx.

TABLE VIREVERBERATION DISTANCES

reverberation distance. At the reverberation distance location,the LOS field and the diffuse field have the same intensity. Itstheoretical expression has been investigated in [7], and is definedas

Rd =12

√DtDrA′

where Rd , Dt , and Dr are the reverberation distance, the trans-mitter, and the receiver antenna directivity, respectively.

In a completely diffuse field, the power density is directionindependent; thus, the directivity of the antennas is unity, i.e.,Dt = Dr = 1. The results of the reverberation distance accord-ing to the Tx–Rx position are shown in Table VI. We obtaina mean reverberation distance of about 5.16 m while a stan-dard deviation of about 0.09 m is obtained. This Rd agreesexcellently with the intersection of the LOS and diffuse powerdensity in Fig. 9. So we conclude that the measurement is ingood agreement with the theory.

The slope of the decrease of the diffuse power derived from

(2) is − 10×log1 0 (e)cτ (in dB), which is only dependent on the

reverberation time, meaning that in a large room the scatteredpower density tends to be constant, or at least within a certainrange of Tx–Rx separation. For the room investigated here (τ ≈45 ns), the slope is about 0.32 dB/m, and hence, we can con-sider the scattered power density as constant—we take the meanvalue—given that a maximal deviation between the extrema isonly about 2 dB.

C. SARwb Calculation and Application

In this section, the whole-body SAR is calculated using themethod in Section III-D. The results will be compared with the

BAMBA et al.: EXPERIMENTAL ASSESSMENT OF SPECIFIC ABSORPTION RATE USING ROOM ELECTROMAGNETICS 755

absorption calculated using a statistical method [9], and with acalculation proposed in [10]. An ACS of about 0.34 m2 (height= 175 cm and weight = 70 kg) at 2.3 GHz has been obtainedin Section V-A. If we assume a total incident power density of1 W/m2 and a mean diffuse power density of about 2.3 mW/m2

(see Section V-B), a whole-body SAR of 2.43 mW/kg is obtainedusing the method proposed in Section III-D.

In [10], the whole-body averaged SAR calculation has beenperformed from 100 MHz to 3 GHz at the basic 2 mm resolu-tion of the voxel model NORMAN using the FDTD algorithm.SARwb of about 3.77 mW/kg has been found at 3 GHz. It isnoteworthy to mention that the NORMAN phantom character-istics used in [10] are different from the characteristics used inthis paper. In [9], a statistical method is applied for the SARwb

calculation in an indoor pico-cell environment at 2.45 GHz witha spheroid average man with same characteristics (weight andheight) as for our experiment and a mean SARwb of about2.7 mW/kg has been obtained. We obtain excellent agreementbetween this result and our measured SARwb . The authorsof [17] investigated the whole-body SAR for different phan-toms from 20 MHz to 2.4 GHz. A whole-body SAR of about3.75 mW/kg is found for the VH, Zubal, and Korean model at2.4 GHz. For the Norman model, a whole-body SAR of 6.25mW/kg is found at 2.4 GHz whereas a value of 7 mW/kg isfound for the female Japan model at the same frequency. Thispaper highlights the variability of the whole-body averaged SARaccording to the phantoms.

The small deviation from our experimental SARwb and theresults in [9], [10], and [17] may be explained by the differencein the phantom shapes and the postures. For instance, for thesame BSA of 1.78 m2 the ACS variation may reach 0.15 m2 fortwo different phantoms shapes and/or postures [12], resulting adifference of 1.07 mW/kg in SARwb . Compared to the resultsobtained in [9], [10], and [17], mention that our method leadsto the lowest value in terms of absorption. This is mainly dueto the fact that we have determined the ACS in an office roomwith people working, meaning all the people in the room weresitting whereas phantoms are standing in the other papers.

As an application, we investigate now SARwb using an actualtransmitted power for WiFi to show that our method enables usto estimate whole-body SAR without the need of simulations.We assume an office scenario with a WiFi access point installedin a room. The maximum allowed effective isotropic radiatedpower (EIRP) for 802.11 wireless LAN in a 2.4 GHz bandis 100 mW [18]. Using this transmitted power and the powerdensity in Section V-B, SARwb can be determined. Fig. 10shows SARwb in a person for different distances from the accesspoint radiating with an EIRP of 100 mW. SARwb in a persondecreases of course with distance with values of 0.17 mW/kg at0.6 m and 0.0012 mW/kg at 10 m. These values are much lowerthan 0.08 W/kg, which is the limitation for the exposure of thepublic [8].

VI. CONCLUSION

Based on a simple theory called room electromagnetics, wehave found interesting properties of the reverberation time. The

Fig. 10. Whole-body SAR at 2.30 GHz for 100 mW input as a function ofdistance (in the same room).

difference in values measured by two systems and differentantennas has been discussed. Results confirming that the rever-beration time is location and antenna independent have beenpresented, although the antenna polarization might have a smallinfluence. It is possible to make use of a virtual channel sounderto measure the reverberation time. Room electromagnetics the-ory has been applied for the first time in adjacent rooms, andthe measurement results are in excellent agreement with the de-veloped theory. Further, a novel and easy method to assess theACS has been proposed. We found an ACS of about 0.34 m2 at2.3 GHz and 0.36 m2 at 3 GHz, confirming that the measurementresults are in good agreement with the literature. The theory forthe power absorption for the LOS component and for the dif-fuse field has been investigated. Using the measurement-basedACS, a whole-body SAR of 2.43 mW/kg is found in a realisticenvironment, in agreement with computational and statisticalmethods. The main advantage of the proposed method is thatit does not require any simulation nor phantom modeling. Themethod developed here holds only for the vertical polarization;our future research will investigate the correlation between theabsorptions induced by vertical and horizontal electromagneticfields. Hence, the present theory can be extended to the hori-zontal polarization case.

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Aliou Bamba was born in Daloa, Ivory Coast, on De-cember 4, 1984. He received the Graduate degree inmobile radio engineering from the National Instituteof Posts and Telecommunications, Rabat, Morocco,in 2009, and the Master degree in advanced tech-niques for mobile communications from the Univer-sity of Lille, Lille, France, in 2010.

Since August 2010, he has been a member of WicaResearch Group with Prof. L. Martens as a ResearchEngineer at the Department on Information Tech-nology (INTEC), Ghent University, Ghent, Belgium.

His research interests include room electromagnetism and the human impact onwireless MIMO channels.

Wout Joseph (M’05) was born in Ostend, Belgium,on October 21, 1977. He received the M.Sc. degree inelectrical engineering from Ghent University, Ghent,Belgium, in July 2000, and the Ph.D. degree fromthe Department of Information Technology (INTEC),Ghent University, in March 2005.

From September 2000 to March 2005, he was aResearch Assistant in the Department of InformationTechnology (INTEC), Ghent University. During thisperiod, his scientific research was focused on elec-tromagnetic exposure assessment. His research work

dealt with measuring and modeling of electromagnetic fields around base sta-tions for mobile communications related to the health effects of the exposure toelectromagnetic radiation. This work later led to the Ph.D. degree. In April 2005,he was a Postdoctoral Researcher at IBBT-Ugent/INTEC (Interdisciplinary in-stitute for BroadBand Technology). In October 2007, he was a PostdoctoralFellow of the FWO-V (Research Foundation-Flanders). Since October 2009, hehas been a Professor of Experimental Characterization of Wireless Communica-tion Systems. His professional interests include electromagnetic field exposureassessment, propagation for wireless communication systems, antennas, andcalibration. Furthermore, he specializes in wireless performance analysis andquality of experience.

Jørgen Bach Andersen (M’68–SM’78–F’92–LF’02) received the M.Sc. and Dr.Techn. degreesfrom the Technical University of Denmark (DTU),Lyngby, Denmark, in 1961 and 1971, respectively.He also received an Honorary degree from Lund Uni-versity, Sweden, in 2003 .

From 1961 to 1973, he was with the Electromag-netics Institute, DTU, and since 1973, he has beenwith Aalborg University, Aalborg, Denmark, wherehe is currently a Professor Emeritus. He has been aVisiting Professor in Tucson, Arizona, Christchurch,

New Zealand, Vienna, Austria, and Lund, Sweden. From 1993 to 2003, he wasthe Head of the Center for Personkommunikation (CPK), dealing with modernwireless communications. He has published widely on antennas, radio wavepropagation, and communications, and has also worked on biological effects ofelectromagnetic systems. He was on the management committee for COST 231and 259, a collaborative European program on mobile communications.

Dr. Andersen was a former Vice President of the International Union ofRadio Science from which he was awarded the John Howard Dellinger GoldMedal in 2005.

Emmeric Tanghe was born in Tielt, Belgium, onAugust 31, 1982. He received the M.Sc. degree inelectrical engineering from Ghent University, Ghent,Belgium, in July 2005, and the Ph.D. degree fromthe Department of Information Technology, GhentUniversity, in May 2011.

From September 2005 to May 2011, he was aResearch Assistant at Interdisciplinary Institute forBroadBand Technology/Department of InformationTechnology, IBBT-Ugent/INTEC, Ghent University.His scientific work focused on the modeling of indoor

and outdoor propagation through field measurements. This work later led to thePh.D. degree. Since May 2011, he has been a Postdoctoral Researcher at thesame institution and continues his research in propagation modeling.

BAMBA et al.: EXPERIMENTAL ASSESSMENT OF SPECIFIC ABSORPTION RATE USING ROOM ELECTROMAGNETICS 757

Gunter Vermeeren was born in Zottegem, Belgium,on March 9, 1976. He received the M.Sc. degree inindustrial engineering from the KAHO Sint-Lieven,Ghent, Belgium, in July 1998, and the M.Sc. degree inelectrical engineering from Ghent University, Ghent,Belgium, in July 2001.

From September 2001 to September 2002, he wasin the Research and Development Department, Net-work Integrator Telindus, Leuven, Belgium. SinceSeptember 2002, he has been a Research Engineerin the WiCa Group, Ghent University, of Prof. L.

Martens, where he is currently involved in several projects in the field of radiofrequency dosimetry, electromagnetic exposure, and on-body propagation. Hisresearch is in the area of numerical modeling as well as measurements of elec-tromagnetic fields in the proximity of humans.

David Plets was born in 1983 in Torhout, Belgium.He received the M.Sc. degree in electrotechnical en-gineering with ICT as the main subject from GhentUniversity, Ghent, Belgium, in July 2006, and thePh.D. degree in May 2011 with a dissertation on thecharacterization and optimization of the coverage ofdigital wireless broadcast and WLAN networks.

He is currently a member of the WiCa ResearchGroup, Department of Information Technology-INTEC, Ghent University, where he mainly focuseson the performance and propagation of wireless tech-

nologies, such as DVB-H and WiFi.

Jesper Ødum Nielsen received the Master’s degreein electronics engineering in 1994 and the Ph.D. de-gree in 1997 both from Aalborg University, Aalborg,Denmark.

He is currently an Associate Professor with theDepartment of Electronic Systems, Aalborg Univer-sity, where main areas of interests are experimentalinvestigation of the mobile radio channel and the in-fluence mobile device users have on the channel. Hehas been involved in MIMO channel sounding andmodeling, as well as measurements using live GSM

and LTE networks. In addition, he has been working with radio performanceevaluation, including over the air testing of active wireless devices.

Luc Martens (M’92) was born in Gent, Belgium,on May 14, 1963. He received the M.Sc. degree inelectrical engineering from Ghent University, Ghent,Belgium, in July 1986, and the Ph.D. degree from De-partment of Information Technology (INTEC), GhentUniversity, in December 1990.

From September 1986 to December 1990, he wasa Research Assistant in the Department of Informa-tion Technology (INTEC), Ghent University. Duringthis period, his scientific research was focused on thephysical aspects of hyperthermic cancer therapy. His

research work dealt with electromagnetic and thermal modeling and with thedevelopment of measurement systems for that application. This work later ledto the Ph.D. degree. In January 1991, he was with Wireless and Cable ResearchGroup, INTEC. Since 2004, this group has been also part of the InterdisciplinaryInstitute for BroadBand Technology. Since April 1993, he has been a Professorin electrical applications of electromagnetism at Ghent University. His researchinterests are related to the physical layer of wired and wireless networks.