Bioelectromagnetics32:209^217 (2011)

Statistical PerturbationsinPersonal ExposureMetersCausedby theHumanBodyin

DynamicOutdoorEnvironments

Bego•aRodr|¤ guez,1* JuanBlas,2 Rube¤ nM.Lorenzo,2 Patricia Ferna¤ ndez,2 andEvaristo J.Abril21Center for theDevelopment ofTelecommunicationsof CastillayLeo¤ n CEDETEL,

Boecillo,Valladolid, Spain2Department of SignalTheory, Communications andTelematics Engineering,

Valladolid, Spain

Personal exposure meters (PEM) are routinely used for the exposure assessment to radio frequencyelectric or magnetic fields. However, their readings are subject to errors associated with perturbationsof the fields caused by the presence of the human body. This paper presents a novel analysismethod forthe characterization of this effect. Using ray-tracing techniques, PEM measurements have beenemulated, with and without an approximation of this shadowing effect. In particular, the GlobalSystem for Mobile Communication mobile phone frequency band was chosen for its ubiquity and,specifically, we considered the case where the subject is walking outdoors in a relatively open area.These simulations have been contrasted with real PEMmeasurements in a 35-min walk. Results showa good agreement in terms of root mean square error and E-field cumulative distribution function(CDF), with a significant improvement when the shadowing effect is taken into account. In particular,theKolmogorov–Smirnov (KS) test provides aP-value of 0.05when considering the shadowing effect,versus a P-value of 10�14 when this effect is ignored. In addition, although the E-field levels in theabsence of a human body have been found to follow a Nakagami distribution, a lognormal distributionfits the statistics of the PEM values better than the Nakagami distribution. As a conclusion, althoughthe mean could be adjusted by using correction factors, there are also other changes in the CDF thatrequire particular attention due to the shadowing effect because they might lead to a systematic error.Bioelectromagnetics 32:209–217, 2011. � 2010 Wiley-Liss, Inc.

Key words: PEM; radiofrequency; exposure assessment; exposimeter

INTRODUCTION

Nowadays, personal exposure meters (PEM) areconsidered one of the most appropriate tools to deter-mine personal exposure to radio frequency (RF) fields.They have been employed in epidemiological researchin recent years [Kuhnlein et al., 2009; Viel et al., 2009;Frei et al., 2009a]. Nevertheless, some constraints havebeen reported in the scientific community, such as theshadowing effect caused by the subject’s body [Blaset al., 2007], false summation of signals within thesame band, out-of-band responses, and high calibrationfactors in a few frequency bands [Neubauer et al.,2010]. In addition, the large proportion of measure-ments below the detection limit makes post-processingand data analysis difficult [Roosli et al., 2008].

To overcome these problems, a profound analysisof the measurement data and exposure simulations arerecommended to improve the quality of the classi-fication of exposed individuals [Knafl et al., 2008].Analyses of field–body interactions by means offinite-difference time-domain (FDTD) simulation havebeen carried out over the last fewyears, showing that the

presence of the human body alters the pattern of wavepropagation in its immediate proximity [Blas et al.,2007; Neubauer et al., 2010], consequently inducingexposure assessment errors. This error is defined to bethe difference between the incident wave power beingmeasured and the RF meter reading. Prior FDTD simu-lations with experimental verification showed that inthe region shadowed by the human body, this error canreach up to 30 dB (only 0.1% of the incident powerwould be detected) in the Global System for Mobile

Grant sponsor: Regional Ministry for Public Works of the Junta deCastilla y Leon.

*Correspondence to: Begona Rodrıguez, Aula CEDETEL, E.T.SIngenieros de Telecomunicacion, Campus Universitario MiguelDelibes, 47011 Valladolid, Spain.E-mail: patfer@tel.uva.es

Received for review 15 March 2010; Accepted 24 September 2010

DOI 10.1002/bem.20627Published online 30 November 2010 in Wiley Online Library(wileyonlinelibrary.com).

� 2010Wiley-Liss,Inc.

Communication (GSM) band in a worst-case scenario[Blas et al., 2007]. Other techniques, such as indoor ray-tracing, documented a 25 dB error (only 0.32% of theincident power would be detected) for a frequency of10 GHz [Ghaddar et al., 2004].

Long-term averaging and scattering tend tosmooth this kind of measurement error and, con-sequently, we do not expect large differences in themean values. Firstly, it is clear that time averagingremoves the short-term oscillations, leaving only thelong-term trend. Secondly, although the location ofthe PEM on the body surface is essential with regardto the illumination directions from isolated sources, thisissue may be less important when the person is movingaround in a realistic field situation with multiple scat-terers [Radon et al., 2005]. However, from an epide-miological point of view, it is also evident that meanvalues are only a first approximation, and exposureassessment should be more carefully managed. Itshould not be forgotten that the biological mechanismby which RF can increase the risk of health endpoints isan active research area; consequently, the eventuallyrelevant metric is unknown. For example, metrics suchas the proportion of measurements above the detectionlimit or themaximumvalue are also normally employed[Viel et al., 2009].

In order to simulate the shadowing effect influenceon the RF meter readings, we need to analyze complexmulti-scale scenarios. On the one hand, the emitters aredistributed over relatively large urban and suburbanareas,wheremultipath effects are dominant.On the otherhand, humanmorphological details are also important inorder to model body-worn meter readings. As a result, itoften becomes necessary to combine different numericalmethods. One possible approach to this problem isthe hybrid FDTD/ray-tracing method that has beenemployed by Neubauer et al. [2008]. The major draw-back of this method is its computational cost, whichlimits the possibility of modeling human motion andreduces the number of cases under study to a few genericsituations. As a result, the impact of a changing environ-ment as the individual moves around is extremelydifficult to analyze using these techniques.

It shouldbenoted that someof the highest environ-mental E-field levels in the downlink band are reportedin open areas, together with churches, schools, andkindergarten buildings [Frei et al., 2009b]. We haveselected an outdoor environment to start with because ahigh percentage of the measurements of the PEM areabove the detection limit. Nevertheless, it should alsobe noted that outdoors the person carrying the PEMwillusually be walking. For this reason, it is important tomodel the relative change of position between theperson and the main elements of the environment under

consideration. Ray-tracing is at present the standardmethod employed to simulate the multipath propa-gation process in urban areas, involving several mech-anisms of interaction between the radio wave and theenvironment. Moreover, ray-tracing techniques havealready been proven to be an effective method to dealwith propagation problems involving human motion inindoor scenarios [Ghaddar et al., 2007].

A pure ray-tracing approach is proposed hereto model the exposure assessment errors caused bythe presence of the body of a PEM user who is inmotion in an approximately static outdoor environment.Theoretical simulations have been contrasted withseveral sets of measurements carried out with aPEM. The experimental environment includes severalbuildings in an open area and the measurements weretaken during a significant time interval. Despite thisspatial diversity and the presence of averaging, we willshow that the body shadowing effect still has clearconsequences that affect the field statistics.

MATERIALS AND METHODS

Experimental Setup

Experimental measurements shown in this paperwere done with a PEM DSP 090 exposimeter (Satimo,Courtaboeuf, France). The minimum measurementcycle of this device is 3 s and the maximum is 4 min15 s. It should also be noted that the dynamic marginof the PEM goes from a minimum of 0.05 V/m up to5 V/m. The DSP 090 sets each value below the detec-tion limit to the value of the detection threshold(0.05 V/m), and each value beyond the dynamicmarginto the detection maximum (5 V/m). Finally, the DSP090 contains a triaxial probe with an axial isotropy of�2 dB (20–25% in voltage) in the GSM band. All themeasurements used in this document were performedusing a sampling rate of 3 s. In addition, the PEM wassynchronized with a GPS receiver in order to geo-position each of the data registers. An EMTACBluetooth GPS receiver (Transplant GPS, Byron,MN) was used together with an IPAQ HP H5500Personal Digital Assistant (PDA) (Hewlett-Packard,Palo Alto, CA), which recorded the log files usingthe IGC format defined by the International GlidingCommission. The GPS receiver and PDAwere locatedin the hands of the user and were checked previouslyto ensure that there was no influence on any of thefrequency bands of the exposimeter under study.

The PEMwas carried by a volunteer (26-year-oldfemale, 1.75 m, 74 kg) in a small backpack centeredon the back at a height of 1.40 m, with its vertical axispointing upward. The other two axes of the device,

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considered in this document as horizontal axes, variedaccording to the relative position of the subject withrespect to the base station. Additional measurementswere performed by dragging a dolly, which was set atthe same height where the individual normally carriesthe exposimeter, in order to provide PEM measure-ments in the absence of the body. In this case, theGPS device was attached to the dolly tripod near thePEM and the dolly was dragged by an operator, separ-ated more than 1 m from the PEM, who was walkingbackwards. The operator also carried a PEM in order toprovide simultaneous measurements impaired by thebody shadowing effect.

The PEM data logs shown in this paper wererecorded at the Miguel Delibes Campus of theUniversity ofValladolid (Valladolid, Spain). The exper-imental environment included several buildings in anopen area. These buildings were made of brick andconcrete and had an approximate height of 15 m. Adual-frequency (950 MHz/2150 MHz) system on a30 m tower was the nearest GSM/Universal MobileTelecommunications System (UMTS) base station inthe testing area. A plane view of the campus with themost relevant buildings is shown in Figure 1. Weassumed that GSM broadcast channels with constant

power were the main contribution in the downlink bandduring the experiment. Aiming to reproduce the DSP090 outcome, it should be noted that a distinctionbetween different sources operating in the same serviceband is not possible. Therefore, additional frequency-selective measurements were performed in the GSMdownlink band (935-960 MHz) to discard the presenceof other possible unknown nearby sources, such as otherbase stations not considered in the simulation or non-GSM sources operating in the same frequency band.Additionally, the measurements did not show suddenmeanvariations that could be associatedwith additionalchannels.

Ray-Tracing Modeling

Measurements were compared with a 2.5D ray-tracer based on image theory. In a 2.5D ray-tracer, thebuildings aremodeled as infinitely tall and the influenceof rooftop diffraction is neglected, but rays are treatedas 3D vectors, taking into account the ground reflectioneffect [Son and Myung, 1999; Athanasiadou et al.,2000]. Although rooftop diffraction can be the maincontributor to the total field generated at a receiver innon-line-of-sight areas, these contributions will usuallybe below the detection limit of the PEM. Thus, neglect-ing this effect has no strong consequences in thisparticular study. Building layouts were provided bythe Geographical Information Center of Valladolid.In the past, results have been reported to improve theaccuracy of the geometry, giving better results with acadastre map rather than a simplified one. In particular,the details of each building block, especially openings,are considered to be an important factor for accuratepredictions.

The electromagnetic parameters employed inthe simulations were as follows. The main buildingmaterial was assumed to be concrete with relative per-mittivity er ¼ 7 and conductivity s ¼ 0.2 S/m. Theground material properties were er ¼ 15 and conduc-tivity s ¼ 7 S/m [Tan and Tan, 1995]. The base stationin the GSM band emitted 950 MHz and had an equiv-alent isotropically radiated power of 193.2 W. Weworked with dual-linear polarizations with angles of�45 degrees. The radiation pattern of the base stationwas also taken into account. The direction of maximumgain is indicated in Figure 1 by a blue dotted line. Fordiffraction modeling, we employed an extension ofHolm’s heuristic diffraction coefficient proposed byNechayev and Constantinou [2006].

Our previous work based on FDTD simulationsshowed that the human body is quite opaque when theRF meter is attached close to the body surface in theGSM band [Blas et al., 2007]. Nevertheless, in a multi-path scenario the human exposure is characterized by a

Fig. 1. PlaneviewoftheMiguelDelibesCampusoftheUniversityofValladolid including the personal exposimeter measurements inRoutes1and2.

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number of waves impinging on the human body withdifferent amplitudes and directions of arrival. It is clearthat a shadow region changes with the angle of arrival(AoA) of themain RF contribution. This shadow regionwould depend on the relative position of the PEM withrespect to the base station and the human body. Insteadof calculating all these possible shadow regions indetail, we simplify the problem by assuming that acertain range of rays in azimuth will be blocked bythe human body, and thus theywill reach the PEMmoreattenuated than the rest of rays, as shown in Figure 2.This approach has the advantage of providing a simplerule to accept or discard the rays, regardless of thesource position.

The main purpose of this experiment was to emu-late the PEM measurements; consequently, all the cal-culations at each location of the routes were basedon the incoming rays at the phase center of the PEMisotropic antenna. The AoA of each ray was computedfor each PEM position. Those rays blocked by thehuman body were attenuated by 30 dB according toBlas et al. [2007], which means that only 0.1% of theinput powerwould be detected. It should be noted that inthis framework, a 30-dB attenuation of a ray is almostequivalent to being rejected. Similarly, E-field levelswere quantified at intervals of 0.01 V/m with the pur-pose of emulating the maximum accuracy of the PEM.Finally, the values below the PEM detection limit weresubstituted for the detection limit value in order toemulate the response of the device. It should be notedthat substitution of the non-detects by the detectionlimit leads to an overestimation of the exposure. Inorder to be more accurate, our analysis should haveincluded the regression on order statistics method pro-posed by Roosli et al. [2008]. Nevertheless, it must bestated that the routes included here were performedmainly in the line-of-sight (LOS) area and the percent-age of non-detects was always lower than 25% in the

GSM downlink band. This percentage of non-detectswas far below 60%, when substitution might be accept-able, as explained by Helsel [2006].

It seems reasonable to think that the azimuthinterval of the rejected rays should be related to theLOS between the PEMand the point fromwhich the rayis coming. Consequently, the limit angle of this regioncould be between 60 and 75 degrees, as shown inFigure 2. Although this angle depends on the influenceof the position of the arms as they are swinging whilewalking, there is not an exact unique value. We startedworking with an angle of 65 degrees without consid-ering the possible influence of the arms in detail. Lateron, a study of the influence of this angle will beaddressed.

RESULTS

Twowalking routes of approximately 5 min each,Route 1 and Route 2, were carried out in predeterminedpaths with the aim of both adjusting the model andtesting the shadowing effect. Additionally, a third routewith a lot more samples and spatial variability wasperformed to address a more general case. In this routethe user was asked towalk around in the environment ina randommanner for up to 30 min. A final route, Route4, was added in order to make clearer the effect ofshadowing without the uncertainty introduced by thesimulator.

Firstly, we are going to analyze the routes wherethe shadowing effect was tested. A representation ofthese two routes with the most important buildingsin the area and the base station position is shown inFigure 1. In Route 1 the volunteer was moving awayfrom the base station following a radial trajectory, sothis route is not affected by the shadowing effect; thePEM is always directly illuminated by the GSM tower.In contrast, in Route 2 the subject was walking towardthe base station in samples 11 to 70, as can be observedin Figure 1. Thus, this case should show the influence ofthe shadowing effect. The results of the ray-tracingmodel and the simulations with and without shadowingeffect for Routes 1 and 2 are shown in Figure 3.

It is almost impossible to get a point-by-pointcoincidence due to several effects such as GPS error,ray-tracing model approximations, as well as the PEMaxial isotropy. In general, but especially in Route 1, itshould be noted that the PEM is in the near field withrespect to the body, if we consider it as a secondarysource of radiation. To be strictly correct our analysisshould take into account the possibility of this effect inrelation to all the secondary sources including the build-ings or the ground [Papkelis et al., 2008]. However, thiseffect is not important in order to test the influence of the

Fig. 2. Personalexposuremeter (PEM)positionwithrespect tothehuman body. Cross section of the human body model at 1.45 m(Visible HumanProject [Spitzeret al.,1996]).

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shadowing effect, which is the aim of the present work.Aswe can observe, the statistical parameters such as themean value (indicated in Fig. 3 as horizontal lines) arebetter approximated when considering the shadowingeffect even in Route 1. More importantly, the fact thatthe user is walking toward the base station, as it happensin samples 11 to 70, ignoring the shadowing effectwhen it actually is taking place, produces a clear localerror.

Figure 4 shows the cumulative distribution func-tion (CDF) of both routes. Firstly, it should be noted thatthe CDF is roughly approximated by the ray-tracingtechniques. Secondly, although in Route 1 the differ-ence between considering the body shadowing effect ornot is minimal, in Route 2 there was a significant devia-tion that does not appear when considering the approxi-mation. Although main contributions arrive from thedirect wave, some of the scatterings in the buildingshave an influence on the final results and the humanbody should attenuate them. Thus, Route 1 also im-proves slightly in its approximation of PEM measure-ments considering the shadowing effect. TheKolmogorov–Smirnov (KS) test will be employed inall the CDF comparisons of this study. It provides theprobability of obtaining the same maximum deviationbetween experimental and simulated CDFs, given thatboth of them come from the same random variable;

the bigger the P-values, the closer the deterministicrelationship between reality and simulations [Blaset al., 2009]. In Route 1, the KS test shows almostno variations, while in Route 2 there is an importantimprovement: The P-value increases from 10�14 to0.0024.

Finally, we studied two more general cases thatcontained more than 714 samples. Consequently, theywere recorded during a time interval of 35.7 min, incontrast with the 5 min of Routes 1 and 2. In Route 3 thePEM user followed a more complex path around thecampus, as shown by the darker color in Figure 5. Inthis case, 74% of the measurements were made in LOSwith respect to the base station. Our aim was to checkwhether our model behaved correctly, taking intoaccount different arrival angles and local scatteringscenarios. Above all, we wanted to confirm whetherscattering and long-term trends tend to hide the import-ance of the shadowing effect as it might be thought. Thestatistical comparison for Route 3 is shown in Figure 7.As before, it is clear that the experimental CDF is muchbetter approximated when we take into account theshadowing effect, therefore, it is by no means negli-gible. In contrast, Route 4 was much simpler; in thisroute the user was walking backwards while dragging adolly with the PEM attached, so the speed was slowerthan normal walking speed.

Fig. 3. Experimentaldata and simulation results for Route1 (Top)and Route 2 (Bottom). Mean E-field levels (in V/m) are shown byhorizontallines.

Fig. 4. CDF for Route1 (Top) andRoute 2 (Bottom).

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DISCUSSION

We have introduced a simple approximation tomodel the shadowing effect and we have analyzedseveral routes in a realistic environment. Two of theseroutes are relatively short in order to calibrate themodel, showing two extreme cases where the shadow-ing effect should have a maximum and a minimuminfluence, while the third case includes a considerableincrease in path length and complexity. We will focusour discussion on Route 3 because it is themore generalcase and shows the effects over a longer interval, as itcould be thought that scattering and long-term trendstend to hide the importance of the shadowing effect.This third route was not chosen for a special predom-inance of the shadowing effect. In fact, E-field depend-ence on the azimuth angle was checked to ensure thatthere was no predominance of any particular directionor directions from which the more energetic raysarrived.

A limit angle of 65 degrees was introduced as amodel parameter to decide whether a particular ray isattenuated or not, due to the shadowing effect. It is a keyissue to test whether a slightly different angle wouldcompromise the results. This angle selection was based

on the LOS between the PEM and the radiation sources.Nevertheless, it is important to know how much theseparameter variationsmight affect the results. In order totest this dependence, we have plotted in Figure 6 twopropagation model quality indicators such as the rootmean square (RMS) error, which compares the resultsusing a point-by-point approach, and the KS test. Bothplots are related to Route 3, which is the one with morestatistical power since Routes 1 and 2 have fixed pre-dominant arrival angles, whichmake themunsuitable totest the limit angle.

From Figure 6, it can be deduced that with a limitangle between 50 and 60 degrees the RMS error reachesits minimum value, which is around 6 dB (50% involtage) versus an error of around 7 dB (55% in volt-age). Nevertheless, this error is normally of the sameorder as the error of the shadowing effect. However, theRMS metric is not the best tool to discuss the resultsbecause it penalizes small spatial displacements relatedto electric path-length uncertainties [Blas et al., 2009].In fact, it is almost impossible to reproduce fast-fadingvariations point by point. As a result, the KS testprovides a far better metric for analyzing the accuracyof our propagation model. In terms of the KS test,the better angles to approach the experimental CDFwould be approximately between 40 and 60 degrees. AP-value between 0.02 and 0.05 is obtained by takinginto account the shadowing effect, versus a P-valueof 10�14 obtained without considering it, which isequivalent to a limit angle of 0 degrees in our shadowing

Fig. 5. PlaneviewoftheMiguelDelibesCampusoftheUniversityofValladolid including the personal exposimeter measurements inRoutes 3 and 4.

Fig. 6. Dependenceof theresultsasa functionof the limit angle inRoute 3:Error (Top) andP-value (Bottom).

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effect approximation. Consequently, the KS testindicates that it is almost impossible that the errorsof the model without the shadowing effect are purelyrandom, and thereforewe incur a systematic error whenneglecting this underlying effect.

Moreover, we can see that there is a reasonablerange of limit angles that provide good results. As canbe seen in Figure 7, a limit angle of 65 degrees alsooffers a much better fit to the CDF of the measurementsthan not considering the shadowing effect at all. Thus,the parameter tolerance is relatively good, although itis also clear that there is a large statistical differencebetween considering the shadowing effect or not. Thebest approximation based on the KS test results wasobtained with an angle of 48 degrees, which is lowerthan the angles obtained with the LOS of the PEM. Thisis due to the diffraction effects, which give the rays acertain capacity to bend around the body. Thus, the LOSof the PEM does not give the azimuth interval in whichrays are highly attenuated; in fact, it is smaller.

In addition, the ray-tracing simulation without theshadowing effect has been found to follow a Nakagamidistribution [Nakagami, 1960] as shown in Figure 8.The Nakagami model has been suggested in the past tobe well suited to approximate the signal envelopefluctuations in suburban and open areas, where the fieldis a combination of a scattered field and a direct wave[Okui, 1992]; indeed, quite similar to the framework ofour measurements. Consequently, our findings arecoherent with previous statistical studies. Note thatthe original PEM measurements did not follow aNakagami distribution. In fact, they fit a lognormaldistribution as shown in Figure 8. To the best of ourknowledge, the shadowing effect distribution has notbeen studied in the case of the outdoor GSM band,although the lognormal distribution has already been

suggested in the literature to fit different shadowingeffects, for example in ultra-wideband body area net-works [Fort et al., 2006].

The difference in the mean values between themeasurements corresponding to the PEM and the simu-lations in the absence of the body is around 2 dB, whichis equivalent to an attenuation factor of 1.29. This erroris lower than in Route 2, which was carried out with theaim of making the shadowing effect clearer. However,the effect is still noticeable, despite the random routeand the scattering in buildings. But the most importantissue is that the differences between theCDFs, as shownin Figure 8, are not only limited to themeanvalue. Thus,averaged correction factors may help in the correctionbut they do not reflect all the implications of the shad-owing effect. In more detail, both PEM measurementsand E-field simulations for absence of the body predictsimilar maximum values (0.87 V/m for the PEM mea-surements and 0.86 V/m for the ray-tracing simu-lation). The main differences in Figure 8 are that thePEM tends to predict a greater number of samples in themean levels (0.1–0.2 V/m) than the simulation withoutthe body.Multiplying by the attenuation factor does notchange this fact; it still slightly underestimates themedium E-field levels. Moreover, it would overes-timate the higher and lower E-field levels (becausethey are multiplied by a factor of 1.29), a fact stronglypenalized by the KS test with a P-value of 10�4, mainlybecause of the overestimation in the lowest E-fieldlevels.

It could be argued that it is problematic to comparetwo uncertain parameters. In order to check this hy-pothesis, Route 4 was performed to enable comparingmeasurements of the PEM with and without thebody. The CDFs for both measurements are shown inFigure 9. Firstly, it has to be pointed out that the

Fig. 7. CDF variationswith thelimit angle. Fig. 8. Results from fitting the experimental and simulated datafromRoute 3 usingcommondistributions.

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attenuation factor has grown to 1.46 and the P-valueshows a difference of 10�46, which seems reasonable asthis route has less complexity than Route 3. PEMmeasurements in the presence of the body still followeda lognormal distribution, while PEM measurements inthe absence of the bodywere better fitted to a Nakagamidistribution. Moreover, this fact was confirmed in theDCS downlink band (1805–1880 MHz) and the UMTSdownlink band (2110–2170 MHz). Both bands showeddifferentiated distributions for the measurements withand without the shadowing effect and were better fittedto lognormal and Nakagami distributions, respectively.

CONCLUSION

This paper provides a useful insight regarding thestatistical perturbations associated to the influence ofthe human body on a PEM. An outdoor scenario hasbeen investigated to model RF exposure assessmentinvolving human motion. Open areas have been con-sidered of special interest because normally, campaignsof measurements report some of the highest E-fieldlevels in the downlink band and a high percentage ofthe measurements of the PEM are above the detectionlimit. A technique has been proposed for the identifi-cation and approximation of samples impaired by theshadowing effect, which is related to the blockage ofsignals by the human body while the user is walking inan outdoor environment. This technique has shown agood agreement with PEM measurements in terms ofstatistical accuracy.

In addition, we have analyzed the differencesbetween the PEM measurements and the exposuresimulation without a human body at a time intervalof 35.7 min, with no special predominance of anazimuth angle in which rays will arrive. This differencehas been found to be significant, especially for the CDF

shape. The exposure in the absence of the body shadow-ing effect in a suburban area has been found to fit aNakagami distribution,which had been suggested in thepast to model propagation in similar conditions. Incontrast, PEM-impaired measurements seem to followa lognormal distribution. Moreover, as a conclusion,realistic simulated CDFs could not be exactly found bymeans of an averaged correction factor, although thatapproach offers a roughly approximate solution, especi-ally when the average error in the band is employed forcorrection.

Our data seem to suggest that ignoring the shad-owing effect is a systematic error, rather than a randomerror. Future work in this area will include the gener-alization of the ray-tracing algorithm to representexposure in the whole body, and the extension of thiswork to cover different morphologies. Although furtherresearch on the broader issue of personal RF electro-magnetic field exposure is necessary, we believe thatthis paper has led to a better understanding of thestatistical consequences of the shadowing effect, pre-senting a newmethodology to deal with such problems.

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