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\DOI{10.5802/crphys.182}
\datereceived{2023-07-27}
\daterevised{2023-12-11}
\datererevised{2024-03-05}
\dateaccepted{2024-03-14}
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\dateposted{2024-05-15}
\begin{document}

\begin{noXML}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{Energy in the heart of EM waves: modelling, measurements and management}
%\def\cdr@specialtitle@french{L'\'energie au c{\oe}ur des ondes \'electromagn\'etiques : mod\'elisation, mesures et gestion}
%\makeatother

\CDRsetmeta{articletype}{research-article}

\title{Monitoring of the exposure to electromagnetic fields with
autonomous probes installed outdoors in France}

\alttitle{Surveillance de l'exposition aux ondes
\'{e}lectromagn\'{e}tiques \`{a} l'aide de sondes autonomes
install\'{e}es en ext\'{e}rieur en France}

\author{\firstname{Ourouk} \lastname{Jawad}\IsCorresp}
\address{ANFR, 78 avenue du g\'{e}n\'{e}ral de Gaulle, 94700
Maisons-Alfort, France}
\email[O. Jawad]{ourouk.jawad@anfr.fr}

\author{\firstname{Emmanuelle} \lastname{Conil}}
\addressSameAs{1}{ANFR, 78 avenue du g\'{e}n\'{e}ral de Gaulle, 94700
Maisons-Alfort, France}
\email[E. Conil]{emmanuelle.conil@anfr.fr}

\author{\firstname{Jean-Beno\^{i}t} \lastname{Agnani}}
\addressSameAs{1}{ANFR, 78 avenue du g\'{e}n\'{e}ral de Gaulle, 94700
Maisons-Alfort, France}
\email[J.-B. Agnani]{jean-benoit.agnani@anfr.fr}

\author{\firstname{Shanshan} \lastname{Wang}\CDRorcid{0000-0002-3784-8924}}
\address{ETIS, UMR 8051, CY Cergy Paris Universit\'{e}, ENSEA, CNRS,
F-95000, France}
\email[S. Wang]{shanshan.wang@ensea.fr}

\author{\firstname{Joe} \lastname{Wiart}\CDRorcid{0000-0002-8902-5778}}
\address{Chaire C2M, LTCI, T\'{e}l\'{e}com Paris, Institut
Polytechnique de Paris, 91120 Palaiseau, France}
\email[J. Wiart]{joe.wiart@telecom-paris.fr}

\begin{abstract} 
The study is based on a new temporal analysis of exposure based on the
deployment of autonomous broadband E-field monitoring probes in many
French cities. The combination of the probe's data with
frequency-selective in situ measurements performed by ANFR and the
knowledge of the nearby base station antennas, allows to draw
statistical conclusions on the exposure of the population. Indeed, the
data collected by the probes reveal that different periodicities exist
(seasonality, day/night). This paper shows that the monitoring probes
are able to detect the seasonality of the exposure and provide analysis
of correlation between monitoring probes and radio environment.
\end{abstract} 

\begin{altabstract} 
L'\'{e}tude repose sur une nouvelle analyse temporelle de l'exposition
se basant sur le d\'{e}ploiement de sondes autonomes large bande pour
la surveillance du champ \'{e}lectrique dans plusieurs villes
fran\c{c}aises. La combinaison des donn\'{e}es issues des sondes avec
les mesures in situ s\'{e}lectives en fr\'{e}quences effectu\'{e}es par
l'ANFR et la connaissance des stations de base avoisinantes permet de
tirer des conclusions sur l'exposition de la population. En effet, les
donn\'{e}es collect\'{e}es des sondes r\'{e}v\`{e}lent que
diff\'{e}rentes p\'{e}riodicit\'{e}s existent (saisonnalit\'{e},
jour/nuit). Cet article montre que les sondes sont capables de
d\'{e}tecter la saisonnalit\'{e}~de l'exposition et de fournir une
analyse de la corr\'{e}lation entre les sondes et l'environnement
radio.
\end{altabstract} 

\shortrunauthors

\keywords{\kwd{Monitoring}\kwd{Exposure}\kwd{EMF}\kwd{In situ
measurement}\kwd{Principal component analysis}}

\altkeywords{\kwd{Surveillance}\kwd{Exposition}\kwd{Champs
EM}\kwd{Mesure in situ}\kwd{Analyse en composante principale}}

\def\thanksname{Note}
\thanks{This article follows the URSI-France workshop held on 21 and 22
March 2023 at Paris-Saclay.}

\thanks{\textbf{Funding.} European Union's Horizon Europe Framework
Programme under Grant Agreement number 101057622 (SEAWave Project)}

\maketitle

\end{noXML}

\section{Introduction}\label{sec1}

The topic of assessing human exposure to electromagnetic waves is a
continuous subject of discussion leading to important debates in
society. Many studies have been conducted worldwide to assess the
downlink human exposure due to mobile phone base stations or the uplink
exposure due to personal equipment such as mobile phones~\cite{1,2}. In
France, the Agence nationale des fr\'{e}quences (ANFR) is responsible
for the surveillance of the exposure of the public to EMF. Thousands of
in situ measurements are carried out every year~\cite{3}, and ANFR has
fine-tuned the level of exposure due to the deployment of 5G NR
technology through measurements and simulations~\cite{4}. Furthermore,
the compact electronic integration enables the development of new
techniques for EMF monitoring. In fact, city councils and ANFR have
installed tens of autonomous monitoring probes that perform broadband
measurements of the electric field (E-field) several times a
day~\cite{5}. This new measurement technique offers the possibility to
analyze spatiotemporal variations of the exposure level in different
radio environments. 

The domain of the continuous monitoring of E-field has achieved several
significant milestones. In~\cite{6,7,8,9,10,11,13}, different networks
of probes monitoring the E-field are presented. They are located in
different countries: Belgium, Greece, Italy, Serbia and Spain. In most
of the studies, probes are positioned at a fix position but in~\cite{6}
they are not fixed. Many of the papers focus on the architecture of the
probe networks such as~\cite{6,9,11} and do not go deeper in the
statistical temporal analysis. In~\cite{7,8,10,13}, temporal analysis
of the exposure reveals some interesting phenomena such as traffic
fluctuation, variation between day and night or variation between urban
and rural area. In~\cite{12}, a systematic literature review was
conducted on EMF exposure monitoring in various countries, the
conclusion suggests that there is a need for a common method of
temporal analysis. In~\cite{13}, an important milestone is presented
regarding the comparison of temporal analysis of the exposure to EMF in
different European countries (Greece, Spain, Romania and Serbia). The
study compares statistical parameters of the E-field on a yearly basis
in different countries, but it does not include France.

For the first time, this paper presents an analysis of the time
variation of the E-field in France by combining measurements by
autonomous probe with other sources of information, including the
database of in situ measurements and the database of base station
antennas. For this purpose, the available data are presented: the
database of in situ measurements, carried out near autonomous probes,
the database of base station antennas and the database of monitoring
probes. Afterwards, the methodologies are presented: a classical
statistical analysis and principal component analysis (PCA) principles.

Then, the data analysis is carried out, beginning with a general
statistical analysis that reveals daily fluctuations. A general
analysis based on PCA is performed to know if there is any correlation
between the evolution of the exposure level and the radio environment
thanks to in situ measurements and the nearby base stations. The PCA is
also used to detect the temporal patterns over 2022 and the spatial
dependence on the radio environment. The results indicate that the
techniques of statistical analysis are promising methods to reveal
global and local patterns of the exposure related to the cellular
network environment. 

This article presents significant findings on the monitoring of the
E-field. The day-and-night fluctuation of the level of exposure is
analyzed, and an empirical day/night hour interval is found. Based on
the monitoring probes data, for the first time, the daily variation is
characterized and confirms the communicated uncertainty contributor.
PCA method is used on two different datasets. First, PCA helps to
identify the probes which are ideally positioned for monitoring of the
exposure due to radio environment, and second, PCA demonstrates the
presence of seasonality throughout the year.

\section{Available data}\label{sec2}
\subsection{ANFR's base station antennas database}\label{ssec21}

ANFR provides open source data regarding exposure of the French
population. There are two types of data available in raw data format or
plotted on a map~\cite{3}. ANFR gives its legal agreement for the
installation of base stations and keeps the French national antenna
database up-to-date (for antennas with EIRP $>$ 5~W). On the Cartoradio
website, it is possible to check the installed base station antennas
everywhere in France, including details such as technology (2G--5G),
frequency band, mobile operator, azimuthal direction, height of the
antenna~\cite{3}. Information is provided for different types of
networks: TV broadcasting, radio broadcasting, point-to-point fixed
radio relay and cellular network. In this article, only base station
antennas are used. The Cartoradio website provides the locations of the
base stations and shows locations where accredited in situ measurements
have been carried out. Details of measurements and base stations are
available by clicking on the indicators. 

\subsection{Monitoring probe database}\label{ssec22}

City councils, ANFR, and the C2M team of Telecom Paris have installed
autonomous monitoring probes. The monitoring probes were designed by
the EXEM company and measure the three components of the E-field
between 80~MHz and 6~GHz~\cite{23}. The autonomous probe measures the
E-field level (equals to the square root of the sum of the squared
components of the E-field) integrated over the whole frequency
band~\cite{14}. Since 2019, 152 autonomous probes have been installed
in different cities in France. In general, the probes are attached to
outdoor electric poles or other street furniture at a certain height to
avoid access by pedestrians (Figure~\ref{fig1}). The probes measure at
several times of the day and night: every two hours between 1:00~AM and
11:00~PM and each measurement is averaged over 6~min. A website
provided by EXEM gives access to the measurement results of the
probes~\cite{5}. Some of the autonomous probe monitoring data are made
publicly available by city councils.

\begin{figure}
\includegraphics{fig01}
\caption{\label{fig1}3D shape of an autonomous probe and a picture
taken during the installation of a probe on a street pole in Paris,
extracted from EXEM datasheet~\cite{23}.}
\end{figure}

Table~\ref{tab1} below shows the number of autonomous probes per city,
the name of the city or conurbation authority where probes are
installed, and the department code. Cities and conurbation authorities
identify interesting probe locations by targeting locations with a high
density of base stations or near children's schools or major public
places located in city centers.

%tab1
\begin{table}
\caption{\label{tab1}Number of probes per city or conurbation
authority}
\begin{tabular}{ccc}
\thead
Number of probes & \parbox[t]{9pc}{\centering Name of city or
conurbation authority} & Department name (number)\vspace*{2pt} \\
\endthead
\05 & Lille M\'{e}tropole & Nord (59) \\ 
\09 & Paris & Paris (75) \\ 
19 & Massy & Essonne (91) \\ 
\04 & Grand Paris Sud &  Essonne (91) and Seine-et-Marne (77) \\
\07 & Orl\'{e}ans M\'{e}tropole & Loiret (45) \\ 
\08 & Eurom\'{e}tropole de Strasbourg & Bas-Rhin (67) \\ 
\03 & Mulhouse & Haut-Rhin (68) \\ 
10 & Rennes & Ille-et-Vilaine (35) \\ 
50 & Nantes M\'{e}tropole & Loire-Atlantique (44) \\ 
33 & Bordeaux M\'{e}tropole & Gironde (31) \\ 
\03 & Marseille & Bouches-du-Rh\^{o}ne (13)
\botline
\end{tabular}
\end{table}

\vspace*{-2pt}

\subsection{Broadband and frequency-selective in situ measurement
database}\label{ssec23}

ANFR and its partners conduct thousands of in situ measurements
annually. Any French resident can request an in situ measurement at
home or in any public space. The accessible results include the
broadband E-field measurement and the frequency-selective E-field
measurement. In situ measurements follow the ANFR protocol~\cite{17},
which is in line with standard EN IEC 62232:2022~\cite{18}. The ANFR
protocol provides a methodology to assess the level of exposure in
France, while standard EN IEC 62232:2022 is the most detailed standard
for determining RF field strength in the vicinity of the
radiocommunication base stations. The ANFR measurement protocol is
divided into two parts. The first part, called ``case A'', consists of
a broadband E-field measurement at three different heights (1.10~m,
1.50~m, 1.70~m); the level of exposure, expressed in V/m, is the root
mean square (RMS) of the E-field measured at the three heights for six
minutes. Usually, the position of the probe position is typically based
on a hot-spot search, and the technician makes a few measurements to
determine where the exposure is maximum. For the measurement at the
ground level beneath the monitoring probe, the hot spot search is
skipped. The second part of the measurement called ``case B'' consists
of a frequency-selective E-field measurement at the same position as in
case A. The results of the measurement provide an overview of the
contributions of the different technologies using any bands between
100~kHz and 6~GHz.

ANFR regularly analyzes, the exposure to EMF due to base station
antennas with:  
\begin{itemize}
\item the yearly report which investigates the evolution of the
exposure based on the outdoor and indoor in situ measurements (the
yearly report is based on the measurement requested by French
citizens)~\cite{19};
\item the report investigating the evolution of exposure specifically
due to the 5G deployment~\cite{20};
\item the ``city hall square'' campaign, which is carried out every
three years in more than 1000 cities (80\% urban areas and sub-urban
areas 20\%)~\cite{21};
\item and other specific campaigns (smart meters, subway etc.). 
\end{itemize}
These reports show that in a very high majority of cases, the largest
contribution to the overall exposure level is due to cellphone networks
(59\% in 2021). In more than 20\% of the in situ measurements in 2021,
there are no major contributions because the measured level is low and
close to the sensitivity threshold of measurement instruments. For the
rest of the in situ measurements, the major contributions can come from
WLAN, HF bands, or private mobile radio.  

\subsection{ANFR database in a glance}\label{ssec24}

In a nutshell, three databases from ANFR are used in this article. For
the sake of clarity, these databases are presented at a glance in
Table~\ref{tab2}.

%tab2
\begin{table}
\caption{\label{tab2}Description of the ANFR databases}
\fontsize{9.5}{11.4}\selectfont
\begin{tabular}{ccll}
\thead
& Type of data & \multicolumn{1}{c}{Description}  & \multicolumn{1}{c}{Applicant} \\
\endthead
\parbox[t]{5pc}{\centering Base station antennas} & Information & 
\parbox[t]{11.5pc}{\raggedright\hangindent.5pc Base station antennas installed
everywhere in France with description of technology (2G--5G), frequency
band, mobile operator, azimuthal direction, height of the antenna} &
\parbox[t]{8.5pc}{\raggedright\hangindent.5pc Mainly network operators request
installation of base station antennas}{\vspace*{5pt}}\\

\parbox[t]{5pc}{\centering Monitoring probes} & Measurement & 
\parbox[t]{11.5pc}{\raggedright\hangindent.5pc Monitoring probes measuring the three
components of the E-field between 80~MHz and 6~GHz at multiple times of
the day and night: every two hours between 1:00~AM and 11:00~PM and
each measurement is averaged over 6~min} & 
\parbox[t]{8.5pc}{\raggedright\hangindent.5pc City councils, C2M team
and ANFR are the main applicants for probe installation}{\vspace*{5pt}} \\

\parbox[t]{5pc}{\centering In situ measurements} & Measurement & 
\parbox[t]{11.5pc}{\raggedright\hangindent.5pc Measurements in two parts:\Lbreak
$\bullet$ Case A: broadband measurement at three heights for 6~min\Lbreak
$\bullet$ Case B: frequency-selective measurement at the same position as
case A from 100~kHz to 6~GHz}
& \parbox[t]{8.5pc}{\raggedright\hangindent.5pc Usually, the applicants are citizens who ask for in situ
measurements. In this study, ANFR asked for in situ measurements at the
ground level under each probe}\vspace*{2pt}
\botline
\end{tabular}
\end{table}

\section{Methodology}\label{sec3}
\subsection{Classical statistical analysis}\label{ssec31}

The large amount of data enables to make classical statistical
observations on the different magnitudes of the E-field measured by the
probes. Since the measurements are made several times per day and per
night, starting from the installation of the probe, it is possible to
see if there is any common temporal behavior. Comparisons can be made
between day and night exposure levels, or between working hours and
off-duty hours. Since the E-field is measured by the probe in volts per
meter, the root mean square is used to evaluate the mean of the
E-field. For a more general analysis of the variation during 2022, a
more sophisticated statistical method must to be used, in particular to
correlate the level of exposure with the radio environment. Indeed, the
first section highlighted that the seasonality of France has never been
shown, and that the correlation with radio environment data has never
been done either.

\subsection{Principal component analysis (PCA)}\label{ssec32}

PCA is a popular method for analyzing high-dimensional data~\cite{15}.
It is an unsupervised statistical method that allows large datasets of
correlated variables to be reduced to a smaller number of uncorrelated
principal components that explain most of the variability in the
original dataset. Suppose that the dataset X is an N-by-P matrix, where
N observations are the rows of the X matrix and P variables are the
columns of the X matrix. There are mainly four steps involved in PCA:
\begin{enumerate}[(1)]
\item Centralization of the dataset X to characterize deviations
between the observations. It consists in subtracting the mean value of
each variable (i.e. column of X).
\item Computation of the covariance matrix.
\item Computation of eigenvalues and eigenvectors of the covariance
matrix to identify the principal components. Our principal components
that maximize the variance of all projected points onto a 2D space is
the eigenvector of the covariance matrix associated with the largest
eigenvalue. There are several techniques to compute eigenvalues and
eigenvectors, one of the most used within PCA and in this study is the
Singular Value Decomposition.
\item Extraction of scores and loadings: the PCA is then based on the
decomposition of the data matrix into two matrices V and U. The matrix
V is a k-by-P (where k is the number of principal components) matrix
and is usually called the loading matrix. The loadings can be
understood as the weights for each original variable in the principal
components space. The matrix U is called the score matrix. It contains
the original observations in a rotated coordinate system. 
\end{enumerate}
PCA is a well-known method to reduce the dimensions of a data set. In
our case, it may be helpful to find the main components that
characterize the time variability between the autonomous probe
measurements. PCA would help to determine whether the recorded shapes
of the monitoring probe level have similarities or differences. 

\section{Data analysis}\label{sec4}
\subsection{Autonomous probe variability analysis}\label{ssec41}

In this section, data from monitoring probes described in
Section~\ref{ssec22} are used. Figure~\ref{fig2} displays the
Cumulative Distribution Function (CDF) of 110 monitoring probes. The
CDF plotted on Figure~\ref{fig2} gather measurements during the year
2022. The average value of the numbers of measurements used to build
CDF is 4325 measurements per probe. This figure shows the extend of
measured values by monitoring probes. It shows that for a large number
of monitoring probes, the measured values are below 1~V/m. These plots
also show that the number of measurements is very high and that
advanced techniques must be used in order to handle the variability
between probes.

\begin{figure}
\includegraphics{fig02}
\caption{\label{fig2}Cumulative Distribution Functions of E-field
measured by probes which were operating during 2022.}
\end{figure}

Raw data of the E-field measured by probes are too difficult to analyze
(raw data of all monitoring probes are presented in Figure~\ref{fig3}
without filtering for the year 2022), then a selection of a few probes
is necessary. As a starting point, the RMS of the E-field of each probe
was calculated, and we selected three probes with the highest RMS
value. The RMS value was calculated over the data measured during the
year~2022.

\begin{figure}
\includegraphics{fig03}
\caption{\label{fig3}Raw data of E-field measured by all the probes
since installation, showing fast variation on a daily basis and very
low variation over long periods of time.}
\end{figure}

A deeper analysis can be made, based on a different time scale
analysis. Indeed, since measurements are made day and night, a
remaining question is how the level of exposure is evolving between day
and night. Figure~\ref{fig4} shows CDF of the 3 selected probes
(highest RMS) with an empirical time separation: day is between 8~AM
and 11~PM and night is between 11~PM and 8~AM. This plot shows that for
the three highest probes the differences are remarkable. In fact, the
ratio of the average day-value over the average night value is 1.30 for
CorbeilEssones\_01, 1.28 for Le~Haillan\_01, 1.42 for Nantes\_01. For
the probes with the lowest RMS level (not presented in this article),
the level of exposure is not different during the night compared to the
day. This is due to the fact that the lowest RMS probes are installed
far from base station antennas and therefore measure very low levels.

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Day and Night CDF of selected probes (Day 8 AM--11
PM and Night 11 PM--8 AM).}
\end{figure}

The number of measurements and the coverage of many different cities
(urban and suburban) allow for another type of analysis.
Figure~\ref{fig5} displays the coefficient of variation (also called
relative standard deviation) calculated on the basis of the
measurements made during working days and hours (Monday to Friday from
8~AM to 5~PM). Figure~\ref{fig5} shows that the coefficient of
variation is less than 30\% for 86\% of the probes. For the 21 probes
with variation coefficients higher than 30\%, most of the probes
measure very low levels of exposure or have large variations due to
repairs. This information is valuable for ANFR because the uncertainty
budget of the accredited in situ measurements includes a specific
contributor for the daily time variation which is equal to 30\%. It
confirms that the uncertainty contributor due to daily variation is up
to 30\% and it is consistent with the information provided by ANFR.

\begin{figure}
\includegraphics{fig05}
\caption{\label{fig5}Relative standard deviation of all probes by
filtering on working hours (Monday to Friday from 8~AM to 5~PM).}
\end{figure}

\subsection{Data preparation prior to PCA}\label{ssec42}
\subsubsection{Dataset No. 1}

The purpose of this study is to correlate E-field measurements from
monitoring probes with the radio environment. The radio environment is
described by two sources of data. The first source of data consists of
the ``case B'' measurement, also known as the frequency-selective
E-field measurement per band. The bands covered are 700~MHz, 800~MHz,
900~MHz, 1800~MHz, 2100~MHz, 2600~MHz and 3600~MHz and they encompass
every technology (GSM/GPRS, UMTS, LTE and 5G EN-DC) available in
France. The second source of data is the number of base station
antennas near the probe's location. The idea is to tally the number of
base station antennas per band that fall within a circle surrounding
each probe. Figure~\ref{fig6} is a schema illustrating how base station
antennas are included in the final count. The antennas are oriented to
radiate towards a specific direction (called azimuthal direction of
radiation, called $\alpha$ and $\alpha'$ in Figure~\ref{fig6}) to cover
a specific cell. Within the circle surrounding the probe, certain base
station antennas are mechanically oriented towards the probe, while
others are not. A base station antenna is considered if the bearing
angle ${\beta}$ (respectively ${\beta}'$) of the vector going from the
antenna to the probe is in the interval [$\alpha - \Delta \phi/2$,
$\alpha + \Delta \phi/2$] (respectively [$\alpha' - \Delta
\phi/2$, $\alpha' + \Delta \phi/2$]). A standard 
120\textdegree{} angular spread (${=}\Delta\phi$) is used. This rule
applied to the base station antennas in Figure~\ref{fig6} means that
only one base station is considered in the final count. Regarding the
radius of the circle, the assumption has been made that antennas
oriented towards the probe and located at a distance of less than 400~m
should be counted for each cellular band. The rationale behind this
assumption is that for a typical antenna EIRP (average EIRP is 32.6~dBm
based on the ANFR base station antenna database) and a distance of
400~m, the E-field in free space can be estimated to be less than
0.02~V/m, which appears to be sufficient to include any contributor per
band.

\begin{figure}
\includegraphics{fig06}
\caption{\label{fig6}Schema explaining how base station antennas are
considered in the final count.}
\end{figure}

For the sake of clarity, Figure~\ref{fig7} represents the matrix X for
dataset No.~1, composed of variables coming from the three databases:
\begin{itemize}
\item squared of the E-field monthly averaged from monitoring probe
database;
\item squared of the E-field per band from case B in situ measurement
database;
\item and, the number of base stations per band surrounding monitoring
probes from the base station antenna database.
\end{itemize}

\begin{figure}
\includegraphics{fig07}
\caption{\label{fig7}Input matrix for PCA on Dataset No.~1 with
indication of the original database.}
\end{figure}

In order to make sure that the measurements of monitoring probes are
comparable to in situ measurements, a comparison has been made. The
Figure~\ref{fig8} presents the comparison of RMS of E-field measured by
probes with in situ case A measurements. It appears that the plot is
almost linear, which means that both techniques of measurement provide
close results. In situ measurement (carried out by ISO17025 accredited
laboratories) uncertainty budget ($k=1.96$) for case A is 2.3~dB and the
monitoring probe estimated uncertainty of measurement is 3.8~dB in case
the entire bandwidth is considered~\cite{3}. The combined uncertainty
is equal to 4.1~dB, based on metrology rules, 95\% of relative
deviation between in situ measurements and E-field measured by the
monitoring probes should be within the combined uncertainty. The
relative deviations between both techniques of measurement reveal that
95.3\% of relative deviations are within the combined uncertainty. This
result means that monitoring probes and in situ measurement results are
close, even if the measurement positions are separated by a few meters.

\begin{figure}
\includegraphics{fig08}
\caption{\label{fig8}RMS value of E-field measured by monitoring probe
(on the same day) in function of in situ broadband E-field measurement
(``case A'') at the ground under the probe.}
\end{figure}

As explained in Section~\ref{ssec31}, the dataset needs to be
standardized, so in our case it is preferable to use the square of the
E-field. The dataset No.~1 is then composed of the following variables:
the square of the E-field averaged for each month from January to
December 2022, the square of the case B in situ E-field measured under
the probes for each band, and the number of base station antennas
within the 400~m radius for each band. To facilitate the interpretation
of the PCA, the monitoring probes that measure relatively low levels of
exposure have been filtered out. The threshold was chosen based on the
average outdoor level of exposure measured by ANFR, based on thousands
of measurements carried out over many years, and the probes with a 99th
percentile below 1~V/m were filtered out. The input matrix is composed
of $P=26$ variables and $N=79$ observation probes.

\subsubsection{Dataset No. 2}

Dataset No.~2 focuses solely on the time domain, i.e. the square of the
E-field measured by the monitoring probes from January to December
2022. The objective is to detect any time patterns along the monitoring
probes, using the same exposure level filter as in dataset No.~1. The
input matrix consists of $P=12$ variables and $N=79$ observation
probes. For the sake of clarity, Figure~\ref{fig9} represents the
matrix X for dataset No.~2, composed of variables coming from the
monitoring probes database.

\begin{figure}
\includegraphics{fig09}
\caption{\label{fig9}Input matrix for PCA on Dataset No. 2.}
\end{figure}

\subsection{PCA's results}\label{ssec43}
\subsubsection{Dataset No.~1}

Figure~\ref{fig10} shows the dataset No.~1 represented in the two main
principal component coordinates. The probes are represented with
different markers for each French department. Table~\ref{tab3} presents
the eigenvalues and the percentage of total explained variance
providing insight into the importance of the components in terms of
variability. The choice has been made to display only six first
parameters in the table. The proportion of total explained variance
shows that the first two components represent 94\% of the variability. 

\begin{figure}
\includegraphics{fig10}
\caption{\label{fig10}Dataset No.~1 represented on the domain composed
by two main principal components.}
\end{figure}

%tab3
\begin{table}
\caption{\label{tab3}Eigen values for each component and proportion of
explained variance for dataset No.~1}
\begin{tabular}{ccc}
\thead
\# Components & Eigenvalue & \parbox[t]{9pc}{\centering Proportion of
total explained variance (\%)}\vspace*{2pt} \\
\endthead
1 & 92.3991\0 & 62.3 \\
2 & 46.8840\0 & 31.6 \\
3 & 3.1131 & \02.1 \\ 
4 & 1.5063 & \01.0 \\ 
5 & 1.0244 & \00.7 \\ 
6 & 0.8020 & \00.5
\botline
\end{tabular}
\end{table}

The point cloud represented in Figure~\ref{fig10} characterizes most of
the variability of the original dataset. It means that distant points
along the first or second components are very different from each other
with respect to their original data. In Figure~\ref{fig10}, some
distant points/probes in the two principal component coordinate systems
are selected. The name of distant probes selected are displayed on the
plot. The selection of these probes (Saint-Aubin-de-M\'{e}doc\_01,
Mulhouse\_03, Nantes\_01, Paris2Connect\_06, Paris\_8e\_02) for deeper
analysis has the advantage of surrounding the point cloud and of giving
a good interpretation on characterized variability. 

Figure~\ref{fig11} shows the correlation circle for the original
variables of dataset No.~1 represented in the domain of two components
found by PCA. The ``Months variable group'' is the average monthly
squared E-field by the probes, the ``in situ frequency selective
squared of the E-field variable group'' comes from the result of case B
measurement per band at the ground level and the ``\#Antennas variable
group'' are the number of base station antennas surrounding the probes.
It shows that the number of base station antennas per band surrounding
the probes is highly correlated with the first component, and that the
level of exposure measured by probes and averaged monthly is highly
correlated with the second component. The level of exposure measured
through case B measurements on the ground is more correlated with the
second component than with the first.

\begin{figure}
{\vspace*{-1pt}}
\includegraphics{fig11}
{\vspace*{-1pt}}
\caption{\label{fig11}Correlation circle for dataset No.~1 representing
variables projected on the two main components.}
\end{figure}

\begin{figure}
\includegraphics{fig12}
{\vspace*{-1pt}}
\caption{\label{fig12}Square of the E-field during 2022 for the probes
surrounding the principal components.}
{\vspace*{-3pt}}
\end{figure}

\begin{figure}
\includegraphics{fig13}
\caption{\label{fig13}Number of base station antennas close to the
probes surrounding the principal components.}
\end{figure}

\begin{figure}
\includegraphics{fig14}
\caption{\label{fig14}Picture of the position of the Paris2Connect\_06
probe~with surrounding base station antennas.}
\end{figure}

\begin{figure}
\includegraphics{fig15}
\caption{\label{fig15}Picture of the location of the Paris8e\_02 probe 
with surrounding base station antennas.}
\end{figure}

To analyze the principal components characterization, the original data
has been plotted for the five probes surrounding the point cloud.
Figure~\ref{fig12} represents the square of the E-field per month minus
its yearly average for the five probes surrounding the two components
space. \mbox{Figure~\ref{fig13}} represents the number of base station
antennas per band for the probes surrounding the two component space.
The PCA reveals that the first component distinguishes between the
probes located near a high number of base station antennas (on the
right side) and those located near very few antennas (on the left
side). The second component separates the probes with a high
variability (top side) from those with very low variability (bottom
side). These interpretations can be confirmed by comparing the
locations of the different probes. Mulhouse\_03, Nantes\_01 and
Paris2Connect\_06 are installed in open areas (in front of a market,
university hospital, or in the middle of a bridge) but with a high
density of base station antennas. The Paris8e\_02 probe is \mbox{located} in a
highly concentrated area of base station antennas near the Avenue des
Champs Elys\'{e}es, despite being situated on a narrow street without
line-of-sight exposure. Figure~\ref{fig14} displays the location of the
Paris2Connect\_06 probe (pink star) with surrounding base station
antennas, the arrows indicating the azimuthal directions of the base
station antennas. Figure~\ref{fig15} displays the location of
probe~Paris8e\_02 with surrounding base station antennas. Since the PCA
shows that there is a correlation (Figure~\ref{fig11}) between the
continuous broadband monitoring of the E-field and the
frequency-selective case B measurements, it is worth investigating the
impact of base station antennas on exposure levels. Figure~\ref{fig16}
presents the frequency-selective\footnote{Detailed frequency bands: HF
$=$\ [100~kHz; 30~MHz], Private Mobile Radio (PMR) $=$\ [30~MHz;
47~MHz] $\cup$ [68~MHz; 87.5~MHz], FM Broadcasting $=$\ [87.5~MHz;
108~MHz] $\cup$ [174~MHz; 223~MHz], PMR/Radio Beacon $=$\ [108~MHz;
880~MHz] $\cup$ [921~MHz; 925~MHz], TV $=$\ [47~MHz; 68~MHz] $\cup$
[470~MHz; 694~MHz], 700~MHz band $=$\ [758~MHz; 788~MHz], 800~MHz band
$=$\ [791~MHz; 821~MHz], 900~MHz band $=$\ [925~MHz; 960~MHz],
Radars/Radio beacon $=$\ [960~MHz; 1710~MHz], 1800~MHz band $=$\
 [1805~MHz; 1880~MHz], DECT $=$\ [1880~MHz; 1900~MHz], 2100~MHz band
$=$\ [2100~MHz; 2170~MHz], 2600~MHz band $=$\ [2620~MHz; 2690~MHz],
3600~MHz band $=$\ [3490~MHz; 3800~MHz], Radars/Wireless local loop
(WLL) $=$\ [2200~MHz; 6000~MHz], WLAN [2400~MHz; 2483.5~MHz] $\cup$
[5150~MHz; 5350~MHz] $\cup$ [5470~MHz; 5725~MHz].} measurements of the
E-field for the surrounding probes of the PCA on dataset No.~1
(Mulhouse~03, Nantes\_01, Paris2connect\_06, Paris\_8e\_02 and
SaintAubindeMedoc\_01). It shows that the main contribution to the
exposure level comes from cellular networks. Moreover, it shows that
Mulhouse\_03, Nantes\_01 and Paris2Connect\_06 have higher
contributions in cellular bands than Paris\_8e\_02 and
SaintAubindeMedoc\_01. The cellular contributions of Paris\_8e\_02 and
SaintAubindeMedoc\_01 are close to the noise level of the measurement
system. It confirms that the PCA on dataset No.~1 reveals:
\begin{itemize}
\item probes located in a dense area of base station antennas and
measuring a high variability of exposure levels (high level on 1st
component and high level on 2{nd} component, for
instance~Paris2Connect\_06);
\item probes located in a dense area of base station antennas and
measuring a low variability of exposure levels (high level on 1st
component and low level on 2{nd} component, for
instance~Paris\_8e\_02);
\item probes located in a relatively dense area of base stations
antennas and measuring a high variability of exposure levels (average
level on 1st component and high level on 2{nd} component, for
instance~Mulhouse\_03 and Nantes\_01);
\item probes located in the vicinity of few base station antennas and
measuring a very low variability of exposure levels (low level on both
components, for instance~SaintAubindeMedoc\_01).
\end{itemize}

\begin{figure}
{\vspace*{2pt}}
\includegraphics{fig16}
{\vspace*{2pt}}
\caption{\label{fig16}Frequency-selective E-field measurements (case B)
for surrounding probes of PCA.}
{\vspace*{2pt}}
\end{figure}

\subsubsection{Dataset No.~2}

In Figure~\ref{fig17}, Dataset No.~2 is represented in the two main
principal component coordinates. Similar to dataset No.~1, the most
distant probes surrounding the point cloud in the principal component
graph are selected to highlight most of the variability.
Table~\ref{tab4} presents the eigenvalues and the percentage of total
explained variance, which gives an idea of how important the components
are in terms of variability. The proportion of total explained variance
shows that the first two components represent 98.5\% of the
variability. Figure~\ref{fig18} displays the correlation circle for the
original variables of dataset No.~2 represented in the domain of two
components found by PCA. It indicates that all months are equally
correlated to the first component but the second component
distinguishes summer months (top side) from winter months (bottom
side). Figure~\ref{fig19} illustrates the original dataset No.~2 for
the five probes surrounding the\break point cloud.

\begin{figure}
\includegraphics{fig17}
\caption{\label{fig17}Dataset No.~2 represented on the domain composed
by two main principal components.}
\end{figure}

\begin{figure}
\includegraphics{fig18}
\caption{\label{fig18}Correlation circle for dataset No.~2 representing
variables projected on the two main components.}
\end{figure}

\begin{figure}
\includegraphics{fig19}
\caption{\label{fig19}Square of the E-field during 2022 for the probes
surrounding the principal components.}
\end{figure}

%tab4
\begin{table}
\caption{\label{tab4}Eigen values for each component and proportion of
explained variance for dataset No.~2}
\begin{tabular}{ccc}
\thead
\# Components & Eigenvalue & \parbox[t]{9pc}{\centering Proportion of
total explained variance (\%)}\vspace*{2pt} \\
\endthead
1 & 50.6853\0 & 97.4\0 \\
2 & 0.6201 & 1.1 \\
3 & 0.2890 & 0.6 \\
4 & 0.1992 & 0.4 \\
5 & 0.0867 & 0.2 \\
6 & 0.0605 & \0\0\00.1163
\botline
\end{tabular}
\end{table}

The PCA on dataset No.~2 shows that the first component distinguishes
probes with high variability from those with low variability. The
second principal component distinguishes probes installed in cities
where the population density is higher in summer compared to winter,
especially cities located in the south of France. Indeed,
Orl\'{e}ans\_01 is located near a skating rink and a school while
B\`{e}gles\_01 is located near a big hub of railway lines connecting to
the Bordeaux-Saint-Jean train station. Marseille\_03 is situated near
the beach in downtown Marseille. It can be assumed that the probes
surrounding the second component of the PCA in Figure~\ref{fig17}
(Marseille\_03, B\`{e}gles\_01) experience a higher level of exposure
during the summer months due to their proximity to frequently used
areas (beach and railway lines) during summer time. The Orl\'{e}ans\_01
probe measures low level of exposure during summer time because the
skating rink and schools are closed during the summer months.

\subsection{Discussion of PCA results}\label{ssec44}
\subsubsection{Dataset No.~1}

Dataset No.~1 includes monthly averaged E-field measurements from
monitoring probes, frequency-selective E-field measurements (case B)
from in situ measurements and the number of base station antennas per
cellular band surrounding each probe. The purpose of this dataset is to
examine the correlation between the level measured by autonomous probes
and the radio environment described by case B in situ measurements and
number of base station antennas surrounding the probe. Principal
component analysis has revealed probes that are located in dense areas
of base station antennas or probes positioned in areas with very few
base station antennas. PCA reveals probes that measure a high level of
variability and are strongly dependent on the radio environment (high
level on 1st component, high level on 2nd component). PCA reveals
probes which measure a low level of variability and are not impacted by
the radio environment (high level on 1st component, low level on 2nd
component). Finally, the PCA of Dataset No.~1 reveals probes that are
positioned correctly to monitor the E-field produced by the radio
environment. Probes measuring a very low level of exposure can then be
identified easily and repositioned to positions that lead to a higher
fluctuation of the exposure levels. However, some probes are positioned
close to specific buildings (such as schools) and their role is to
monitor low levels of exposure. 

\subsubsection{Dataset No.~2}

Dataset No.~2 contains monthly averaged squared E-field measurements
from monitoring probes. The purpose is to analyze whether there is a
seasonal pattern within the monitoring probes. The principal component
analysis on dataset No.~2 highlights probes that measure temporal
E-fields that present a seasonal pattern. Indeed, probes with 1st
component value higher than zero show a seasonal pattern, probes with
high value on the 2nd component show a higher average level of exposure
during summer time compared to winter time. Probes with negative level
on the 2nd component present a higher averaged level of exposure during
winter compared to summer. Finally, PCA helps us to identify the probes
measuring seasonal patterns (1st component ${>}$ 0), but also identifies
how the summer season is compared to the winter. It shows that the type
of neighborhood where the probe is installed plays a significant role. 

\section{Conclusion and perspectives}\label{sec5}

This study introduces a novel method for monitoring exposure to
electromagnetic fields emitted by radio base stations. It shows that
monitoring probes installed by ANFR, the C2M team of T\'{e}l\'{e}com
Paris, city councils or metropolitan authorities enable the analysis of
the time domain aspect of exposure and the extraction of several
noteworthy observations.

The analysis indicates that the monitoring probes have varying exposure
levels. Probes measuring significant levels show a difference in
exposure between day and night, a phenomenon observed for the first
time in France. An empirical time interval from 8~AM to 11~PM enables
to calculate the ratio of averaged E-field levels between day and
night. This ratio is between 1.28 and 1.42 for the three probes with
the highest RMS level. Several papers, such as~\cite{8,9,10}, have
characterized the day and night fluctuation, but this has never been
demonstrated using French data.

For the first time, the variability of daily working hours has been
quantified for all the probes installed in France. The data shows that
most of the probes exhibit a 30\% variation percentage based on the
data gathered from 8~AM to 5~PM. Based on our knowledge, this is the
first time that the assessment of the daily variation contributor based
on more than 150 probes installed in different environments is
achieved. It confirms the level of daily variation contributor to the
in situ measurement uncertainty budget, as communicated in the
accredited in situ measurement reports~\cite{3,17,18}.

In this study, one of the goals was to correlate different sources of
measurement: monitoring probe measurements and in situ measurements.
In~\cite{13}, an attempt was made to compare different types of
monitoring probes installed in various countries. However, in this
study, we compare in situ measurements to monitoring probes. It has
been shown that measurements by monitoring probes installed on street
furniture and in situ measurements on the ground level beneath the
probes are nearly linear and that the relative deviations are bounded
by the combined uncertainty. This is a satisfactory result,
particularly given that the in situ measurement is taken only a few
meters below the monitoring probe.

The published literature has shown several examples of monitoring
probes~\cite{6,7,8,9,10,11,12,13}, but for the first time a methodology
based on PCA on dataset No.~1 has enabled the detection of probes that
are in the best position to monitor radio environment radiation.
Although the effect of antenna density on the measured field has been
addressed in many studies mentionned in the introduction, for the first
time, a methodology is proposed to detect which probes present a strong
correlation with antenna density. This methodology can also be useful
to displace some of the probes which are installed in high density of
base station area but not in a good configuration of exposure.

For the first time, the seasonality of the level of exposure has been
analyzed at the French national level. The PCA on dataset No.~2
emphasizes the observation that the positioning of the probe is crucial
to observe a remarkable variation of the exposure level. The probe must
not only be installed in an area with many base stations, but also in
close proximity to them and in a line-of-sight position for the
exposure. A large number of probes measuring low exposure levels can be
explained by the fact that the probes are not in a line-of-sight
situation. In some cities, probes were installed in low-density areas
rather than in front of base stations due to public concern over
electromagnetic waves. Upon analysis, we find that some probes measure
a lower level of exposure in summer time. This interpretation was
confirmed with the Principal Component Analysis, which showed that the
second component of the PCA characterizes the difference between probes
with higher exposure in summer or winter. This phenomenon can be
explained by the fact that some of the cities are very touristic during
the summer, leading to increased use of the telecommunication
infrastructure. In general, the exposure levels measured by the
autonomous probe are very low compared to the limits. The increase of
the exposure level is relatively slow, as it has been shown in several
ANFR studies~\cite{4,19,20,21}. 

In future work, statistical clustering methods can be used to group
probes in PCA coordinates and enhance the methodology for detecting
probes with the same E-field pattern. 

\section*{Declaration of interests}

The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

\section*{Funding}

Funding for this research was provided by the European Union's Horizon
Europe Framework Programme under Grant Agreement number~101057622
(SEAWave Project)~\cite{16}. 

\section*{Acknowledgments}

We thank C2M Telecom Paris for their very valuable input. We greatly
acknowledge EXEM company (ANFR's subcontractor) for conducting in situ
measurements, installing monitoring probes, and sharing all the probe
results with ANFR. 

\CDRGrant[EU]{101057622}

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