AL HAJJ 2022 Archivage

Radio frequency exposure analysis in 5G massive MIMO
systems
Maarouf Al Hajj
To cite this version:

Maarouf Al Hajj. Radio frequency exposure analysis in 5G massive MIMO systems. Networking and
Internet Architecture [cs.NI]. Institut Polytechnique de Paris, 2022. English. �NNT : 2022IPPAT003�.
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NNT : 2022IPPAT003
Radio Frequency Exposure Analysis in

5G Massive MIMO Systems
Thèse de doctorat de l’Institut Polytechnique de Paris
préparée à Télécom Paris
École doctorale n◦ 626 École doctorale de l’Institut Polytechnique de Paris (EDIPP)

Spécialité de doctorat : Information, communications, electronique
Thèse présentée et soutenue à Palaiseau, le 13/01/2022, par
M AAROUF A L H AJJ
Composition du Jury :
Philippe De Doncker
Professeur, Université Libre de Bruxelles Président
Laurent Clavier
Professeur, IMT Nord Europe Rapporteur
Christian Person
Directeur du Lab-STICC, IMT Atlantique Rapporteur
Philippe Martins
Professeur, Télécom Paris Examinateur
Lina Mroueh
Professeur, Institut Supérieur d’Electronique de Paris Examinateur
Emmanuelle Conil
Ingénieure de recherche, Agence Nationale des Fréquences Examinateur
Marceau Coupechoux
Professeur, Télécom Paris Examinateur
Joe Wiart
HDR, Titulaire de la Chaire C2M, Télécom Paris Directeur de thèse
626
1
Acknowledgements
First of all, I would like to express my sincerest gratitude towards my supervisor Joe
Wiart for his support and advice throughout this PhD.
I also thank the ANFR team, and especially Dr. Emmanuelle Conil, for the valuable
collaboration during this PhD. The priceless expertise, and the great perspective they
shared with me paved the way towards completing this PhD.
My thanks also go towards Prof. Philippe Martins and Prof. Laurent Clavier for evalu-
ating this dissertation. Also to Prof. Lina Mroueh, Prof. Marceau Coupechoux, and Dr.
Emmanuelle Conil for examining the dissertation.
Furthermore, I thank Dr. Shanshan Wang for her valuable advice and input, and also
my other colleagues that I have known throughout the years at C2M, for their help and
support: Amirreza, Bader, Nihal, Seyedfaraz, Sirine, Soumaya, Taghrid, Xi, Yuanyuan,
and Zicheng. And to my friends back at home and abroad who are too many to list.
And finally, I am forever grateful to my parents, Sana and Anas, to my siblings, Noema,
Hassan, and Mariam, and to my fiancee Maryame, for being by my side throughout this
journey.
2
3
Abstract
Assessment of electromagnetic field (EMF) exposure is key in the deployment of wire-

less systems, and it has been grabbing more attention in the context of future wireless sys-
tems, mainly fifth generating (5G) and massive multiple-input multiple-output (MIMO)
cellular networks. This is due to network densification, high-gain transmitting devices,
and usage of high frequencies with higher bandwidth. Both measurement procedures and
analytical models are being developed and tested for 5G and massive MIMO wireless
networks to properly characterize their induced exposure.
In this dissertation, we estimate and study the EMF exposure in 5G massive MIMO
antenna networks. We first present the different characteristics of 5G, relevant to the
EMF exposure, specifically the downlink signaling and transmission, and we also present
the different measurement procedures to measure the EMF. We show that using current
measurement methods, measuring the exposure in a 5G network may result in a signif-
icant information loss, due to the large sweep time required to measure the whole 5G
band in comparison to the transmission beam allocation. We also show that the 5G syn-
chronization signal block (SSB) can be measured in zero-span, and used to extrapolate
its power to the whole bandwidth. However, this signal alone is not sufficient for the esti-
mation of the EMF exposure, due to beam refinement, channel boosting, and multi-user
communication.
We then analytically analyze the 5G massive MIMO network in the millimeter wave
(mmWave) band by modeling it as a Poisson point process (PPP) and using stochastic
geometry tools to determine the total power received which is modeled as a shot-noise
process with a modified power law. We fit the mmWave channel model into statistical
distributions with data obtained from the NYUSIM channel simulator [1]. The fitted
distributions, e.g., exponential and gamma distribution for antenna and channel gain
respectively, were then implemented into an analytical framework. We obtain the closed-
form expression of the moment-generating function (MGF) for the total power received in
the network at the typical MT. The framework is then validated by numerical simulations
and a sensitivity analysis is carried out to investigate the impact of key parameters, e.g.,
BS density, path loss exponent, and transmission probability. We then prove and quantify
the significant impact the transmission probability on global exposure, which indicates
the importance of considering the network usage in 5G exposure estimations.
4
And finally we develop a statistical model for both the exposure and the ratio of the
exposure to SIR at the nearest MT to its serving BS in a multi-user massive MIMO
network deploying MRT and max-min fairness downlink power control. We determine
the closed-form expression of the exposure and the expression of the exposure to SIR
ratio for MTs being in LoS/NLoS of the BS with LoS probability, pL . We show that the
exposure at the nearest MT to the serving is higher in denser cells, however it decreases
with the number of served MTs if the MT density remained constant. It also increases
with the number of antenna elements, M due to the increase in the transmission gain. We
also show that the exposure strictly increases with the density of the BSs in the network
and that the rate of increase is higher in networks with higher pL in all scenarios. As for
the ratio between the exposure and the SIR, we confirm that it increases linearly with
the transmit power, and with the BS density, meaning that the exposure increases more
than the SIR in these scenarios. However, we show that it decreases with the increase
of number of antenna elements in mostly NLoS environments, and that at sufficiently
large number of antenna elements, the ratio between the exposure and the SIR would be
practically independent from the number of served MTs. This shows that the system is
more efficient in terms of coverage considering the EMF exposure in NLoS and less so in
increasingly LoS environments.
5
6
Résumé
L’évaluation de l’exposition aux champs électromagnétiques (CEM) est de plus en

plus importante pour les futurs systèmes sans fil, principalement les réseaux cellulaires
de cinquième génération (5G) et les réseaux Multiple Input Multiple Output (MIMO).
Cela est à cause de la densification du réseau, des dispositifs de transmission à gain élevé
et de l’utilisation de hautes fréquences de transmission. Des procédures de mesure et des
modèles analytiques sont développés et tests afin d’assurer une charactérisation précise
de l’éxposition des réseaux 5G.
Dans cette thèse, nous estimons et étudions l’exposition aux CEM dans les réseaux
5G massive MIMO . Nous présentons d’abord les différentes caractéristiques pertinentes
de la 5G pour l’exposition aux CEM, surtout la signalisation et la transmission de li-
aison descendante, ainsi que les différentes procédures de mesure CEM. Nous montrons
qu’en utilisant les methodes de mesure actuelles, la mesure de l’exposition dans un réseau
massive MIMO entraı̂nera une perte d’informations importante, en raison du temps de
balayage requis pour mesurer l’ensemble de la bande 5G qui est large par rapport à
l’allocation des faisceux de transmission. Nous montrons également que la synchroniza-
tion signal block (SSB) 5G peut être mesurée à l’aide de mesures zero-span et utilisée pour
extrapoler sa puissance pour toute la bande passante. Cependant, ce signal seul ne peut
pas être suffisant pour l’estimation de l’exposition aux champs électromagnétiques en
raison du raffinement du faisceau, de l’amplification des canaux, et de la communication
multi-utilisateurs.
Nous analysons ensuite, analytiquement, le réseau 5G massive MIMO dans la bande
des ondes millimétriques (mmWave) en le modélisant comme un processus de point de
Poisson (PPP) et en utilisant des outils de géométrie stochastique pour déterminer la
puissance totale reçue, modélisée comme un processus de bruit de grenaille avec un loi
de puissance modifiée. Nous adaptons le modèle de canal mmWave à des distributions
statistiques avec des données obtenues à partir du simulateur de canal NYUSIM [1].
Les distributions sont ajustées à la distribution exponentielle et gamma pour le gain
d’antenne et de canal respectivement, et ils ont ensuite été mises en œuvre dans un cadre
analytique. Nous obtenons l’expression sous forme fermée de la fonction génératrice
des moments (MGF) pour la puissance totale reçue dans le réseau au MT typique. Le
cadre est ensuite validé par des simulations numériques et une analyse de sensibilité est
7
effectuée pour étudier l’impact de la densité des BSs, l’exposant de perte de trajet et
la probabilité de transmission. Nous prouvons et quantifions ensuite l’impact significatif
de la probabilité de transmission sur l’exposition globale, ce qui indique l’importance de
prendre en compte l’utilisation du réseau dans les estimations d’exposition 5G.
Et enfin, nous développons un modèle statistique pour l’exposition et le rapport de
l’exposition au SIR au MT le plus proche à sa BS de service dans un réseau massive
MIMO multi-utilisateurs déployant maximum-ratio transmission (MRT) et le contrôle
de puissance de liaison descendante max-min fairness. Nous déterminons l’expression de
forme fermée de l’exposition, et l’expression du ratio exposition/SIR pour les MT étant
en LoS/NLoS de la BS avec une probabilité de LoS pL . Nous montrons que l’exposition
augmente avec le nombre de MT desservis, K, en raison de cellules plus denses, et avec le
nombre d’éléments d’antenne, M . Nous montrons également que l’exposition augmente
strictement avec la densité des BS dans le réseau et que le taux d’augmentation est plus
élevé dans les réseaux avec des pL plus élevés dans tous les scénarios. Nous montrons
également que le rapport augmente linéairement avec la puissance d’émission, et avec la
densité des BSs, signifiant que l’exposition augmente plus que le SIR dans ces scénarios.
Cependant elle diminue avec l’augmentation du nombre d’éléments d’antenne.
8
9
Contents
1 Introduction 22
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2 Objectives and outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Introduction To 5G New Radio 26

2.1 5G massive MIMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1.1 Array structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.2 Analog beamforming . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.3 Digital beamforming . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.4 Hybrid Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.5 Beam management . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 5G network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Millimeter wave Communications . . . . . . . . . . . . . . . . . . . . . . 36
2.4 Physical layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.1 Numerology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.2 Frame structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.3 Duplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.4 Synchronization signal block (SS/PBCH block) . . . . . . . . . . 40
2.4.5 Channel state information - reference signal . . . . . . . . . . . . 42
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 In-Situ Exposure Assessment of 5G Networks 46

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Electromagnetic field exposure metrics . . . . . . . . . . . . . . . . . . . 47
3.2.1 Specific absorption rate . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.2 Power density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 5G NR measurement methods and scenarios . . . . . . . . . . . . . . . . 48
3.3.1 Full spectrum measurement . . . . . . . . . . . . . . . . . . . . . 49
3.3.2 SSB measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.3 Beam refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 5G massive MIMO measurements . . . . . . . . . . . . . . . . . . . . . . 52
10
3.4.1 Measurement setup and scenario . . . . . . . . . . . . . . . . . . 53
3.4.2 Demodulation domain measurements . . . . . . . . . . . . . . . . 54
3.4.3 Frequency domain measurements . . . . . . . . . . . . . . . . . . 58
3.4.4 Time domain measurements . . . . . . . . . . . . . . . . . . . . . 61
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4 Introduction to Stochastic Geometry in Wireless Networks 65

4.1 Mathematical background . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.1.1 Poisson point process . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.1.2 Useful theorems and definitions . . . . . . . . . . . . . . . . . . . 68
4.2 Cellular network modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.1 Path-loss model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.2 Small-scale channel fading . . . . . . . . . . . . . . . . . . . . . . 71
4.2.3 The total received power . . . . . . . . . . . . . . . . . . . . . . . 72
5 A Statistical Estimation of 5G Massive MIMO Networks’ Exposure

Using Stochastic Geometry in mmWave Bands 75
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.1.1 Our approach and contributions . . . . . . . . . . . . . . . . . . . 77
5.2 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2.1 Path Loss Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.2 Antenna model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.3 Channel model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3 Exposure estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6 Performance and EMF Exposure Analysis of Massive MIMO Networks

With Max-Min Power Control in LoS/NLoS Scenarios 95
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.1 Massive MIMO Network Modeling . . . . . . . . . . . . . . . . . 98
6.2.2 Downlink Transmission . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2.3 Max-Min Fairness Power Control . . . . . . . . . . . . . . . . . . 103
6.3 Average Power Received . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.4 Exposure to SIR Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.5.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.5.2 Average Power Received . . . . . . . . . . . . . . . . . . . . . . . 116
11
6.5.3 Exposure to SIR Ratio . . . . . . . . . . . . . . . . . . . . . . . . 122
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7 Conclusions and Future Work 128

7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.2.1 Non-PPP models . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.2.2 Compliance boundary estimation . . . . . . . . . . . . . . . . . . 130
7.2.3 Joint optimization of EMF exposure and performance . . . . . . . 130
12
List of Figures
2.1 Multi-Cell MU MIMO Model . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2 Massive MIMO Array Structure [8] . . . . . . . . . . . . . . . . . . . . . 28
2.3 Massive MIMO Array Gain [8] . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Analog Beamformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5 Digital Precoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6 5G BS-MT Connection scenarios [16] . . . . . . . . . . . . . . . . . . . . 32
2.7 Non-standalone 5G Network [17] . . . . . . . . . . . . . . . . . . . . . . . 33
2.8 Homogeneous deployment of the 5G network . . . . . . . . . . . . . . . 34
2.9 Heterogeneous 5G Network with NR Small Cells . . . . . . . . . . . . . . 34
2.10 Heterogeneous 5G Network with LTE Small Cells . . . . . . . . . . . . . 34
2.11 Massive MIMO Deployment Scenarios [8] . . . . . . . . . . . . . . . . . . 35
2.12 Atmospheric and molecular absorption in mmWave [18] . . . . . . . . . . 36
2.13 Rain attenuation in mmWave [18] . . . . . . . . . . . . . . . . . . . . . . 37
2.14 5G Downlink Channel Mapping . . . . . . . . . . . . . . . . . . . . . . . 39
2.15 5G SSB Structure per Numerology . . . . . . . . . . . . . . . . . . . . . 41
2.16 Beam Sweeping [16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.17 Periodic and Aperiodic CSI-RS [23] . . . . . . . . . . . . . . . . . . . . . 43
2.18 Single CSI-RS Signaling [22] . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.19 Multiple CSI-RS Signaling [22] . . . . . . . . . . . . . . . . . . . . . . . . 43
2.21 codebook-based beamforming massive MIMO cell Architecture . . . . . . 44
2.20 SRS Based Signaling [22] . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1 Zero-Span (Time Domain) measurement when data is being transmitted

over a single beams showing the SSB power and data in time when mea-
suring over 1 MHz bandwidth at the center frequency . . . . . . . . . . . 50
3.2 Demodulation domain measurement when data is being transmitted over
the SSB beam 3, showing measured powers of the SSBs, the channel power
and the power per resource element (PPRE) of signaling and data channels 51
3.3 Representation of the beam refinement procedure as a second step of the
signaling after the SSB selection [8] . . . . . . . . . . . . . . . . . . . . . 52
3.4 Representation of the measured massive MIMO’s beamforming code-book 53
13
3.5 Demodulation domain measurement for 0% traffic load being transmitted
on the data channel and only the SSB channel is on . . . . . . . . . . . . 54
3.6 Demodulation domain measurement when we send 100% traffic load of
data at beam 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.7 Demodulation domain measurement for 100% traffic load transmitted over
beam 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.8 Demodulation domain measurement for 100% traffic load transmitted over
beam 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.9 Demodulation domain measurement for 100% traffic sent over 4 different
beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.10 Frequency domain measurement over the whole 100 MHz band for 0%
traffic load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
traffic load transmitted over beam 3 . . . . . . . . . . . . . . . . . . . . . 58
traffic load transmitted over beam 11 . . . . . . . . . . . . . . . . . . . . 59
traffic load sent over 4 different beams . . . . . . . . . . . . . . . . . . . 60
3.16 Time domain measurement for 100% traffic load transmitted over beam 11 61
3.19 Time domain measurement for 100% traffic load sent over 4 different beams 63
4.1 Representation of a Voronnoi tessellation of a Poisson Point Process . . . 68

4.2 Representation of the Rayleigh distribution for σ = 0.5 . . . . . . . . . . 71
4.3 Cumulative distribution function of the total power received . . . . . . . 74
5.1 2D slice of the 3D antenna pattern realization of the 3GPP active antenna
array model with 256 antenna elements directed perpendicularly to the
antenna array over the steering angles in the azimuth and elevation. . . . 82
5.2 Illustration of our mmWave model (left) and the channel model (right).
The channel model follows the NYU Wireless Group mmWave channel
model in [46]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3 Plot of the fit of the antenna array gain into an exponential distribution
for a rectangular uniform antenna array with Ntx = 256 antenna elements. 84
14
5.4 Channel gain fit into a gamma distribution for MTs uniformly distributed
on a 2D plane and having a single element antenna array. . . . . . . . . . 85
5.5 Verification of the analytical expression of the CDF of the power received
versus a Monte-Carlo simulation. . . . . . . . . . . . . . . . . . . . . . . 89
5.6 90th percentile of the exposure as function of BS Density λ for different
values of the path loss exponent η. . . . . . . . . . . . . . . . . . . . . . 90
5.7 90th percentile of the exposure as function of system utilization α for
different values of the BS density λ. . . . . . . . . . . . . . . . . . . . . . 90
5.8 Comparison between the current model developed in this chapter (red
circles), its verification using Monte-Carlo simulations assuming the gain
distributions from Section 5.3 (dashed line), and the model assuming a
constant gain presented in 4.2 (blue diamonds), versus a Monte-Carlo sim-
ulation of the exposure using gain values simulated by NYUSIM (solid
line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.1 Antenna gain pattern and the side-lobe approximation in the LoS link
between the BS and the MT . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2 Verification of the power control coefficient by comparison between the
a Monte-Carlo simulation of the useful signal power and the proposed
asymptotic approximation in 6.25 . . . . . . . . . . . . . . . . . . . . . . 110
6.3 Average power received as function of the number of antenna elements M
for different values of (a) pL for K = 15 and (b) K for M = 256. Markers
represent the Monte-Carlo simulation results and the dotted line represents
the result from the analytical framework. . . . . . . . . . . . . . . . . . . 117
6.4 Average power received as function of the BS density for different values
of (a) pL for K = 15 and (b) K in LoS. Markers represent the Monte-
Carlo simulation results and the dotted line represents the result from the
analytical framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.5 Average power received as function of the number of antenna elements M
for different values of K where the MT density in the cell is constant in (a)
NLoS and (b) LoS. Markers represent the Monte-Carlo simulation results
and the dotted line represents the result from the analytical framework. . 120
6.6 Expectation of the total power received at MT0 as function of the BS
density λBS and different number of served MTs K, for M = 16 (a),
M = 64 (b), and M = 128 (c) antenna array elements. Markers represent
the Monte-Carlo simulation results and the dotted line represents the result
from the analytical framework. . . . . . . . . . . . . . . . . . . . . . . . . 121
15
6.7 Expectation of the ratio of the exposure to SIR at MT0 versus the transmit
power, ρdl , for different number of served MTs, K in (a) NLoS and (b) LoS.
Markers represent the Monte-Carlo simulation results and the dotted line
represents the result from the analytical framework. . . . . . . . . . . . . 123
6.8 Ratio between the total power received and SIR as function of M for
different pL and K = 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.9 Ratio between the total power received and SIR as function of M for
multiple values of K in (a) LoS and (a) NLoS. Markers represent the
Monte-Carlo simulation results and the dotted line represents the result
from the analytical framework. . . . . . . . . . . . . . . . . . . . . . . . . 125
6.10 Ratio between the total power received and SIR as function of M for multi-
ple values of K in (b) LoS and (a) NLoS, while maintaining a constant MT
density in the cell. Markers represent the Monte-Carlo simulation results
and the dotted line represents the result from the analytical framework. . 126
16
List of Tables
2.1 5G Numerology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2 5G Physical Layer Duration per Numerology . . . . . . . . . . . . . . . . 38
2.3 Number of Frames and Slots in 5G per Numerology . . . . . . . . . . . . 38
2.4 The ratio of PDSCH EPRE to DM-RS EPRE . . . . . . . . . . . . . . . 45
5.1 List of symbols used in antenna pattern and model derivation . . . . . . 79

5.2 NYUSIM simulation parameters used for the channel simulations. . . . . 83
5.3 Parameters of the fitted distributions. a for the exponential distribution
and b, c for the gamma distribution . . . . . . . . . . . . . . . . . . . . . 83
5.4 Simulation Parameters used for the verification of the analytical equation
with Monte-Carlo simulations . . . . . . . . . . . . . . . . . . . . . . . . 89
5.5 Parameters used in the analysis simulations for Figure 5.6 and Figure 5.7. 91
5.6 Total Sobol indices of the inputs contributing to the 90th percentile of the
exposure in the network. . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.1 List of symbols and abbreviations used in the document . . . . . . . . . . 102

6.2 Summary of default parameters used in the Monte-Carlo simulations (un-
less otherwise stated) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
17
Acronyms
5G fifth generation
BPP binomial point process
BS base station
CCDF complementary cumulative distribution function
CDF cumulative distribution function
CSI channel state information
CSI-RS channel state information-reference signal
DL downlink
EMF electromagnetic field
EPRE energy per resource element
FCC federal communication commission
FD full dimension
fidi finite-dimensional distribution
i.i.d. independent and identically distributed
ICNIRP international commission on non-ionizing radiation protection
IEEE Institute of Electrical and Electronics Engineers
LoS line-of-sight
LTE Long Term Evolution
MGF moment generating function
18
MIMO multiple-input multiple-output
mmWave millimeter-wave
MRT maximum-ratio transmission
MT mobile terminal
MU multi-user
NLoS non-line-of-sight
NR New Radio
NSA non-standalone
OFDM orthogonal frequency division multiplexing
PBCH Physical broadcast channel
PDF probability density function
PDSCH physical downlink shared channel
PGFL probability generating functional
PL path loss
PPP Poisson point process
PPRE power per resource element
PSS Primary synchronization signal
RAN radio access network
RB resource block
RBW resolution bandwidth
RF radio frequency
SA standalone
SAR specific absorption rate
SCC standards coordinating committees
SIR signal to interference ratio
19
SSB synchronization signal block
SSS Secondary synchronization signal
TTI transmission time interval
ZF zero-forcing
20
21
Chapter 1
Introduction
Contents
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2 Objectives and outline . . . . . . . . . . . . . . . . . . . . . . 24
22
1.1 Background
Throughout the last few decades, communication systems have been rapidly evolv-
ing with new technologies being developed at an accelerating pace to accommodate the
increasing demand on communication technologies [2]. This demand has pushed the in-
dustry towards high spectrum usage, paired with an increase of transmitting elements
to achieve capacity requirements. However, not only that the transmitting elements are
being deployed more densely, but the mechanisms of the new generations of wireless com-
munication systems are significantly different than previous ones [3]. For these reasons,
the already existing concerns have increased with regards to the effect of EMF radiation
on the public health [4]. Therefore, regulatory bodies, alongside constructors and oper-
ators, have already started testing their newly developed antennas for compliance with
EMF regulations like what’s presented in [5]. Measurement procedures of the EMF ex-
posure have been already put in place to use for older communication systems, however,
the fundamental difference between newer and older technologies calls for revisiting these
procedures to ensure their reliability [6].
Moreover, cellular networks based on large (macro) base stations are expected to not
be sufficient in fulfilling the additional demands of high-data-rate users. Instead, tech-
nologies like small-cells and distributed antenna networks, are expected to be deployed,
creating ultra-dense networks.
In addition to that, in 5G and beyond systems, new frequency bands, like millimeter-
wave (mmWave) bands, are being investigated to exploit their large available spectrum,
largely increasing the data rate and capacity of the transmission. However, higher fre-
quency channels have different characteristics than lower frequency ones. Penetration
loss, propagation loss, and antenna design will have significant impact on the commu-
nication channel at higher frequencies. The effect of these characteristics need to be
considered during exposure assessment.
One of the most promising technologies for 5G systems, in mmWave bands, and lower,
is massive MIMO antennas. Beamforming, being the act of concentrating the transmitted
signal towards the served user is one of the key solutions to meet the demands of future
wireless networks and overcome the high path loss of higher frequency bands, however, it
proved to be one of the main challenges for EMF regulation bodies. Using a large number
of transmitting and/or receiving antennas transforms the omnidirectional radiation of a
classical antenna onto a lobe pattern that is both time and space varying. This spatio-
temporal variation needs to be accounted for when evaluating the EMF exposure of newer
generation systems to ensure its accuracy.
23
1.2 Objectives and outline
Methods developed in this dissertation serve the purpose of characterizing the down-
link exposure in a 5G massive MIMO network. It also serves to analyze the exposure
as function of network and MT parameters. This characterization will aid direct the
regulatory efforts by giving a more realistic scenario of studying 5G exposure even before
its deployment.
Chapter 2 introduces the 5G New Radio (NR) radio access technology and its char-
acteristics relevant for the exposure estimation. We present the massive MIMO array
structure which is one of the most prominent technologies for 5G then we discuss the
different beamforming techniques for different types of antennas. We also discuss the
network architecture, propagation in mmWave frequencies and the physical layer and
frame structure alongside the signaling and data transmission channels in 5G.
Chapter 3 presents in-situ measurements of a 5G massive MIMO antenna’s downlink
transmission using a PXA signal analyzer. We present measurements in the time domain
(zero-span), in the frequency domain (spectrum measurement) and in the demodulation
domain. We measure the received signal’s entire spectrum and also measure the signaling
channel separately and show the beam selection process and its mapping to the synchro-
nization signal block (SSB). We show different transmission scenarios and compare them
while also discussing the benefits and shortcomings of each measurement method.
Chapter 4 introduces the concepts of stochastic geometry in wireless communication
systems. It presents the mathematical background of modeling the base station (BS)s
and the MTs as point processes, the different path loss models used, and introduces the
essential tools of the mathematical formulation. In it we also present a simple case of
determining the closed-form equation of the exposure’s distribution in a cellular network.
Chapter 5 addresses the analytical modeling of the total power received in a mmWave
massive MIMO 5G network using stochastic geometry. The BSs are modeled following a
PPP and the total power received is considered at the typical MT. The mmWave channel
was estimated using the NYUSIM mmWave channel simulator and the 3GPP antenna
array model, and their values were fitted into statistical distributions then integrated
into the framework to get the distribution of the total power. A sensitivity analysis
of the power received is also performed to assess the importance of different network
characteristics on the exposure.
Chapter 6 investigates both the analytical EMF exposure and its relation to the
performance, by considering the exposure to signal to interference ratio (SIR) ratio, of
the 5G MU massive MIMO network where the scheduled MTs are being served in the same
time-frequency block. The exposure and the SIR in this chapter, however, are considered
at the nearest MT to its serving BS, not at the typical MT in the cell. The model
considers both LoS and NLoS scenarios and their respective beamforming patterns. We
24
also consider max-min fairness power control that ensures fair resource allocation between
simultaneously scheduled MTs to guarantee equal SIR for all MTs. The expressions of
the total power received and the exposure to SIR ratio are then verified and analyzed for
different network deployment scenarios.
Chapter 7 concludes the dissertation and suggests future research directions following
the work accomplished during this PhD.
25
Chapter 2
Introduction To 5G New Radio
Contents
2.1 5G massive MIMO . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1.1 Array structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.2 Analog beamforming . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.3 Digital beamforming . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.4 Hybrid Beamforming . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.5 Beam management . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 5G network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Millimeter wave Communications . . . . . . . . . . . . . . . . 36
2.4 Physical layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.1 Numerology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.2 Frame structure . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.3 Duplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.4 Synchronization signal block (SS/PBCH block) . . . . . . . . . 40
2.4.5 Channel state information - reference signal . . . . . . . . . . . 42
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
26
Figure 2.1: Multi-Cell MU MIMO Model
Since 5G networks are fundamentally different than previous generations, it is im-

portant to distinguish the differences between them in order to have representative mea-
surements of the EMF. In this section we present and explain the parameters that are
necessary in the characterization of the 5G exposure.
2.1 5G massive MIMO

MIMO antenna is a technology in which multiple antenna elements are used at the
transmitter and receiver side of the communication channel. Using multiple antenna
elements can increase the capability of the RF system by virtue of spatial diversity,
spatial multiplexing, or MU transmission.
A MIMO antenna can be called full dimension (FD) MIMO, meaning that it can form
beams in both horizontal and vertical directions so it can focus on anywhere in the 3D
space. The antenna is basically a rectangular array with dimensions typically 8x8 or
more. FD-MIMO is designed to operate in lower frequency bands (sub 6 GHz) [7].
The MIMO is called multi-user (MU), if more than 2 MTs can be served simultane-
ously. The difference between the already available MU-MIMO and the MU-MIMO for
5G NR systems is that it will be on a much higher scale, thus, massive.
Massive MIMO, also called path-loss MIMO, is an array system with a large set of
antennas. The number of antennas required for the system to be called Massive depends
on the receiver (equalizer) algorithm. But typically, a system consisting of 64 antennas
(8x8) can be considered massive. Massive MIMO is becoming more and more important
in both bands of 5G NR deployment (Below and above 6 GHz). It generally aims to
serve multiple users in the same time-frequency resource block (RB). When a network
is communicating simultaneously with multiple users in a cell, as illustrated in Figure
2.1, the signal would various types of interference from other MTs within the same cell
and interference from neighboring cells. Transmission algorithms usually aim to optimize
transmission parameters (Tx power, Resource Allocation) for each MTs to maximize the
total throughput of a cell.
27
Figure 2.2: Massive MIMO Array Structure [8]
Figure 2.3: Massive MIMO Array Gain [8]
2.1.1 Array structure

The massive MIMO array structure is typically that of a rectangle as shown in Figure
2.2, to enable high gain beamforming and to allow the steering of the beams [8]. The gain
is constructed by combining the signals from the different antenna elements. The more
antenna elements in the array, the higher is the gain of the beams formed. The offset
angle of the beams is formed by controlling the amplitude and the phase of smaller parts
of the antenna array. The antenna is divided into sub-arrays (group of non-overlapping
elements), and by applying one RF chain per polarization for each sub-array, multiple
beams can be formed containing independent data streams.
The total number of elements determines the maximum gain and the sub-array parti-
tioning allows steering of the high-gain beams over the range of angles as shown in Figure
2.3. The sub-array radiation pattern determines the envelope of the narrow beams. It is
important to consider the division of the array since extra RF chains impose important
additional computational and construction costs.
Even with the same number of served MTs and the same number of Tx/Rx, different
modes of implementation can be used. Some of the factors affecting implementation:
28
1. Number of MTs covered.
2. Number of Tx and Rx antennas used.
3. Receiver design.
4. Precoding algorithm.
Antenna architecture in 5G systems are generally divided into three types, analog,
digital, and a hybrid of both. To model the radiation of the antennas, different charac-
teristics affect the radiated power in different ways.
Analog massive MIMO antennas, use phased antenna array elements to create a single
steerable beam towards a certain angular direction in the azimuth, elevation, or both.
The steering dimensions depend on the antenna construction, which is explained in 2.1.1.
Analog massive MIMO also uses a precoding, also called beamforming, codebook [9] as
shown in figure 2.21, in which a predefined array of beamforming vectors are stored,
and where a vector is chosen based on the estimated channel between the BS and the
MT. This channel estimation is performed following a procedure called beam steering, in
which the BS sends the signaling frames to all served MTs successively, and on different
beams. The BS then estimates the beam that best serves each MT based on a feedback
signal from it. The number of precoded beams is not onlt dependent on the antenna’s
architecture, but also on the numerology that is chosen for transmission. The numerology
specifies the sub-carrier spacing, i.e. the separation in frequency between sub-carriers,
which affects the number of signaling blocks used when estimating the serving beam.
Moreover, the numerology also affect the transmission time interval (TTI), which is the
minimal transmission duration between the BS and the MT.
On the other hand, digital and hybrid massive MIMO antennas are more complicated
to characterize than analog ones. This type of antennas can simultaneously create multi-
ple beams for each antenna element in the array. The precoded beams are also more likely
than not to not be directed, especially in NLoS scenarios. The channel is estimated using
uplink pilots sent from the MT and the beams are formed using precoding techniques
like zero-forcing (ZF) [10] or maximum-ratio transmission (MRT) [11]. The transmission
resources are then distributed according to a power control scheme like max-min fairness.
Other characteristics present in analog massive MIMO antennas are also present in digital
and hybrid ones, like numerology. Each of these characteristics will be discussed in its
own section.
Massive MIMO is not necessarily a way to increase throughput by MIMO/Spatial
Multiplexing, but massive MIMO in 5G has the purpose of implementing beamforming
to help increase the gain in the direction of transmission and reduce the interference in
other directions.
29
Figure 2.4: Analog Beamformer
The implementation of Massive MIMO/Beamforming is not specified in the 3GPP

specifications for 5G NR. The implementation remains up to each equipment construc-
tor/vendor. There are multiple methods for the implementation of massive MIMIO, but
it will be most likely the Hybrid mode that will be dominant in the future.
2.1.2 Analog beamforming

Analog beamforming, illustrated in Fig. 2.4, has the advantage of having a simple
RF chain for the transmitter system. Lots of antenna test papers and bibliography items
focused on the analog transmitters instead of the more complex hybrid. It functions by
shifting the phase of the emitted signal in the RF domain at each antenna element to cre-
ate an effect similar to a phased antenna array and thus changing the directivity/pattern
of the antenna.
Analog beamformers are limited in terms of beamforming, they have fixed precoded
beams and can emit only one beam per time slot. Some research suggests that analog
beamforming will be used for one dimensional sweeping and transmission and for imple-
mentations with a lower number of beams (<6 GHz). But in the previously mentioned
papers, Ericsson has performed its measurements in 14.5, 15.2 GHz [12] and 28 GHz [13].
2.1.3 Digital beamforming

In digital beamforming (also known as precoding), illustrated in Fig. 2.5, the signals
are shifted in phase/amplitude in the baseband before the RF transmission which requires
an A/D converter for each element, making a full high dimension digital massive MIMO
expensive to implement. Amplitudes and phases and also frequency bands (subcarriers)
can be assigned to each antenna element thus enabling higher flexibility. Digital beam-
forming is particularly desirable for spatial multiplexing where the system transmits a
superposition of signals with different directivities (channel conditions) especially in wide-
band scenarios (frequency-selective fading). The two most popular precoding methods
30
Figure 2.5: Digital Precoder
are zero-forcing and maximum ratio processing.

Zero-forcing, also called null-steering, nominally eliminates the multi-user interference
among the multiplexed signals in a multi-user MIMO. In the condition of perfectly-known
CSI at the transmitter, the precoding matrix can be expressed as the pseudo-inverse of
the channel matrix [10]. As a general rule, an antenna having N elements, can create N-1
independent nulls in the radiation pattern.
As for maximum ratio processing, also called maximum-ratio transmission (MRT) [11],
is an implementation of the maximum-ratio combining technique used at the receiver
side to exploit diversity. MRT aims to maximize the power received at the MT by
exploiting channel diversity. This can be explained by focusing the transmit power in
specific directions so that it adds up at the receiver. in LoS, it can be equated to analog
beamforming where the transmitted power is directed towards the LoS path.
2.1.4 Hybrid Beamforming

Hybrid beamforming can allow, at the cost of a more complex system, the formation
of multiple transmission beams while maintaining a level of multiplexing/multiple access.
The power emitted from the antenna is divided by the beams formed. Typically, and
as seen in some presentations by constructors/operators, the hybrid antennas can have
up to 8 transceiver units (TXRUs) in the case of cross polarization [14] and 4 TRXUs
when using a single polarization [15], to emit simultaneously to four MTs in the case
of MU-MIMO, or transmit four beams to a single MT in the case of SU-MIMO, or one
beam per panel, and will be most likely used for applications in the spectrum above 6
GHz [15].
In over-6 GHz channels, antennas are usually separated into multiple, widely sepa-
rated, panels. And the characteristics are not in specifications and can vary depending
on the constructor.
31
2.1.5 Beam management
The defining characteristics of the 5G NR and its challenges reside in its deployment
in the mmWave frequency band (while its deployment in sub 6 GHz is possible and very
likely). The management can be separated into multiple parts depending on the state of
connection (cell search/initial access, connected state. . . ). Beam management for specific
connection phases are explored in its own sections. Here is the discussion of the general
idea. The most general scenarios for BS-MT connection, illustrated in figure 2.6 can be
summarized by four examples:
1. MT and Network are connected through a single TRP (Tx/Rx Point) and a single
beam.
2. MT and Network are connected through multiple TRP (Tx/Rx Point) and a single
beam for each TRP.
3. MT and Network are connected through a single TRP (Tx/Rx Point) and multiple
beams
4. MT and Network are connected through multiple TRP (Tx/Rx Point) and multiple
beams for each TRP
Figure 2.6: 5G BS-MT Connection scenarios [16]
32
2.2 5G network
Generally, the network will either be homogeneous where 4G and 5G cells are co-
located or heterogeneous where 5G will be deployed on small cells managed by the 4G
network (or vice versa) as shown in figures 2.8, 2.9, and 2.10. The exposure in a network
is affected mostly by network structure and density, the type of antennas used in the
network and the distribution and density of the MTs.
The densification of the network will undoubtedly result in an increase in the total
received power and consequently the exposure. However, it is important to estimate the
effect this densification on the total received power, especially since the network will have
many small cells being added. The same behaviour can be expected by increasing the
number of antenna elements on the serving BS which has to be also studied.
5G NR networks can be deployed as standalone (SA) and non-standalone (NSA). The
first phase of 5G deployment will be the NSA, where the 5G connection will be dependent
on the already established Long Term Evolution (LTE) network. Regarding cell layout,
there are two general cases of deployment, homogeneous and heterogeneous.
NSA NR is a deployment method of NR in its early stages, when it’s dependent on
the already present LTE network. The MT communicates with both LTE eNB and NR
gNB in the site. While the LTE core network is used for signaling/data, the gNB and
eNB will use each their own PHY/MAC layer. The overall network architecture will
be equivalent to Figure 2.7. In NSA, the MT communicates with the gNB for data-
throughput improvement (User Plane) but still use 4G for control and signaling (Control
Plane).
Figure 2.7: Non-standalone 5G Network [17]
Even though the gNB will be dependent on the LTE core, the radio interface should
33
not be any different from the standalone deployment. The difference in the radio interface
between the standalone and the non-standalone deployment of NR can be introduced if
each deployment used different frequency bands (sub 6 GHz for NSA and mmWave for
SA) which can heavily affect the usage of the radio channel.
Homogeneous deployment, presented in figure 2.8, is when LTE, and NR cells cover
the same areas. This also implies that the NR and LTE systems are operating in the
same frequency bands and have co-located cells.
Figure 2.8: Homogeneous deployment of the 5G network
Heterogeneous deployment, presented in figures 2.9 and 2.10, has two scenarios, NR
small cells, or NR macro cells. In this kind of deployment LTE cell is large cell size to
meet coverage requirement while NR cell size is small to meet the capacity requirements.
Here the NR cell can be deployed as a co-located cell or a non-located cell as a hot spot.
Figure 2.9: Heterogeneous 5G Network with NR Small Cells
Figure 2.10: Heterogeneous 5G Network with LTE Small Cells
The illustration in Figure 2.11 highlights the three basic deployment scenarios: Dense
urban high-rise, Urban low-rise, and rural environments.
34
Figure 2.11: Massive MIMO Deployment Scenarios [8]
Dense urban environments are characterized by high-rise building and high BS density
of 2 × 10−3 -5 × 10−3 . They are also characterized by the large traffic volume due to high
MT density and MT spread in the vertical plane. This requires small sub-arrays with
wide beams in the vertical direction, which produces high-gain beams that can be steered
over a large range of angles. This also means that the antenna should have a sufficiently
large number of RF chains to support all the sub-arrays. A proposed architecture is to
have 64 radio chains controlling the sub-arrays.
The urban scenario represents most of the cities worldwide, including the outskirts of
dense urban cities. Base stations are typically deployed on rooftops and are separated by
few hundred meters. Traffic per unit area is lower than dense urban scenarios. And since
the heights of the buildings is lower than dense urban, it allows larger vertical subarrays
meaning fewer radio chains are required. Reciprocity-based beamforming schemes will
work for most users, but there will be users with poor coverage that need to rely on
techniques such as feedback-based beamforming. MU MIMO is also appropriate at high
loads due to the multi-path propagation environment, good link qualities and MT pairing
opportunities.
In rural and suburban environments, antennas are mounted on rooftops of on towers
and separated by few kilometers. Low or medium population density and very small ver-
tical MT distribution. This scenario calls for an antenna with a large area and supporting
horizontal beamforming. Since the vertical distribution of users is very small, vertical
beamforming does not provide significant gains and large antenna subarrays with small
vertical coverage are suitable. In this scenario, MU-MIMO gains are less important.
35
Figure 2.12: Atmospheric and molecular absorption in mmWave [18]
2.3 Millimeter wave Communications

Millimeter wave is the EM wave having a wavelength into the scale of millimeter (10
∼ 1 mm or 30 GHz ∼ 300 GHz). The actual range of frequencies of the millimeter
wave signals is not clearly defined, so the waves with frequencies > 20 GHz can also be
considered in the mmWave band. mmWave communication systems have fundamental
differences from their RF counterparts which impose challenges in the physical, MAC
and routing layers of mmWave communications.
mmWave signals suffer from big propagation loss compared to signal with lower car-
rier frequencies in addition to rain attenuation and atmospheric absorption as shown in
figures 2.12 and 2.13. Smaller cell sizes are being deployed to combat the effect of rain
attenuation and atmospheric absorption. NLOS channels also suffer more attenuation
from atmospheric absorption than LOS. To combat the severe path loss in mmWave
propagation directional antennas at both the transmitter and receiver are being used.
Moreover, electromagnetic waves don’t have the ability to diffract around objects with
sizes significantly larger than its wavelength. For this reason, waves in the 60 GHz band
are susceptible to blockage by obstacles like humans and furniture.
On the other hand, the small wavelengths of mmWave signals allows the construction
of antennas with a large number of elements, and by controlling the phase at each (or
some) elements of the array, the direction of propagation of the antenna can be steered
towards the desired direction of emission creating high gains towards the served MT, while
having lower gain towards the interferers. The directivity of the transmission reduces the
interference between the MTs in the cell, and also reduces inter-cell interference. However
due to the fast growth of connected and IoT devices being deployed, especially in indoor
environments, interference becomes a large problem to manage.
36
Figure 2.13: Rain attenuation in mmWave [18]
µ f =2µ .15 [KHz] Cyclic Prefix Supported for Data Supported for Sync
0 15 Normal Yes Yes
1 30 Normal Yes Yes
2 60 Normal, Extended Yes No
3 120 Normal Yes Yes
4 240 Normal No Yes
Table 2.1: 5G Numerology
2.4 Physical layer

2.4.1 Numerology
NR operates in two frequency ranges, FR1 (450 MHz – 6 GHz), and FR2 (24.25 GHz
– 52.6 GHz)- millimeter wave. Scalable and flexible frame structure is a key to implement
the NR deployment in such broad and diverse spectrum. Numerology is a new concept
created in the 3GPP specifications for NR and its most representing of the subcarrier
spacing in the 5G frame [19]. In LTE, this terminology was not necessary because there
was only one subcarrier spacing (15 KHz), while in NR there are multiple subcarrier
spacings that can be used. The supported numerologies are summarized in Table 2.1,
timings and durations in Table 2.2 and number of slots in Table 2.3.
37
Subcarrier 30 kHz (2 ×15 60 kHz (4 ×15 15×2n kHz(n =
15 kHz
Spacing kHz) kHz) 3, 4, . . . )
OFDM symbol
66.67 µs 33.33 µs 16.67 µs 66.67/2n s
duration
Cyclic prefix
4.69 µs 2.34 µs 1.17 µs 4.69/2n s
duration
OFDM symbol
71.35 µs 35.68 µs 17.84 µs 71.35/2n s
including CP
Number of
OFDM
7 or 14 7 or 14 7 or 14 14
symbols per
slot
500 µs or 1,000 250 µs or 500 125 µs or 250
Slot duration 1, 000/2n s
µs µs µs
Table 2.2: 5G Physical Layer Duration per Numerology
As shown in Table 2.1, not every numerology can be used for every physical channel
and signals, though most of the numerologies can be used for both. The multiple nu-
merologies (subcarrier spacings) are motivated by the changing characteristics of the 5G
channel depending on the operation frequency (sub 6 GHz or mmWave).
Slot f rame subf rame
µ NSymb Nslot Nslot
0 14 10 1
1 14 20 2
2 14 40 4
3 14 80 8
4 14 160 16
Table 2.3: Number of Frames and Slots in 5G per Numerology
2.4.2 Frame structure

Depending on the numerology used, the slot changes in length. Lower subcarrier
spacing will result in the orthogonal frequency division multiplexing (OFDM) symbols
being closely positioned in the time domain. And since the number of OFDM symbols is
fixed in a slot (14 symbols/slot for normal CP, and 12 symbols/slot for extended CP) at
all the numerologies, the slot duration gets lower with wider subcarrier spacing. However,
the duration of the radio frame does not change (10 ms).
The main differences between the legacy LTE TDD Subframe configuration and the
NR slot configuration are [20]:
38
Figure 2.14: 5G Downlink Channel Mapping
1. In NR, the DL/UL assignment changes at symbol level compared to assignment at

subframe level in LTE
2. Slot format patterns in NR are much more diverse than LTE.
3. Symbol assignment for NR can be UL, DL, or flexible.
The resource grid for NR is almost identical to the LTE resource grid but differs in
its physical dimension (i.e. Subcarrier spacing, number of OFDM symbols per frame)
since the dimension in NR is depending on the numerology. A slot is typically the unit
for transmission used for scheduling, but in NR the system has the ability to start and
end the transmission at any OFDM symbol (non-slot based scheduling) necessary and
can utilize mini-slots that can occupy 2, 4 or 7 OFDM symbols to facilitate very low
latency for critical data transmissions and minimize interference [21]. The Transmission
Time Interval (TTI) can be considered as the slot duration as considered in [12]; in the
paper the TTI is considered as the duration of the subframe. However, in the 3GPP
specifications, the duration of the subframe is constant and the duration of the slot is
the one dependent on the numerology/SCS. The 5G NR channel mapping is presented
in Figure 2.14.
2.4.3 Duplexing
The duplexing schemes supported in NR are Frequency Division Duplex (FDD), Time
Division Duplex (TDD) with semi-statically configured UL/DL configuration, and Dy-
namic TDD. For TDD operation, each OFDM symbol in a slot can be configured as DL,
UL, or flexible. Where a symbol configured as flexible can be used in either DL or UL op-
erations. The allocation of UL and DL symbols happens in cell-specific and MT-specific
Radio Resource Control (RRC) configurations. Dynamic TDD is the case where there is
no configuration for the slot and all the symbols are defaulted to flexible and whether
the symbol is used for UL or DL can be dynamically determined according to layer 1/2
signaling of DL control information (DCI) [21].
39
2.4.4 Synchronization signal block (SS/PBCH block)
In LTE, the signaling block had only one pattern of transmission. While in NR, the
transmission pattern of SSB is more complicated as it depends on different parameters
(numerology, frequency range. . . ) as illustrated by Figure 2.15. While the SSB set is
always sent in the first half frame (first 5 ms), its periodicity is not fixed. The SSB set
period can be {5, 10, 20, 40, 80, 160 ms}. An SSB is mapped to 4 OFDM symbols in
time and 240 subcarriers (20 RBs) in frequency. The location of the SSB in the frequency
domain is also flexible, but in its default, it is mapped to the center frequency. Figure
2.14 shows the mapping between the logical, transport, and physical channels in 5G NR.
The SSB is contains three different physical channels:
Primary synchronization signal (PSS) at symbol zero and occupies 127 consec-
utive subcarriers. It is used for downlink frame synchronization.
Secondary synchronization signal (SSS) at symbol two and occupies 127 con-
secutive subcarriers. And also used for frame synchronization.
Physical broadcast channel (PBCH) at symbols one, two and three, and occupies
240 consecutive subcarriers in symbols one and three each, and ninety-six in symbol two.
Its used mainly to broadcast the master information block (MIB).
40
Figure 2.15: 5G SSB Structure per Numerology
Beam sweeping (Idle state)
The SSB plays a crucial role in beam management and resource allocation, as part
of the beam sweeping procedure. Beam sweeping is implemented by assigning each SSB
to a specified beam. The beams carrying the SSB are swept in time and transmitted
towards MTs on different locations in the coverage area at regular intervals based on a
set periodicity {5/10/20/40/80/160 ms}. Beam sweeping procedure is illustrated in the
figure below.
41
Figure 2.16: Beam Sweeping [16]
Each SSB is identified by a unique number called SSB index. MTs located in the
coverage area around the gNB receive the SSBs and measures the signal strength of each
SSB. Each MT then selects its preferred beam as a result from its measurements and
communicates it back to the gNB. We note that the number of beams in the sweeping
procedure is directly related to the number of SSBs in an SSB set which is also directly
related to the numerology and frequency of operation used by the gNB. The maximum
number of SSBs in a set (max number of beams) is called Lmax . We can conclude, from
the predefined numerologies discussed above, that for sub 6 GHz frequencies Lmax can be
either 4 or 8 and can be swept in one dimension only, while in mmWave it is 64 and can
be swept in two dimensions.
2.4.5 Channel state information - reference signal

Like in LTE, channel state information-reference signal (CSI-RS) reporting is used in
connected mode to regularly estimate the channel conditions for mobility management
purposes. The CSI-RS spans {1, 2, 4} OFDM symbols and they are transmitted following
one of two modes: periodic, semi-persistent/aperiodic. The CSI-RS is a downlink signal
sent by the gNB and multiple CSI-RS can be configured to the same SS burst. CSI-RS is
also used for beam management purposes in sub 6 GHz for analog beamforming. In the
42
Figure 2.17: Periodic and Aperiodic CSI-RS [23]
downlink, for analog massive MIMO systems, there are multiple schemes that can be used
for beam management either replacing SSB based beam management or complementing
it [22].
Single CSI-RS Analogous to LTE Class A, the CSI-RS may or may not be beamformed
an its typically intended for arrays having 32 TXRUs or less with no beam selection (no
CRI). Its process is for the gNB to transmit the CSI-RS to the MT that in turn computes
and sends the Rank Indicator (RI)/ Precoding Matrix Indicator (PMI)/Channel Quality
Indicator (CQI) to the gNB.
Figure 2.18: Single CSI-RS Signaling [22]
Multiple CSI-RS It combines beamforming with CSI-RS and CSI-RS Resource Indi-
cator (CRI) feedback. The gNB transmits one or more CSI-RS each in different direction,
the MT then computes the CRI /PMI/CQI and transmits it to the gNB. It supports ar-
rays having arbitrary number of TRXUs and can be used as beam refinement in P-2 after
SSB sweeping.
Figure 2.19: Multiple CSI-RS Signaling [22]
43
Figure 2.21: codebook-based beamforming massive MIMO cell Architecture
SRS-Based Designed for TDD systems. The MT sends the SRS signal and the gNB
computes the precoding weights. Since in TDD the DL and UL channels can be assumed
identical, the UL channel characteristics calculated by the gNB can be assumed for DL
also.
Figure 2.20: SRS Based Signaling [22]
Cell architecture
In NR, the sector-based cell architecture is no longer applicable in order to overcome

the disadvantages of the usage of the mmWave band by using beamformed transmission.
The cell architecture will be dependent on the characteristics of the massive MIMO
antenna used at the gNB. It has been reported in that Nokia, for example, had a system
with 128 antennas that can produce 32 beams, thus, a 32 beams massive MIMO system,
with the aim to schedule up to 4 beams simultaneously. Below is an example of a 20
beams cell sector, spanning over an angle of 120° . Note that the predefined beams are
those used for signaling and control, and the data beams can be dynamically formed
depending on the cell usage.
EPRE and power allocation
The energy per resource element (EPRE) was a part of LTE power control before 5G
and signifies the energy allocated to each resource element in a physical channel. Some
of the relations of allocated power per resource element are highlighted in the 3GPP
specifications [20] 15]. These relations can help in estimating the increase of the antenna
44
Number of DM-RS CDM DM-RS configuration type DM-RS configuration type
groups without data 1 2
1 0 dB 0 dB
2 -3 dB -3 dB
3 - -4.77 dB
Table 2.4: The ratio of PDSCH EPRE to DM-RS EPRE
gain between the data and the signaling beams. The downlink EPRE directly specified
are below. physical downlink shared channel (PDSCH) EPRE to DM-RS EPRE varies
with the number of DM-RS CDM groups without data and given by Table 2.4 [15]. SSS,
PBCH DM-RS and PBCH have the same EPRE. The ratio of PSS EPRE to SSS EPRE
in a SS/PBCH block is either 0 dB or 3 dB. The ratio of PDCCH DMRS EPRE to SSS
EPRE is within -8 dB and 8 dB [20].
2.5 Conclusion
In this chapter, we introduced the 5G NR physical layer and radio access network
(RAN) technologies. We also introduced massive MIMO antennas, discussing their dif-
ferent possible architectures, deployments, and beamforming techniques. The high paryh-
loss in mmWave bands will require high transmitted power to ensure SIR threshold, which
can be achieved using massive MIMO antennas. Massive MIMO antennas can have many
array structures that may allow multi or single user transmission, and digital, analog or
hybrid beamforming. Different strategies of downlink power control can also be used like
zero-forcing or max-min fairness. 5G networks will also be deployed in heterogeneous
networks with small-cells and macro-cells, and as NSA and SA technology. Moreover,
different sub-carrier spacings can be assigned at the 5G frames which affect slot timings
and physical channels’ bandwidth. Uplink and downlink assignment can also be done at
symbol level and can be assigned flexibly by the operator.
It is apparent from this chapter, that measurement procedures need to be revisited for
5G systems to get an accurate EMF values. The main challenges for 5G measurements
stem from the spatio-temporal variation of the emission alongside the effects of beam-
forming and beam refinement. In the next chapter, we introduce the metrics specified for
EMF exposure estimation, and we discuss the different types of measurement techniques
that can be used for 5G systems. We also present the results of an in-situ measurement,
using the Keysight PXA signal analyzer, of a 5G massive MIMO antenna in different
scenarios and using different methods.
45
Chapter 3
In-Situ Exposure Assessment of 5G

Networks
Contents
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Electromagnetic field exposure metrics . . . . . . . . . . . . 47
3.2.1 Specific absorption rate . . . . . . . . . . . . . . . . . . . . . . 47
3.2.2 Power density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 5G NR measurement methods and scenarios . . . . . . . . . 48
3.3.1 Full spectrum measurement . . . . . . . . . . . . . . . . . . . . 49
3.3.2 SSB measurements . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.3 Beam refinement . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 5G massive MIMO measurements . . . . . . . . . . . . . . . 52
3.4.1 Measurement setup and scenario . . . . . . . . . . . . . . . . . 53
3.4.2 Demodulation domain measurements . . . . . . . . . . . . . . . 54
3.4.3 Frequency domain measurements . . . . . . . . . . . . . . . . . 58
3.4.4 Time domain measurements . . . . . . . . . . . . . . . . . . . . 61
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
46
3.1 Introduction
Since its emergence and spread, the human exposure to EMFs from wireless communi-
cations and radio technologies have been a source of worry for both the general public and
for health professionals. And with each generation, and with the increasing deployment
of transmitting devices to meet the ever-increasing demand, the demand for more precise
studies, and clearly defined constraints grows larger. To give assurance to the public,
and to maintain safe levels of EMF exposure, national and international standardization
bodies such as ICNIRP, FCC, the European Council, and IEEE-SCCs emerged to stan-
dardize and to give guidelines on evaluation tests and limits ensuring no effect on the
users.
In this chapter, we present the metrics of EMF exposure measurements used for com-
pliance assessment. We then present signal power measurements of 5G massive MIMO
antennas while discussing the different measurement methods presenting their advantages
and disadvantages and highlighting areas where more improvements should be made for
proper characterization of the exposure.
3.2 Electromagnetic field exposure metrics

The increase of deployment of cellular base stations and advanced wireless antennas,
like large-array antennas and small cells, have increased the public dislike of these struc-
tures and made more countries concerned for the public health. This has led legislators to
put forward restrictive limits on RF emissions. ICNIRP provides widely-accepted limits
[24] through out the scientific community and constitutes the current scientific consensus
[25]. Limits can be defined differently depending on the scenario in question with the
main two metrics being the specific absorption rate (SAR) and the power density.
3.2.1 Specific absorption rate

The highest exposure for the general public is handheld devices and near-field emis-
sions. The limits for such scenarios, the limits that are mainly considered by the SAR
value, where the body configuration, the emitting device’s positioning, and the device’s
design have strong impact on the absorbed power. The whole-body SAR can be defined
as follows
Pabs
SARW B = , (3.1)
m
where Pabs is the absorbed power by the body in W and m is its mass in Kg. SAR can
also be evaluated locally for specific body parts. Another way to express the SAR is by
47
linking it directly tot the incident electric field
σE 2
SAR = , (3.2)
2ρ
where E is the incident electric field in (V /m), σ is the conductivity in (S/m), and ρ is the
density of the tissue in (Kg/m3 ). The SAR is the quantity used for exposure evaluation
mainly in frequencies below 6 GHz in the IEEE standard and 10 GHz in the ICNIRP
standard.
3.2.2 Power density

While the notation of SAR is mostly used in the near-field region of EMFs, the power
density is the commonly used unit for exposure characterization in the far-field, especially
in frequencies higher than 6 GHz that will be used in 5G. Power density is described by
the power per unit area and is usually expressed in terms of watts per meters squared
(w/m2 ). In the IEEE-C95.1 standard the power density limit is considered for frequencies
above 3 GHz, and for frequencies above 10 GHz in ICNIRP (1998). The power density
is averaged over an area of 20 cm2 and the limit for averaging it over an area of 1 cm2
should not exceed 20 times the limit. The limit for the average power density has been
specified in ICNIRP (1998) are 50 and 10 (W/m2 ) for occupational exposure and general
public, respectively.
3.3 5G NR measurement methods and scenarios

5G systems are being designed to be extremely flexible in terms of both the antennas
used, the resource allocation, and the cellular system architecture. NR will have major
differences in handling data transmission and reception. Moreover, the exact architecture
and models are still being developed, and each constructor/operator can develop vastly
different technologies of antennas and RAN architecture. This diversity in implementa-
tion possibilities makes the characterization of the emission more challenging than for
older technologies, since it can be affected by many variables. Moreover, the EMF expo-
sure in a 5G network will be highly dependent, much more so than older generations, on
parameters that can only be represented statistically, e.g. MT distribution and density in
the cell. This shifts the focus of EMF exposure estimation from the theoretical maximum
to statistical percentiles of the possible exposure values [26].
Although the 5G waveform that has been decided by 3GPP specifications is OFDM
based, and shares some characteristics with its predecessor in LTE, the 5G Massive
MIMO antennas will require the development of a new approach to estimate the downlink
exposure. Unlike in LTE, the emission of a 5G antenna, seen from a certain location in
48
space, is not continuous. The beamforming from a hybrid massive MIMO antenna allows
the formation of up to n beams simultaneously at a certain point in time. In order to
estimate the actual exposure induced by a 5G antenna, this variation must be considered.
In order to properly estimate the exposure of a 5G antenna, the following issues must be
tackled: The estimation of the exposure under maximum traffic conditions, estimation
of the spatio-temporal variation of the antenna’s serving beam, and the increase in gain
due to beam refinement in the connected state. The following sections will review some
measurement methods and check their compatibility with 5G systems.
3.3.1 Full spectrum measurement

Frequency domain and channel power
Frequency domain measurements are possible with current widely available spectrum
analyzers which allows the measurement of the received power at a selected frequency
range. This however can be operated in two scenarios, swept and real-time.
Swept spectrum analyzer This mode occurs when the selected measurement fre-
quency is larger than the spectrum analyzer’s resolution bandwidth (RBW). This will
will divide the measurement bandwidth into sections that will get measured successively,
and will take a duration denoted by ”sweep time” to complete a sweep over the whole
band.
Measuring the 5G transmission channel in the frequency domain will introduce inac-
curacies in the measurement, for 5G more so than LTE, due to the high variability of the
beamformed emissions and its dependence on the traffic variations, and the impossibility
of the separation of the downlink from the uplink symbols in TDD. Since the sweep time
is usually large compared to beam assignment frequency which can be done at subframe
level.
Real-time spectrum analyzer This mode occurs when the measurement bandwidth
is equal or less than the RBW of the spectrum analyzer. This condition, while not easily
available in current hand-held measurement equipment, allows the real-time measurement
of the whole bandwidth without loss of information.
Wile real-time spectrum analyzer will overcome data loss due to sweeping, it will still
raise questions on the measurement performed in a 5G massive MIMO network. The
power received at a certain location in the cell depends on the traffic and MT density
in that specific location. An area with large number of active MTs will have a higher
average power value in the transmission channel than an area with low number of served
MTs. Moreover, the power hot-spots for a code-book based massive MIMO can easily be
missed when performing the measurement.
49
3.3.2 SSB measurements
Since full spectrum measurements of the 5G does not give a sufficient representation
of the received power, an alternative method has been suggested to get a conservative
estimation of the received power. It consists of measuring the the always on downlink
channels, then extrapolating it over the whole band. The Synchronization Signal Block
(SSB) is the only downlink channel that is independent of the traffic and is periodically
emitted with period T= {5, 10, 20, 40, 80, 160 ms} and is emitted in bursts depending
on the numerology used.
SSB signals are composed of three physical channels (PBCH, PSS, SSS) spanning
over 20 RBs in frequency and four OFDM symbols in time. The number of SSBs is also
specified by the used numerology and each SSB is mapped to a signaling beam in case of
beamforming. SSBs are located by default around the center frequency of the emission,
and it can be measured over a specified bandwidth less or equal to its bandwidth.
Time domain
Measurements in the time domain (zero-span), as in Figure 3.1, gives the instanta-
neous power received over the measurement bandwidth. Measuring the SS block requires
a RBW of around 7.2 MHz for 30 KHz subcarrier spacing, but a lower RBW (e.g. 1
MHz) can be used since the power of the SS block is constant (assuming no boosting of
the PSS channel relative to SSS) and not dependent on the traffic.
Figure 3.1: Zero-Span (Time Domain) measurement when data is being transmitted over
a single beams showing the SSB power and data in time when measuring over 1 MHz
bandwidth at the center frequency
Demodulation domain
Demodulation domain measurement, shown in Figure 3.2 produce the most accurate
results when measuring the SSB power. In addition to that, demodulating the signal
allows the access to some extra information like beam and cell identification. Demod-
ulation domain measurements also help measure the PDSCH - DMRS signal useful in
estimating the beam refinement gain explained below in section 3.3.3.
50
Figure 3.2: Demodulation domain measurement when data is being transmitted over the
SSB beam 3, showing measured powers of the SSBs, the channel power and the power
per resource element (PPRE) of signaling and data channels
Extrapolation
Be it in the time domain or demodulation domain, the measured instantaneous power

of the SSB channels can be extrapolated to the whole transmission bandwidth to estimate
the maximum possible received power from a specific beam at the measurement location.
The extrapolation can be done by multiplying the power per RB of the measured signal
RB
by the extrapolation factor K = NRB × Nsc , where K = NRB is the number of resource
RB
block (RB)s and Nsc is the number of subcarriers per RB, to obtain the power over the
whole band.
3.3.3 Beam refinement

One of the characteristics of 5G radio access is beam refinement, illustrated in Figure
3.3, which is the second step in establishing the connection between the gNB and the
MT for data transmission. This dictates that the antenna will adapt its beamforming
to be more suitable for the specific served MT. Therefore, the gain of the antenna when
transmitting in the signaling channel will not be the same as when transmitting in the
data channel.
Beam refinement, if used, means that we can’t simply measure the SSB channel
and extrapolate it to the transmission bandwidth, since the gain will be higher when
transmitting data. And the refinement gain cannot be necessarily obtainable from the
manufacturer/operator when doing in-situ measurements thus making it necessary to
estimate the increase in gain to avoid the underestimation of the emission.
This refinement gain can be estimated by measuring the difference in the received
instantaneous power in a small frequency band (e.g. 1 MHz) between the SSB and the
51
Figure 3.3: Representation of the beam refinement procedure as a second step of the
signaling after the SSB selection [8]
PDSCH. Since power control is not necessary in 5G (static or semi-static, if present),

the allocated Energy Per Resource Element (EPRE) is either constant or has a static
offset between SSB subcarriers and PDSCH subcarriers [27]. The measured received
instantaneous power per resource element should differ between the SSB channel and the
data channel only due to the gain of beam refinement. To determine the increase in gain
due to refinement, it is sufficient to determine the ratio of the received instantaneous
power in a resource element between the PDSCH and SSB channels as follows
P DSCH SSS
GBR = PRE − PRE dB (3.3)
We can assume that EPRESSS = EPREP DSCH [28], which is not necessarily true for
every scenario, but seems to be the default if no downlink power control is deployed.
Beam refinement gain can also be determined by calculating the power ratio between
the PDSCH-DMRS and SSB in demodulation domain, and accounting for the suitable
power control ratios if present. Refinement gain can be hard to detect if the PDSCH
EPRE is lower than the SSS EPRE. The ratio of PDSCH EPRE to DM-RS EPRE (same
as SSS EPRE) is stated in [27].
Beam refinement varies with the location of measurement since the refined beams are
generally precoded and can sometimes be used for vertical steering of the antenna beam,
as will be shown in section 3.4. Measuring in a real network however, makes it hard to
distinguish data channels for each beam in the time domain thus deducing the refinement
becomes more difficult.
3.4 5G massive MIMO measurements

In this section we present multiple measurements done on a 5G massive MIMO an-
tenna. We present exposure measurements in frequency (channel power) domain and by
52
extrapolating the SSB power done in both time domain (zero-span) and demodulation
domain. We analyze these measurement methods and compare them, we also present the
advantages and disadvantages of each of them.
3.4.1 Measurement setup and scenario

In this section we present measurements done on a 5G massive MIMO antenna, emit-
ting over a 100 MHz bandwidth at the 3.65 GHz center frequency, using Keysight’s
PXA signal analyzer co-located with a receiving MT. It involved a 64-elements antenna
transceiver capable of 1-D sweeping in the horizontal direction using SSBs, and capable
of 2-D beamforming in both horizontal and vertical directions for data transmission using
CSI-RS. The beamforming vectors were predefined in a 7 × 4-beam code-book as shown
in figure 3.4 for data transmission with IDs ranging from 0 to 30 divided into 7 rows
and 4 columns. The PXA was installed at a fixed distance directly in face of the MIMO.
We measure the power received at the PXA when data is transmitted over beams 3, 11,
19, and 27. The measurements were performed to test different characteristics of the
5G antenna for different transmission scenarios. We present measurements in the time
domain (zero-span), frequency domain (spectral analysis), and demodulation domain.
We analyze the observations from the measurements and discuss their advantages and
shortcomings.
Figure 3.4: Representation of the measured massive MIMO’s beamforming code-book
53
3.4.2 Demodulation domain measurements
Figure 3.5: Demodulation domain measurement for 0% traffic load being transmitted on
the data channel and only the SSB channel is on
In Figure 3.5, we measure the downlink transmission of the 5G antenna in the de-
modulation domain when no traffic load is present. In this type of measurement, we can
get the power per resource element (PPRE) of each signaling block corresponding to each
beam formed at the BS. The main serving beam is the one that has the highest power,
which is at −70.65 dBm in this measurement and corresponds to the fourth SSB/beam,
the number of RB can then be used to extrapolate the total power.
54
Figure 3.6: Demodulation domain measurement when we send 100% traffic load of data
at beam 3
In Figure 3.6 3.7 and 3.8, the downlink transmission is measured also in the demod-
ulation domain for 100% traffic load and where the data is being sent on beams 3, 11,
and 19 consecutively, which represents the same horizontal direction, i.e. SSB beam, but
several elevation angles. We notice that the ranking of the SSB beams remains unchanged
even with slight changes in power values, which is to be expected. In this case, it is also
possible to measure the PPRE of the downlink data channel, PDSCH, and we notice the
difference in power between the SSB and PDSCH, and we notice that the ideal serving
beam for the MT is 11. This difference is due to the beam refinement gain done after the
signaling phase.
55
Figure 3.7: Demodulation domain measurement for 100% traffic load transmitted over
beam 11
Figure 3.8: Demodulation domain measurement for 100% traffic load transmitted over
beam 19
In Figure 3.9, we measure in the demodulation domain while transmitting data in

four randomly selected beams that are allocated every 20 ms. We notice that, while the
PPRE remains unchanged for the signaling channels, the PPRE drops significantly for the
PDSCH. This measurement scenario is more representative of the actual deployment of
the MIMO antenna in a 5G system, since many MTs will have to be served simultaneously
56
Figure 3.9: Demodulation domain measurement for 100% traffic sent over 4 different
beams
using different beams. In this scenario, the power allocated to each MT/beam, likewise
the frequency resources, depends on the MT’s requirement and the BS capability.
Figure 3.10: Frequency domain measurement over the whole 100 MHz band for 0% traffic
load
57
3.4.3 Frequency domain measurements
In Figure 3.10, we measure the channel power when no traffic is present. We notice the
power values at the center of the spectrum, which corresponds to the SSB signal power.
The channel power measured is, as expected, low at −63.5 dBm measuring the whole 100
MHz band, and the peak power value is measured at −35 dBm. A waterfall display is
also presented on the bottom half which shows the periodicity of the SSB channel.
Figure 3.11: Frequency domain measurement over the whole 100 MHz band for 100%
traffic load transmitted over beam 3
In Figure 3.11, 3.12, 3.13, and 3.14, we measure the channel power for 100% traffic
load being sent on beams 3, 11, 19, and 27, respectively. Just like in demodulation
domain measurements, we deduce that the optimal beam to the served MT, co-located
with the PXA, is beam 11 since it has the highest channel power. We also notice the
channel becoming more frequency selective, and more prone to fading, the more we move
away from the optimal beam and the transmission is moving away from being in LoS.
58
59
We also measure the spectrum when we emit simultaneously on four different beams
as shown in Figure 3.15. In this mode, we are measuring the power received from the
optimal serving beam to the MT and PXA, in addition to the multi-beam interference
which can be equated to multi-user interference in an actual deployment of the antenna.
traffic load sent over 4 different beams
60
3.4.4 Time domain measurements
We measure the received signal power in zero-span configuration over a RBW of 1
MHz, centered around the center frequency of the transmission. This bandwidth will
allow the measurement of the SSB in time-domain. In this measurement, since we are
emitting over the whole spectrum, and the RBW is fully covered by the SSB channel, the
measured power values in zero-span are distributed over the same bandwidth and thus
the power values at the SSB can be compared to the values of the data (PDSCH). We
also recall that the SSBs are associated to beams 0 to 7, and the optimal SSB corresponds
to beam 3.‘
Figure 3.16: Time domain measurement for 100% traffic load transmitted over beam 11
In Figure 3.16, we present the time domain measurement of the received power for
100% traffic load when transmitting at beam 11. In the figure, we measure the SSBs
alongside the PDSCH over a 1 MHz bandwidth. We notice the difference in measured
power between the optimal SSB beam, 3, and the power received from the optimal beam,
11, which is in this case 4.5 dB.
61
In figures 3.17 and 3.18, we perform the same measurement when transmitting in
beams 19 and 27. The SSB power values are the same, but the PDSCH power is lower,
in accordance with the other measurement types.
We also measure in zero-span, like with previous types of measurements, when trans-
mitting in four different beams, presented in Figure 3.19. We notice the the different
62
power values of the different beams received at the PXA. Measuring the PDSCH seems
straightforward from this configuration, however, the PDSCH is not necessarily sent over
the whole bandwidth, nor is it necessarily present around any specific frequency. In this
figure, we also notice the presence of periodic power spikes which can be attributed to
the CSI-RS channel. This channel spans only over 1, 2, or 4 OFDM symbols, meaning
that the instantaneous power measured in zero-span would not give visually-comparable
values to the SSB and PDSCH, their power values however can be extrapolated if their
configuration was known.
Figure 3.19: Time domain measurement for 100% traffic load sent over 4 different beams
3.5 Conclusion
From these measurements, we can predict the challenges when measuring a 5G massive
MIMO network’s exposure when actually deployed. Utilizing a swept spectrum analyzer
will introduce a loss in information when measuring the power in frequency domain since
the beam does not necessarily emit over the whole bandwidth. This loss can be significant
since the difference in power between beams can be very large in a network. Moreover,
measuring the channel power without loss of information due to sweeping requires a large
RBW, which may not be available for handheld analyzers or otherwise, since, for 5G
networks, transmission bandwidth can go up to 400 MHz.
The alternative way of measuring the SSBs and extrapolating the power to get a con-
servative estimation, while seemingly promising, can largely underestimate the received
power due to beam refinement after the initial SSB beam selection. The refinement gain
63
can be very significant, like in our case here, where the refinement is done at another
dimension completely, and cannot be reliably measured in a realistic network. Also ex-
trapolating the SSB power would give the highest possible power value at the location
of measurement itself, and can vary significantly between the locations since we would
not be sure of the specific location of the power hot-spot, especially in NLoS scenarios
where a beam does not necessarily have a single angle of departure. In addition to that,
multi-user antennas serving more than one MT in the same time-frequency block will
reduce the gain of the data channel without necessarily affecting the SSB this will further
add more uncertainty to the measurement since the gain will depend on the number of
MTs served.
For all the reasons above, and since there haven’t been a real deployment of 5G
massive MIMO network, characterizing and studying the exposure of massive MIMO
networks using in-situ measurements will be lacking. We believe it is essential to study
the exposure analytically to investigate the different characteristics of the network and its
antennas. It is also necessary to characterise the exposure under a more realistic network
scenario, in this dissertation, we opted to do that using stochastic geometry, which is
what we present in the following chapters.
64
Chapter 4
Introduction to Stochastic Geometry

in Wireless Networks
Contents
4.1 Mathematical background . . . . . . . . . . . . . . . . . . . . 66
4.1.1 Poisson point process . . . . . . . . . . . . . . . . . . . . . . . 66
4.1.2 Useful theorems and definitions . . . . . . . . . . . . . . . . . . 68
4.2 Cellular network modeling . . . . . . . . . . . . . . . . . . . . 69
4.2.1 Path-loss model . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.2 Small-scale channel fading . . . . . . . . . . . . . . . . . . . . . 71
4.2.3 The total received power . . . . . . . . . . . . . . . . . . . . . . 72
65
Both the performance and the EMF exposure in a wireless network depend largely
on the locations of the BSs and the MTs. This is especially the case for 5G and beyond
networks where the spatial distribution of emission is even more prominent than previ-
ous generations. In modern networks, with the number of transmitting nodes greatly
increasing and small cells are being deployed to increase capacity in low-coverage areas,
the network architecture can no longer be assumed as regular or deterministic. This has
prompted the modeling of the network not as regular cells, but as a stochastic process of
points either in two-dimensional or three-dimensional space.
Stochastic geometry is the area in mathematics that allow the analysis of such ran-
dom models and as such, it is the go-to for more realistic representations of the wireless
network. As such, it has been widely studied in the last decade by researchers in wire-
less networks mainly to study the performance of the network. In this dissertation, we
introduce using the same method to study the EMF exposure in the 5G massive MIMO
network.
4.1 Mathematical background

4.1.1 Poisson point process
Point processes are a collection of points randomly located on a mathematical space.
Therefore, they have been widely used to model wireless network components like BSs,
MTs, WiFi access points, etc. A point process can formally defined by [29] as follows:
A point process is a countable random collection of points residing in a measure space,
usually the Eucledian space Rd . The associated σ−algebra is the Borel sets B d , and the
measure is the Lebesgue measure.
Point processes can be characterized by counting the number of points falling in a set
A ⊂ R as
Φ = {x ∈ Rd : N ({x}) = 1} (4.1)
In wireless networks applications, the formalism of the simple point process, or sometimes
called orderly point process, is usually used where a single point can exist at a given
location. The counting measure of such point process is
N ({x}) ∈ {0, 1} a.s. ∀x ∈ Rd (4.2)
For simple point processes, the notion of boundedly finite point process is usually used.
A point process is boundedly finite if and only if
|A| < ∞ =⇒ Φ(A) < ∞ (4.3)
66
The simplest point process to consider is the homogeneous Poisson point process (PPP)
where for every compact set A, the point process Φ(B) has a Poisson distribution
with mean λ|B| where λ is the expected number of points per unit area, also known
as the intensity of the PPP. Moreover, if the sets A1 , A2 , . . . , An are disjoint, then
N (A1 ), N (A2 ), . . . , N (An ) are independent random variables. The PPP Φ with inten-
sity measure Λ can be defined by the joint probability distribution, for Ai , ∀i = 1, . . . , k
being compact sets, as
k
−Λ(Ai )xi
Y
Pr [Φ(A1 ) = x1 , . . . , Φ(An ) = xk ] = exp −Λ(Ai ) , (4.4)
i=1
xi !
for k being a finite positive integer. This distribution is also called the finite-dimensional
distribution (fidi) distribution.
The PPP, shown in Figure 4.1, has been widely used in many practical applications
for the mathematical tractability of the models it produces. One expression resulting
from 4.4, for n = 0 and k = 1, is of particular interest and is called the void probability
function. It gives that for any subset A of Φ,
Pr [Φ(A) = 0] = exp−Λ(A) . (4.5)
The void probability gives the probability that no points exist in A. It also represents
the complementary cumulative distribution function (CCDF) of the contact distance dis-
tribution, or empty space distribution defined for a generap point process as
F (r) , Pr[ku, Φk ≤ r]. (4.6)
The void probability function describes the distance distribution between a typical point
and its nearest point in the PPP.
A homogeneous PPP can also be stationary if its distribution is translation-invariant,
implying a constant intensity. It can be formulated as the following
Pr[Φ ∈ E] = Pr[Φx ∈ E] ∀E, x, (4.7)
where Φx is the point process Φ translated by x ∈ Rd . Similarly, a PPP is isotropic if

its distribution is rotationally invariant about the origin. A PPP that is both stationary
and isotropic is called a motion-invariant point process.
A special case of the PPP for a fixed number of points n is the uniform binomial point
process (BPP) ΦB . The number of points in C ⊂ W are identically and independently
distributed on a compact set B ⊂ Rd according to a binomial distribution on B with
|C|
parameters n = ΦB (B), and p = |W |
. And since the number of points is finite, the point
67
Figure 4.1: Representation of a Voronnoi tessellation of a Poisson Point Process
processes ΦB (W \ C) = n − ΦB (C) and are therefore not independent.

In the last decade, modeling wireless nodes as PPP has been widely studied in the
literature. Its mathematical tractability has allowed its usage in analyzing and optimizing
the performance of said wireless networks. Many emerging technologies have also been
studied by means of random distribution of wireless nodes to prove their functionalities,
some notable examples are massive MIMO networks [30], [31], distributed antenna arrays
[32], cell free massive MIMO [33]–[36], and heterogeneous networks [37], [38].
4.1.2 Useful theorems and definitions

Modeling the network as a point process, sums and products of functions evaluated
at these points is essential. An obvious example is the interference on a wireless network
is a sum over all interfering nodes. Equivalently, the total exposure at a particular MT
is the sum of all emissions from all active transmitting nodes in the network. Ideally, we
would like a complete statistical characterization of these sums and products, we often
opt to obtain transforms of the random variables.
Campbell’s theorem
Campbell’s theorem is the most important result about the expectation of a sum on
a point process. For a point process Φ on Rd and for f : Rd 7→ R being a measurable
P
function, the random sum S = x∈Φ f (x) is a random variable with mean
Z
E [S] = f (x)Λ(dx). (4.8)
Rd
68
For a stationary point process Φ ⊂ Rd with intensity λ, Campbell’s theorem reduces to
Z
E [S] = λ f (x) dx. (4.9)
Rd
Probability generating functional
For a non-negative integer-valued random variable X, the moment generating function

(MGF) MX is defined as
Z
X
MX (t) = E[t ] = tn fX (x) dx. (4.10)
Rd
This function can be used to compute the moments of the function. Most notably, the
2
mean E[X] = dM dt
X
|t=0 , and the variance Var[X] = d dtM2X |t=0 . We note that for X
having a continuous PDF, fX (x), MX (t) is the two-sided Laplace transform of fX (x),
and MX (−jt) is the characteristic function of X.
For a measurable function v : Rd 7→ [0, 1], the probability generating functional
(PGFL) of a point process Φ is defined as
!
Y
G[v] , E v(x) (4.11)
x∈Φ
for Φ being a PPP, the PGFL can be expressed as

Z
G[v] = exp − [1 − v(x)]Λ(dx) . (4.12)
Rd
4.2 Cellular network modeling

For the last few years, cellular network modeling is shifting from the classical hexag-
onal model to a more random distribution of wireless nodes. In fact, It has been shown
in [39] that the hexagonal model of modeling the BSs provides an upper bound of the
coverage probability whereas PPP models provide the lower bound. Stochastic geometry,
as a tool to analyze these random distributions, have shown great promise in describing
an actual implementation of wireless networks. In [40] the distribution of the BSs of
Paris has been shown to fit a β−Ginibre point process. And in [41] a promising method,
called the inhomogeneous double thinning approach, have been developed that aims to
represent existing wireless networks as known point processes.
These models of the spatial distribution of the BSs in the network can be comple-
mented by realistic and/or relevant channel and transmission models to get a more realis-
tic representation of the wireless network, or to study the behaviors of certain technologies
or scenarios. In this section, we introduce the different concepts of modeling a wireless
69
network, like antenna gains, transmission channels, path loss models, and other relevant
parameters. We then derive an expression for the average total power received in a simple
network.
4.2.1 Path-loss model

Single-state unbounded PL Model
The unbounded path-loss model, also called unbounded PL model, is the most com-
mon and simplest one. Defining r as the distance between the transmitting BS and the
receiver, we can define the path-loss as follows
β(r) = κr−α , (4.13)
where κ is the PL constant, and α > 2 is the path-loss coefficient, also called the path
loss exponent.
While this model is the simplest for the mathematical framework, it introduces a
singularity for the received power at the MT when r → 0. This model also assumes
transmission in the far-field which is not the case for lower values of r. To overcome
these shortcomings, we opt to use a bounded path-loss model. Another problem with this
model is the shortcoming when considering the LoS and NLoS since it assumes the same
exponent αLoS = αN LoS = α.
Single-state bounded PL model
A solution to the singularity problem in unbounded PL models is its bounded coun-

terpart. The bounded PL model can be achieved either by using the max function or
adding a factor to the distance between the BS and the MT. A bounded PL model can
be formulated as
β(r) = κ max(d, r)−α . (4.14)
Other forms of bounded PL models exist like β(r) = κ max(d, r−α ), or β(r) = κ(1 + r−α ).
Dual-state PL model
The dual state PL model assumes two path loss exponents, αL and αN for LoS and
NLoS propagation channels respectively. The model is expressed as follows

κ r−αL in LoS
L
β= (4.15)
κ r−αN in NLoS
N
70
Figure 4.2: Representation of the Rayleigh distribution for σ = 0.5
where κs is the path-loss constant for s ∈ L, N . Each state has a probability PL which is
the probability that the MT is in LoS or NLoS of the BS. The dual-state PL model can
be either bounded or unbounded by using any of the techniques presented before in this
section.
4.2.2 Small-scale channel fading

A fading model is the mathematical formulation of the effects of the transmission
channel on the amplitude and phase of the transmitted signal. While path-loss, which
represents slow changes in the signal, is represented by the path-loss model previously
discussed, small-scale fading represents the rapid changes of amplitude and phase of the
signal usually due to multi-path and is commonly represented by statistical distributions.
The most popular distribution for modeling the small-scale fading is the Rayleigh distri-
bution presented in Figure 4.2, and is used to represent what is called Rayleigh fading
channel [42]. The Rayleigh distribution has the PDF
x −x22
f (x) = e 2σ (4.16)
σ2
Multi-path propagation results from the signal getting reflected by numerous obsta-
cles between the transmitter and the receiver. Each path will have its own Doppler shift,
path attenuation, and time delay resulting in a linear, time-varying channel. Such chan-
nel, when no dominant path exists, can be represented by the Rayleigh fading channel.
This results from the fact that the envelope of the received signal follows the Rayleigh
distribution. When a dominant path exists, usually a LoS path, the small-scale fading
71
channel is often described by the Rician distribution [43].
4.2.3 The total received power

We consider a two-dimensional downlink (DL) cellular network where the BSs are
distributed according to a PPP denoted by Φ having an intensity λ. Base stations are
distributed in a 2D plane following a PPP ΦBS with intensity λBS . The MTs are assumed
to be uniformly distributed in the cell. The system is assumed to be in full buffer mode,
which is an acceptable conservative assumption for exposure estimation, and users are
being served over the whole transmission period.
The simplest path-loss coefficient model a single-slope path loss model, β = max(m, r−α ).
Where, α is the path loss exponent and r is the distance between the MT and the BS.
We also ignore the transmission noise and shadowing effects. We also assume a constant
antenna gain G.
For a NLoS channel, the default small-scale fading coefficient is assumed to vary
according to a Rayleigh distribution. A Rayleigh fading channel can be modelled by
independent and identically distributed (i.i.d.) complex Gaussian random variable with
zero mean and variance σ, h ∼ CN (0, σ). For this type of channel, the channel gain,
|h|2 ∼ Ex(1/σ), will be exponentially distributed with mean σ.
The exposure can be calculated by summing the received power at a certain point in
space from the serving base station and from all other interferers. The expression of the
total received power at a typical MT is as follows
X
E= Ptx |h|2 Gtx r−α , (4.17)
ri ∈ΦBS
where Ptx is the transmit power from the BSs, |h|2 is the small-scale fading channel
gain, and Gtx is the antenna array gain. To determine the CDF of the exposure, we
first determine the MGF defined as ΦE (t) = E[exp(jtE)]. The MGF can be expressed as
72
follows
" !#
X 2 −α
ϕ (t) = E exp jt Ptx |h| Gtx r (4.18)
ri ∈φBS
" #
(a) Y
E|h|2 exp j t Ptx |h|2 Gtx r−α

= Er (4.19)
x∈ΦBS
" #
(b) Y 1
= Er (4.20)
x∈ΦBS
1 − jtPrtxαGtx
i
Z ∞
(c) jtPtx x
= exp 2πλ α
dx (4.21)
m x − jtPtx
"
jtPtx Gγ̄m2−α
= exp − 2πλBW G PG ×
α−1
!# (4.22)
α−2 2
2 F1 1, , 2 − , jtPT x G BW PG γ̄m−α
α α
Here, (a) follows from conditioning |h|2 and r, (b) follows from the PDF of the exponential
distribution, and (c) from the PGFL 4.12 of a PPP. Where 2 F1 (a, b, c, z) is the Kummer
confluent hypergeometric function defined in [44], α is the path loss exponent, BW is the
beamwidth, λ is the PPP intensity, G is the average gain, Ptx the transmit power, and
m the minimum separation distance between the BS and the MT to avoid infinite values
at the BS location.
The CDF of the exposure can be determined using the Gil-Peleaz theorem [45] defined
as follows
1 1 ∞ Im [e−jtx ϕ (t)]
Z
F (x) = − dt. (4.23)
2 π 0 t
The result obtained from applying the PGFL to 4.22 is verified with Monte-Carlo simu-
lations as shown in Figure 4.3. In the Monte-Carlo simulation, the network was modeled
as having 2000 points, on average, representing the BSs randomly distributed in the two-
dimensional plane following a PPP in an area Rnetwork satisfying BS density λ. The total
power is the sum of all powers received from the different BSs using the already defined
path-loss model and modeling each channel as complex Gaussian. The simulation was
performed over 5 × 104 runs and lasted ∼ 1 minute.
73
Figure 4.3: Cumulative distribution function of the total power received
Using this approach, studying the trends of the EMF exposure for different BS densi-
ties. The superposition of multiple independent networks is also simple just by summing
the multiple BS point processes. This model however, is representative of the 5G network.
As we discussed in the previous chapters, the usage of massive MIMO antennas will be
widespread in future network. Here, the characteristics of massive MIMO antennas and
5G, like beamforming, MIMO channels, mmWave, and multi-user transmission, are not
considered. In the following chapters we introduce more relevant models that considers
important 5G network parameters.
74
Chapter 5
A Statistical Estimation of 5G
Massive MIMO Networks’ Exposure
Using Stochastic Geometry in
mmWave Bands
Contents
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.1.1 Our approach and contributions . . . . . . . . . . . . . . . . . 77
5.2 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2.1 Path Loss Model . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.2 Antenna model . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.3 Channel model . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3 Exposure estimation . . . . . . . . . . . . . . . . . . . . . . . . 84
5.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
75
As discussed in the previous chapter, a simplistic classical network model is not repre-
sentative of 5G massive MIMO transmission and will result in over-conservative exposure
values. In this chapter, we aim to prove this claim by using more realistic channel and
antenna models to derive a closed-form expression of the distribution of the total power
receiver at the typical user in a massive MIMO network in mmWave, and by comparing
the obtained results to the simplistic model derived in the previous chapter. In this chap-
ter, we assume that the BSs and the MTs are distributed following a PPP. The power
received at the transmitter is modeled as a shot-noise process with a modified power law.
The distributions of 5G massive MIMO antenna gain and channel gain were obtained
by fitting simulation results from the NYUSIM mmWave channel simulator [46]. The
fitted distributions, e.g., exponential and gamma distribution for antenna and channel
gain respectively, were then implemented into an analytical framework and validated by
Monte-Carlo simulations. We then perform sensitivity analysis to investigate the impact
of key parameters, e.g., BS density, path loss exponent, and transmission probability.
5.1 Introduction
The explosive growth in communication devices in the last decade pushed the industry
towards exploiting the existing communication spectrum. The recent mass-deployment
of Internet of Things (IoT) devices paired with increasing demand for quality in the
streaming and entertainment industries made satisfying these requirements using the
same spectrum particularly challenging. To ensure that the huge spectrum capacity re-
quired to maintain a stable communication system is met, the industry started shifting
with the design of 5G networks to millimeter-wave (mmWave) frequency bands. For in-
door communication, mmWave bands are already in use, e.g., IEEE 802.11ad [47]. How-
ever, mmWave channels are fundamentally different from Ultra High Frequency channels
used for existing cellular communication protocols, they have higher propagation loss
in air, and low penetration for construction materials and foliage [48]. The high path
loss in mmWave frequencies makes it necessary to implement methods to increase the
received power at the mobile terminal (MT) in order to maintain an acceptable signal-to-
noise ratio (SNR) to decode the signal. One way of increasing the SNR is by increasing
the gain at the base station (BS). Therefore, beamforming became one of the essential
technologies for 5G mmWave communication. The usage of a large number of radiating
elements at the antennas will allow them to emit signals in fast-varying, high-gain beams
focused on the desired MT, while simultaneously decreasing the interference to other
MTs. Exposure compliance assessments are performed by manufacturers and operators
to ensure that emitting devices are compliant with safety regulations concerning human
exposure to electromagnetic fields. Safety regulations concerning human exposure to EM
fields have been specified by International Commission on Non-Ionizing Radiation Pro-
76
tection (ICNIRP) [49] and IEEE [50]. Multiple studies have been made over the years to
characterize the exposure in current and legacy communication systems which are based
on assuming the maximum theoretical power emitted for the antenna. However, these
characterizations struggle to stay accurate for 5G and future technologies due to the
fundamental differences between the systems. In [51] and [52], it has been shown that
the actual power contributing to the electromagnetic field exposure is much lower than
the theoretical maximum. This is due to the uncertainty in the values of the emitted
and received power from a massive MIMO antenna deploying beamforming. The spatio-
temporal variation of the antenna pattern, and its dependency on the MT distribution
and channel characteristics make the transition to statistical methods for the exposure
estimation a necessity if accurate estimations are desired. Statistical analysis of cellular
networks’ exposure has been a case study for the last couple of years, using simulations
to model the behavior of the channel and the transmission e.g., in [53], but accurate
analytical analysis is yet to be performed.
5.1.1 Our approach and contributions

The mathematical approach to analyzing cellular systems is often considered as a
promising solution [54]. However, for cellular networks, analytical tractability has been
proven by relying on the methodology of stochastic geometry while modeling the BSs us-
ing point processes. Stochastic geometry has been widely applied in the field of communi-
cation theory, and it has proven that it is a powerful approach in conducting performance
analysis and solving optimization problems. Examples of the usage of stochastic geom-
etry in modeling cellular networks can be found in [19–24]. In this study, we model the
locations of the base stations in the network as identically and independently distributed
following a homogeneous Poisson point process (PPP).
In this chapter, we use the active antenna model developed by 3GPP [55], [56], which
assumes a uniform rectangular array antenna, for communication in bands above 6 GHz.
As for the channel model, we use the NYUSIM statistical mmWave channel simulator
[1], which is backed by extensive measurements in the mmWave band, and was shown
to be better suited for above 6 GHz frequencies [57]. Multiple large-scale channel mea-
surements have been performed in the mmWave band over the last few years [14], [58]–
[60], and multiple studies compared the different channel models used by the different
standardization bodies as in [54], [57].
In this chapter, we fitted the channel gain and the antenna gain into statistical distri-
butions based on channel simulations from NYUSIM and the 3GPP antenna array model.
We determined the closed-form expression of the MGF for the exposure in the network,
which is equivalent to the total power received at a certain MT location, with which we
compute its cumulative distribution function (CDF). We analyzed the behavior of the
77
90th percentile of the exposure for different network parameters. We showed the compar-
ison between this model and a simplified, less accurate, model with simple antenna and
channel models in [61]. We performed a sensitivity analysis on the exposure expression
to show the impact of each parameter on the global exposure. The list of the symbols
used in the chapter is presented in Table 5.1.
5.2 System model

The aim of this study is to determine the closed-form equation of the electromagnetic
field exposure in a 5G massive MIMO cell emitting in the mmWave band. The base
stations are modeled as points of a stationary and isotropic Poisson point process ΨBS
with density λBS . The locations of said points are denoted by x ∈ ΨBS ⊆ R2 . The
MTs are distributed uniformly and independently in a bounded region of R2 and thus, in
addition to the assumption on the BS distribution, we can generalize the distribution of
the exposure over the whole cell area and the framework can be developed for a typical
MT denoted by MT0 located at the origin without losing generality. To investigate the
effect of the network load on the exposure, we assume that the BSs emit with probability
α, i.e., at a certain time-frame the number of active MTs is less than the number of
base stations λactive
MT ≤ λBS , which means that the BSs will have an effective density
of λef f = α λBS . Since line-of-sight (LOS) paths are the highest contributors to the
exposure, we assume that all the paths between the BS and the MT are LOS paths.
The BSs will emit with a constant power denoted by Ptx . We assume a 5G massive
MIMO network where the BSs are composed of antenna arrays with identical structure,
and thus identical radiation patterns. The BS is assumed as single-user MIMO, and
it emits towards one MT in a single time slot. We assume no downlink power control
exist in the network, which seems to be the case for 5G networks [62], so every MT is
being allocated the whole power resource for each transmission slot. We implement the
channel model NYUSIM, developed by New York University Wireless Group [46] which
divides the channel power into clusters and paths between the BS and the MT. The
BSi
received power Prx at each MT is dependent on the transmitted power, the propagation
t
distance, the channel gain, and the antenna gain. The global exposure Prx can then be
t BSi
P
defined as Prx = BSi ∈ΨBS Prx and it can be rewritten as
X
t
Prx = Ptx Hi Gi Li , (5.1)
BSi ∈ΨBS
where Hi , Gi , and Li are the link’s channel gain, antenna gain, and path loss, for the
link between the MT to the ith BS, respectively. To better analyze the distribution of
t
total received power Prx , we focus on studying the CDF of total received power, which
is defined as
78
Symbol Description
t
Prx Total Power Received at the center of the cell
BSi
Prx Power received from the ith BS at the center of the cell
Ptx Transmitted power from all the BSs
Hi , Gi Channel and antenna gain from the ith BS to the MT
Path loss experienced by the transmitted signal from
Li
the ith BS to the MT
Zenith and azimuth angles in the local coordinate
θ, φ
system centered at the origin of the array
Radiation pattern and its vertical and horizontal
AE , AE,V , AE,H (θ, φ)
components respectively
Vertical and horizontal beamwidths of the antennas in
θ3dB , φ3dB
degrees
min [x1 , x2 . . . ] Numerically smallest number of xk
Am Antenna’s front-to-back ratio
SLAV , SLAH Vertical and horizontal sidelobe attenuation levels
AA (θ, φ) Array pattern of the antenna
Phase shift due to the [m, n] antenna element
vm,n
placement
wm,n Weighting factor due to the [m, n] antenna element
NH , NV Number of horizontal and vertical antenna elements
θetilt , φescan Zenith and azimuth electrical down-tilt steering angle
dv , d H Vertical and horizontal antenna
R∞ element spacing
Γ (b) Gamma function Γ (b) = 0 xb−1 e−x dx, R (b) > 0
The Poisson point process and its density describing
ΨBS , λBS
the BS distribution in the cell
Ek [.] Expectation with respect to the random variable k
λactive
MT Density of the active MTs in the cell
α Emission probability of the BSs
M T0 Mobile terminal at the center of the cell
ri the distance between BSi and MT0
η Path loss exponent assumed constant in the whole cell
MGF and characteristic function of the random
ϕX , ΦX
variable X
FX (x) CDF of the random variable X
Γ (a, x) Upper incomplete gamma function
γ (a, x) Lower incomplete gamma function
Iid random variable describing the channel and
K
antenna gains
2 F2 (a1 , a2 , b1 , b2 , z) Generalized hypergeometric function
Table 5.1: List of symbols used in antenna pattern and model derivation
79
t
t (x) = P r
FPrx Prx ≤ x , x ∈ [0, +∞) (5.2)
In the following subsections, we describe the system model, including the antenna
array gain, the channel gain, and derive the expression to compute the CDF of the
exposure of the assumed network.
5.2.1 Path Loss Model

In this chapter, a two-state path loss model is considered. It is modeled as a shot
noise process with a modified power law [63]. We divide path loss into two regions, with
r < R0 and r ≥ R0 . The explicit expression for path loss Li (ri ) for the link between MT
and ith BS is denoted as
Li (ri ) = (Ki , ri < R0 Ki ri−η , ri ≥ R0 ) (5.3)
where ri is the distance between BSi and MT0 , and η is the path loss exponent assumed
constant in the network. K is an independently distributed random variable drawn from
a common distribution and independent of r. It accounts for the transmitted power, the
channel gain and the antenna gain for the ith link, defined as Ki = Prx Hi Gi . The details
of Hi and Gi are presented in the following subsections.
Remark 1. In this chapter, we adopt this two-state path loss model, which has already
included the simpler case by setting K(r < R0 ) = 0 used in the authors’ previous work
[61]. In the region where r < R0 , we approximate the path loss with a constant which
can be interpreted as a rough average of the attenuation in the near-field region while for
r > R0 , the power law decay model is used.
5.2.2 Antenna model

We implement the 3GPP active antenna model used to model the channels above 6
GHz [55]. The model can be used on frequencies up to 100 GHz. We have implemented
the 3D model (2D steering) with steering in both elevation and azimuth since both scan-
ning directions will be exploited in mmWave antennas [64]. The total antenna radiation
pattern is the combination of the radiating element’s radiation pattern and the array
factor. The modeling of the antenna array is explained in the following subsections.
Element pattern
By denoting θ and φ as the zenith and azimuth angles in the local coordinate system
centered at the center of the antenna array, respectively, and defined as 0° < θ < 180°
80
and −180° < φ < 180°, we can express the radiation pattern AE of an antenna element
as
AE (θ, φ) = − min [AE,V (θ) + AE,H (φ) , Am ] (5.4)
where AE,V and AE,H are the vertical and horizontal radiation patterns of the array
element, expressed as
AE,V (θ) = −min[12((θ − 90°)/θ3dB )2 , SLAV ] (5.5)
and " 2 #
φ
AE,H (φ) = −min 12 , Am (5.6)
φ3dB
where, θ and φ are the zenith and azimuth angles respectively in the local coordinate
system centered at the center of the antenna array and defined as 0° < θ < 180° and
−180° < φ < 180°. θ3dB = φ3dB = 65° are the 3 dB vertical and horizontal beamwidths of
the antenna, SLAV = SLAH = 30 dB are the vertical and horizontal sidelobe attenuation
levels, respectively, and Am = 30 dB is the antenna’s front-to-back ratio.
Array pattern
Implementing a large number of antenna elements in the array will allow high-gain
transmission of power towards the served MT by concentrating the field intensity in the
direction of transmission [65]. The interference of the transmitted electromagnetic fields
will form points of high intensity in certain directions, while producing low intensity
transmissions towards unwanted directions. The array pattern is determined according
to the physical implementation of the antenna elements and the electrical steering of the
main beam. The array’s radiation pattern AA is determined using the element radiation
pattern AE in (5.4), and assuming a uniformly spaced rectangular array (URA) in the
horizontal and vertical dimensions with identical element radiation pattern as in
  2

NH X
X NV
AA (θ, φ) = AE (θ, φ) + 10log 10 1 + ρ  wm,n vm,n − 1, (5.7)
m=1 n=1
where vm,n is the phase shift due to the antenna element placement, wm,n is the
weighting factor which provides the electrical down-tilt and attenuation of the antenna’s
sidelobes, and NH and NV are the number of horizontal and vertical antenna elements
respectively. As it is shown in (5.9), w is dependent on the antenna steering angles, the
electrical down-tilt steering angle θetilt and the electrical horizontal steering angle ϕescan ,
and since we assume that the main beam of the antenna is centered towards the receiving
MT, the antenna array will have a different radiation pattern towards each MT depending
on their location. The 2D slice of the antenna pattern on the azimuth plane for a 16 ×
81
Figure 5.1: 2D slice of the 3D antenna pattern realization of the 3GPP active antenna
array model with 256 antenna elements directed perpendicularly to the antenna array
over the steering angles in the azimuth and elevation.
16 array can be presented as in Figure 5.1.

dV dH
vm,n = exp 2πi (n − 1) cos(θ) + (m − 1) sin(θ)sin(φ) (5.8)
λ λ

1 dV dH
wm,n =√ exp 2πi (n − 1) sin(θetilt ) − (m − 1) cos(θetilt )sin(φescan )
NH NV λ λ
(5.9)
m = 1, 2, . . . NH (5.10)
n = 1, 2, . . . NV (5.11)
5.2.3 Channel model

In our model, we separate the two gains obtained from the channel simulation into
channel gain obtained directly from the NYUSIM channel simulation, and antenna gain
obtained by determining the antenna radiation pattern for every scanning angle after
each channel simulation. Using the NYUSIM channel simulator, we determine, in each
simulation, the LOS link characteristics between the serving antenna and the receiving
MT. From that link, we can determine the channel gain, and the angles of departure
(AoD) from the BS towards the MT. The AoDs are then used to determine the array
gain using the 3GPP active array model [55], modeled in Section 5.2.2 The antenna gain
for each beam can be determined from this model, according to its AoD, as shown in
the realization in Figure 5.1. We assume that the antennas are deployed in an urban
82
Figure 5.2: Illustration of our mmWave model (left) and the channel model (right). The
channel model follows the NYU Wireless Group mmWave channel model in [46].
Parameter Value
Frequency 28 GHz
Scenario UMI
Tx Power 0 dBm
Array type U RA
Number of elements 256
Antenna spacing 0.5 λ
Half-Power Beamwidth 10◦
Link Type LOS
RF Bandwidth 800 M Hz
MT Terminal Height 1.5 m
Base Station Height 35 m
Table 5.2: NYUSIM simulation parameters used for the channel simulations.
microcell (UMI) scenario. The channel model is presented in Figure 5.2. The parameters
used for the channel simulation are presented in Table 5.2. Running a large number of
simulations, we empirically fitted the distributions of the gain components into statistical
models. We chose the distributions for the channel and antenna gain by determining the
best fit out of the common distributions using MATLAB. The distributions’ parameters
summarized in Table 5.3 were determined accordingly.
Parameter Value Description

a 0.57 Gamma distribution shape parameter
b 1.45 Gamma distribution scale parameter
c 966.5 Exponential distribution exponent
Table 5.3: Parameters of the fitted distributions. a for the exponential distribution and
b, c for the gamma distribution
83
Figure 5.3: Plot of the fit of the antenna array gain into an exponential distribution for
a rectangular uniform antenna array with Ntx = 256 antenna elements.
Array gain
Using the AoDs from the simulated paths in NYUSIM we have determined, for each
path, the array gain g towards each specific MT. The distributions of the array gain G
using the 3GPP active antenna array model, presented in Figure 5.3, has been fit into an
exponential distribution with probability density function (PDF) fG defined as
fG (g) = ae−ag . (5.12)
Channel gain
Channel gain h is the gain produced by the exploitation of the channel between the
Tx and Rx such as the diversity gain, multipath, hardening, etc. [46]. This corresponds
to the sum of the gains of the different subpaths in NYUSIM channel model. We fitted
the channel gain H into a gamma distribution, as shown in Figure 5.4, with PDF fH
given in (5.13). The parameters for the fit gain distributions are summarized in Table
5.3.
1
fH (h) = hb−1 e−h/c (5.13)
Γ (b) cb
5.3 Exposure estimation

In this section, we derive the analytical framework based on the system model of the
t
5G network given in Section . Since the distribution of Prx is unknown, we adopt the
Gil-Pelaez inversion theorem [66] to compute the CDF defined in (5.2), which is based
t t
on characteristic function of random variable Prx . The CDF Prx is given by
84
Figure 5.4: Channel gain fit into a gamma distribution for MTs uniformly distributed on
a 2D plane and having a single element antenna array.
Z ∞
1 1 1
Im e−jtx ΦPrx

FPrx
t (x) = − t (t) dt (5.14)
2 π 0 t
t
where ΦPrxt (t) represents the characteristic function of P
rx , which can be derived from
moment-generating function as ΦPrx t (t) = ϕPrx t (jt). The MGF (MGF) of a random
tX
variable, defined as ϕX (x) : =E e , ∀ t ∈ R, is an aLTErnative representation of the
random variable other than its probability distribution. It can be used to determine the
n
distribution’s moments as E [X n ] = d ϕdxXn(x) , ∀ n ∈ R . Since the expected value of
0
the distribution is determined by derivation of the MGF in comparison to integrating
the probability density, using the MGF becomes more attractive for complicated random
variables thanks to the simpler operation. Following the path loss model defined in (6.2),
t
P
the total power at the MT0 can then be represented by: Prx (t) = i∈Π Bi f (Ki , ri ).
Where Bi is a set of random variables such that P (Bi = 1) = 1 − P (Bi = 0) = α. Since
we divided the space into two regions, the total power received in the whole region can
t in out in
be written as Prx = Prx + Prx where Prx is the total power received from transmitters
out
within distance R0 from the MT, and Prx is the total received power from transmitters
at distances greater than R0 . To account for transmission gain, we assume that Ki is
drawn from the distribution having the PDF: fK (k) = fG (g) .fH (h). Where, G and H
are the antenna gain and the channel gain distributions, respectively. As mentioned in
2.2., we fit the antenna gain into an exponential distribution with PDF fG (g) = ae−ag ,
1 k−1 −h/c
and the channel gain into a gamma distribution with PDF fH (h) = Γ(k)θ kh e . The
MGF of this model is presented in Theorem 1.
Theorem 1. The MGF of the exposure in the network modeled in Section 5.3, given the
85
array gain and channel gain in (10) and (11) is formulated as:
ϕ (s) = exp (πλαΘ), (5.15)
where,
! η2
2 2
b
a a

a

2 P e csc π η
Γ b + η
Θ=1− e Pe Γ 1 − b, −π
Pe Pe η a Γ (b)
πb c η2

2 a
+ (−1)b − csc (πb)γ b + , −
Γ (b) a η Pe
"
c 21 x η2 (5.16)
η b 2 2 a
+ − (−1) − π csc (πb)γ 1 + b + , −
2Γ (b) x η a η Pe
η2 ! #
xc
− Ω (b + 1) + Ω (b)
aPe
and a 2/η
a
Ω (x) = Γ(x) 2 F2 {1, 2/η} , {1 − x, 1 + 2/η} , (5.17)
c s c Ptx
R∞
and where, Pe = scPtx , Γ (a, x) = x ta−1 e−t dt is the upper incomplete gamma func-
Rx
tion, γ (a, x) = 0 ta−1 e−t dt is the lower incomplete gamma function [67], 2 F 2 is the
P∞ Qpj=1 (aj )k zk
generalized hypergeometric function defined as p Fq = k=0
Qq , and Γ (x) =
R ∞ x−1 −t j=1 (bj )k k!
0
t e dt is the standard gamma function.
Proof. The total exposure assuming the emission as shot noise process f (K, r) = Kr−η
t
for A < r < B, and Poisson distribution of transmitters, can be written as Prx (r) =
P −η
Ptx BSi ∈ΨBS Ki ri continuing from (5.1) for Ki = Hi Gi . We let Ki be drawn from a
discreet set {Ki } so that the shot noise process can be written as sum of independent shot
i i
P
noise processes Prx (r) = Ptx j f (Ki , r − rj ). The MGF of Prx can be determined by
solving (5.20). As per the result in [63], we can obtain the form in (5.21) for a continuous
set of Ki , and using the probability generating functional (PFGL) of a poisson point
process. Simplification by integrating by parts gives the form in equation
h i
i
ϕ (s) = E e−sPrx (r) (5.18)
  
X X
= EK exp −sPtx Ki (r − rj )−η  (5.19)
BSi ∈ΨBS j
Z B
PGFL
EK 1 − exp −sPtx Kr−η dr

= exp −µ (5.20)
A
The MGF of the exposure then can be represented by the product of the two independent
MGFs ϕ (s) = ϕin (s) ϕout (s), where ϕin can be obtained by substituting A = 0, and
86
B = R0 = 1 in (5.20). Likewise, for A = 1 and B = ∞, ϕout can be expressed by
"
h i
ϕout (s) = exp πλα EK 1 − e−sPtx K − s2/η EK (P tx K)2/η Γ (1 − 2/η)

#! (5.21)
h i
+ s2/η EK (Ptx K)2/η Γ (1 − 2/η, sPtx K)
The expression of ϕout , (5.21) can be rewritten into (5.22), replacing the expectations
with their integral forms. Each component can then be determined as presented below
to obtain the closed-form expression
" Z ∞ Z ∞
−skPtx 2/η
ϕout (s) = exp πλα 1 − e fK (k) dk − Γ (1 − 2/η) (sPT X ) k 2/η fK (k) dk
0 0
#!
Z ∞
+ (sPtx )2/η k 2/η Γ (1 − 2/η, skPtx ) fK (k) dk
0
(5.22)
To determine the PDF of K, fK (k), we first determine the CDF FK (k) of K as follows
def
FK (k) = P (K < k) (5.23)
= P (GH ≤ k) (5.24)
= P (GH ≤ k, G ≥ 0) + P (GH ≤ k, G ≤ 0) (5.25)
= P (H ≤ k/G, G ≥ 0) + P (H ≥ k/G, G ≤ 0) (5.26)
Z ∞ Z k/g Z 0 Z ∞
= fG (g) fH (h)dh dg + fG (g) fH (h)dh dg (5.27)
0 −∞ −∞ k/g
The PDF fK (k) can then be obtained by differentiating the CDF with respect to k using
the chain rule. Where, Kb−1 is the modified Bessel function of the second kind, and Γ (b)
is the gamma function.
Z ∞
1
fK (k) = fG (g) fH (k/g) dg (5.28)
|g|
Z−∞∞
1 1
g b−1 e− /θ ae− /g dg
g ak
= − b
(5.29)
0 |g| Γ (b) θ
b−1
q
2a (kθa) Kb−1 2 ka
2
θ
= b
(5.30)
Γ (b) θ
The 2/η th moment of k can then be expressed by the closed-form equation by solving
(5.31) knowing that K = PT X G H. Since we assume that Ptx is constant, the integral
87
can be solved to give (5.32).
Z ∞
2/η
EK K 2/η = Ptx k 2/η fK (k) dk

(5.31)
0
2/η
θ Γ (1 + 2/η) Γ (b + 2/η)
= Ptx , f or2/η < 1 (5.32)
a Γ (b)
MK (t) = EK e−sK is the MGF of K. The MGF can be determined by solving (5.33)

using the PDF expression from (5.32).
MK (t) = EK e−sPtx K

(5.33)
Z ∞
= e−skP T X fK (k) dk (5.34)
0
∞ b−1
e−su
Z r
(a)1 uθa 2 ua
= 2a Kb−1 2 du (5.35)
Ptx 0 Γ (b) θb Ptx Ptx θ
a
ae θs Ptx ∞ 1 θs−aP t
Z
= e tx dt (5.36)
Ptx θs 1 tb
a Z 1 −2
(b) ae θs Ptx w −a
= −b
e wθs Ptx dw (5.37)
Ptx θs 0 w
a 1−b
ae Ptx θs Ptx θs a
= Γ 1 − b, (5.38)
Ptx θs a Ptx θs
Step (a) follows from a change of variables as u = kPtx . To determine the closed-form
expression of the exponential integral in (5.36) we perform, in step (b), another change
of variables as w = t−1 and we obtain in (5.38) the incomplete upper gamma function
R∞
defined as Γ (a, x) := x ta−1 e−t dt. The expectation EK K 2/η Γ (1 − 2/η, sK) can be

determined using the law of the unconscious statistician [68] as in (5.40).

Z ∞
2/η
k 2/η Γ (1 − 2/η, sk) fK (k) dk

Ek K Γ (1 − 2/η, sK) = (5.39)
0
"
a
a b+2/η a
= csc (πb) e θs − − nΓ (b + 2/η) + nΓ b + 2/η, −
θs θs
#
a 2/η h ai
+ a (−1)b − Γ(b − 1) 2 F2 {2, 2/η + 1} , {2 − b, 2 + 2/η} ,
θs θs
(5.40)
Qp
P∞ (aj )k z k
where, 2 F 2 is the generalized hypergeometric function defined as p Fq := Qj=1
q .
k=0 j=1 (bj )k k!
Just by observing the exposure definition in (5.1), we notice some of the effects the
parameters will have on the total exposure. However, we are also interested in estimating
88
Figure 5.5: Verification of the analytical expression of the CDF of the power received
versus a Monte-Carlo simulation.
Parameter Value
λ 2 × 10−5
α 0.5
η 4
Ptx 1 mW
Table 5.4: Simulation Parameters used for the verification of the analytical equation with
Monte-Carlo simulations
the importance of each parameter on the total exposure and analyzing the way these
parameters affect the total exposure. In the next section, we first verify our model with
a Monte-Carlo simulation, then we investigate the variation of the 90th percentile of the
exposure, we perform a sensitivity analysis to quantify the importance of each parameter
on the total exposure, and then we compare the model we developed in this chapter with
the old model developed in [61].
5.4 Numerical results

In this section, we validate the model against numerical simulations, and we present
some numerical results of the variation of the 90th percentile of the exposure against
different network parameters. In Figure 5.5, we validate the CDF from with ϕ (s) given
by Theorem 1, with Monte-Carlo simulations of the same scenario, to verify the model
we developed while the parameters used in the validation are presented in Table 5.4.
The expression derived above has an indeterminate expectation, but from the de-
termined CDF we can easily determine the 90th percentile of the exposure, which is a
percentile that is often used to express the exposure in a network. We determine the
90th percentile as function of the base station density for different values of the path loss
89
Figure 5.6: 90th percentile of the exposure as function of BS Density λ for different values
of the path loss exponent η.
Figure 5.7: 90th percentile of the exposure as function of system utilization α for different
values of the BS density λ.
exponent η, the results are presented in Figure 5.6. We also determined the variation of
the 90th percentile of the exposure as a function of the system utilization α in Figure 5.7.
The parameters used to simulate the results of Figure 5.6 and Figure 5.7 are presented
in Table 5.5.
We also perform a comparison between the newly created model and the model in
our previous work [61] versus the exposure simulation derived directly from the NYUSIM
data in Figure 5.8. This comparison shows that the old model overestimates the exposure
especially at the lower percentiles. This overestimation can be attributed to the fact that
the old model assumes uniform array pattern, which is equivalent of having an isotropic
antenna gain at the transmitter, and gain values towards the MT. It is also apparent,
in the model derived in this study compared to the simulations, the small error between
the simulation and our model which can be attributed to the error in fitting finite gain
data into infinite distributions alongside the errors from the imperfect fitting. The former
90
Parameter Value
b 1.45
c 966.5
a 0.57
λ 2 × 10−5
α 0.5
η 3
Table 5.5: Parameters used in the analysis simulations for Figure 5.6 and Figure 5.7.
Figure 5.8: Comparison between the current model developed in this chapter (red cir-
cles), its verification using Monte-Carlo simulations assuming the gain distributions from
Section 5.3 (dashed line), and the model assuming a constant gain presented in 4.2 (blue
diamonds), versus a Monte-Carlo simulation of the exposure using gain values simulated
by NYUSIM (solid line).
error can be calculated depending on the maximum gain the antenna can produce as in
(5.41) where fX (x) is the probability density function of the fitted distribution, and Gmax
is the maximum gain the antenna array can produce.
Z ∞
erf it = fX (x) dx (5.41)
Gmax
Since massive MIMO will be implemented in really diverse scenarios, it is impor-

tant to investigate the effect of each variable on the exposure. For this, we perform a
variance-based sensitivity analysis on the calculated model which estimates the effect of
the variance of the inputs on the variance of the output as form of indices called Sobol
indices [69] . Sensitivity analysis is often performed to determine the importance of the
input variables on the output of the model. nth degree Sobol indices S1,2...n determine
the fraction of the output variance attributed to the set of inputs of degree n. We are
interested here in determining the total Sobol indices which can be defined as in (5.42).
The total Sobol indices determine the variance of the output due to the variance of an
input, in addition to the interactions between the specified input variable and the other
91
Input Variable Total Sobol Indices
α 0.447
η 0.932
λ 0.365
P 0.254
Table 5.6: Total Sobol indices of the inputs contributing to the 90th percentile of the
exposure in the network.
input variables. It is an alternative to computing the higher-order Sobol indices for every
variable.
EX i (V arXi (Y | X i ))
ST i = (5.42)
V ar (Y )
Since obtaining the exposure from the CDF requires solving an inverse function, it
takes a long time to determine the Sobol indices and it may introduce inaccuracies at
extreme input values. To avoid this, we use polynomial chaos expantion (PCE) using
Latin Hypercube samples to estimate a metamodel to represent the 90th percentile of
the exposure in the cell. PCE approximates the relation between the model’s output to
its inputs by expanding it in an orthogonal polynomial basis [69]. The metamodel can
be denoted as
X
Υ (ζ) = aβ Ψβ (ζ), (5.43)
β∈N d
where Ψβ are miltivariate polynomials defined as the product of univariate polyno-

mials of degrees (β1 , . . . , βd ) and aβ are the polynomial’s coefficients. The fit model has
a leave-one-out error of 0.14%. Using this metamodel we estimate the Sobol indices for
each one of the variables and we obtain the results in Table 5.6. We can see that the sum
of the total Sobol indices is greater than one, showing the interactions between the input
variables in determining the percentile.
5.5 Discussion
In this section, we discuss the results of the numerical outcomes of our model. We
discuss the effect of some of the network parameters considered throughout this study
on the exposure, and we discuss the result of the sensitivity analysis considering the
importance of each parameter on the global exposure. From the results presented in
Figure 5.5, we can show the accuracy of the developed model in estimating the total
exposure in the cell. The result shows a good overlap between the analytical framework
and the numerical validation. Here, the blue solid line is obtained by considering the
fitted distribution of the channel and antenna gain, i.e., (5.12) and (5.12). The purpose
92
of Figure 5.5 is to verify the correctness of the analytical framework. It should be noted
that the execution time in obtaining results from the analytical framework is much quicker
than the numerical simulations. The sensitivity analysis shows the big effect the path
loss exponent has in comparison to the other variables. In terms of exposure, this effect
is desirable especially knowing that the path loss exponent is relatively high in mmWave
channels leading to lower power in the cell. Although, since cellular networks are usually
designed to maintain a sufficient SNR, it would give clearer insight analyzing the exposure
in relation with the SNR. On the other hand, our study sheds the light on a usually
ignored, but increasingly discussed, aspect of cellular network design and analysis which is
the total electromagnetic wave power present in the cell area. As previously mentioned in
Section 1.1., the 5G NR architecture make it difficult to accurately measure the exposure
because of its beam behavior. In terms of in-situ measurements of the exposure, they
are being performed without consideration of the variability in the system utilization in
order to have constant beam behavior. This assumption will ignore the effect the system
usage will have on the actual exposure in the cell. As we can see from our analysis,
the transmission probability, which is directly related to the system utilization, it is the
second-most important variable affecting the exposure since it accounts for 0.44 of the
total exposure’s variance, and simply measuring at constant full transmission may lead
to major overestimation of the exposure.
5.6 Conclusion
In this study, we have determined a closed-form analytical representation of the down-
link exposure of a 5G massive MIMO network distributed following a PPP with realistic
transmission gain and channel representation using statistical distributions instead of
approximated value. We have analyzed the distribution of the exposure for different im-
plementation scenarios and we have shown the impact that the network characteristics
have on the exposure in the cell. This approach allows the accurate study of the massive
MIMO network without the need for costly simulations. We have also shown the signif-
icance of using a realistic antenna model as compared to a simple one. We also studied
the significance of the key parameters in the network, and we showed the importance
the network usage has on the total exposure and the importance of considering it when
conducting exposure analysis.
Even though downlink EMF exposure estimation is increasing in importance, most
network deployment planning and analysis focuses more on the network performance.
And since the goal of future wireless networks is to provide better performing networks,
it is of importance to study the EMF exposure jointly with the network performance.
Moreover, it is necessary to consider the worst case scenario of the EMF exposure in the
network, which is at the nearest MT to the serving BS, which is the focus of the next
93
chapter.
94
Chapter 6
Performance and EMF Exposure

Analysis of Massive MIMO
Networks With Max-Min Power
Control in LoS/NLoS Scenarios
Contents
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.1 Massive MIMO Network Modeling . . . . . . . . . . . . . . . . 98
6.2.2 Downlink Transmission . . . . . . . . . . . . . . . . . . . . . . 101
6.2.3 Max-Min Fairness Power Control . . . . . . . . . . . . . . . . . 103
6.3 Average Power Received . . . . . . . . . . . . . . . . . . . . . 103
6.4 Exposure to SIR Ratio . . . . . . . . . . . . . . . . . . . . . . 110
6.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.5.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.5.2 Average Power Received . . . . . . . . . . . . . . . . . . . . . . 116
6.5.3 Exposure to SIR Ratio . . . . . . . . . . . . . . . . . . . . . . . 122
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
95
In this chapter, we analyze the EMF exposure, in terms of total received power, in a
massive multiple-input multiple-output (MIMO) network at the nearest MT to the serving
BS. With the recent deployment of 5G networks, the potential risks of EMF exposure
are gaining increasing attention. However, most of the current research that focuses on
the mathematical modeling of 5G networks ignore downlink power control. Therefore, we
derive the framework of the average power received at the nearest MT under max-min
fairness power control using stochastic geometry, where MTs in the cell can be in either
LoS and NLoS channel conditions. In addition to that, we derive the expression of the
average exposure to SIR ratio at the nearest MT. We propose a tight approximation on
the power control coefficient. The framework on total received power and the ratio are
then validated by Monte-Carlo simulations. The results show that the average received
power monotonically increases as the density of the base station increases and the number
of users increases. It is also shown that the system is increasingly efficient in terms of
SIR considering the EMF exposure with the increase in the number of antenna elements
in the MIMO in NLoS environments, but less so in LoS.
6.1 Introduction
Radio frequency (RF) electromagnetic field (EMF) compliance assessments are critical
for manufacturers and operators to prove that the transmitting equipment is compliant
with safety regulations on human exposure [51] and to determine exclusion bounds around
base stations (BS)s. For this reason, metrics, and measurement procedure, were stan-
dardized to ensure proper estimation of the EMF exposure. In the far field, the EMF
exposure metric is usually the power density which is directly proportional to the re-
ceived power [70]. Traditionally, RF EMF exposure assessments are performed assuming
the maximum theoretical transmit power at the BS [71]. This will introduce an unnec-
essary bottleneck when deploying large, high-gain, antenna arrays for 5G networks, also
called massive multiple-input multiple-output (MIMO) antennas, which concentrate the
transmit power towards the desired MT.
Massive MIMO antennas have become a key technology in 5G systems for both sub-
6GHz and millimeter-wave bands [72]. The large number of transmitting elements in
one antenna array create a robust transmission channel [73] with high directed gain
which results in high throughput, spectral efficiency and energy efficiency at the receiving
MT [74]. The large massive MIMO allows the simultaneous transmission to multiple
MTs in the cell in the same time-frequency resource block, through spacial multiplexing
[75]. Power control schemes exist to ensure coverage for all the MTs in the cell, either
by allocating a minimal signal to interference and noise ratio (SINR) targets [76] or
ensuring equal SINR between MTs using max-min fairness power control [77]. Massive
MIMO has been extensively studied throughout the years with the main focus being the
96
performance [34], and efficiency. However, the RF EMF exposure cannot be overlooked
[78]. Moreover, statistical studies of the EMF exposure have mostly ignored the network
performance aspect. Since network planning is done mainly considering the performance,
the deployment of future networks should be studied in relation to their induced EMF
exposure.
Multiple precoding schemes exist to create signals with high directive gain, with the
goal of focusing the transmitted signal towards the served user while simultaneously
decreasing the interference [79]. When the MT is in line-of-sight (LoS) with the BS, the
precoded signal is sent over a single lobe directed at the MT, however, in non-line-of-sight
(NLoS), the precoded signal is sent over several different paths depending on the channel.
This spatial variation of the emitted power, while well studied in the domains of coverage
and throughput, is introducing new challenges for exposure estimations.
Many papers have addressed modeling the 5G network using stochastic geometry,
however, power control was mostly missing since they considered the typical MT. In [80]
a millimeter-wave network has been shown to outperform the ultra-high frequency one
for a dense 5G network. And in [81], 5G heterogeneous networks were modeled by PPP
and K-means clustering methods and their performance analyzed. As for EMF exposure
studies of 5G networks, statistical studies were performed to estimate more realistic power
levels [26] for simple network architecture. And recently, some studies opted to analyze
the average EMF exposure in the cell for randomly distributed BSs following a Poisson
point process (PPP) [82], [83].
In this chapter, we aim to characterize the power received and the SIR at the nearest
MT to the serving BS in a 5G massive MIMO network in LoS/NLoS scenarios. We
consider a more realistic channel model with max-min power control amongst all MTs.
Then, a tight approximation of the power control coefficient is proposed and validated
by Mon-Carlo simulations in order to obtain closed-form expression on the total received
power at MT0 .
The contributions of this chapter can be summarized as follows:
1. We derive a closed-form expression of the average received power for the signal, and
the inter-cell and multi-user interference, with max-min fairness power control in
LoS/NLoS scenarios.
2. We derive an expression allowing the evaluation of the average ratio between the
total power and the SIR in a single cell.
3. We analyze both the average received power and the ratio between it and the SIR for
multiple scenarios and show different behaviors in relation to different parameters.
We also propose a robust framework, which has big distinctions from the ones used in
exposure studies of massive MIMO networks, that can be considered for future research
97
on exposure assessment and complicance studies in highly variable networks.
The rest of this chapter is organized as follows. We present the system model in Section
II. We derive the expressions for the average total received power and the average ratio
between the total power and the SIR in Section III. In Section IV, we apply the models
and present the results to analyze the trends of behavior of the power received and SIR.
Finally, we give the conclusions and perspective based on the work in Section V.
Vectors and matrices are expressed by boldface lowercase and uppercase letters. (·)∗
denotes the complex conjugate of a matrix, and k·k is the euclidean norm of a vector. The
probability of an event and the expectation are denoted by Pr[·] and E[·]. The notation
a ∼ CN (0, IM ) represents a circularly symmetric complex Gaussian random vector with
zero-mean and a covariance matrix IM being an M × 1 identity matrix.
6.2 System Model

In this section, we present the system model that we use to evaluate the performance
of a massive MIMO network. We focus on some standard modeling assumptions for
BS and MT distributions since our aim in this study is to introduce a more relevant
scenario of evaluating the exposure in the cell, in addition to performance analysis in
this same scenario. Throughout this study, we assume the MRT precoding scheme at the
transmitting BS.
6.2.1 Massive MIMO Network Modeling

We consider a downlink multi-cell, multi-user massive MIMO network. This network
consists of BSs distributed following a homogeneous PPP ΦBS ⊂ R2 with density λBS .
The MTs are modeled as another homogeneous PPP, ΦM T with density λM T . We assume
the zero-cell to be a disk centered around the BS and having a radius of R = √πλ1 BS , which
is the average size of the voronoi cell of a homogeneous PPP. Since ΦBS is stationary and
isotropic, the MTs will be distributed inside the cell also following a homogeneous PPP

ΦlM T = Xkl , where Xkl is the k + 1-th nearest MT from its serving BS in cell l. We
condition ΦM T on having fixed number of points K in a single cell, representing the served
MTs in a single time-frequency block. The MTs in a single cell l are therefore distributed
following a binomial point process (BPP) [84] ΦlM T with density λlM T = K/R. We denote
by Rlk the distance between the k-th MT to the l-th BS, and by Rk the association
distance of the k-th MT. Each BS is equipped with M antenna elements and each MT is
equipped with a single omnidirectional antenna.
98
Channel Modeling
In this study, we consider both small-scale fading and uncorrelated path-loss for both
LoS and NLoS paths. We assume that the network operates using a time-division duplex
(TDD) scheme, to exploit channel reciprocity [85]. Thanks to these assumptions, the BS
will be able to estimate the downlink channel matrix using a pilot signal sent from the
MT. We assume a cell where each MT can be either LoS or NLoS independently from
each-other and independently from the distance to the serving BS, thus we can denote
KL and KN = K − KL as two binomial random variables representing the number of
MTs in LoS and NLoS conditions to the serving BS, respectively. The probability mass
function (PMF) of KL is that of the binomial distribution fKL (x) = Kx pxL (1 − pL )K−x .

The LoS and NLoS probabilities are PL and PN respectively. We assume that LoS paths
can occur exclusively between an MT and its serving BS. We justify this assumption since
the inter-cell interference occurs over high distances where the channel is progressively
more likely to be in NLoS condition. Same argument applies for denser small cell BSs
that are distributed on lower altitudes. We also present distinct path-loss models for
both LoS/NLoS channel conditions.
p
S S S
We denote by glk = βlk hlk , for S ∈ {L, N }, the M × 1 downlink random channel
S
vector between M Tk and BSl for a LoS/NLoS link, where βlk and hSlk are the path-loss
and small-scale fading vectors respectively. We introduce both vectors in the following.
path-loss
We introduce a two-slope path-loss model that represents LoS/NLoS channel condi-

tions. We express the fading exponents by αL , with probability pL and αN with probabil-
ity pN . Furthermore it is important, for modeling the total power received, to consider a
two-region path-loss coefficient to avoid the singularity for Rlk = 0. The path-loss vector
is expressed by
S
βlk (Rlk ) = max (d, Rlk )−αS (6.1)
= 1ΦLoS
MT
(k) (d, Rlk )−αL + 1ΦNMLoS
T
(k) (d, Rlk )−αN (6.2)
where αS is the path-loss exponent for LoS/NLoS, and d ∈ R+ is the distance of the
guard zone around the BS.
Small-Scale Fading
For a generic link between MTk and BSl we assume that hSlk ∼ CN (0, IM ) is an M × 1
i.i.d. Rayleigh fading vector representing the small-scale fading of the NLoS link between
an MT and a BS.
99
When transmitting in a LoS massive MIMO channel, the small scale fading is de-
terministic with very high correlation between the paths between the different antenna
elements and the served MT. Therefore, it cannot be expressed as i.i.d. Rayleigh, but its
small-scale fading can be represented by a deterministic model. The performance of such
case is investigated in [86] and [87] where it is shown that favorable propagation can be
obtained for LoS paths, and where a performance analysis is also performed. The M × 1
small-scale fading vector hLlk between BSl and MTk in the far-field can be expressed as
2π (M ) T
2π (2)
hLlk := eiθk e−i δ ∆k . . . e−i δ ∆k ∈ CM , (6.3)
where δ is the carrier wavelength, θk is the phase shift between the BS and user k assumed
(m)
to be uniformly distributed on [−π, π], and ∆k is the distance differential between the
mth antenna array element and the kth user as in
(m)
∆k := d(k, 1) − d(k, m), m = 1, . . . , M (6.4)
Assuming that the users are uniformly distributed on the circle of radius R, and the
antenna elements spacing between antenna elements is λ2 , (6.3) can be written as [88]
T
hLlk := eiθk e−iπ sin ψk . . . e−i(M −1)π sin ψk ∈ CM (6.5)
Channel Gain
The channel gain between a BS and an MT in a LoS path depends on the correlation
between the channel vector obtained from the uplink pilot and the precoding vector at the
BS. The function of this correlation is an intractable function, which is why we propose
a simplification of this gain. We divide the space around BS0 into two angular regions:
Main-lobe region where the user is in the main beam of the antenna i.e., the angular
separation between MTk and BS0 is less than the beamwidth, and side-lobe gain when
MTk is elsewhere. We can easily determine q the angular coordinates of the first nulls in
the antenna pattern from (6.5) to be θ0 = ± M3 . The gain function can be represented
by [89]
 √
M,
 |θ0,k | ≤ √3
√ √ √ M
Gk (M ) = M − 2π3 M sin √3 (6.6)
2 M
Gk (M ) =
 √ √ √ , elsewhere
M − 2π3 sin √3
2 M
The signal gain is identical for LoS and NLoS links. However, the interference gain at
MTk will be one of two cases, either aligned interferers when MTk is in the angular region
of the main-lobe or misaligned interference when MTk is elsewhere. Since the MTs are
uniformly distributed in the cell, the probability that a user is aligned with the beam of
100
Figure 6.1: Antenna gain pattern and the side-lobe approximation in the LoS link between
the BS and the MT
q
an interferer is PA = π1 M3 . A representation of the antenna pattern and the proposed
approximation in (6.6), for M = 256, is given in figure 6.1.
6.2.2 Downlink Transmission

In this study, we assume perfect CSI at the transmitter and no pilot contamination.
The perfect CSI assumption produces a conservative estimation of the downlink exposure.
The signal received at the nearest MT to the typical BS, MT0 is given by
√ X
H S
y0 = ρdl gl0 sl + w 0 , (6.7)
l∈ΦBS
where ρdl is the downlink transmit power, gl0 is the M × 1 channel gain vector at MT0
taking into account the path-loss and the small-scale fading, and sl is the transmitted
√
signal from the BS in cell l. It can be expressed as sl = K
P
k=1 ηlk alk qk , with ηlk being
the power control coefficient, and qk ∼ CN (0, 1) the transmit data symbols for the kth
MT in cell l. Moreover, alk represents the vector of the linear precoder. Under MRT,
the M × 1 precoding vector alk = [a1lk , ..., aM T
lk ] is
1
aSlk = H
hH
lk , (6.8)
E tr(Al Al )
1 √1
where Al is the M × K precoding matrix, the term E[tr(Al AH
is the normalization
=
l )]
M

parameter insuring the constraint on the transmit power E ρdl sl (sl )H = ρdl .
Taking into account the previous assumptions, the signal received at MT0 in cell l, is [85]
p  
S
ρdl ηlk βl0  S 2 X X
y0 = √ khl0 k + hl0 hH
lk
 qk , (6.9)
M l∈ΦBS k∈Φl
MT
101
Table 6.1: List of symbols and abbreviations used in the document
Symbol Description
ΦBS , λBS , ΦlM T , λlM T Point process and density of the BSs and MTs respectively
R Radius of the 0-cell
Number of MTs simultaneously served in a cell, number of
K, KL , KN
served MTs in LoS/NLoS respectively
M Number of antenna elements at each BS
BSl , M Tk BS in cell j and user k in the 0-cell
αS Path-loss exponent
d radius of the guard zone around the BSs
S S M × 1 channel, path-loss, and small scale gain vectors between
glk , βlk , hSlk
user k and its associated BS in cell l
ηlk Power control coefficient for MTlk
Distance between MTk and BSl , and association distance of
Rlk , Rk
user k in the 0-cell
Complex conjugate and conjugate transpose of a matrix, re-
(·)∗ , (·)H , | · |
spectively
PA Aligned probability
Average power received at a the typical MT and nearest MT
El , El0
to BSl respectively
and the total power received at MT0 in cell l can be written as
X
S S
Pl0 =M ρdl ηl0 βl0 + ρdl βi0 + ρdl βl0 ×
i∈ΦBS \{l}
(6.10)
 
X X
 ηlk + ηlk Gk (M ) ,
k∈ΦN LoS
M T \{X0 } k∈ΦLoS
M T \{X0 }
Where the first term in (6.10) represents the received signal, the second term repre-
sents the inter-cell interference, and the last term represents the multi-user interference
from users in LoS and NLoS. Similarly, the SIR can be written as follows
S
M ηl0 βl0
Ξ0 = P S
P . (6.11)
βi0 + βl0 ηlk Gk (M )
i∈ΦBS \{l} k∈ΦS
M T \{X0 }
We note from (6.11) that unlike the traditional approach, the SIR at MT0 decreasing
with K is not apparent since βl0 is also dependent on K. This will be presented further
on when analyzing the expression.
102
6.2.3 Max-Min Fairness Power Control
Max-min power control seeks to maximize the worst SINR in the cell by providing
equal SINR for all the terminals in ΦlM T [85]. The proposed model assumes no coordi-
nation between the BSs so that the power control coefficient is computed solely based
on the multi-user channel inside the cell, and the coefficient is determined independently
in each cell. This results in a simple optimization problem that produces a closed-form
solution for this particular scenario. We can write the power control coefficient at the
nearest MT to its BS as
1 + ρdl βlk
ηlk = P 1+ρdl βlk . (6.12)
βlk βlk
k∈ΦS
MT
This power control scheme introduces an important trade-off in the power received at
MT0 . Even though MT0 has the smallest path-loss coefficient out of all MTs in the cell,
it will have fewer high-gain resources allocated to it, as per (6.10).
We note that the power control coefficient ηlk is chosen under the constraint allowing

maximum power usage at each BS, i.e. E ksl k2 = 1, ∀l, giving
X
ηlk = 1, ∀l. (6.13)
k∈ΦlM T
6.3 Average Power Received

In this section, we derive the closed-form expressions of the average received power at
the nearest MT in cell l, MT0 , using an approximation of the power control coefficient.
From this section onward, we ignore the noise factor w0 in the evaluation of the total
power received. And without loss of generality, we assume that the typical BS is located
at the origin (Slivnyak theorem [29]). From (6.10), knowing that the precoding gain is
independent of the power control coefficient and the path-loss coefficient, and substituting
ηl0 by its expression in (6.12), we divide the expectation of the power received at MT0 to
its associated BS as
El0 = S + IM + II , (6.14)
where,
S = ρdl M E [ηl0 βl0 ] , (6.15)
103
is the average useful signal power,
 
X
S
IM = ρdl E βl0 ηlk Gk (M ) , (6.16)
k∈ΦS
M T \{X0 }
is the average multi-user interference power, and

 
X
II = E  βl0  , (6.17)
i∈ΦBS \{l}
is the average inter-cell interference power. The sum in the denominator of the power
control coefficient (6.12) makes the derivation of the expectations intractable. For this
reason, we propose an approximation for this parameter in the following proposition.
Proposition 1. For an MT k in cell l, the power control coefficient ηlk can be approxi-
mated, for large number of served users K, using the weak law of large numbers [90] as
in
1 + ρdl βlk
ηlk = ! (6.18)
(βljL )−1 + (βljN )−1
P P
βlk ρdl K +
j∈ΦL
MT j∈ΦN
MT
1+ρ β
L dl lk (6.19)
βlk ρdl K + KL E (βlj )−1 + KN E (βljN )−1
1 + ρdl βlk
= (6.20)
βlk ρdl K + KL Ῡ(αL ) + KN Ῡ(αN )
where Ῡ(αS ) is the expectation of the inverse of the path-loss coefficient from a typical
MT in the cell for S ∈ {L, N }. We validate this proposition for our model with a Monte-
Carlo simulation in Fig. 6.2. For minimal error, we assume K > 10 throughout this
chapter.
We present the expression of the expectation of the path-loss for MTs for either LoS
or NLoS, Ῡ(αS ), in the following lemma.
Lemma 2. The average of the inverse of the path-loss coefficient from a typical MT,
Ῡ(αS ), can be formulated as follows,
αdαS +2 + 2RαS +2
Ῡ(αS ) = (6.21)
(αS + 2)R2
Proof. We denote by FRk (x) = P (k ∈ Bd ) the CDF Rk which is the probability that the
104
user k falls inside the ball Bd = {b(0, x) : x ≤ R}. Its PDF can be determined as follows
d Pr [k ∈ b(0, x)] 2x
fRk (x) = = 2. (6.22)
dx R
Using the path loss model in (6.2) the nth moment of the distance between the origin
and a point distributed according to a BPP in a ball b(0, R) centered at the origin is
Z R Z d
E [Rkn ] = n
x fRk (x) dx + dn fRk (x) dx (6.23)
d 0
n dn+2 + 2Rn+2
= , (6.24)
(n + 2) R2
replacing n with αS completes the proof.
From proposition 1, the power control coefficients of the interfering users can be
assumed independent of the path-loss of the corresponding user so that their expectations
can be determined separately. We determine the expectation of the signal power received
at MT0 in the following theorem.
Theorem 3. The expectation of the useful signal power received at MT0 can be expressed
as follows
S = M ρdl 1 + ρdl pL QLl0 + ρdl pN QN

l0 L, (6.25)
where QSl0 is the expectation of the path-loss fading from hthe multi-user interference
i at
1
MT0 , determined in the following lemma, and L , EKL Kρdl +KL Ῡ(αL )+KN Ῡ(αN ) is the
expectation of the denominator of the power control coefficient.
Proof. Since the LoS probability of MT0 is independent of the distance, we can simply
write from (6.15)
S

S = ρdl M E ηl0 βl0 (6.26)
" #
S
1 + ρdl βl0
= ρdl M E (6.27)
ρdl K + KL Ῡ(αL ) + KN Ῡ(αN )
" S #
1 + ρdl ES,Rlk βl0
= ρdl M EKL (6.28)
" #
L N
1 + ρdl ERlk pL βl0 + pN βl0
= ρdl M EKL , (6.29)
h i
1

definingQSl0, S
ERl k βl0 and L , EKL Kρdl +KL Ῡ(αL )+KN Ῡ(αN )
and substituting them in
the equation gives (6.25) and concludes the proof.
105
Lemma 4. The expectation of the path-loss fading for the nearest MT to its serving BS,
Ql0 with path loss model defined in (6.2) is
K !
d−αS −1 d2 2

1 1 d
QSl0 = d2 (2K − 1) + R2 − R2 2 F1 − , 1 − K; ; 2

1− 2
4K 2 − 1 R 2 2 R
!
Γ −α2S +3

Γ(K)R−αS +3 2

−α S + 3 −α S + 5 d
+ − d−αS +3 2 F̃1 1 − K, ; ; 2 ,
2R2 Γ K + −α2S +3 2 2 R
(6.30)
where Γ(x) is the gamma function, B(a, b) is the binomial function, and 2 F̃1 is the regu-
larized hypergeometric function.
Proof. In a point process consisting of K uniformly distributed points in a 2-dimensional

ball of radius R centered at the origin, we denote by F̄Rl0 the complementary cumulative
distribution function (CCDF) of Rl0 for 0 < r ≤ R which is the probability that there
are less than n points in b(0, r). It can be written as [84]
k−1
X K
F̄Rk (r) = p (1 − p)K−1 , (6.31)
k=0
1
where p = r2 /R2 . F̄r0 can also be represented by the regularized incomplete beta function
[91].
F̄Rl0 (r) = I1−p (K, 1), (6.32)
The Euclidean distance Rl0 from the origin to the nearest neighbor follows a generalized
beta distribution of the first kind, the PDF can then be derived by differentiating the
CDF w.r.t. r as follows
fRl0 (r) = −dF̄r0 (r)/dr (6.33)

K−1
dp (1 − p)
= (6.34)
dr B(K, 1)
!
B(3/2, K) r 2
= β ; 3/2, K , (6.35)
B(K, 1) 2
where β(x; a, b) = (1/B(a, b))xa−1 (1 − x)b−1 is the generalized beta function. The nth
n
moment of Rlk , E [Rlk ] for d < rk < R can then be determined as
2
Z R r 2 K−1
n n+2
E [Rl0 ] = 3 r 1− dr (6.36)
R B(K, 1) d R
!
Γ n+3

n+3 2

Γ(K)R n + 3 n + 5 d
= 2 − dn+3 2 F̃1 1 − K, ; ; 2 , (6.37)
2R2 Γ K + n+3 2
2 2 R
106
for 0 < rk < d, E [βk ] can be determined likewise by replacing rn with dn inside the
integral. The summation of the expression in the two ranges gives (6.30) for n = −αS ,
and completes the proof.
We now determine the expectation of the multi-user interference at MT0 defined in

(6.16). This expression takes into account the different states an interfering MT can be
in, in terms of LoS/NloS, which produces different gains for the interfering signal at MT0 .
The derivation of the expectation is presented in the following lemma.
Theorem 5. The expectation of the multi-user interference at MT0 is
(1 − pL )K
IM = ρdl pL QLl0 + pN QN

l0
K(ρdl + Ῡ(αN ))
(6.38)
K(ρdl + Ῡ(αN )) Kρdl + Ῡ(αL ) + (K − 1)Ῡ(αN ) pL
× 2 F1 −K, ; ;
Ῡ(αL ) − Ῡ(αN ) Ῡ(αL ) − Ῡ(αN ) pL − 1
Proof. Knowing that βl0 and ηlk are independent for k 6= 0, and the array gain is inde-
pendent of the distance, we can write
 
h i
S0
X
IM = ρdl EKL QSl0 E ηlk Gk (M )  (6.39)
k∈ΦS
M T \{X0 }
We determine the expectation of the multi-user interference at MT0 conditioned on be-

ing in LoS by splitting the sum of the interference power to LoS interferers and NLoS
interferers as follows
   
X X
LoS
= ρdl ES,KL QSl0   S 0 = L
L N
IM E ηlk Gk (M ) + E ηlk (6.40)
k∈ΦL
M T \{X0 } k∈ΦN
MT
N 0
= ρdl ES,KL QSl0 (KL − 1)E ηlk
L
Gk (M ) + KN E ηlk S =L , (6.41)
since we have a finite number of MTs, the number of interfering MTs in LoS and NLoS
are not independent. Then uncoditioning from the LoS probability of MT0 , we determine
IM as
LoS
IM = ρdl ES IM (6.42)
= ρdl pL QLl0 + pN Ql0 EKL
N
L N
(KL − 1)E ηlk Gk (M ) + KN E ηlk (6.43)
Moreover, the interference gain from LoS MTs, Gk (M ), is independent of the distance
L
and the number of LoS MTs. Thus, we can get its expectation independently from ηlk as
107
follows
(6.43) = ρdl pL QLl0 + pN QN

L N
l0 (pA M + pN A Gk (M )) EKL (KL − 1)ERlk ηlk + EKL KN ERlk ηlk
(6.44)
We can express the expectation of the power control coefficient of interfering MTs in
either LoS or NLoS as follows
S −1
S ERlk (βlk ) + ρdl
ERlk ηlk = , (6.45)
Kρdl + KL Ῡ(αL ) + KN Ῡ(αN )
substituting this expression in (6.44) we get the following

Ῡ(αL ) + ρdl
pL QLl0 pN QN

(6.44) = + (pA M + pN A Gk (M )) EKL (KL − 1)
l0
!
Ῡ(αN ) + ρdl
+ EKL KN
(6.46)
= ρdl pL QLl0 + pN QN

l0 (pA M + pN A Gk (M )) Ῡ(αL ) + ρdl
!
KL 1
× EKL − EKL
Kρdl + KL Ῡ(αL ) + KN Ῡ(αN ) Kρdl + KL Ῡ(αL ) + KN Ῡ(αN )

K
+ Ῡ(αN ) + ρdl EKL
!!
KL
− EKL
(6.47)
= ρdl pL QLl0 + pN QN (pA M + pN A Gk (M )) Ῡ(αL ) + ρdl (L∗ − L)

l0
! (6.48)
+ Ῡ(αN ) + ρdl (KL − L∗ ) ,

h i
KL
where we define L∗ , EKL Kρdl +KL Ῡ(αL )+KN Ῡ(αN )
, ending the proof.
The number of MTs in LoS state can be represented by a binomial random variable
KL ∼ B(K, pL ) with probability mass function (PMF), fKL (k) = Kk pk (1 − p)K−k , and

the number of NLoS MTs is KN = K − KL . We determine the expressions of L and L∗

in the following lemma.
108
Lemma 6. The expressions of L defined in theorem 3, L∗ defined in theorem 5, and L∗∗
defined in theorem 8 in the following section below, can be expressed as follows
(1 − pL )K

K(ρdl + Ῡ(αN )) Kρdl + Ῡ(αL ) + (K − 1)Ῡ(αN ) pL
L= 2 F1 −K, ; ; ,
K(ρdl + Ῡ(αN )) Ῡ(αL ) − Ῡ(αN ) Ῡ(αL ) − Ῡ(αN ) pL − 1
(6.49)
KpL (1 − pL )K−1
L∗ =
Kρ + (K − 1)Ῡ(αN ) + Ῡ(αL )

Ῡ(αL ) + (K − 1)Ῡ(αN ) + Kρ 2Ῡ(αL ) + (K − 2)Ῡ(αN ) + Kρ pL
× 2 F1 1 − K, ; ; ,
Ῡ(αL ) − Ῡ(αN ) Ῡ(αL ) − Ῡ(αN ) pL − 1
(6.50)
and
¯ L )+(K−1)Υ(α ¯ N )+Kρ

K−1 Υ(α
KpL (1 − pL ) Γ ¯ L )−Υ(α
Υ(α ¯N )
L∗∗ = ¯ L ) − Υ(α¯N)
Υ(α
¯ L ) + (K − 1)Υ(α
Υ(α ¯ N ) + Kρ ¯ L ) + (K − 2)Υ(α
2Υ(α ¯ N ) + Kρ pL
× 3 F̃2 2, 1 − K, ¯ L ) − Υ(α
¯N) ; 1, ¯ L ) − Υ(α
¯N) ; .
Υ(α Υ(α pL − 1
(6.51)
Proof. The number of LoS MTs, KL , follows a binomial distribution in B. Following

from proposition 1, we can write

1
L = EKL (6.52)
Kρdl + KL Ῡ(αL ) + (K − KL )Ῡ(αN )
K
(a) X 1 K x
= pL (1 − pL )K−x (6.53)
x=0
Kρdl + x Ῡ(αL ) + (K − x)Ῡ(α N ) x
Where (a) comes from the expectation of a function of a binomial random variable. The
sum in this expression has the form of a hypergeometric function defined as 2 F1 (a, b; c; z) =
P∞ zn (a)n (b)n
n=0 n!(c)n
, where (x)n ≡ Γ(x+n)
Γ(x)
is the Pochhammer symbol. Similarly for L∗ and
L∗∗ ,
K
∗
X x K x
L = pL (1 − pL )K−x , (6.54)
x=0
Kρdl + xῩ(αL ) + (K − x)Ῡ(αN ) x
and
K
x2

∗∗
X K x
L = p (1 − pL )K−x . (6.55)
x=0
Kρdl + xῩ(αL ) + (K − x)Ῡ(αN ) x L
Substituting the equations accordingly gives (6.49) and (6.50) concluding the proof.
Theorem 7. We present the expression of the expected value of the inter-cell interference
109
Figure 6.2: Verification of the power control coefficient by comparison between the a
Monte-Carlo simulation of the useful signal power and the proposed asymptotic approx-
imation in 6.25
at the nearest MT to BSl , MT0 , as follows
d2−αN d2−αN

− pL QLl0 + pN QN

II = 2πλBS ρdl + l0 (6.56)
2 αN − 2
Proof. This expression can be simply determined by applying Campbell’s theorem for
sums over stationary PPP [92] as follows
 
X
II = ρdl E  βi0  (6.57)
i∈ΦBS \{l}
" #
X
S
= ρdl E βi0 − βl0 (6.58)
i∈ΦBS
Z d Z ∞
PGFL −αN 1−αN
dr − pL QLl0 + pN QN

= 2πρdl λBS d r dr + r l0 , (6.59)
0 d
solving the integrations gives (6.56) and concludes the proof.
6.4 Exposure to SIR Ratio

Cellular network design is usually optimized to maximize the coverage probability,
which is directly related to the received SIR at the MT. The exposure to SIR ratio will
give insight on how the exposure varies in a massive MIMO cell when the SIR varies due
to changes in different network parameters. We determine the PDF of the ratio between
110
the total power received and the SIR at MT0 for either LoS and NLoS networks in the
following theorem. In this section, we consider only the multi-user interference in the cell
for two reasons; the first being that it has the most contribution to the exposure, and the
other being the simplification of the formulation. We define the expectation of the ratio
between the total power received and the SIR in the following theorem, and we present
its derivation in the rest of this section.
Theorem 8. The expectation of the ratio of the exposure to SIR at the nearest MT to
the serving BS is presented as follows
ρdl
(KL − L∗ ) ρdl + Ῡ(2αN ) + K 2 + K − Var[KL ] Ῡ(αN ) + L∗∗ − 2KL∗

Rl0 = IM +
M
!
+ E Gk (M )2 (L∗∗ − L∗ ) Ῡ(αL ) + L∗ Ῡ(2αL ) + Var[KL ]LῩ(αL )

α+2
!
∞ − α+2
ρ2 x2 + 2x
Z
2 α K p
2 x + 4) + x
α
× 2
x p + x x (ρ
αR 0 x (ρ2 x + 4)
 p −2/α K−1
1/α 2 x + 4) + x
4 x (ρ
× 1 −
 
R 2 
(6.60)
where E [Gk (M )2 ] = pA M 2 + pN A Gk (M ), Var[K

h L2] =i KpL (1 − pL )) is the variance of the
K
binomial random variable KL , and L∗∗ , E νS (KLL ) previously determined in lemma 6.
Proof. The proof is provided in the rest of this section below.
Proposition 2. We can express the expectation of the ratio Rl0 as follows

" S 2
#
ρdl 1 S 2
β l0
Rl0 = IM + E E I(βlk ) KL E S
(6.61)
M νS (KL ) ρdl βl0 +1
Proof. We define the ratio of the exposure to SIR at MT0 as follows
I(βl0 , βlk )2
Rl0 , I(βl0 , βlk ) + . (6.62)
S(βl0 )
To simplify this expression, we separate the path-loss coefficient of MT0 , βl0 , and that of
the interfering MTs, βlk in I by defining the random variable I(βlk ) = I(βl0βl0,βlk ) νSρ(K
dl
L)
, it
can be expressed as follows
X
Sk −1
I(βlk ) = ρdl + (βlk ) Gk (M ). (6.63)
k∈ΦS
M T \{X0 }
111
Rl0 can then be expressed by
ρdl (I(βlk )βl0 )2

Rl0 = I(βlk )βl0 + (6.64)
M νS (KL ) ρdl βl0 + 1
The expectation of (6.64) between the total power received and the SIR at MT0 can be
written as follows
" #
ρdl (I(βlk )βl0 )2
Rl0 = E I(βlk )βl0 + . (6.65)
M νS (KL ) ρdl βl0 + 1
Since βl0 and I are independent, and conditioning on the number of MTs in LoS, we can
write
" S 2
#
ρdl 1 S 2
β l0
Rl0 = IM + E E I(βlk ) KL E S
, (6.66)
M νS (KL ) ρdl βl0 +1
completing the proof.

2

(βl0S )
First, we derive the expression of the second expectation in (6.66), E S +1
ρdl βl0
. This
can be expressed by integrating its PDF as follows
S 2
" # Z ∞
βl0
E = xf βS 2 (x) dx. (6.67)
S
ρdl βl0 +1 0
( l0 )
ρdl β S +1
l0
We determine the expression of the PDF of βl0 in the following lemma, and the PDF of
2
(βl0S )
ρdl β S +1
in the corollary following it.
l0
Lemma 9. The PDF of the path-loss coefficient at MT0 , fβl0 , can be expressed as follows
K−1
− α2 −1

x−2/αS
2Kx S 1− R2
fβl0 (x) = (6.68)
αS R 2
Proof. We determine the CDF of the path-loss fading from (6.2) at MT0 as

S −αS

Fβl0 (x) = P max d, Rl0 <x (6.69)
= 1 − P max d, Rl0 < x−1/αS S

(6.70)
= F̄Rl0 (x−1/αS ), ∀ x > d−αS (6.71)
K
x−2/α

= 1− , ∀ x > d−αS (6.72)
R2
The PDF can then be obtained by differentiating Fβl0 (x) with respect to x giving (6.68)
and completing the proof.
112
2
(βl0S )
Corollary 9.1. The PDF of Y = S +1
ρdl βl0
in proposition 2 can be expressed as follows
α+2
!
2 αρ2 x2 + 2x
K p − α+2
α
fY (x) = p +x 2
x (ρ x + 4) + x
αR 2 2
x (ρ x + 4)
 p −2/α K−1 (6.73)
1/α 2
4 x (ρ x + 4) + x
× 1 −
 
R2

2
(βl0S )
Proof. We first determine the CDF of Y = S +1
ρdl βl0
as follows
S 2
" #
βl0
FY (x) = Pr S
<x (6.74)
ρdl βl0 +1
" p #
2
S ρ dl x + x(4 + ρdl x
= Pr βl0 < (6.75)
2
p !
ρdl x + x(4 + ρ2dl x
= Fβl0S , (6.76)
2
and substituting in (6.68) and differentiating for x completes the proof.
To determine the expectation of the square of the random sum in the interference
part in Rl0 , we first present a theorem simplifying the expression below. This theorem
Theorem 10. Where N is a random variable, we can write

 !2 
N
X
 = E[Xi ]2 E[N ]2 − E[N ] + E[N ]E Xi2

E Xi (6.77)
i=1
PN
Proof. We define the random variable Y = i=1 Xi , so we can then write
E Y 2 = Var[Y ] + E[Y ]2

(6.78)
we determine the variance of Y as

" N
#
X
Var[Y ] = Var Xi (6.79)
i=1
" " N
##
(a) X
= EN Var Xi N (6.80)
i=1
= E[N ] Var[Xi ] + Var[N ]E[Xi ] (6.81)

= E[N ] E Xi2 − E[Xi ]2 + Var[N ]E[Xi ]

(6.82)
113
where (a) follows from conditioning and unconditioning on N and the fact that Xi are
iid random variables. We can then write (6.78) as follows
E Y 2 = E[N ] E Xi2 − E[Xi ]2 + Var[N ]E[Xi ] + E[N ]2 E[Xi ]2 ,

(6.83)
and completing the proof.
Using the result from theorem 10, we can determine a closed-form expression of the
first expectation in (6.66) as presented in the following lemma.
Lemma 11. The expectation of the square of the interference divided by the path-loss
coefficient of MT0 can be expressed as follows
S 2
h i
N −1
h i
N −2
h i
N −1
) = ρ2dl + 2ρdl E βlk KL2 − KL

E I(βlk + E βlk KL + ρdl + E βlk
h i
N −1
+ ρdl + E βlk Var[KN ]
2
2 h i
N −1
h i
N −2
+ E Gk (M ) ρdl + 2ρdl E βlk + E βlk KL
!
h i h i
N −1 2 N −1
+ ρdl + E βlk KL − KL + ρdl + E βlk Var[KN ]
#
N −1 L −1

+ 2 E [Gk (M )KL (K − KL )] E ρdl + (βlk ) ρdl + (βlk ) KL
(6.84)
Proof. Using the result in theorem 10, we can write

 2 
X
S 2 Sk −1

E I(βlk ) KL = E  ρdl + (βlk ) Gk (M ) KL  (6.85)
k∈ΦS
M T \{X0 }
Separating the MTs in LoS and in NLoS of the BS, the expression becomes
 2 
X X
N −1 L −1

(6.85) = E  ρdl + (βlk ) + ρdl + (βlk ) Gk (M ) KL  ,
k∈ΦN
M T \{X0 } k∈ΦL
M T \{X0 }
(6.86)
114
and expanding the square of the sum we get
" 2  2
X X
N −1  L −1

=E  ρdl + (βlk ) + ρdl + (βlk ) Gk (M )
k∈ΦN
M T \{X0 } k∈ΦL
M T \{X0 }
   #
X X
N −1   L −1

+ 2 ρdl + (βlk ) ρdl + (βlk ) Gk (M ) KL
k∈ΦN
M T \{X0 } k∈ΦL
M T \{X0 }
(6.87)
 2   2 
X X
N −1  L −1

= E  ρdl + (βlk ) KL  + E  ρdl + (βlk ) Gk (M ) KL 
k∈ΦN
M T \{X0 } k∈ΦL
M T \{X0 }
   
X X
N −1 L −1

+ 2 E  ρdl + (βlk )  ρdl + (βlk ) Gk (M ) KL  .
k∈ΦN
M T \{X0 } k∈ΦL
M T \{X0 }
(6.88)
And since the conditional sums over the MTs in LoS and NLoS are independent of each
other, we can separate the expectation of their products as such
 2   2 
X X
N −1  L −1

k∈ΦN
M T \{X0 } k∈ΦL
M T \{X0 }
N −1 L −1

+ 2 E [Gk (M )KL (K − KL )] E ρdl + (βlk ) ρdl + (βlk ) KL
(6.89)
 2   2 
X X
N −1  L −1

k∈ΦN
M T \{X0 } k∈ΦL
M T \{X0 }
N −1 L −1

+ 2 E [Gk (M )KL (K − KL )] E ρdl + (βlk ) ρdl + (βlk ) KL .
(6.90)
Following from theorem 10 we can write

 2 
h i
N −1 2
X
N −1 

E  ρdl + (βlk ) KL  = E ρdl + (βlk ) KN
k∈ΦN
M T \{X0 } (6.91)
N −1
KN2

+ E ρdl + (βlk ) − KN
N −1

+ E ρdl + (βlk ) Var[KN ],
115
and similarly
 2 
X
L −1
2
h i
L −1 2
E  ρdl + (βlk ) Gk (M )  KL = E Gk (M )
 E ρdl + (βlk ) KL
k∈ΦL
M T \{X0 }
L −1
2
+ E ρdl + (βlk ) K L − KL
!
L −1

+ E ρdl + (βlk ) Var[KL ] .
(6.92)
Substituting in the expressions in (6.90) completes the proof.
The expression of the ratio can then be represented by an almost closed-form equation
by substituting the expressions obtained in corollary 9.1 and lemma 11, and by further
averaging for KL giving the result presented in theorem 8.
6.5 Numerical Results

In this section, we present the numerical results of the proposed frameworks with their
validations using Monte-Carlo simulations. We present the results of the average power
received first, and then we present those of the exposure per SIR ratio.
6.5.1 Simulation Setup

We verify the analytical framework by comparing it to a Monte-Carlo simulation.
This simulation was performed assuming K MTs distributed in a circle centered around
the BS of the zero-cell, and the BSs being distributed following a PPP with intensity
λBS with an average of 2000 BS in the network. The received power is the sum of the
transmitted powers from all BSs subject to the path loss model previously introduced.
The beamforming gains and power control coefficients are modeled as presented in (6.10)
and (6.12) respectively. We also assume the proposed approximation of LoS gain where
the gain of the interference power from serving non-aligned MTs corresponds to the
adjacent beams’ gain, which will produce a conservative scenario. The simulation was
performed over 105 iteration and took around 30 minutes to complete. The parameters
used for the simulation are summarized in table 6.2.
6.5.2 Average Power Received

In Fig. 6.3, we plot the average received power as function of the the number of
antenna elements, M , for different LoS probabilities and for different number of served
MTs. We notice in Fig. 6.3a that the average power received at MT0 increases with M ,
116
(a)
(b)
Figure 6.3: Average power received as function of the number of antenna elements M
for different values of (a) pL for K = 15 and (b) K for M = 256. Markers represent
the Monte-Carlo simulation results and the dotted line represents the result from the
analytical framework.
117
Parameter Value
λBS 10−4
K 10
ρdl 1 mW
M √256
R 1/ 2πλBS
αL , αN 3, 4
d 5m
pL 0.5
Number of realisations 105
Table 6.2: Summary of default parameters used in the Monte-Carlo simulations (unless
otherwise stated)
and at a much higher rate the higher pL is, even though the interference gain is lower for
LoS channels, and it is inversely proportionate to the number of antenna elements M .
The number of antenna elements affects mainly the gain of the useful signal towards MT0 ,
and on a smaller scale, the gain of the aligned interference when the interferer is in LoS
to the BS and is aligned with MT0 . The small increase with M for lower pL indicates
that the major contributing factor to the exposure at MT0 with this high number of
served MTs, is not the useful signal, but the interference, thus the path-loss exponent
contributes more to the exposure than the transmission gain. Similarly, in Fig. 6.3b,
we see that the average power received is increasing with M even with. However, it also
increases with the density of served MTs the cell λ0M T , where the average distance of MT0
to the serving BS is higher, even though the high-gain useful signal power decreases with
K increasing.
In Fig. 6.4 we see similar behavior to Fig. 6.3 concerning LoS probability, however
for different reasons. Denser networks will increase the possibility of MTs being close
to the serving BS. Even though the power control will lower the received signal power
at closer distances to keep a uniform SIR throughout the cell, the increased interference
power will produce higher power received while degrading the signal quality.
To determine the effect of increasing the number of served MTs in the cell, and thus
the number of multi-user interferers, we increase K while maintaining a fixed MT density
in the cell without affecting the distance of MT0 to its BS. We do this simply by changing
the BS density λBS , and thus changing the radius of the cell. The BS density will satisfy
λBS (K) = KK0 λ0BS where K0 and λ0BS are the initial number of MTs and the initial BS
density producing the MT density to maintain. In Fig. 6.5, we plot the expectation of
the total received power as function of the number of antenna elements M under these
conditions. We notice, as expected, that increasing the number of served MTs decreases
the total received power in both LoS and NLoS, and at similar rate.
Setting pL = 0.5, in Fig. 6.6, we notice that the power received is higher for larger
118
(a)
(b)
Figure 6.4: Average power received as function of the BS density for different values of
(a) pL for K = 15 and (b) K in LoS. Markers represent the Monte-Carlo simulation
results and the dotted line represents the result from the analytical framework.
119
(a)
(b)
Figure 6.5: Average power received as function of the number of antenna elements M for
different values of K where the MT density in the cell is constant in (a) NLoS and (b)
LoS. Markers represent the Monte-Carlo simulation results and the dotted line represents
the result from the analytical framework.
120
(a)
(b)
(c)
Figure 6.6: Expectation of the total power received at MT0 as function of the BS density
λBS and different number of served MTs K, for M = 16 (a), M = 64 (b), and M = 128
(c) antenna array elements. Markers represent the Monte-Carlo simulation results and
the dotted line represents the result from the analytical framework.
121
numbers of served MTs in denser networks. However for sparse networks, this behavior
changes and the power received decreases with the number of served MTs. We also notice,
from the different sub-figures, that the BS density at which this change occurs depends on
the value of M , and thus the beamforming gain. The higher number of antenna elements,
the denser the network is when behavior changes.
6.5.3 Exposure to SIR Ratio

In this section we analyze the ratio between the total power received and the SIR
at MT0 . This ratio gives insight on how different network parameters and transmission
scenarios jointly affects both the EMF exposure and the coverage in the cell. It represents
how many milliwatts of total power is received at MT0 per unit SIR.
In Fig. 6.7, we plot the expectation of the ratio Rl0 as function of the transmit power
in mW in a LoS (b) and an NLoS (a) environment. The plot in 6.7 shows that the ratio
grows linearly with the increase in transmit power and with an equal slope for all values
of K. However, the increase in Rl0 increases with the increase of K. This is, as explained
before, due to the increase in the MT density in the cell, thus lower distance of MT0 . Just
like for the average power received, the same behavior can be expected from increasing
the BS density λBS since it will reduce the cell radius R and thus increasing λM T .
In Fig. 6.8, we evaluate the ratio as function of the antenna elements, M . We notice
that the ratio decreases with M , and it decreases further in mostly NLoS environments
compared to LoS ones. This decrease indicates that the SIR gained by increasing the
number of transmitting elements is larger than the amount of EMF exposure gained.
In Fig. 6.9, we evaluate the ratio at different user load in the cell. We plot the
average ratio as function of M for different number of MTs simultaneously served in the
cell taking pL = 0.5. As expected, the increasing number of served MTs will degrade the
communication quality by increasing the interference as well as increasing the exposure
by increasing the MT density λ0M T . However, the trend of the ratio is monotonically
decreasing with M , this is due to an increase in the transmission gain in the useful signal
part without an increase in multi-user interference. On the contrary, a large number of
antenna elements produces a lower interference gain when the interferers are in LoS of
the BS and a lower alignment probability.
Just like in section 6.3, we want to study the scenario where different number of
served MTs are being served without increasing λ0M T . In Fig. 6.10, we plot Rl0 under
this condition and we notice that, the ratio keeps decreasing with M in both LoS and
NLoS scenarios, unlike in 6.9a where the ratio increases in LoS. However, the expectation
of the ratio, same as in Fig. 6.9, always increases with K.
122
(a)
(b)
Figure 6.7: Expectation of the ratio of the exposure to SIR at MT0 versus the transmit
power, ρdl , for different number of served MTs, K in (a) NLoS and (b) LoS. Markers
represent the Monte-Carlo simulation results and the dotted line represents the result
from the analytical framework.
123
Figure 6.8: Ratio between the total power received and SIR as function of M for different
pL and K = 15
6.6 Conclusion
In this chapter, we have we derived the expression of the average power received
at nearest MT to its serving BS, MT0 , under max-min fairness power control using
stochastic geometry. We also determined the expression of the ratio of the exposure to
SIR at MT0 in a single cell scenario. We determined the closed-form expressions of the
useful received signal, the multi-user interference and inter-cell interference. We proposed
a tight approximation on the power control coefficient, and based on it, the framework
on total received power is then validated by Monte-Carlo simulations.
The results show that the average received power at MT0 monotonically increases
as, the density of the base station, the number of antenna elements, and the MT density
increases. The results also show that the more the environment is LoS, the increase of the
power received is greater. In addition to that, we show that, for dense environments, the
power received for different MT densities changes its trend and higher MT densities will
result in lower power received. This change is also dependent on the number of antenna
elements M .
As for the ratio of the exposure to SIR, we show that increasing the transmit power
at the BSs will result at a higher increase in exposure than in SIR, likewise is seen
in a purely LoS environment versus M . On the other hand, in the cases where the
environment is not purely LoS, the results show that as M increases, the SIR increases
at a higher rate than the exposure, and more so in increasingly NLoS environments. We
also show that increasing the number of MTs in the cell, and increasing the number
of served MTs without changing the MT density, increases the exposure more than the
SIR. This increase is reduced however the higher M is. This shows that antennas with
124
(a)
(b)
Figure 6.9: Ratio between the total power received and SIR as function of M for multiple
values of K in (a) LoS and (a) NLoS. Markers represent the Monte-Carlo simulation
results and the dotted line represents the result from the analytical framework.
125
(a)
(b)
Figure 6.10: Ratio between the total power received and SIR as function of M for multiple
values of K in (b) LoS and (a) NLoS, while maintaining a constant MT density in the
cell. Markers represent the Monte-Carlo simulation results and the dotted line represents
the result from the analytical framework.
126
higher antenna elements will be increasingly efficient to the coverage in the 5G network
considering the EMF exposure in NLoS environments, however, decreasingly so the more
LoS the environment is.
127
Chapter 7
Conclusions and Future Work
Contents
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.2.1 Non-PPP models . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.2.2 Compliance boundary estimation . . . . . . . . . . . . . . . . . 130
7.2.3 Joint optimization of EMF exposure and performance . . . . . 130
128
7.1 Conclusions
In this dissertation, we present the EMF measurement methods applied to 5G massive
MIMO networks and we analyze their advantages and disadvantages in relation to the
different characteristics of 5G NR. We also present a new methodology for studying
the EMF exposure in a wireless network using stochastic geometry, where the different
characteristics of the 5G network can be modeled mathematically and studied for different
deployment scenarios.
Second, we study the 5G massive MIMO network in mmWave frequency bands. We
model the cellular network’s BSs as randomly placed points in the 2D space following a
stationary PPP and the power is then modeled as shot-noise process. We get the sta-
tistical channel and antenna gain distributions from fitting the data obtained from the
NYUSIM channel simulator which is itself based on measurements in the mmWave fre-
quency band. These distributions were then integrated into the mathematical framework
to obtain a closed-form equation of the MGF of the total received power at the typical
MT in the cell. The CDF of this distribution is then analyzed for different scenarios and
sensitivity analysis performed to investigate the impact of different network parameters
on the total exposure, and it has been shown that the network utilization will have the
highest impact on the exposure.
Third, we present a more relevant scenario in studying the EMF exposure in a 5G
massive MIMO networks using stochastic geometry which is by considering the nearest
MT to its associated BS, MT0 , instead of the typical MT in a MU network wehere many
MTs are being served by a single BS in the same time-frequency block. We distribute
the BSs following a PPP and the MTs inside a single cell following a BPP. We consider
a network deploying max-min fairness power control to distribute the downlink resources
fairly between the simultaneously-served MTs ensuring equal SIR throughout the cell. We
consider both LoS and NLoS channels and their respective antenna gains. We determine
the closed-form equation of the total power received and the expression of the exposure to
SIR ratio at MT0 . We analyze the total power received for multiple network parameters
and for different LoS probabilities, we also analyze the exposure to SIR ratio. We analyze
the results of the power received and we deduce that, in this system, the increase of the
SIR, by either network densification or by deployment of larger arrays, is always larger
than the increase of the electromagnetic field (EMF) exposure.
7.2 Future work

Many extensions in the field of exposure analysis can be made based on this disserta-
tion for analytical studies of the EMF exposure. We present some of them below.
129
7.2.1 Non-PPP models
We chose the stationary in this dissertation PPP for its mathematical tractability
and its generality. However, many more point processes can be considered to represent
different different network architectures. Clustered point processes, e.g. Matérn cluster-
ing process (MCP), can be considered to model clusters of small-cell transmitters, access
points, or MT distributions. Repulsive point processes, e.g. Matérn hard-core process
(MHCP) or β-Ginibre point process, can be considered to model the spatial repulsion
that exists between BSs. An interesting research path would be to compare these dif-
ferent deployment scenarios in the context of EMF exposure jointly with the network
performance.
7.2.2 Compliance boundary estimation

Compliance boundary can be equated to the exclusion zone considered for the bounded
path-loss models used throughout this dissertation. This boundary is essential for con-
structors to define in order to deploy a certain antenna. Since for 5G systems assuming
maximum radiated power in a specific beam is over-conservative and may introduce un-
necessary restrictions, statistical limits can be better studied for different scenarios to get
more accurate estimations.
7.2.3 Joint optimization of EMF exposure and performance

While the main focus when developing massive MIMO antennas is the spectral and
energy efficiency through beamforming techniques, these need to take into consideration
the EMF exposure so it doesn’t exceed regulatory limits. Optimization problems can be
formulated using the developed framework to improve the performance while simultane-
ously limiting human exposure to EMFs.
130
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Titre : Analyse De L’exposition Radio Fréquence Dans Les Systèmes 5G Massive MIMO
Mots clés : Télécommunications, Statistiques, 5G, Massive MIMO, Communication sans fil
Résumé : Cette thèse présente des mesures in- Un autre modèle de réseau massive MIMO
situ d’une antenne massive MIMO et analyse les multi-utilisateurs déploiyant le précodage MRC et
différents paramètres pertinents pour l’estimation de le contrôle de puissance max-min fairness est
l’exposition aux CEM dans un réseau 5G. De mul- également développé, et où les MTs sont distribués
tiples méthodes sont présentées et discutées pour es- suivant un PPP soit en LoS ou NLoS. Une expression
timer la puissance reçue dans le réseau tout en se sous forme fermée de l’espérance de la puissance
concentrant sur les avantages et les inconvénients de totale reçue et l’expression du rapport entre la puis-
chacune d’elles. sance totale et le SIR à la MT la plus proche de sa BS
Cette thèse propose également une nouvelle de desserte, où l’exposition est la plus élevée. L’ex-
méthode analytique pour étudier l’exposition position moyenne est ensuite étudiée par rapport aux
moyenne, représentée par la puissance totale reçue, paramètres du réseau en tenant compte des compro-
dans un réseau 5G massive MIMO dana la bande mis présentés par le modèle de contrôle de puissance
mmWave. En utilisant la géométrie stochastique, et les gains d’antenne. De même, le rapport entre l’ex-
une équation de forme proche de l’exposition est position et le SIR est également analysé pour étudier
développée et étudiée en adaptant un modèle de ca- l’augmentation de l’exposition par l’augmentation du
nal mmWave utilisant NYUSIM dans des distributions SIR à la MT la plus proche de sa BS. Et il est montré
statistiques et en modélisant les BS en tant que PPP. que plus le nombre d’éléments d’une antenne mas-
Une analyse de sensibilité est effectuée pour quanti- sive MIMO est élevé, plus elle est efficace en termes
fier l’influence des variables d’entrée sur l’exposition. de SIR considérant l’exposition produite.
Title : Radio Frequency Exposure Analysis In 5G Massive MIMO Systems

Keywords : Telecommunications, Statistics, 5G, Massive MIMO, Wireless Communications
Abstract : This dissertation presents in-situ measu- work is also developed deploying maximum-ratio
rements of a massive MIMO antenna and analyses combining precoding and max-min fairness downlink
the different parameters pertinent to the estimation of power control, and where MTs are distributed follo-
the EMF exposure in a 5G network. Multiple methods wing a PPP and can be either LoS or NLoS. A closed-
are presented and discussed to estimate the power form expression of the expectation of the total power
received in the network while focusing on the advan- received and the expression of the ratio between the
tages and inconveniences in each of them. total power and the SIR at the nearest MT to its ser-
This dissertation also proposes a new analytical me- ving BS, where the exposure is highest. The average
thod for studying the average exposure, presented by exposure is then studied in relation to network para-
the total power received, in a 5G mmWave massive meters taking into account the trade-offs presented by
MIMO network. Using stochastic geometry, a close- the power control model and antenna gains. Likewise,
form equation of the exposure is developed and stu- the ratio between the exposure and SIR is also ana-
died by fitting a mmWave channel model using NYU- lyzed to study the increase of exposure per the in-
SIM into statistical distributions and by modeling the crease of the SIR at the nearest MT to its BS. And it
BSs as a PPP. A sensitivity analysis is performed to is shown that the higher the number of antenna ele-
quantify the influence of the input variables onto the ments a massive MIMO antenna has, the more effi-
exposure. cient it is in terms of SIR considering the produced
Another model for a multi-user massive MIMO net- exposure.
Institut Polytechnique de Paris

91120 Palaiseau, France

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Radio frequency exposure analysis in 5G massive MIMO

To cite this version:

HAL Id: tel-04148055

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est

Radio Frequency Exposure Analysis in

École doctorale n◦ 626 École doctorale de l’Institut Polytechnique de Paris (EDIPP)

Thèse présentée et soutenue à Palaiseau, le 13/01/2022, par

Assessment of electromagnetic field (EMF) exposure is key in the deployment of wire-

L’évaluation de l’exposition aux champs électromagnétiques (CEM) est de plus en

2 Introduction To 5G New Radio 26

3 In-Situ Exposure Assessment of 5G Networks 46

4 Introduction to Stochastic Geometry in Wireless Networks 65

5 A Statistical Estimation of 5G Massive MIMO Networks’ Exposure

6 Performance and EMF Exposure Analysis of Massive MIMO Networks

7 Conclusions and Future Work 128

2.1 Multi-Cell MU MIMO Model . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1 Zero-Span (Time Domain) measurement when data is being transmitted

4.1 Representation of a Voronnoi tessellation of a Poisson Point Process . . . 68

5.1 List of symbols used in antenna pattern and model derivation . . . . . . 79

6.1 List of symbols and abbreviations used in the document . . . . . . . . . . 102

BPP binomial point process

CCDF complementary cumulative distribution function

CDF cumulative distribution function

CSI channel state information

CSI-RS channel state information-reference signal

EMF electromagnetic field

EPRE energy per resource element

FCC federal communication commission

fidi finite-dimensional distribution

i.i.d. independent and identically distributed

ICNIRP international commission on non-ionizing radiation protection

IEEE Institute of Electrical and Electronics Engineers

LTE Long Term Evolution

MGF moment generating function

MRT maximum-ratio transmission

OFDM orthogonal frequency division multiplexing

PBCH Physical broadcast channel

PDF probability density function

PDSCH physical downlink shared channel

PGFL probability generating functional

PPP Poisson point process

PPRE power per resource element

PSS Primary synchronization signal

RAN radio access network

RBW resolution bandwidth

SAR specific absorption rate

SCC standards coordinating committees

SIR signal to interference ratio

SSS Secondary synchronization signal

TTI transmission time interval

Introduction To 5G New Radio

Since 5G networks are fundamentally different than previous generations, it is im-

2.1 5G massive MIMO

Figure 2.3: Massive MIMO Array Gain [8]

2.1.1 Array structure

2. Number of Tx and Rx antennas used.

The implementation of Massive MIMO/Beamforming is not specified in the 3GPP

2.1.2 Analog beamforming

2.1.3 Digital beamforming