University of Southern California Dissertations and Theses

Channel sounding for next-generation wireless communication systems

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Channel sounding for next-generation wireless communication systems

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Content Channel Sounding for Next-Generation Wireless Communication Systems
by
Jorge Luis Gomez Ponce
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
May 2023
Copyright 2023 Jorge Luis Gomez Ponce
Dedication
To myHeavenlyFather for being with me every day. To my family: my wife Evelyn, my daughter Catalina,
my parents, Haydeé and Jorge, my sisters Jennifer, Susan, and Erika, my aunts Elizabeth and Jackeline, and
my grandmothers Lourdes, Amarilis, and Magdalena for supporting me during this journey. Without you,
I would not be here. This work is yours as it is mine.
Do not fear: I am with you;
do not be anxious: I am your God.
I will strengthen you, I will help you,
I will uphold you with my victorious right hand.
Isaiah 41:10
ii
Acknowledgements
First and foremost, I would like to express my deepest gratitude to my research advisor Prof. Andreas F.
Molisch. His advice and guidance were essential for me in every work step. I would also like to thank
my dissertation and qualification exam committee members: Prof. Alan Willner, Prof. Keith Chugg, Prof.
Leana Golubchik, Prof. Remigijus Mikulevicius, and Prof. Mahta Moghaddam.
Next, I would like to thank my fellow research group members with whom I shared great mementos
working together: Dr. Daoud Burghal, Dr. Rui Wang, Dr. Umit Bas, Thomas Choi, Guillermo Castro, and
Hussein Hammoud. Special thanks to Dr. Naveed A. Abbasi for his advice and remarkable contributions
to the work presented in this thesis. It has been a great pleasure working with all of you. I would also
like to acknowledge our administrative staff: Susan Wiedem, Gerrielyn Ramos, Corine Wong, and Diane
Demetras, for their help throughout my doctoral degree.
Additionally, I would like to thank my colleagues at ESPOL, Washington, Carlos, and especially Fran-
cisco, for encouraging me to follow this path; despite the many challenges ahead, you provided the spark
to achieve this goal.
Finally, my deepest gratitude and appreciation to my family: my wife Evelyn, for your love and support
throughout this journey; to my daughter Catalina, for being the joy of my life. To my parents, Jorge and
Haydeé, for their unconditional love and support, and my grandmas Amarilis, Lourdes, and Magdalena,
for being that wise voice and giving me advice encouraging me to pursue my dreams.
iii
TableofContents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Rapid Growth Trends in Wireless Communications . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Overview of Wireless Communication Channels . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Impact of Channel Characteristics on a Systems Design . . . . . . . . . . . . . . . . . . . . 8
1.4 Overview of Channel Sounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 Thesis Outline and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5.1 Estimation of condensed propagation channel parameters from noisy
measurement data with Fourier-based evaluation . . . . . . . . . . . . . . . . . . . 15
1.5.2 Multi-band-WLAN systems for ultra-high troughput . . . . . . . . . . . . . . . . . 16
1.5.3 Impact of Common Reflecting and Absorbing Building Materials on THz
Multipath Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.5.4 Directionally Resolved Measurement and Modeling of THz Band Propagation
Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6 Other Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Chapter 2: Estimation of condensed propagation channel parameters from noisy measurement
data with Fourier-based evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Signal model & Synthetic channel description . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Proposed Evaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.1 Processing of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Theoretical Analysis and MC Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4.1 Noise impact on parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4.2 Analytical computation of impact of threshold on delay spread . . . . . . . . . . . 37
2.5 Evaluation with synthetic channel data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.5.1 Impact of frequency/delay points,N
f
. . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5.2 Impact of angular points,N
az
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
iv
2.5.3 Impact of DMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.6 Evaluation with measured channel data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Chapter 3: Multi-band-WLAN systems for ultra-high throughput . . . . . . . . . . . . . . . . . . . 55
3.1 Introduction and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Setup and Extraction Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.1 Antennas and directionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3 Key Measurements and Modeling Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Chapter 4: Impact of common reflecting and absorbing building materials on THz multipath
channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Measurement equipment and site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.1 Testbed description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.2 Experiments and scenario description . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Parameters and processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3.1 Path loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3.1.1 Delay spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3.2 Power distribution over MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3.3 Angular spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4 Measurement results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4.1 VHE outdoor measurement scenario . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4.2 EEB5
th
floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4.3 EEB 539 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4.4 EEB 110 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Chapter 5: Directionally Resolved Measurement and Modeling of THz Band Propagation Channels 86
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.1.1 THz applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.3 Structure of chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2 THz propagation effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4 Parameters and their system impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.5 The measurement environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.6 Sample results and impact of specific environments . . . . . . . . . . . . . . . . . . . . . . 104
5.7 Statistical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.7.1 Path loss and shadowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.7.2 Delay dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.7.3 Angular Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.8 System performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Chapter 6: Conclusions and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
v
ListofTables
2.1 Setup parameters for PDP, theory analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2 Setup parameters for synthetic MIMO channel . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1 VNA Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1 Common setup parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 Additional setup parameters for VHE outdoor scenario. . . . . . . . . . . . . . . . . . . . . 67
4.3 Additional setup parameters for EEB5
th
floor scenario. . . . . . . . . . . . . . . . . . . . . 68
4.4 Additional setup parameters for EEB 539 scenario. . . . . . . . . . . . . . . . . . . . . . . . 69
4.5 Additional setup parameters for EEB 110 scenario. . . . . . . . . . . . . . . . . . . . . . . . 70
4.6 Estimated parameters for all measurement points . . . . . . . . . . . . . . . . . . . . . . . 85
5.1 Path loss parameters in the different environments. . . . . . . . . . . . . . . . . . . . . . . 116
5.2 σ τ parameters in the different environments. . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.3 Q window parameters in the different environments. . . . . . . . . . . . . . . . . . . . . . 122
5.4 Q-tapnumber parameters in the different environments. . . . . . . . . . . . . . . . . . . . . 125
5.5 log
10
(AS) parameters in the different environments. . . . . . . . . . . . . . . . . . . . . . 125
vi
ListofFigures
1.1 5G bands versus coverage, [36] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Data rate requirements per application, [27] . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 6G envisioned features, [151] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 6G spectrum grouping, [122] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Reflection of an EM, [131] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.6 Wireless system design flow diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.7 Frequency domain channel sounder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.8 Time domain channel sounder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.9 Rotating virtual array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.10 Cylindrical switched array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.11 Parallel links and antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.12 5-7 GHz channel allocation in the US,[103] . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.13 5G & 6G Key Performance Indicators,[162] . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Critically sampled PDPs with and without oversampling. For visualization purposes, the
values of−∞ dB are instead shown at− 50dB. . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2 PDP Rectangular approximation models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3 Comparison of MC simulation and theoretical values, single-cluster case. . . . . . . . . . . 39
2.4 Comparison of MC simulation and theoretical values, 2 clusters case. . . . . . . . . . . . . 40
2.5 Single exponential cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
vii
2.6 Comparison of MC simulation and theoretical values, single cluster exponential PDP case. 41
2.7 ¯σ τ (mean) values for max-dir case with a different number of frequency points. NLoS
scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.8 ¯σ τ (mean) values for omni case with a different number of frequency points. NLoS scenario. 44
2.9 Mean estimated values of
¯ Q
win
and
¯ Q
tap
forN
f
= 2001,N
az
= 18 case. NLoS scenario,
max-dir case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.10 ¯σ ◦ (mean) values for Tx with a different number of frequency points. LoS scenario. . . . . 46
2.11 Mean estimated values forN
az
=72,N
f
=1001 . . . . . . . . . . . . . . . . . . . . . . . . 47
2.12 Impact of DMC onσ omni
τ for a fixed γ ′
=40dB,N
f
=1001,N
az
=18. . . . . . . . . . . . 49
2.13 d
Tx− Rx
=93m,N
f
=1001,N
az
=36, LoS scenario . . . . . . . . . . . . . . . . . . . . . . 51
2.14 N
f
=1001,N
az
=36, LoS scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.15 d
Tx− Rx
=10.49m,N
f
=1001,N
az
=36. NLoS scenario. . . . . . . . . . . . . . . . . . . . 52
2.16 N
f
=1001,N
az
=36, NLoS scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.1 Channel sounding setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 VHE outdoor measurement scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 EEB5
th
floor scenario. EEB 539 can also be seen in the figure. . . . . . . . . . . . . . . . . 68
4.4 EEB 539 measurement scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.5 EEB 110 measurement scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.6 PDP and APS comparisons for the scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.7 Omnidirectional PDP observed by a system withS =− 132 dB . . . . . . . . . . . . . . . . 77
4.8 PDP comparison for LoS measurement of EEB5
th
floor. . . . . . . . . . . . . . . . . . . . . 78
4.9 Omnidirectional PDP comparison for LoS case of EEB 539. . . . . . . . . . . . . . . . . . . 79
4.10 APS for LoS case of EEB 539. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.11 APS for NLoS case of EEB 539. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.12 PDP comparison for NLoS measurement of EEB 539. . . . . . . . . . . . . . . . . . . . . . . 80
viii
4.13 APS for LoS case of EEB 110. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.14 PDP comparison for LoS case of EEB 110. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.15 APS for NLoS case of EEB 110. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.16 PDP comparison for NLoS case of EEB 110. . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1 Block diagram of the measurement setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 Comparison of measurement with and without the RoF extension in an indoor environment
for a channel length of 2.4 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3 Delay filtering process in sample OTA calibration. . . . . . . . . . . . . . . . . . . . . . . . 97
5.4 Map of the indoor environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5 Map of the Conference room environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.6 Map of the outdoor intersection environment. . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.7 Map of the outdoor plaza for D2D environment. . . . . . . . . . . . . . . . . . . . . . . . . 104
5.8 Map of the outdoor plaza for microcellular environment. . . . . . . . . . . . . . . . . . . . 105
5.9 APDS of outdoor microcellular LOS link, TX1-Rx1 ford
Tx− Rx
=82.5m. . . . . . . . . . . 106
5.10 ADPS of indoor LoS link, TX2-Rx8. d
Tx− Rx
=32m. . . . . . . . . . . . . . . . . . . . . . . 107
5.11 PDP of indoor LoS link, TX2-Rx8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.12 APS of indoor LoS link, TX2-Rx8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.13 ADPS of outdoor D2D NLoS link, TX6-Rx32 ford
Tx− Rx
=97.59m. . . . . . . . . . . . . . 108
5.14 PDP of outdoor D2D NLoS link, TX6-Rx32. . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.15 ADPS of indoor NLoS link, TX2-Rx6 ford
Tx− Rx
=34.4m. . . . . . . . . . . . . . . . . . . 109
5.16 ADPS of outdoor NLoS link, TX3-Rx14 ford
Tx− Rx
=62.6m. . . . . . . . . . . . . . . . . . 110
5.17 PDP of outdoor NLoS link, TX3-Rx14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.18 APS of outdoor NLoS link, TX3-Rx14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.19 ADPS of a link with and without reflectors, Conference room scenario (see [50] for details). 112
5.20 PDP of long-distance measurement (70 m link) with 10 GHz bandwidth. . . . . . . . . . . 113
ix
5.21 Path loss as a function of distance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.22 CDF of the rms delay spread. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.23 CDF of the Q window, SINR = 15 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.24 CDF of the Q window, SINR = 20 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.25 CDF of the Q window, SINR = 25 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.26 CDF of the Q-tapnumber, SINR=15dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.27 CDF of the Q-tapnumber, SINR=20dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.28 CDF of the Q-tapnumber, SINR=25dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.29 CDF of the AS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.30 Comparison of digital and analog beamforming in a piconet controller scenario. . . . . . . 126
5.31 Comparison of digital beamforming in a piconet controller scenario. . . . . . . . . . . . . . 126
5.32 Comparison of analog beamforming in a P2P scenario. . . . . . . . . . . . . . . . . . . . . 127
x
Abstract
Next-generation wireless communication systems are envisioned to support new services with high data-
rate demands. Consequently, it is necessary to use accurate channel models based on detailed measure-
ments to make realistic assessments. This dissertation presents the results of extensive measurement cam-
paigns in the sub-7GHz (2.4 GHz and 5-7 GHz) and THz (145-146 GHz) bands in multiple scenarios and
performed a Fourier-based statistical channel model on both.
In the first chapter, we explore the current state of the art in channel sounding, the motivation for
bands to be reassigned (e.g., 6 GHz), and new spectrum bands to be opened for new applications (e.g., THz).
Next, a framework to analyze the impact of noise on the Fourier-based estimation of channel parameters
(e.g., delay spread, angular spread) is presented. The most notorious effect is overestimation because a
Fourier-based analysis does not distinguish between signal and noise; consequently, it can mislead the
proper design of a wireless system envisioned for the environment. A reasonable margin in the noise
thresholding can improve the estimation.
Additionally, the diffuse multipath components (DMC) play a significant role in the estimate because
they are part of the channel. The DMC statistical properties are similar to the noise, and a Fourier-based
analysis cannot distinguish between DMC and noise contrast to High-Resolution Parameter Extraction
techniques. Thresholding can allow excessive noise or eliminate too much DMC, affecting the estimation;
for this reason, a proper threshold is necessary for a correct analysis.
xi
In the following chapter, we discuss the results of an extensive sub-7GHz campaign carried out in typ-
ical WiFi deployment scenarios (e.g., Food courts, Offices, Open cafes, and Plazas), obtaining 400 points
between SIMO, MISO, and MIMO measurements. We observe the benefits of applying directional tech-
niques for performance improvement; for instance, the use of beamforming can help overhead reduction
by reducing the impact of a reduced cyclic prefix. The path loss observed in the 6-7 GHz band has no
significant difference compared to the 5-6 GHz. However, the delay spread differs in open office scenarios,
allowing delay diversity and, if combined with the 2.4 GHz, could lead to significant improvement. Fi-
nally, considerable beamdiversity is observed in the 5-7 GHz, which is helpful for MU-MIMO capabilities,
a feature envisioned in future versions of WiFi.
Similarly, in the THz band, the scenarios selected for analysis were Indoor, D2D, and Microcellular
(reaching up to 100 m Tx-RX distance in the last 2 cases). In chapter four, we analyze in depth the impact
of passive reflectors in THz channels. When these reflectors were placed, we observed additional multipath
components (MPCs) in the scenarios, leading to greater frequency, temporal, and angular diversity; this
is a premise for using Intelligent Reflective Surfaces (IRS). This change can impact the design of wireless
communication systems (e.g., equalizers) because of the number of taps for optimal design changes.
In the next chapter, multiple compound parameters such as Path Loss, RMS delay spread, and angular
spread are modeled. The Path Loss (PL) in LoS is close to Friis; for the NLOS, the excess PL is between 10
and 30 dB over Friis. From the systems design perspective, it is noted that the Q-window and Q-tapnumber
values are larger in NLoS and Indoor scenarios due to the large number of MPCs observed at the receiver,
increasing the complexity for an optimal receiver at these frequencies. Finally, in the angular domain,
we observe that the angular spread at the base station side is smaller than the user equipment due to
interacting objects. This behavior will significantly affect the signal-to-noise ratio (SNR) when a blockage
obstructs the strongest path in a link.
xii
Finally, in chapter six, we discuss the conclusions and future work; for the sub-7GHz band, a full-band
analysis is envisioned to evaluate channel and system parameters. Given that future WiFi systems will use
channels with 80, 160, and 320 MHz bandwidth, a sliding window analysis is necessary to evaluate how
parameters such as delay spread,Q
window
, andQ
tapnumber
behave as a function of frequency. Furthermore,
a time domain channel sounder is necessary for the THz band to measure dynamic scenarios, such as
obstruction, foliage attenuation, and moving objects. An exciting application for communication systems
in the THz band is localization because it can provide a highly accurate estimation. A multiband analysis
comparing the sub-7GHz and THz bands would provide valuable insight when comparing channel and
systems parameters for multiband systems using both bands. Determining the capacity with different
beamformers and power control schemes is also necessary to assess the maximum data rates achieved on
both bands under real scenarios.
xiii
Chapter1
Introduction
1.1 RapidGrowthTrendsinWirelessCommunications
The trend for wireless communication systems shows a constant increase in data traffic. According to
[36], the number of connections will increase significantly; for instance, by 2028, more than 300 million
subscribers (80% with 5G technology) will have Fixed Wireless Access, and Broadband IoT applications
will dominate 4G/5G connections. The current average data consumption per smartphone is 19 GB per
month, with 80% of this total comprising video.
Therefore, multiple bands have been opened to provide the resources for 5G features. 5G networks
can be deployed in three bands: Low-band for extensive coverage but small capacity (<7 GHz), mid-band
for increased bandwidth and higher capacity than the low band, and high-band or mm-wave (>24 GHz),
which offers the highest rates and lowest latencies at the cost of less coverage (see Figure 1.1)
This trend of growing data consumption is not only for smartphone use; [27] forecasts that household
demand will also increase. Current applications, such as gaming, UHD video, and smart TVs, require speeds
of 100 Mbps, and future applications, such as augmented reality and self-driving vehicles, will require more
than 500 Mbps to work correctly (see Figure 1.2). New services will place significant demands on mobile
networks, and current bandwidths will not suffice to provide the necessary resources to support new
applications.
1
Figure 1.1: 5G bands versus coverage, [36]
Figure 1.2: Data rate requirements per application, [27]
Figure 1.3: 6G envisioned features, [151]
2
Figure 1.4: 6G spectrum grouping, [122]
Next-generation wireless communication systems (i.e., 6G) must provide the necessary features to
ensure the quality of new applications and services. Peak rates of 1 Tbps and user experience rates of
1 Gbps are foreseen from 6G; additional features like ultra-low latency, more reliability, higher density
of devices, and energy efficiency are outlined (see Figure 1.4). Currently, the sub-6GHz band is wholly
used, and the mm-wave band is insufficient to provide the bandwidth to ensure 6G provides everything it
promises; therefore, searching for new bands is necessary.
The search for available bands has led national frequency regulators to access spectrum for research
purposes which have helped the development of new technology. For instance, the THz band has been
opened and multiple frequency regulators such as FCC, OFCOM, CEPT, and MIC have begun opening
frequency bands between 100 and 300 GHz [38, 107, 21]. The current use for this band is radio astronomy,
passive sensing, and satellite communications. For frequencies above 275 GHz, there is no ITU allocation
registered; therefore, the 100-300 GHz band is underused [122].
Another frequency band to be explored is the 6-7 GHz band. In 2020, the FCC opened the 6GHz band
for Wi-Fi and unlicensed systems[39]. According to the Wi-Fi Alliance, opening the 6GHz band addresses
the Wi-Fi spectrum shortage by providing more spectrum for high bandwidth applications. With the
opening of 6GHz for unlicensed applications, new technologies, such as WiFi6E or newer versions, can
use bandwidths up to 320 MHz, with OFDMA, directional beams, and MU-MIMO to ensure Gigabit speeds,
extremely low latency, and high capacity[15]. Regulators like OFCOM share an interest in exploiting
3
the 6 GHz band for unlicensed users[108]. However, international entities, like the GSMA Alliance, are
advocating this band for 5G services in the mid-band [54]. The motivation for further analyzing the 5-7GHz
and THz bands will be detailed in future sections.
Regardless of the frequency, it is necessary to evaluate the wireless communication channel to properly
design systems that ensure the quality of service and the user experience.
1.2 OverviewofWirelessCommunicationChannels
The wireless propagation channel is the linking medium between the transmitter (Tx) and receiver (Rx);
its main characteristic is the multipath propagation, i.e., the existence of multiple paths leading from the
Tx to the Rx. We sometimes have a direct line-of-sight (LOS) path; however, the paths can reach the Rx
by interacting with objects (e.g., buildings, mountains, houses). A complete description of the channel is
represented by the multipath components (MPCs) combination, also known as double directional impulse
response (DDIR) as detailed in [99, 146].
h(t,τ, Ω ,Ψ)=
L
X
l=1
ρ l
δ (Ψ − Ψ l
)δ (Ω − Ω l
)δ (τ − τ l
) (1.1)
where l is the path index, ρ l
,τ l
are the complex gain and delay of the l
th
path, Ω l
is the direction of
departure (DOD)Ω = [ ϕ,θ ] of thel-th path, whereϕ,θ are the azimuth and elevation, respectively, and
Ψ l
is the direction of arrival (DOA); similarlyΨ=[ ϕ,θ ].
An observation of the wireless channel transfer function H(f) in multiple input multiple output
(MIMO) systems can be captured by using directional antennas (e.g., horn antennas or beams) pointing at
different angular directions (i.e., azimuth and elevation) in the Tx side ( ϕ Tx,i
,θ Tx,j
) and the receiver end
(ϕ Rx,k
,θ Rx,l
) as well. [51]
4
For a given Tx-Rx horn orientation, a full-frequency scan is performed over the bandwidth of interest
usingN
f
frequency points (f
k
). As a result of the capture on a single location, a five-dimensional tensor
with dimensions [N
f
× N
Tx
az
× N
Tx
el
× N
Rx
az
× N
Rx
el
] is generated per measurement location.
∗
Each propagation path, regardless of its direction, can be affected by the following propagation effects:
• Free Space: The power radiated by the transmitter is distributed over a larger area, and thus the
power density decays as the signal travels further from the Tx. The energy collected by a receiver
with constant-gain antenna is lower as the distance between the Tx and Rx increases [99].
PL(d,f)=

4πfd
c
0

2
(1.2)
whered is the distance between Tx and Rx,f is the system’s operating frequency, andc
0
is the speed
of light.
Intuitively we can determine that if frequency or distance increases, then PL also increases. How-
ever, by analyzing the antenna gain at an endpoint (e.g., Rx), we obtain the following mathematical
relationship:
G
Rx
=
4πf
2
A
Rx
c
2
0
(1.3)
The abovementioned equation indicates that the antenna’s gain increases with frequency if the area
is constant. This is crucial for future wireless communication systems working at high frequencies
(e.g., THz). For antenna arrays, which can adapt to signals coming from different directions, constant
area of the array means that the number of array elements increases at higher frequency (i.e., smaller
wavelength).
• ReflectionandTransmission : Electromagnetic (EM) waves interact with multiple objects before reach-
ing the Rx. Each time an EM wave hits a new object, a reflection occurs. The reflected energy and
∗
given the fact that the channel is static when referring to the channel frequency response asH(f) instead ofH(f,t)
5
Figure 1.5: Reflection of an EM, [131]
direction depend on the object’s characteristics. Two mechanisms are in effect: reflection and trans-
mission. The first consists of energy bouncing back from the object. If the surface is smooth and
large (compared to the wavelength), a specular reflection occurs. For this particular case, the angle
of reflection and incidence are equal ( Φ e
= Φ r
). However, the angle of refraction for the portion of
energy moving into the object is determined by Snell’s Law:
sinΦ t
sinΦ e
=
r
δ 1
δ 2
(1.4)
whereΦ e
,Φ t
,Φ r
represent the angle of incidence, transmission, and reflection, respectively. δ is the
complex dielectric constant of the material and can be obtained as
δ =ϵ 0
δ r
=ϵ − j
σ e
2πf
c
(1.5)
wheref
c
is the carrier frequency,ϵ is the dielectric constant of the material,σ e
is the conductivity
of the material and j is the imaginary unit. Some examples of material properties to evaluate the
reflection and transmission characteristics are shown in [69, 127, 87].
• Scattering: When the surface is rough, the reflection in the specular direction has reduced strength
(compared to the smooth-surface case), due to angular the dispersion produced by the surface, as
seen in Figure 1.5
6
This energy dispersion is proportional to the variation of the surface roughness. The rougher the
surface, the more dispersed the EM wave will be. In this case, dispersion redirects radiation in mul-
tiple directions, and only a portion of the total power is reflected in the specular direction. A surface
can be considered rough (i.e., the percentage of dispersed radiation is significant) if the variation of
the surface roughness is larger than the Rayleigh roughness.
∆ h=
λ 8sinΦ e
(1.6)
This formula indicates that the roughness effect is more noticeable at higher frequencies. The degree
of scattering depends on the angle of incidence and the roughness of the surface in comparison to
the wavelength. There are multiple analyses such as [12, 135] where the scattering effect and its
impact in modeling are analyzed for mm-wave and the THz bands.
• Diffraction : This phenomenon refers to the effect when an EM wave encounters obstacles, corners,
or openings. When an EM wave hits an edge or wedge, it does not produce a sharp shadow but rather
an interference pattern produced by the constructive and destructive combination of the spherical
waves that can thought of as constituting the EM wave. This effect is delineated by the Huygens
principle.
This propagation mechanism allows bending around objects to reach the Rx, which helps improve
coverage in NLOS scenarios at low frequencies. However, when the frequency increases, the shad-
ows produced by objects such as buildings or humans are sharper, producing a higher attenuation
given the object. Studies such as [82, 96] show experimental results of this effect for 60GHz, 73GHz,
and 300GHz.
7
1.3 ImpactofChannelCharacteristicsonaSystemsDesign
The channel frequency responseH(f,ϕ Tx,i
,θ Tx,j
,ϕ Rx,k
,θ Rx,l
) possesses the information of the propaga-
tion channel.
†
However, describing the channel in the delay domain is more common. To further simplify
the description, the first step is to compute the double-directional Power Delay Profile (PDP) obtained via
IFFT.
P(τ,ϕ Tx,i
,θ Tx,j
,ϕ Rx,k
,θ Rx,l
)=|H(f,ϕ Tx,i
,θ Tx,j
,ϕ Rx,k
,θ Rx,l
)|
2
(1.7)
whereτ is the delay between the Tx and Rx.
Using this description of the channel, we can compute the following parameters:
• Path Gain/Path Loss, PL: When analyzing the received power in a system, it varies greatly due to
multiple effects at different spatial scales [99]:
– Asmallscale effect is observed in one wavelength range, a product of the interactions of differ-
ent MPCs. These fluctuations can be delineated by their mean value and the variation around
the mean. This phenomenon is called small-scale fading
– Variations are observed by calculating the average power over ten to forty wavelengths. The
cause of these variations is the amplitude change of the individual MPCs, caused, e.g., by the
shadowing produced by large objects, e.g., buildings and houses. Similar to the previous case,
this behavior can be represented by its mean and the variations around the mean. This is
referred to as large-scale fading
– Finally, the previously obtained large-scale mean shows a monotonically decreasing behavior
with respect to the distance. This effect is called average path loss.
†
This description excludes polarization, Doppler, and wavefront curvature, a complete description of the channel is detailed
in [123]
8
A spatial average over the local area is necessary to eliminate variations in the received power (i.e.,
fading) before computing the path loss, which thus shows the shadowing variations. The pathloss av-
eraged over the shadowing is called theaveragepathloss, although it is often simply called "pathloss"
when it is clear from the context that the shadowing has been averaged out.
• Delay Spread, σ τ : this is a measure of the power dispersion in the delay domain; it is computed
as the second central moment of the Power Delay Profile. Delay spread is related to the coherence
bandwidth and provides an indirect measure of the frequency diversity of the channel.
• Angular Spread,σ ◦ : Like the delay spread, angular spread measures the power dispersion over the
angular domain (azimuth or elevation). It is directly related to the angular diversity of the channel
(i.e., the number of distinguishable paths reaching the Rx). However, depending on the scenario’s
specific characteristics and the system under consideration, a larger value cannot be assessed as
"beneficial" or "detrimental" depending on the scenario’s specific characteristics. This quantity can
be computed as the second central of Angular Power Spectrum (APS). Nevertheless, this approach
can generate ambiguities and inconsistencies; to avoid these issues, we can use Fleury’s definition
to have a unique quantity [42].
• Q-window,Q
win
: Quantifies the minimum window such that the ratio of the energy of the impulse
response within the window to that outside of it reaches a particular valueQ.
• Q-tapnumber,Q
tap
: Defines the minimum number of arbitrarily-placed taps (by enforcing that they
are at integer multiples of the sampling interval) that guarantees a signal-to-interference ratio be-
tween the energy collected on those taps by the rest of the delay bins in the power delay profile is
equal toQ.
• Interference Quotient,Q
T
: Similar to the Q-tapnumber, the Q-window, and Delay spread, the inter-
ference quotient is the energy ratio between the signal within a time window of duration T and the
9
energy arriving outside of that window. In other words, it describes the self-interference produced
by the delay dispersion of the channel. The signal inside the window is considered useful while the
signal outside will produce intersymbol interference.
In addition to describing the quantitative channel parameters, it is essential to understand their im-
pact on designing a wireless communications system. However, these parameters are intrinsic to each
scenario, and their impact can vary. For this reason, it is essential to remember that to design a good
wirelesssystem,considerthechannelinwhichitwilloperate. The main parameter that describes the
fundamental limit of any system operating in the channel iscapacity. [134]. This parameter sets the limit
of the maximum data rate that a channel can support with a vanishing error probability.
In addition to the capacity, other parameters can also impact the design of a wireless communication
system, for instance:
• PathLoss: This parameter relates to the system’s coverage and capacity via the SNR. Its variation,
together with the small-scale fading, impacts temporal diversity and requires speed of feedback and
repetition.
• Delay spread: As noted above, frequency diversity is measured in terms of its relationship to the
channel’s coherence bandwidth. Additionally, it can impact the duration of cyclic prefixes and equal-
izers to minimize or suppress Intersymbol Interference (ISI) and channel selectivity, respectively.
• Angular Spread: This parameter impacts MIMO capacity because it relates to the number of dis-
tinguishable directions reaching the Rx. It is essential when designing a beamformer (analog, digital
or hybrid) used in the scenario.
• Interference Quotient: As a measure of delay dispersion, Q
T
can be helpful to determine the
minimum amount of cyclic prefix that allows a certain Q
T
level. An example of this type of study is
shown in [48].
10
Figure 1.6: Wireless system design flow diagram
• Q-window: This quantity is most beneficial to assess OFDM and single-carrier systems where the
equalizer taps are at regular locations, nT
c
, n = 1,2,..... In both cases, Q describes the SIR since
the window contains a desired signal, and the energy outside the window contains intersymbol
interference.
• Q-tapnumber: This quantity is helpful to assess Rake receivers and equalizers with dynamically-
placeable taps.
1.4 OverviewofChannelSounding
The previous section focused on analyzing the different parameters used to quantify the channel char-
acteristics and their impact on systems design. Estimating path loss, delay spread, angular spread, and
other parameters is essential to developing a reliable wireless communication system. However, we need
to compute channel parameters obtained from double-directional channels to design a reliable system.
Therefore, obtaining double-directional channel information is vital for a sound wireless communication
system design. Figure 1.6 shows a flow diagram where the causality of the design process is established.
Channel sounding is the starting point for the design of a wireless system. This procedure is used to
collect double-directional channel data. To collect the data, the wireless channel is excited with a known
11
Figure 1.7: Frequency domain channel sounder
signal x(t); the received signal y(t) is collected to estimate the channel response h(t) (see Figure 1.6). The
equipment used to collect the channel data is calledsounder[99].
Sounders can be categorized by use into two principal groups
• Frequency domain channel sounder: As its name suggests, this sounder performs a frequency
scan to measure the channel. These sounders are usually based on vector network analyzers (VNA)
capable of performing a frequency sweep and calculating the parameter S21 with extremely low
noise[48]. Commercially available VNAs have an upper frequency limit around 65 GHz; however,
it can be extended by adding frequency extenders. Channel sounders based on them can further
improve their sensitivity by adding amplifiers and can be extended to measure MIMO/directional
channels by use of positioners to create virtual antenna arrays [10]. Some advantages of these sys-
tems are their low sensitivity, extensive dynamic range, and high-quality measurement. However,
frequency domain sounders based on VNAs are slow due to the frequency scan time, so it is recom-
mended to be used in "quasi-static" scenarios (see Figure 1.7).
Another limitation of this kind of sounder is that the Tx and Rx must be connected to the ports of
the VNA, which constrains the measurement range. This could be an issue for systems measuring
extreme frequencies (e.g., THz) due to the attenuation in RF cables.
12
Figure 1.8: Time domain channel sounder
• Timedomainchannelsounder: Time domain sounders differ from frequency domain sounders, in
that they generally use two separate units for the transmitter and receiver. On the Tx side, a pulse- or
arbitrary waveform generator sends a signal with the bandwidth of interest. Conversely, a digitizer
or a digital sampling oscilloscope receives the signal. RF units (up/down converters) translate the
signal from the baseband to RF and vice versa. The most important feature of this sounder is the
synchronization between the Tx and RX; without this, such an approach would not be possible. An
advantage of this approach is real-time measurement capabilities, useful for dynamic scenarios (e.g.,
V2V, moving objects). Another advantage is that Tx and Rx do not need to be connected with cables.
On the other hand, a disadvantage of this approach is susceptibility to synchronization errors. In
some cases, the dynamic range is lower than for VNAs (see Figure 1.8).
Both approaches characterize the sounding procedure for a SISO channel; however, multiple wireless
technologies are MIMO; hence adding multiple antennas to the sounders is necessary. Four well-known
strategies can be used to add MIMO capabilities to sounders.
• Virtual antenna arrays: A virtual antenna array can be created by moving or rotating a single
antenna with a positioner in any direction. The measurement duration per physical location can
take hours due to the movement speed of the antenna. Hence, it is only recommended for static
scenarios (see Figure 1.9, [50])
13
Figure 1.9: Rotating virtual array
Figure 1.10: Cylindrical switched array
• Switchedantennaarrays: In this approach, the sounder has a high-speed switch (or switches) that
allows switching between the antennas of an array following a predefined pattern. It is essential to
mention that theentire MIMO capture must be done within the channel’s coherence time to measure
the scenario’s dynamics correctly. Two critical challenges for this approach are the tight synchro-
nization between the Tx and Rx to ensure accurate capture of the entire sequence and transmit power
limitations due to the switches. Figure 1.10 shows an example of this sounder, [26]
• Parallel antennas and links: A different approach for MIMO measurements involves multiple
dedicated SISO RF channels working in parallel. This approach is recommended for highly dynamic
scenarios. However, its cost and complex calibration procedure are constraints to its development.
14
Figure 1.11: Parallel links and antennas
• Switchedbeamarray: The final approach consists of a phased array or any array that steers beams
in different directions. This allows a high-speed system to perform measurements in dynamic sce-
narios. Like the switched antenna array, a tight synchronization between Tx and Rx is required for
its operation. An example of this approach is shown in [17].
The approach chosen to carry the measurements in this thesis is thevirtualarraywithafrequency
domain channel sounder. This approach was selected because it provides high-quality measurements
with reduced effort for constructing the sounder. The range of the system will be extended by using
RFoF ([10]) for long-distance measurements at very high frequencies. With this system outlined above,
measurements will be carried out in 2 spectrum bands sub-7GHz (5-7GHz) and THz. The reasons both
bands were selected are discussed in the next section.
1.5 ThesisOutlineandContributions
1.5.1 Estimationofcondensedpropagationchannelparametersfromnoisy
measurementdatawithFourier-basedevaluation
Condensed channel parameters, such as power delay profiles, RMS delay spread, and angular spread, are
essential ways of representing results from the measurement of wireless propagation channels. However,
15
real-world measurements are invariably affected by noise, which is not inherently reduced by the Fourier
processing - in contrast to high-resolution parameter estimation. Even when the signal-to-noise ratio is
relatively high, e.g., 20 dB, the impact of the noise on the condensed parameters can be significant and lead
to erroneous estimates. This can be explained, e.g., for the computation of the RMS (root mean squared)
delay spread, where long delays (which often carry noise only) are "up-weighted" by the square of the
delay. While techniques like noise thresholding are often applied, the reasons for choosing thresholds
are usually not described in detail. In this chapter, we will provide a systematic analysis of the choice of
threshold for joint delay-angle measurements and derive equations of thresholds for the computation of
delay and angle RMS spreads and window parameters under various measurement circumstances. The
results are based on closed-form equations, Monte Carlo (MC) simulations, and real measurements.
The following publication is related to this topic:
1. J.Gomez-Ponce et al., Estimation of condensed propagation channel parameters from noisy mea-
surement data with Fourier-based evaluations, submitted to Transaction on Wireless Communica-
tions.
1.5.2 Multi-band-WLANsystemsforultra-hightroughput
Wireless communication systems are evolving rapidly; according to [27], IP traffic is expected to double by
2022, and the compound annual growth rate is 30% (i.e., internet traffic increases 30%, an exponential rate).
The estimated total traffic for 2022 is 350 Exabytes per month, distributed to 5 Billion users. This trend
is due to the increasing demand for wireless devices and high-data-rate applications. Unlicensed systems
like Wi-Fi and licensed systems like 4G support these services. All systems have a common constraint
on their performance: the spectrum of licensed and unlicensed bands assigned by government entities to
offer the services. Since the spectrum is limited, it is necessary to exploit new frequency bands to ensure
that new applications (e.g., IoT, Virtual Reality) with higher data rate requirements operate correctly.
16
Figure 1.12: 5-7 GHz channel allocation in the US,[103]
Multiple studies have focused on analyzing licensed and unlicensed systems’ traffic or interference
levels. For instance, [47] studies the interference of Wi-Fi systems into Bluetooth using the 2.4 GHz band.
The effect of this saturation is observed as an increment in packet error probability in Bluetooth systems. To
overcome this problem in the unlicensed bands, the Federal Communications Committee (FCC) approved
the opening of 1.2 GHz in the 6GHz band to support the increasing demand for unlicensed systems ([39]).
This will allow larger channels for high-speed data applications (up to 320 MHz), as shown in Figure 1.12
Using the new open bands, new systems likeIEEE 802.11be are envisioned to work and provide new
features like spatial multiplexing, beamforming, and faster speeds ([77]).
For the previously described reasons, achannelsounding campaign of the 2.4 GHz and 5-7 GHz bands
in multiple indoor and outdoor scenarios (e.g., offices, corridors, indoor environments, and cafeterias) was
carried out to compare and assess performance in both bands. This campaign was executed in a hotspot
configuration where the transmitter was set higher than the receiver to emulate a common Wi-Fi scenario.
The main contributions of this work are:
1. Ultrawideband channel measurement in the 5-7GHz band in different scenarios (e.g., offices, corri-
dors, libraries, open plaza, cafeteria) in a hotspot configuration was performed.
2. A more accurate channel modeling for the 5-7GHz band was developed
17
3. The impact of using directional beams for spectral efficiency in the 5-7GHz band in indoor and
outdoor scenarios was evaluated.
Publications related to this part of the work are shown below:
1. J.Gomez-Ponce et al., "Directional Delay Spread and Interference Quotient Analysis in sub-7GHz
Wi-Fi bands," GLOBECOM 2020 - 2020 IEEE Global Communications Conference, Taipei, Taiwan,
2020, pp. 1-6, doi: 10.1109/GLOBECOM42002.2020.9322252
2. Andreas F. Molisch,J.Gomez-Ponce et al., "Multi-band-WLAN systems for ultra-high throughput",
Project report for year 1, CISCO, November 1, 2019
1.5.3 ImpactofCommonReflectingandAbsorbingBuildingMaterialsonTHz
MultipathChannels
THz band communication has the potential to meet the high data rate demands of many current and future
applications. However, extensive channel measurements are needed to characterize the wireless channel at
these frequencies before these networks can inform system design and deployment. This chapter presents
a set of double-directional channel measurements conducted in several relevant indoor and outdoor sce-
narios. The goal is to identify the effect of common building materials that might be particularly reflective
or absorptive (such as energy-saving glass, window blinds, or metallic reflectors) and how their presence
changes the channel characteristics. Among other effects, we find that - depending on the considered dy-
namic range - the presence/absence of these materials can increase the required equalizer length by an
order of magnitude.
The following publications are related to this topic:
18
Figure 1.13: 5G & 6G Key Performance Indicators,[162]
1. J.Gomez-Ponce, Abbasi, N. A., Kondaveti, R., Kumar, A., Abu-Surra, S., Xu, G., et al. (2022). Impact
of common reflecting and absorbing building materials on THz multipath channels. Radio Science,
invited paper, 57, e2021RS007412. https://doi.org/10.1029/2021RS007412
1.5.4 Directionally Resolved Measurement and Modeling of THz Band Propagation
Channels
Several new and upcoming applications require ultra-high data rates beyond the capabilities of mmWave-
based 5G communication systems (see Figure 1.13). To meet these requirements, higher frequencies such
as the THz band (0.1-10 THz) are being investigated because of the availability of considerable amounts
of unused spectrum in these bands [151, 62, 63, 121]. Therefore, numerous studies have explored the THz
band, especially the frequencies between 0.1-0.5 THz, e.g., [88, 80, 76, 74]. The recent decision of the
Federal Communication Commission (FCC), the US spectrum regulator, to provide experimental licenses
in this band has fostered additional research interest [38]. This band is widely expected to be an essential
part of 6G wireless systems [151].
19
Channel sounding measurements and their statistical analyses are a vital first step towards understand-
ing a channel and, consequently, towards designing and deploying a wireless system [99]. Since channel
characteristics depend highly on the operating frequency range, environment, and scenarios a wireless
channel operates in, channel-sounding campaigns must be performed in the critical scenarios of interest.
Consequently, this chapter focuses on channel sounding for possible new bands in the THz spectrum
opened by FCC that will be used in ultra-high-speed applications[38]. This is crucial in the particular case
of THz due to the enormous data rates required by 6G applications ([151]), where current mm-wave bands
might not be enough to supply the ever-increasing demand. The main contributions of this analysis are:
1. Performance of THz channel measurement in multiple scenarios (e.g., D2D, Microcellular, Indoor)
allows computing more realistic models useful for systems design.
2. Deployment of the first double-directionallong-distance (up to 100m) in D2D and microcellular
scenarios. Single-directional measurements, such as directional links with horns, have been car-
ried out for many years to measure atmospheric attenuation. Additionally, the configuration in the
microcellular case places the base station at the height of11.5m following 3GPP modeling recom-
mendations for this kind of scenario [1]. Compared to measurement campaigns performed in similar
bands (such as [156]), the base station is almost three times higher than other campaigns.
3. Development of systems design using actual measurement data and performance assessment under
real conditions.
The list of publications related to this topic is shown as follows:
1. J. Gomez-Ponce et al., Beamdiversity in sub-THz communication channels, approved to ICC WC
Symposium 2023.
2. F. Sheikh, J. Gomez-Ponce et al., "THz Measurements, Antennas, and Simulations: From the Past
to the Future," in IEEE Journal of Microwaves, 2022, doi: 10.1109/JMW.2022.3216210.
20
3. J.Gomez-Ponce et al., "Directionally Resolved Measurement and Modeling of THz Band Propaga-
tion Channels," in IEEE Open Journal of Antennas and Propagation, vol. 3, pp. 663-686, 2022, doi:
10.1109/OJAP.2022.3181326.
4. N. A. Abbasi,J.Gomez-Ponce et al., "THz Band Channel Measurements and Statistical Modeling for
Urban Microcellular Environments," Submitted to IEEE Transactions on Wireless Communications.
https://arxiv.org/abs/2112.01770
5. N. A. Abbasi, J. Gomez-Ponce et al., "THz Band Channel Measurements and Statistical Model-
ing for Urban D2D Environments," in IEEE Transactions on Wireless Communications, 2022, doi:
10.1109/TWC.2022.3184929.
6. N. A. Abbasi, J. Gomez-Ponce et al., "Double-Directional Channel Measurements for Urban THz
Microcellular Communications in a Street Canyon," ICC 2022 - IEEE International Conference on
Communications, 2022, pp. 2876-2881, doi: 10.1109/ICC45855.2022.9838551.
7. N. A. Abbasi, J. Gomez-Ponce et al., "Ultra-Wideband Double Directional Channel Measurements
for THz Communications in Urban Environments," ICC 2021 - IEEE International Conference on
Communications, 2021, pp. 1-6, doi: 10.1109/ICC42927.2021.9500510.
8. N. A. Abbasi, J. Gomez-Ponce et al., "Double-Directional Channel Measurements for Urban THz
Communications on a Linear Route," 2021 IEEE International Conference on Communications Work-
shops (ICC Workshops), 2021, pp. 1-6, doi: 10.1109/ICCWorkshops50388.2021.9473566.
9. J. Gomez-Ponce, N. A. Abbasi, Z. Cheng and A. F. Molisch, "Directional characteristics of THz
outdoor channels - measurement and system performance implications," 2021, 55th Asilomar Con-
ference on Signals, Systems, and Computers, 2021, pp. 658-663,
doi: 10.1109/IEEECONF53345.2021.9723253.
21
10. N. A. Abbasi, J. Gomez-Ponce et al., "Double-Directional Channel Measurements for Urban THz
Microcellular Communications in a Street Canyon," ICC 2022 - IEEE International Conference on
Communications, 2022, pp. 2876-2881, doi: 10.1109/ICC45855.2022.9838551.
11. Z. Cheng, J.Gomez-Ponce, N. A. Abbasi and A. F. Molisch, "A High-resolution Parameter Extrac-
tion Algorithm for Multiple Clusters Channels," 2022 IEEE 23rd International Workshop on Signal
Processing Advances in Wireless Communication (SPAWC), 2022, pp. 1-5,
doi: 10.1109/SPAWC51304.2022.9834031.
1.6 OtherPublications
1. J.Gomez-Ponce et al., "Air-to-Ground Directional Channel Sounder With Drone and
64-antenna Dual-polarized Cylindrical Array," 2021 IEEE International Conference on Communica-
tions Workshops (ICC Workshops), 2021, pp. 1-6, doi: 10.1109/ICCWorkshops50388.2021.9473627.
2. T. Choi,J.Gomez-Ponce et al., "Using a Drone Sounder to Measure Channels for Cell-Free Massive
MIMO Systems," 2022 IEEE Wireless Communications and Networking Conference (WCNC), 2022,
pp. 2506-2511, doi: 10.1109/WCNC51071.2022.9771649.
3. T. Choi,J.Gomez-Ponce et al., "Energy Efficiency of Uplink Cell-Free Massive MIMO With Transmit
Power Control in Measured Propagation Channel," in IEEE Open Journal of Circuits and Systems,
vol. 2, pp. 792-804, 2021, doi: 10.1109/OJCAS.2021.3125894.
4. T. Choi, J. Gomez-Ponce et al., "Experimental Investigation of Frequency Domain Channel Ex-
trapolation in Massive MIMO Systems for Zero-Feedback FDD," in IEEE Transactions on Wireless
Communications, doi: 10.1109/TWC.2020.3028161.
22
5. Thomas Choi, Francois Rottenberg, J. Gomez-Ponce, Akshay Ramesh, Peng Luo, and Andreas
F. Molisch, Channel Extrapolation for FDD Massive MIMO: Procedure and Experimental Results,
2019 IEEE 90th Vehicular Technology Conference: VTC2019-Fall 22-25 September 2019, Honolulu,
Hawaii, USA
6. R. Wang, J. Gomez-Ponce et al, "Enabling Super-Resolution Parameter Estimation for mm-Wave
Channel Sounding," in IEEE Transactions on Wireless Communications, vol. 19, no. 5, pp. 3077-
3090, May 2020
23
Chapter2
Estimationofcondensedpropagationchannelparametersfromnoisy
measurementdatawithFourier-basedevaluation
2.1 Introduction
Many emerging multimedia-rich applications such as high-fidelity holograms, immersive reality, and haptic-
based communications are beyond the capabilities of the current 5G wireless systems [151, 162, 121, 45].
To satisfy the demands of these new applications, 6G systems currently under discussion consider a di-
verse number of frequency bands that range from below 6 GHz up to 1 THz. A key step in successfully
realizing the upcoming 6G ecosystem is the characterization and understanding of the propagation chan-
nels in these bands through channel sounding measurements, followed by the evaluation and analysis of
essential channel parameters [153, 71, 58].
A standard method to characterize and describe wireless channels is the utilization of Fourier eval-
uations of channel measurements to obtain power angular delay profiles (PADPs) similar to the results
described in [164, 143, 120, 64, 159, 18, 74, 3]. Compared to the extraction of multipath components (MPCs)
from channel responses by high-resolution parameter extraction (HRPE) methods such as CLEAN, SAGE,
or RiMAX, Fourier evaluations are inherently simple and easy to conduct. However, the results of Fourier
24
analysis are limited by the properties of the measurement systems themselves and the chosen measurement
parameters, such as bandwidth, aperture, dynamic range, and angular spacing of the captures.
Another challenge for Fourier-based evaluation is the impact of the measurement noise. While HRPE
aims to eliminate the noise as part of the MPC extraction, Fourier techniques do not make a distinction
between noise-caused and MPC-caused parts of the PADPs. The measurement noise can thus lead to a
significant distortion of the PADPs, and the condensed parameters derived from them.
A popular channel parameter that is frequently used for wireless wideband system design is the RMS
delay spread [19, 101, 99, Chapter 6]. Moreover, traditionally in systems design, we are also interested in
the optimal estimation of the necessary delay taps or rake fingers that can allow us to equalize the channel
response properly [99, Chapter 6]. These parameters are often derived from the Fourier-based channel
analysis; however, as discussed earlier, without proper countermeasures, they can significantly deviate
from the ‘real’ parameter values and thus have detrimental effects on system design.
’Noise thresholding’ of Power Delay Profiles (PDPs) is widely used in SISO (single-input - single-
output) measurements to limit the error due to noise in the analysis. In this method, a threshold is selected
some dB above the noise floor, and all measured samples below the threshold are set to zero. The choice
of the threshold value is critical since parameter values may be distorted by both too-high and too-low
values. For very low threshold values, parameters such as delay spread may be over-estimated since some
noise peaks are retained and consequently are interpreted as parts of the PDP. Conversely, a very high
threshold may underestimate parameter values because parts of the actual channel PDPs are lost. Though
noise thresholding is widely used, and different authors choose values according to their respective ex-
perimental settings, a general analysis of threshold choice impact is - to the best of our knowledge - not
present in the literature.
This challenge has been compounded in recent years by increasing interest in the angular character-
istics of propagation channels. For the lower frequency ranges, such measurements are often performed
25
with real, switched, or virtual antenna arrays, with an FFT providing a transformation to beamspace [89].
For higher frequencies, measurements with a rotating horn have been extensively used, in particular for
measurements in the mm-wave regime [143, 120, 84, 18], but also more recently for THz [74, 10, 3]. How-
ever, using such beamspace measurements complicates the analysis of thresholding, both for the delay
domain parameters and also for condensed parameters in the angular domain such as the RMS angular
spread. In fact, the relation between the noise threshold and the distortion of the condensed parameters
depends on the specific type of evaluation of the measurements, e.g., whether the "maximum beam di-
rection" characteristics of the channel are evaluated or the "quasi-omni-directional" parameters [119] are
chosen.
Based on the discussion above, firstly, it is important to analyze how specific parameter estimations are
affected by measurement setup parameters and threshold choices, and then, to evaluate the use of process-
ing techniques that can help us manage this. Therefore, in the current chapter, we present a study of the
impact of factors such as dynamic range, noise, diffuse multipath components (DMC), and the number of
frequency and angular points in measurements on parameter evaluation. We then present a mathematical
background for threshold selection to minimize the impact of noise. Finally, we perform evaluations on
synthetic and real measured data. Our results show that the measurement system parameters discussed
above can significantly affect the estimation of condensed channel parameters such as delay and angular
spread. We stress thatthegoalofthisworkisnottoadvocateordiscourageusingparticularthresholdvalues
for analysis but rather to provide a framework for analyzing the impact of noise and thresholds in Fourier
analysis and condensed parameter estimation.
The rest of this chapter is organized as follows. Section II presents our signal model and the parameters
for the synthetic MIMO channel. Data processing and parameter definitions are discussed in Section III.
The impact of noise and dynamic range on parameter estimation is described in Section IV. Evaluations
26
with synthetic and measured channels are presented in Section V and Section VI, respectively. Finally,
conclusions are drawn in Section VII.
2.2 Signalmodel&Syntheticchanneldescription
The complete description of a wireless channel is given by the double directional impulse response and is,
in its simplest form
∗
[146, 119, 99] is the following sum of discrete MPCs:
h(t,τ, Ω ,Ψ)=
L
X
l=1
ρ l
δ (Ψ − Ψ l
)δ (Ω − Ω l
)δ (τ − τ l
) (2.1)
where l is the path index, ρ l
,τ l
are the complex gain and delay of the l
th
path, Ω l
is the direction of
departure (DOD)Ω = [ ϕ,θ ] of thel-th path, whereϕ,θ are the azimuth and elevation, respectively, and
Ψ l
is the direction of arrival (DOA); similarlyΨ=[ ϕ,θ ].
We further assume that an observation of the wireless channel transfer function H(f) in a multiple
input multiple output (MIMO) system is done by using a directional antenna (e.g., horn antenna) pointed
at different angular directions; since the channel is also assumed to be static, we refer to the channel fre-
quency response as H(f) instead of H(f,t). To simplify notation, we henceforth assume the angular
measurements are performed only in azimuth - as is indeed often done in practice, e.g., [10, 93, 92], such
that measurements are done at (ϕ Tx,i
,ϕ Rx,j
), wherei∈{1,··· ,N
Tx
az
} andj∈{1,··· ,N
Rx
az
}; generaliza-
tion to the 3D case is straightforward. Therefore, theestimateddouble-directional channel transfer function
H
spec,ij
(f) (which has finite resolution due to the finite beamwidth of the horn antennas) is described as
follows:
∗
This representation ignores the polarization, as well as wavefront curvature; for simplicity, we will ignore those aspects
henceforth, though generalization is straightforward [99]. It furthermore ignores the diffuse multipath (DMC), which will be
discussed in greater detail in Sec. V.C
27
H
spec,ij
(f)=
L
X
l=1
ρ l
b
Tx
i
(ϕ d
l
)b
Rx
j
(ϕ a
l
)e
− j2πfτ l
(2.2)
whereb
Tx
i
is the gain of the Tx directional antenna centered at thei
th
orientation,b
Rx
j
is the Rx antenna
gain centered at thej
th
orientation, andϕ d
l
,ϕ a
l
are the azimuth of departure and arrival of thel
th
MPC. Fi-
nally, the frequency is discretized intoN
f
frequency points (f
k
) over the entire bandwidth (BW) of interest,
making thefull observed MIMO channel transfer function (H) a three-dimensional tensor with dimensions
[N
f
× N
Tx
az
× N
Rx
az
]. The MIMO channel is furthermore impacted by additive white Gaussian noise (i.e.,
H(f
k
) = H
spec
+N, which is zero-mean circularly symmetric on each frequency sample and antenna
orientation (i.e.,N(f
k
,ϕ Tx,i
,ϕ Rx,j
)∼CN (0,σ 2
n
)), where2σ 2
n
is the average noise power.
For the analysis in Sec. V.C, we assume that the MIMO channel has contributions not only from the
discrete MPCs (specular components) shown in (1) but also diffuse multipath components (DMC), such that
H(f
k
)=H
spec
+H
dmc
+N [124]. The statistical behavior of the DMC is assumed to follow a zero-mean
complex circularly symmetric Gaussian distribution with covariance matrixR, i.e., H
dmc
∼ CN (0,R),
with the correlation being determined by the dispersion in the delay and angular domains. For this analysis,
we assume the DMC to be exponentially decaying in delay and following aLaplaciandistribution in angle
[60, 56, 128].
P
DMC
(τ,ϕ Tx,i
,ϕ Rx,j
)=α 1
e
− B
d(τ − τ DMC
0
)
µ
τ − τ DMC
0

e
− |ϕ Tx,i
− ϕ DMC
Tx
0
|
σ DMC− d
ϕ e
− |ϕ Rx,j
− ϕ DMC
Rx
0
|
σ DMC− a
ϕ (2.3)
where α 1
corresponds to the peak power of the DMC, B
d
is the coherence bandwidth of the DMC, and
β d
=B
d
/BW is the normalized coherence bandwidth of the DMC.σ DMC− a
ϕ andσ DMC− d
ϕ are the angular
decay parameters for the DMC for the DOA and DOD.µ (.) is the Heaviside step function;τ DMC
0
,ϕ DMC
Tx
0
and
ϕ DMC
Rx
0
represents the mean time delay of arrival (TDOA), azimuth DOD and DOA of the DMC respectively.
Consequently, the covariance matrix,R, is decomposable as the Kronecker-product of covariance matrices
28
in the frequency domain,R
f
∈C
N
f
× N
f
, Rx antenna elements,R
R
∈C
N
Rx
az
× N
Rx
az
and Tx antenna elements
R
T
∈C
N
Tx
az
× N
Tx
az
, asR=R
T
⊗ R
R
⊗ R
f
, where⊗ denotes the Kronecker product [124].
In the subsequent sections, we will use the above generic model to perform our analysis and MC sim-
ulations, generating synthetic MIMO channel realizations that (unless stated otherwise) are exponentially
distributed in delay and Laplacian distributed in the angular domain [60, 56, 128]. DMC and noise are
added in the synthetic channel as described previously. These channels will be used to evaluate the impact
of different measurement features in the parameter estimation.
2.3 ProposedEvaluations
2.3.1 Processingofdata
Starting from the estimated double-directional transfer function, we next obtain the power delay profile
(PDP) by applying the Inverse Fourier Transform (IFFT) and taking the squared magnitude:
P
pr
(τ,ϕ Tx,i
,ϕ Rx,j
)=|F
− 1
f
{H(f,ϕ Tx,i
,ϕ Rx,j
)}|
2
, (2.4)
whereF
− 1
f
is the inverse fast Fourier transform (IFFT) with respect tof. From thisdouble-directional PDP,
the minimum spacing between two consecutive resolvable samples is defined as angular/delay bin. In the
delay domain it is equal to the inverse of the bandwidth, and in the angular domain it is the beamwidth.
Since the following discussion covers the case with and without oversampling in the delay domain, we
write the discrete delay values as generic variableτ .
We use in the following examples a Hann window [110] to strongly suppress the sidelobes in the PDP
created by each MPC, and in particular, to eliminate the skirt produced by thesinc function arising from
the IFFT using a rectangular window. Other types of windows (e.g., Hamming [65], Kaiser [144], Raised-
Cosine) can be used; the selection will depend on a trade-off between the width of the main lobe and the
29
decaying speed and height of the sidelobes. If a filter is not used, the impact of the skirt (i.e., sidelobes)
would significantly distort the delay parameters. For instance, the second central moment of a (continuous)
|sinc|
2
function over[−∞ ,∞] is infinity. Windowing also makes the noise samples correlated as well as
leads to an MPC impacting multiple delay bins (though only to a small degree) because of the wider main
lobe width (> 1/BW ). Selecting a proper window implies a trade-off between higher sidelobes versus a
shorter impact on adjacent bins. The impact of an MPC on several delay bins is compounded if the MPC
does not fall into the center of a bin. Note that all of these effects will lead to a correlation of the fading in
adjacent bins in those cases where time-variant channels are analyzed; for example, the WSSUS condition
[99, Chapter6] will not strictly hold for the sampled values even if different MPCs are fading independently.
We also perform oversampling in the delay domain when computing the channel delay parameters (σ τ ).
Channel parameters like σ τ are defined for continuous waveforms, and to approximate the continuous
PDP by a discrete one, we increase the number of samples by oversampling. We use in this chapter an
oversampling factor 10 (this particular value is a heuristic compromise between computational effort and
accurate approximation of the continuous waveform). This oversampling avoids problems in estimating
σ τ when the PDP is critically sampled. For instance, in the case of a PDP centered in the middle of two
(critical) sampling points,σ τ will be overestimated compared to the estimated value obtained if we sample
the same function centered on a sampling point (see Figure 2.1) [51].
Next, the PDP needs to be delayed gated. The delay-gating threshold is strongly related to the filtering
function (i.e., windowing) since it must eliminate the significant sidelobes originating from strong early
components and are wrapped around by the FFT. In some situations, the delay gating can also be used to
eliminate delay regions of the PDP where it is known from physical considerations that no MPCs occur;
this can impact the choice of the noise threshold described below. Subsequently, one needs to perform
noise thresholding with a cutoff level P
λ selected to minimize the impact of noise and dynamic range of
30
(a) PDP centered between two sampling points. (b) PDP centered in a sampling point
†
.
Figure 2.1: Critically sampled PDPs with and without oversampling. For visualization purposes, the values
of−∞ dB are instead shown at− 50dB.
the system in the parameter estimations; concrete selection criteria will be discussed in the next section.
The PDP has thus computed as:
P(τ )=[P
pr
(τ ):(τ ≤ τ gate
)∧(P
pr
(τ )≥ P
λ )] (2.5)
or0 otherwise.
These PDPs are now evaluated for two specific configurations. The max-dir case is computed as fol-
lows:
P
max
(τ )=P(τ,ϕ ˆ
i
,ϕ ˆ
j
); (2.6)
where(
ˆ
i,
ˆ
j)=argmax
i,j
P
τ P(τ,ϕ i
,ϕ j
), i.e.,(
ˆ
i,
ˆ
j) is the horn orientation pair with the largest path gain.
The second case is the omnidirectional PDP, which reconstructs the PDP an omni-directional antenna
would see from full double-directional measurements. There are a number of different approaches for the
31
reconstruction [64, 59, 149]; we choose here an approach similar to [64, 17, 5], i.e., selecting the direction
of the highest contribution per delay bin
‡
:
P
omni
(τ,d )= max
ϕ Tx
,ϕ
Rx
P(τ,ϕ Tx
,ϕ Rx
,d). (2.7)
The first parameters to compute using the previously obtained PDPs are the delay parameters: delay-
spread, Q-tapnumber, and Q-window. Delay spread is calculated as the second central moment of the PDP
[19, 99] as:
σ τ =
s
P
τ P
m
(τ )τ 2
P
τ P
m
(τ )
− P
τ P
m
(τ )τ P
τ P
m
(τ )

2
, (2.8)
where m can be "omni" or "max-dir". Note that long-delayed samples with small power (e.g., noise) can
disproportionately impact the delay spread; therefore, selecting proper thresholding is critical in estimating
delay spread.
The next delay parameter is the Q-window, which quantifies the minimum window such that the ratio
of the energy of the PDP within the window to that outside of it reaches a particular value (i.e., signal to
(self-)interference ratioSIR
ISI
). To compute this parameter, we define a threshold γ = 1− 10
− SIR
ISI
/10
related to the desiredSIR
ISI
for the system [31, 99]
Q
win
= argmin
x,
P
T
0
+x
τ =T
0
P(τ )≥ γE
T
0
+x
X
τ =T
0
P(τ ), (2.9)
where E is total path gain of the PDP (E =
P
τ P(τ )).
The last considered delay parameter is the Q-tapnumberQ
tap
, which represents the minimum number
ofarbitrarily-placed taps (more precisely, at arbitrary integer multiples of the inverse bandwidth) necessary
to ensure minimum signal-to-interference ratio (i.e., SIR
ISI
) for the system (e.g., equalizer taps or Rake
fingers). In this case, the selected delay bins of the PDP are considered the signal while the rest are the
‡
Given this approach, windowing can affect the best direction per delay bin because of the wider mainlobe
32
noise + intersymbol-interference. For this study, the use of a Hann window for the PDP combines the
signal of two adjacent delay bins: since the windowed channel has an effective bandwidth of 500 MHz
instead of the 1GHz of the measurements, for the analysis ofQ
win
andQ
tap
the duration of each delay bin
is doubled.
For the computation of Q
tap
, the delay bins are ordered according to their strength; i.e.,
˜
P(τ k
) =
sort(P(τ k
)), wheresort is a sorting function that reorders the taps in descending order. Using
˜
P(τ k
), the
delay window is estimated as follows:
Q
tap
= argmin
x,
P
x
m=1
˜
P(τ m)≥ γE
x
X
m=1
˜
P(τ m
), (2.10)
where againγ is the SIR threshold. Similar toσ τ , bothQ
tap
andQ
win
are also sensitive to noise because
if the number of delay bins is large, that may lead to an overestimation of the number of Rake fingers or
window size to ensure the necessarySIR
ISI
.
The next type of parameter is the angular spread, which needs to be computed from the double-
directional angular power spectrum (DDAPS), which in turn is computed as [119, 10, 99]:
DDAPS(ϕ Tx
,ϕ Rx
)=
X
τ P(τ,ϕ Tx
,ϕ Rx
). (2.11)
Like for the delay parameters, performing noise thresholding and delay gating before computing the
DDAPS reduces noise accumulation from directions without significant MPC.
By summing overϕ Rx
orϕ Tx
we obtain the (single-directional) angular power spectrum (APS) for the
Tx or Rx, respectively. Using the APS, we compute the angular spread according to Fleury’s definition [42]
as:
σ ◦ =
v
u
u
t
P
ϕ |e
jϕ − µ ϕ |
2
APS
p
(ϕ )
P
ϕ APS
p
(ϕ )
, (2.12)
33
wherep can be Tx or Rx for the departure or arrival APS andµ ϕ is
µ ϕ =
P
ϕ e
jϕ APS
p
(ϕ )
P
ϕ APS
p
(ϕ )
. (2.13)
2.4 TheoreticalAnalysisandMCSimulation
This section will discuss the theoretical basis of the noise and dynamic range impact on parameter estima-
tion. The following sections compare the results against MC simulations in synthetic and real measured
MIMO channels.
2.4.1 Noiseimpactonparameterestimation
The theoretical analysis starts by investigating the statistical behavior of the noise in each delay/angle bin.
Each delay/bin is assumed to have noise statistically distributed aszeromeancircularlysymmetricallycom-
plex Gaussian (N(τ )=N
I
(τ )+jN
Q
(τ ),N ∼ CN(0,σ 2
n
)). From this assumption, we can derive that the
noise amplitude (|N(τ )|=
q
N
2
I
(τ )+N
2
Q
(τ )) to follow a Rayleigh distribution (|N(τ )|∼ Rayl(σ n
)). By
squaring the magnitude, we obtain the noise power, which is exponentially distributed (P
l
n
(τ )=|N|
2
,P ∼ Exp(
¯ P
l
n
),
¯ P
l
n
=2σ 2
n
) [99, 109].
Applying thresholding, either for noise reduction, or due to limitations of the dynamic range of the
measurement system, is equivalent to applying an indicator function to each delay bin allowing only delay
bins with power higher thanP
λ to be retained; the thresholded noise is thus:
˜
P
l
n
(τ )=1
Pn(τ )≥ P
λ P
l
n
(τ ) (2.14)
34
where the threshold is selected as the larger of (i) the average noise power per delay bin plus a margin
and (ii) the peak amplitude of the PDP minus the dynamic range of the system; thus,P
λ on a dB scale is
obtained as:
P
λ =max{
¯ P
n
+M,P
pk
− DR}. (2.15)
The probability that a delay bin containing only noise has an amplitude larger than the threshold (and
is thus nonzero after the thresholding operation) is:
Pr(P
l
n
≥ P
l
λ )=
Z
∞
P
l
λ e
− y/
¯ P
l
n
¯ P
l
n
dy =e
− P
l
λ /
¯ P
l
n
(2.16)
where
e
− P
l
λ /
¯ P
l
n
=











e
− 10
M
10
, P
λ =
¯ P
n
+M
e
− 10
P
pk
− DR− ¯Pn
10
, P
λ =P
pk
− DR
(2.17)
and the expected noise power for
˜
P
l
n
is obtained as:
E[
˜
P
l
n
]=
Z
∞
P
l
λ y
e
− y/
¯ P
l
n
¯ P
l
n
dy =e
− P
l
λ /
¯ P
l
n

P
l
λ +
¯ P
l
n

. (2.18)
The above approach is valid for the max-dir case, which analyzes a single PDP. However, the omnidirec-
tional analysis differs due to the strategy used to obtain the omnidirectional PDP. As explained in Sec.
IV.2.3.1, the omni PDP is obtained by selecting on each delay bin the strongest power from all the possible
directions. This procedure alters the noise statistics on each delay for the omni PDP. Let us define a vari-
ableP
l
n− omni
(τ ) to represent the noise power in a delay bin (τ ) for the omni case. Then, it can be defined
as follows:
P
l
n− omni
(τ )=max

P
l
n,(1,1)
(τ ),··· ,P
l
n,(N
Tx
az
,N
Rx
az
)
(τ )

(2.19)
35
where P
l
n,(i,j)
(τ ) is the noise power in the direction (ϕ Tx,i
,ϕ Rx,j
) at delay bin τ . Each observation of
P
l
n,ij
(τ ) is independent and identically exponentially distributed (i.e., P
l
n,ij
(τ ) ∼ Exp(
¯ P
l
n
)). Therefore,
the probability density function ofP
l
n− omni
(τ ) is
f
P
l
n− omni
(z)=
N
T
¯ P
l
n
e
− z/
¯ P
l
n

1− e
− z/
¯ P
l
n

N
T
− 1
(2.20)
whereN
T
=N
Tx
az
N
Rx
az
. The probability that a noise delay bin survives the thresholding
Pr

P
l
n− omni
≥ P
l
λ
=1−
1− e
− P
l
λ /
¯ P
l
n

N
T
(2.21)
and the expected power after thresholding
˜
P
l
n− omni
(τ )=

1
P
n− omni
(τ )≥ P
λ P
l
n− omni
(τ )

is:
E
h
˜
P
l
n− omni
i
=
Z
∞
P
l
λ zN
T
¯ P
l
n
e
− z/
¯ P
l
n

1− e
− z/
¯ P
l
n

N
T
− 1
dz . (2.22)
Finally, for areal omnidirectional antenna, the equivalent statistical model for the noise power is exponen-
tial. However, the system no longer uses a directional horn antenna with gainG
ant
; which is equivalent to
retaining the same signal power but using larger noise power (i.e.,P
l
n− romni
(τ )∼ Exp(G
ant
¯ P
l
n
)) where
G
ant
is the gain of the horn antenna.
§
For this case, the probability that a noisy delay bin survives the
thresholding is:
Pr

P
l
n− romni
≥ P
l
λ
=e
− P
l
λ /Gant
¯ P
l
n
(2.23)
and the expected power after the thresholding
˜
P
l
n− romni
(τ )=

1
P
n− romni
(τ )≥ P
λ P
l
n− romni
(τ )

is:
E[
˜
P
l
n− romni
]=e
− P
l
λ /Gant
¯ P
l
n

P
l
λ +G
ant
¯ P
l
n

. (2.24)
§
The dynamic range threshold might also need to be adjusted, depending on the system settings.
36
2.4.2 Analyticalcomputationofimpactofthresholdondelayspread
We next analyze the impact of the thresholded noise on the parameter estimation. Let us define two
variables, γ ′
,∆ ′
which represent the difference between P
pk
and
¯ P
n
(γ ′
= P
pk
− ¯ P
n
) and the difference
between P
λ and
¯ P
n
(∆ ′
= P
λ − ¯ P
n
), respectively. γ ′
can be interpreted as a type of SNR (the height of
the strongest signal bin over the average noise bin power in the delay domain - though note that this is
not the actual SNR of the raw signal, which is defined as the average signal power over the average noise
power (in either delay or frequency domain).∆ ′
is the offset of the threshold from the average noise level,
irrespective of whether it is due to a "safety margin" for the noise thresholding or stems from the dynamic
range limitation.
We turn now to the computation of the RMS delay spreadσ τ . We first assume the shape for the PDP
depicted in Fig. 2.2a: the PDP of the multipath is modeled as a rectangle, approximating a single cluster case
PDP.
¶
Note that in the following, we perform an expectation operation over theσ 2
τ that are obtained in
different measurements. However, note that the expectation is taken over the different noise realizations,
while no averaging is done over various fading realizations (i.e., the PDP describes aninstantaneous PDP).
Real-world instantaneous PDPs will deviate from the assumed rectangular shape chosen to enable closed-
form analysis that helps better understand the various parameters’ impact. For this analysis, the PDP has
a delay bin resolutionδ τ = 1/BW whereBW is the measurement bandwidth andN
f
delay samples, as
defined in Table 2.2.
The depicted PDP shows the original PDP including noise: the green rectangle (from 0 toτ 1
) contains
MPCs plus noise and thus has powerP
pk
+
¯ P
n
, and the blue rectangle fromτ 1
toτ 2
is the noise-only region
¶
The superscript()
l
indicates that the value is in linear scale (not dB)
37
(a) Single cluster. (b) Multi-cluster (two) case.
Figure 2.2: PDP Rectangular approximation models.
Table 2.1: Setup parameters for PDP, theory analysis
Parameter Symbol Value
Duration of first cluster τ 1
100 ns
Duration of second cluster [τ 2
,τ 3
] [300, 400] ns
Maximum measurable delay τ 4
1µs
PDP exponential decay factor S 15 ns
Difference between P
pk
and
¯ P
n
γ ′
[10, 20, 30] dB
Offset between P
λ and
¯ P
n
∆ ′
0:2:12 dB
∗ For the single cluster and exponential cases,τ 2
is the maximum measurable delay (i.e.,τ 4
).
with power
¯ P
n
. In the no-noise case, it is well known thatσ τ =
τ 1
√
12
. When noise is taken into account,
the estimated noisyσ τ is computed as follows:
˜ σ 2
τ =E{σ 2
τ }≈ P
l
pk
τ 3
1
+
ˆ
P
l
n
τ 3
2
3
ˆ
P
T
−
P
l
pk
τ 2
1
+
ˆ
P
l
n
τ 2
2
2
ˆ
P
T
!
2
(2.25)
where
ˆ
P
l
n
=E[
˜
P
l
n
] and
ˆ
P
T
=P
l
pk
τ 1
+
ˆ
P
l
n
τ 2
.
∥
Using the parameters in Table 2.1, Fig. 2.3 compares the results obtained from (2.25) with MC simula-
tions. Results for the MC simulations provide adistribution or errors, thus providing the smooth (solid-line)
cdfs, since each noise realization can give a different value. The theoretical result only provides the mean
(and thus is represented as step function cdfs (vertical lines). The theoretical value of ˜ σ τ closely matches
the mean of the distribution; nevertheless, there is a residual difference, which increases as P
λ increases.
∥
˜ σ τ in (2.25) is an approximation of the new averageσ τ with noise. A difference from the average of the MC realizations is
expected because theE[Y/X] is not equal toE[Y]/E[X] for everyX,Y random variables. A similar approximation is used in
(2.26) and (2.27).
38
(a)γ ′
=20dB. (b)γ ′
=30dB.
Figure 2.3: Comparison of MC simulation and theoretical values, single-cluster case.
This deviation is due to a "sampling bias" produced by the thresholding operation and the fact that the
number of "noisy" delay bins surpassing the threshold becomes smaller. This sampling bias decreases as
the number of noise-only bins increases.
More importantly, we see that the deviation between the noisy RMS delay spread and the actual value
can be very significant (factor 2 for γ ′
= 30dB, more than factor 4 for γ ′
= 20 dB) if the threshold is
chosen too low; see Fig. 2.3a. While stricter delay gating reduces τ 2
, and thus the impact of noise, this
would require a priori knowledge of the delay regions not containing MPCs.
Since real-world channels often exhibit (at all frequency ranges) multiple clusters [99, 58], we also
analyze a PDP with two rectangles, as shown in Fig. 2.2b. The delay spread for this case is:

˜ σ 2c
τ
2
≈ P
l
pk
1
τ 3
1
+P
l
pk
2
(τ 3
3
− τ 3
2
)+
ˆ
P
l
n
τ 3
4
3
ˆ
P
2c
T
−
ˆ
T
2c
m

2
(2.26)
where
ˆ
P
l
n
=E[
˜
P
l
n
],
ˆ
T
2c
m
=
P
l
pk
1
τ 2
1
+P
l
pk
2
(τ 2
3
− τ 2
2
)+
ˆ
P
l
n
τ 2
4
2
ˆ
P
2c
T
and
ˆ
P
2c
T
=P
l
pk
1
τ 1
+P
l
pk
2
(τ 3
− τ 2
)+
ˆ
P
l
n
τ 4
.
The impact of the noise on the RMS delay spread is generally smaller in the case of multiple clusters.
While in the single-cluster case all long-delayed PDP components (which by definition of the second central
moment have a high impact) stem from noise, in the multi-cluster case, long-delayed components can be
39
(a)γ ′
=10dB. (b)γ ′
=30dB.
Figure 2.4: Comparison of MC simulation and theoretical values, 2 clusters case.
actual MPCs. This is confirmed by Fig. 2.4b, which again has a γ ′
= 30 dB, but where now delay spread
variations as a function of the threshold are less than 5%. Another noteworthy effect is that increase of
the threshold does not always lead to a convergence of the result to the ground truth. As is also intuitive,
a higher threshold can cut off significant MPCs, and thus lead to an underestimation of the delay spread.
An extreme case is shown in Fig. 2.4a. since γ ′
= 10 dB. The second cluster peak power is lower by 5
dB compared to the first cluster; progressively increasing the noise threshold will cut off first the weaker
cluster and (for∆ ′
≥ 10 dB) even the strongest cluster, reducing the delay spread to zero. However, ifγ ′
is larger, this effect does not appear within the range of considered parameters. Generally, both γ ′
and the
ratio of the cluster powers play a role here.
Another popular model for the PDP is a single-sided exponential decay, i.e.,P(τ )=P
pk
e
− τ/ S
, where
S is the decay constant of the PDP; again noise is added as depicted in Fig. 2.5.
Similar to the previous case, we can compute the RMSDS for this case as follows:
(˜ σ exp
τ )
2
≈ 3P
l
pk
(2S
3
− Se
− τ 2
/S
(2S
2
+2Sτ 2
+τ 2
2
))+
ˆ
P
l
n
τ 3
2
3
ˆ
P
exp
T
−
ˆ
T
exp
m

2
(2.27)
where
ˆ
P
l
n
=E[
˜
P
l
n
],
ˆ
T
exp
m
=
2P
l
pk
S(S− e
− τ 2
/S
(S+τ 2
))+
ˆ
P
l
n
τ 2
2
2
ˆ
P
exp
T
and
ˆ
P
exp
T
=P
l
pk
S(1− e
− τ 2
/S
)+
ˆ
P
l
n
τ 2
.
40
Figure 2.5: Single exponential cluster.
(a)γ ′
=10 dB. (b)γ ′
=20 dB.
Figure 2.6: Comparison of MC simulation and theoretical values, single cluster exponential PDP case.
As shown in Figure 2.6, the theoretical and MC values agree for low margin values; however, a gap
increases as the margin gets larger. Like the previous case, this effect is due to the reduced number of
surviving noisy delay bins after the thresholding.
It is important to highlight again that if the margin is large, it can affect not only the noisy delay bins
but the non-noisy ones (i.e., bins containing actual MPCs), altering the estimation and even eliminating
the PDP, as can be observed in Figure 2.6a.
2.5 Evaluationwithsyntheticchanneldata
This section will continue evaluating the noise impact on condensed parameter estimation using more
realistic channel models. We generate syntheticdouble-directional MIMO channel responses following the
41
parameters shown in Table 2.2, mimicking a typical measurement campaign (e.g., [10]). For this analysis
each azimuthal capture, either in Tx or Rx, will be done atHPBW degrees of separation, which provides
N
az
=360
◦ /HPBW captures (i.e.,N
az
={72,36,18} for each value ofHPBW described in Table 2.2).
The simulated scenarios are multi-cluster MIMO (covering LoS and NLoS) with specular MPCs and DMC
at different delays and angles.
∗∗
The results will be evaluated for the purely specular cases using the mean
values from the MC simulation to analyze the behavior. For the cases involving DMC, the CDF of the MC
runs will be compared directly, given the statistical behavior of the scenario.
2.5.1 Impactoffrequency/delaypoints,N
f
We start by analyzing the impact of the number of frequency points in the MIMO channel response. The
synthetic channels used here only have specular MPCs; for the impact of DMC see Sec. V.C.
Several effects are observed when the frequency points are doubled and quadrupled (i.e., x2,x4). The
main impact is the overestimation in the parameters such as σ τ ,Q
win
,Q
tap
because denser frequency
points correspond to larger delay range. For a limited support of the ground truth PDP, increasing the
observed delay range increases the number of noise-only delay bins. Suitable delay gating can mitigate or
eliminate this effect, though care must be taken not to eliminate actual MPCs when the gating interval is
too short.
An example of this effect is given in Figure 2.7, which shows the values for RMSDS in the max-dir
case (N
f
) for1001 and4001 frequency points, in sub-figure a and b, respectively. For the maximum value
ofσ τ (obtained at low values ofγ ′
,∆ ′
), the ratio is approximately four, i.e., the same ratio as the number
of frequency points. As∆ ′
orγ ′
increase, the estimated value decreases, converging to the actual value;
the decay in the estimated parameter is also slower for higher N
f
. The plot shows that ∆ ′
dominates
the estimation compared toγ ′
, i.e., increasing∆ ′
provides a faster drop in the overestimation. However,
for power distributions of the MPC with considerable support (i.e., wide spread of the occurring powers),
∗∗
For this analysis, we assume that the number of angular scans is the same for Tx and Rx (i.e.,N
Tx
az
=N
Rx
az
=Naz)
42
(a)N
f
=1001,N
az
=18 (b)N
f
=4001,N
az
=18.
Figure 2.7: ¯σ τ (mean) values for max-dir case with a different number of frequency points. NLoS scenario.
increasing the threshold can purge valid delay bins in addition to the noise-only ones and so produce the
opposite effect in the estimated parameter, as discussed in Sec. III.
We stress that a largeγ ′
alone might not guarantee an accurate estimation; for instance, ifγ ′
= 40dB
and ∆ ′
= 6dB, the values for σ md
τ ≈ 13.49 and 223.44 ns compared to the actual value on each case,
meaning that for this case, the estimated values are 23 and 487 times larger than the actual value (σ ori
τ =
0.59ns). This ratio can change depending in the scenario (e.g., LoS, NLoS) whereσ ori
τ can change. WhenN
f
increases, the probability of a noisy long delay bin increases, and it can increase the estimatedσ τ because
it depends on the square of the delay.
††
The impact of the number of frequency points on the omnidirectional PDP is different compared to the
max-dir case due to the strategy used to generate the omni PDP from the directional captures (explained
in Section 2.3.1). Even though from the measurement point of view, selecting the maximum power from
all azimuthal directions per delay bin is a sound strategy [64], from the noise perspective, it might change
the statistical behavior because the maximum value is always selected from theN
Tx
az
N
Tx
az
possible azimuth
combinations, and so enhance the noise. Therefore, the total noise observed in the omni PDP is larger or
equal to that observed in the max-dir case.
††
The definition of σ τ contains a square root function; however, the argument requires to compute the PDP’s second moment,
which requires multiplying the power times the square of the delay. For this reason, longer delay bins have more considerable
impact in the estimation
43
Table 2.2: Setup parameters for synthetic MIMO channel
Parameter Symbol Value
Frequency points N
f
1001
Frequency Range [f
start
,f
stop
] [145, 146] GHz
Bandwidth BW 1 GHz
Antenna 3 dB beamwidth HPBW [5
◦ ,10
◦ ,20
◦ ]
Tx/Rx rotation range ϕ Tx
,ϕ Rx
[0
◦ ,360
◦ ]
Tx/Rx rotation resolution ∆ ϕ Tx
,∆ ϕ Rx
[5
◦ ,10
◦ ,20
◦ ]
Number of clusters N
cl
3
Number of MPCs per cluster N
mpc− cl
3
Cluster mean delay ¯τ cl
[100, 120, 160] m
Cluster delay spread σ cl
τ [3, 5, 5] m
Cluster AOA mean
¯ ϕ cl− a
[0
◦ ,50
◦ ,130
◦ ]
Cluster AOA spread σ cl− a
ϕ [20
◦ ,30
◦ ,30
◦ ]
DMC AOA decay parameter σ DMC− a
ϕ 10
◦ Cluster AOD mean
¯ ϕ cl− d
[0
◦ ,− 50
◦ ,230
◦ ]
Cluster AOD spread σ cl− d
ϕ [20
◦ ,30
◦ ,30
◦ ]
DMC AOD decay parameter σ DMC− d
ϕ 10
◦ (a)N
f
=1001,N
az
=18 (b)N
f
=4001,N
az
=18.
Figure 2.8: ¯σ τ (mean) values for omni case with a different number of frequency points. NLoS scenario.
Figure 2.8, shows the decrease of σ omni
τ with increasing γ ′
.
‡‡
In contrast to the max-dir case, the
differences between the curves ∆ ′
∈ [0,6] dB is negligible. This is because the probability that a noise
delay bin survives (see Eq. 2.21) for ∆ ′
∈ [0,6] dB only changes from 1 to 0.9978. However, significant
differences are observed for ∆ ′
≥ 8 dB. Like in the max-dir case, increasingN
f
will lead to overestimation
even for larger values ofγ ′
; in other words a large value is require to approximate the ground truth closely.
‡‡
In the noise-free case, the number of samples (in delay or angle) may have an impact in the estimation of the delay spread
(omni case) and angular spread (Tx or Rx) due to the sampling of the MPCs.
44
(a)
¯ Q
win
. (b)
¯ Q
tap
.
Figure 2.9: Mean estimated values of
¯ Q
win
and
¯ Q
tap
forN
f
= 2001,N
az
= 18 case. NLoS scenario, max-
dir case.
For instance, ifγ ′
= 40 dB and ∆ ′
= 8dB, the estimated value forσ omni
τ is less than5% larger than the
actual value whenN
f
= 1001 and approximately 8 times larger whenN
f
= 4001; in this particular case,
it is necessary to increase∆ ′
to 10 dB to reduce the estimate toσ τ =145 ns (almost as twice as the value
ofσ ori
τ =84.95 ns).
Next we analyze the noise impact onQ
win
andQ
tap
. Q
win
has a strong correlation withσ τ : a larger
σ τ indicates that the power is more dispersed in delay; so we require a larger window Q
win
to capture
more energy of the channel. Therefore, we expect a similar behavior toσ τ . On the other hand,Q
tap
is not
dependent on the delay of the MPCs but rather their number and power distribution; still, a larger number
of noisy delay bins can affect the total power of the PDP, and so require a larger number of delay bins to
achieve the desiredSIR
ISI
.
The conjecture about the behavior ofQ
win
being similar to that ofσ τ is confirmed in Figure 2.9a, which
shows the max-dir case forN
f
=2001. Asγ ′
and∆ ′
decrease,Q
win
increases because the additional noisy
delay bins in the PDP increase the overall available power, thus necessitating a larger window (remember
that the receiver cannot distinguish between the noise and multipath in the thresholded PDP). These extra
delay bins increase the total energy of the PDP; so, to collect the targetedSIR
ISI
(e.g., SIR
ISI
= 15 dB
equivalent to≈ 97% of the total energy of the PDP), a larger number of delay bins need to be collected. In
45
(a)N
f
=1001,N
az
=18. (b)N
f
=4001,N
az
=18.
Figure 2.10: ¯σ ◦ (mean) values for Tx with a different number of frequency points. LoS scenario.
the case ofQ
tap
, the expectation is to behave similarly toQ
win
. The additional noisy delay bins will affect
the total power of the channel, and so increasing the number of needed taps (e.g., Rake fingers) to reach
the requiredSIR
ISI
(see Fig. 2.9b).
We can also expect the estimated angular spreadσ ◦ to be impacted by the noise and, in particular, lead
to increased values when more noise-only bins exist, e.g., due to increased frequency points. This effect
is because the APS is computed as the sum of the power on each delay bin per angle. A larger number of
noise-only delay bins, equally likely to occur at any angle, tends to increase the angular spread except in
some special cases (e.g., equally strong contributions from the front and back).
This effect is confirmed in Fig. 2.10. For instance, ∆ ′
= 6dB andγ ′
= 40 dB generateσ ◦ = 0.85,0.99
(forN
f
=1001,4001 respectively), which is almost twice the original values. A∆ ′
=10dB allows a value
closer to the ground truth at the sameγ ′
value. Similar behavior is observed on the Rx side. Comparing
LoS and NLoS, we noticed similar behavior in both cases; like the delay parameters, a large∆ ′
allows to
minimize the impact; however, ifγ ′
is low, likeσ τ , the value is underestimated because non-noisy delay
bins get eliminated in the thresholding. Also, suitable delay gating can significantly decrease the impact
of the noisy bins for the angular spread.
46
(a) ¯σ omni
τ , NLoS. (b) ¯σ ◦ Tx
, LoS.
Figure 2.11: Mean estimated values forN
az
=72,N
f
=1001
2.5.2 Impactofangularpoints,N
az
Next we analyze the impact of the number of angular captures of the MIMO channel, i.e., the density of
the angular grid on which the measurements are done. Increasing density will usually, but not always, be
associated with reduced beamwidth of the antennas. The conjecture for this case is that the noise in the
max-dir PDP will remain unchanged because the number of frequency/delay samples remains constant;
therefore σ τ ,Q
win
and Q
tap
will remain unchanged as N
az
increases. This conjecture is confirmed in
simulations, which are not shown here for conciseness. However, in practice γ ′
may increase when the
beamwidth decreases, since the antennas provide higher gain.
On the other hand, the omni PDP is affected by the change of N
az
because there are more angular
captures from which a noisy delay bin can be selected, producing a noise enhancement. This effect will be
noticeable in all delay parameters such asσ τ ,Q
win
,Q
tap
. Figures 2.11a and 2.8a showσ omni
τ for two cases
ofN
az
. We observe that the maximum value estimated is similar because it is limited by the total number
of samples in the PDP; however, juxtaposing both figures, the curves for different ∆ ′
are different. The
curves for∆ ′
≤ 8dB are closer to each other forN
az
=72 compared toN
az
=18, which is in agreement
with the previous conjecture. This fact also indicates that a higher∆ ′
is required to estimate close to the
ground truth; nevertheless, the impact depends onγ ′
as in previous cases.
47
Finally, it is expected that the estimate of the angular spread is impacted by changes in N
az
. The
increment of this parameter implies more points where a noisy delay bin can appear; hence the angular
spread increases. This effect is mitigated when ∆ ′
increases; nevertheless, like the previous cases, whenγ ′
is low, it can produce an underestimation because delay bins containing low-power MPCs are eliminated
together with the noise. Figure 2.11b showsσ ◦ for Tx - LoS scenario where, as expected, the curves with
lower ∆ ′
have larger values when N
az
increases. For example, when γ ′
= 40 dB and ∆ ′
= 6dB the
estimated σ ◦ are 0.99 (increment of 10%). In this case, ∆ ′
≥ 10 dB generated σ ◦ values lower than the
ground truth forγ ′
≤ 50 dB.
2.5.3 ImpactofDMC
In this section, we evaluate the impact of the DMC in the estimation. We will focus on the impact of am-
plitude and decay characteristics of the DMC in the estimation; for this reason, the specular characteristics
of the MPCs in the synthetic channel remain unchanged for this analysis. The decaying parameters to be
changed for this analysis areα 1
, which corresponds to the magnitude of the DMC in the delay domain, and
β d
which is the normalized coherence bandwidth of the channel, which determines the decaying of the
DMC [130, 72]. The values forα 1
,β d
are inspired by a measurement campaign in the THz band described
in [130]. To be on the same order, we use values forα 1
=[− 15,0] dB below the strongest peak of the PDP,
a normalized decaying parameter ofβ d
=[0.01,1], andτ DMC
0
is set to be equal to the LoS delay.
First, we evaluate the impact ofβ d
while maintaining a constant value ofα 1
=− 5dB andγ ′
=40dB.
A larger β d
indicates a faster decay of the DMC, leading to a smaller no-noise delay spread, as indicated
in Fig. 2.12a. From the plot, a large ∆ ′
> 10dB is required to estimate close to the no-noise case for all
values ofβ d
. However, for small∆ ′
, the delay spread first decreases but then increases with increasing β d
.
This behavior can be explained by the fact that a largerβ d
implies a smaller energy carried by the DMC,
so that noise contribution dominates the delay spread. In contrast, for smaller beta, the DMC component
48
(a)α 1
=− 5dB. (b)β d
=0.01.
Figure 2.12: Impact of DMC onσ omni
τ for a fixed γ ′
=40dB,N
f
=1001,N
az
=18.
dominates (we can see that for very smallβ d
all curves follow the "no-noise" curve), where the deviation
starts to become significant depending on the ∆ ′
. Similar to the specular case, the curves for ∆ ′
≤ 6dB
are close due to the noise statistics in the omnidirectional case.
Next, we evaluate the impact of α 1
while keeping constant β d
= 0.01 and γ ′
= 40. For a small α 1
,
the estimated delay spread may be too low (for high∆ ′
, which cuts off not only the noise but also much
of the DMC) or too high (for high∆ ′
, so that too much noise remains after the thresholding). As theα 1
increases, the estimates for all ∆ ′
become close to the true value, even though there is up to 20% error
even forα 1
=0dB (see Fig. 2.12b).
From all the cases analyzed, we observed that the DMC could significantly change estimated delay
spread values even though the DMC’s statistical properties are similar to the noise. This behavior is be-
cause the DMC carries the actual signal from the channel. However, a Fourier-based analysis of a channel
measurement cannot distinguish between DMC and noise and interprets all of the delay bins as part of the
PDP. Thus, thresholding tends to allow too much noise or eliminate too much DMC. This effect contrasts
High-Resolution Parameter Extraction techniques (e.g., CLEAN, SAGE, or RIMAX [fleury1999channel ,
124]) which separate the DMC and specular MPCs from the noise only and generally allow a more precise
suppression of the noise.
49
2.6 Evaluationwithmeasuredchanneldata
In this final section, we analyze the impact of noise in real measured channel transfer functions. A sub-THz
(145-146 GHz) "device-to-device" campaign performed at the University of Southern California, University
Park Campus (UPC) will be used for this purpose. Two locations were selected for this analysis, a line-of-
sight (LoS) scenario with a 93 m distance between Tx and Rx and a 10.49 m non-LoS (NLoS) scenario. This
campaign used a frequency domain channel sounder with two horn antennas. Both antennas were placed
on precision rotors to scan every 10
◦ allowingN
Tx
az
= N
Rx
az
= N
az
= 36 angular samples on each end.
The sounder performed a frequency sweep ofN
f
=1001 frequency points over the measured bandwidth
of 1GHz, which leads to a maximum resolvable excess delay of 300 m. Delay gating could only be applied
to eliminate delays > 290m to eliminate the skirts of the FFT; no tighter gating was possible because
of MPCs’ delays on this order. Further details of the sounder and campaign can be found in [10]. The
chosen measurements had very high (60 dBγ ′
); for the following analysis, noise will be added artificially
to observe its impact on the estimated parameters.
The PDP and APS for the LoS scenario are shown in Figure 2.13. The environment is a quad where
trees and buildings are on both sides of the link and behind the receiver. As expected, the max-dir PDP (red
dotted line) shows a strong peak at the LoS distance and sparse delay bins with significantly lower power
than the LoS delay bin for longer delays. The omni PDP, on the other hand, has more MPC-carrying delay
bins corresponding to reflections coming from buildings in the area. The LOS is observed in the APS at
the large red spot atϕ Tx
= ϕ Rx
= 0
◦ ; another direction with significant energy is ϕ Tx
= 0,ϕ Rx
= 180
◦ which is a reflection coming from a building located behind the receiver.
The first parameter to analyze is σ τ . The conjecture is that the noise will increase the estimated value
for both cases (max-dir and omni), and it will be reduced when γ ′
or ∆ ′
increase. For the omni case,
a similar behavior to the synthetic channel case is expected as a result of noise enhancement for this
case. Figure 2.14a shows the average behavior ofσ τ , where the curve for the omni PDP case follows the
50
(a) PDP. (b) APS.
Figure 2.13: d
Tx− Rx
=93m,N
f
=1001,N
az
=36, LoS scenario
(a) ¯σ omni
τ . (b) ¯σ ◦ Tx
.
Figure 2.14: N
f
=1001,N
az
=36, LoS scenario.
conjectures, and as expected, when∆ ′
=12dB, the estimated parameters were lower than the original for
γ ′
≤ 50dB.
We expect a similar impact in the angular domain as in the synthetic case for estimatingσ ◦ . For small
∆ ′
, noise is accumulated, increasing the estimated value, and decaying asγ ′
or∆ ′
increases. However, even
for an LoS scenario, a largeγ ′
and∆ ′
is required for a good estimation. From Figure 2.14b we observe that
aγ ′
≥ 50dB and a∆ ′
≥ 10dB are required. Like our previous analysis, the angular spread is overestimated
(e.g.,γ ′
=50dB,∆ ′
=6dB) and underestimated (e.g.,γ ′
=40dB,∆ ′
≥ 10dB) for other cases.
51
(a) PDP. (b) APS.
Figure 2.15: d
Tx− Rx
=10.49m,N
f
=1001,N
az
=36. NLoS scenario.
For the NLoS scenario, the Tx and Rx are located at the entrance of the Vivian Hall of Engineering (VHE)
building at UPC. This area has tall wide pillars, metal benches, walls, and glass doors. In this case, the Tx
and RX were blocked by two pillars between them. The PDPs exhibited in Figure 2.15a show the strongest
delay bin at approximately 50 m, indicating the complete line-of-sight blockage. The omni PDP shows ad-
ditional delay bins with considerable arriving between 18 and 50 m from reflections in the walls and pillars
surrounding the Tx and Rx. This effect is also observed in the angular domain by checking Figure 2.15b.
The strongest power in this case comes fromϕ Tx
=− 90,ϕ Rx
= 90. Still, we also distinguish significant
power (within 10dB below strongest angular bin) from other directions such asϕ Tx
=120,ϕ Rx
=40 and
ϕ Tx
=− 50,ϕ Rx
=− 130 which implies a large value in the angular spread.
Analyzing the delay parameters for the NLoS scenario, we expect larger values because of the more
spread-out power of the delay bins. Figure 2.16a shows the curves of the average values ofσ τ andQ
win
for the omnidirectional case. The behavior is similar to the LoS case; however, for the max-dir case, we see
that∆ ′
≥ 8dB produces underestimated values forγ ′
≤ 40dB, which is a result of the low-power delay
bins being covered up by the noise and also eliminated by the thresholding, leaving the strongest delay
bin only for that particular case (Figure is not shown for space reasons). The omni case is different due
to the delay bin atτ = 227m with power 8dB lower than the strongest one. This MPC dominates theσ τ 52
(a) ¯σ omni
τ . (b) ¯σ ◦ Tx
.
Figure 2.16: N
f
=1001,N
az
=36, NLoS scenario.
estimation and is only affected when γ ′
=20dB and∆ ′
≥ 10dB. When these cases happen, we can expect
underestimation onσ τ .
Finally, in the angular domain, we expect large values in the estimation and the noise increasing the
estimated value; however, it is also susceptible to underestimation when∆ ′
is large. Figure 2.16b shows
the values for Tx and Rx, the high values of∆ ′
make the parameter underestimated because of the power
reduction on each angle due to the threshold. For instance, when∆ ′
= 10dBσ ◦ is underestimated for all
values ofγ ′
, it closes up to the actual value asγ ′
increases. A similar behavior is observed on the Rx side
because of the scenario’s similarities in the angular power spectra.
2.7 Conclusions
We analyzed the effects of noise and the choice of noise thresholding on condensed channel parameters
for joint delay-angle measurements. We observed that the noise could lead to dramatic overestimation of
channel parameters such as delay spread and angular spread, as well as systems design parameters such
as Q
win
,Q
tap
. For all parameters, the impact of the noise depends on its strength (γ ′
). The larger the
value, the lower the impact and the overestimation; asγ ′
becomes enormous, the values converge into the
ground truth. Increasing the frequency points led to more noisy delay bins and significant overestimation.
53
Current measurement campaigns at mm-wave and sub-THz are performed using rotating horns point-
ing in different directions capturing MPCs. In this case, we observed that the noise in the omnidirectional
power delay profile is more prominent compared to the max-dir because the noise from directions with no
signal components can enhance the noise in the omni PDP. A similar behavior is observed in the angular
spread and design parameters likeQ
win
,Q
tap
, which could lead to overestimating the required number of
taps for a receiver, increasing its complexity. If a system requires a considerably large SIR (e.g., > 15dB
for high-capacity systems), the impact of noise in estimating taps is more noticeable.
We also focused on the impact of threshold, where a large value (∆ ′
) did not guarantee to reach the
correct value in all cases but instead can cause underestimation when MPCs with low power are suppressed
together with the noise. This scenario is common in communication devices with low dynamic range,
contrary to what is encountered in equipment for sounding purposes.
It is essential to mention that the goal of this analysis is not to encourage or discourage the use of
particular values for analysis but rather to provide a framework for the analysis of the impact of noise and
thresholds in Fourier analysis and condensed parameter estimation.
54
Chapter3
Multi-band-WLANsystemsforultra-highthroughput
3.1 IntroductionandMotivation
Wi-Fi has become the dominant mode in which computers and most smartphones are connected to the
internet. New frequency ranges and physical-layer technologies are required to handle the concomitant
increase in traffic load. Regarding physical-layer technology, Wi-Fi is more heavily exploiting multiple
antenna elements at both link ends – increasing the number of antenna elements that access points and
end devices can enable multi-user MIMO. In terms of the frequency range, an important step has been
the recent approval of the 6-7 GHz band for Wi-Fi, more than doubling the available bandwidth of UnII.
Furthermore, the presence of three main Wi-Fi bands, namely 2.4, 5-5.8 GHz (henceforth just called the 5
GHz band(, and 6-7 GHz (henceforth called the 6 GHz band), suggests the use of multi-band technology,
i.e., exploiting the fact that the propagation conditions in those bands are correlated, but not identical. To
assess the impact of these developments and enable the design of new equipment that can best exploit
them, we first need to understand the propagation channel. The main focus of this chapter is thus to in-
vestigate the propagation channel in the 2.4, 5, and 6 GHz bands concerning path loss (which determines
coverage and modulation+coding scheme), delay spread (which impacts cyclic prefix and channel estima-
tion), and in particular directional characteristics. The channel measurements investigate the properties
55
in the three bands in environments most relevant for enterprise Wi-Fi deployment, including various of-
fice structures (small offices and cubicles), cafeteria/lounge environments, and outdoor courtyards. The
resulting statistical channel models can be used as more general versions of the existing Wi-Fi models.
Furthermore, the detailed results show the relationship between environmental and specific propagation
characteristics. This will help with the deployment planning of future single-band or multi-band Wi-Fi
systems and developing new, more efficient Wi-Fi devices. We stress that our measurement setup and ex-
traction are designed to allow the extraction of the pure channel properties, i.e., exclude all the effects due
to the measurement system. Consequently, the results can be used to provide system performance results
for any antenna design and RF system. In other words, our results are not just an assessment of how a
specific current system works but can serve as the basis for future device and system development. [157,
140, 57, 30, 112, 99, 78, 95, 79, 94]
3.2 SetupandExtractionProcedure
We used a frequency domain channel sounder for our measurement campaign based on a Vector Network
Analyzer, VNA (Agilent model E5080A). The transmit signal from the VNA is amplified by a WENTEQ
ABP1500-03-3730 power amplifier (PA) to a level of 29/27 dBm at the output (for 2.4/5-7 GHz respectively)
and then transmitted from the TX antenna. On the other link end, the signal from the TX antenna goes
through a bandpass filter in order to eliminate interference from adjacent bands, after which it is boosted
by WENTEQ ABL0800-12-3315 LNAs (amplification 35/33 dB, noise figures 1.5/2 dB in 2.4/5-7 GHz band
respectively) and sent through an RF cable (attenuation 9/15 dB/50ft) to port 2 of the VNA. Different settings
of the VNA were chosen for the two bands; see Table 3.1. Since the subcarrier spacing determines the
maximum measurable excess delay, we aimed for similar spacings in the two bands (though somewhat
smaller in the 2.4 GHz band); yet, due to the different available bandwidths, this resulted in a much larger
number of subcarriers in the 5-7 GHz band. The TX power was changed to get the maximum possible
56
power from the PA. An IF bandwidth of 500 kHz for both bands was chosen as a compromise between
measurement speed and noise power. Since the duration of a measurement sweep is larger than the typical
channel coherence time in the presence of human movement, the setup can only be used under quasi-static
conditions, which were ensured throughout our campaign.
Table 3.1: VNA Settings
Band 2.4GHz 5-7GHz
StartFrequency 2.4 GHz 5 GHz
StopFrequency 2.5 GHz 7 GHz
NumberofPoints 201 1601
Txpower 7 dBm 12 dBm
3.2.1 Antennasanddirectionality
Given the wide separation between the 2.4 and 5-7 GHz bands, we must use separate antennas. Further-
more, we need directional (horn) and omnidirectional antennas to investigate directional vs. omnidirec-
tional spreads. The omnidirectional antenna selected for this experiment is the COBHAM XPO2V-0.3-
10.0/1381. It has a non-uniform beampattern in elevation, with a beamwidth (full-width half-maximum,
FWHM) of∼ 90°.
∗
The directional antennas are a Cast Mini Reflector Grid Antenna (sold by L-com) for
the 2.4-2.5 GHz beamwidth of 12° in the E-Plane and 19° in the H-Plane, and 20dBi gain. For the 5GHz
band, antennas from A-INFO with beam width ranging from 13° to 17° in E-plane and 16° to 19° for the
H-Plane, and the gain ranges between 19 and 21 dB. The directional antennas were mounted on precision
rotation stages from Diamond Engineering to point the main beam into different azimuths and elevations
and obtain the directional impulse responses [146]. Since a sweep of all combinations of TX and RX di-
rections (full MIMO) would take more than 4 hours and thus significantly limit the number of locations
that can be measured, we instead captured SIMO (omniantenna at the TX and horn at the RX) and MISO
∗
One limitation of our setup was the frequency variations of the gain of the omnidirectional antenna in the bands of interest
(especially in the band of 5 -7 GHz), on the order of 6 to 8 dB, as well as deviations from a truly omnidirectional pattern of up to
4dB in azimuth. These variations in the pattern may impact the results obtained in post-processing.
57
(vice versa) configurations. Equivalent SISO (omni at both link ends) channel characteristics are obtained
by post-processing.
A comprehensive analysis was performed for some select measurement points for each location, and
the results were analyzed closely in comparison with the channel geometry. These results gave us a timely
sanity check for the long measurement campaign. As can be expected with many locations, the final hurdle
was offered by a large amount of data processing required to process and analyze the current measure-
ments. The processed data were analyzed to provide path loss and shadowing models, rice factor, angular
and delay spreads, beamforming, and parameter extraction algorithms.
3.3 KeyMeasurementsandModelingResults
The main results of our measurements, and the resulting models, are summarized in the following.
PathlossandShadowing:
Pathloss and shadowing are the critical parameters for wireless system deployment, as they determine
the signal-to-noise ratio and the interference to/from other systems. While small-scale fading also impacts
SNR and interference, it is somewhat less critical in wideband systems because it can be eliminated through
frequency/delay diversity. It is pertinent to note that higher frequencies naturally have a higher free-
space path loss. However, our current analysis goes beyond this simplistic analysis and looks at in-depth
characteristics of the channel.
For the Indoor corridor to office environment line of sight (LOS) scenarios, the path gain coincides with
free space path gain (FSPG) for shorter channel lengths. However, the gain decreases less with distance
than FSPG, indicating a waveguiding effect in the corridor environment. The benefit of this effect increases
as the frequency increases from 2.4 GHz to 6-7 GHz. Similarly, shadowing standard deviation, though
quite similar, also increases with frequency. We do not observe the waveguiding effect in non-line of sight
58
(NLOS) cases. The shadowing remains relatively similar for all the bands though it is much higher than in
the LOS case.
The waveguiding effect is not visible in the LOScafeteriascenario since the environment is more open.
The path gains thus closely follow the FSPG for all the bands under consideration. The NLOS signals are
more attenuated over shorter distances since the open environment reduces reflections. The shadowing
values are roughly independent of the band that is considered in this environment.
The Open office blockages cause higher losses for the NLOS scenario. The shadowing is highest in the
2.4GHz bands, followed by the 5GHz bands and the nearly equal 6GHz bands.
For the Outdoor courtyard, path gains for LOS are slightly less than FSPG. Both the higher frequency
bands suffer higher attenuation than the 2.4GHz NLOS scenario. LOS in the 5GHz and 6GHz bands show
smaller shadowing compared to 2.4 GHz; however, this situation is reversed for the NLOS case.
In conclusion, in the path loss analysis, we see that waveguiding happens for indoor scenarios with
corridors, and this effect benefits higher frequencies more; relatively open indoor areas follow the FSPG
models quite closely though a reduction of reflections causes higher attenuation in NLOS scenarios, blocker
affects the performance for both the LOS and NLOS cases in indoor scenarios, and outdoor scenarios
do slightly worse than FSPG. Shadowing is generally more significant in NLOS scenarios than the LOS
scenarios and reduces with frequency in indoor scenarios. Though the LOS-NLOS trend of shadowing
follows that of indoor environments, the trend with respect to frequency reverses here.
Delay, Angular Spread and Rice Factor: As mentioned above, a key of our measurement setup is
isolating channel properties from the effects of the measurement system. The latter is eliminated by careful
calibration and signal processing. From the calibrated data, an evaluation was performed by analyzing the
2.4 GHz data, as well as the 5-6 and the 6-7 GHz bands.
In the case of delay spread, it can be seen that the 2.4 GHz band has more delay dispersion in outdoor
scenarios and open indoor areas compared to 5 to 6 and 6 to 7 GHz. However, the difference is slight:
59
on average, the difference between corridors was 5 ns for NLOS scenarios and less than 2 ns for LOS.
Comparing the bands 5-6 and 6-7 showed that the behavior is quite similar for the indoor corridor and
outdoor scenarios. However, in the case of the open office environment, differences in the behavior of the
delay spread in these two bands occur, though they are not systematic (this indicates a good possibility for
diversity).
For the case of the Rice factor, it is essential to highlight that the precision of the estimation depends on
the available measurement bandwidth and, thus, is considerably lower at 2.4 GHz. Given this, the results
show differences in the K factor for 2.4 GHz and 5 to 6 and 6 to 7 GHz for all the bands. The values for
2.4 GHz are between the results obtained from 5-6 and 6-7 GHz. For all the scenarios, Rice factor values
between the 5-6 GHz band and 6-7 GHz are different; in fact, the 5 to 6 GHz distribution is always higher
than the one from 6 to 7. This phenomenon is observed clearly in LOS cases; in NLOS cases, the difference
is minimal.
In the case of angular spread, there are differences between the behavior of 2.4 GHz and the 5- 6 and
6 -7 GHz bands, this difference can be up to 10 degrees in LOS scenarios (e.g., outdoor environment), but
in NLOS the difference is tiny. An important fact to analyze is that the statistical behavior of the angular
spread for LOS cases shows an essentially uniform spreading over a range. However, some scenarios, like
the cafeteria and open office area for NLOS, showed a distribution function skewed towards high values.
When analyzing the bands 5 to 6 and 6 to 7 GHz in the angular domain, the difference between them is
not significant.
To summarize the frequency dependence of the various considered parameters: There are (slight) dif-
ferences between the bands 5-6 and 6-7 GHz when there is an open area scenario (e.g., open office). These
effects are more noticeable in scenarios with good reflectors (glass, metallic surfaces). In the case of the
Rice factor, there is a difference between the bands. There is a difference in path loss between 5 - 6 and 6
- 7 GHz; this effect is even more noticeable when comparing 2.4 GHz against the higher bands. Finally, in
60
the case of angular spread, comparing 2.4 GHz and the 5 - 6 and 6 - 7 GHz shows a clear difference that
can reach the order of 10 degrees. The effect in NLOS scenarios is reduced compared to the variation seen
in the LOS cases. Comparing the 5 - 6 and 6 - 7 GHz show no significant variation in the angular spread.
3.4 Conclusions
The differences in propagation effects are minor concerning the difference between the 5 and the 6 GHz
bands. This leads us to conclude that current deployment guidelines and tools can be adapted relatively
straightforwardly for the new 6 GHz frequency band. As was expected, more significant differences can
be identified between the 2.4 and the 6 GHz bands. The different electromagnetic properties of objects at
those frequencies and the lower effectiveness of diffraction at 6 GHz means that 2.4 GHz will remain the
most robust band but may suffer from increased interference and low bandwidth. Combining the two (or
3) frequency bands thus enables performance advantages and even systems that, e.g., use low-data rate
control signaling (such as RTS/CTS in one band and use the 6 GHz band as a pure data carrier without
significant overhead) appear feasible.
61
Chapter4
ImpactofcommonreflectingandabsorbingbuildingmaterialsonTHz
multipathchannels
4.1 Introduction
The high data rate requirements for many upcoming applications such as virtual reality and immersive
environments cannot be met with current and proposed 5G networks [133]. Moreover, these requirements
are envisioned to grow even further in near future. Communications in the THz band (0.1-10 THz) is a key
candidate to meet these requirements because of the availability of a large amount of unused spectrum
in this band [14]. The topic has thus seen a lot of recent interest, especially in the 0.1-0.5 THz range as
pointed out by some recent survey papers on the future of THz communications [88, 24, 121, 58]. This
interest is in part fostered by the recent decision of the US spectrum regulator, the Federal Communication
Commission (FCC), to provide experimental licenses in the 140-220 GHz band, and the expectation that
this band is to be an important part of 6G wireless systems [151]
The design of any communication system, regardless of its frequency of operation or bandwidth, de-
pends on the channel it is to operate in. Therefore, the first key step in order to move towards the develop-
ment of THz systems is to perform measurements that allow understanding and realistic assessment and
modeling of the channels. A number of such studies have been recently performed in particular at the lower
62
end of this band (0.1-0.5 THz). A propagation system for channel measurements at 300 GHz is discussed
in [116]. Statistical analysis for a desktop THz channel at 300 GHz is discussed in [80]. Recent papers by
our group cover channel measurements and statistical analysis for urban outdoor device-to-device [6, 8,
10] and microcell scenarios [3] at 140 GHz. Also, recently the authors of [155, 156] have performed and
analyzed channel measurements above 140 GHz. A detailed survey covering various indoor and outdoor
scenarios is given in [58]. Yet, the understanding of the key channel characteristics in this band is still very
preliminary since the overall number of directionally-resolved channel measurements is still very small
and it needs to be explored further before an eventual development and deployment can be considered.
Environmental objects, by virtue of their presence, absence or change in reflection/transmission char-
acteristics, play an important role for the communication channels since they partially govern the eventual
multipath component (MPC) structure of the channel. This is especially true for higher frequencies such
as the THz band because they are more directional and a large percentage of their energy can be blocked
more easily than their lower frequency counterparts. The placement of such objects can be deliberate, e.g.,
to enhance coverage in a particular area. Passive reflectors placed at the intersection of corridors to extend
coverage into non-line-of-sight (NLoS) corridors was suggested more than 40 years ago [66] and explored
since, e.g., [150].
∗
The placement of objects can also be co-incidental, such as the placement of furniture
[55, 29, 161].
These and other studies such as [139, 161, 32] have looked at the impact the presence or absence of
common objects in the environment have on channel characteristics, however, they have - to the best of our
knowledge - all been limited to lower frequency bands so far. Furthermore, they investigated the impact of
adding new objects to the environment, but not the change of the reflection/transmission characteristics
of existing objects that occur when they are covered with a different material.
∗
This topic is related to the recently popular subject of intelligent reflective surfaces , see [wu2021intelligent], but different
in that those reflectors do not have any adaptivity.
63
On the other hand, several studies have looked at the material properties of various common objects
in various sub-bands of the larger THz band. Reflection coefficients for some common indoor building
materials were analyzed in [113]. Indoor materials such as wood, plastic, paper, brick, glass, and leather
were analyzed in [137] for material characteristics. Penetration loss and attenuation as a result of several
common constructional materials were discussed in [34]. The radar cross-section of the human body was
measured in [9]. The above-discussed studies have measured isolated samples of these materials but have
not looked at their impact in the larger context of multi-path channel characteristics. To bridge this gap
under the considerations stated above, the aim of the current study is to explore the impact of various
common environmental objects on THz channels, specifically in the 145-146 GHz band.
†
For the current chapter, we choose scenarios and objects that represent common indoor and outdoor
communication applications for the THz band. We first revisit a set of outdoor measurements (previously
described in our conference paper [5]) and discuss the results and the scenario in more detail. We then
describe several indoor measurements where we assess the impact of energy-saving (low-e) glass vs com-
mon glass, open windows vs blinds, and the impact of using high-tint glass inside buildings. Besides the
analysis of angular power spectra (APS) and power delay profiles (PDP), various condensed channel pa-
rameters such as path loss, delay spread, MPC power distribution, and angular spread are also investigated
to see how they are affected in the various scenarios discussed above.
The remainder of this chapter is organized as follows. In Section II, we describe the channel-sounding
setup and the measurement scenarios. Key parameters of interest and their processing is described in
Section III. The results of the measurements and modeling are presented in Section IV. We finally conclude
the manuscript in Section V.
†
Some authors prefer to use the term "THz" to identify with 300 GHz and beyond while using "sub-THz" or ‘low-THz’ for
frequencies between 100-300 GHz whereas other authors use the term "THz" for both these cases. For the current work, we will
use the term "THz" since it is more widely used in the literature for the band of interest.
64
IF IF
Frequency Extender
Tx
Tx Antenna
Frequency Extender
Rx
Frequency Synthesizer
(within VNA)
Rx Antenna
Vector Network Analyzer
THz Channel
RFoF Tx
(OZ1840)
Fiber Amp1
USB over
Fiber
Extension
USB USB
Positioner Positioner
LO LO
Amp2
RFoF Rx
(OZ1840)
Figure 4.1: Channel sounding setup.
4.2 Measurementequipmentandsite
4.2.1 Testbeddescription
We used a frequency-domain channel sounder shown in Fig. 5.1 to perform the current measurement
campaign. The setup is based on Vector Network Analyzer (VNA) which uses frequency extenders to
reach frequencies in the THz range. An RF-over-fiber (RFoF) (introduced in [7]) system allows the system
to operate over longer measurement distances (up to 100 m) in comparison to typical systems (less than
10 m). For further details of the setup, please see [6, 10]. While the complete configuration of the sounder
varies over the various experiments due to the requirements of each particular measurement, some of the
common parameters are summarized in Table 4.1. Please note that while our setup allows measurements in
the full 140-220 GHz band, we have limited the bandwidth for the current measurements to 1 GHz because
of the extensive time requirements for the experiments. For a frequency domain setup, such as the one
used for the current measurements, measurement time for an impulse response increases linearly with
an increase in the measurement bandwidth. For logistical reasons, extending the measurement time per
location significantly beyond 1 GHz was not feasible for us.
All experiments were done for quasi-static scenarios since the low measurement speeds coupled with
the overheads due to mechanical rotation do not allow the measurements of channel dynamics. Addition-
ally, we perform an over-the-air calibration (OTA) for every measurement which consists of a (delay-gated)
65
Table 4.1: Common setup parameters
Parameter Symbol Value
Start frequency f
start
145 GHz
Stop frequency f
stop
146 GHz
Bandwidth BW 1 GHz
IF bandwidth IF
BW
1 KHz
THz IF f
THzIF
279 MHz
Antenna 3 dB beamwidth ϕ 3dB
13
◦ line of sight (LoS) measurement at a known distance to eliminate the system’s behavior and normalize the
antenna gain.
4.2.2 Experimentsandscenariodescription
Overall, in the current study, we perform experiments in four different locations where on each one of them
some environmental objects are modified or added to analyze their impact on the channel. Specifically, we
measure the impact of (i) increasing the reflection coefficient of columns in a courtyard by metallic foil,
(ii) placing pieces of tinted glass (similar to picture frames) in a corridor), (iii) analyzing various types of
glass windows in the entrance door of a conference room, and (iv) (un)covering windows in a conference
room with blinds. These scenarios will be now described in detail.
The first measurement scenario is located at the entrance of the Vivian Hall of Engineering (VHE)
building in the USC University Park Campus, Los Angeles, CA, USA. It is an open area with equally-
spaced pillars. The front area faces buildings with low height and the back side faces an open area with
trees, chairs, and a water fountain (see Fig. 4.2).
In this scenario, the transmitter (Tx) and the receiver (Rx) are in a non-line of sight (NLoS) scenario,
blocked by 2 pillars, with a distance of 15.94 m between them. Both horn antennas face entrance A. The
modification applied in this scenario was to increase the reflectivity of the pillars by wrapping them with
an aluminum foil centered at 1.65 m height (as explained in [5]). The specific configuration for this scenario
is shown in Table 4.2. The antennas were set to 1.65 m height where the Rx performs a full azimuth scan
66
Figure 4.2: VHE outdoor measurement scenario.
Table 4.2: Additional setup parameters for VHE outdoor scenario.
Parameter Symbol Value
Measurement points N 1601
Tx - Rx distance d
NLoS
Tx− Rx
15.9 m
Tx rotation range Tx
AZ
[-45
◦ ,45
◦ ]
Tx rotation resolution ∆ Tx
AZ
5
◦ Rx rotation range Rx
AZ
[0
◦ ,360
◦ ]
Rx rotation resolution ∆ Rx
AZ
6
◦ with an angular resolution of6
◦ . On the other hand, the Tx illuminates a sector, from− 45
◦ to45
◦ with
an angular resolution of5
◦ . The number of frequency points per sweep is 1601 which allows a maximum
measurable distance of 480 m in delay. The orientation of the positioners for this measurement is looking
towards the west as the origin direction (ϕ Tx
=ϕ Rx
=0) as shown in Fig. 4.2.
The next scenario is on the 5th floor of Hughes Aircraft Electrical Engineering Center (EEB) at 3740
McClintock Ave, Los Angeles, CA 90089, which is a 5-story (plus a basement) building. The floor is an
office environment with several offices having wooden doors (and glass windows on a few of them). The
walls of the building are made of drywall alongside metallic elevators while the floor has tile flooring and
the roof has a false ceiling (with acoustical tiles) at a height of 2.45 m. The floor has two long corridors that
are around 36 m long and 1.5 m wide. In the first one (bottom hallway in Fig. 4.3), henceforth identified as
67
Figure 4.3: EEB5
th
floor scenario. EEB 539 can also be seen in the figure.
Table 4.3: Additional setup parameters for EEB5
th
floor scenario.
Parameter Symbol Value
Measurement points N 1001
Tx - Rx distance, LoS d
LoS
Tx− Rx
20.12 m
Tx rotation range Tx
AZ
[0
◦ ,360
◦ ]
Tx rotation resolution ∆ Tx
AZ
10
◦ Rx rotation range Rx
AZ
[0
◦ ,360
◦ ]
Rx rotation resolution ∆ Rx
AZ
10
◦ EEB5
th
floor (since no other corridor measurements were done in the campaign), there are offices located
on both sides. The second corridor is similar to the first one except for the fact that there are notice boards
and paintings with glass lamination on the walls alongside two elevators (see Fig. 4.3).
To see the effect of more reflective high-tint glass in the environment, we modify the scenario by
placing high-tint glasses on the walls in the corridor. We place 4 pieces of glass, 2 at the doors located on
the edges of the corridors and 2 additional ones on both side walls. The antenna height is set to 1.7 m.
Both antennas perform a full azimuth scan with an angular resolution of10
◦ and the number of frequency
points per sweep is selected to be 1001 allowing a maximum measurable distance of 300 m which is more
than sufficient for the scenario (see Table 4.3).
68
Figure 4.4: EEB 539 measurement scenario.
Table 4.4: Additional setup parameters for EEB 539 scenario.
Parameter Symbol Value
Measurement points N 301
Tx - Rx distance, LoS d
LoS
Tx− Rx
3.36 m
Tx - Rx distance, NLoS d
NLoS
Tx− Rx
3.89 m
Tx rotation range Tx
AZ
[-60
◦ ,60
◦ ]
Tx rotation resolution ∆ Tx
AZ
10
◦ Rx rotation range Rx
AZ
[0
◦ ,360
◦ ]
Rx rotation resolution ∆ Rx
AZ
10
◦ The third scenario is an office of 7.22 m by 3.78 m located at EEB 5
th
floor, henceforth specifically
named EEB 539. The room has a large table, a cabinet, and 2 whiteboards. The Tx horn was placed outside
the room, 45 cm from the door, the LoS scenario Rx is placed at 3.37 m from the Tx, meanwhile, the NLoS
scenario Rx is placed inside the room at 3.89 m such that the line-of-sight is blocked by a wall, a whiteboard,
and the frame (see Fig. 4.4). A platform is placed at the door which allows us to emulate a glass opening
in the door and thus allows us to see the effect of using different types of glasses in the door. For this set
of measurements, the number of frequency points per sweep is 301 which allows a maximum measurable
distance of 90 m which is more than sufficient for the scenario. Like the previous case, the Rx performs a
full scan with a10
◦ angular resolution, however, the Tx performs an angular scan from− 60
◦ to60
◦ with
the same angular resolution since this is the major portion that covers the glass opening in the door (see
Table 4.4).
69
Table 4.5: Additional setup parameters for EEB 110 scenario.
Parameter Symbol Value
Measurement points N 1001
Tx - Rx distance, LoS d
LoS
Tx− Rx
3.98 m
Tx - Rx distance, NLoS d
NLoS
Tx− Rx
4.05 m
Tx rotation range Tx
AZ
[0
◦ ,360
◦ ]
Tx rotation resolution ∆ Tx
AZ
10
◦ Rx rotation range Rx
AZ
[0
◦ ,360
◦ ]
Rx rotation resolution ∆ Rx
AZ
10
◦ The last scenario is another office located at the EEB building, however, it is on the 1
st
floor (EEB
110) in this instance and has dimensions of 7.19 m x 3.94 m. The room has a whiteboard, a large table, a
bookshelf, and a large window with blinds facing the street (see Fig. 4.5). For this case, we wanted to see
the effect of the presence of blinds in the room. We, therefore, perform measurements with and without
the blinds pulled down on the windows. The Tx is placed outside the room, the LoS Rx is placed nearly in
the middle of the room at 3.98 m from the Tx facing the window, and the NLoS Rx is placed at the opposite
side of the room facing in the same direction as the LoS Rx, looking towards a whiteboard (in front of
the large window that Tx faces). For both Tx and Rx, we performed a full azimuth scan with an angular
resolution of10
◦ and 1001 frequency points to have a maximum measurable distance of 300m (see Table
4.5).
4.3 Parametersandprocessing
The sounder described in the previous section produces a collection of frequency scans for each Tx-Rx loca-
tion. Each one can be represented as a three-dimensional tensor (as described in [2])H
meas
(f,ϕ Tx
,ϕ Rx
;d)
wheref is the frequency point within the 1GHz bandwidth (145-146 GHz),ϕ Tx
,ϕ Rx
are the azimuth ori-
entations for Tx and Rx respectively, and d is the Euclidean distance between Tx and Rx. The matrix
H
meas
has dimensions(N,N
Tx
,N
Rx
) whereN is the number of frequency points,N
Tx
andN
Rx
are the
70
Figure 4.5: EEB 110 measurement scenario.
number of azimuth scans at the Tx and Rx respectively. The first step of the analysis is to calibrate the mea-
surements (eliminate the effects of the system and antennas) by dividing the measured channel transfer
function by the OTA calibrationH
OTA
(f): H(f,ϕ Tx
,ϕ Rx
;d) = H
meas
(f,ϕ Tx
,ϕ Rx
;d)/H
OTA
(f). This
calibrated channel frequency response is the input to the estimation of the different parameters described
in the following.
The directional power delay profile is:
P
calc
(τ,ϕ Tx
,ϕ Rx
;d)=|F
− 1
f
{H(f,ϕ Tx
,ϕ Rx
;d)}|
2
(4.1)
71
whereF
− 1
f
is the inverse fast Fourier transform (IFFT) with respect tof, andτ is the delay, with samples
spaced 1 ns apart. Delay gating and noise thresholding are implemented to minimize the impact of the
noise (similar to [48]):
P(τ )=







P
calc
(τ ) if(τ ≤ τ gate
)∧(P
calc
(τ )≥ P
λ )
0 otherwise
(4.2)
τ gate
is the delay gating threshold set to avoid using points with "wrap-around" effect of the IFFT. P
λ is
the noise threshold, selected to avoid counting delay bins with noise which could distort the estimation
of parameters such as delay spread and angular spread. P
λ is selected to be 6 dB above the noise floor
(average noise power) of the PDP andτ gate
is selected depending on the number of frequency pointsN.
Using the entire set of directional PDPs, we select the "strongest beam" as the beam pair Tx-Rx with
the highest power (integrated over delay). The PDP in this beam called the Max-Dir PDP, is:
P
max
(τ ;d)=P(τ,ϕ ˆ
i
,ϕ ˆ
j
;d);(
ˆ
i,
ˆ
j)=max
i,j
X
τ P(τ,ϕ i
,ϕ j
,;d). (4.3)
Another kind of PDP to be computed is the "omnidirectional" PDP. It is constructed by selecting the
strongest azimuth direction per delay bin to reconstruct the PDP similar to [64]
P
omni
(τ ;d)= max
ϕ Tx
,ϕ
Rx
P(τ,ϕ Tx
,ϕ Rx
;d). (4.4)
Using the Max-Dir and Omni-directional PDPs, we estimate parameters such as Path Loss, delay and
angular spread, and power distribution over the MPCs.
72
4.3.1 Pathloss
Path Loss is computed as the sum of powers in all delay bins in the PDP (see [99]).
PL
i
(d)=

X
τ P
i
(τ,d )
!
− 1
, (4.5)
wherei can denote omnidirectional (omni) or strongest beam (Max-Dir).
4.3.1.1 Delayspread
The (RMS) delay spread is the second central moment of the PDP [99]:
σ τ =
s
P
τ P
i
(τ )τ 2
P
τ P
i
(τ )
− P
τ P
i
(τ )τ P
τ P
i
(τ )

2
, (4.6)
wherei can be "omni" or "Max-Dir".
‡
4.3.2 PowerdistributionoverMPC
To determine the concentration of power in the strongest MPC versus the rest present in the channel we
define a parameter κ 1
:
κ 1
=
P
i
(˜ τ 1
)
P
˜ τ N
˜ τ =˜ τ 2
P
i
(˜ τ )
, (4.7)
wherei can be "omni" or "Max-Dir", and ˜ τ k
is the location of thek-th local maximum of the PDPP
i
(˜ τ ),
ordered by magnitude so that ˜ τ 1
signifies the location of the largest local maximum. This definition is
different from the "Rice Factor" because in the Fourier analysis, it is not possible to differentiate between
closely spaced MPCs, so the local maximum of the PDP is not strictly identical to an MPC, as explained in
[7].
‡
Note that long-delayed samples with small power can disproportionately impact the delay spread; for this reason, noise
thresholding is especially important in assessing delay spread.
73
4.3.3 Angularspread
The double-directional angular power spectrum (DDAPS) describes the power distribution over different
Tx-Rx angular orientations (since our measurement setup scans only the horizontal plane, a distinction
between angular and azimuthal power spectrum is moot). The DDAPS is computed as
DDAPS(ϕ Tx
,ϕ Rx
,d)=
X
τ P(τ,ϕ Tx
,ϕ Rx
,d). (4.8)
The resolution of this function is proportional to the spacing between angular captures performed during
the measurement. Since the DDAPS is computed from the PDP, it benefits from the noise thresholding
and delay gating procedures applied there. This is important to suppress noise power accumulation in the
directions in which no significant MPCs occur.
To obtain the (single-directional) angular power spectrum (APS) at the Tx we integrate the DDAPS
function overϕ Rx
, and similarly for the APS at the Rx. Using these quantities, we proceed to compute the
angular spread by applying Fleury’s definition [42]
σ ◦ =
v
u
u
t
P
ϕ |e
jϕ − µ ϕ |
2
APS
k
(ϕ )
P
ϕ APS
k
(ϕ )
, (4.9)
wherek can be Tx or Rx indicate departure or arrival APS andµ ϕ can be computed as
µ ϕ =
P
ϕ e
jϕ APS
k
(ϕ )
P
ϕ APS
k
(ϕ )
. (4.10)
The finite horn antenna beamwidth leads to an over-estimation of the channel’s angular spread, as ex-
plained in [8]
74
4.4 Measurementresults
In this section, we describe our results, emphasizing the changes observed when the modifications in the
scenario were applied.
4.4.1 VHEoutdoormeasurementscenario
Since the scenario is NLoS, we can expect to have multiple MPCs, which are coming from directions dif-
ferent from the LoS. In this case, the strongest MPC comes from the direction (ϕ Tx
=− 20,ϕ Rx
=− 18),
where the Tx and Rx are looking towards a glass door on the opposite side of the entrance of VHE (see Fig.
4.2). Analyzing the corresponding Max-Dir PDP in Fig. 4.6 (a) we observe that the strongest component
has a detour of 46.5 m (consistent with the reflection coming from the entrance A), and thus shows a delay
much larger than the LoS component at 15.9 m. The distance and direction were verified using Google
Earth software. Additionally, we observe more MPCs with detours between 20 m to 40 m corresponding to
reflections at the pillars in the area. However, the reflected power is low due to the small cross-section of
the area where the beam can hit the object. Additional MPCs can be observed atϕ Tx
=− 30,ϕ Rx
=− 12
(1 in Fig. 6), ϕ Tx
=− 30,ϕ Rx
=− 54 (2 in Fig. 6), andϕ Tx
= 30,ϕ Rx
=− 66 (3 in Fig. 6). For the first
two cases, the Tx and Rx horns look towards the pillars located in the middle area. The third MPCs occur
when the Tx looks to the last row of pillars and the Rx similarly to the previous cases looks towards the
pillars. Additional components in this scenario show larger detours, larger than 100 m in some cases, as
observed in Fig. 4.6 (b) (blue line).
The impact of the foil can be seen more clearly in the APSs shown in Fig. 4.6 (c) and (d) where the
MPCs 1, 2, and 3 increase their power by 6 dB on average. In Fig. 4.6 (c), we observe these MPCs in the
delay domain with the omnidirectional PDP. The delay for these 3 cases is at 33.6, 27, and 20.4 respectively.
All of them have detours of less than 46 m because they come from reflections of the pillars located closer
75
Figure 4.6: PDP and APS comparisons for the scenario.
to the antennas. As expected, adding the foil in the pillars increased the reflected power coming from them.
The comparison between the condensed channel parameters for the foil and no foil cases is shown
in Table 4.6. Adding foil decreases the path loss, increases delay spread, reducesκ 1
and increases in the
angular spread at both Tx and Rx due to the increase in power of the MPCs. For pathloss andκ 1
, the impact
is smaller for the Max-Dir case than for the omni-case, because most of the column-reflected components
do not fall into the Max-Dir beam. However, for the RMS delay spread, the impact is larger in the Max-Dir
case: while there is only two (relatively weak) column-reflected component in the Max-Dir beam, they are
76
20 25 30 35 40 45 50
[m]
-135
-130
-125
-120
-115
|h( )|
2
[dB]
No Foil Foil
DR = 15dB
S=-132 dB
3
2
1
4
Figure 4.7: Omnidirectional PDP observed by a system withS =− 132 dB
the second- and third-most significant MPCs in this setting, thus driving the RMS delay spread from an
extremely small value to a (still small, but) significantly higher value.
If the channel is analyzed from a systems design point of view, the impact of the foil is more noticeable.
Wireless communication systems do not have a large/infinite dynamic range. For instance, if we set a
dynamic range of 15 dB in the system, we observe the large impact of the foil on the MPC components,
as shown in Fig. 4.7. The impact on system design becomes immediately clear: instead of a single MPC
carrying all the power, now at least two MPCs are present - this can be a drawback because an equalizer
is required, but also an advantage because it provides diversity. The existence of additional MPCs in other
directions also enables beam diversity, so that the system can switch directions when the strongest MPC
is blocked. Assuming that the system sensitivity limit (S) is at− 132 dB path gain, then the no-foil case
has no beam diversity, while the foil case does provide three alternative beams (1,2 and 4; 3 is excluded
because its associated power is lower than S).
4.4.2 EEB 5
th
floor
The EEB5
th
floor scenario is an indoor corridor, therefore, we can expect a waveguiding effect with the
signals concentrated along the axis of the corridor. A large concentration of power is observed in the LoS
direction and close toϕ = 180
◦ because of the reflections coming from the door at the other end of the
77
0 20 40 60 80 100
[m]
-130
-125
-120
-115
-110
-105
-100
|h( )|
2
[dB]
No Glass Glass
45 50 55
-130
-120
-110
-100
No Glass Glass
Figure 4.8: PDP comparison for LoS measurement of EEB5
th
floor.
corridor. When we add the glass to the experiment, the reflected components are increased since the glass
is placed behind the antennas and on both sides of the wall.
Fig. 4.8 shows components with 22.2 m and 24 m detours with a small increment due to the reflected
power on the glasses along the corridor. The largest impact is observed with the MPC at 50.7 m, showing
an increase of 4 dB due to the glass placed at the end of the corridor, in the direction towards the back of
the Rx. Subsequent MPCs also show an increment compared to their counterparts without glass.
These impacts are also observed when analyzing the estimated parameters. There is a decrease in the
PL and angular spread due to the reduction of MPCs by the glass. On the other hand,σ τ andκ 1
showed
an increment, due to the same reduction of MPCs. The full description of the estimated parameters for the
LoS and NLoS measurement in this scenario is shown in Table 4.6.
4.4.3 EEB539
In this scenario, a glass rectangle was placed at the entrance of the room, therefore, the beam has to go
through the glass to enter the room. The anticipated effect of this experiment is to observe a significant
reduction in power of the MPCs since the glass will reflect most of the power away from the room. Fig 4.9
shows the omnidirectional PDP where we observed the power reduction of MPCs by approximately 8 dB
78
0 5 10 15 20
[m]
-130
-120
-110
-100
-90
-80
|h( )|
2
[dB]
No Glass Glass
2 4 6
-120
-100
-80
No Glass Glass
1 1
2
2
Figure 4.9: Omnidirectional PDP comparison for LoS case of EEB 539.
Figure 4.10: APS for LoS case of EEB 539.
when the glass is placed. Fig. 4.10 shows APSs for both cases, where we observe a clear reduction in the
power of the LoS MPC.
The estimated parameters in this case show different behavior. Delay spread is only reduced by 1 dBs,
andκ 1
only changes by 2 dB because all the MPCs are attenuated at the same time. However, the biggest
impact is observed in the path loss with 8 dB attenuation due to the penetration loss of the glass.
The NLoS case shows a similar behavior as the LoS. Here we observe a reduction of power in the MPCs
as well. The APS shown in Fig. 4.11 demonstrates the reduction of the main MPC. Similarly, the Max-Dir
79
Figure 4.11: APS for NLoS case of EEB 539.
Figure 4.12: PDP comparison for NLoS measurement of EEB 539.
direction shows the attenuation of the MPCs due to the glass (see Fig. 4.12). In the case of the estimated
parameters, the largest impact is observed in the delay spread, angular spread, andκ 1
. The details about
the estimated parameters for the LoS and NLoS case for this scenario are shown in Table 4.6.
4.4.4 EEB110
For the EEB 110 measurements, we investigate the impact of drawing the blinds. We can anticipate that
the LoS MPC should not be affected by this change but MPCs involving reflections from the windows will
80
Figure 4.13: APS for LoS case of EEB 110.
suffer an impact from the blinds. Since the blinds are metallic, but do not have a flat surface, it is not clear
from inspection whether they will increase or decrease the reflections from the window area.
Indeed, analyzing the APSs in Fig. 4.13 we see no significant impact on the LoS MPC located at ϕ Tx
=
− 40
◦ ,ϕ Rx
= 40
◦ (denoted by 1). There is an MPC at ϕ Tx
= 50
◦ ,ϕ Rx
= 50
◦ (denoted by 3); this MPC
is produced by the reflection of the signal on the channel sounder, which was placed 1m to the left of the
antenna. However, the MPCs atϕ Tx
=− 20
◦ ,ϕ Rx
= 150
◦ (denoted by 2) andϕ Tx
=− 10
◦ ,ϕ Rx
= 10
◦ (denoted by 4) show a change in the received power, in this case, attenuation, when the blinds were drawn.
The attenuation most likely is a result of how the curved surface of the blinds affects the reflection of the
ray coming from the Tx antenna, and so attenuating it when reaching the Rx.
Analyzing this effect from the delay domain, we observe in Fig. 4.14 the attenuation of delay bins
between 5-15 m coming from reflections at the window and whiteboard. Looking at the estimated pa-
rameters, we observe small variations in delay spread, path loss, and κ 1
because the impact is only in
low-power MPCs instead of the LoS. The Rx angular spread is reduced due to the attenuation in the power
of the MPCs reflected from the window behind the antenna. However, when considering a system with a
81
Figure 4.14: PDP comparison for LoS case of EEB 110.
limited (20 dB) dynamic range, we find that the presence of the blinds eliminates the two available beam
diversity directions, making the system more sensitive to LoS blockage.
For the NLoS case, the impact of the blinds is larger, because the MPCs are mainly produced by re-
flections from the window behind the antenna. Fig. 4.15 shows the APS when the blinds are drawn and
when they are not. As can be observed, the main MPCs showed an increment in power. For instance, the
MPC located atϕ Tx
=− 20
◦ ,ϕ Rx
=20
◦ (denoted by 2) is a double reflection from the Tx to the Rx hitting
the window behind and the whiteboard in front of the antenna; when the blinds are used we observed an
increase of power. This effect is related to the scattering produced by the curved blinds, which change the
reflection coming from the window which is reflected by the whiteboard in front of the antenna. Another
MPC located atϕ Tx
=− 30
◦ ,ϕ Rx
= 150
◦ (denoted by 1), where the Rx looks towards the back window,
has the opposite effect with a reduction of 11dB approximately.
When analyzing the delay domain, the strongest delay bins changed completely when using the blinds.
In Fig. 4.14 (b) the strongest delay bin changed from 8.4 m to 9.9 m indicating an additional delay provided
by the blinds. Fig. 4.16 (a) also presents additional delay bins that were changed by the blinds. In summary,
the blinds altered MPCs differently, increasing power in some cases and doing the opposite in other because
82
Figure 4.15: APS for NLoS case of EEB 110.
Figure 4.16: PDP comparison for NLoS case of EEB 110.
of the curvature of the blinds, affecting the specular reflection coming from the back window. This clearly
shows that the blinds not only change the strength of the MPCs but also the directions.
Our conjecture for the estimated parameters is to observe significant changes in the estimated param-
eters. The most significant changes are observed in κ 1
due to the variation in the power of the MPCs.
Path loss, delay spread, and angular spread were not significantly affected even though the MPCs showed
a significant change when the blinds were used. Table 4.6 shows a summary of all the parameters for the
83
LoS and NLoS cases for this scenario.
Applying the systems design criteria used in the VHE measurement, we observed that for both LoS and
NLoS cases, the MPCs within a limited dynamic range changed significantly. For the LoS case applying a
20 dB dynamic range, we observe that without the blinds we see 4 MPCs at the Rx but when the blinds are
used, the number of MPCs is reduced to 1. Similarly, in the NLoS case, the impact is also noticeable, when
the blinds were used, the number of MPCs increased and some of them increased their power, impacting
the estimated characteristics.
4.5 Conclusions
In this chapter, we covered a number of interesting scenarios from the perspective of THz communica-
tions and performed measurements to investigate how changes in the environment affect the channel.
We showed that with the addition of passive reflectors in outdoor scenarios, MPC powers (up to 6 dB
on average were observed) and angular diversity increased. Our indoor measurements showed that the
addition of reflecting surfaces such as glass in corridors also increases MPC powers (up to 4 dB in some
cases). Further indoor experiments showed that transmission through high-tint glass caused significant
attenuation(8-10 dB), and the presence or absence of window blinds significantly changed the channel
characteristics. Variations in the scenario may not necessarily offer an impact on the condensed channel
parameters that are commonly used for concise channel description. However, from a systems point of
view, the channel changes induced by the scenario variations might have a significant impact, particularly
in the presence of a limited dynamic range. It is important to emphasize that our work does not imply that
all systems will show a drastic variation when variations in the scenario happen. Rather, we show that it
can occur in at least some scenarios and that a robust system design has to work also in those. Thus, our
84
Table 4.6: Estimated parameters for all measurement points
σ τ PL κ 1
σ ◦ Omni Max-Dir Omni Max-Dir Omni Max-Dir Tx Rx
VHE
Nofoil -74.98 -83.12 114.81 115.51 9.21 16.15 0.22 0.35
Foil -74.12 -81.62 113.54 115.26 4.57 15.13 0.26 0.4
EEB5F
LoS,Noglass -74.51 -86.4 96.35 99.39 3.78 13.24 0.9 0.99
LoS,Glass -73.47 -86.82 95.99 100.11 1.55 10.84 0.94 1
EEB539
LoS,Noglass -86.22 -87.68 86.57 86.74 12.27 16.15 0.18 0.53
LoS,Glass -87.41 -89.56 94.92 95.24 12.84 19.54 0.17 0.56
NLoS,Noglass -78.79 -79.86 103.63 106.67 -2.07 4 0.23 0.88
NLoS,Glass -79.85 -96.46 104.58 114.59 -7.4 5.79 0.44 0.83
EEB110
LoS,Noblinds -82.87 -87.49 87.22 88.27 7.67 20.66 0.57 0.48
LoS,Blinds -84.06 -88.55 86.72 87.22 13.35 21.23 0.57 0.31
NLoS,Noblinds -79.12 -86.52 93.26 97.5 -3.16 10.14 0.48 0.93
NLoS,Blinds -79.23 -84.22 92.81 96.13 -0.96 14.53 0.47 0.91
focus has been on showing sample scenarios in which this effect is noticeable and analyzing its impact on
channel characteristics and a possible system that can be used in these scenarios.
85
Chapter5
DirectionallyResolvedMeasurementandModelingofTHzBand
PropagationChannels
5.1 Introduction
Over the past decades, a general trend has been for wireless communications to move to higher and higher
frequency bands. This trend is motivated by three factors: (i) the available absolute bandwidth, which de-
termines the feasible data rates, increases with the carrier frequency; (ii) there is much fallow spectrum in
higher frequency bands - either it is not assigned at all, or not effectively utilized; (iii) progress in semi-
conductor technology has made it possible to create transceivers for frequency bands that were previously
not accessible with low-cost (CMOS) technology. Thus, cellular communications expanded from 450 MHz
(used in 1G) to 900 MHz, 2 GHz, and 3.5 GHz, and - in a major step in 5G - to the 24-90 GHz band. The
next generation, 6G, will be marked by the use of even higher frequencies, namely the THz spectrum, in
particular, 0.1-0.5 THz [151, 162, 121].
∗
The three trends we mentioned above as generally driving the use of higher-frequency bands are also at
work specifically for the THz band: (i) new applications, such as holographic communications or extended
reality, may require up to 1 Tbit/s data rate, thus greatly exceeding what can be realized in currently used
∗
This spectrum is sometimes called sub-THz, and the 100-300 GHz band may be called high-mmWave; however for brevity
and in line with most papers in this area, we will call it THz spectrum.
86
bands [147, 28]. (ii) actions by frequency regulators in various countries (e.g., MIC in Japan, FCC in the USA,
OFCOM in the UK, and CEPT in Europe) are making large swaths of spectrum in the THz band available for
communications applications [97], and (iii) improvements in circuit design and semiconductor technology
enable manufacturing of critical RF components, such as phased arrays [91, 142]. Power amplifiers [53,
73] with low-cost technology. Consequently, THz communications have greatly interested the community
over the past 10 years [40, 83, 13] and are anticipated to be a major part of 6G systems.
It is axiomatic that the design and evaluation of new wireless systems requires an understanding of,
and models for, the wireless propagation channels those systems operate in. The channel determines the
fundamental performance limits both for single-user systems (e.g., Shannon capacity [134]) and multi-
user systems (multi-access and broadcast capacity) [46]. Furthermore, channel characteristics determine
which transceiver structures, modulation methods, and signal processing techniques can be used advan-
tageously [99]. An understanding of channel characteristics and suitable channel models must be based
on (or verified by) measurements. Since the underlying multipath propagation of the propagation pro-
cesses is frequency dependent, using a new frequency band, such as the THz band, requires new channel
measurements and derived models.
In this spirit, the WiDeS (Wireless Devices and Systems) group at the University of Southern California
(USC), in collaboration with Samsung Research USA and the Optical Communications group at USC has
performed, over the past three years, several extensive measurement campaigns in three types of environ-
ments and configurations: indoor, outdoor microcell, and outdoor device-to-device (D2D). While detailed
description and key results were published in a series of research papers [10, 3, 49, 50, 4], the current
chapter aims to systematically summarize the results, provide comparisons between channels in different
environments, and quantify several channel parameters beyond those provided in the original papers.
87
5.1.1 THzapplications
The extremely high data rates enabled by THz communications enable various applications. One critical
use case is ultra-high-speed wireless local area networks (WLANs) and personal area networks (PANs),
generally in indoor, primarily residential or office environments. These networks can be used for holo-
graphic communications [28], wireless connections of extended-reality headsets to their associated pow-
erful computation engines [37], information kiosks that allow ultra-fast downloading of large amounts of
content [145], and similar applications for office use and entertainment. While current WLAN systems
are limited to about 10 Gbit/s (both in the 6 GHz bands and the 60 GHz band), THz applications envision
faster speeds between one and two orders of magnitude. The typical placement of an access point is near
the ceiling,2− 3 m above the floor.
High-rate communications are also desirable in outdoor scenarios. In a cafe, city square, or sports sta-
dium, applications like extended reality, watching high-resolution replays or holographic re-enactments,
and real-time gaming will create demand for THz communications systems [20]. In addition to the high
data rate, these systems will have a higher user density, necessitating multi-user MIMO and making infor-
mation about angular dispersion particularly relevant [98]. The typical height of base stations (BSs) ranges
from2− 4 m (typical WLAN access point height) to10− 20 m (a typical microcellular BS height [1]).
Gaming, social networking, and real-time sensing and control for autonomous driving and similar
applications also motivate the use of D2D communications, where two user devices communicate directly
with each other [163]. This reduces the strain on the infrastructure nodes and latency - an aspect of
particular importance in the above-mentioned applications [22]. In D2D settings, the transmitter and
receiver (Tx and Rx) are at the same height, typically between1 and1.8 m above the ground. In particular,
for outdoor environments, the difference in the height of such a device compared to a BS is quite significant
and leads to fundamentally different propagation channel characteristics.
88
For both outdoor and indoor applications, research and standardization activities have begun. In partic-
ular, the IEEE 802.15.3d standard has been recently established for indoor applications. It specifies switched
point-to-point links using single-carrier modulation (up to 64 QAM) or on-off keying. It operates in the
250-320 GHz band, which can be used entirely or divided into sub-bands [111]. Theoretically, more than
300 Gbit/s can be achieved. However, future work will be needed to realize actual practical systems. Sev-
eral large-scale research projects have started all over the world to bring THz systems to reality, both in
industry and in academia.
Besides the above-discussed applications, THz communications is also envisioned for several other
applications, such as backhaul links for cellular applications, connections between servers in data centers,
and other high-speed point-to-point links [125, 25, 148]. THz links are also helpful for wireless connec-
tions between computer boards and even between chips on the same board [43, 44, 160]. Finally, on-body
networks, in-body networks, and related medical applications are anticipated. Those topics are beyond
the scope of the current chapter, and we refer to the survey papers [40, 83, 13, 121] for a description.
5.1.2 Literaturereview
There have been several directional or double-directional (i.e., directionally resolved at one or both link
ends, respectively) channel measurements in indoor environments. The earliest we are aware of are from
TU Braunschweig, which measured in a variety of indoor environments [117, 118].The measurements were
done with a vector network analyzer (VNA) in a static environment. Emphasis was on the frequency range
around 300 GHz, in line with the band for IEEE 802.15.3d devices. Further measurements were done by
various research groups, e.g.,[156, 105, 104, 35, 114, 132, 81, 76, 23, 75].
For outdoor measurements, the number of available double-directional measurements is much smaller.
Our measurements in [6, 7] were the first long-distance double-directional measurements. Recently, NYU
[155, 154, 74] presented a measurement campaign, and a channel model derived from it; measurements are
89
done in the 140 GHz range, and the BS height is4 m, i.e., a typical access point height (while our outdoor
measurements are with a BS height of 1.6 m for the D2D scenario, and 11 m for the microcell scenario).
The measurements of [152] is for a street canyon at 300 GHz.
A variety of channel models has been developed based on measurements, as well as deterministic
simulations ranging from a finite-difference time-domain to point-cloud-based ray tracing to simple ray
launching. For a comprehensive survey, the reader is referred to [58].
5.1.3 Structureofchapter
The remainder of the chapter is organized as follows: Section II reviews the fundamental propagation
processes and their frequency dependence. This is followed by a description of our measurement setup
in Section III. Next, Section IV discusses the condensed channel parameters we analyzed and their impact
on system design. The measurement environments are described in Sec. V. In Sec, several sample impulse
responses, angular spectra, and their physical interpretation. The statistics of the channel parameters in
the investigated environments in Section VII follow VI. Section VIII then analyzes system performance in
the measured channels, including the impact of various beamforming strategies. Conclusions and outlook
to future work wrap up the chapter.
5.2 THzpropagationeffects
In a wireless channel, signals can propagate via different routes from the Tx to the Rx, interacting with
objects in the environment along the way. The different signal echoes or multipath components (MPCs)
thus undergo different propagation processes along the way, in particular one or more of the following (i)
free-space path loss, (ii) atmospheric attenuation, (iii) specular reflection/transmission, (iv) diffraction, (v)
diffuse scattering, and (vi) Doppler shift. In the following, we review the frequency dependence of each of
those processes, which will help later to interpret the measurement results.
90
Free-space path loss describes the "thinning out" of the area power density as the distance between Tx
and the observation point increases. In the far field (beyond the Rayleigh distance), the ratio of receive
power to transmit power in free space is [99]
P
Rx,FS
P
Tx
=G
Tx
G
Rx

c
0
4πfd

2
=A
Tx
A
Rx

f
c
0
d

2
, (5.1)
wherec
0
is the speed of light,G
Tx
andG
Rx
are the antenna gains at Tx and Rx respectively,A
Tx
andA
Rx
are the antenna area at Tx and Rx respectively,f is the considered frequency, andd the distance between
Tx and Rx. The term

4πfd
c
0

2
is known as the free-space path loss. The left equality, also known as
Friis’ law, is more commonly used and indicates that when the antenna gain is independent of frequency,
path gain decreases with the square of the carrier frequency. However, the right equality shows that for
constant antenna area, the path gain actually increases with the square of the frequency. This is because
of the constant form factor (i.e., geometric area), an antenna becomeselectrically larger, and thus increases
gain and reduces beamwidth.
For mobile and nomadic access scenarios, the antennas have to be adaptive arrays that can steer the
narrow beam in the correct direction. Thus, array antennas with a fixed area have to increase the number
of antenna elements with the square of the frequency.
Consequently, when considering possible antenna gain, two limitations need to be considered: (i)
limited antenna area due to constraints on the form factor and (ii) limited gain due to constraints on
the number of antenna elements, which arises from cost and energy consumption considerations. In our
campaigns, we measured with (horn) antennas with21 dB gain, which phased arrays could achieve with
approximately 64 antenna elements (assuming an element gain of 3 dB). Link budgets and achievable
distances discussed later assume this value, which might be realistic for early deployments of THz systems.
91
During propagation through the atmosphere, THz radiation can also be absorbed or scattered by oxy-
gen, and water molecules [158, 67]. One of the most challenging atmospheric effects for this band is rain.
In [106, 16], a thorough study in the sub-THz band is shown. This study analyzes its behavior concerning
rainfall rate; it indicates that the attenuation can reach up to 20dB/km for extreme rain cases. These values
are reduced tenfold due to the maximum considered distance (≈ 100)m. For these reasons, in the 140
GHz band, which is the band of interest in this chapter, the attenuation due to atmospheric effects is not
significant over the measured range.
Many materials used in building construction have high reflection coefficients for THz signals, includ-
ing glass, steel concrete, and gypsum boards. However, reflection might occur as either specular or diffuse
reflection, and the relative importance of those contributions depends on the smoothness of the surface.
Note that the definition of roughness is relative to the wavelength; for THz frequencies, even minor rough-
nesses (order of mm) have a significant impact [70, 135]. The diffuse scattering might be radiated into a
continuum of directions; the simplest model is a Lambertian radiator [136], while more involved models
may assume ”beams" centered on the direction of specular reflection, and possibly the direction of inci-
dence [33]. Transmission loss is generally quite high; even drywall can attenuate the signal by more than
20 dB [34].
It is well known that the effectiveness of diffraction processes decreases with frequency, i.e., objects
throw ”sharper shadows" at higher frequencies. Thus, while the uniform theory of diffraction [86] provides
a good mathematical description of the diffraction coefficient [115] for practical purposes, the diffraction
at 140 GHz can be mostly neglected, except for very shallow diffraction angles. For instance, [96, 82, 85]
show diffraction analysis between 73 GHz and 2 THz. In these studies, the attenuation shown can reach
up to 40dB, depending on the angle, and the relative gain obtained by diffraction is ≤ 2dB in small angles,
congruent with our previous statement.
92
IF IF
Frequency Extender
Tx
Tx Antenna
Frequency Extender
Rx
Frequency Synthesizer
(within VNA)
Rx Antenna
Vector Network Analyzer
THz Channel
RFoF Tx
(OZ1840)
Fiber Amp1
USB over
Fiber
Extension
USB USB
Positioner Positioner
LO LO
Amp2
RFoF Rx
(OZ1840)
Figure 5.1: Block diagram of the measurement setup.
Finally, Doppler spread may be a significant factor in THz systems, due to the fact that Doppler shifts
increase linearly with the carrier frequency. Note, however, that beamforming in particular at a moving
device reduces the angular range from which signals are incident and thus reduces the Doppler spread.
Consequently, the Doppler spread might increase sublinearly with frequency if the beamwidth changes
with frequency, e.g., in a constant-area antenna. Our measurements were done with static Tx and Rx so that
no Doppler shifts occur during the measurements. However, since we measured the angular power spectra
at both link ends, a Doppler spectrum can be synthesized from those measurements from the well-known
relationship between angular spectrum and Doppler spectrum [68].
†
5.3 Measurementsetup
Our measurement system is based on a combination of (i) VNA, (ii) frequency-extenders, and (iii) rotat-
ing horn antenna, as well as Radio-over-fiber connections to enable large distances between Tx and Rx
antennas, see Fig. 5.1.
At the core of the sounder is a 4-port VNA, model Keysight PNAX N5247A, which covers a frequency
range of up to 67 GHz. It is combined with VNA extenders WR-5.1VNAX from Virginia Diodes. These
extenders receive an external local oscillator (LO) signal in the range of11.33− 18.33 GHz and multiply
it internally with a multiplication factor of12, and furthermore mix it with an IF signal that is at 279 MHz.
†
Note that this requires that the beamwidth of the analyzed device is significantly larger than the beamwidth of the antenna
in our measurement system.
93
We configure the setup such that both the intermediate frequency (IF) and the LO signals are generated by
the ports of the VNA, and thus derived from the same precision clock, leading to the high phase stability
of the setup.
The transmit power of the frequency extender is -1 dBm where, as discussed in the previous section,
the horn antennas for the Tx and Rx provide a gain of 21 dB. For an IF bandwidth (IFBW) of 10 Hz, the
system’s dynamic range is nearly 120 dB. The Rx frequency extender uses a high-sensitivity waveguide
that enhances this dynamic range by a further 20 dB. The dynamic range of the setup can be adjusted by
the choice of the IFBW, trading off measurement sensitivity with measurement duration. In most of our
measurements,1 kHz was chosen as IFBW. For outdoor measurements, we use frequency steps of1 MHz
spacing for the VNA, leading to a maximum resolvable excess run-length of300 m, which is sufficient for
all the scenarios we investigated - while longer-delayed MPCs might exist, their power is too low to play a
significant role. For indoor, we use a step width of 625 kHz, in order to retain comparability to our existing
indoor measurements at lower frequencies. We measure over a1 GHz bandwidth; while larger bandwidths
might be of interest for THz systems, the time required for a frequency sweep is linearly proportional to the
bandwidth, and larger bandwidths would have increased the total measurement time (see below) beyond
the feasibility limits.
The feasible distance from the VNA to the Tx and Rx antennas in measurements from the literature
is limited by the cable losses at the LO frequency (in our case at nearly 12 GHz), resulting in a maximum
measurement range of around10 m.
‡
To circumvent this problem, we introduced in [6] a radio-over-fiber
(RoF) setup that modulates the LO signal to the optical domain, where it is transported by a low-loss fiber.
We downconverted at the LO port of the remote antenna. While our earliest measurements [6] were done
with an RoF setup that was created from available discrete components, our later measurements [10, 3,
50, 4] used a more robust commercial RoF setup (Optical Zonu OZ1840). Fig. 5.2 compares measurements
‡
We assume here that the frequency extenders are co-located with the antennas so that only the LO signal must be transmitted
to the remote location. Transmission of the actual THz RF signal would be affected by even higher losses
94
141 142 143 144 145 146 147 148
Frequency (GHz)
14
16
18
20
22
24
26
28
30
Pathloss (dB)
Without RFoF for 5m IF
Without RFoF for 105m IF
With RFoF for 5m IF
With RFoF for 105m IF
Figure 5.2: Comparison of measurement with and without the RoF extension in an indoor environment
for a channel length of 2.4 m.
made with the RoF connection to a conventional cable connection.
§
We see that the shapes of the measured
path loss curves agree, and a suitable calibration can account for the attenuation difference related to the
RoF and the IF cable [6].
The directional characteristics were measured by mechanically rotating horn antennas to cover the
desired range in azimuth and elevation. Our horns have a beamwidth (full-width half maximum, FWHM)
of 13°. In azimuth, the antennas were rotated in steps of 10° for all our measurement cases, though the
range over which rotation occurred varied from case to case, see below. By definition, 0° azimuth corre-
sponds to the case where both the Tx and Rx face each other - this is the definition irrespective of whether
the optical LoS is obstructed or not.
¶
To maintain a uniform definition of elevation in all measurement
campaigns regarding the elevation, we define the "co-elevation" as the "initial elevation" orientation (i.e.,
offset) from which the measurement is performed. This offset depends on the specific campaign. For D2D
measurements, both Tx and Rx were always oriented in the horizontal plane (co-elevation
˜
θ =0°), and the
azimuth range for both Tx and Rx is[0°,360°]. For the microcellular measurements, the co-elevation was
defined such that the geometrical connection between Tx and Rx was
˜
θ = 0°, irrespective of whether a
line of sight existed or not. We performed measurements with both Tx and Rx in positions
˜
θ = 0°,± 13°,
§
To enable measurement with the conventional connection, the distance from Tx to Rx was kept to 2.4 m; however, the optical
fiber between VNA and Rx still had a length of 105 m also in this case.
¶
Deviations from this convention for indoor corridor measurements will be discussed separately in Sec. VI.
95
leading to a total of 9 elevation combinations. The azimuth rotation range for the Tx covered a 120°
sector from [− 60°,60°] while the Rx scanned the entire azimuth range ([0°,360°]). For the indoor mea-
surements, co-elevation is defined with respect to the horizontal plane, and we performed elevation scans
for
˜
θ = 0°,− 10°,− 20° on the Tx since the Tx is already almost at ceiling height and looking up does
not provide significant information (more in Sec. V) whereas at the Rx we have three elevations with
˜
θ = 0°,±− 10°. Overall, the indoor measurements also result in 9 elevation combinations, just like the
microcellular measurements. The azimuth scan resolutions for the indoor measurements are similar to the
microcellular measurements.
The reason for choosing 13° resolution in elevation for the microcellular is that the spacing is equal
to the FWHM beamwidth, and thus the addition of the elevation measurements results in an effective
antenna pattern that is uniform over the range they are combined, collecting all the multipath energy
overall (practically relevant) elevation angles.
∥
For microcellular measurements the range is [− 13°,13°]
the effective FWHM beamwidth is 39 degrees, whereas, for the indoor measurements, the range is[0°,20°]
at the Tx and[− 10°,10°] on the Rx resulting in an effective FWHM beamwidth of 33 degrees (with some
overlap in beams) on both sides.
The measurement setup was calibrated at the beginning of each measurement day, to account for
possible changes of the electronic components. Due to the use of the high-sensitivity waveguide, a true
”back-to-back" calibration, where Tx and Rx are connected via cable, is not permissible (would overload
and damage the Rx). Therefore, ”over-the-air" (OTA) calibration was performed, with Tx and Rx antennas
aligned along LoS direction over a short distance. For the indoor and D2D measurements, this distance
was chosen to be between0.5 m and2.5 m (ensuring antenna far field), while for the microcellular mea-
surements, it was larger (between20 and40 m), due to the significant height difference between Tx and
Rx (and the resulting impossibility of placing the Rx in closer proximity to the Tx without disconnecting
∥
The motivation for using10° in indoor measurement spacing stems from retaining comparability to our earlier 5GHz mea-
surements in the same environment. The non-uniformity introduced by this revised spacing into the effective antenna pattern is
less than 0.1 dB.
96
0 200 400 600 800 1000
[sample]
-80
-70
-60
-50
-40
-30
-20
-10
[dB]
Raw
Clean
540 550 560 570
-50
-40
-30
-20
-10
Long delay reflections
System's
response
Figure 5.3: Delay filtering process in sample OTA calibration.
the cables and thus destroying the calibration). Delay filtering was used in either case to eliminate residual
MPCs. We apply the CLEAN algorithm [61] in the inverse Fourier transform of the OTA calibration with a
narrow delay window centered in the delay bin corresponding to the LOS. Applying this strategy, we elim-
inate long delay bins in the calibration that do not constitute the system’s response but rather multipath.
An example of this procedure is shown in Fig. 5.3.
Besides measurements with a VNA-based setup, other arrangements using pn-sequences, chirps, or
multi-carrier signals as sounding signals are possible for THz channel sounding [119]. We chose the VNA
setup both because of its flexibility and the high phase stability that can be used for high-resolution pa-
rameter estimation. The two main drawbacks of the VNA setup are the long measurement time and the
need for a cable/fiber connection between Tx and Rx. The former issue is of limited concern as long as
the measurement duration is dominated by the mechanical rotation time. The latter issue is overcome by
measuring in locations that stay under our control (e.g., campus) for the duration of the measurement, and
a suitable ”over-the-air" calibration, as described above. Note that due to the long measurement time of a
mechanically rotating horn, the environment needs to remain quasi-static over several hours (i.e., absence
of pedestrians and vehicles), and thus has to be under the control of the experimenters.
97
5.4 Parametersandtheirsystemimpact
For each pair of horn orientations (ϕ Tx,i
,θ Tx,j
), (ϕ Rx,k
,θ Rx,l
) the measurement setup provides a trans-
fer function H
meas
(f) at the discrete frequency points f
n
through which the VNA steps. The transfer
function is first corrected by the back-to-back calibration, to get H
(
f) = H
meas
(f)/H
cal
(f). This is then
transformed to the delay domain (with the inverse Fourier transform implemented as an IFFT) to obtain
the impulse response
˜
h(τ ). The instantaneous power delay profile, PDP, is then further delay-gated and
noise-thresholded
P(τ )=[|
˜
h(τ )|
2
(τ ):(τ ≤ τ gate
)∧(|
˜
h(τ )|
2
(τ )≥ P
λ )] (5.2)
or0 if it does not fulfill these conditions. Here τ gate
is the delay gating value selected to avoid using long
delay points and points with a "wrap-around" effect of the IFFT, and P
λ is the noise threshold, which is
chosen as 9.5 dB above the average noise level. The margin value was selected by analyzing the noise distri-
bution in the PDP. Assuming the noise iszeromeancircularlysymmetricallycomplexGaussian distributed
(N = N
I
+jN
Q
,N ∼ CN(0,σ 2
I)), where I is an identity matrix; the amplitude of the noise follows
a Rayleigh (|N| =
q
N
2
I
+N
2
Q
,|N| ∼ Rayl(σ )). Thus, the power follows an exponential distribution
(P =|N|
2
,P ∼ Exp(Ω) ) [99, 109].
Pr(P ≥ M
¯Ω)=
Z
∞
M
¯Ω e
− P
¯Ω ¯Ω dP =e
− M
(5.3)
where
¯Ω = E(P) = P
N
is the average noise power
∗∗
andM = 10
M[dB]/10
. This margin value ensures
that the probability of accepting a delay bin with noise is roughly10
− 4
, i.e., approximately one delay/angle
bin within each snapshot. For the analysis of the delay parameters,H(f) is multiplied with a Hann win-
dow before the Fourier transformation since the sidelobes of thesinc function arising from the IFFT would
∗∗
Further details on how to compute the average noise power will be explained in future papers
98
lead to a significant distortion of the delay parameters.
††
Furthermore, the PDPs are computed with over-
sampling since, e.g., the delay spread of a critically sampled PDP can deviate considerably from the value
of the underlying continuous profile.
‡‡
All the above quantities depend oni,j,k,l, as well as the particular locations of the Tx and Rx. In case
measurements in multiple elevations are available, the PDPs are summed overj andl, as discussed in Sec.
III. From the resulting elevation-integrated PDPs, we obtain the following three quantities:
1. max-dirPDP: we determine the horn azimuth combination
ˆ
i,
ˆ
k that provides the largest total power
(integrated overτ ) and call it the max-dir PDP. The max-dir PDP and all parameters derived from it
are below, depending on the beamwidth of the used horn.
2. omnidirectionalPDP: we combine all directional azimuth PDPs to synthesize a PDP that emulates the
result we would get if we measured with an omnidirectional antenna. This is done by the method of
[64], where for each delay the maximum of the received power (over all azimuth angles) is identified,
and the maxima are used to generate a total PDP.
3. angular power spectrum: by integrating the (directional) PDPs over the delay, a discretized form of
the angular power spectrum, APS, is obtained.
§§
From these quantities, we can further obtain condensed parameters:
• Path gain, PG: The PG is obtained by integrating the PDP over the delay, providing the omnidirec-
tional PG or the max-dir PG, depending on which PDP is used as the basis for the computation. The
path gain is of fundamental importance for the link budget, SNR, and thus the capacity of a (single-
stream) link. Scatter plots of the measurements, as well as functional fits, of PG as a function of
distance, will be provided in Sec. VII. However, two major caveats must be noted: (i) any fit is valid
††
For example, the second central moment of a (continuous)|sinc|
2
function over[−∞ ,∞] is infinity.
‡‡
Consider, for example, a PDP centered in the middle between two (critical) sampling points: its delay spread will be much
larger than that of the same function centered on a sampling point.
§§
Obviously, all measured PDPs and APSs are discrete; however, the figures below will show interpolated versions.
99
only within the range of distances in which it is done, (ii) the selection of Tx/Rx locations impacts the
overall results. In our campaigns, measurement points were selected where it could be reasonably
anticipated that the received signal was strong enough for the channel to be estimated. Thus, the
results are not suitable to assess the outage probability of cellular/WLAN/D2D THz systems, which
should be based on measurements where at least one link end is placed at random, or on a regular
grid.
• RMS Delay Spread, DS: The DS is defined as the second central moment of the PDP, and can thus be
computed easily [99], though care must be taken to account for sidelobes stemming from the IFFT,
and impact of MPCs whose delay is between sampling points, as discussed above. Depending on
whether max-dir or omni PDP underlies the computation, we obtain the max-dir or omni DS. The
DS is a common measure to describe the results of measurement campaigns, and can be tied (via
uncertainty relations [41]) to the coherence bandwidth of the channel, and thus provide an indirect
measure of the achievable frequency diversity.
• Q-window: Another quantity describing the delay dispersion is the Q-window, which quantifies the
minimum window such that the ratio of the energy of the impulse response within the window to
that outside of it reaches a particular value Q. This quantity is most useful to assess OFDM and
single-carrier systems where the equalizer taps are at regular locations,nT
c
,n=1,2,..... In both of
these cases,Q describes the SIR, since the window contains a useful signal, and the energy outside
the window contains intersymbol interference.
• Q-tapnumber: A related quantity is the Q-tapnumber, which defines the minimum number of arbi-
trarily placed taps (by enforcing that they are at integer multiples of the sampling interval) in order
that the energy collected on those taps divided by those at other locations is Q. This quantity is
useful to assess Rake receivers and equalizers with dynamically-placeable taps.
100
• RMSangularspread,AS: The AS quantifies the angular dispersion and is thus a measure of the avail-
able angular diversity, the possibility of spatial multiplexing, and interference between links with
different horn directions. Thus, it is not possible to classify large angular dispersion as "beneficial" or
"detrimental" to system performance; rather the particularities of the analyzed system configuration
need to be taken into account. While the definition of angular spread (AS) as the second central mo-
ment of the angular power spectrum (APS) is common in the literature, this definition suffers from
ambiguity, since (due to the periodicity of the angular coordinates) the choice of the origin of the
coordinate system has a major impact on the result. Instead, the definition of Fleury ([42], see also
[10] and [99]) will be used in the following. In this definition, the range of possible values is [0,1];
for small values the (dimensionless) Fleury AS has the same numerical value as a (suitably centered)
second central moment expressed in radians. Finally, we note that the AS values are lower-bounded
by the beamwidth of the horn used in our measurements.
5.5 Themeasurementenvironments
The environments in which the measurements are done govern which propagation processes occur, and
what parameters of the MPC channel we can expect. Our measurements were done in the following sets
of environments:
Indoor corridor and conference rooms: the indoor measurements were conducted in an office
building. Tx and Rx were located either in a corridor (1.78m wide,2.45 m high), or a variety of offices, see
Figs. 5.4 and 5.5. The walls are made of post-and-drywall, and the windows are of the non-energy-saving
type. In all the measurements, the Rx was at1.55 m height while the Tx was at a height of2.18 m, which
corresponds to the height of a typical hotspot/indoor access point. The distance between Tx and Rx varied
between 8 and 35 m. Overall, we measured 4 LoS links in the corridors, as well as 5 NLoS links in the
101
Figure 5.4: Map of the indoor environment.
corridors and 2 NLoS links in the offices. A map of the environments markings of the Tx and Rx locations
is given in Figs. 5.5 and 5.4.
Outdoor plaza and street crossing: the D2D outdoor measurements were performed in two areas
of the USC campus that are a plaza and a street crossing, respectively. The plaza encompasses an open
area with concrete pillars, bounded by building walls on two sides, as well as a larger L-shaped space
with trees, umbrellas, and tables. For the street intersection, there were buildings, and various amounts of
vegetation, at three corners of the intersection, while at the fourth corner was a sports field surrounded
by a metal fence. In all the measurements both Tx and Rx were at1.6 m in height. The distance between
Tx and Rx varied between 1 and 93 m. Overall, we measured 12 LoS links in the plaza and 9 LoS links in
the intersection, as well as 14 NLoS links in the plaza and 3 NLoS links in the intersection. A map of the
environment marking the Tx and Rx locations is given in Figs. 5.6 and 5.7.
Streetcanyonandparkinglot: the microcellular measurements were performed in an urban envi-
ronment, with the Tx located at11.6 m height essentially at the facade of a building, and the Rx located
at various positions in a parking lot and in street canyons. Since the Tx was on a building facade (more
102
Figure 5.5: Map of the Conference room environment.
Figure 5.6: Map of the outdoor intersection environment.
103
Figure 5.7: Map of the outdoor plaza for D2D environment.
precisely at openings in the building facade), its antenna was chosen to only illuminate a120
°
sector. Dif-
ferent mounting positions on different walls of the building, pointing in different directions, were used.
The 3D distance between the Tx and Rx varied between 20 and 85 m. Overall, we measured 13 LoS links
and 13 NLoS links. A map of the environment with markings of the Tx and Rx locations is given in Fig.
5.8.
More details about the environments, and a listing of all measured links, can be found in [10, 3, 50, 4],
respectively.
5.6 Sampleresultsandimpactofspecificenvironments
The following figures show, for a number of sample cases, the angular delay power spectrum, ADPS,
(where an integration over the transmit directions has been done since four-dimensional descriptions are
difficult to display), as well as the PDP and the APS at the Rx side derived as the marginal distributions of
104
Figure 5.8: Map of the outdoor plaza for microcellular environment.
this ADPS.
¶¶
The delays are given in units of meter (i.e., multiplied by the speed of light) for easier geo-
metric interpretation. From these results, we can intuit a number of insights into the relevant propagation
processes.
Fig. 5.9 shows the results for a microcellular LoS link. From the plot, we can firstly see that - as expected
- the LoS component carries the strongest power, arriving from0° azimuth, and with a delay equal to the
Euclidean Tx-Rx distance. We also see that there are a number of significant MPCs at later delays (around
100 m) that come from different directions and thus will be filtered out by a directional antenna pointing
only in the LoS direction. Finally, reflections from the back (at ϕ RX
=180°) can be noted at a delay of160
m. Please note that the reflections from the back are not the effects of the backlobe of the antenna, since
such backlobes would show up at the LoS delay.
It is interesting to compare this outdoor LoS scenario to the indoor LoS example shown in Fig. 5.10,
which was measured in a building corridor. We first note the significantly larger dispersion, both in the
delay and the azimuth domain. This is related to the walls lining the corridor at the side and the back, thus
¶¶
Note that the PDP shown as the marginal distribution of the ADPS (i.e., ADPS integrated over all Rx angles) is defined
slightly differently from the omni-PDP computed by the method of [64] as shown in the ”standalone" PDP figures. However, the
differences in the results are minor.
105
Figure 5.9: APDS of outdoor microcellular LOS link, TX1-Rx1 ford
Tx− Rx
=82.5m.
giving rise to many MPCs and extended ”ringing" of the echoes. Thus, even though the distance between
Tx and Rx is much shorter than in the outdoor case, the delays of the echoes extend over a longer time
(distance). We also note major differences in the APS: firstly, the main peak (around 0°) is broader than
in the previous case because the waves are guided by the corridor, and thus reflected repeatedly at the
sidewalls. Secondly, the power of the components arriving from the back (ϕ RX
= 180°) is significantly
higher than in the outdoor case, because the wall terminating the corridor is closer to the Rx, oriented
perpendicular to the direction of LoS propagation, and has a high reflectivity.
Fig.5.11 shows, in greater detail, the PDP, distinguishing between the omnidirectional and the max-dir
PDP for an indoor measurement. We can clearly see that omni case provides a much richer multipath,
but that even the max-dir case has a quite significant delay dispersion. The omni-PDP can be described
as a single-exponential decay, with several additional pronounced discrete components. The joint APS at
Tx and Rx side, depicted in Fig. 5.12, shows a significant broadening of the main beams, and that energy
arrives at the Rx both from the front and the back (note that the Tx only swept the 120° sector looking
towards the Rx, so it does not illuminate the corridor wall behind it).
We next investigate the results for an outdoor NLoS scenario. An example ADPS from a D2D mea-
surement is shown in Fig. 5.13. We first note that the PDP shows multiple peaks, most with a considerable
delay with respect to the direct distance between the Tx and Rx. The absence of a pronounced component
106
Figure 5.10: ADPS of indoor LoS link, TX2-Rx8. d
Tx− Rx
=32m.
0 100 200 300 400
[m]
-170
-160
-150
-140
-130
-120
-110
-100
-90
|h( )|
2
[dB]
Omni Max-Dir
15 20 25 30 35
-140
-120
-100
Omni Max-Dir
Figure 5.11: PDP of indoor LoS link, TX2-Rx8.
Figure 5.12: APS of indoor LoS link, TX2-Rx8.
107
Figure 5.13: ADPS of outdoor D2D NLoS link, TX6-Rx32 ford
Tx− Rx
=97.59m.
100 120 140 160 180 200
[m]
-170
-160
-150
-140
-130
-120
|h( )|
2
[dB]
Omni Max-Dir
Figure 5.14: PDP of outdoor D2D NLoS link, TX6-Rx32.
at/near the LoS delay confirms that diffraction is not an efficient propagation process, as discussed in Sec.
II. Note also that the strongest signal does not come fromϕ RX
=0°, which by definition is the geometrical
LoS direction. We furthermore note significant components near 180°, which means that waves reflected
by the building at the back of the Rx (buildings on the right side of the cross street in which the Rx is
located) are important. More details of the PDP can be seen in Fig. 5.14. Again the omni-PDP shows a
much larger multipath richness than the max-dir one.
Waveguiding also leads to interesting effects, both in outdoor environments (not shown for space
reasons) and especially in indoor corridor environments, where it is very pronounced. A sample ADPS is
shown in Fig. 5.15. In this case, we use a coordinate system where 0/0 points in the direction of the corridor
108
Figure 5.15: ADPS of indoor NLoS link, TX2-Rx6 ford
Tx− Rx
=34.4m.
containing the Tx. We first observe that the strongest directions at the Rx are near 90° and - somewhat
weaker -− 90°. Thus, at the Rx the waves are coming down the corridor in which the Rx is located (and
which is perpendicular to the corridor in which the Tx is located); with additional components that are
first guided down the Rx corridor, and then reflected at the back wall of that corridor. Consistent with this
interpretation, the first significant component with ϕ RX
= − 90° angle has a larger delay than the first
component with theϕ RX
= 90°. We also see a very pronounced cluster structure in the PDP, with each
cluster decaying exponentially with a short time constant, and the power of the clusters decaying with a
longer time constant. This is similar to the famous Saleh-Valenzuela (SV) model [126], though the cluster
delays are deterministically periodic and not random as in the SV model.
Finally, we inspect an example of a microcellular NLoS scenario in an open square surrounded by
buildings. Here the APS at the Rx (as seen in Fig. 5.16) shows several MPCs coming from positive angles,
i.e., from scatterers located in the parking lot. Indeed, there were not only cars, but also multiple other
objects like lantern masts, and signs, in the parking lot, which are effective reflectors at THz frequencies. In
contrast, little power is coming from negative angles, which is where the building wall of USC Michelson
Center for Convergent Bioscience (MCB) extends. The strongest - and first arriving - component has a
slightly positive angle. We conjecture that it is diffraction. While diffractions normally have extremely
small power, in this case, the diffraction angle is shallow. Furthermore, we see that the absolute power is
109
Figure 5.16: ADPS of outdoor NLoS link, TX3-Rx14 ford
Tx− Rx
=62.6m.
50 100 150 200 250 300
[m]
-165
-160
-155
-150
-145
-140
-135
|h( )|
2
[dB]
Omni Max-Dir
60 65 70 75 80
-160
-155
-150
-145
-140
-135
Figure 5.17: PDP of outdoor NLoS link, TX3-Rx14.
indeed small; we conjecture that it is the largest one only because of the absence of buildings that could
provide effective reflection processes larger than the diffracted component.
The NLoS characteristics also have a significant impact on localization. Most precision localization
methods (including GPS) are either based on time-of-arrival, time-difference-of-arrival, or combinations
thereof with signal strength and/or Direction of Arrival DoA. The discrepancy between the nominal Eu-
clidean distance between Tx and Rx on one hand, and the delay of the strongest (or the first measurable
component) on the other hand thus impacts the accuracy of the measurements. Determination of which
links are NLoS - information that can be used as a basis for either discarding those links or subjecting
110
Figure 5.18: APS of outdoor NLoS link, TX3-Rx14.
them to more advanced signal processing - is thus important for precision localization [11]. For this pur-
pose, statistics of the excess delay of first/strongest components, and their correlation with other channel
parameters such as excess path loss, need to be analyzed, which we will do in future work.
Since reflections are the dominant propagation process in NLoS situations, it is also interesting to
investigate the impact of reflection coefficients and additional (passive) reflected objects on the received
signal. We have performed such an experimental study in [50]. An example result is shown in Fig. 5.19,
specifically showing the ADPS in an NLoS office channel in which the windows are either covered with
blinds or not. The presence of the blinds changes the strength of some of the longer-delayed echoes (10
m delay and more), indicating that the specific furnishing of a room might influence the ADPS. In further
measurements (see [50] for details), we found that the introduction of additional metallic objects can lead
to an increase in the number of MPCs, and thus coverage and angular and delay diversity; however, this can
also possibly increase multi-user interference. The choice of placement thus has to be handled carefully.
We finally analyze the potential impact of ground reflections. For short distances ( < 20 m) and D2D
settings, the elevation angle of the ground reflection is outside the main beamwidth of the horn antenna
and is thus significantly attenuated. For larger distances, ground reflection might be received, but cannot
be resolved for 1 GHz bandwidth in the delay domain due to the small excess runlength (10 cm, which
is significantly smaller than the resolvable binwidth of 1 ns = 30 cm) of the ground reflection. We thus
111
(a) with blinds (b) without blinds
Figure 5.19: ADPS of a link with and without reflectors, Conference room scenario (see [50] for details).
performed long-distance measurements with a bandwidth of 10 GHz. Since a full angular scan is neither
possible for this bandwidth (due to the long measurement time) nor necessary to analyze the ground reflec-
tion of the LoS component, we only measured the PDP with the two horns pointing directly at each other.
An example PDP in Fig. 5.20 shows a ground reflection at the excess delay to be expected from the geom-
etry. We performed these measurements at a variety of distances between 15 and 70 m; the amplitude of
the ground reflection is between 2 and 10 dB weaker than the LoS, with the specific attenuation depending
on the surface structure at the reflection point (e.g. asphalt versus brick tiles). The ground reflection has
little impact on the path loss measurements, which, within our distance measurement range, do not show
a transition to thed
4
path loss law that is postulated when a ground reflection with reflection coefficient
− 1 destructively interferes with the LoS, see [99], Chapter 4.
5.7 Statisticalresults
For system design, the statistics of the different MPC-channel characteristics are discussed in Sec. IV
needs to be analyzed. The following subsections and tables provide the ”best fit" in terms of probability
density function (for the distribution of parameters over the ensemble of measured points) and the distance
dependence of the parameters. Details about the fitting procedures, as well as the confidence intervals
112
68 68.5 69 69.5 70 70.5 71 71.5 72 72.5
Delay (m)
-75
-70
-65
-60
-55
-50
-45
-40
-35
-30
Power (dB)
X 69.683
Y -28.9643
X 69.773
Y -38.3658
Figure 5.20: PDP of long-distance measurement (70 m link) with 10 GHz bandwidth.
of the fitting parameters, are given in [10, 3, 4]. We stress again that the distance dependence of the
parameters is only valid for the distance range in which the measurements were made.
5.7.1 Pathlossandshadowing
Fig. 5.21 shows the path loss as a function of the Euclidean distance between Tx and Rx. In particular, Fig.
5.21a and b aggregate the results for LoS scenarios, and also shows the best fit for the α − β model
P
Tx,dB
+G
Tx,dB
+G
Rx,dB
− P
Rx,dB
=α +10βlog
10

d
1m

+ϵ, (5.4)
where ϵ is a lognormally distributed random variable with standard deviation σ ϵ . We can see that in all
environments, the path loss coefficient β is slightly smaller than2, as can be expected for an LoS environ-
ment, due to the contribution of the LoS component itself that has path loss coefficient 2, and is augmented
by other MPCs. We also see that the path loss is smaller in indoor than in outdoor environments, which
is in line with the physical insight that a corridor (with highly reflecting and (almost) continuous walls)
guides power better than an open square or even a street canyon. Comparing the omni and the max-dir re-
sults, we see that the difference is relatively small since most of the power is carried in the LoS component.
The shadowing standard deviation is on the order of1− 2 dB, indicating that an accurate prediction of the
113
LoS signal strength can be realized. Again, this mainly rests on the dominance of the (highly predictable)
LoS component compared to all other MPCs. If the antenna is not pointing towards the LoS component,
or it is shadowed off by, e.g., a human body, the received power is dominated by indirect (i.e., non-LoS)
MPCs, and exhibits considerably larger variations.
Figs. 5.21c and d show the path loss for the NLoS situations. We first of all notice that the path loss is
almost always larger than the free-space path loss. Secondly, the excess path loss is significantly larger for
the max-dir case than for the omnidirectional case, indicating that a significant percentage of the energy
comes from directions other than the max-dir direction.
∗∗∗
Thirdly, for the microcellular case, the excess
path loss increases with distance for the max-dir case, while itdecreases for the omnidirectional case. This
indicates that the multi-path richness increases with increasing distance, leading to stronger contributions
from different directions, again aligned with intuition. For the D2D case, the excess path loss decreases
both for the max-dir and the omni case. For the indoor environment, trends are difficult to judge due to
the relatively small range of distances (the largest distance is only a factor of 3 larger than the smallest
distance). The shadowing standard deviation is significantly larger in the NLoS case than for LoS, ranging
between 4 and 8 dB.
Table 5.1 summarizes the results for path loss coefficients and shadowing in all the environments. It
shows the fitting parameters not only for the α − β model but also for the CI model (5.5), with the following
formula:
P
Tx,dB
+G
Tx,dB
+G
Rx,dB
− P
Rx,dB
=FPSL(f,d
0
)+10nlog
10

d
1m

+ϵ, (5.5)
whereFPSL(f,d
0
) =− 20log
10
(
c
4πf
) is the Free space path loss at 1m distance, thus leaving only one
parameter to optimize
∗∗∗
Of course, the receive SNR is higher in the max-dir case than in the omni case, due to the gains of the directional antennas
at the two link ends.
114
1 2 5 20 50 100
d [m]
70
80
90
100
110
120
PL [dB]
Friis
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
20 40 60 80
100
105
110
115
(a) LoS, max-dir
1 2 5 20 50 100
d [m]
70
80
90
100
110
120
PL [dB]
Friis
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
20 40 60 80
95
100
105
110
115
(b) LoS, omni
2 5 10 20 50 100
d [m]
80
90
100
110
120
130
140
PL [dB]
Friis
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(c) NLoS, max-dir
2 5 10 20 50 100
d [m]
80
90
100
110
120
130
140
PL [dB]
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
Friis
(d) NLoS, Omni
Figure 5.21: Path loss as a function of distance.
Note that the shadowing variance is computed as the standard deviation with respect to theα − β fit.
5.7.2 Delaydispersion
We next analyze the various measures for the delay dispersion, namely DS, Q-window, and Q-tapnumber.
Fig. 5.22 shows the results in the various environments, separately for LoS and NLoS, and for max-dir
and omnidirectional antenna configuration. Due to the limited bandwidth and the Hann filter operation,
the minimum measurable spread is around− 93 dBs. For LoS situations, the DS generally remains below
− 80 dBs, while for NLoS, it can reach up to− 68 dBs for the omnidirectional case and− 75 dBs for the
max-dir case. A comparison of these values to those at lower frequencies can be done mainly for the omni
case, since, for the max-dir case, the results depend on the beamwidth, and lower frequencies generally
use larger beamwidth. We find that for the omni case, the results are in the same order as those obtained in
115
α max− dir
β max− dir
n
max− dir
α omni
β omni
n
omni
σ ϵ max− dir
σ ϵ omni
Range[m]
IndoorLoS 77.35 1.5 1.62 79.01 1.25 1.49 1.69 1.67 [16-32]
D2DLoS 76.68 1.84 1.9 76.86 1.77 1.85 1.63 1.28 [1-100]
MicrocellLoS 76.93 1.91 1.99 73.84 2 1.89 1.04 0.91 [20.4-82.5]
IndoorNLoS 108.67 1.33 3.93 97.91 1.86 3.61 4.36 4.32 [8.94-34.17]
D2DNLoS 89.76 2.18 3.16 89.22 1.99 2.93 7.53 5.37 [2-100]
MicrocellNLoS 85.22 2.5 3.1 91.65 1.86 2.86 7.34 6.1 [18.3-83]
Table 5.1: Path loss parameters in the different environments.
similar environments (and similar antenna placements) at both mmWave [100] and cmWave frequencies
[102].
The results also indicate that the coherence bandwidth is significantly smaller than the assumed sys-
tem bandwidth of 1 GHz. This can be advantageous in terms of the available frequency diversity and, thus,
robustness against small-scale fading. However, it also implies that the small-scale fading characteristics,
and thus (digital) beamforming coefficients, vary significantly over the bandwidth. This not only means
that (for a beamformer based on feedback) higher overhead for the feedback is required, but also that ana-
log beamformers, which usually can only form a subcarrier-independent beampattern, may significantly
underperform in a number of situations, a conclusion we will find confirmed in Sec. VIII.
When comparing the DS in the different environments, the microcellular case leads to the smallest DSs
in all cases (LoS and NLoS, omni and max-dir). Outdoor D2D provides somewhat larger values, which can
be explained by interacting objects being in the vicinity of both Tx and Rx, thus enabling richer multipath
and stronger delayed components. Indoor environments provide the largest values; we conjecture that
this is due to the specific type of indoor environment, namely a long corridor with well-reflecting walls,
in which most of our indoor measurements were done. This conjecture is supported by the fact that the
difference between outdoor and indoor DSs is largest for the LoS case (where the signal can be reflected
multiple times between walls at the two ends of the corridor).
The CDF of the DS over the ensemble of measured points can be well fitted by a lognormal distribution,
a finding that is consistent with the well-known model of Greenstein [52] that has been validated in a
116
-95 -90 -85 -80 -75
[dBs]
0
0.2
0.4
0.6
0.8
1
F( )
D2D
Microcell
Indoor
D2D model
Microcell Model
Indoor Model
(a) LoS, max-dir
-90 -85 -80 -75 -70
[dBs]
0
0.2
0.4
0.6
0.8
1
F( )
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(b) LoS, omni
-95 -90 -85 -80 -75 -70
[dBs]
0
0.2
0.4
0.6
0.8
1
F( )
D2D
Microcell
Max-Dir
D2D Model
Microcell Model
Indoor Model
(c) NLoS, max-dir
-85 -80 -75 -70 -65
[dBs]
0
0.2
0.4
0.6
0.8
1
F( )
D2D
Microcell
Omni
D2D Model
Microcell Model
Indoor Model
(d) NLoS, Omni
Figure 5.22: CDF of the rms delay spread.
variety of environments and frequency ranges. The DS also tends to increase with distance for most
environments and antenna settings, but the confidence intervals of the estimated slopes are relatively
wide and often encompass both positive and negative values, for details see [10, 3]. Future measurements
with larger numbers of points will be needed for a more definitive assessment.
We next turn to the Q-window, analyzing with a threshold SIR of15,20, and25 dB. We consider here
a tap size of2ns since we use a Hann window to obtain the impulse response (see Sec. IV), which broadens
µ max− dir
(dBs) σ max− dir
(dBs) µ omni(dBs) σ omni(dBs)
IndoorLoS -76.41 0.67 -74.71 0.95
D2DLoS -84.7 4.16 -76.8 3.04
MicrocellLoS -85.54 2.53 -77.7 4.06
IndoorNLoS -75.76 1.91 -74.91 1
D2DNLoS -81.84 4.33 -71.76 2.09
MicrocellNLoS -86.76 4.06 -76.98 4.43
Table 5.2: σ τ parameters in the different environments.
117
the main beam while suppressing sidelobes. CDFs are shown in Figs. 5.23. 5.24, and 5.25, respectively. As
expected, the windows are larger for NLoS than for LoS, and for omni than for max-dir, and increase with
increasing threshold SIR. Far more surprising is the range of absolute values of the windows: between 2
and 250 ns for the max-dir case (keeping in mind that the max-dir results are specific to the given antenna
beamwidths) and up to 900 ns for the omni case. In the outdoor max-dir case, the Q-window is below
about 80, 140, and 200 ns, respectively, in about 90% of all cases, These results have a significant impact
on system design; in particular, they indicate that the width of the cyclic prefix in an OFDM system has to
be on the order of tens or even hundreds of ns, implying (for good spectral efficiency) at most hundreds of
kHz of subcarrier spacing. Furthermore, for single-carrier systems with regularly-spaced equalizers, tens
of, or even one hundred, taps are required, even in the max-dir case.
To model the statistical behavior of the Q-window parameter, we use a Gamma distribution, which has
the following probability density function (pdf):
f(x;κ,λ )=
1
Γ( κ )λ κ x
κ − 1
e
− x/λ
, (5.6)
whereΓ( x) is Euler’s Gamma function. For a Gamma pdf, the mean and variance are calculated as:
E[x]=κλ, (5.7)
V[x]=κλ 2
, (5.8)
whereE[·],V[·] are the expected value and the variance of the random variablex, andκ,λ are the param-
eters of the distribution, whose values in different environments are tabulated in Table 5.3.
We finally turn to the Q-tapnumber. Again we observe similar trends as for the Q-window, namely
that max-dir PDPs have a much smaller number of relevant taps, and that the number of taps is lower in
118
0 2 4 6 8 10
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(a) LoS, max-dir
0 20 40 60 80 100
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(b) LoS, omni
0 20 40 60 80
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(c) NLoS, max-dir
0 100 200 300 400
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(d) NLoS, Omni
Figure 5.23: CDF of the Q window, SINR = 15 dB.
LoS than in the NLoS situations - not because there are fewer MPCs, but because the LoS component is
much stronger, and thus fewer taps are needed to collect a total percentage of energy. In absolute terms,
the number of taps is much smaller than the length of the Q-window divided by the delay binwidth, which
indeed indicates that the PDPs are sparse in the sense that the percentage of taps containing significant
energy is small; however they are not sparse in the sense that the absolute number of taps is small. For
the outdoor cases, the number of taps at the (approximate) 90% level are 10, 25, and 40, respectively -
considerably smaller than the Q-windows, but still a significant number.
Similar to the previous parameter, we used a Gamma distribution to model the statistical behavior of
the Q-tapnumber and the parameters of the distribution are tabulated in Table 5.4.
119
0 20 40 60 80 100
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor model
(a) LoS, max-dir
0 50 100 150 200
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(b) LoS, omni
0 50 100 150
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(c) NLoS, max-dir
0 100 200 300 400 500
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(d) NLoS, Omni
Figure 5.24: CDF of the Q window, SINR = 20 dB.
5.7.3 AngularDispersion
We next move to measures for the angular dispersion, in particular the AS. For the D2D scenarios (both
outdoors and indoors), there is no need to distinguish between AS at the Tx and Rx. For those scenarios,
the CDFs of the AS are shown in Fig.5.29. The logarithm of the AS is bounded on the lower limit by
approximately− 0.8, due to the finite beamwidth of the horn antennas. When analyzing the CDFs of the
AS, we can observe 3 clusters of curves in the LoS case: (i) AS at the microcellular and indoor Tx (i.e.,
the BS or access point); due to the elevated position and the limited angular range during scanning, the
values are small and range from− 0.8 to− 0.6 for LoS. In the NLoS case, the variations are much larger
(-0.8 to -0.2). (ii) AS for the microcell Rx, and the D2D Rx and Tx (remember that in the D2D case, there
is on average no difference between the environment that Tx and Rx see). Here, in the LoS case values
120
0 50 100 150
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(a) LoS, max-dir
0 50 100 150 200 250
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell model
Indoor Model
(b) LoS, omni
0 50 100 150 200
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor model
(c) NLoS, max-dir
0 100 200 300 400 500
Q
win
0
0.2
0.4
0.6
0.8
1
F(Q
win
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(d) NLoS, Omni
Figure 5.25: CDF of the Q window, SINR = 25 dB.
vary between− 0.8 and− 0.05, with a mean around− 0.5; in the NLoS case it varies between− 0.6 and
0. The fact that we observe larger values of the AS can be explained by the richer scattering environment
around the (outdoor) device at1.6 m height, compared to an elevated BS. (iii) indoor Rx shows the largest
AS (between− 0.2 and 0, due to strong signals incident from the front and the back (again, due to the
corridor structure in which we measured).
The CDFs can be fitted well by lognormal distributions, as shown in Fig. 5.29; the parameters of these
distributions are given in Table 5.5.
121
κ 15dB
max− dir
λ 15dB
max− dir
κ 15dB
omni
λ 15dB
omni
κ 20dB
max− dir
λ 20dB
max− dir
κ 20dB
omni
λ 20dB
omni
κ 25dB
max− dir
λ 25dB
max− dir
κ 25dB
omni
λ 25dB
omni
IndoorLoS 17.14 0.35 6.59 6.79 15.15 4.41 26.3 3.72 8145.5 0.004 1000.4 0.13
D2DLoS 53 0.06 1.05 22.29 23.78 0.15 1.38 31.98 8.2 0.62 2.05 37.45
MicrocellLoS 15.09 0.24 0.65 37.53 8.63 0.6 0.68 76.74 7.29 0.91 1.12 60.08
IndoorNLoS 3.28 11.32 15.66 3.07 5.3 15.4 60.27 1.49 10.67 9.79 184.88 0.68
D2DNLoS 1.29 7.83 2.2 63.15 1.24 14.05 4.07 44.5 1.16 50.44 4.97 47.67
MicrocellNLoS 2.18 3.11 1.29 34.58 2.11 4.15 1.41 49.27 2.32 4.43 1.74 64.15
Table 5.3: Q window parameters in the different environments.
0 2 4 6 8 10
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(a) LoS, max-dir
0 10 20 30 40
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(b) LoS, omni
0 10 20 30 40 50
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(c) NLoS, max-dir
0 50 100 150 200
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(d) NLoS, Omni
Figure 5.26: CDF of the Q-tapnumber, SINR=15dB.
5.8 Systemperformance
The impact of the angular dispersion on the system performance depends on the specific beamforming
algorithms. In [49], we evaluated both analog and digital beamforming with measured outdoor D2D prop-
agation channels for both ”piconet-controller" and ”peer-to-peer" scenarios. In the former case, different
devices are all talking to a single device, e.g., a piconet controller, which uses beamforming to spatially
122
0 10 20 30 40 50
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor model
(a) LoS, max-dir
0 20 40 60 80
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(b) LoS, omni
0 20 40 60 80 100
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(c) NLoS, max-dir
0 50 100 150 200
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor model
(d) NLoS, Omni
Figure 5.27: CDF of the Q-tapnumber, SINR=20dB.
separate the different users. In the latter case, pairs of devices are talking to each other, and pointing beams
towards each other.
For the analog beamformer, we assume that the receiving device simply selects the beam that provides
the highest power of the desired signal. This beam selection takes into account that an analog beamformer
can only form a beam that is valid for all incident signals, but it is actually more restrictive in that it allows
only the selection of a fixed beam and not the forming of an arbitrary beamshape. It is, however, a simple
structure and in line with simple phased arrays in cellular handsets that typically also step (and not sweep)
over different angles.
For the digital beamformer, we assume that all 36 receive signals (one from each of the Rx antenna
directions) are processed with either maximum-ratio combining (MRC). zero-forcing (ZF), or minimum
123
0 20 40 60 80 100
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(a) LoS, max-dir
0 50 100 150
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(b) LoS, omni
0 20 40 60 80 100
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(c) NLoS, max-dir
0 50 100 150 200 250 300
Q
tap
0
0.2
0.4
0.6
0.8
1
F(Q
tap
)
D2D
Microcell
Indoor
D2D Model
Microcell Model
Indoor Model
(d) NLoS, Omni
Figure 5.28: CDF of the Q-tapnumber, SINR=25dB.
-1 -0.8 -0.6 -0.4 -0.2 0
log
10
( ° )
0
0.2
0.4
0.6
0.8
1
F(log
10
( ° ))
D2D
Microcell Tx
Microcell Rx
Indoor Tx
Indoor Rx
D2D Model
Microcell Tx Model
Microcell Rx Model
Indoor Tx Model
Indoor Rx Model
(a)σ ◦ for LoS
-1 -0.8 -0.6 -0.4 -0.2 0
log
10
( ° )
0
0.2
0.4
0.6
0.8
1
F(log
10
( ° ))
D2D
Microcell Tx
Microcell Rx
Indoor Tx
Indoor Rx
D2D Model
Microcell Tx Model
Microcell Rx Model
Indoor Tx Model
Indoor Rx Model
(b)σ ◦ for NLoS
Figure 5.29: CDF of the AS.
mean square error (MMSE). Since different beamformers on different subcarriers (or more generally, dif-
ferent parts of the band) are possible, better performance can be anticipated.
124
κ 15dB
max− dir
λ 15dB
max− dir
κ 15dB
omni
λ 15dB
omni
κ 20dB
max− dir
λ 20dB
max− dir
κ 20dB
omni
λ 20dB
omni
κ 25dB
max− dir
λ 25dB
max− dir
κ 25dB
omni
λ 25dB
omni
IndoorLoS 11.94 0.34 8.56 2.54 4.7 3.62 29.44 1.87 24.27 2.13 118.22 0.78
D2DLoS 31.54 0.07 3.49 1.6 8.99 0.33 2.92 5.32 7.77 0.54 2.85 13.83
MicrocellLoS 14.59 0.18 7.02 0.64 14.85 0.25 3.41 2.86 7.97 0.69 3.73 5.98
IndoorNLoS 4.47 5.88 15.37 2.71 6.08 8.66 35.7 2.01 11.33 7.29 103.73 1.01
D2DNLoS 3.63 1.2 2.52 23.4 2.13 4.19 4.92 20.12 2.81 6.49 8.56 16.29
MicrocellNLoS 2.35 2.26 1.39 23.29 1.95 3.9 1.49 35.11 2.08 4.52 1.95 37.55
Table 5.4: Q-tapnumber parameters in the different environments.
µ Tx
/µ D2D
σ Tx
/σ D2D
µ Rx
σ Rx
IndoorLoS -0.7 0.05 -0.12 0.07
D2DLoS -0.49 0.2 N.A. N.A.
MicrocellLoS -0.73 0.06 -0.53 0.15
IndoorNLoS -0.6 0.21 -0.14 0.06
D2DNLoS -0.23 0.17 N.A. N.A.
MicrocellNLoS -0.5 0.19 -0.36 0.21
Table 5.5: log
10
(AS) parameters in the different environments.
∗ The values in this table are dimensionless, as explained in Section 5.4
Figs. 5.30-5.32 compare the performance achieved with those beamforming schemes in a piconet con-
troller and a peer-to-peer scenario, respectively. The results in Fig. 5.30 assume a network consisting of
peer devices (i.e., D2D channels), where one of the peer devices serves as piconet controller. In this exam-
ple, we see that in two cases (PnC7 and PnC8), analog beamformer provides a capacity that has a similar
behavior (as function of the transmit power) as digital beamforming, and generally shows an offset of
about 1-2 bit/s/Hz; this might be an acceptable loss in many situations, given the much lower complexity
of the analog beam selection. However, we also see that in one example (PnC5), the analog beamformer
has a much worse performance; capacity as function of SNR essentially saturates at a low level, as does
digital MRC combining. In contrast, for digital beamforming with ZF or MMSE, capacity increases with
the Tx power. This is due to the fact that several devices are in one beam of the piconet controller, so that
their transmissions collide. Better scheduling would reduce this problem, but still the use of beam selection
instead of creation of complex weights that optimize reception, exerts a significant performance penalty.
Similar results occur in a microcellular setup where multiple devices access the BS, see Fig. 5.31.
In the P2P scenario, the capacity considerably depends on the directions into which the interfering
devices transmit. Since the different devices are assumed not to coordinate their transmissions with each
125
-20 -10 0 10 20
P
UE
[dBm]
0
10
20
30
40
C
Sum
[bps/Hz]
Analog, PnC
5
MRC, PnC
5
ZF, PnC
5
MMSE, PnC
5
Analog, PnC
7
MRC, PnC
7
ZF, PnC
7
MMSE, PnC
7
Analog, PnC
8
MRC, PnC
8
ZF, PnC
8
MMSE, PnC
8
Figure 5.30: Comparison of digital and analog beamforming in a piconet controller scenario.
-20 -10 0 10 20
P
UE
[dBm]
0
10
20
30
40
C
Sum
[bps/Hz]
MRC, PnC
1
ZF, PnC
1
MMSE, PnC
1
MRC, PnC
5
ZF, PnC
5
MMSE, PnC
5
MRC, PnC
7
ZF, PnC
7
MMSE, PnC
7
Figure 5.31: Comparison of digital beamforming in a piconet controller scenario.
other, we can assume that transmissions occur into random directions. For this case, Fig. 5.32 shows the
CDF of the capacity (over the ensemble of interference directions), for a variety of devices. Only analog
beamforming is considered in this case. We can see that the considerable angular dispersion leads to more
interference than what one could expect if THz links consisted only of LoS components. More examples
and details of the configurations are discussed in [49].
5.9 Conclusions
This chapter has provided an overview of extensive channel-sounding campaigns in the THz band, specif-
ically at 145 GHz. We have described our measurement setup, the measurement environments (outdoor
126
Figure 5.32: Comparison of analog beamforming in a P2P scenario.
microcell, outdoor D2D, and indoor), and the parameters extracted from the measurements. Most impor-
tantly, we surveyed the numerical results for path loss, delay dispersion, and angular dispersion. Some of
the key insights are as follows:
• For LOS, the path loss coefficient is on the order of 1.8, similar to what is observed in lower frequency
bands. The impact of ground reflections is minor in the situations we analyzed.
• For NLOS, the excess path loss (compared to free-space) is on the order of 10-30 dB, and generally
decreases with increasing distance between Tx and Rx in particular in the omnidirectional case, due
to the rich multipath. However, this result does not incorporate heavily shadowed locations.
• For the considered beamwidth (≈ 13°), delay dispersion is considerable. When considering the max-
dir delay spread, values are up to30 ns in D2D and indoor environments, and10 ns in microcellular
environments, with values up to150 ns for the omnidirectional case.
• Q-windows, which indicate the necessary length of cyclic prefixes, can be tens or even hundreds of ns
long for the max-dir case (and larger for the omni-case). Q-tapnumbers, which indicate the required
number of arbitrarily spaced equalizer taps, is considerably lower than that, indicating sparsity of
the channels, but still tens of taps might be required for, e.g.,20 dB signal-to-self-interference ratio.
127
• Angular spreads are smallest at elevated BSs, either indoor or outdoor. At the UE location, which
is usually surrounded by scattering objects, large ASs (many multiples of the antenna beamwidth)
were observed.
• The angular dispersion has a significant impact on the multi-user capacity. For dispersive channels,
digital beamforming to separate users coming from similar directions results in significant perfor-
mance advantages compared to simple beam selection.
While the measurement campaigns are among the largest ever done in this frequency range, the num-
ber of points and variety of investigated environments is still quite limited. Thus, the results presented
here can be considered a useful starting point for reality-based values of system design and performance
assessment but will be augmented by future measurement campaigns.
128
Chapter6
ConclusionsandFutureDirections
This dissertation presented the results of a Fourier-based analysis of extensive campaigns in the sub-7GHz
and THz in multiple scenarios. To evaluate the large dataset using Fourier-based analysis, it was necessary
to analyze the impact of the noise captured in the measurements and how it affected the estimated param-
eters. In Chapter 2, it was observed that the major impact of the noise is the overestimation in parameters;
the larger the noise, the larger the overestimation. To overcome this issue, noise thresholding was used
to minimize noise; however, the threshold is critical because it can impact the estimation by allowing too
much noise or discarding signal delay bins with noisy ones. This framework can also be helpful for HRPE
analysis to improve the estimation of parameters by noise reduction.
The first evaluated campaign is the sub-7GHz described in Chapter 3. A total of 400 measurements
were captured between SIMO, MISO, and MIMO points in two bands (2.4 GHz and 5-7 GHz) in different
LOS and NLOS environments, including Indoor, Indoor Office, and Outdoor Hotspots. The current state
of the art of analysis in the sub-7GHz does not show (to the best of our knowledge) a thorough channel
analysis with actual data for the 5-7GHz band. From this campaign, it was observed that the propagation
characteristics between the 5-6 GHz and 6-7 GHz are similar, allowing a more straightforward implemen-
tation of systems design for the 6-7 GHz. Additionally, an improvement in the signal-to-self-interference
ratio (i.e., Q
t
) was observed when using directional antennas. This effect is significant because it can
129
improve the spectral efficiency of OFDM systems when a reduced cyclic prefix is applied, an envisioned
feature of future versions of Wi-Fi.
Future work in this band is a window analysis of the channel parameters, given that the subsequent
WiFi systems [77] are expected to use channels up to 320 MHz (80,160, 320 MHz). The focus will be
to analyze channel parameters such as delay spread, Rice factor, interference quotient, or Qwindow or
Qtapnumber as a function of frequency. Even though the sub-7GHz campaign is vast, it does not include
trajectory routes or measurements in dynamic scenarios, which are also crucial for multiple applications
(e.g., Industry applications). Therefore, measurements must be conducted to evaluate channel parameters
and design optimal systems to overcome issues in dynamic scenarios (e.g., LoS-NLoS transitions in human
blockages, object obstructions, or turning around corners).
Next, we analyzed the THz campaign. This campaign covered multiple scenarios, like Microcellular,
D2D, and Indoor, where double-directional channel measurements inquasi-static scenarios were obtained
for posterior analysis. We first focused on the impact of environmental changes in the design of THz
communication systems (Chapter 4). Changing reflectors can increase MPCs power ( ≈ 4 dB in some
cases) angular and delay diversity of systems with limited dynamic range. Furthermore, we inspected
Indoor and office scenarios where small changes like using blinds or not or using e-glass in windows can
significantly impact the powers and angles of MPCs. It is essential to highlight that these changes may not
be significant when computing channel parameters, but they may affect the optimal design of a system
envisioned in those scenarios.
Chapter 5 detailed a Fourier-based analysis of the THz band measurement campaigns. Key insights
of the analysis are that the path loss coefficient for LoS is similar to free space propagation in lower fre-
quency bands. In the NLoS case, the excess loss (compared to free space) is between 10 to 30 dB. We
observed considerable delay dispersion even in the case of the strongest direction (i.e., max-dir), and it
was more significant for NLoS. This effect impacts the design of optimal receivers in the THz band; for
130
instance, it might affect the cyclic prefix duration if an OFDM system is implemented in these scenarios
(Q
win
). Similarly, Q
tap
values were smaller than Q
win
, but still quite significant. This parameter affects
the design of a Rake receiver structure because it will require a large number of fingers to collect the nec-
essary to satisfy theSIR
ISI
condition. We observed a significant spread in the UE location in the angular
domain because close objects interact with the receiver. This behavior is closely related to the multi-user
capacity, which should be considered when implementing beamforming strategies to improve the system’s
performance.
The THz campaign in Chapter 5 is the largest ever done in the 145-146 GHz range [51]. However,
the total number of points is still quite limited (e.g., 38 for D2D, 26 for Microcellular, and 4 for Indoor)
to produce models with statistical significance. The main reason for the limited number of points is the
considerable measurement time per location due to the VNA frequency scan and mechanical rotation of
the positioners. A Time-Domain (TD) sounder can obtain faster captures by sending a wideband OFDM
sounding signal over the bandwidth of interest. This allows us to measure dynamic scenarios with moving
objects, evaluate human blocking, and assess foliage absorption. For a double-directional channel capture
in dynamic scenarios, it is necessary to use horn antennas or phased arrays, allowing for a much faster
angular sweeping [90, 141].
Studies involving the analysis of the sub-7GHz and THz bands in the same location are also of great
interest. A multiband comparison to assess the behavior and similarities between sub-7GHz and THz bands
in multiple scenarios can provide insight for systems using both bands together, as discussed in Chapter
3 with the 2.4 GHz and 5-7 GHz bands. Similar studies have been carried out to compare sub-6GHz and
mm-wave bands [129]. Another application for multiband analysis is localization; for instance, new WiFi
systems are envisioned to work with channels up to 320 MHz [77]; a study to assess the impact on the
accuracy of localization systems given the channel’s bandwidth is essential for such applications. In the
THz band case, a higher accuracy (e.g., centimeter-level) can be achieved due to the large bandwidth (of
131
the order of GHz) ranging signal that can be used in these channels. A desirable feature that provides fine
time resolution, improving the range measurements’ accuracy [138]. To evaluate the accuracy, a study of
the1
st
and2
nd
components in the PDP concerning the actual Euclidean distance of the link is crucial. This
analysis can estimate the impact of time-of-arrival-based and time-difference-of-arrival-based localization
strategies.
Finally, to determine the maximum achievable data rate in both bands, evaluating the capacity in MU-
MIMO under different beamforming strategies (digital, analog) and power control schemes are necessary.
A study of this kind can help assess the performance of wireless communication under real conditions to
choose the best beamforming and power control strategy in MU-MIMO scenarios.
132
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Abstract (if available)

Abstract Next-generation wireless communication systems are envisioned to support new services with high data-rate demands. For this purpose, it is necessary to use accurate channel models based on detailed channel measurements to make realistic assessments. This dissertation presents the results of extensive measurement campaigns in the sub-7GHz (2.4 GHz and 5-7 GHz) and sub-THz (145-146 GHz) bands in multiple scenarios and a Fourier-based statistical channel model. First, a framework to analyze the impact of noise in channel parameters is presented. The most notorious effect is the overestimation of estimated parameters. Additionally, noise thresholding is analyzed, observing that a proper margin to minimize the noise can improve the estimation. Next, we evaluate a sub-7GHz campaign done in typical WiFi deployment scenarios (e.g., Food courts, Offices, Open cafes, and Plazas), obtaining 400 points between SIMO, MISO, and MIMO points.
Similarly, in the THz band, the scenarios selected for analysis were Indoor, D2D, and Microcellular (reaching up to 100 m Tx-RX distance in the last 2 cases). In both campaigns, multiple compound parameters such as Path Loss, RMS delay spread, and angular spread were modeled. Finally, the impact of building materials at the THz band and its implications in systems design is investigated; we found that modifying the MPCs can significantly impact diversity, temporal and angular. Similarly, the blockage impact on THz channels is analyzed from the UE side. The angular power distribution significantly affects the SNR loss when a blockage obstructs the strongest path in a link.

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Asset Metadata

Creator Gomez Ponce, Jorge Luis (author)

Core Title Channel sounding for next-generation wireless communication systems

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2023-05

Publication Date 04/18/2023

Defense Date 03/27/2023

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag 5G,5G and beyond,6G,channel modeling,channel sounding,Communications,OAI-PMH Harvest,propagation,RF,systems design,WiFi,wireless

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Molisch, Andreas F. (committee chair), Willner, Alan (committee member), (Golubchik, Leana)

Creator Email gomezpon@usc.edu,jolugome1989@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113038247

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