University of Southern California Dissertations and Theses

Multidimensional characterization of propagation channels for next-generation wireless and localization systems

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Multidimensional characterization of propagation channels for next-generation wireless and localization systems

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Content MULTIDIMENSIONAL CHARACTERIZATION OF PROPAGATION CHANNELS FOR
NEXT-GENERATION WIRELESS AND LOCALIZATION SYSTEMS
by
Seun Sangodoyin
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)
August 2018
Copyright 2018 Seun Sangodoyin
Dedication
To my mom, dad, sister and brother.
ii
Acknowledgments
Many people have contributed, either directly or indirectly, to this dissertation. The
research work presented herein has been carried out under the supervision of my academic
advisor Prof. Andreas F. Molisch at the department of Electrical Engineering, University of
Southern California.
First and foremost, I would like to express my deepest gratitude to my advisor Prof.
Andreas F. Molisch. The guidance, constructive criticism, technical insight and most espe-
cially patience afforded by Prof. Molisch are truly remarkable. He has patiently molded a
modest researcher out of miry clay and taught me the important principle of always asking
"why" whether you get the correct result or the incorrect one, and for this I will forever be
grateful. Secondly, I would like to express my sincere gratitude to Dr. Niranjayan Somasun-
daram for his help when I was in a dark cloud of uncertainty, his guidance on how to be a
scientific researcher and maturity expected for this type of work was absolutely invaluable.
Thirdly, I will like to express my gratitude to Dr. Jussi Salmi, who introduced to me to
the field of channel measurement and parameter extraction. He gave me the tools needed to
succeed in this field. Its rather unfortunate that I only got to work with him at a time when
I was not apt enough for the task at hand, nevertheless, his contributions to my growth will
always be cherished.
IwouldliketothankallmycollaboratorsandcolleaguesespeciallythosefromtheWireless
devices and systems group (WiDES) at the University of Southern California for their help
over the years.
iii
Finally and most importantly, I would like to thank my family for their unconditional
support and sacrifice during my studies.
iv
Contents
Dedication ii
Acknowledgments iii
List of Tables ix
List of Figures xii
Abstract xviii
1 Motivation 1
1.1 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Dissertation structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 List of publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Impact of Body Mass Index on UWB BAN Channels 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Measurement Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Limitations of our study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.1 Limitation of population . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.2 Limitation of BMI as a measure . . . . . . . . . . . . . . . . . . . . . 18
2.4.3 Limitation due to channel configuration and environment . . . . . . . 20
2.5 Data Evaluation and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.5.1 Mode of propagation of MPCs . . . . . . . . . . . . . . . . . . . . . . 23
2.5.2 Path gain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5.3 Shadowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5.4 Delay Dispersion Statistics . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5.5 Amplitude Fading Statistics . . . . . . . . . . . . . . . . . . . . . . . 31
2.5.6 Spatial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6 Implementation Recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.7 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.7.1 Capacity Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
v
2.7.2 Sub-group Analysis Approach . . . . . . . . . . . . . . . . . . . . . . 38
2.8 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3 A Measurement-Based Model of BMI Impact on UWB Multi-antenna
PAN and B2B Channels 42
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.1 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1.2 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Measurement Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.1 PAN setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3.2 B2B setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.3 Human subject selection . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 Limitations of our study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5 Data Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5.1 PAN Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5.2 B2B Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.6.1 PAN Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.6.2 B2B Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.7 Implementation Recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.8 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.8.1 Baseline path gain and shadowing modeling approach . . . . . . . . . 68
3.8.2 Sub-group Analysis approach . . . . . . . . . . . . . . . . . . . . . . 71
3.8.3 Capacity Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.9 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4 A Measurement-based Model for Outdoor Near-ground Ultrawideband
Channels 77
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1.1 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.2 Measurement Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4 Measurement Data Processing and Results . . . . . . . . . . . . . . . . . . . 86
4.4.1 Pathloss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.4.2 Shadowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.4.3 Fading Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.4.4 Delay Dispersion Statistics . . . . . . . . . . . . . . . . . . . . . . . . 97
4.5 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.6 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
vi
5 Statistical Modeling of Ultrawideband MIMO Propagation Channel in a
Warehouse Environment 105
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.1.1 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2 Measurement Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.3 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4 Measurement Data processing and Results . . . . . . . . . . . . . . . . . . . 111
5.4.1 Path Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4.2 Shadowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.5 Angular Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.5.1 MPC parameter extraction using CLEAN . . . . . . . . . . . . . . . 116
5.5.2 Clustering of MPCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.5.3 LOS Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.5.4 NLOS Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.6 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.7 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6 Cluster Characterization of 3D MIMO Propagation Channel in an Urban
Macrocellular Environment 142
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6.1.1 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.1.2 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.2 Measurement campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.2.1 Measurement environment . . . . . . . . . . . . . . . . . . . . . . . . 145
6.2.2 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.3 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.3.1 Time-domain representation . . . . . . . . . . . . . . . . . . . . . . . 149
6.3.2 Parameter extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.4.1 Path distribution in the environment . . . . . . . . . . . . . . . . . . 152
6.4.2 Clustering analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.4.3 Clustering statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.4.4 Cluster polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.4.5 Pathloss and shadowing model . . . . . . . . . . . . . . . . . . . . . . 162
6.4.6 Dense multipath component (DMC) . . . . . . . . . . . . . . . . . . 164
6.5 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.5.1 RMS delay spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.5.2 Directional spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.6 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
7 Conclusion 175
vii
Reference List 177
viii
List of Tables
2.1 Hardware used in the channel measurement . . . . . . . . . . . . . . . . . . . . 14
2.2 Measurement parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Channels on the body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 International classification according to BMI . . . . . . . . . . . . . . . . . . 17
2.5 Parameters extracted for various channels and BMI categories . . . . . . . . 26
2.6 Average path gain values for sample channel from measurement with harness
alone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7 Passing rate of K-S test at 5% significance level for BMI 1 F2F channel . . . . . 31
2.8 Passing rate of K-S test at 5% significance level for τ
rms
for BMI 1 F2H channel . 31
2.9 Passing rate of K-S test at 5% significance level . . . . . . . . . . . . . . . . 32
2.10 Maximum deviationD
v
values for Capacity CDFs for BMI 1, 2, 3 F2F channels 38
2.11 Parameters extracted from BMI categories sub-groups . . . . . . . . . . . . . 39
3.1 Measurement parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2 Hardware used in the channel measurement . . . . . . . . . . . . . . . . . . . . 50
3.3 International classification according to BMI . . . . . . . . . . . . . . . . . . 51
3.4 Path gain and shadowing parameters (obtained from sub-banding processing
approach) for channels from various BMI categories in PAN . . . . . . . . . 57
3.5 Linear fit parameters for
˜
G
L
and ˆ μ
ˆ s
over sub-bands in B2B network. . . . . 62
3.6 Passing rate of K-S test at 5% significance level for X
env
. . . . . . . . . . . . . 70
ix
3.7 Comparison of parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.8 Parameters extracted from BMI categories sub-groups in PAN measurements . . . 71
3.9 Parameters extracted for various channels and BMI categories in PAN and B2B
networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.10 Parameters extracted for various channels and BMI categories in the B2B
channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.11 Capacity values for various channels and BMI categories in the PAN and B2B
network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.1 Hardware description of the UWB channel sounder . . . . . . . . . . . . . . 84
4.2 Antenna height configurations . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3 UWB Multitone Signal Parameters . . . . . . . . . . . . . . . . . . . . . . . 86
4.4 distane-dependent pathloss exponent γ . . . . . . . . . . . . . . . . . . . . . 90
4.5 Passing Rate of K-S Hypothesis test at 5% Significance Level . . . . . . . . . 95
4.6 Regression line parameters for m-parameter charcterization . . . . . . . . . . 97
4.7 Passing Rate of K-S Hypothesis test at 5% significance level . . . . . . . . . 99
4.8 rms delay-spread-distance dependent parameters . . . . . . . . . . . . . . . . 100
4.9 Results of Channel extracted parameters at USC campus . . . . . . . . . . . 101
4.10 Results of Channel extracted parameters from Catalina Island . . . . . . . . 101
4.11 Comparing Near-ground channel parameters from different papers . . . . . . 102
5.1 Channel measurement parameters . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2 Hardware used in the UWB MIMO channel measurement . . . . . . . . . . . 112
5.3 Extracted Large Scale Channel Parameters . . . . . . . . . . . . . . . . . . 114
6.1 Channel sounder configuration. . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.2 Passing rate of K-S test at 5% significance level. . . . . . . . . . . . . . . . . 161
6.3 Passing rate of K-S test at 5% significance level. . . . . . . . . . . . . . . . . 164
6.4 Extracted parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
x
6.5 Comparing extracted channel parameters from different papers. . . . . . . . 174
xi
List of Figures
2.1 (a) anechoic chamber (b) indoor lab environment in the Ultralab at USC . . 13
2.2 UWB BAN measurement setup with harness on the body . . . . . . . . . . 15
2.3 Sample Antenna and harness setup on the body . . . . . . . . . . . . . . . . 16
2.4 (a) F2F (b) F2S (c) F2H (d) H2S (e) F2B (f) H2B (g) H2L . . . . . . . . . 16
2.5 PDF of the path gain in the (a) H2S in the anechoic chamber (b) F2S channels
in the indoor lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 APDP from sample measured channels in the indoor lab environment . . . . 23
2.7 Empirical CDF and corresponding Gaussian fit of path gain for F2H channel
in (a) anechoic chamber (b) indoor lab environments. . . . . . . . . . . . . . 25
2.8 Antenna placement for measurements with harness alone . . . . . . . . . . . 28
2.9 Empirical CDF and corresponding Gaussian fit for the shadowing gain in the
F2F channel of BMI 1 in both anechoic and indoor lab environments. . . . 29
2.10 Empirical CDF and corresponding Gaussian fit of τ
rms
in the F2H channel in
(a) anechoic chamber (b) indoor lab environment . . . . . . . . . . . . . . . 30
2.11 Ricean distribution fit for small-scale amplitude fading in F2F anechoic chan-
nel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.12 Emprical CDF of the correlation magnitude for (a) TX array for BMI 1 in
anechoic for F2F channel (b) RX array for BMI 1 in anechoic for F2F channel 35
2.13 Emprical CDF and model fit of capacity for (a) BMI 1 F2F (b) BMI 2 F2F
(c) BMI 3 F2F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
xii
3.1 (a) TX antenna placement in the anechoic chamber (b) platforms for test
subject placements for PAN and B2B setups . . . . . . . . . . . . . . . . . . 46
3.2 (a) UWB SIMO PAN measurement setup (b)UWB MIMO B2B measurement
setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 (a) hip (b) front (c) back Channels . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 Empiricalcumulativedistributionfunction(CDF)oforientation-averagedmean
path gain Φ (dB) over ensembles of test subjects with corresponding Gaussian
fit for (a) hip (b) back channels for PAN. . . . . . . . . . . . . . . . . . . . . 56
3.5 Linear fit for EBSG (μ
s
) at various BMI categories (a) hip (b) front channels
in PAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6 Empirical CDF over of the correlation magnitude for RX array over ensemble
of test subjects and body orientations for BMI 1 category in the back channel
in PAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.7 Linear fit for EPBSG (ˆ μ
ˆ s
) in the (a) intra- (b) inter-BMI categories in B2B
network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.8 Empricial CDF of the correlation magnitude for (a) TX array (b) RX array
over ensemble of test subjects and body orientations for BMI 1 for Front
Channel in B2B network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.9 Linear regression fit for path gain over distance . . . . . . . . . . . . . . . . 69
3.10 Empirical CDF and corresponding Gaussian fit for (a) shadowing (X
env
) due to the
environment (b)X
b
at a select distance (c) standard deviation of X
b
for all distances 70
3.11 Emprical CDF and model fit of capacity for (a) BMI 1 (b) BMI 2 (c) BMI 3 72
4.1 The Measurement Site at USC Wrigley Marine Science Center on Catalina
Island. CA . USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Flat terrain Measurement site . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.3 Hilly terrain Measurement site . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4 UWB Channel Sounder setup . . . . . . . . . . . . . . . . . . . . . . . . . . 84
xiii
4.5 Antennas at 20cm height above ground . . . . . . . . . . . . . . . . . . . . . 85
4.6 Channel Impulse response for Tx,Rx separation of 20m antenna height Tx
10cm-Rx 10cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.7 Channel Impulse response for Tx,Rx separation of 200m antenna height Tx
10cm-Rx 10cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.8 Scatterplot of normalized pathloss for all measurements at Tx200cm-Rx200cm
antenna height configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.9 Scatterplot of normalized pathloss for all measurements at Tx10cm-Rx10cm
antenna height configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.10 CDF plot of frequency-dependent pathloss exponent (κ) . . . . . . . . . . . 93
4.11 CDF plot of shadowing component atTx200cm_Rx10cm antenna height con-
figuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.12 CDF of the RMS delay-spread for antenna height Tx20cm_Rx_20cm . . . . 98
4.13 CDF of the RMS delay-spread for antenna height Tx50cm_Rx_50cm . . . . 99
4.14 RMS delay-spread as a function of distance at Tx50cm_ Rx50cm . . . . . . 100
5.1 USC Warehouse Facility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.2 Floor map of the first floor of the warehouse. . . . . . . . . . . . . . . . . . 109
5.3 Floor map of the basement of the warehouse. . . . . . . . . . . . . . . . . . 110
5.4 Channel sounder measurement setup in the warehouse environment. . . . . 111
5.5 Distance dependency of the path gain in the LOS and NLOS scenarios. . . 114
5.6 Frequency dependency of the path gain in the LOS and NLOS scenarios. . . 116
5.7 Scatter plot of the unclustered MPCs. (5 m LOS measurement.) . . . . . . 118
5.8 Clustered MPCs with KPowerMeans algorithm. (5 m LOS measurement.) . 119
5.9 Figure demonstrating that the intra-cluster DoD and DoA are independent,
in the LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.10 Figure demonstrating that the intra-cluster DoD and ToA are independent,
in the LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
xiv
5.11 Intra-cluster DoD and DoA for the LOS cluster, in the LOS environment. . 122
5.12 Intra-cluster DoD and DoA for the NLOS clusters, in the LOS environment. 122
5.13 Intra-cluster ToA modeling for the LOS and NLOS clusters, in the LOS envi-
ronment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.14 Intra-cluster power decay constant for different cluster ToA, in the LOS envi-
ronment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.15 Figure demonstrating that the cluster DoD and DoA are not independent, in
the LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.16 Figure demonstrating that the cluster DoD and ToA are not independent, in
the LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.17 Cluster DoD modeling in the LOS environment. . . . . . . . . . . . . . . . 125
5.18 Figure comparing the measured and simulated conditional densityDoA|DoD,
for the LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.19 Modeling the Excess cluster ToA for different propagation scenarios in the
LOS environment (a) Backwall reflection (b) Double bounce scattering with
DoD∗DoA< 0 (c) Double bounce scattering with DoD∗DoA> 0. . . . . 127
5.20 Inter-cluster power decay for different propagation scenarios in the LOS envi-
ronment (a) Backwall reflection (b) DoD∗DoA < 0 (c) DoD∗DoA > 0.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.21 Average number of clusters as a function of measurement distance in the LOS
environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.22 Intra-cluster DoD and DoA modeling in the NLOS environment. . . . . . . 131
5.23 Intra-cluster ToA modeling in the NLOS environment. . . . . . . . . . . . . 132
5.24 Intra-cluster power decay modeling in the NLOS environment. . . . . . . . 133
5.25 Cluster DoD modeling in the NLOS environment. . . . . . . . . . . . . . . 133
5.26 Figure comparing the measured and simulated conditional densityDoA|DoD,
for the NLOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
xv
5.27 Modeling the excess cluster ToA for different propagation scenarios in the
NLOS environment (a) Backwall reflection (b) Double bounce scattering with
DoD∗DoA< 0 (c) Double bounce scattering with DoD∗DoA> 0. . . . . 135
5.28 Inter-cluster power decay for different propagation scenarios in the NLOS
environment (a) Backwall reflection (b) DoD∗DoA< 0 (c) DoD∗DoA> 0. 136
5.29 Capacity and RMS delay spread validation for the LOS channel model. . . . 138
5.30 Capacity and RMS delay spread validation for the NLOS channel model. . . 139
6.1 Map of measurement area in Cologne. . . . . . . . . . . . . . . . . . . . . . . 143
6.2 TX view of the urban macrocell in Cologne. . . . . . . . . . . . . . . . . . . 146
6.3 Illustration of channel measurement sounder. . . . . . . . . . . . . . . . . . . 148
6.4 TX antenna array (PULPA) and RX antenna array (SPUCPA) . . . . . . . 148
6.5 System diagram of the channel sounder setup and data processing. . . . . . . 149
6.6 Illustration of receiver position 47. . . . . . . . . . . . . . . . . . . . . . . . 153
6.7 (a) DoD (az-delay) plot of extracted MPCs. (b) DoD (el-delay) plot of
extracted MPCs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.8 Clusters at RX position 47. . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.9 Distribution of the intra-cluster angular (centered) parameters of rays for a
sample location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.10 Distribution of the inter-cluster angular parameters. . . . . . . . . . . . . . . 159
6.11 Distribution of the number of clusters. . . . . . . . . . . . . . . . . . . . . . 160
6.12 PDF of cluster shadowing gain. . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.13 Distribution of the XPR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
6.14 Linear regression fit for pathloss and delay. . . . . . . . . . . . . . . . . . . 162
6.15 CDF of the bulk shadowing gain. . . . . . . . . . . . . . . . . . . . . . . . . 163
6.16 Comparison of (a) measured (h) (b) residual ( h− (S(θ
sp
))) and (c) modeled
DMC Power-azimuth-delay-profile (PADP) at Tx end for Rx Position 47. . . 164
6.17 Empirical CDF of the fraction of power contained in the DMC. . . . . . . . 167
xvi
6.18 Empirical CDF of DMC (a) delay parameter ˜ α
1
(dB) (b) spatial parameter
κ
ϕ,T
(dB) with corresponding Gaussian fit. . . . . . . . . . . . . . . . . . . . 168
6.19 Empirical CDF of rms-delay spread computed from measurement and corre-
sponding simulated rms-delay spread obtained from the channel model. . . 169
6.20 Empirical CDF of the (a) DoD σ
el
(b) DoD σ
az
computed from measurement
data and corresponding simulation values obtained from the model. . . . . . 170
xvii
Abstract
Propagation channel measurement and modeling are essential for design, simulation and
deployment of wireless systems for communication, localization and ranging. These channel
models typically provide a closed-form description for complicated electromagnetic transmis-
sion process of reflection, scattering, diffraction and shadowing. Most channel models are
empirically parameterized while the statistics of these parameters can be inferred as well.
Since wireless systems are deployed in several scenarios and environments, designers of wire-
less systems/networks are typically interested in scenario-specific models, which allows the
optimization of their system for that particular scenario or environment. These scenarios
range from indoor to outdoor, human body and or even some with geographical variations
at times.
With the growing demand for higher data rate, improved precision in localization systems
and reliable communication infrastructure in different applications, more advanced wireless
architectures will be needed in the nearest future. The development of any such future
wireless system will require new propagation channel models to either complement existing
ones or as new stand-alone models.
This thesis deals with measurement-based modeling of wireless propagation channels.
Since channel measurement and modeling is a very broad field (albeit one in which few
institutions or companies are working), I have concentrated on the following three areas:
• Channels for "wireless healthcare" applications. It is expected that the human
body tissues will have a significant effect on electromagnetic wave propagation around
xviii
the human body especially when various body types with different dimensions and
tissue properties are considered. Therefore, the impact of Body Mass Index (BMI)
on ultrawideband multi-antenna Body Area Network (BAN), Personal Area Network
(PAN) and Body-to-Body (B2B) network propagation channels was investigated in
this thesis. A large number of human test subjects that is statistically sufficient for
creating a comprehensive channel model, which had otherwise not been done in prior
research in the literature were considered. The test subjects were divided into cate-
gories based on their BMI values. A comparison of statistics among the BMI categories
reveals considerable differences emphasizing the fact that the classic propagation chan-
nel parameters are in fact BMI dependent. Parameters such as path gain showed a
monotonic decrease across the BMI categories with values ranging from 1-2 dB to
almost 13 dB in some channels. In this thesis, I have propose a propagation channel
model for the BMI dependent parameters and validated that this model can reproduce
the measured channel capacities.
• Ultrawideband(UWB)and/ormultiple-input-multipleoutput(MIMO)chan-
nels in the context of localization and ranging systems. A statistical channel
model of UWB and/or MIMO in the context of localization and ranging systems is pro-
vided in this thesis by studying electromagnetic wave propagation when transceivers
are i) near-ground i.e., in close proximity to the ground and ii) in a warehouse envi-
ronment.
– In the near-ground case, transceiver heights were varied from 200 cm to 10 cm
with measurement conducted over distances ranging 10 m to 200 m. Distance-
and frequency-dependent pathloss component and shadowing gain were found to
increase with increasing antenna proximity to the ground with values ranging
from 2.14 to 3.60 in distance-dependent pathloss component, 0.98 to 1.24 in the
frequency-dependent pathloss exponent while shadowing gain varied 2.8 to 8.52
xix
dB. Also, a 1 ns ranging accuracy was achieved from the measurement setup used
for this work.
– AUWBMIMOdouble-directionalchannelmodelwasdevelopedforthewarehouse
environment. The model is especially important for Radio Frequency Identifici-
ation (RFID) tag localization in the warehouse environment. Multipath compo-
nents were found to naturally grouped into clusters in the warehouse environment
and as such the statistics of the cluster parameters observed has been provided.
The cluster channel model proposed in this warehouse environment simplifies sim-
ulation and systems development.
• Three-dimensional (3D) MIMO channels for urban macro/micro cellular
networks. Using an advanced antenna array (3D massive MIMO) system, an exten-
sive propagation channel measurement campaign in an urban macrocellular environ-
ment was conducted and a comprehensive channel model that includes both specular
and diffuse contributions of multipath components in this type of environment has
been provided in this thesis. A cluster-based approach was also implemented since
multipath components were found to naturally grouped into clusters in type of urban
environment. Cluster angular and delay spread parameters were modeled using a log-
normal distribution while cluster angle-of-arrival and departure were modeled using a
Laplacian distribution. The diffuse component were found to be a crucial part of the
propagation channel with fraction power contribution of about 15 %, therefore diffuse
component modeling is essential in an urban macro/micro cellular environment.
In all of these areas, there are very few (or none) existing measurement results. An
extensive description of all measurement campaigns and relevant channel models inferred
(with validation) has been provided in this thesis. Results of this work can be used for
realistic system design in 4G LTE-Advanced and 5G networks and has also found its way
into the 3GPP standardization work.
xx
Chapter 1
Motivation
Wireless communications has had an immeasurable impact on our everyday lives. It
affords benefits that range from the convenience provided by the traditional cellular commu-
nication, which has changed the habits and mobility of workers, to wireless sensor networks
monitoring factory equipment and wireless positioning systems localizing trucks that have
goods identified by wireless RF (Radio Frequency) tags. However, increasing demand for
higherdata-rate, lowernetworklatencies, betterenergyefficiency, reliableubiquitousconnec-
tivity and improved precision in localization systems coupled with the shortage of available
spectrum has resulted in the pursuit of new ways to improve the wireless communication and
localization systems. A lot of ideas have been proposed for solving these challenges towards
the next-generation (5G and beyond) wireless architecture. These ideas include; wireless
software-defined networks; use of millimeter wave spectrum; big data and mobile cloud com-
puting; scalable Internet of Things (IoTs); device-to-device connectivity and deployment
of massive MIMO systems. In addition, the signal processing methods widely discussed
towards the next-generation wireless implementation include adaptive beam forming, joint
space-time equalization, multi-user detection, interference cancellation, and spatial diversity.
The development of any such future wireless and localization systems or signal processing
method will require new propagation channel models.
This thesis deals with measurement-based modeling of wireless propagation channels,
particularly those geared towards next-generation applications. It mostly comprises of mea-
surementofthewirelesschannelsusingpropagationchannelsounderswithadvancedantenna
systems. In addition to this is the estimation of the space, time, frequency and polarization
dependent double direction MIMO radio channel model parameters from these extensive
1
channel sounding measurements using high resolution parameter extraction algorithms such
as RIMAX (an iterative maximum likelihood algorithm). The term "double-directional"
refers to the fact that the channel is characterized by directional properties at both ends of
the radio link, revealing the overall spatio-temporal multipath structure of the MIMO propa-
gation channel. An advanced channel sounding measurement setup along with sophisticated
estimation techniques allows separation of the influence of the measurement equipment from
the properties of the wireless channel itself. Such technique provides a general character-
ization of the radio channel at a certain signal bandwidth and specified carrier frequency,
withoutimposinganyrestrictiveassumptionsonaspecificcommunicationschemeorantenna
configuration. The obtained results of such a measurement-based multidimensional channel
modeling (MBMDCM) scheme can be later applied for analyzing specific, realistic wireless
and localization systems with given antennas and other operational parameters in any given
(specific) scenario or environment.
The specific areas considered in this work are discussed below:
• Channels for "wireless healthcare" applications: Wireless Body Area Network
(BAN), Personal Area Network (PAN) and Body-to-Body (B2B) networks have many
important applications such as wearable communications devices, vital sign monitor-
ing and Internet-of-Things. Wireless propagation in on/off-body channels has been
measured and modeled in the past. However, a crucial element that is usually ignored
is the impact of the body size of the user – a 50 kg person obviously creates a different
channel than a 150 kg person. The status-quo ’one-size-fits-all’ approach to channel
characterizationinBAN,PAN,andB2Bnetworksisthusincomplete. Hence, achannel
model that takes this BMI dependency into consideration is needed.
• Ultrawideband (UWB) and/or multiple-input-multiple output (MIMO)
channels in the context of localization and ranging systems:
2
– Localization in warehouse channels: UWB systems have many envisioned applica-
tions including real-time tracking of assets, personnel, and hospital patients and
could especially be of great use in locating items in a warehouse environment. For
example, UWB as of late has found use in radio-frequency identification (RFID)
technology, which is naturally deployed in warehouse environment, and in UWB-
basedwirelesssensornetworks, whichcouldeventuallyfinduseinawarehouse-like
environment. However, there are no wireless propagation channel models avail-
able for the warehouse environment. The warehouse environment is unique in its
geometric/structural layout, which is often sparse with storage racks or shelves
all demarcated into aisles. This constitute a unique propagation channel, whose
properties need to be explored for system design and simulation. The task of
providing such as channel model has been undertaken in this thesis.
– Ranging in Near-ground channels: Deployment of wireless devices with
transceivers in close proximity to the ground has become increasingly attractive
for a wide range of applications such as distributed sensor networks and broad-
band tactical communications. Furthermore, the use of UWB signals is attractive
for these communications due to their robustness and their suitability for preci-
sion ranging and localization. For the development and performance analysis of a
UWB near-ground system, accurate channel models are required. Since there are
no measurements and/or models detailing ultrawideband, near-ground channels
in an outdoor environment, this is remedied with results provided in this thesis.
• Three-dimensional (3D) MIMO channels for urban macro/micro cellular
networks: Multidimensional characterization of outdoor urban macro/micro cellular
propagationchannelsisessentialfortheanalysisanddesignofnext-generation(5Gand
beyond) cellular massive MIMO systems. Since most massive MIMO arrays will extend
into two or three dimensions, an understanding of three dimensional (3D) parameters
(i.e., azimuth and elevation) of the multipath components (MPCs) is required. There is
3
a dearth of investigations of 3D MIMO propagation channel measurements and model-
ing in urban environment, therefore our work fills this gap by provided a comprehensive
measured-based channel model with the inclusion of the Dense Multipath Components
(DMC), which has never been included in modeling of this type .
1.1 Challenges
The Challenges in performing channel measurements arises from a number of factors:
• Dealing with sensitive measurement equipment in a complex environment that can give
rise to a lot of different effects requires an extremely careful planning and execution of
all measurement campaign.
• High-resolution extraction is difficult and time-consuming, but should be done because
it results in a description that is much more flexible and genral than a "straighfroward
measurement if transfer function between arrays in particular, this description becomes
independent of the antennas that were used during the measurements.
1.2 Contributions
The details of the contributions from each area of work in this thesis are provided below;
• Channels for "wireless healthcare" applications: Impact that BMI has on BAN, PAN
and B2B networks was investigated. Extensive report of the various channel measure-
ments conducted that employed UWB multi-antenna array setup has been provided
in this thesis. Estimates and statistics of extracted propagation channel parameters
such as path gain, shadowing gain and rms delay spread, amplitude fading and spatial
correlation coefficients are provided. Results from system performance analysis has
also been provided.
4
• Ultrawideband(UWB)and/ormultiple-input-multipleoutput(MIMO)channelsinthe
context of localization and ranging systems was investigated.
– Details on a MIMO channel measurement campaign performed in a warehouse
environment for Line-of-sight and Non-line-of-sight (NLOS) scenarios have been
provided in this thesis along with all large scale parameters extracted. A cluster-
based closed form model for the warehouse environment was also provided in this
work.
– An extensive report on the channel measurement campaign performed using a
developed channel sounder which allows UWB measurements at distances up to
several hundred meters has been presented in this thesis. Estimates of chan-
nel parameters extracted are also provided while observing their dependency on
antenna heights.
• Three-dimensional (3D) MIMO channels for urban macro/micro cellular networks: In
this work, a detailed description of the measurement setup and procedure using an
advanced polarimetric wideband Full-dimensional MIMO channel sounder with mas-
sive number of antenna elements is provided. Multipath components (MPCs) were
extracted through a high-resolution algorithm, and grouped into clusters, from which
intra- and inter- cluster statistics were derived. Parameterization of the model for
the Dense Multipath Components (DMC) in the measured environment was also per-
formed.
In all these areas, there are very few (or none) existing measurements results. Output of
this work serves to enable more realistic system design especially in these scenario-specific
cases.
5
1.3 Dissertation structure
This thesis has been mainly written based on publications [1]-[12], which all have been
previously authored by this author. In particular, all the research results presented in this
thesis have been previously reported in those publications.
The content of this thesis is organized in seven chapters as follows. Chapter 1 introduces
the context of the research field of this thesis, and provides an overview and principles
of MIMO channel measurement and modeling while giving short insight into challenges
experienced and finally itemizing contributions of each aspect of the research area looked
into. In Chapter 2 and 3, the impact of body mass index on BAN, PAN and B2B network
channels has been investigated based on extensive measurements on 60 human test subjects
in different environments – anechoic and indoor Lab. A comprehensive channel model was
presented, which factors in the BMI dependence of channel parameters. The channel model
presented in BAN, PAN and B2B models were validated using channel capacity. In Chapter
4, thecharacteristicsofMPCinawarehouseenvironmentareestablishedwithacluster-based
channel model while propagation channel model with antenna proximity to the ground are
alsodevelopedandpresentedinchapter5. Chapter6isdedicatedforchannelcharacterization
in an 3D urban macro/micro-cellular environment, with specular modeled using a cluster-
based approach while diffuse components in the environment was also modeled. Conclusions
are inferred in chapter 7.
1.4 List of publications
Selected publications relevant to this thesis have been presented below.
1. S. Sangodoyin , S. Niranjayan, A.F. Molisch, "A Measurement Based Model for Out-
door Near-ground Ultrawideband Channels" IEEE Transaction on Antennas and Prop-
agation, Vol. 64 No. 02, February 2016.
6
2. S. Sangodoyin, R. He, V. Kristem, A.F. Molisch, "Statistical Ultrawideband Propa-
gation Channel Model for a Warehouse Environment" IEEE Transaction on Antennas
and Propagation, Vol. 64 No. 09, September 2016.
3. S.Sangodoyin,V.Kristem, C.U.Bas, M.Kaeske, J.Lee, C.Schneider, G.Sommerkorn,
J. Zhang, R. Thomae, and A. F. Molisch, "Cluster Characterization of 3D MIMO Prop-
agation Channel in an Urban Macrocellular Environment" accepted to IEEE Transac-
tions on Wireless Communications.
4. S. Sangodoyin and A. F. Molisch, "Impact of Body Mass Index on Ultrawideband
MIMO BAN Channels - Measurements and Statistical Model" accepted to IEEE Trans-
actions on Wireless Communications.
5. S. Sangodoyin and A. F. Molisch, "A Measurement-Based Model of BMI Impact on
UWBMulti-antennaPANandB2BChannels"acceptedtoIEEETransactionsonCom-
munications.
6. S. Sangodoyin, V. Kristem, C. U. Bas, M. Kaeske, J. Lee, C. Schneider, G. Som-
merkorn, J. Zhang, R. Thomae, and A. F. Molisch, "Cluster-based Analysis of 3D
MIMO Channel Measurement in an Urban Environment", MILCOM 2015, Tampa.
FL, 26-28 October 2015
7. S. Sangodoyin, S. Niranjayan and A. F. Molisch, "Ultrawideband Near-Ground Out-
doorPropagationChannelMeasurementsandModeling"inProc. 7thEuCAP,Gothen-
burg, Sweden. April 2013, pp.3034-3038
8. S. Sangodoyin, R. He, A. F Molisch, V. Kristem and F. Tuvesson, "Ultrawideband
MIMO Channel Measurements and Modeling in a Warehouse Environment"in Proc
IEEE ICC 2015, London, UK, 8- 12 June 2015
9. S. Sangodoyin and A.F Molisch, "Body Mass Index Effect on Ultrawideband MIMO
BAN Channel Characterization"in Proc VTC Fall 2017, Montreal, CANADA)
7
10. S. Sangodoyin and A.F Molisch, "Capacity Measurements for Body Mass Index Depen-
dent Ultrawideband MIMO BAN Channels"in Globecom Dec. 2017, Singapore
11. S. Sangodoyin and A.F Molisch, "Experimental Characterization of the Dependence of
UWB Personal Area Networks Channels on Body Mass Index" accepted at IEEE ICC
2018, Kansas City, Missouri, May 20-24 2018.
12. S. Sangodoyin and A.F Molisch, "Experimental Investigation of the Impact of BMI
on Ultrawideband MIMO Body-to-Body Networks" accepted at VTC Fall 2018, Porto,
Portugal.
8
Chapter 2
Impact of Body Mass Index on UWB
BAN Channels
2.1 Introduction
In recent years, there has been an increased interest in Wireless Body Area Networks
(BANs) because of their potential application in areas such as healthcare monitoring, surveil-
lance and sports. Vital medical information of patients such as body temperature, heart rate
and blood pressure can be obtained through biomedical sensors attached to the human body
and wirelessly transmitted to a hub node (typically a cellphone) carried on the body [1].
Some of these sensors have already started to permeate the market in the form of pulse mon-
itoring gloves, daily-exercise tracking wristbands and other wearable IoT devices. Additional
devices, particularly in patient monitoring, are expected to emerge in the near future.
Ultrawideband(UWB)radiotechnologyhasbeenconsideredovertheyearsasapromising
candidate to enhance communication and localization in scientific, military, and industrial
applications [2, 3, 4, 5]. UWB signals are defined as either having more than 20% relative
bandwith or more than 500 MHz absolute bandwidth [6] and are permitted to operate in the
3.1-10.6 GHz frequency band by the Federal Communications Commission [7] in the USA,
while occupying 4.2-4.8 and 6-8.5 GHz bands in Europe, and 3.4-4.8 and 7.25-10.25 GHz
bands in Japan [8]. UWB radio, due to its low power, high data rate, and robustness to
fading has been suggested as the technology of choice for implementing BANs. Also, recent
9
suggestions for improving BAN communications includes the use of Multiple-Input-Multiple-
Output (MIMO) antennas to increase channel capacity [9] and robustness of the channel to
fading [10].
In order to develop any reliable wireless system, it is essential that the channel in which
thesystemwilloperatebecharacterized. Hence, comprehensiveandrealisticcharacterization
of the on-body channel with a realistic model is essential.
It has been established through theoretical and practical investigation that the character-
istics of narrowband and UWB channels are remarkably different [11, 12, 13, 14, 15, 16, 17].
Furthermore, in BANs, electromagnetic (EM) waves transverse the human body either via
surface waves or diffraction mechanisms [10] and it is expected that the human body tissues
will have a significant effect on the propagation especially when various body types (with dif-
ferent dimensions and tissue properties) are considered [18]. The Body Mass Index (BMI) is
a measure of human body fat based on height and weight [19, 20] and can thus be anticipated
to be a contributing factor to the characteristics of any on/off body wireless propagation.
For medical applications, modeling the BAN on people with very high BMI is particularly
important, since it is exactly this user group for whom medical BANs are especially relevant.
However, most previous measurements and models considered test subjects with BMI < 25.
2.1.1 Related works
A number of papers [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 18, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47] in the literature have provided BAN models in the cm (below
10 GHz) frequency range.
1
These models range from narrowband to ultrawideband and were
derived either analytically, through numerical simulation or by actual measurements.
We can categorize existing results as:
1
There are also models for mm-wave BAN channels; due to the significantly different propagation char-
acteristics in that frequency range, we do not survey them here.
10
• Narrowband models: Refs. [21, 22, 23, 24, 25, 26, 27, 28, 30, 29, 31, 32] provide path
gain models for propagation along/around the human body. These papers are based on
analyticalcomputation[21,22,23,24,25,26], numericalsimulation[27], measurements
with phantoms [28], measurements with human test subjects in an anechoic chamber
[29], [30], indoor environment [31] and outdoor environment [32]. The most common
frequency band for those measurements is 2.45 GHz [21, 22, 23, 24, 25, 28, 32, 31, 30]
although 915 MHz [26] and 4.5 GHz [29] have been measured as well. A Finite-
dimension time-domain (FDTD) simulation was done to develop BAN models at 400
MHz and 900 MHz in [27]. Narrowband static and dynamic measurements were
conducted around 402, 900 and 2400 MHz frequency bands in [44]. These measure-
ments made use of 20 human test subjects – both male and female. Also, a dynamic
characterization of BAN communication channel at 2.4 GHz was conducted on 8 adult
subjects in [45]. Narrowband measurements were conducted at 2.36 GHz using 5 adult
test subjects performing ’everyday’ activity in [46] while 3 adult subjects were used for
narrowband measurement at 2.36 GHz in [47]. An open-access database, which con-
tains hundreds of hours of all narrowband measurements conducted in [44, 45, 46, 47]
can be accessed in [48].
• Ultrawideband models: Refs. [33, 38, 34, 35, 36, 18, 37, 39, 40] also provides pathloss
models. Analytical derivations are provided in [37], numerical simulations are done in
[18] while other papers were based on measurements in anechoic chamber [38, 34, 36]
and indoor/office are provided in [33, 38, 34, 35]. The frequency bands used varies
from 3-6 GHz in [33, 35] to 2-8 GHz in [36] and 3-10 GHz in [38], [42, 43].
Most of the above models, irrespective of the frequency band, are based on measurements
or analysis on a single person or single phantom with the exception of [44, 45, 46, 47, 48], in
which narrowband measurements were conducted on a larger sample size of test subjects.
Furthermore, [39] analyzed the difference between propagation characteristics of three people
11
with different weights. The measurement was conducted in the UWB frequency band of 3-
5 GHz in an anechoic chamber, however the number of samples measured is too small to
render the results statistically significant. [41] studied the effects of body shape and gender
on BAN by conducting measurements on a total of 16 people (8 males and 8 females),
however this was done for a narrowband channel (centered at 2.36 GHz). [40] conducted
UWB measurements in the 3-10 GHz frequency band using 8 different human body sizes
and shapes. This was done using a small sample size and also only the pathloss analysis was
provided in the paper. We are unaware of any ultrawideband measurement-based model that
characterizes the propagation channel responses based on the BMIs of a number of people
sufficiently large to render results statistically significant.
2.1.2 Contribution
As can be seen from the literature review above, there exist, to the best of my knowledge,
no measurements detailing ultrawideband MIMO BAN channels with a large sample size of
human subjects that allow analysis of different BMI categories in an anechoic and indoor
environment. This is remedied by investigating the impact that BMI has on UWB-MIMO
BAN channels. The contributions of this work can be summarized as follows:
1. Providing an extensive report on the channel measurement campaign that employs
our UWB MIMO array system to perform the BAN propagation channel measurement
both in an anechoic chamber and indoor laboratory environments.
2. Providing estimates and statistics of extracted propagation channel parameters such
as path gain, frequency-dependency coefficient of the path gain, shadowing gain, rms
delay-spread, amplitude-fading and spatial correlation coefficient.
3. Proposing a UWB MIMO BAN propagation channel model that takes the BMI of
various people into consideration. The model is validated by comparing derived MIMO
capacity values to those of the original measurements.
12
4. Providing an implementation recipe, which can be used to simulate BAN channels.
The measurement environment, measurement setup, limitations of my study on BAN
and results from the measurement campaign are discussed in subsequent sections.
2.2 Measurement Environment
ThemeasurementswereconductedattheUltRaLabfacility[49]locatedattheUniversity
of Southern California (USC) in Los Angeles, CA, USA. The experiments were performed
in both an anechoic chamber and indoor lab environments, which are shown in Figs. 2.1(a)
and 2.1(b) respectively. The anechoic chamber is a 9.1 x 4.6 x 4.6 m Radio Frequency (RF)
shielded room, which serves as a controlled environment with no reflections while the indoor
lab is a 13.1 x 15.2 x 6.0 m room mostly populated with plastic chairs, computers, metallic
workbench (labeled A) and two metallic pillars (labeled B), and also houses the anechoic
chamber.
The human subject was positioned on a floor tile (labeled F) in the indoor lab while a
platform (labeled P in Fig. 1) was used in the anechoic chamber. Additional details about
the measurement environment are presented in [50].
(a) (b)
Figure 2.1: (a) Anechoic chamber (b) Indoor lab environment in the Ultralab at USC
13
Table 2.1: Hardware used in the channel measurement
Item Manufacturer Model No.
VNA Agilent 8720ET
TX/RX RF switch Pulsar Microwave SW8RD13
coaxial cables RF Industries RFW-5950-96
UWB antennas XY XY3
Parameter Setting
Bandwidth 8 GHz (2-10 GHz)
Center frequency, f
c
6 GHz
Transmitted Power -10 dBm
Total number of Channels 16
Number of sub-carriers 801
delay resolution 0.125 ns
Frequency resolution 9.98 MHz
Table 2.2: Measurement parameters
Channel Location
1 Front-to-Front (F2F)
2 Front-to-Shoulder (F2S)
3 Front-to-back (F2B)
4 Front-to-Hip (F2H)
5 Hip-to-Shoulder (H2S)
6 Hip-to-Back (H2B)
7 Hip-to-Leg (H2L)
Table 2.3: On-body Channels
2.3 Measurement setup
A task specific propagation channel sounder system was developed for our BAN mea-
surement campaign. Fig. 2.2 illustrates our setup. The measurements were performed in
the frequency domain using a vector network analyzer (VNA, Agilent 8720ET) for a stepped
frequency sweep conducted for 801 frequency points within a range of 2-10 GHz. A 4-element
switched uniform linear antenna (ULA) array configuration was used at both the TX and
RX ends with an in-house developed XY3 omni-directional antennas [51]. The antennas
were placed 7.5 cm apart in the linear array configuration in most instances while switching
between array elements was performed by Pulsar Microwave (SW8RD13) RF switches [52].
14
The test subjects wore a harness (see Fig. 2.3) on the body to avoid the antenna directly
contacting the body surface. Measurements were conducted on the harness alone (without
the human body) so as to establish a baseline for comparison. Results from this will be sub-
sequently discussed in later subsections. A list of all equipment is given in Table 2.1 while
all parameter settings for the channel measurement are shown in Table 2.2. An extensive
description of the channel sounding setup has been provided in [50].
Different on-body channels measured in our campaign are listed in Table 2.3, while
antenna placements on the body for these channels are shown in Figs. 2.4(a) to 2.4(g).
A total of 60 male subjects with ages 18 years or older with various BMIs were considered.
We could not conduct experiments with female subjects since no female research personnel
qualified to work on this Instituitional Review Board (IRB) - approved project were available
to work with female test subjects. The male test subjects were categorized according to their
BMI values following a conventional medical classification [53] as shown in Table 2.4. The
recruited subjects were later grouped such that there were 20 candidates per BMI category.
!"#$%&'()#
!"#*++*,#
-"#$%&'()#
!"
!"
./0#
-"#*++*,#
1*+23$$#
4%&'()#(52'+56#(&+(7&'#
8*9'59#+722&2:####
8*;<&3%#$5=%*+3#
(5223('5+#
Figure 2.2: UWB BAN measurement setup with harness on the body
15
Figure 2.3: Sample Antenna and harness setup on the body
(a) (b) (c) (d)
(e) (f) (g)
Figure 2.4: (a) F2F (b) F2S (c) F2H (d) H2S (e) F2B (f) H2B (g) H2L
A key assumption for our measurement is that the channel is static, which is fulfilled if
there are no posture variations/movements from the human subject or moving scatterers in
the environmental. We thus made sure of this in our experiment. We made sure there
16
Table 2.4: International classification according to BMI
Category BMI Value Classification
1 18.5-24.9 normal
2 25-29.5 overweight
3 ≥ 30 obese
were no moving scatterers in the vicinity of our measurement setup, and also monitored and
instructed all test subjects to keep still while the measurements were being conducted.
2.4 Limitations of our study
While this study is, to the best of our knowledge, the first of its kind (see Sec. I.A), the
limited population used in our study, the use of BMI as a suitable measure for categorizing
human body sizes and our choice of channel configuration and measurement environment
merits a discussion.
2.4.1 Limitation of population
One issue is the limited number (60) of test subjects. Obviously, a larger number would
result in a better statistical viability of the model, but, the number of test subjects is
limited both by difficulties in recruiting, and the time effort of measurements (see below).
Furthermore, the current number gives reasonable reliability (see Sec. VI.A).
A more serious constraint is the limited diversity of the test population, specifically, our
experiment used male subjects between the ages of 18 and 24. It can be expected that in
particular women, with an inherently different body shape, and children under the age of
18 (with unusual body shapes during spurts of growth) could lead to significantly different
results. However, extending the test population was not possible for two reasons: (i) having
a statistically significant number in each of the mentioned population groups would mean
at least tripling the number of measurements, leading to an impractical time effort (just the
measurementsreportedhereextendedoverayear, withthemeasurementoneachtestsubject
17
taking three hours, and considerable coordination effort to accommodate the volunteer test
subjects). Furthermore, since we had no female IRB (Institutional Review Board)-qualified
researcher on our team, we could not measure on female test subjects; and measuring with
underage test subjects creates obvious permission issues.
To provide a comprehensive channel model that factors in a larger and more diverse
population, additional channel measurements will need to be done. We encourage other
research using the population groups not considered in this work to serve as a complement
to our current work. Our setup and analysis as described in Secs. III & V will easily transfer
to other groups/subpopulation of test subjects.
2.4.2 Limitation of BMI as a measure
The debate over the suitability of the BMI as a measure for quantifying the human body
fat has been going on for a while and has been critically discussed in different works. While a
lot of works such as [54], [55], [56] and [57] have oppposed the use of BMI as a valid measure
for obesity, some works such as [58] and [59] have supported it.
We can categorize the differing opinions as:
• Opposed: Ref. [54] tested the accuracy of the BMI by comparing the adiposity status
defined by BMI and dual-energy X-ray absorptiometry (DXA) in a large population.
The conclusion of the work was that BMI misclassified adiposity status in approxi-
mately one-third of women and men compared with DXA. [55] also inferred that the
accuracy of BMI in diagnosing obesity is limited, particularly for individuals in the
intermediate BMI ranges, in men and in the elderly. [56] stated that BMI has vari-
ous deficiencies as a measure of obesity and is an indirect measure of body fat when
compared with more direct approaches such as bioelectrical impedance. Moreover,
BMI does not necessarily reflect the changes that occur with age in a population. The
proportion of body fat increases with age, whereas muscle mass decreases, but corre-
sponding changes in height, weight and BMI may not reflect changes in body fat and
18
muscle mass. [57] stated that consideration of changes in body composition rather
than BMI should be used as a measure for determining obesity since weight variations
have a bigger impact on the BMI values even when the individual’s height remains the
same, which is especially common in adults.
• Support: In analyzing the measure of obesity and cardiovascular risk among men and
women, [58] compared the waist-to-height (WHtR) ratio and BMI and concluded that
BMI remained the most clinically practical measure of adiposity. [59] argues for the
use of BMI as the principal and universal measure of obesity. [57] in contrast to its
eventual assertion, stated that in a large population, BMI provides a useful surrogate
index of obesity because it corrects for individuals who are heavy by virtue of the
fact that they are also tall and that while BMI provides no information regarding the
composition of the weight, or its distribution, it does not matter so much when the
study is conducted on a large population.
Many other works (not mentioned here for space reasons) have provided various refine-
ment of the BMI. In addition to the contrasting opinions in different works, it suffices to
recall that the BMI is essentially height divided by weight. In adults, height is a fixed
quantity
2
, so BMI serves as a proxy for weight. In children/adolescents, both height and
weight are variable, thus a much more diverse range of body types can be observed for a
given BMI. Also, BMI has limitations not only on quantifying body fat but also composition
(muscle vs fat as well as where the body fat is located). In a ’very large-framed’ or muscular
person, BMI may overstate body fat, while conversely it may understate body fat for a ’very
small-framed’ person, someone with little muscle mass, or an individual with excess body
fat around the belly or midsection with very small limbs.
We use BMI for categorizing different body sizes in BAN propagation channel measure-
ments and model for the following pragmatic reasons: (i) it provides a single-parameter
2
Note that the height of the test subjects used in our work ranges from about 160 to about 187 cm.
19
description of human body shape. This is vital for this measurement campaign, because
a description with a larger number of parameters would need a larger number of test sub-
jects to obtain statistically viable results; yet for practical reasons a significant increase in
that number of subjects is not feasible as discussed above. (ii) it can be measured in a
standardized way (as opposed, e.g., to torso circumference), and cheaply (as opposed, e.g.,
to DXA). (iii) it is available for a very large population group since weight and height is
measured at every doctor’s visit and often at home. Perhaps most importantly, our mea-
surements demonstrate that the standard deviation of channel parameters, such as path gain
within each BMI category, is (slightly) less than the deviation between different categories
as shown in the probability distribution functions (PDFs) plotted in Figs. 2.5(a) and 2.5(b).
This demonstrates that the BMI is a relevant metric for the impact of body shape on radio
propagation.
-100 -80 -60 -40
path gain (dB)
0
0.05
0.1
0.15
0.2
0.25
PDF
BMI 1
BMI 2
BMI 3
(a)
-70 -60 -50 -40
path gain (dB)
0
0.05
0.1
0.15
0.2
0.25
0.3
PDF
BMI 1
BMI 2
BMI 3
(b)
Figure 2.5: PDF of the path gain in the (a) H2S in the anechoic chamber (b) F2S channels
in the indoor lab
2.4.3 Limitation due to channel configuration and environment
On-body propagation channels measured in this work can be categorized into Line-of-
sight (LOS) channels (e.g., F2F, F2H, F2S) and Non-line-of-sight (NLOS) channels (e.g.,
F2B,H2B).Itisimportanttonotethatinon-bodypropagation, theterm"LOS"and"NLOS"
channels are only valid for static measurements such as the ones presented in this paper. As
20
stated in [60], these terms are not valid in a dynamic scenario as body movement would sig-
nificantlychangethechannel–obscuringthedistinctionbetweenthesetwotypesofchannels.
Also, some of the parameters extracted in this work such as shadowing, amplitude fading
and delay dispersion (to be discussed in subsequent sections) are all empirically determined
in a static scenario.
Due to the amount of effort involve in this type of measurement campaign and the
configuration of our measurement setup, some channels such as TX or RX at lower leg or
lower arm to other parts of the body were not measured. This could prove insightful for the
UWB wireless BAN modeling, we hope any future research conducted in this field would
take these channels into consideration to complement the results provided in this paper.
One important conclusion from the results of the current measurements is that they
provide a quantitative estimate of the BMI influence in two "extreme" environments with no
(anechoic chamber) or very rich (indoor lab) scattering. BAN channel measurements results
conducted in other real-world environments are anticipated to lie between those extremes.
It would indeed be interesting to measure the BMI impact in a range of other environments
as well. The logistics and the sheer time effort of such measurements would have been
prohibitive in the current campaign, but we hope that this paper can encourage studies of
other researchers along those lines.
2.5 Data Evaluation and Results
The transfer function of each on-body channel can be represented as H
i,j,k,z,q,ψ,ξ
, where
i∈ [1, 2,...,I = 4] and j∈ [1, 2,...,J = 4] denote the TX and RX antenna position indices
within the array, k∈ [1, 2,...,K = 801] represents the frequency points, z∈ [1, 2,...,Z = 7]
is the type of on-body channel measured (see Table 2.3), q∈ [1, 2,...,Q = 20] represents
the index of people within a BMI category, ψ∈ [1, 2,...Ψ = 3] indicates the BMI categories,
and ξ ∈ [1,..., Ξ = 2] represents the environments with ξ = 1 as the anechoic chamber
21
and ξ = 2 as Indoor Lab environment, respectively. The transfer function H
i,j,k,z,q,ψ,ξ
was
transformed to the delay domain by using an inverse Fourier transform and a Hanning
window (to reduce side-lobes). The resulting impulse response is denoted ash
i,j,n,z,q,ψ,ξ
, using
similar index parameters representation as those of the transfer function with the exception
of the frequency bin index changed ton∈ [1, 2,...,N = 801], wheren indicates the delay bin
index. The instantaneous power-delay profiles (PDP) are derived from the impulse responses
by taking the magnitude squared (P
i,j,n,z,q,ψ,ξ
=|h
i,j,n,z,q,ψ,ξ
|
2
) of the impulse response. The
influence of small-scale fading is reduced by averaging the PDP over all MIMO channels so
as to obtain the average power-delay-profile (APDP) as shown in (2.1). Sample APDP plots
obtained from some of the channels in the BMI categories are shown in Figs. 2.6(a) & 2.6(b)
below.
ˆ
P
n,z,q,ψ,ξ
=
1
I
1
J
I
X
i=1
J
X
j=1
P
i,j,n,z,q,ψ,ξ
(2.1)
To minimize the influence of noise in our data evaluation, we implemented a noise thresh-
olding filter that sets all APDP samples whose magnitudes are below a certain threshold to
zero. Thethresholdvalueischosentobe6dBabovethenoiseflooroftheAPDP[11]. Finally,
a delay-gating filter was implemented for the anechoic chamber measurements only, which
eliminated MPCs with an excess runlength (difference between runlength and Euclidean dis-
tance between TX and RX) larger than 4 m. The value 4 m was chosen because there were
no observable reflector/scatterer that could cause a MPC with such a large excess runlength
in the on-body channels.
Inourdataevaluation, wediscussthemode-of-propagationofMPCsinon-bodychannels,
path gain, shadowing, delay dispersion, amplitude fading and spatial correlation. Extraction
procedureandresultsforeachofaforementionedparametersarediscussedinsubsequentsub-
sections.
22
2.5.1 Mode of propagation of MPCs
In BAN, the Mode of Propagation (MOP) of an electromagnetic (EM) wave around the
body has been classified as either through-body penetration or via creeping waves on the
surfaceofthebody, diffractionaroundthebodyorasaresultofreflectionsintheenvironment
[27], [61], [24], [33], [26]. Whiledifferenton-bodychannelshavedifferentprimarypropagation
mechanisms, subsequently received MPCs could stem from a combination of various MOPs.
For example, the F2F channel in an indoor lab environment, as shown in Fig. 2.4(a) and
APDP shown in Fig. 2.6(a), is more likely to be dominated by the creeping waves on
the surface of the body while occurence of other MPCs is as a result of on-body and indoor
reflections[33], [62]. FortheF2Bchannel(seeFig. 2.4(e)), itcanbededucedfromtheAPDP
(shown in 2.6(b)) that the first strongest peak corresponds to the MPC diffracted around
the human body while the second strongest peak is mainly the result of ground reflection
and subsequent MPCs are due to reflections in the environment. This characterization of
the APDP from the F2B channel had been previously mentioned in [33]. It is important to
note that the general shape of the APDP was the same at a particular on-body channels
in the different BMI categories, which simply implies a common mode of MPC propagation
within a channel irrespective of the body type.
0 1 2 3 4 5
delay(s)
×10
-8
-110
-100
-90
-80
-70
-60
-50
Power(dB)
(a) APDP of F2F Channel
2 4 6 8
delay(s)
×10
-8
-105
-100
-95
-90
-85
-80
-75
Power(dB)
(b) APDP of F2B Channel
Figure 2.6: APDP from sample measured channels in the indoor lab environment
23
2.5.2 Path gain Analysis
Intheliterature, pathgaininnarrowbandchannelsisusuallymodeledasbeingdependent
on distance only; while path gain in the UWB channel exhibits both distance and frequency
dependency [17], [62] and is written as
G
L
(f,d) =
1
Δf
·E





f+Δf/2
Z
f−Δf/2

H(
e
f,d)

2
d
e
f





, (2.2)
where H(
˜
f,d)
3
is the channel transfer function. E{·} is the expectation taken over the
fading.
4
The frequency range, Δf is chosen small enough so that diffraction coefficients,
dielectric constants, etc., can be considered constant within that bandwidth. For our mea-
surement, Δf is chosen to be 200 MHz, which is sufficient to average out frequency-selective
fades.
As a consequence of the nature of our work, there are no distance dependencies of path
gain for each channel since the channels were measured at a fixed TX-RX separation. The
path gain can be expressed as
G
L
(f,d
0
) = G
0
·X
σ
·G
L
(f), (2.3)
where G
0
, X
σ
and G
L
(f) are the average path gain at a fixed distance (d =d
0
), shadowing
gain and frequency-dependent path gain respectively. These parameters will be discussed in
detail subsequently.
Fixed distance path gain
For each test subject, we compute the local mean power (M
z,q,ψ,ξ
0
) as shown in (2.4))
3
We have used the transfer function notation as stated in [62].
4
Note that due to the nature of our setup, there is no large-scale fading created by movement along
a trajectory; rather the "shadowing" variable introduced below describes as the different "realizations" the
results on the different users. To simplify notation, we henceforth speak of "fading" when we mean small-scale
fading arising from interference between multipath components
24
M
z,q,ψ,ξ
0
=
N
X
n=1
ˆ
P
n,z,q,ψ,ξ
, (2.4)
from which we then compute G
0
as
G
z,ψ,ξ
0
=
1
Q
Q
X
q=1
M
z,q,ψ,ξ
0
. (2.5)
Values for G
0
obtained from our measurements are provided in Table 2.5. Sample cumulative
distribution function (CDF) plots for M
0
in different BMI categories and environments for
example channel F2H are shown in Figs. 2.7(a) and 2.7(b).
-90 -80 -70 -60 -50 -40 -30 -20
path gain (dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
BMI 1 Measured
BMI 1 Gaussian fit
BMI 2 Measured
BMI 2 Gaussian fit
BMI 3 Measured
BMI 3 Gaussian fit
(a)
-90 -80 -70 -60 -50 -40 -30 -20
path gain (dB)
0
0.2
0.4
0.6
0.8
1
BMI 1 Measured
BMI 1 Gaussian fit
BMI 2 Measured
BMI 2 Gaussian fit
BMI 3 Measured
BMI 3 Gaussian fit
(b)
Figure 2.7: Empirical CDF and corresponding Gaussian fit of path gain for F2H channel in
(a) anechoic chamber (b) indoor lab environments.
It can be observed from Table 2.5 that G
0
values differ by only about 2 dB between BMI
1 and BMI 2 while the difference to BMI 3 is much larger, namely 3-13 dB. It is intuitive
that the path gain is lower for BMI 3, since more body mass needs to be transversed with
exposure to more body tissue, which will likely attenuate the transmitted signal. Also, for
channels on the front of the body, protruding bellies of the BMI 3 subjects decrease the
average path gain while the variation (shadowing) is increased. Path gain in the two different
environments(anechoicchamberandindoorlab)aresimilarexceptforthe"Non-Line-of-Sight
(NLOS)" channels (F2B, H2B), where path gain values in the indoor lab environment are
actually higher than those of the anechoic chamber. This can be explained by the fact that
additional propagation paths (from the TX via scatterers in the environment to the RX) can
25
be more efficient than the creeping/diffracted waves that constitute the only propagation
path in the anechoic chamber.
Average path gain, G
0
(dB)
F2F F2B F2H F2S H2B H2L H2S
Anec. Ind. Anec. Ind. Anec. Ind. Anec. Ind. Anec. Ind. Anec. Ind. Anec. Ind.
BMI 1 -39.40 -40.78 -72.68 -63.62 -49.23 -50.69 -54.14 -55.63 -60.80 -58.61 -40.52 -41.14 -55.49 -61.29
BMI 2 -41.91 -41.66 -72.17 -65.98 -50.90 -50.18 -56.28 -56.43 -62.64 -61.21 -42.40 -41.69 -62.31 -62.16
BMI 3 -47.55 -45.76 -86.37 -74.57 -63.58 -62.32 -61.88 -61.68 -66.58 -65.44 -45.93 -49.64 -72.20 -71.26
Frequency-dependent decay factor (κ)
BMI 1 1.05 1.06 1.21 1.22 1.20 1.22 1.28 1.25 1.23 1.20 1.03 1.18 1.31 1.48
BMI 2 1.04 1.05 1.31 1.36 1.21 1.21 1.29 1.30 1.30 1.16 1.23 1.26 1.42 1.54
BMI 3 1.04 1.13 1.86 1.57 1.46 1.43 1.43 1.38 2.03 1.88 1.40 1.59 1.50 1.92
Shadowing gain, σ
s
(dB)
BMI 1 2.69 4.55 8.57 6.65 5.88 7.12 5.26 5.61 6.67 7.04 5.24 4.48 3.20 4.00
BMI 2 3.50 4.21 5.54 3.77 5.61 6.06 5.13 5.34 7.21 2.91 4.06 6.11 2.90 5.33
BMI 3 4.27 2.55 2.90 5.88 5.22 3.54 3.07 3.40 8.07 3.16 3.16 1.90 4.37 2.59
mean rms delay-spread, μ
τ
rms (dBs)
BMI 1 -90.74 -86.93 -91.28 -84.68 -91.94 -85.97 -89.84 -84.81 -92.13 -83.81 -90.62 -87.12 -88.62 -81.32
BMI 2 -90.82 -86.25 -93.06 -84.39 -91.53 -87.02 -88.28 -82.03 -90.11 -84.14 -90.76 -87.23 -88.18 -81.83
BMI 3 -96.09 -86.22 -102.81 -86.10 -94.52 -85.78 -92.52 -76.66 -88.83 -80.13 -116.28 -87.01 -90.85 -81.38
std. dev rms delay-spread, σ
τ
rms (dBs)
BMI 1 3.06 4.11 4.92 1.83 3.65 4.63 3.01 3.61 3.86 3.36 3.19 3.98 3.40 2.12
BMI 2 2.39 2.55 5.30 1.77 2.71 5.26 2.63 3.74 3.90 4.83 3.01 3.01 3.91 2.67
BMI 3 3.33 5.39 2.71 1.21 1.69 5.62 0.85 2.78 2.19 4.76 3.62 4.13 5.50 3.61
meanK-factor, μ
K
(dB)
BMI 1 2.30 2.05 2.01 2.13 2.82 1.24 1.12 1.31 2.28 0.94 2.10 3.10 1.80 0.92
BMI 2 3.06 2.88 3.11 3.21 2.69 1.69 1.31 1.02 -1.23 -0.80 1.80 2.90 -1.23 -1.20
BMI 3 3.66 2.78 4.72 1.91 1.70 2.14 1.21 1.43 2.53 1.03 2.40 1.10 -1.56 1.27
std. devK-factor, σ
K
(dB)
BMI 1 0.58 0.89 1.39 0.67 2.27 1.11 0.80 1.04 0.32 0.84 0.55 1.40 1.70 2.34
BMI 2 1.53 1.19 2.22 3.06 1.11 1.19 1.19 1.93 2.12 1.08 1.10 0.82 1.80 2.30
BMI 3 3.04 0.83 0.78 2.11 1.08 1.18 1.07 3.20 1.12 0.67 1.72 0.93 3.1 2.10
Table 2.5: Parameters extracted for various channels and BMI categories
Frequency-dependent path gain
The frequency dependency in the BAN UWB channel arises primarily from the frequency
dependency of the antenna power density and gain variation [63], [64], the tissue constituents
of the human body, and the physical propagation phenomena such as scattering and diffrac-
tion [65] in the channel.
Following [66, 67], we model G
L
(f) as
G
L
(f) =ζ

f
f
0
!
−2κ
, (2.6)
26
where κ is the frequency decay factor, ζ is a normalization constant, f
0
is the center fre-
quency. In our analysis, the average of the frequency-decay factors, extracted separately
for each candidates in each BMI category is used for modeling κ. While [68] has shown
that κ can be different for each multipath component, we use here (like most other papers
describing frequency dependence) a "bulk" model because we did not have sufficient number
of measurement points to extract it for each path separately. All extracted κ values are
provided in Table 2.5.
Although there has been some recent work done aimed at de-embedding the antenna
effect from the on-body propagation channel [69], [70], it is important to note that any
results in our analysis represent the behavior of the radio channel including both the physical
propagation channel (human body) and the antennas. Different antennas with consequently
different frequency dependent behavior could lead to significantly different results. All other
measurement campaigns that do not use calibrated antennas have the same limitation.
Path gain with Harness
We conducted additional channel measurements in the anechoic chamber with harness
alone i.e., without the human body present. This was mainly done as part of a sanity check
(due diligence in measurement) and to also establish a baseline for comparison purposes
for some of the on-body channels measured in our campaign. A sample figure showing the
antenna arrangements on the harness is shown in Fig. 2.8 while the average path gain values
obtained from some of the sample channels measured has been provided in Table 2.6 below.
Channel average path gain (dB)
F2F -39.22
F2S -44.73
F2B -45.27
Table 2.6: Average path gain values for sample channel from measurement with harness
alone.
27
Figure 2.8: Antenna placement for measurements with harness alone
2.5.3 Shadowing
Shadowing gain (X
σ
) accounts for the fluctuations of the received power for a given
channel and environment type, as well as BMI category, between different test subjects.
The standard deviation (std. dev) of shadowing gain computed from all channels and BMI
categories in the anechoic and indoor lab environments are shown in Table 2.5; it mainly
ranges from 2.55 to 8.57 dB. There is very little difference between these std. dev values
among BMI categories and the environments.
In generic UWB propagation channel measurements [71], [72], the shadowing gain has
been characterized as a lognormal distributionN(0,σ
s
(dB)). This distribution for the shad-
owing gain was also used in our work, even though the generating mechanism is different.
The lognormal distribution was validated by matching the empirical data to some typical
theoretical distribution such as lognormal, Nakagami, Rayleigh, Ricean, and Weibull. The
Kolomogorov-Smirnov (K-S) hypothesis test was used to determine the goodness-of-fit of
these distribution at 5% significance level (Table 6.2).
As can be observed from Table 6.2, the lognormal distribution gives the highest passing
rate for both anechoic and indoor lab environments. This observation holds for all BMI
28
-20 -15 -10 -5 0 5 10 15 20
shadowing std (σ)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Anechoic Measured
Anechoic Gaussian fit
Indoor Measured
Indoor Gaussian fit
Figure 2.9: Empirical CDF and corresponding Gaussian fit for the shadowing gain in the
F2F channel of BMI 1 in both anechoic and indoor lab environments.
categories and channels. A sample distribution for a select channel (F2F) is shown in Fig.
2.9.
2.5.4 Delay Dispersion Statistics
The rms delay-spread, τ
rms
is defined as the square-root of the second central moment
of the normalized APDP. This parameter serves to compactly describe the effects of delay
dispersion in multipath propagation environments [73]. The rms delay-spread was computed
directly from the APDP as described in [74].
We found rms delay-spread to be lognormally distributed (with respect to the ensemble
of subjects within a BMI category). The CDF plots in Figs. 8(a) and 8(b) show that
the logarithmic value of τ
rms
z,ψ,ξ
(with respect to 1 s) is well approximated by a Gaussian
distribution; this holds for all the other BAN channels measured in various environments as
well. This was again validated with a K-S test using the same distributions and significance
level as for the shadowing. Table 2.8 compares the passing rate of the aforementioned
distributions for a sample channel (F2H-BMI 1) in both anechoic and indoor environments.
It can be observed from the result that the lognormal distribution has the highest passing
rate. The statistical parameters (second-moment) for the rms delay-spread values (expressed
in dB) for all BAN channels are shown in Table 2.5. BMI 3 categories typically have the
29
smallestτ
rms
values. Also, as a consequence of the environment, comparing rms delay-spread
values between BMI categories is more difficult in the indoor Lab environment as scattered
and reflected MPCs drown out the impact of creeping or diffracted waves. Conversely, the
measurements in the anechoic chamber show a stronger dependence on BMI, since there
exist few or no reflections in the channel. Also, the rms delay-spread values in the indoor lab
environment are larger than the anechoic due to the rich scattering environment. Impact of
MPC delay dispersion on BAN or Personal Area Network (PAN) system performance have
been studied in papers such as [75] and [76].
Figure 2.10: Empirical CDF and corresponding Gaussian fit of τ
rms
in the F2H channel in
(a) anechoic chamber (b) indoor lab environment
-110 -105 -100 -95 -90 -85 -80 -75
τ
rms
(dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
BMI 1 Measured
BMI 1 Gaussian fit
BMI 2 Measured
BMI 2 Gaussian fit
BMI 3 Measured
BMI 3 Gaussian fit
(a)
-110 -105 -100 -95 -90 -85 -80 -75 -70 -65
τ
rms
(dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
BMI 1 Measured
BMI 1 Gaussian fit
BMI 2 Measured
BMI 2 Gaussian fit
BMI 3 Measured
BMI 3 Gaussian fit
(b)
30
Distribution K-S (anechoic) K-S (indoor)
Weibull 78.28 57.00
Rayleigh 16.17 15.23
Rician 16.17 15.23
Lognormal 98.37 89.36
Nakagami 27.87 36.59
Table 2.7: Passing rate of K-S test at 5% significance level for BMI 1 F2F channel
Distribution K-S (anechoic) K-S (indoor)
Weibull 55.16 45.24
Rayleigh 3.82 9.14
Rician 3.82 9.14
Lognormal 93.00 89.32
Nakagami 69.71 52.40
Table 2.8: Passing rate of K-S test at 5% significance level for τ
rms
for BMI 1 F2H channel
2.5.5 Amplitude Fading Statistics
The variation in the received signal amplitude over the 4× 4 MIMO UWB channel can
be attributed to the small-scale fading (SSF) on the body. This variation stems from MPC
interaction with local scatterers such as head, arm, etc (depending on the channel measured),
which exist within the vicinity of the receiver.
Several channel measurements [77, 78, 79, 11, 80, 74] have described the SSF statistics
as either lognormal, Rician, Rayleigh or m-Nakagami distributed. In our work, the SSF
statistics was found to follow a Ricean distribution. This was investigated by considering
fading on sub-carriers in different sub-bands over MIMO sub-channels. The chosen sub-
carriers in contiguous sub-bands are 200 MHz apart so to reduce the bias introduced by
possible correlation between sub-carriers [81]. An ensemble of the amplitude at each such
chosen sub-carrier and MIMO sub-channels are used in modeling the Ricean distribution.
TheK-factor is essentially constant over frequency, as verified by computingK-factor for
1-GHz sub-bands (not shown here for space reasons). TheK-factor parameter of the Ricean
distriibution was computed using the method of moments as described by (1)-(9) in [82].
A distribution fit from sample measurement data is provided in Fig. 2.11 below. Also,
31
a K-S hypothesis test at 5% significance level was used to determine a goodness-of-fit for
the aforementioned empirical data as compared to typical theoretical distributions such as
Rayleigh, Ricean, Lognormal, Nakagami, and Weibull. Table 3.6 compares the passing rate
of these tests for our measurement data. It is clear that the Ricean distribution has a much
higher passing rate.
0 0.2 0.4 0.6 0.8 1 1.2
amplitude
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Measured
Ricean Fit (K = 2.3 dB)
Figure 2.11: Ricean distribution fit for small-scale amplitude fading in F2F anechoic channel
Table 2.9: Passing rate of K-S test at 5% significance level
Distribution K-S
Weibull 84.89
Rayleigh 58.43
Rician 98.50
Lognormal 75.78
Nakagami 92.58
TheK-factor parameter of the Ricean distribution was found to be lognormally dis-
tributed over the ensemble of all subjects within a BMI category for each channel measured
for different environments. First and second moment values for a logarithmic equivalent,
i.e., Gaussian distributedK-factorN (μ
κ
(dB),σ
κ
(dB)) statistics are provided in Table 2.5.
We did not observe a significantK-factor dependency on BMI values in our analysis.
32
2.5.6 Spatial Correlation
Correlation of the signals at different antenna elements could have an adverse effects on
thechannelcapacityofaMIMOsystem. Correlationisinfluencedbytheangularspectrumof
the channel as well as the arrangement and spacing of antenna elements [83]. For antennas
that have been spaced half a wavelength apart, a uniform angular power spectrum leads
approximately to a decorrelation of incident signals. A smaller angular spread of the channel
leads to an increase in correlation. For a given Signal-to-Noise Ratio (SNR), maximum
capacity is achieved when the channel transfer matrix has full rank and the singular values
of the MIMO channel matrix are equally strong. If the fading of the channel coefficients is
correlated, this will lead to reduction in the MIMO system capacity.
We approximated the spatial correlation matrix of the non-LOS part of the channel (i.e.,
after the subtraction of the LOS component) channel as the Kronecker product of the spatial
correlation matrix at the TX and RX sides such that
R =R
TX
⊗R
RX
(2.7)
where⊗ denotes that Kronecker product and the matrices R
TX
has as their entries the
complex correlation coefficient ρ
j,i
between two sub-channels with ith and jth TX antenna
element.
5
This approach is similar to what has been implemented for different wireless
channels in the literature [84], [85], [86] and [87]; it is furthermore necessary in our case
to obtain an ensemble over which the expectation can be taken. We note that even with
this approximation, the ensemble size is on the low side. Furthermore, we do not model the
dependence of the correlation on delay, but assume it is identical for all delay bins (note
that we have already subtracted the impact of the LOS component, so that we only assume
that the diffuse components are delay-independent). With this assumption, we can then use
the ensemble of subcarriers (with similar constraints as in Sec. V-E), at all RX antennas,
5
and vice-versa in the RX case
33
as the ensemble, thus greatly increasing the ensemble size and reducing random variations.
It must be noted, however, that by the very nature of this process, we cannot extract delay
dependence of the correlation matrix.
For the various on-body channels analyzed, the spatial correlation coefficients were usu-
ally approximately uniformly distributed between 0 and 0.5-0.6. For example, in the F2F
channel (which can be considered a LOS channel - antenna arrangements on the human body
are shown in Fig. 2.4(a)), the CDF plots of the spatial correlation between sub-channels at
the TX and RX, respectively over an ensemble of human subjects within a BMI are shown
in Figs. 2.12(a) and 2.12(b). A simplified approach was used in modeling R
TX
and R
RX
by
having correlation coefficient value of 1 in the diagonal of the correlation matrix while all
off-diagonal matrix values are set to 0.3. We compared this approach to a more complicated
approach in which each correlation coefficient was modeled by a uniform random distribution
(over the ensemble of test subjects), and the correlation between the correlation coefficients
of one user were taken into account (thus ensuring, e.g., thatρ
12
was always larger thanρ
14
).
We found that both the capacity distribution and the distribution of the eigenvalues in the
two modeling approaches (the simple constant off-diagonal, and the more involved one) gave
almost the same results, and were well aligned with the correlation coefficients as directly
extracted from the measurements. We also compared to the simple i.i.d. assumption, but
found significant differences in both the capacity distribution and eignevalue cdf.
We did not observe any impact of BMI on the correlation coefficient values. Given the
fact that most of the sub-channel exhibit low correlation coefficient, it is fair to expect a high
capacity value even for the LOS channels in all the environments. An extensive discussion
on the MIMO channel capacity values obtained in our work has been presented in [88].
34
0 0.1 0.2 0.3 0.4 0.5
|ρ|
0
0.2
0.4
0.6
0.8
1
CDF
|ρ
j,12
TX
|
|ρ
j,13
TX
|
|ρ
j,14
TX
|
|ρ
j,23
TX
|
|ρ
j,24
TX
|
|ρ
j,34
TX
|
(a)
0 0.1 0.2 0.3 0.4 0.5 0.6
|ρ|
0
0.2
0.4
0.6
0.8
1
CDF
|ρ
j,12
RX
|
|ρ
j,13
RX
|
|ρ
j,14
RX
|
|ρ
j,23
RX
|
|ρ
j,24
RX
|
|ρ
j,34
RX
|
(b)
Figure 2.12: Emprical CDF of the correlation magnitude for (a) TX array for BMI 1 in
anechoic for F2F channel (b) RX array for BMI 1 in anechoic for F2F channel
2.6 Implementation Recipe
During simulations, we aim to create a frequency-selective MIMO fading channel (
¯
H)
withN
T
transmit andN
R
receive antennas for BAN channels. The channel realizations can
thus be generated as follows:
1. Select an on-body channel, BMI category and environment desired.
2. Select a suitable frequency band and delay window for the simulation. Also, select
appropriate sampling grid to create taps in delay.
3. From Table 2.5, select corresponding values for G
0
, κ and σ
s
and then generate
G
L
(f,d
0
) by using (2.3) .
4. Generate P
n
for each delay tap using
P
n
= G
L
(f,d
0
)·η·e
−
τn−τ
0
α
(2.8)
where η is a normalization constant such that
P
∞
n=0
e
−
τn−τ
0
α
=
1
η
andα is a realization
of the τ
rms
. The pdf of the rms delay-spread is lognormal; its parameters are give in
Table 2.5. Note that this shape of the PDP is not necessarily the one that was observed
35
in our measurements; however, due to the restriction on the number of scenarios we
could measure, a more detailed modeling of the PDP is beyond the scope of the paper.
5. Compute the Fourier transform (F{·}) of P
n
such that
P
f
=F{P
n
} (2.9)
6. Generate a matrix
ˆ
H
LOS
for the LOS component using (2.10) and (2.11).
ˆ
H
LOS
=a(p)a(q)
T
(2.10)
a(r) =e
−j
2π
λ
|
− →
r
i
−
− →
r
j
|
(2.11)
where|
− →
r
i
−
− →
r
j
| is the location vector of the array antenna elements
7. Generate a residual matrix
ˆ
H
res
as shown in (3.15).
vec(
ˆ
H
res
) =R
1/2
vec(H
w
) (2.12)
where the N
T
N
R
×N
T
N
R
matrix R
1/2
is obtained by factoring the total correlation
matrixR, i.e.,R =R
1/2
R
1/2
. The spatial correlation matrixR can be generated using
the simplified approach described in Sec. IV-F. H
w
is a complex i.i.d white Gaussian
random matrix.
8. Generate a linear equivalent of theK (dB) from the Gaussian distribution using cor-
responding moment values in Table 2.5.
9. Generate a realization of the propagation channel
˜
H in (3.16) by combining all the
parameters above.
˜
H =
q
P
f


s
K
K + 1
ˆ
H
LOS
+
s
1
K + 1
ˆ
H
res


(2.13)
36
10. Multiply
˜
H by

f
fc

−κ
to obtain
¯
H as shown in (2.14)
¯
H =
˜
H·

f
f
c
!
−κ
(2.14)
2.7 Model Validation
The model presented in this work was validated by using the channel capacity and by
dividing each BMI category randomly into two subgroups, extracted parameters for each of
the sub-groups, and comparing these parameters.
2.7.1 Capacity Approach
For each channel measured, an equal power capacity [42] was computed by using the
channel coefficients from
¯
H. The CDF of the capacity (TX SNR = 68 dB) obtained from
data generated synthetically from our model and that computed from the measurement data
for each BMI category for the F2F channel are compared in Figs. 3.11(a)-3.11(c) below. The
CDF was derived using an ensemble from candidates within each BMI categories.
0 10 20 30 40
capacity(b/s/Hz)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Simulated
(a)
0 10 20 30 40
capacity(b/s/Hz)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Simulated
(b)
8 10 12 14 16 18 20
capacity(b/s/Hz)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Simulated
(c)
Figure 2.13: Emprical CDF and model fit of capacity for (a) BMI 1 F2F (b) BMI 2 F2F (c)
BMI 3 F2F
Visually, it is clearly observable (from the CDFs plots in Figs. 3.11(a) to 3.11(c)) that the
capacityresultsfromthemodeldoeshaveagoodfittothatobtainedfromthemeasureddata.
37
In addition to this visual confirmation, a maximum deviation (D
v
= Maximum
x
|F
model
(x)−
F
empirical
(x)|) value
6
metric, which describes how closely the model and the empirical data
match was implemented. D
v
is equivalent to the Kolmogorov-Smirnov test statistic and has
been extensively discussed in [89]. The values ofD
v
between the CDFs for BMI 1, 2 and 3 as
shown in Figs. 3.11(a) to 3.11(c) are small – confirming a good fit and have been provided
in Table 2.10.
Table 2.10: Maximum deviationD
v
values for Capacity CDFs for BMI 1, 2, 3 F2F channels
Category D
v
BMI 1 0.18
BMI 2 0.12
BMI 3 0.16
2.7.2 Sub-group Analysis Approach
For each BMI category, we randomly divided the measurement data into two sub-groups
(having equal number of candidates) and extracted parameters such as G
0
and mean delay-
spread τ
rms
for comparison in the F2F, F2H and H2S channels. Similar parameters values
between the two sub-groups, which are also in agreement with the overall results shown in
Table 2.5 would corroborate the accuracy of our result irrespective of the data size used.
These parameters are shown in Table 3.8 below.
It can be observed from Table 3.8 that the parameters from different sub-groups for these
channels in the same environments are similar (with a few exceptions, e.g., G
0
for BMI 3
F2F, F2H Anechoic and H2S Indoor Lab) and are also close to values provided in Table 2.5,
which supports the notion that number of samples used in our analysis is in fact sufficient.
6
where F
model
(x),F
empirical
(x) are the distributions obtained from model and the empirical data.
38
Table 2.11: Parameters extracted from BMI categories sub-groups
Anechoic - Average path gain, G
0
(dB)
F2F F2H H2S
BMI 1 BMI 2 BMI 3 BMI 1 BMI 2 BMI 3 BMI 1 BMI 2 BMI 3
Sub-group 1 -39.72 -43.57 -44.13 -50.90 -51.04 -65.36 -59.14 -65.04 -67.90
Sub-group 2 -40.60 -44.21 -51.44 -50.74 -51.51 -60.75 -60.89 -63.39 -68.01
Indoor Lab - Average path gain, G
0
(dB)
F2F F2H H2S
BMI 1 BMI 2 BMI 3 BMI 1 BMI 2 BMI 3 BMI 1 BMI 2 BMI 3
Sub-group 1 -42.60 -43.95 -47.02 -50.39 -51.35 -61.40 -60.17 -64.44 -73.10
Sub-group 2 -42.36 -43.40 -48.32 -48.80 -50.10 -63.59 -60.44 -62.30 -69.88
Anechoic - mean rms delay-spread, μ
τ
rms (dBs)
F2F F2H H2S
BMI 1 BMI 2 BMI 3 BMI 1 BMI 2 BMI 3 BMI 1 BMI 2 BMI 3
Sub-group 1 -90.19 -91.02 -96.70 -91.81 -90.89 -94.37 -89.19 -88.44 -91.87
Sub-group 2 -90.50 -91.15 -95.48 -91.72 -92.38 -94.04 -88.35 -87.95 -90.15
Indoor Lab - mean rms delay-spread, μ
τ
rms (dBs)
F2F F2H H2S
BMI 1 BMI 2 BMI 3 BMI 1 BMI 2 BMI 3 BMI 1 BMI 2 BMI 3
Sub-group 1 -87.88 -87.52 -86.14 -86.63 -86.27 -85.55 -80.91 -82.16 -82.52
Sub-group 2 -86.15 -86.40 -86.89 -85.71 -87.19 -86.21 -82.03 -81.55 -79.18
2.8 Summary and Conclusion
We conducted a BAN measurement campaign using a UWB MIMO (4 x 4) antenna
array channel sounder setup for various on-body channels for different BMI categories in an
anechoic chamber and indoor lab environments. We extracted parameters used for modeling
a UWB BAN channel characteristics with respect to various BMI categories. A summary of
our findings is presented as follows:
1. We observed that parameters such as path gain do in fact vary for different BMI
categories. The path gain values were lower in BMI 3 than for BMI 1 and 2 by almost
13 dB in some channels.
2. Frequency-decay factor κ ranged from 1.03 to 1.92 and did not vary much over BMI
categories. However, this parameter is notably a function of the antenna used in our
measurement.
39
3. Shadowing gain was modeled as lognormal distribution with standard deviation values
ranging from 2.5 to 8.5 dB. We observed that there were very little differences between
the std. dev values among BMI categories and the environments.
4. The delay-spread statistics showed that the rms delay-spread values tends to follow a
lognormal distribution, which is consistent with the previous literature. We observed
that BMI 3 categories typically have the smallest τ
rms
values. Also, τ
rms
values are
higher in the indoor lab environment than in the anechoic chamber.
5. The amplitude fading statistics was modeled using a Ricean distribution while theK-
factor parameter was found to be lognormally distributed over an ensemble of subjects
and did not show any dependence on BMI category.
6. A Kronecker approach was used in modeling the spatial correlation of the MIMO
channel. A low correlation was generally observed between the sub-channels. This
implies that a high capacity value can be obtained with spatial multiplexing.
7. Based on these results, we provide a complete UWB MIMO BAN channel model
and give a step by step modeling procedure. The results were validated by using
MIMO capacity values as a comparison metric and also agreement between parame-
ters extracted from sub-groups of the data at each BMI category.
8. It is important to note that the modeling technique used in this work is generic and
can be adapted to any multi-paramater body composition metric (other than the BMI)
in any future research.
Overall, it is clearly observable from the results and statistics presented in this paper
that the propagation channel parameters for the UWB BAN channel does in fact differ
for different BMI categories. The status-quo BAN models are incomplete, hence our work
serves as either a complement to pre-existing models or a replacement. Details such as those
40
provided in this work will be of great help for BAN systems design and simulation in various
environments.
41
Chapter 3
A Measurement-Based Model of BMI
Impact on UWB Multi-antenna PAN
and B2B Channels
3.1 Introduction
RECENT years have seen an increasing interest in short-range "off-body" communica-
tions, where wireless devices positioned on the body communicate with devices in a different
physical location [90]. Off-body communications can be categorized into wireless Personal
Area Networks (PANs), i.e., links between a person and a nearby local Access Point (AP)
and Body-to-Body (B2B) communication networks, i.e., from a wearable device on one body
to that on another body. PANs and B2B networks are usually defined as networks where
transmitter (TX) and receiver (RX) are within a range of about 10 m [91]. They differ from
traditional Wireless Local Area Networks (WLAN), which have a larger coverage area and
are not as susceptible to the human body influence. PAN applications include communica-
tions from APs to body-mounted devices for medical monitoring, entertainment (gaming)
and computation, while B2B applications are prevalent in emergency services such as on-
body sensor node communication between firefighters, medical monitoring, communication
between military personnel, and sports and entertainment [92, 93, 94, 95].
Ultrawideband(UWB)radiotechnologyhasbeenconsideredovertheyearsasapromising
candidate to enhance communication and localization in scientific, military, and industrial
applications [2, 3, 4, 5]. UWB signals are defined as either having more than 20% relative
42
bandwidth or more than 500 MHz absolute bandwidth [6] and are permitted to operate in
the 3.1-10.6 GHz frequency band in the USA [7], while occupying the 4.2-4.8 and 6-8.5 GHz
bands in Europe and 3.4-4.8 and 7.25-10.25 GHz bands in Japan [96]. UWB radio, due to
its low power, high data rate, and robustness to fading has been suggested as the technology
of choice for implementing PANs and B2B networks. Also, the use of multiple antennas
has been suggested for both PAN and B2B to increase channel capacity and robustness to
fading.
Knowledge of the channel in which any wireless system will operate is essential for devel-
oping a reliable system. Hence, comprehensive and realistic characterization of off-body
channels is crucial to the development of any wireless PAN and B2B system. Furthermore,
theoretical and practical investigations have revealed that the behavior of narrowband and
UWB channels are remarkably different [11, 17], hence the need for a proper characterization
of the UWB PAN and B2B channels.
Due to the short distance between PAN and B2B TX and RX, user proximity-induced
effects such as human body blockage have been identified as a critical issue in these channels.
Forthehumanbodyinteractionwiththeelectromagneticwavepropagation, thehumanbody
size and tissue types, which can be compactly described by the Body Mass Index (BMI),
have an important impact [19, 20, 97, 18]. Although the dielectric properties of biolog-
ical tissues from different human body parts and (electromagnetic wave) frequency ranges
have been described in [98], yet, to the best of our knowledge, the impact of different BMI
categories on propagation in PAN and B2B channels has not yet been investigated in the
literature. Most existing measurements only involve test subjects with BMI values < 25,
and furthermore have a very limited number of test subjects (one or two).
43
3.1.1 Related works
Although several publications [90, 99, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108,
109, 110, 111, 112, 113, 114, 115, 116, 117, 44, 45] have dealt with PAN and B2B chan-
nel measurements and modeling, none of these have considered the effect of body size on
propagation channel parameters. We categorize existing results as:
• PAN works
1. Narrowbandsingle-antennameasurements: [90]studiedthereceivedsignalcharac-
teristics in an indoor environment at 5.8 GHz. [99] investigated the characteristics
of the shadow fading observed in off-body communications channels at 5.8 GHz.
Narrowband static and dynamic on-body to off-body channel measurements were
conducted at 427, 820 and 2360 MHz frequency bands in [44].
2. Narrowband MIMO measurements: path gain model and shadowing correlation
with respect to the user orientation at 5.8 GHz were provided in [91]. The impact
of human body shadowing on PAN MIMO channels at 2.45 GHz were studied
in [100] and [101]. [102] and [103] studied the spatial diversity and correlation
for off-body communications in indoor environments at 868 MHz and 5.8 GHz
respectively. The interaction between the human body and handheld transceivers
at 5 GHz in a PAN channel was investigated in [104]. Narrowband characteriza-
tion of off-body communication channels at 2.4 GHz was conducted on 8 adult
subjects in [45]. An open-access database, which contains hundreds of hours of
all narrowband measurements conducted in [44, 45] can be accessed in [48].
3. UWB single-antenna measurements: UWB channel measurements from different
parts of the body to an access point were provided in [105]. The effect of human
presence in PAN channels was investigated in [106] using a UWB (3.1-10.6 GHz)
setup while path gain model for UWB off-body (3.5-6.5 GHz) was presented in
[107].
44
4. UWB MIMO measurements: In our conference paper [76], we provided prelim-
inary results for the channel measurement campaign that underlies the current
paper, in particular, mean path gain and shadowing gain, however, we did not
provide other parameters (and their statistics) needed to fully model the BMI
dependent PAN channel.
With the exception of our conference paper [76] and refs. [44, 45], all other mea-
surements (in the literature) were done with only a single test subject. Even for the
single-subject case, we are not aware of UWB SIMO or UWB MIMO PAN measure-
ments.
• B2B works
1. Narrowband single-antenna measurements: [112] provided a path gain model for
B2B channels at 2.45 GHz.
2. Narrowband MIMO measurements: The mean path gain and body shadowing in a
B2B channel were characterized at 2.45 GHz in [109]. Fading in B2B channels was
investigated in [110], also at 2.45 GHz, while characterization of channel transfer
functions for B2B channels at 2.48 GHz was conducted in [111]. A channel model
whose components and parameters directly depend on the mutual body position
in terms of distance and orientation was provided in [113] while macro- and micro-
diversity in indoor B2B channels at 2.48 GHz were studied in [114].
3. Wideband MIMO measurements: A detailed system analysis for B2B channels in
a wideband 80 MHz (centered at 3.6 GHz) multi-antenna setup was provided in
[115], while an indoor multi-antenna channel characterization was provided using
a 100 MHz bandwidth (centered at 5.5 GHz) in [108].
4. UWBMIMOmeasurements: In[116], measurementswereconductedwithaUWB
setup with frequency ranging from 2 to 8 GHz. In our conference paper [118],
45
(a) (b)
Figure 3.1: (a) TX antenna placement in the anechoic chamber (b) platforms for test subject
placements for PAN and B2B setups
sampleresultsofthemeanpathgain,shadowinggainanddelaydispersionanalysis
were provided for the channel measurement campaign that underlies the current
paper. However, we did not provide other parameters (and their statistics) needed
to fully model the B2B channel.
All measurements in the papers listed were done with a single pair of test subjects with
the exception of [109] in which a combination of two pairs of human test subjects were
used and our conference paper [118], in which a total of 9 test subjects were used.
3.1.2 Contribution
As can be seen from above, with the exception of [44, 45] (in the narrowband PAN case),
all other models provided in the literature, irrespective of the frequency band, are based on
measurements or analysis on a single person. We are unaware of any measurements detailing
UWB MIMO PAN or B2B channels with a large sample size of human subjects that allow
for the analysis of different BMI categories. In this paper, we remedy this by investigating
the impact that BMI has on UWB SIMO/MIMO PAN/B2B channels. Measurements are
done in an anechoic chamber, in order to clearly work out the impact of the human body (as
opposed to environmental scattering). The contribution of this paper can be summarized as
follows.
46
1. Weprovideanextensivereportonthechannelmeasurementcampaignthatemploysour
UWB multi-antenna array system to perform the PAN and B2B propagation channel
measurements in an anechoic chamber.
2. We provide estimates of extracted propagation channel parameters such as path gain,
shadowing gain ("bulk" and "sub-band"), rms delay spread, amplitude fading statistics,
spatial correlation and channel capacity values in both PAN and B2B channels for
various BMI categories.
3. We propose a UWB multi-antenna model for the PAN and B2B channels that takes the
BMI into consideration. The model is validated by showing that parameters extracted
in two different sub-groups of human subjects are similar and comparable to results
when all sub-groups are combined. Furthermore, we demonstrate that the capacity
CDF (Cumulative distribution function) generated from our model shows good agree-
ment with the capacity CDF obtained from from the raw measurement data.
3.1.3 Organization
This paper is organized as follows. Sections II and III describe the measurement environ-
ment and measurement setup, respectively. Limitations of our study are discussed in section
IV. Section V details the data evaluation. Results are discussed in section VI while model
validation is provided in section VII. Conclusions are drawn in section VIII.
3.2 Measurement Environment
The measurements were conducted at the UltRa Lab facility [49] of the University of
Southern California (USC) in Los Angeles, CA, USA. The experiments were performed in
an anechoic chamber (Fig. 1), a 9.1 x 4.6 x 4.6 m Radio Frequency (RF) shielded room,
which serves as a controlled environment with no reflections.
47
(a)
(b)
Figure 3.2: (a) UWB SIMO PAN measurement setup (b)UWB MIMO B2B measurement
setup
ForthePANmeasurementsthehumansubjectswereplacedonabsorberplatformslabeled
as ’P’ in Fig. 1, at a distance 4.5 m from the TX antenna while for the B2B measurements
TX and RX antenna array bearers where positioned on absorber platforms labeled ’P’ and
’Q’, separated by 1.35 m.
3.3 Measurement setup
Two propagation channel sounder systems were developed for the PAN and B2B mea-
surement campaigns as shown in Figs. 3.2(a) and 3.2(b). Both systems are based on a vector
48
network analyzer (VNA, Agilent 8720ET) for a stepped frequency sweep using 801 frequency
points over a range of 2-10 GHz.
3.3.1 PAN setup
In the SIMO setup used for the PAN measurements, a UWB TEM horn antenna [119]
was used at the TX end while a 4-element switched uniform linear antenna (ULA) array
configuration was used at the RX end whose elements are in-house developed XY3 omni-
directional antennas [51]. The TX and RX were separated (in distance) by about 4.5
m. The RX antennas were placed 7.5 cm apart in a linear array configuration. Switch-
ing between array elements was performed by Pulsar Microwave (SW8RD13) RF switches
[52] with switching time of 100 ns and insertion loss of 3.5 dB. The RF switches were cali-
brated separately with their system response subtracted from the channel sounder response.
Although there has been some recent work aimed at de-embedding the antenna effect from
the on-body propagation channel [70], [69], antennas are interpreted as part of the propaga-
tion channel in this work. This is necessary because the presence of large dielectric objects
(the human body) throughout the relevant propagation channel makes difficult the extrac-
tion of a double-directional channel representation [120]. The antenna arrays were placed on
a harness that was worn by the test subjects on their bodies to avoid the antenna directly
contacting the body as this would cause degradation in performance of the antenna and
significantly influence the path gain. Effects of antenna proximity to the body in human
body related measurements have been extensively discussed in [88].
The channels measured in this setup are the hip, front and back channels, with antenna
placements shown in Fig. 3.3(a)-3.3(c). For each measured channel, the human subject was
asked to rotate his orientation at 45
◦
increments from 0
◦
to 315
◦
. The rotation is such that
the subject starts at 0
◦
orientation with the broadside of the RX antenna array perpendicular
to the TX and moving in a clockwise direction; for example in the hip and front channels,
49
Parameter Setting
Bandwidth 8 GHz (2-10 GHz)
Center frequency, f
c
6 GHz
No. of Channels PAN/B2B 4/16
No. of sub-carriers 801
delay resolution 0.125 ns
Frequency resolution 9.98 MHz
Table 3.1: Measurement parameters
Item Manufacturer Model No.
VNA Agilent 8720ET
TX RF switch Pulsar Microwave SW8RD13
RX RF switch Pulsar Microwave SW8RD13
coaxial cables RF Industries RFW-5950-96
UWB Omni antennas XY XY3
UWB Horn antenna TL TS1
Table 3.2: Hardware used in the channel measurement
the LOS to the TX will only occur when the TX is at 270
◦
orientation while a complete
NLOS is expected at 90
◦
orientation (see Fig. 3.2(a)).
3.3.2 B2B setup
For the B2B measurement, a MIMO setup comprising of a 4-element switched ULA
configuration was used at both the TX and RX ends using the aforementioned XY3 omni-
directional antennas. The antennas were also placed 7.5 cm apart in a ULA configuration at
the TX and RX ends (see Fig. 3.2(b)) while switching between array elements was performed
by TX and RX RF switches. The channels measured in this setup are the front and back
channels. As in the PAN case, each human subject was asked to rotate his orientation in
90
◦
increments (clockwise direction) from 0
◦
to 270
◦
relative to the other human subject’s
current orientation such that a 0
◦
to 270
◦
orientation will be covered at both TX and RX
ends.
A list of all equipment is given in Table 3.2 while all parameter settings for the channel
measurement are shown in Table 3.1.
50
(a) (b) (c)
Figure 3.3: (a) hip (b) front (c) back Channels
3.3.3 Human subject selection
A total of 60 male subjects with ages 18 years or older with various BMIs participated in
the PAN measurements. The test subjects were categorized according to their BMI values
following a conventional medical classification [53] as shown in Table 3.3. There were 20 can-
didates per BMI category
1
in the PAN measurements. For the B2B measurements 9 subjects
(3 per BMI category) were used. Both intra- and inter-BMI categories measurements were
conducted. We could not conduct experiments on female subjects since no female research
personnel qualified to work on this Institutional Review Board (IRB)-approved project were
available to work with female test subjects.
Table 3.3: International classification according to BMI
Category BMI Value Classification
1 18.50-24.90 normal
2 25.00-29.50 overweight
3 ≥ 30.00 obese
A key assumption for our measurement is that the channel is static. To fulfill this, we
made sure that there were no moving scatterers in the vicinity of our measurement setup,
and also monitored and instructed all test subjects to keep still while the measurements were
being conducted.
1
Note that the range of height of our test subjects within each BMI category are: BMI 1 = (min –
165cm, max – 187 cm), BMI 2 = (min – 159cm, max – 186cm), BMI 3 = (min – 161cm, max – 178cm).
51
3.4 Limitations of our study
The limited test population size and lack of diversity, i.e., absence of women (with an
inherently different body shape) and children under the age of 18 (with unusual body shapes
during spurts of growth) constitute limitations of our study. Measurements on the afore-
mentioned subpopulation could lead to significantly different results from what is presented
in this paper.
Another limitation is the use of BMI as a suitable measure for categorizing human body
sizes in clinical and scientific research. This has been deemed debatable in a number of
works such as [57] and [59]. While caution should be taken when BMI is used in clinical
and scientific research, we use it here for categorizing different body sizes in the PAN and
B2B propagation channel measurements and model for the following pragmatic reasons: (i)
it provides a needed single-parameter description of human body shape (a description by
more parameters would require more test subjects for statistical significance), (ii) it can be
measured and categorized in a standardized way (as opposed to, e.g., torso circumference)
(iii) it is available for a very large population group since the underlying parameters, height
and weight, are measured both at home and at every doctor’s visit.
Finally, some of the propagation channels measured in this work can be categorized into
Line-of-sight (LOS) channels and Non-line-of-sight (NLOS) channels as will be discussed in
subsequent sections. It is important to note that the term "LOS" and "NLOS" channels are
only valid for static measurements such as the ones presented in this paper. As stated in
[60], these terms are not valid in a dynamic scenario as body movement would significantly
change the channel – obscuring the distinction between these two types of channels. The
parameters extracted in this work such as path and shadowing gain (also to be discussed in
subsequent sections), etc., are all empirically determined in a static scenario and are thus
only relevant in a static scenario.
Future work will be needed to overcome issues particularly in limited population used
in our study and the use of BMI as a suitable measure for categorizing human body sizes.
52
An extensive discussion about the limitations of this study and other body-related channel
measurements can be found in [97].
3.5 Data Evaluation
Duetodifferingmeasurementsetupanddatastoragestructure, theevaluationprocedures
for PAN and B2B channels are discussed separately.
3.5.1 PAN Channel
For this measurement, the transfer function of each SIMO channel can be represented
as H
j,k,z,q,ψ,o
, where j∈ [1, 2,...,J = 4] denotes the RX antenna position within the array,
k ∈ [1, 2,...,K = 801] indexes the frequency points, z ∈ [1, 2,...,Z = 3] is the type of
off-body channel measured (with 1 denoting hip, 2 front and 3 back), q∈ [1, 2,...,Q = 20]
represents the index of people within a BMI category, ψ∈ [1, 2,...Ψ = 3] indicates the BMI
category and o∈ [1, 2,...O = 8] indicates body orientation. The transfer function H
j,k,z,q,ψ,o
was transformed to the delay domain by using an inverse Fourier transform and a Hanning
window (to reduce side-lobes). The resulting impulse response is denoted ash
j,n,z,q,ψ,o
, using
similar index parameters representation as those of the transfer function with the exception
of the frequency bin index changed ton∈ [1, 2,...,N = 801], wheren indicates the delay bin
index. The instantaneous power-delay profiles (PDP) are derived from the impulse responses
by taking the magnitude squared (P
j,n,z,q,ψ,o
=|h
j,n,z,q,ψ,o
|
2
) of the impulse response. The
influence of small-scale fading is reduced by averaging the PDP over all SIMO channels so as
to obtain the average power-delay-profile (APDP,
ˆ
P
n,z,q,ψ,o
). Sample APDP plots obtained
from different human body orientations are provided in [76].
53
3.5.2 B2B Channel
ThetransferfunctionfortheMIMOchannelintheB2Bmeasurementscanberepresented
as H
0
i,j,k,υ,κ
ζ
,ξ,r,w
, which is similar to that defined for the PAN (SIMO) with the addition of
i∈ [1, 2,...,I = 4] denoting the TX antenna position indices within the array, the ξ ∈
[1,..., Ξ = 2] denoting the B2B channels measured (1 denoting front and 2 the back), υ
indicates the counting index of the candidate within each BMI category, κ
ζ
denoting the
BMI categories with ζ = 1 indicating intra-BMI category and ζ = 2 indicating inter-BMI
category. r∈ [1, 2,...,R = 4] and w∈ [1, 2,...,W = 4] indicates the body orientation of TX
and RX arrays respectively. An inverse Fourier transform and a Hanning window approach
is used to compute the impulse response from which the instantaneous PDP (P
0
i,j,n,υ,κ
ζ
,ξ,r,w
) is
derived while the APDP (
¯
P
n,υ,κ
ζ
,ξ,r,w
) in this case can be obtained by averaging over antenna
elements at both TX and RX. Sample APDP plots obtained from different human body
orientations are provided in [118].
3.6 Results
Wenextdiscussresultsofchannelparameterssuchaspathgainandshadowinggainusing
bulk (aggregation of all frequency bands) and sub-band (computations over select frequency
bands) approaches in both PAN and B2B channels. We also discuss the rms delay spread,
spatial correlation, amplitude fading statistics and capacity of all channels measured.
3.6.1 PAN Modeling
For the PAN and B2B evaluations, no distance dependence of path gain was considered,
since measurements were done only at a single distance. Since measurements were done in
an anechoic chamber, we conjecture that a simple d
2
scaling of the results would be valid,
but this could not be verified experimentally due to the limitations of chamber.
54
Path gain analysis
For each test subject, we compute the orientation-dependent path gain (M
z,q,ψ,o
) as
shown in (3.1) from which we derive a test subject-dependent mean (over an ensemble
of orientations) path gain (Φ) and an orientation-dependent mean (over an ensemble of
test subjects) path gain (β) as shown in (3.2) and (3.3) respectively. The variation in
orientation-dependent mean path gain values over different body orientations can be seen
in Table 3.9.
M
z,q,ψ,o
=
N=801
X
n=1
ˆ
P
n,z,q,ψ,o
, (3.1)
Φ
z,q,ψ
=
1
O
O=8
X
o=1
M
z,q,ψ,o
(3.2)
β
z,ψ,o
=
1
Q
Q=20
X
q=1
M
z,q,ψ,o
(3.3)
G
z,ψ
L
=
1
O
O=8
X
o=1
β
z,ψ,o
. (3.4)
The mean path gain (G
L
) is then computed by averaging β over different body orienta-
tions as shown in (3.4). The values for G
L
) is also shown in Table 3.9. From the values in
the Table 3.9, it can be observed thatβ changes over body orientation (from LOS to NLOS)
by about 8-9 dB in the hip channel and 11-14 dB in the front and back channels across all
BMI categories. Sample plots of Φ for the hip and back channels in various BMI categories
are shown in Figs. 3.4(a) and 3.4(b) in which it is clearly observable that values of Φ are
much lower in the BMI 3 category than BMI 1 and 2.
Also from Table 3.9,G
L
generally changes over the BMI categories with BMI 3 being 3-4
dB less than BMI 1 & 2.
Shadowing analysis
Since the measurements were done in an anechoic chamber, no environmental shadowing
occurred; "shadowing" and "human body shadowing" becomes synonymous henceforth. For
each test subject, a distribution of the (normalized) shadowing gain over an ensemble of
55
-80 -75 -70 -65 -60 -55
Φ (dB)
0
0.2
0.4
0.6
0.8
1
CDF
Measured BMI 1
Gaussian Fit BMI 1
Measured BMI 2
Gaussian Fit BMI 2
Measured BMI 3
Gaussian Fit BMI 3
(a)
-80 -75 -70 -65 -60 -55
Φ(dB)
0
0.2
0.4
0.6
0.8
1
CDF
Measured BMI 1
Gaussian Fit BMI 1
Measured BMI 2
Gaussian Fit BMI 2
Measured BMI 3
Gaussian Fit BMI 3
(b)
Figure 3.4: Empirical cumulative distribution function (CDF) of orientation-averaged mean
path gain Φ (dB) over ensembles of test subjects with corresponding Gaussian fit for (a) hip
(b) back channels for PAN.
orientations is derived as shown in (3.5). This shadowing gain follows a zero-mean lognormal
distribution with standard deviation S [76]. The standard deviation itself is a random
variable (over an ensemble of test subjects), which is characterized by its mean (μ
s
) and
standard deviation (σ
s
) as shown in (3.6). The values ofμ
s
andσ
s
for the different channels
and BMI categories shown in Table 3.9. To ease further discussions, we will henceforth refer
toμ
s
as the "effective body shadowing gain (EBSG)" andσ
s
as the "effective body shadowing
deviation (EBSD)." From Table 3.9 it can be observed that EBSG is about 3 dB for the hip
channel while ranging from 6-7 dB in the front and back channels. A slightly increase (≈ 1
dB) in EBSG value can be observed over BMI categories.
S
z,q,ψ
=D
o
(
10·log
10

M
z,q,ψ,o
E
o
{M
z,q,ψ,o
}
!)
(3.5)
μ
z,ψ
s
=E
q
n
S
z,q,ψ
o
, σ
z,ψ
s
=D
q
n
S
z,q,ψ
o
(3.6)
where D{·} and and E{·} are the standard deviation and the expected value operators
respectively.
Path gain analysis over sub-bands
Further insights to the path gain can be obtained by considering the channel responses
within frequency sub-bands (Δf). Δf needs to be chosen small enough so that diffraction
56
coefficients, dielectric constants, etc., can be considered constant within that bandwidth; we
chose Δf to be 1 GHz. The extraction of channel impulse responses and path gain within
each sub-band are similar to the procedure in Sec. V-A and Sec. VI-A.1.
Following the IEEE 802.15.4a standard model [67], a linear regression fit of the path gain
over the sub-band frequencies was performed as
ˆ
G(f)(dB) = A· 10·log
10

f
f
0
!
+B(dB), (3.7)
where
ˆ
G(f)(dB) is the frequency-dependent mean path gain andf
0
is the reference frequency
2.5 GHz, which corresponds to the center frequency of the first sub-band. A is the slope
and B is the intercept to the ordinate at the reference frequency; the parameters A and B
are tabulated in Table 3.4. We find that BMI 3 tends to show a larger slope than the other
channels. This is intuitive, as the blocking by a large body is especially significant at higher
frequencies.
Mean path gain (G
L
) from sub-banding Shadowing (μs) from sub-banding
hip front back hip front back
A B (dB) A B (dB) A B (dB) As Bs (dB) As Bs (dB) As Bs (dB)
BMI 1 -0.14 -62.41 -0.05 -64.92 -0.04 -65.40 1.06 1.92 0.99 5.22 0.96 6.32
BMI 2 -0.07 -64.28 -0.02 -65.54 -0.34 -65.72 0.83 3.45 0.85 5.78 1.05 6.28
BMI 3 -0.97 -62.04 -0.56 -65.36 -0.50 -65.84 1.54 1.89 1.09 6.72 1.07 7.50
Table 3.4: Path gain and shadowing parameters (obtained from sub-banding processing
approach) for channels from various BMI categories in PAN
Shadowing analysis over sub-bands
For each sub-band, the EBSG, i.e., μ
s
, was computed using a similar procedure as done
in Sec.VI-B.2. A linear regression fit was also implemented to observe the variation of EBSG
over the frequency sub-bands. Sample channels (hip and front) are shown in Figs. 3.5(a)
and 3.5(b) while all fitting parameters are provided in Table 3.4.
It can be observed from Figs. 3.5(a) and 3.5(b) and parameters in Table 3.4 that EBSG
tends to increase with increasing frequency for all BMI categories. However, no unambiguous
trend over BMI indices could be observed.
57
0 1 2 3 4 5 6
Frequency Sub-band (dBHz)
2
4
6
8
10
12
14
16
18
EBSG
Body Shad 1
Body Shad 2
Body Shad 3
LS Fit 3
LS Fit 2
LS Fit 1
(a)
0 1 2 3 4 5 6
Frequency Sub-band (dBHz)
6
8
10
12
14
16
EBSG
Body Shad 1
Body Shad 2
Body Shad 3
LS Fit 3
LS Fit 2
LS Fit 1
(b)
Figure 3.5: Linear fit for EBSG (μ
s
) at various BMI categories (a) hip (b) front channels in
PAN
Delay dispersion analysis
The RMS delay-spread, τ
rms
is defined as the square-root of the second central moment
of the normalized APDP [83]. This parameter serves to compactly describe the effects of
delay dispersion in multipath propagation environments [73].
The delay dispersion in the PAN channel mainly stems from the interaction of the MPCs
with different human body parts such as head, hands and torso [97]. The rms delay-spread
was computed directly from the APDP as described in [74]. The logarithmic values of the
mean (averaged over all orientation and ensemble of test subjects within each BMI category)
τ
rms
computed for various channels and BMI categories are provided Table 3.9. There is a
considerable difference in delay dispersion between the BMI categories, with BMI 1 having
a higher dispersion than BMI 2, while BMI 3 had the least dispersion. This trend was also
observed in on-body channels as reported in [97]. The trend can be explained physically by
the fact that bodies with higher BMI shadow off parts of the body farther away from the
TX (e.g., the belly of a BMI 3 subject would more strongly shadow off the head from the
TX at the hip), thus reducing the impact of delayed MPCs.
58
Spatial Correlation
It is well established that the correlation of signals at different antenna elements could
have adverse effects on the diversity in SIMO/MISO, and the channel capacity of a MIMO
system [83]. Correlation is influenced by the angular spectrum of the channel as well as the
arrangement and spacing of antenna elements. A uniform angular power spectrum leads
approximately to a decorrelation of the incident signal for antenna spacing≥
λ
2
.
In our analysis, the magnitude of the correlation coefficients
2
(|ρ
RX
e,l
|) between sub-
channels of the RX array were computed. For each pair of sub-channels, the correlation
coefficient was computed for each body orientation measured, while observing if these coef-
ficient varied as the test subject changes his orientation. We found these sub-channels to
be uncorrelated (with an average correlation coefficients of approximately 0.1) even as the
test subject rotated his body orientation. We observed that there was very little variation
(< 0.03) in the values of the coefficient for different angles measured. We generated the CDF
of|ρ
RX
e,l
| by using an ensemble of values over all test subjects within each BMI categories and
angles measured with a sample plot for the back channel in a BMI 1 category provided in
Fig. 3.6.
0 0.2 0.4 0.6 |ρ|
0
0.2
0.4
0.6
0.8
1
CDF
|ρ
RX
12
|
|ρ
RX
13
|
|ρ
RX
14
|
|ρ
RX
23
|
|ρ
RX
24
|
|ρ
RX
34
|
Figure 3.6: Empirical CDF over of the correlation magnitude for RX array over ensemble of
test subjects and body orientations for BMI 1 category in the back channel in PAN
We did not observe any impact of BMI on the correlation coefficient values.
2
Note that e and l are indexes of different sub-channels.
59
Amplitude fading statistics
Fluctuation in the received signal amplitude over the 1× 4 SIMO sub-channels can be
attributed to the small-scale fading (SSF) on the body. This fluctuation also stems from
MPC interaction with local scatterers such as head, arm, etc (depending on the channel
measured), which exist within the vicinity of the receiver [97].
In our work, the SSF was investigated by considering fading on sub-carriers in different
sub-bands (Δf = 1 GHz) over the SIMO sub-channels. The choice of 1 GHz sub-band is due
to the non-stationarity of path gain observed over the measured bandwidth thereby leading
to a sub-division of the bandwidth into 1 GHz sub-bands with less path gain variation.
Within each sub-band, sub-carriers which are 330 MHz apart were chosen so as to reduce
the bias introduced by possible correlation between sub-carriers. The SSF statistics was
found to follow a Ricean distribution in our analysis with the RiceanK-factor for each
sub-band computed by using the methods of moments as described by (1)-(9) in [82]. This
RiceanK-factorwassubsequentlyaveragedovertheensembleofsub-bands. Foreachchannel
measured and body orientation, the equivalentK-factor was modeled as a random variable
using the ensemble of test subjects within each BMI category. TheK-factor was found to
be lognormally distributed with the logarithmic equivalent of its mean (μ
K
) and standard
deviation (σ
K
) provided in Table 3.9. The results in Table 3.9 seems intuitive since a high
RiceanK-factor is expected for the LOS angle (i.e., 270
◦
), while smaller values are expected
for other body orientations. Also, we did not observe any significant dependence of the
RiceanK-factor on BMI.
Channel capacity
We analyzed the SIMO channel capacities for the PAN channels measured for different
BMI categories in the anechoic environment. The SIMO channel capacity was derived for
two different TX power policies:
60
1. constant TX power (this would be used, e.g., when TX does not have channel state
information (CSI)).
2. fixed RX Signal-to-Noise Ratio (SNR), i.e., perfect power control.
The UWB capacity is computed as
C =
1
B
Z
B
log
2
|I
N
R
+
γ
N
T
H(f)H(f)
†
|df, (3.8)
where H(f) is the un-normalized transfer function of the channel under consideration, I
N
R
represents an identity matrix with sizeN
R
xN
R
(N
R
– number of RX antenna array element,
N
T
– number of TX antenna array elements) and B is the bandwidth of the considered
system. † denotes the Hermitian transpose. With the constant TX power assumption case
(listed above) the transmit SNR used was γ = 75 dB and is calculated from
P
TX
N
0
where P
TX
is the transmitted power and N
0
is the noise power per sub-carrier, while a receiver SNR,
γ = 22 dB+

10·log
10
n
R
f
|
˜
H(f)·
˜
H(f)
†
|df
o
is used in the case where a constant RX power
is assumed. This means that the power control compensates for the SNR variations due to
the body rotation and different test subjects. Note that in the constant RX power case a
normalized transfer function
˜
H(f) was used for the analysis. The mean (average over the
ensemble of test subjects) of the capacity (μ
capacity
) values are shown in Table 3.11 below.
It can be observed from the results in the constant TX power case that the channel
capacity values do in fact decrease when going from LOS to NLOS orientation, with a
difference of about 3 b/s/Hz, which can be attributed to human body shadowing. The
capacity values also decrease with increasing BMI. In the constant RX power analysis, the
channel capacity values do not exhibit a significant variation over the body orientation.
61
Mean path gain (
˜
G
L
, intra-BMI) from sub-banding Mean path gain (
˜
G
L
, inter-BMI) from sub-banding
front back front back
BMI A B A B BMI A B A B
1 -0.13 -75.71 -0.04 -75.34 {1 - 2} -0.80 -73.39 -0.14 -75.51
2 -0.26 -75.45 -0.04 -77.38 {1 - 3} -0.47 -73.15 -0.30 -73.38
3 -0.01 -75.84 -0.32 -77.63 {2 -3 } -0.37 -73.75 -0.38 -73.44
Shadowing parameters (ˆ μ
ˆ s
, intra-BMI) from sub-banding Shadowing parameters ( ˆ μ
ˆ s
, inter-BMI ) from sub-banding
front back front back
BMI A B A B BMI A B A B
1 0.01 7.57 0.10 9.26 {1 - 2} 0.38 7.27 0.03 8.98
2 0.14 6.18 -0.04 6.39 {1 - 3} 0.15 6.42 0.11 7.95
3 -0.22 10.79 -0.04 10.64 {2 -3 } 0.12 7.67 0.05 8.96
Table 3.5: Linear fit parameters for
˜
G
L
and ˆ μ
ˆ s
over sub-bands in B2B network.
3.6.2 B2B Modeling
Path gain analysis
For a pair of test subjects either belonging to the same intra-BMI category or different
inter-BMI categories, we compute the orientation-dependent mean power (
˜
M
υ,κ
ζ
,ξ,r,w
) as
shown in (3.9) from which we derive the mean path gain
˜
G
κ
ζ
,ξ
L
(see (3.10)) over an ensemble
of test subjects and body orientations.
˜
M
υ,κ
ζ
,ξ,r,w
=
N=801
X
n=1
¯
P
n,υ,κ
ζ
,ξ,r,w
, (3.9)
˜
G
κ
ζ
,ξ
L
=
1
W
·
1
R
·
1
Υ
W =4
X
w=1
R=4
X
r=1
Υ=3
X
υ=1
˜
M
υ,κ
ζ
,ξ,r,w
(3.10)
The computed path gain for channels and BMI categories measured are provided in Table
3.10. A difference of about 3-4 dB was observed between the mean path gain values in the
intra-BMI category from BMI 1 to BMI 2 & 3 while a difference about 2-3 dB was observed
in the inter-BMI case.
Shadowing analysis
The definition of the shadowing gain is the same as for the PAN case; though evaluations
are done relative to a pair of test subjects and separately for intra- and inter-BMI channels.
We compute the mean of the (normalized) shadowing standard deviation (ˆ μ
ˆ s
) here as the
averageoverensembleoftestsubjects(asshownin(3.11))withvaluesprovidedinTable3.10.
Also, for simplicity we refer to the mean of the (normalized) shadowing standard deviation ˆ μ
ˆ s
as the "effective pair body shadowing gain (EPBSG)". Due to the small number of subjects
62
here, we could only provide a mean value (i.e., EPBSG) as we could not compute the
cumulative distribution function (CDF). It can be observed that in the intra-BMI category,
EPBSG is about 3 dB higher for BMI 3 than BMIs 1 and 2 while a slight difference of about
0.5 to 1 dB exists in the inter-BMI category.
ˆ
S
υ,κ
ζ
,ξ
=D
r,w



10·log
10


˜
M
υ,κ
ζ
,ξ,r,w
E
r,w
n
˜
M
υ,κ
ζ
,ξ,r,w
o





, ˆ μ
κ
ζ
,ξ
ˆ s
=E
υ
n
ˆ
S
υ,κ
ζ
,ξ
o
(3.11)
Path gain analysis over sub-bands
The path gain analysis for different sub-bands was derived through a similar procedure to
Sec. VI-A.3 using a linear regression fit to estimate the relationship between path gain over
the different sub-bands. All parameters related to our analysis for both intra- and inter-BMI
categories are provided in Table 3.5.
Shadowing analysis over sub-bands
Alinearregressionanalysiswasalsoimplementedtocharacterizetherelationshipbetween
EPBSG (ˆ μ
ˆ s
) and the sub-bands. Sample plots of ˆ μ
ˆ s
over different sub-bands for the front
channel measured in both intra- and inter-BMI categories are shown in Figs. 3.7(a) and
3.7(b) below, while all parameters from the regression fit are provided in Table 3.5.
0 2 4 6
Frequency Sub-band (dBHz)
5
6
7
8
9
10
11
12
EPBSG
BMI 1
BMI 2
BMI 3
Fit BMI 3
Fit BMI 2
Fit BMI 1
(a)
0 2 4 6
Frequency Sub-band (dBHz)
5
6
7
8
9
10
EPBSG
BMI 1 - 2
BMI 1 - 3
BMI 2 - 3
Fit BMI 1 - 2
Fit BMI 1 - 3
Fit BMI 2 - 3
(b)
Figure 3.7: Linear fit for EPBSG (ˆ μ
ˆ s
) in the (a) intra- (b) inter-BMI categories in B2B
network
63
It can be observed from the results in Table 3.5 that ˆ μ
ˆ s
generally increased with frequency
with the exception of BMI 3 measurement, which showed a decrease over frequency in the
intra-BMI case for the front and back channels measured.
Delay dispersion analysis
Using a similar procedure as in the PAN analysis, the logarithmic values of the mean
(averaged over all orientation and ensemble of test subjects within each BMI category)
˜ τ
rms
computed for the intra- and inter-BMI categories are provided in Table 3.10 below.
Considerable difference in delay dispersion between the BMI categories exists in this case
as well, with BMI 1 having a higher dispersion than BMI 2, while BMI 3 had the least
dispersion. The dispersion in the inter-BMI categories seems fairly similar.
Spatial correlation
Using a similar approach to the PAN SIMO case, the spatial correlation of the sub-
channels in the B2B channels was analyzed. The magnitude of the correlation coefficients
at the TX array (|ρ
TX
α,ω
|) and the RX array (|ρ
RX
e,l
|) were computed. For each fixed antenna
element at the TX, correlation between a pair of sub-channelse,l at the receiver is computed
for each body orientation of both the TX and RX antenna array bearer, while observing if
these coefficients varied as the test subjects changed their orientation. We found these
sub-channels to be uncorrelated (irrespective of the orientation) with an average correlation
coefficients of approximately 0.1. To generate the CDF of these coefficients, we used an
ensemble of coefficient values obtained over different test subjects within a BMI category,
sub-channels and orientations measured. A sample CDF plot for|ρ| at the TX and RX
arrays are shown in Figs. 3.8(a) and 3.8(b). We did not observe any impact of BMI on the
correlation coefficient values in both the intra- and inter-BMI categories.
64
0 0.2 0.4 0.6 0.8
|ρ|
0
0.2
0.4
0.6
0.8
1
CDF
|ρ
TX
12
|
|ρ
TX
13
|
|ρ
TX
14
|
|ρ
TX
23
|
|ρ
TX
24
|
|ρ
TX
34
|
(a)
0 0.2 0.4 0.6 0.8
|ρ|
0
0.2
0.4
0.6
0.8
1
CDF
|ρ
RX
12
|
|ρ
RX
13
|
|ρ
RX
14
|
|ρ
RX
23
|
|ρ
RX
24
|
|ρ
RX
34
|
(b)
Figure 3.8: Empricial CDF of the correlation magnitude for (a) TX array (b) RX array over
ensemble of test subjects and body orientations for BMI 1 for Front Channel in B2B network
Amplitude fading statistics
Using a similar modeling approach from Sec. VI-A.7, a Ricean distribution fit was also
found as a fit for the SSF in the B2B measurements. The RiceanK-factor was computed
for the intra- and inter-BMI categories with results provided in Table 3.9. Note that only
specific orientations; body facing each other (FEO), backing each other (BEO) and right
angle to each other (RAEO) where chosen to reflect cases that results in the best, worst
and "typical"K-factor values. From both intra- and inter-BMI results, the highestK-factor
occur in the LOS scenario while the lowest values occur in the NLOS scenarios, i.e., when
the two bodies (TX and RX bearers) serves as obstructions. This result agrees well with
intuition. We did not observe any dependence of the RiceanK-factor on BMI (in both intra-
and inter- cases).
Channel Capacity
In this analysis, we have used the assumption that the TX does not have CSI, and the
UWB capacity is computed for the B2B channels for the intra- and inter-BMI categories by
using (3.8). Capacity results are provided in Table 3.9. Also, only specific orientations; body
facing each other (FEO), backing each other (BEO) and right angle to each other (RAEO)
were chosen to reflect cases that results into the best, worst and "typical" capacity values here
65
as well. The results from both intra- and inter-BMI analysis show that the highest capacity
occur in the LOS scenario while the lowest capacity values occurs in the NLOS scenarios,
i.e., when the two bodies (TX and RX bearers) serves as obstructions, which agrees well
with intuition.
3.7 Implementation Recipe
The simulation objective is to create a frequency-selective SIMO (in PAN) or MIMO (in
B2B networks) fading channel (
˜
H) withN
T
transmit andN
R
receive antennas for PAN and
B2B channels. The channel realizations can thus be generated as follows:
1. Select body channel and BMI category desired.
2. Select a suitable frequency band and delay window for the simulation. Also, select
appropriate sampling grid to create taps in delay.
3. From Table 3.9, select corresponding values forG
L
(dB) as in (3.4) for PAN simulation
while using equivalent parameters from Table 3.10 for the B2B simulation.
4. Generate P
n
for each delay tap using
P
n
=G
L
·S·η·e
−
τn−τ
0
α
(3.12)
where S is a zero-mean lognormal random variable (i.e., shadowing) having a deter-
ministic variance in the B2B networks, however, the variance ofS is actually a random
variable in the PAN with second moment values provided in Table 3.9. α is the rms
delay spread obtained from Table 3.9 while η is a normalization constant such that
P
∞
n=0
e
−
τn−τ
0
α
=
1
η
.
5. Compute the Fourier transform (F{·}) of P
n
such that P
f
=F{P
n
}.
66
6. Generate a matrix
ˆ
H
LOS
for the LOS component using (3.13) and (3.14)
ˆ
H
LOS
=a(p)·a(q)
T
, (3.13) a(r) =e
−j
2π
λ
|
− →
r
i
−
− →
r
j
|
(3.14)
where|
− →
r
i
−
− →
r
j
| is the location vector of the array antenna elements.
7. Generate a residual matrix
ˆ
H
res
as shown in (3.15).
vec(
ˆ
H
res
) =R
1/2
vec(H
w
) (3.15)
where the N
T
N
R
×N
T
N
R
matrix R
1/2
is obtained by factoring the total correlation
matrix R, i.e., R = R
1/2
R
1/2
. The spatial correlation matrix R can be generated
using the coefficients described in Sec. VI-A.6 and VI-B.6. H
w
is a complex i.i.d white
Gaussian random matrix.
8. Generate a linear equivalent of theK (dB) from the Gaussian distribution using cor-
responding moment values in Table 3.9.
9. Generate a realization of the propagation channel
¯
H in (3.16) by combining all the
parameters above.
¯
H =
q
P
f


s
K
K + 1
ˆ
H
LOS
+
s
1
K + 1
ˆ
H
res


(3.16)
10. Multiply
¯
H by

f
f
0

−κ
to obtain
˜
H as shown in (3.17)
˜
H =
¯
H·

f
f
0
!
−κ
(3.17)
where the exponent−κ is equivalent to A from Tables 3.4 and 3.5 for PAN and B2B
networks respectively.
67
3.8 Model Validation
The model presented in this work was validated by comparing:
• Abaselinemodelderivedfromanotherexperimentweconductedwithourmeasurement
setup, to an existing work in the literature with a similar setup.
• The mean path gain (G
L
) and EBSG (μ
s
) from the PAN measurements in a sub-
group analysis approach. Specifically, we divided each BMI category randomly into
two subgroups, extracted parameters for each of the groups, and compared them.
• Capacityvaluesgeneratedfromthemeasurementdatatothosefromthedatagenerated
synthetically from our model.
We do not provide a model validation for the B2B channel model using an analysis of
statistical significance, due to small ensemble size of test subjects used.
3.8.1 Baseline path gain and shadowing modeling approach
Path gain and shadowing in PAN and B2B channels have been discussed in the literature
showing that the variation in the received power, i.e., shadowing can be separated into that
due to the environment and that due to the human body [91]. As a sanity check in our
work, we undertook an experiment with a setting similar to [91], namely in an indoor lab
environment (as opposed to the anechoic chamber used elsewhere in our measurements), and
at different distances between TX and RX. We then compare parameters such as distance-
dependent path gain exponent (n) and shadowing gain (X
env
– due to environment, X
b
–
due to the body) to those in [91].
We conducted a UWB (2-10 GHz) SIMO measurement in an indoor lab environment
with TX antenna (using a UWB TEM horn antenna) placed on a 1.4 m high pole while a
4-element receiver array was mounted on the torso of a human subject (Fig. 3.2(a)). The
humansubjectremainedatafixedlocationwhiletheTXwasmovedtodifferentdistances(for
68
0 2 4 6 8 10
−75
−70
−65
−60
−55
−50
−45
−40
10log
10
(d)
Path gain (dB)
Pathloss for PAN Indoor Lab

G
tot
(d)
n=1.42
G
i
(d,o)
Figure 3.9: Linear regression fit for path gain over distance
TX-RX separation). At each measured distance, the human subject rotated his orientation
at 45
◦
increments from 0
◦
to 315
◦
, similar to the description in Sec. III. The measured
distances covered 16 values in the range 1 to 8 m.
Path gain model derivation
Firstly, wedevelopapathgainmodelinwhichthetotalpathgainG
tot
(d)isdefinedasthe
average of the local path gain (G
i
(d,o)) over body orientation at each distance measured,
where G
i
(d,o) is defined as the aggregate power of the APDP (over delay bins) at each
distance and body orientation.
The distance-dependent path gain can be visualized from the scatter plot of both G
tot
(d)
and G
i
(d,o) at each measured distance shown in Fig. 3.9. A linear regression fit was imple-
mented to create a power-decay model in (dB) as shown in (3.18). This linear fit emphasizes
monotonic dependence of the total path gain on distance with parametersn and G
0
provided
in Table 3.7. Note that at each distance (d) in Fig. 3.9 G
tot
(d) was obtained by averaging
G
i
(d,o) on a linear scale while the display is plotted in decibels.
G
det
(d) = G
0
− 10·n·log
10

d
d
0
!
+X
env
(3.18)
69
-10 -5 0 5 10
shadow gain (dB)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Gaussian Fit
(a)
-20 -10 0 10 20 30
shadow gain (dB)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Gaussian Fit
(b)
2 3 4 5 6 7 8
shadow gain (dB)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Gaussian Fit
(c)
Figure 3.10: Empirical CDF and corresponding Gaussian fit for (a) shadowing (X
env
) due to the
environment (b)X
b
at a select distance (c) standard deviation of X
b
for all distances
Shadowing Model derivation
From Fig. 3.9, the deviation of the total path gain (G
tot
(d)) from the linear (determinis-
tic) fit stems from the shadowing (X
env
) caused by the environment, while the variation of
the G
i
(d,o) around the G
tot
(d) is a consequence of the human blockage effect (shadowing,
X
b
) at different orientations. This blockage effect will henceforth be referred to as "human
body shadowing". This shadowing have been stated to be zero-mean lognormal distributed
random variable in the literature; we also find this to be true in our work. Fig. 3.10(a)
shows the CDF of a Gaussian distribution fit for a logarithmic fit of X
env
, while a match
of X
env
to some other commonly used distributions such as Rayleigh, Rician, lognormal,
Nakagami, and Weibull were implemented by using the K-S hypothesis test to determine
the goodness-of-fit at 5% significant level; the passing rates are given in Table 3.6. It is clear
that the lognormal distribution has the highest passing rate.
Table 3.6: Passing rate of K-S test at 5% significance level for X
env
Distribution K-S
Weibull 76.05
Rayleigh 50.61
Rician 50.61
lognormal 88.03
Nakagami 73.63
The body shadowing X
b
was found to be zero mean lognormally distributed at different
distances (see Fig. 3.10(b)). The standard deviation ofX
b
differed from location to location
and has been modeled as a random variable. A Gaussian fit was found to be adequate for
70
the distribution of these standard deviation values (in dB) as shown in Fig.3.10(c) with
second-order parameters (mean (μ
σ
b
(dB)), standard deviation (σ
σ
b
(dB))) provided in Table
3.7.
Table 3.7: Comparison of parameters
Parameters Our work ref [91] (LOS AP2HH
2.6
)
n 1.42 1.40
σenv (dB) 1.89 2.30
μσ
b
(dB) 5.05 2.30
3
σσ
b
(dB) 0.64 N/A
G
0
(dB) -50.96 -43.00
From Table 3.7, we see that the path gain coefficient and environment shadowing are
similar to that in the literature (ref. [91]), while the body shadowing variance in our case is
considerably larger. We conjecture that this might be due to the different used antennas, as
well as the different mounting on the body. In summary, while not a conclusive proof, the
similarity of our results with the literature tends to support our measurement and extraction
procedure.
3.8.2 Sub-group Analysis approach
For each BMI category, we randomly divided the measurement data into two sub-groups
(having equal number of candidates) and extracted parameters such as G
L
and μ
s
for com-
parison in the hip, front and back channels. Similar parameter values between the two
sub-groups, which are also in agreement with the overall results shown in Table 3.9, would
corroborate the accuracy of our result. All extracted parameters from our sub-group analysis
approach are presented in Table 3.8.
Table 3.8: Parameters extracted from BMI categories sub-groups in PAN measurements
Sub-group 1 - G
L
(dB) Sub-group 1 - μs (dB)
hip front back hip front back
BMI 1 -65.06 -67.66 -67.74 2.35 4.64 5.41
BMI 2 -65.55 -68.16 -68.08 2.71 5.72 5.73
BMI 3 -69.54 -72.35 -71.41 2.65 6.21 6.31
Sub-group 2 - G
L
(dB) Sub-group 2 - μs (dB)
hip front back hip front back
BMI 1 -64.05 -66.38 -66.48 2.61 4.87 4.94
BMI 2 -64.25 -67.94 -68.30 3.02 5.47 5.72
BMI 3 -67.84 -70.85 -69.96 2.64 6.80 6.40
71
It can be observed from Table 3.8 that the parameters from different sub-groups for these
channels are similar to each other, and are close to the values provided in Table 3.9. This
indicates the reliability of our model.
3.8.3 Capacity Approach
For each channel measured, an equal power capacity [42] was computed by using the
channel coefficients from
¯
H. The CDF of the capacity (TX SNR = 75 dB) obtained from
data generated synthetically from our model and that computed from the measurement data
for each BMI category for the Front channel are compared in Figs. 3.11(a)-3.11(c) below.
The CDF was derived using an ensemble of candidates (within each BMI categories) and all
orientations measured.
2 4 6 8 10
capacity (b/s/Hz)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Simulated
(a)
2 4 6 8 10
capacity (b/s/Hz)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Simulated
(b)
2 4 6 8 10
capacity (b/s/Hz)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Simulated
(c)
Figure 3.11: Emprical CDF and model fit of capacity for (a) BMI 1 (b) BMI 2 (c) BMI 3
Visually, it is clearly observable (from the CDFs plots in Figs. 3.11(a) to 3.11(c)) that
the capacity results from the model does have a good fit to that obtained from the measured
data.
3.9 Summary and Conclusion
We conducted a measurement campaign using UWB multi-antenna channel sounders (a
SIMO (1× 4) antenna array for PAN measurements and a MIMO (4× 4) antenna array for
B2B measurements) in various off-body channels for different BMI categories in an anechoic
72
PAN path gain (β (dB))
hip channel
Angles 0
◦
45
◦
90
◦
135
◦
180
◦
225
◦
270
◦
315
◦
β
BMI 1
-65.55 -66.56 -69.41 -66.19 -63.34 -62.64 -62.43 -62.80
β
BMI 2
-65.62 -67.12 -70.53 -66.17 -63.72 -62.46 -62.40 -63.12
β
BMI 3
-69.23 -67.93 -73.93 -68.77 -67.02 -67.43 -65.15 -66.70
front channel
β
BMI 1
-64.10 -67.05 -72.35 -68.45 -65.30 -62.93 -62.48 -63.09
β
BMI 2
-63.28 -68.72 -76.83 -68.93 -64.11 -62.55 -62.07 -61.82
β
BMI 3
-68.08 -68.82 -84.64 -75.90 -68.76 -66.27 -67.23 -64.95
back channel
β
BMI 1
-64.38 -61.58 -62.32 -62.77 -64.47 -70.65 -74.21 -70.71
β
BMI 2
-64.70 -61.63 -61.40 -62.35 -63.88 -71.29 -75.63 -71.85
β
BMI 3
-67.57 -64.21 -65.23 -65.88 -66.74 -74.03 -79.31 -76.38
PAN Mean path gain (G
L
(dB)) and shadowing gain Modeling
Mean path gain (G
L
(dB)) (Shadowing parameters (μs (dB),σs (dB) ))
Channel hip front back hip front back
BMI 1 -64.86 -65.72 -64.91 μs=3.35, σs=1.25 μs=6.26, σs=2.64 μs= 6.12, σs= 2.05
BMI 2 -65.14 -66.04 -65.59 μs=3.65, σs=1.59 μs=6.65, σs=1.84 μs= 6.52, σs=2.24
BMI 3 -68.18 -70.58 -69.92 μs=3.73, σs=0.94 μs= 7.64, σs=2.33 μs=7.75, σs=2.70
PAN rms delay spread (τrms (dB))
Channel hip front back
BMI 1 -93.00 -94.29 -94.61
BMI 2 -93.28 -94.02 -95.01
BMI 3 -93.64 -97.29 -96.82
RiceanK-factor (dB) from PAN
hip channel
Angles 0
◦
45
◦
90
◦
135
◦
180
◦
225
◦
270
◦
315
◦
μ
K,BMI 1
-2.01 -0.95 -2.54 -3.20 -2.37 -0.43 2.85 -1.07
σ
K,BMI 1
2.82 0.61 0.50 1.00 0.21 1.21 1.59 0.84
μ
K,BMI 2
-1.47 -1.54 -2.09 -1.18 -1.99 -1.20 2.53 -0.75
σ
K,BMI 2
0.81 0. 37 0.84 0.70 0.72 1.74 2.03 1.60
μ
K,BMI 3
-0.91 -1.03 -3.22 -0.58 -2.31 -2.51 1.09 -1.81
σ
K,BMI 3
1.11 0. 32 0.52 1.43 2.31 2.10 0.25 1.03
front channel
μ
K,BMI 1
-1.64 -0.73 -0.95 -2.71 -0.96 -0.78 1.70 -0.90
σ
K,BMI 1
0.42 0.91 0.22 1.12 0.52 0.50 0.66 0.37
μ
K,BMI 2
-3.25 -1.14 -1.22 -1.75 -2.39 -1.04 1.24 -0.04
σ
K,BMI 2
0.33 0.81 0.73 1.02 0.53 0.61 0.73 0.30
μ
K,BMI 3
-1.91 -1.49 -1.66 -1.24 -2.23 -0.61 0.77 -1.06
σ
K,BMI 3
0.21 0.34 1.50 0.21 1.03 1.00 0.11 1.02
back channel
μ
K,BMI 1
-3.41 -2.09 1.20 -0.70 -2.15 -3.06 -1.91 -2.78
σ
K,BMI 1
1.71 1.37 0.23 0.11 1.11 1.34 0.40 1.39
μ
K,BMI 2
-0.41 -0.37 1.71 -1.03 -1.24 -1.65 -1.58 -1.61
σ
K,BMI 2
0.42 0.61 0.40 1.00 1.01 1.39 0.32 0.23
μ
K,BMI 3
-0.62 -0.54 2.21 -0.74 -1.43 -1.00 -2.00 -1.34
σ
K,BMI 3
0.11 0.41 0.32 0.43 0.50 0.23 1.11 1.03
RiceanK-factor (dB) from intra-BMI in B2B network
front back
FEO BEO RAEO FEO BEO RAEO
BMI 1 1.38 -1.32 -1.01 -2.77 0.89 -1.08
BMI 2 1.49 -1.13 -0.97 -1.67 0.92 -1.28
BMI 3 1.22 -1.83 -1.20 -2.01 1.37 -1.16
RiceanK-factor (dB) from inter-BMI in B2B network
front back
FEO BEO RAEO FEO BEO RAEO
BMI {1 - 2} 1.36 -2.34 0.80 -2.14 1.50 1.18
BMI {1 - 3} 1.16 -1.04 -1.61 -1.65 0.85 -1.35
BMI {2 - 3} 1.95 -2.47 1.09 -2.24 1.62 -0.09
Table 3.9: Parameters extracted for various channels and BMI categories in PAN and B2B
networks
Intra-BMI
front channel back channel
Parameters BMI 1 BMI 2 BMI 3 BMI 1 BMI 2 BMI 3
˜
G
L
(dB) -73.98 -76.39 -76.66 -74.5 -76.29 - 78.88
ˆ μ
ˆ s
(dB) 7.10 7.99 10.29 9.75 9.38 11.28
˜ τrms (dB) -94.87 -97.37 -99.17 -96.20 -97.91 -99.60
Inter-BMI
front channel back channel
Parameters BMI {1 - 2} BMI {1 - 3} BMI {2 - 3} BMI {1 - 2} BMI {1 - 3} BMI{ 2 - 3}
˜
G
L
(dB) -76.41 -74.58 -74.55 -75.43 -74.21 - 74.19
ˆ μ
ˆ s
(dB) 9.44 8.92 8.30 9.45 8.30 9.04
˜ τrms (dB) -96.77 -96.71 -96.72 -97.86 -98.47 -97.35
Table 3.10: Parameters extracted for various channels and BMI categories in the B2B chan-
nels
73
PAN Channel Capacity (b/s/Hz), Constant TX Power, TX SNR = 75 dB
hip channel
Rot. angles 0
◦
45
◦
90
◦
135
◦
180
◦
225
◦
270
◦
315
◦
μ
BMI 1
capacity
5.67 5.33 4.58 5.38 6.15 6.58 6.72 6.51
μ
BMI 2
capacity
5.71 5.20 4.23 5.27 6.29 6.46 6.64 6.59
μ
BMI 3
capacity
5.57 6.30 4.64 4.63 5.68 5.78 6.43 6.34
front channel
μ
BMI 1
capacity
6.15 5.49 4.20 4.93 6.02 6.36 6.62 6.44
μ
BMI 2
capacity
6.25 4.96 3.61 4.69 6.17 6.57 6.73 6.79
μ
BMI 3
capacity
5.91 6.15 3.16 3.26 5.44 6.44 6.40 6.55
back channel
μ
BMI 1
capacity
6.06 6.59 6.67 6.58 6.08 4.62 3.78 4.19
μ
BMI 2
capacity
5.90 6.76 6.80 6.61 6.09 4.08 3.60 4.15
μ
BMI 3
capacity
5.62 6.75 6.67 6.63 6.30 3.32 3.31 3.25
PAN Channel Capacity (b/s/Hz), Constant RX Power, RX SNR = 22 dB
hip channel
μ
BMI 1
capacity
6.27 6.39 6.18 6.33 6.26 6.28 6.18 6.33
μ
BMI 2
capacity
6.32 6.09 5.98 6.23 6.29 6.26 6.23 6.24
μ
BMI 3
capacity
6.14 6.14 5.79 6.33 6.28 6.39 6.50 6.29
front channel
μ
BMI 1
capacity
6.20 6.06 5.32 5.92 6.30 6.27 6.20 6.22
μ
BMI 2
capacity
5.86 5.84 5.19 6.13 6.20 6.31 6.10 6.17
μ
BMI 3
capacity
6.26 5.50 4.83 5.33 6.37 6.34 6.26 6.43
B2B Capacity (b/s/Hz) of intra-BMI
front back
FEO (b/s/Hz) BEO (b/s/Hz) RAEO (b/s/Hz) FEO (b/s/Hz) BEO (b/s/Hz) RAEO (b/s/Hz)
BMI 1 8.70 2.34 5.34 1.98 8.41 5.30
BMI 2 8.79 2.19 5.26 2.06 7.50 4.70
BMI 3 8.54 1.82 5.81 1.95 8.45 4.88
B2B Capacity of inter-BMI
front back
FEO (b/s/Hz) BEO (b/s/Hz) RAEO (b/s/Hz) FEO (b/s/Hz) BEO (b/s/Hz) RAEO (b/s/Hz)
BMI {1 - 2} 8.56 2.11 4.66 1.94 8.61 5.60
BMI {1 - 3} 8.31 2.41 5.33 2.17 8.95 5.70
BMI {2 - 3} 8.80 2.19 5.51 1.99 8.41 5.49
Table 3.11: Capacity values for various channels and BMI categories in the PAN and B2B network
chamber environment and extracted the relevant channel parameters. The main findings
are:
1. The mean (average over the ensemble of test subjects) path gainβ in the PAN channel
changes over body orientation (from LOS to NLOS) with variation of about 8-9 dB in
the hip channel, and 11-14 dB in the front and back channels across all BMI categories.
We observed that the mean (average over an ensemble of test subjects and rotation)
path gain G
L
varied over the BMI categories with BMI 3 being 3-4 dB less than BMI
1 & 2 in the PAN channel while for the B2B channel, a difference of about 3-4 dB was
observed between
˜
G
L
values in the intra-BMI categories with 2-3 dB observed in the
inter-BMI.
2. We observed in the PAN channel that the human body shadowing gain followed a zero-
mean lognormal distribution with a standard deviation modeled as a random variable
74
(using an ensemble of test subjects). The mean of the standard deviation (denoted as
EBSG) was found to be about 3 dB for the hip channel and about 6-7 dB for the front
and back channels while also showing a variation of about 1 dB between the various
BMI categories. For the B2B channel, the mean of the standard deviation (denoted as
EPBSG) ranges from about 7-12 dB in the front and back channels for the intra-BMI
category and about 8-9 dB in the inter-BMI category. Also a variation was observed
in the BMI categories, which was about 3 dB higher for BMI 3 than BMI 1 and 2 in
the intra-BMI category and about 0.5 to 1 dB in the inter-BMI category.
3. The mean path gains G
L
,
˜
G
L
generally decreased over frequency of sub-bands (Δ =
1 GHz) while the EBSG/EPBSG increased over the frequency sub-bands in both PAN
and B2B channels with the exception of BMI 3 category in the intra-BMI 3 (in the
B2B channel), which decreased over the frequency sub-bands.
4. The RMS delay spread values show a considerable difference among the BMI categories
in both PAN and B2B channels with BMI 1 having a higher dispersion than BMI 2,
while BMI 3 had the least dispersion.
5. Thespatialcorrelationcoefficientbetweensub-channelsinbothPANandB2Bchannels
shows a low correlation with a mean value of about 0.1. We did not observe any impact
of BMI on the correlation coefficient values from both PAN and B2B channels.
6. From the SSF analysis, the RiceanK-factor over different body orientation (in both
PAN and B2B channels) differ considerably, and are lowest when the antennas are in a
NLOS scenario. We did not observe any significant dependence of the RiceanK-factor
on BMI.
7. The capacity values (without Channel State Information at TX (CSIT)) over different
body orientation (in both PAN and B2B channels) differ considerably, and are lowest
when the antennas are in a NLOS scenario. This is especially prevalent in BMI 3,
75
which also happens to typically have the smallest capacity. The capacity values are
fairly constant in the PAN channels when power control is used. In the B2B channels
withoutCSITthemean(overanensembleoftestsubjects)capacityvaluesaretypically
strongest in the LOS and weakest in the NLOS scenario for both intra- and inter-BMI
categories.
8. The results were validated firstly, by measuring (for a single person) the channels at
different distances. The extracted path gain coefficient, environment shadowing and
body shadowing agreed reasonably well with the literature [91]. This serves as a sanity
check for our measurement setup and procedure. Secondly, the agreement between
parameters extracted from sub-group of the data at each BMI category also validates
the results.
Overall, it is clearly observable from the results and statistics presented in this paper
that the propagation channel parameters for the UWB PAN and B2B channel do in fact
differ for different BMI categories. The present PAN and B2B models do not take this
into account; hence our work serves as either a complement to pre-existing models or a
replacement. Details such as those provided in this work will be of help for PAN or B2B
systems design and simulation in various environments.
76
Chapter 4
A Measurement-based Model for
Outdoor Near-ground Ultrawideband
Channels
4.1 Introduction
Ultrawideband (UWB) wireless communications has garnered considerable amount of
attention over the years for robust communication and precision ranging/localization. UWB
signals are commonly defined as either having more than 20% relative bandwidth or more
than 500 MHz absolute bandwidth [6]. The approval of the 3.1-to-10.6 GHz as a dedicated
spectrum for UWB communications by the Federal Communication Commission (FCC) gave
rise to a large volume of theoretical and practical work on system designs using UWB
signaling [7]. Communications systems based on time-hopping impulse radio [121], [122],
direct-sequence spread spectrum [123], and frequency-hopping OFDM systems [124] have
been proposed. Advantages of UWB include robustness to frequency-selective fading [2],
[125], efficient use of radio spectrum through underlaying techniques [122], robustness to
narrowband interference [126], and capability for precision ranging and localization [127].
UWB communication systems are designed to operate in different environments ranging
from residential, office, industrial, warehouse, to outdoor environments. For the design of
suitable systems, it is essential that the channel in which these systems would operate be
duly characterized and a proper model established, since the propagation channel ultimately
determinestheperformanceofanywirelesssystems. Bydefinition, narrowbandor"standard"
77
wideband channel models are insufficient to characterize UWB channels, so that new models
have to be established. Over the past 15 years, a considerable number of measurement
campaigns and models have been published (see, e.g., [128, 129, 130] and references therein).
Lately, there has been a significant growth in the use of wireless systems whose
transceivers are in close proximity to the ground. While some systems have already been
deployed for use in different fields, some are still just envisioned. These systems are/could
be used in a variety of applications including: Outdoor wireless broadband systems [131];
Perimeter monitoring and security related applications [132]; Localization of rescue workers
in emergency or disaster relief zones [133]; Wireless sensor networks deployment in outdoor
environments [134]; Navigation and localization for robots [135]; Tactical communications
[136].
4.1.1 Related work
It has been indicated that wireless propagation channel parameters vary according to
Tx/Rx antenna heights proximity to the ground [137, 138, 139]. Hence, it is important that
these propagation channel parameter variations be characterized. Several publications have
addressed near-ground channel measurements and modeling, though none of those consider
ultra-wide bandwidth. An empirical study of the propagation losses that is associated with
fixed wireless services from near-ground base stations to homes in suburban environment
was considered in [138] using a 200kHz bandwidth at 3.5 GHz center frequency. Urban
propagation measurements were conducted using mainly the military Ultra-High-frequency
(UHF) bands (between 225MHz and 450MHz) in [139], which does not fall into the UWB
spectrum range being considered in our work. Near-ground propagation channel measure-
ments at a 900 MHz center frequency in a yard/park environment was also explored in [140],
with a 50 MHz bandwidth. Temporal variations of near-ground channels induced by mov-
ing scatterers (with static Tx/Rx locations) were explored in [141], using a 2.6 GHz center
frequency and 200 MHz bandwidth. This measurement was done with the sensor nodes at
78
Figure4.1: TheMeasurementSiteatUSCWrigleyMarineScienceCenteronCatalinaIsland.
CA . USA
only a few meters apart. Outdoor measurement and modeling of near-ground scenarios were
also conducted in a large plaza, a straight sidewalk and an open grassland in [142], with
a narrowband setup with center frequency at 2.4 GHz. [143] showed results from a nar-
rowband and wideband measurements conducted at 300 MHz and 1900 MHz investigating
effects of transmit and receiver antenna heights, antenna radiation patterns as well as effects
of foliage in a forest environment. [144] explored propagation of ground lying antennas over
the 800-1000 MHz frequency range. [145] conducted measurements and proposed a model
for near-ground short-range propagation loss in forested areas at the Ultra-High-frequency
(UHF) and Very-High-frequency (VHF) bands. [137] also investigated short-range, narrow-
band near-ground scenarios using portable transceivers and noticed a significant decrease in
power as these transceivers got closer to the ground. Also, [146] studied the effects of placing
a cellular/PCS near the ground. [147] performed outdoor UWB channel measurement in a
rural environment, measuring over a bandwidth of 1.3 GHz. [148] also performed outdoor
UWB channel measurements mainly for the 3-6 GHz frequency range, while most recently,
are measurements from [149] and [150], but none of these measurements were for transmit-
ter/receivers near ground. Extensive Channel measurements for both indoor and outdoor
UWB channels are reviewed in [62] and [128]. Although [151] performed a near-ground UWB
measurement campaign, it was done in an indoor environment, over short distances.
79
4.1.2 Contributions
As can be seen from the literature review above, there exist, to the best of our knowledge,
no measurements detailing ultrawideband, near-ground channels in an outdoor environment.
In this paper, we remedy this by investigating the effect near-ground antennas have on
UWB propagation channel parameters. The contributions of this paper can be summarized
as follows:
• Weprovideanextensivereportonthechannelmeasurementcampaignperformedusing
a newly developed channel sounder setup, which allows for UWB measurements at
distances up to several hundred meters.
• We provide estimates and statistics of extracted propagation channel parameters such
as pathloss exponent (γ), frequency-dependence coefficient of the pathloss (κ), rms-
delay-spread (τ
rms
), shadowing variance and amplitude fading statistics.
• We explore the relationship these parameters have with other parameters and observe
their dependency on antenna heights.
4.1.3 Organization
This paper is organized as follows. Section II describes the measurement environment
investigated in this campaign. Section III describes the measurement setup. Section IV
describes the data evaluation procedure used in obtaining parameter estimates as well as
the extracted results. Section V provides a model validation, while conclusions are drawn in
Section VI.
4.2 Measurement Environment
In order to ensure the accuracy of the measurements, we were striving to measure in
a static (time-invariant) environment that had as little man-made interference as possible.
80
We thus chose the secluded USC Wrigley marine science facility (see Fig. 4.1) on Catalina
Island; this facility is located off the coast of California about 47 miles from downtown Los
Angeles.
The measurements were performed in two different environments, which can be best
described as rural flat and hilly terrains (see Figs. 4.2 & 4.3). The flat terrain is an almost
level surface with some small unevennesses. Typical features in this environment include 10
cmhighgrass(patchyinmostplaces), occasionalshrubsnohigherthan3-4m, andresidential
and aquatic research labs at distances over 30 m, which may serve as scattering/shadowing
objects. Most part of the hilly terrain was covered by 20-30 cm high dry grass and very little
scattered vegetation with 3-5 m height. We chose to measure the fairly accessible part of the
hilly terrain. It can be observed from Fig. 4.3 that the hilly terrain site, which was originally
used as a wreck yard (by the Institute), has man-made objects in the valley. These include
abandoned boats, vehicles, large storage containers; a few mobile homes were also adjacent
to the hilly terrain. These objects were deemed as probable reflection points and scatterers
in the channel.
The month in which the measurement campaign was performed corresponds to the the
wet season on the island, therefore we often experienced rain showers during the day. The
grass as well as soil is usually moderately moist as a result of these showers and partly due
to the early morning dew. Measurement campaigns were usually suspended on days with
rainy weather forecast.
The measurement was performed for a Line-of-sight (LOS) scenario. Therefore we made
sure none of the aforementioned objects in the environment caused an obstruction of the LOS
between the transmitter and receiver setup in the channel. However, minor obstructions are
probable in the first Fresnel zone of the propagation channel based on the placement of the
Tx and Rx antennas.
81
Figure 4.2: Flat terrain Measurement site
Figure 4.3: Hilly terrain Measurement site
4.3 Measurement Setup
We designed and assembled a task-specific propagation channel sounder system for this
measurement campaign. The block diagram for the system is shown in Fig. 4.4; detailed
information about the components are provided in Table 6.1. Note that the components
are all commercially available; it is the specific combination thereof, and the waveform
design and signal processing, that makes the setup uniquely suited for UWB long-distance
measurements.
At the heart of the transmitter is an arbitrary waveform generator (AWG), which is
used for generating multitone (OFDM-like) sounding waveforms as well as triggering the
digital sampling oscilloscope (DSO) that is used at the receive end for data acquisition and
display. The AWG was operated in an interleaved mode to utilize the maximum available
82
bandwidth. The interleave mode creates signals from two 12 GS/s digital-to-analog (D/A)
channels, offset in time by half the sampling period and combined to reach a higher sampling
rate of 24 GS/s. A 22 dB gain pre-amplifier was used together with a 10W 40dB high power
amplifier (HPA) designed to operate in the frequency range of the transmitted signal. A
pair of UWB Skycross omni-directional antennas [152] were used at both transmitter and
receiver side of the channel sounder.
The core component at the receiver side is the digital sampling oscilloscope (DSO) oper-
ating at 40 GS/s. A 30 dB low noise amplifier (LNA) is placed between the receiver antenna
and the DSO. AWG marker channels were configured to send control/trigger signals to the
DSO at the receiver side. Since the channel sounder was designed for long- distance mea-
surements, the trigger signal from the AWG was transported to the DSO (which could be up
200m away) using an RF-over-fiber link: the RF trigger signal from the AWG was sent to
an electro-optical converter unit (Tx Module in Fig. 4.4), which converts the RF signal into
an optical signal and then transmits this through an optical fiber. The RF-over-fiber link’s
Rx module converts the signal back to the RF domain and is connected to a designated
trigger input port of the DSO. The decision to use an RF-over-fiber approach (and not a
coaxial cable) stems from the fact that losses incurred in any commercial coaxial cable would
have been too high to allow successful transmission of the trigger signal over the targeted
measurement distances.
The channel measurement campaign was performed over a 3− 10 GHz frequency range
using a 1 x 4 SIMO virtual antenna array setup. For each measurement, the Tx antenna
remained fixed, while the Rx antenna was placed at virtual array positions horizontally
separated by 5 cm, corresponding to half a wavelength at the lower band edge. Four Rx
antenna positions were used in our measurement due to logistical reasons and some limita-
tions imposed by our measurement setup.
Antenna proximity to the ground is expected to have an impact on the different channel
parameters extracted, hence, various antennas height combination for Tx and Rx antennas
83
Figure 4.4: UWB Channel Sounder setup
havebeenconsideredforthechannelmeasurement. Theantennaheightcombinationusedare
stated in Table 4.2. The antenna heights are chosen to match probable antenna deployment
heights in a tactical or outdoor environment. Also, Fig. 4.5 shows the Tx antenna at close
proximity (at about 20cm) to the ground. The transmitter and receiver antennas were placed
onastand,whichwasfabricated,usingfiber-glassmaterial,intoarodwithatelescopicheight
reduction mechanism such that various antenna heights could be easily selected, while also
ensuring that antenna RF cables used are undisturbed especially as antennas get closer to
the ground.
Table 4.1: Hardware description of the UWB channel sounder
Item Manufacturer Model No.
AWG Tektronix AWG 7122c
DSO Agilent DSA91304A
HPA Gigatronics 10W GT1000A
Pre-Amp Sonoma custom 3XX
Tx, Rx Antenna Skycross SMT-3TO10M-A
LNA RFLambda RLNA05M12GA
Tx, Rx modules OpticalZonu OZ516
For the excitation of the propagation channel, the channel sounder uses a multitone
waveform [153], [154]. This waveform has been thoroughly described in [153], [155], [156],
[157]. The multitone waveform in general is a linear combination of sinusoidal waveforms
that are mutually orthogonal in the time support [t,t +T ], and can be written as
84
y(t) =
i=ku
X
i=k
l
w
i
·sin(2πf
i
t +φ
i
). (4.1)
The multitone waveform, which typically has a flat spectral shape and low-crest factor
at the transmitter, is designed to maximize the SNR at the receiver. The weights w
i
are
generally equal to unity (the phase functions used here are intended for w
i
= 1), however, in
some cases, w
i
can be adjusted to equalize the signal in the frequency domain. This turns out
to be useful when the front-end analog hardware introduces phase distortion (e.g., from the
filters) and even nonlinear distortion from the power amplifier [157]. Due to nonlinearities at
the front-end of the AWG that was used for our experiment, a non-ideal frequency response
was observed at select frequency points. This effect was corrected by using polynomial
interpolation to compute proper values of w
i
with i = [k
l
...,k
u
] used for pre-equalization
in the frequency domain. With that correction, excellent spectral flatness of the excitation
signal radiated from the transmitter-end was achieved. Waveform parameters used in the
experiment are provided in Table 4.3; for additional information about the waveform see
[156].
Figure 4.5: Antennas at 20cm height above ground
85
Table 4.2: Antenna height configurations
Configuration Tx-Rx Height
1 200cm-to-200cm
2 200cm-to-50cm
3 200cm-to-10cm
4 50cm-to-50cm
5 20cm-to-20cm
6 10cm-to-10cm
Table 4.3: UWB Multitone Signal Parameters
Parameter Settings
Bandwidth, (B =f
u
−f
l
) 7GHz
Center frequency, f
c
6.5GHz
Number of multitones (k
u
−k
l
+ 1) 9559
Number of waveforms (n) 1800
Number of Channels 4
Frequency tones spacing 732.42kHz
4.4 Measurement Data Processing and Results
We estimate the channel transfer function at each multitone frequency (see [156] for
details), and denote by H
j,k,ψ,d,z
the estimate, where the indices j∈ [1, 2,..J = 4] denote
the antenna element position used in the virtual Rx array for the 1 x 4 SIMO setup, k∈
[1,...,K = 9559] the multitone frequency, ψ ∈ [1,..Ψ = 10] the "shadowing points" (see
below for definition), d∈ [1,..D = 5] the distances between Tx and Rx, respectively. Also,
z∈ [1,...Z = 6] indicates various antenna heights considered in our measurement, namely
z = 1 is Tx200cm-Rx200cm,z = 2 is Tx200cm-Rx50cm,z = 3 is Tx200cm-Rx10cm,z = 4 is
Tx50cm-Rx50cm,z = 5 is Tx20cm-Rx20cm ,z = 6 is Tx10cm-Rx10cm height configuration.
Measurements were performed at five different distances (where distance index d = 1
is 10m, d = 2 is 20m, d = 3 is 50m, d = 4 is 100m , d = 5 is 200m). For each of these
86
distances, measurements were performed at 10 (a combination
1
of 5 in flat terrain, 5 in hilly
terrain) widely separated points for a total of 50 measurement locations (with a 1 x 4 SIMO
channel in each location). This allowed to extract shadowing variances as well as pathloss,
as described below.
The measured transfer function H
j,k,ψ,d,z
is further transformed into its delay domain
equivalent, the impulse response, using an inverse Fourier transform with a Hanning window.
The impulse response is represented as h
j,n,ψ,d,z
, with similar index parameters representa-
tions as those of the transfer function with the exception of the frequency bin indicator k
changedton∈ [1,...N = 9559]forthedelaydomainbins. Instantaneouspower-delayprofiles
(PDP) are obtained from the impulse responses by taking the magnitude squared (P
j,n,ψ,d,z
=|h
j,n,ψ,d,z
|
2
) of the impulse response. The influence of small-scale fading is reduced (though
not perfectly removed) by averaging the PDP over the four SIMO channels to obtain the
average power-delay-profile (APDP):
ˆ
P
n,ψ,d,z
=
1
J
J
X
j=1
P
j,n,ψ,d,z
(4.2)
To minimize the influence of noise on our data evaluation, we implement a noise thresh-
olding filter that sets all APDP samples whose magnitude is below a certain threshold equal
to zero. The threshold value is chosen to be 6dB above the noise floor of the APDP. In
our setup, the noise floor is computed by averaging the energies in all bin before the first
multipath component of the APDP. Also, we subjected the APDP to a delay-gating filter,
which is implemented by using a 150 m delay-window. The reason for this filter is so as to
eliminates all MPCs that are 150 m in excess of the Tx-Rx separation. The value 150 m
was chosen because there are no observable reflectors/scatterer that could cause a MPC with
that much of a runtime in excess of the time-of-arrival of the Line-of-Sight (LOS) component
in our channels.
1
Wecombinedmeasurementsintheevaluationoftheruralflatandhillyterrainsbecauseoftheinsufficient
number of points in each environment
87
0 50 100 150 200 250 300 350 400 450
0
1
2
3
4
5
6
7
x 10
!6
Magnitude of the Impulse response function (h)
distance (m)
|h|
Figure 4.6: Channel Impulse response for Tx,Rx separation of 20m antenna height Tx 10cm-
Rx 10cm
0 50 100 150 200 250 300 350 400 450
0
0.5
1
1.5
2
2.5
3
x 10
!7
Magnitude of the Impulse response function (h)
distance (m)
|h|
Figure 4.7: Channel Impulse response for Tx,Rx separation of 200m antenna height Tx
10cm-Rx 10cm.
The measurement was conducted for large Tx-Rx separation ranging from 10m to 200m
with antenna height at close proximity to the ground. Even at low antenna heights (about
10cm) and large distances (200m Tx-Rx separation), we indeed did obtain impulse responses
with good SNR at all measurements points (see Figs. 4.6 & 4.7).
4.4.1 Pathloss
Pathloss (G
L
) of a channel typically refers to the difference between the received and the
transmitted power [83]. While in narrowband/wideband systems the pathloss is distance
dependent, the pathloss in a UWB system actually exhibits both distance and frequency
dependency. Define
G
L
(f,d) =
1
Δf
E





f+Δf/2
Z
f−Δf/2

H(
e
f,d)

2
d
e
f





(4.3)
88
where H(
˜
f,d)
2
is the channel transfer function. E{·} is the expectation taken over the
small- and large-scale fading. The frequency range, Δf is chosen small enough so that
diffraction coefficients, dielectric constants, etc., can be considered constant within that
bandwidth. Forourmeasurement, Δf ischosentobea500MHzsub-band, whichissufficient
to average out frequency-selective fades. To simplify the modeling, the distance-dependence
of pathloss G
L
(d) is considered to be independent of the frequency-dependence of pathloss
G
L
(f) , hence can be written as
G
L
(f,d) = G
L
(d)·G
L
(f) (4.4)
This simplification is based on previous work reported in [62] and [67].
Distance-dependent pathloss
The distance-dependent pathloss is computed by summing the power in the small-scale
averaged PDP (i.e APDP) over all delay bins for all points measured. This term is commonly
referred to as the local mean power (E
tot
). The local mean power is computed separately for
measurements at different shadowing points (ψ), Tx-Rx separations (d) and antenna height
combinations (z):
E
tot
ψ,d,z
=
1
J
J
X
j=1
N
X
n=1
P
j,n,ψ,d,z
(4.5)
where N is 9559, which corresponds to the maximum number of delay bins used in our
measurement analysis. Following the literature, we use a conventional power law equation
[62], [83] (see eq. 6.14);
G
L
(d) = G
0
− 10·γ·log
10

d
d
0
!
+S
σ
(4.6)
2
using transfer function notation as stated in [62]
89
where,d
0
is the reference distance at 1 m, G
0
is the pathloss at the reference distance, γ
is the pathloss exponent and S
σ
is a lognormal distributed random variable describing large-
scale variations due to shadowing. We have assumed a unit gain for Tx and Rx antenna in
our model. Figs. 4.8 and 4.9 show scatter plot examples of the normalized pathloss for all
measurements conducted at different distances for select antenna heights. G
0
has been used
as a normalization factor for the pathloss values on these plots. The normalization is done
by subtracting G
0
from the overall pathloss value G
L
(d) i.e G
L
(d)−G
0
3
from our model
(see eq.(6.14)) leaving 10·γ·log
10
(d/d
0
) +S
σ
as the attenuation value plotted in Figs. 4.8
and 4.9. A linear regression fit for the scatter plot does show the anticipated monotonic
dependence of pathloss on distance. The distance-dependent pathloss coefficient obtained
for different antenna heights in our measurements are shown in Table 4.4 below;
Table 4.4: distane-dependent pathloss exponent γ
Antenna Height γ
Tx 200cm-Rx 200cm 2.14
Tx 200cm-Rx 50cm 2.91
Tx 200cm-Rx 10cm 3.11
Tx 50cm-Rx 50cm 3.30
Tx 20cm-Rx 20cm 3.60
Tx 10cm-Rx 10cm 3.33
Frequency-dependent pathloss
The received power in an ultrawideband propagation channel does exhibit a dependence
on frequency [62, 66, 67]. The dependence arises primarily from the antenna power density
and gain variation with frequency [63], [64] and additionally from frequency dependence of
physical propagation phenomena such as scattering and diffraction [65].
For the computation of pathloss in our measurement, the frequency-dependent pathloss
3
since they are both in log-scale
90
10 12 14 16 18 20 22 24
20
25
30
35
40
45
50
10log
10
(d/d
0
)
Attenuation(dB)
Figure 4.8: Scatterplot of normalized pathloss for all measurements at Tx200cm-Rx200cm
antenna height configuration
10 12 14 16 18 20 22 24
10
20
30
40
50
60
70
80
10log
10
(d/d
0
)
Attenuation(dB)
scatter plot of Large−scale attenuation Tx10cm−Rx10cm
Figure 4.9: Scatterplot of normalized pathloss for all measurements at Tx10cm-Rx10cm
antenna height configuration
(G
L
(f)) as a function of frequency is expressed as a logarithmic expansion of a power-law
decay model [66, 67]:
G
L
(f) = G
ϑ
(f
0
)− 20·κ·log
10

f
f
Mc
!
(4.7)
where κ is the frequency decay factor, G
ϑ
(f
0
) is the power of the lowest frequency sub-
band and is equivalent to G
0
from eq.(6.14), f
Mc
is the center frequency of each selected
sub-band (each sub-band is 500MHz). Note that we find a fit for κ in the dB (logarithmic
power) domain. In our analysis, we extracted κ separately for each shadowing point, and
then integrate over frequency so as to be able to fit the distance-dependent pathloss with
(frequency-independent)d
γ
andshadowing. Alsonote-worthyisthatalthough[68]hasshown
thatκ can be different for each multi-path component, however a "bulk" model has been used
91
in our analysis because we did not have sufficient number of measurement points to extract
it for each path separately.
From our measurements, we find that for given antenna height configurations, κ follows
a Gaussian distribution (over the ensemble of distance points and shadowing points). We
couldnotanalyzethedependenceofκonthedistanceduetothelownumberofmeasurement
points. As an example, the CDF plot for antenna height configuration Tx50cm-Rx50cm is
shown in Fig. 4.10. A similar distribution fit for the frequency-dependent decay component
of pathloss was arrived at in [65]. The values of κ for different antenna heights is shown
below;
κ =∼N[μ,σ]
∼







































N[1.16, 0.33], Tx200cm_Rx200cm
N[0.98, 0.34], Tx200cm_Rx50cm
N[0.98, 0.37], Tx200cm_Rx10cm
N[1.05, 0.28], Tx50cm_Rx50cm
N[1.17, 0.32], Tx20cm_Rx20cm
N[1.24, 0.23], Tx10cm_Rx10cm
(4.8)
Note that in a classical free-space model, we would obtainN(1, 0). To attest to the accuracy
of our measurement, the value of κ extracted from measurement at antenna height close to
free-space condition and short distance separation of 1 m between Tx and Rx antennas was
1.07. This value is close to the aforementioned theoretical free-space value.
It is important to note that these results represent the behavior of the radio channel
including both the physical propagation channel and the antennas. Different antennas (with
consequently different frequency dependent behavior), could lead to significantly different
results. All other measurement campaigns that do not use calibrated antenna arrays have
the same limitation.
92
0 0.5 1 1.5 2 2.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
κ
Pr(κ ≤ abscissa)

measurement
Gaussian Fit
Figure 4.10: CDF plot of frequency-dependent pathloss exponent (κ)
4.4.2 Shadowing
The shadowing gain (denoted as S
σ
in eq. 6.14) accounts for the large-scale fluctuations of
the received power. This phenomenon has been reported in the literature [71], [72] to follow
a lognormal distribution. For each antenna height (z) configuration in our measurement,
S
σ
is obtained by computing the deviation of power gain at each measured shadowing point
from the linear regression fit over distance.
The logarithmic values of the power deviation observed closely match a zero-mean
Gaussian distribution N(0,σ
s
(dB)), which is the standard model for shadowing. As an
example, a typical distribution fit for a measurement performed at with antenna heights
Tx200cm_Rx10cm is shown in Fig.4.11. The standard deviation values for all other antenna
height configurations range from 2.80 dB to 8.52 dB as shown below; we find that the stan-
dard deviation increases as the height of the antennas decreases. This is in agreement with
intuition, as links with low antenna heights are more susceptible to small unevennesses in the
ground as well as exposure to more obstacles and as a consequence site-specific variations,
whichconstitutetheshadowingobserved. Itissafetosaythateventhoughthesenear-ground
links are LOS, a significant obstruction may occurs within the first Fresnel zone in the prop-
agation channel.
4
Channels with antenna height closer to free-space condition experience
smaller shadowing effects than the near-ground channels. The shadowing observed from the
4
especially at locations with 20-30cm high dry grass for example.
93
−20 −15 −10 −5 0 5 10 15
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
S
σ
(dB)
Pr(S
σ
(dB) ≤ abscissa)

measurement
Gaussian Fit
Figure 4.11: CDF plot of shadowing component at Tx200cm_Rx10cm antenna height con-
figuration
aforementioned channels mostly stems from observable structures/scatterers present in the
environment (shown in Figs. 4.2 & 4.3).
S
z
=∼N[0,σ(dB)]
∼







































N[0, 2.80], Tx200cm_Rx200cm
N[0, 4.33], Tx200cm_Rx50cm
N[0, 5.22], Tx200cm_Rx10cm
N[0, 4.39], Tx50cm_Rx50cm
N[0, 8.52], Tx20cm_Rx20cm
N[0, 7.31], Tx10cm_Rx10cm
(4.9)
The lognormal distribution of the shadowing gain was validated in this measurement by
matching empirical data from the measurement to some typical theoretical distributions
such as lognormal, Nakagami, Rayleigh, Ricean and Weibull. The Kolmogorov-Smirnov
(K-S) hypothesis test was used to determine the goodness-of-fit of these distributions at
5% significance level. We have used 50 data sample points for this test, as this includes
values for all shadowing and distance points measured for each antenna height configuration.
Table.4.5 below compares the passing rate of the aforementioned distribution for a typical
measurement height (Tx50cm-Rx50cm). As can be observed from Table.4.5, the lognormal
94
distributiongivesthehighestpassingratefromK-Sresulthencethechoiceforshadowinggain
distribution fit. This observation holds for all other antenna heights as well. It is important
Table 4.5: Passing Rate of K-S Hypothesis test at 5% Significance Level
Distribution K-S
Rayleigh 29.00
Nakagami 43.50
Rician 29.10
lognormal 85.51
Weibull 63.68
to note that, the few (J = 4) number of small-scale measurement points used in deriving
the APDP (from eq.4.2) could influence the extraction of the shadowing variance. Increase
of the shadowing variance estimate (for the variances encountered in the measurements) due
to the small number of points is less than 0.7 dB for the case of Rayleigh fading and smaller
for Rician fading.
4.4.3 Fading Statistics
The variation in the received signal amplitude over the 1 x 4 SIMO channel can be
attributed to the small-scale fading (SSF) in the environment. In many UWB measurements,
the SSF statistics are described as m-Nakagami distributed [158], [11], [62]. We use this
assumption as well - note that the number of SSF realizations (for each shadowing point) is
too small to reliably test the distribution of the SSF; rather we extract a (rough) estimate
for the m-parameter for each delay bin using an ensemble of the small-scale measurement
points.
To ensure a proper characterization of the fading statistics per delay bin in our analysis,
a runtime compensation for every MPC in impulse response was performed by translating
the bin with the quasi-LOS component to first bin of the impulse response; this follows the
procedure of [11]. The m-parameter was computed using the inverse normalized variance
(INV) estimator [159]
95
ˆ m
INV
=
μ
2
2
μ
4
−μ
2
2
(4.10)
where, μ
ˆ
k
=
1
N
P
N
i=1
Q
ˆ
β
i
, Q is the observed amplitude vector of the measurement data and
N = 4 in this case,
ˆ
β-moment order.
Them-parameters for each bin are random variables and are typically modeled by a trun-
cated Gaussian distribution [11] denoted bym − T
N
(μ
m
,σ
2
m
). Using a similar assumption
in our measurement, we came up with a truncated Gaussian distribution model for the
m-parameter using the probability density function in eq. (4.11);
f
m
(x) = ∼







ρ
m
e
−((x−μm)
2
/2σ
2
m
)
, if x≥ 0.5
0, otherwise
(4.11)
where ρ
m
is the normalization constant chosen so that the integral over f
m
(x) is unity.
To parameterize the proposed truncated Gaussian distribution the mean (μ
m
) and variance
(σ
m
) values of the m-parameter as a function of excess delay were obtained by using a linear
regression fit
μ
m
(τ
n
) = A−
1
B
τ
n
(4.12)
σ
m
(τ
n
) = C−
1
D
τ
n
(4.13)
where the units of τ
k
5
are in nanoseconds. The slope and intercept values for different
antenna height configurations used in our experiments are stated below in Table 4.6. It is
important to note that due to the delay-gating filter used in our processing, the analysis
done here is only for τ < 500ns.
The estimates A, B, C, D are indeed within the range one would expect. These values
indicate that the MPCs arriving with large excess delay are likely to be more diffuse that
5
Note that the k subscript indicates the delay bin index
96
Table 4.6: Regression line parameters for m-parameter charcterization
Antenna Height A B C D
Tx 200cm-Rx 200cm 2.49 972 4.84 1958
Tx 200cm-Rx 50cm 2.05 737 3.43 221
Tx 200cm-Rx 10cm 2.51 575 4.61 679
Tx 50cm-Rx 50cm 2.31 1673 4.52 738
Tx 20cm-Rx 20cm 2.50 291 4.75 140
Tx 10cm-Rx 10cm 2.42 638 4.98 153
the first arriving components. It can be deduced from the small slope values,
1
B
, in Table
4.6, that even though them-parameter values are crude estimates, there seems to be a fairly
similar distribution across all delay bins. Similar findings in a UWB channel have also been
reported in [11].
4.4.4 Delay Dispersion Statistics
The RMS delay-spread, τ
rms
is defined as the square-root of the second central moment
of the normalized APDP [83]. This parameter serves to compactly describe the effects of
delay dispersion in multi path propagation environments [73]. The rms delay-spread was
computed for each shadowing point measured at the different Tx-Rx distance separations
and different antenna height configurations hence denoted as τ
rms
ψ,d,z
. It can be computed
directly from the APDP
τ
rms
ψ,d,z
=
v
u
u
u
u
u
u
t
N
P
n=1
(nΔτ)
2ˆ
P
n,ψ,d,z
P
tot
ψ,d,z
−





N
P
n=1
(nΔτ)
ˆ
P
n,ψ,d,z
P
tot
ψ,d,z





2
(4.14)
where,
P
tot
ψ,d,z
=
N
X
n=1
ˆ
P
n,ψ,d,z
(4.15)
97
−105 −100 −95 −90 −85 −80 −75 −70
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
10Log
10
(τ
rms
)
Pr(τ
rms
≤ Abscissa)
CDF of rms delay spread

Measurement
Gaussian Fit
Figure 4.12: CDF of the RMS delay-spread for antenna height Tx20cm_Rx_20cm
is the time integrated power of the APDP and Δτ (0.1428ns) is the delay resolution. Previ-
ous narrowband measurements [73], [160] have found the rms delay-spread to be lognormally
distributed. We found this to hold true also in our measurements. The cumulative distribu-
tion function (CDF) plots in Figs. 4.12 & 4.13 show that the logarithm ofτ
rms
ψ,d,z
(with respect
to 1s) is well approximated by a Gaussian distribution; this holds for all other antenna height
configurations measured as well (not shown here for space reasons). The statistical parame-
ters for the rms delay-spread (expressed in dB) for all antenna heights in our measurement
are shown below;
τ
rms
z
=∼N[μ
dB
,σ
dB
]
∼







































N[−82.67, 3.06], Tx200cm_Rx200cm
N[−81.64, 1.98], Tx200cm_Rx50cm
N[−82.14, 3.40], Tx200cm_Rx10cm
N[−83.71, 2.03], Tx50cm_Rx50cm
N[−83.69, 4.75], Tx20cm_Rx20cm
N[−82.42, 4.61], Tx10cm_Rx10cm
(4.16)
98
−90 −88 −86 −84 −82 −80 −78 −76
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
10Log
10
(τ
rms
)
Pr(τ
rms
≤ Abscissa)
CDF of rms delay Spread

Measurement
Gaussian fit
Figure 4.13: CDF of the RMS delay-spread for antenna height Tx50cm_Rx_50cm
To validate the assumption that the rms-delay spread follows a lognormal distribution,
empirical data from the measurement were matched to some typical theoretical distributions
such as lognormal, Nakagami, Rayleigh, Ricean and Weibull. The Kolmogorov-Smirnov (K-
S) hypothesis test was then used to determine the goodness-of-fit of these distributions at
5% significant level. As before we have used all 50 data sample points. Table.4.7 below
compares the passing rate of the aforementioned distribution for a typical measurement
height (Tx50cm-Rx50cm) and it is clearly obvious that the lognormal distribution is the
choice that best fits our data.
Table 4.7: Passing Rate of K-S Hypothesis test at 5% significance level
Distribution K-S
Rayleigh 32.43
Nakagami 44.30
Rician 32.42
lognormal 94.91
Weibull 80.61
According to [73, 158], the rms delay-spread increases with distance between Tx and Rx.
Assuming that this dependency can be modeled using eq. (4.17), the decay exponent can
be extracted to give information about the relationship between the τ
rms
and distance at
each antenna height configuration.
Let ˆ τ
rms
d,z
be the rms delay-spread averaged over all shadowing points, then model
99
10·log
10
(ˆ τ
rms
d,z
) = G
T
0
+ 10··log
10
(d) +L
T
(4.17)
where d - is the distance between Tx and Rx, G
T
0
the intercept of the ordinate, the slope
parameter and L
T
a normally distributed random variable N(0,σ
2
L
T
),
A linear regression fit approach was used to estimate all parameters. A scatterplot for
a sample antenna height configuration is shown in Fig. 4.14, all exponents () extracted are
shown in Table 4.8 below. Exponents () for different antenna height configurations are
positive as expected, which implies that the τ
rms
increases with distance irrespective of the
antenna height configuration. Numerical values for all other parameters extracted are given
in Table. 4.14.
10 12 14 16 18 20 22 24
−88
−86
−84
−82
−80
−78
−76
10Log10(d)
10Log10(τ
rms
)
Figure 4.14: RMS delay-spread as a function of distance at Tx50cm_ Rx50cm
Table 4.8: rms delay-spread-distance dependent parameters
Antenna Height G
T
0
(dB) σ
L
T
(dB)
Tx 200cm-Rx 200cm 0.18 -82.40 2.10
Tx 200cm-Rx 50cm 0.43 -88.95 2.30
Tx 200cm-Rx 10cm 0.38 -88.72 2.05
Tx 50cm-Rx 50cm 0.17 -92.70 1.48
Tx 20cm-Rx 20cm 0.48 -91.00 3.63
Tx 10cm-Rx 10cm 0.09 -91.32 3.31
100
Table 4.9: Results of Channel extracted parameters at USC campus
Antenna Height γ κ σ[dB] ¯ τ
rms
(ns)
Tx 100cm-Rx 100cm 2.86 0.88 2.20 10.45
Tx 10cm-Rx 10cm 3.80 1.13 1.27 18.44
Table 4.10: Results of Channel extracted parameters from Catalina Island
Antenna Height γ κ σ[dB] ¯ τ
rms
(ns)
Tx 200cm-Rx 200cm 2.14 1.16 2.80 9.79
Tx 200cm-Rx 50cm 2.91 0.98 4.33 8.54
Tx 200cm-Rx 10cm 3.11 0.98 5.22 7.03
Tx 50cm-Rx 50cm 3.30 1.05 4.39 5.14
Tx 20cm-Rx 20cm 3.60 1.17 8.52 7.65
Tx 10cm-Rx 10cm 3.33 1.24 7.31 6.97
4.5 Model Validation
To validate the proposed model, we conducted additional outdoor near-ground propaga-
tion channel measurements in a different outdoor environment with a similar UWB chan-
nel sounding configuration. The additional measurements were conducted on the campus
grounds of the University of Southern California (USC) in downtown Los Angeles. The
environment had a similar geographical-terrain (flat) structure to that of Catalina Island,
however, the nearby scatterer distribution were different.
From the antenna height measured, as shown in Table 4.9, it can be observed that
parameters such as distance-dependent pathloss exponent (γ) and the frequency-dependent
pathloss exponent (κ) do in fact behave as expected in that they have similar values to those
extracted from Catalina Island outdoor near-ground experiments shown in Table 4.10, also
these parameters exhibit an increase in value as the antenna height to the ground decreases,
in a fashion similar to results from Table 4.10. The average rms delay-spread values and
shadowing standard deviation are slightly different from those of the previous performed
measurement, mainly because the scatterers and obstruction in the environment are quite
different in the two cases.
101
Table 4.11: Comparing Near-ground channel parameters from different papers
Papers γ σ[dB] ¯ τ
rms
(ns) κ
this paper (UWB outdoor) 3.33 7.31 6.97 1.24
Ref. [151](UWB indoor) 2.50 2.59 8.77 N/A
Ref. [144](wideband outdoor) 3.0 - 4.6 2.89 - N/A
Ref. [138](narrowband outdoor, LOS) 2.00 2.30 N/A N/A
4.6 Summary and Conclusion
We successfully conducted a measurement campaign in an outdoor UWB near-ground
environment using a newly assembled channel sounder structure we designed specifically for
long range measurements. We succeeded in extracting parameters used for modeling the
propagation channel characteristics. A summary of our findings is presented as follows:
• We find that the distance-dependent pathloss (γ) shows considerable dependence on
antenna height, as its value tends to increase with antennas increased proximity to the
ground. The pathloss exponent values extracted ranged from 2.14 to 3.60.
• The frequency decay coefficient (κ) of the pathloss values were around 1, these values
also tend to slightly increase when the antenna is in close proximity to the ground. A
statistic distribution fit over the ensemble of the parameter extracted shows a Gaussian
distribution fit with mean values ranging from 0.98 to 1.24, while the variance ranged
from 0.23 to 0.37.
• The shadowing variance in the channel increases as the antennas get closer to the
ground. We also confirmed the statistical distribution of the shadowing gain as being
lognormal distributed, with standard deviations ranging from 2.8dB to 8.52dB.
• The small-scale amplitude fading statistics were modeled (using the general convention
foundintheUWBliterature)asm-Nakagamidistribution. Them-parameterestimates
extracted were rough estimates due to limitation of the number of measurement points.
102
Them-parameter estimates themselves are random variables and as such were modeled
as truncated Gaussian distribution; mean and variance decreased with delay.
• The delay-spread statistics show that the rms delay value tends to follow a lognormal
distribution, consistent with previous literature. The distance dependency of the rms
delay-spread was also observed and modeled, as the rms delay-spread tends to increase
with distance. Also, mean rms delay-spread values (averaged over all distances) tend
to decrease as the antennas got closer to the ground.
It is important to note that although parameters such as pathloss exponent do not differ
too much from those of narrowband measurements done with near-ground antennas such as
[138], the overall pathloss value expressed in eq. (6.15) does in fact differ due to the inclusion
ofthefrequency-dependencyofpathlosssimplybythenature
6
ofthechannelbeingmeasured.
These measurement results indicate that outdoor near-ground UWB propagation channels
are described by parameters that are quite different from those of narrowband and wideband
channels. A comparative table of parameter values from near-ground measured channels
7
in
our work and that obtained from other works such as [151] , [144] and [138] is provided in
Table. 4.11.
Overall, we find that the qualitative behavior of "standard" channel parameters (distance-
dependent pathloss exponent (γ), rms delay spread (τ
rms
) and shadowing variance (σ
2
))
extracted in this paper is comparable to those existing in the literature [138],[140],[151],[67].
However, new aspects that are particular to the outdoor near-ground UWB environment
6
Ultrawideband channel
7
Note that the comparison done here is for the Tx10cm - Rx10cm channel in our case (as it is the lowest
antenna height we measured) while the antenna was placed directly on the ground in [151] to realize their
near-ground (NG) LOS channel. The "dry tall underbrush" outdoor channel and the "Sandy Flat Beach"
was used for comparison in [144] also with Tx, Rx antennas placed directly on the ground, while the LOS
scenario with Tx antenna at 0.3m height was considered in [138].
103
using different antenna height combinations are provided, and are in agreement with intu-
ition. While a single measurement campaign like this cannot provide a complete character-
ization of the whole "near-ground outdoor" environment, we believe that these results are
useful for understanding and simulating outdoor UWB near-ground channels.
104
Chapter 5
Statistical Modeling of Ultrawideband
MIMO Propagation Channel in a
Warehouse Environment
5.1 Introduction
Ultra-wideband (UWB) technology has emerged as one of the most promising candidates
for communication and localization systems and has attracted great interest from the sci-
entific, military and industrial communities [2, 3, 4, 5]. UWB signals are defined as either
having more than 20% relative bandwidth or more than 500 MHz absolute bandwidth [6]
and are permitted to operate in the 3.1–10.6 GHz frequency band by the Federal Commu-
nication Commission (FCC) [7] in the USA, while occupying 4.2–4.8 GHz and 6–8.5 GHz
band in Europe, according to the European conference of postal and telecommunications
Administrations (CEPT) and 3.4 – 4.8 GHz, 7.25 – 10.25 GHz bands in Japan. UWB sig-
nals show a number of important and attractive qualities such as, accurate position location
and ranging due to its fine time resolution [127, 161], robustness to frequency-selective fad-
ing [2, 162], possibility of extremely high data rates for communications [124], efficient use
of radio spectrum through underlaying techniques [122] and easier material penetration due
to the presence of energy at different frequencies. Ultra-wideband systems have many envi-
sionedapplicationsincludingreal-timetrackingofassets, personnelandhospitalpatientsand
could especially be of great use in locating items in a warehouse environment. For example,
UWB as-of-late has found use in Radio-frequency identification (RFID) technology, which is
105
naturally deployed in warehouse environment, and in UWB-based wireless sensor networks,
which could eventually find use in a warehouse-like environment as well.
The warehouse environment is unique in its geometric/structural layout, which is often
sparse with storage racks or shelves all demarcated into aisles. This constitutes a unique
propagation channel, whose properties need to be explored for system design and simulation
purposes.
5.1.1 Related work
UWBsystemsarebeingdesignedtooperateindifferentenvironmentsandassuchchannel
models have been provided for several environments ranging from indoor–residential [12, 11,
163, 164] to offices [165], factories or industrial [166, 79] and outdoor environment [147,
148, 149, 167]. However, there is a dearth of propagation channel models for warehouse
environments in the literature. In fact, to the best knowledge of the authors, there are
hardly any channel models dealing with warehouse environments. Channel measurements
were conducted in a warehouse environment in [168], however, the results provided were only
for a single-input-single-output (SISO) channel model. Ref. [169], deals with channel models
in the frequency range from 0.5 to 1.5 GHz, intended for UHF RFID systems at a warehouse
portal. A warehouse channel measurement was also done in [170] to enhance a ray-tracing
tool, but the measurements was only performed for 0.8–2.5 GHz.
5.1.2 Contributions
In this paper, we remedy this gap by investigating the propagation channel parameters
in a typical warehouse environment. The contributions of this paper can be summarized as
follows:
• We report the details of a MIMO channel measurement campaign performed in a
warehouse environment for a LOS and NLOS scenario in the 2–8 GHz frequency range.
106
• We extract the large scale propagation channel parameters such as distance-dependent
path gain exponent (n), frequency-dependent path gain coefficient (κ) and shadowing
variance (σ
2
) for the LOS and NLOS environments.
• Using the high-resolution CLEAN algorithm, the temporal and directional parameters
of the multipath components (MPCs) are extracted.
• InlightoftheobservationthatMPCstypicallycanbegroupedintoclusterscorrespond-
ing to the scatterers and interacting objects (IO) in the environment, we performed a
cluster analysis and derive both intra- and inter- cluster statistics.
• The inter-cluster DoA, DoD and ToA are observed to be dependent; and we develop a
suitable model to capture this effect.
• The developed channel models are validated using capacity and root-mean-square
(RMS) delay spreads as the validation metrics.
The developed model can be used for realistic performance evaluations of UWB systems in
warehouse environments.
5.1.3 Organization
The rest of the paper is organized as follows. Sec. 5.2 describes the measurement envi-
ronment. Sec. 5.3 describes the measurement setup. The large scale parameter extraction
is described in Sec. 5.4. The intra-cluster and inter-cluster channel models for LOS and
NLOS environments is developed in Sec. 5.5. The developed channel models are validated
in Sec. 5.6.
5.2 Measurement Environment
MeasurementswereperformedattheUniversityofSouthernCalifornia(USC)mainware-
house facility (shown in Fig. 5.1). The warehouse structure has four floors (including the
107
basement) with each floor comprising of large open halls, which were mainly used for storing
items such as books, computers and other office stationery. The ceiling, floor and walls
surrounding each large open hall on each floor were made of reinforced bricks and concrete,
while concrete pillars (labeled A in Fig. 5.1) served as structural supports for the ceiling (and
could also contribute to shadowing effects in the propagation channel). Typically, the stor-
age areas on each floor were often demarcated into aisles, with each aisle containing rows of
two layered metallic storage racks (labeled B in Fig. 5.1). There also exists walkways/paths
between these aisles to ease the movement of people and forklift trucks. To store sensitive
material such as medical equipment or non-toxic laboratory chemicals, and old computer
parts, special demarcations were made with barb-wired fences. Access to each storage hall
is mainly through steel garage doors, which could serve as a source of reflections.
The measurements were conducted on the first floor and basement storage halls, see
Figs. 5.2 & 5.3 for the floor plans. The use of the basement storage hall (with similar layout
to the first floor, but with slightly different geometrical structures, i.e no concrete pillars
or metallic garage doors) provided more measurement points, especially for large distance
separations between transmitter (Tx) and receiver (Rx) ends.
For both LOS and NLOS scenarios, measurements were taken for Tx-Rx separation dis-
tances of 5 m, 10 m, 15 m, 20 m and 25 m. Multiple measurements were taken for a given
separation distance, by placing the Tx and Rx arrays at different positions. For each Tx-Rx
separation distance, 5 and 8 positions were selected respectively for the LOS and NLOS
scenarios. These positions provide different realizations of the shadowing effects and other
distance-dependent large-scale effects. A total of 65 positions were measured in our cam-
paign. The measured positions are indicated in the Figs. 5.2 & 5.3. The Tx/Rx array
locations for the LOS/NLOS measurements are indicated on the floor maps with the abbre-
viations: TXL1 (Tx LOS position 1), TXN1 (Tx NLOS position 1), etc. A similar format
is used for the Rx positions. To avoid congesting the floor schematic, only a subset of the
measured positions are marked in the figures.
108
Figure 5.1: USC Warehouse Facility.
Figure 5.2: Floor map of the first floor of the warehouse.
5.3 Measurement Setup
A frequency domain channel sounder setup with an 8 x 8 virtual MIMO antenna array
configuration (see Fig. 5.4) was used to perform the measurement campaign. At the heart
of the channel sounder setup is a vector network analyzer (VNA, HP 8720ET) [171], which
is used for obtaining the complex transfer function (H(f)) of the propagation channel. The
VNA was calibrated with the inclusion of a 20 m long coaxial cable (to connect the Tx, Rx
109
Figure 5.3: Floor map of the basement of the warehouse.
ends) rated at 1.22 dB/m at 8 GHz [172] and a 30 dB low noise amplifier (LNA) [173],
which was used at the Rx to boost the received signal power. A stepped frequency sweep
was conducted for 1601 points within the 2–8 GHz frequency range. The settings for the
VNA are shown in Table 5.1 and a list of all equipment used is given in Table 5.2.
The MIMO antenna array was implemented by using a virtual antenna array at both
Tx and Rx. An omni-directional antenna [64] was attached to a 1.78 m high support pole
and then fastened to a stepper motor controlled by linear positioner. Using a linear posi-
tioner controlled by LabView software, the single antenna was moved to different positions,
thus creating a virtual uniform linear array (ULA), which allows determination of angular
characteristics of the MPCs. Note, however, that a ULA does not allow extraction of the
elevation of the MPCs, and the azimuth of MPCs incident from nonzero elevation is dis-
torted. Due to the building structure, this effect did not play a major role. The separation
between antenna elements is 50 mm, hence by moving each antenna over a distance of 400
mm at both ends, 8 antenna positions at each link end are measured, providing a total of
64 channel realizations. Due to array positioner movement time and VNA frequency sweep
time (over a 6 GHz bandwidth), the total measurement time for each position (64 channels)
was about 48 minutes. A key requirement for evaluations based on virtual arrays is that
the channel is static during a measurement run. Several precautions were taken to ensure
110
Figure 5.4: Channel sounder measurement setup in the warehouse environment.
this including making certain that the cables used in the measurement setup do not twist
and turn during the positioner movements, and that there were no moving objects, forklift
trucks or personnel in the warehouse during the measurement.
5.4 Measurement Data processing and Results
The channel transfer function of each measured location was extracted from the VNA
data. The transfer function can be denoted as H
d,s,m,n,f
k
, wherem = 1...N
T
andn = 1...N
R
respectively denote the Tx and Rx antenna positions in the array,{f
k
,k = 1...N
F
} represents
the measured frequencies, d denotes the Tx-Rx separation distance, and s = 1...N
S
denote
the shadowing position. For our measurement setup, N
T
= 8, N
R
= 8, N
F
= 1601, N
S
Table 5.1: Channel measurement parameters
Parameter Setting
Bandwidth 6 GHz (2–8 GHz)
Transmitted Power 5 dBm
Center frequency, f
c
5 GHz
Total number of channels 64
Number of sub-carriers 1601
Delay resolution 0.167 ns
Frequency resolution 3.74 MHz
Maximum path length 80 m
111
Table 5.2: Hardware used in the UWB MIMO channel measurement
Item Manufacturer Model No.
VNA Agilent 8720ET
LNA JCA JCA018-300
Stepper motor control Velmex VMX-2
Coaxial cable Flexco Microwave FC-195
is 5 and 8 respectively for LOS and NLOS measurements, the set of distances measured
are d ={5, 10, 15, 20, 25} m. The transfer function H
d,s,m,n,f
k
was transformed to the delay
domain by using an inverse Fourier transform with a Hann window to suppress sidelobes.
The resulting impulse response is denoted as h
d,s,m,n,τ
, where τ indicates the delay index.
The magnitude squared of the impulse response is computed to derive the instantaneous
power-delay-profile (PDP), i.e., P
d,s,m,n,τ
=|h
d,s,m,n,τ
|
2
. The influence of small-scale fading
is removed by averaging the instantaneous PDPs over the 8× 8 Tx/Rx positions, to obtain
the average-power-delay-profile (APDP,
ˆ
P
d,s,τ
).
ˆ
P
d,s,τ
=
1
N
T
N
R
N
T
X
m=1
N
R
X
n=1
P
d,s,m,n,τ
. (5.1)
Sample APDP plots for both LOS and NLOS measurements at 5 m and 25 m distances
are given in [168].
To reduce the influence of noise, we implement a noise-threshold filter, which sets all
APDP samples whose magnitude is below a certain threshold to zero. The threshold value
is chosen to be 6 dB above the noise floor of the APDP. This noise floor is computed by
averaging the energies in all bins with delays shorter than that of the first MPC of the APDP.
Also, the APDP was subjected to a delay-gating filter, which eliminates all MPCs whose
delays are 60 m or more in excess of the Tx-Rx separation. The APDP is used for RMS
delay spread computations, which is further used for model validation in Sec. 5.6.
112
5.4.1 Path Gain
Path gain is typically defined as the difference between the received and transmitted
power [83]. It has been established through theoretical and practical investigation that the
behavior of narrowband and UWB path gains are remarkably different [11, 12, 13, 14, 15,
16, 17]. An example of this is the fact that for frequency-independent receive antenna area,
path gain in narrowband channels is only distance dependent [83], [17], [62]. A generic path
gain can be defined as
G
L
(f,d) =
1
Δf
E





f+Δf/2
Z
f−Δf/2
|H(f,d)|
2
df





. (5.2)
whereH(f,d) is the channel transfer function. E{·} is the expectation taken over the small-
scale and large-scale fading. In this case, the frequency range Δf is chosen small enough so
that the physical parameters such as diffraction coefficients, dielectric constants, etc., can be
considered constant within that bandwidth. The modeling can be simplified by considering
the distance-dependent path gainG
L
(d) to be independent of the frequency-dependent path
gain G
L
(f), and hence the overall path gain can be written as
G
L
(f,d) =G
L
(d)·G
L
(f) . (5.3)
Distance-dependent path gain
In order to obtain the distance-dependent path gain, we first sum the power in the small-
scale averaged PDP (i.e APDP) over all delay bins. The result is commonly referred to as
the local mean power (P
tot
). The local mean power is computed separately for measurements
at different shadowing points (s) and Tx-Rx separation distances (d):
P
tot
s,d
=
T
X
τ=1
ˆ
P
s,d,τ
(5.4)
113
5 10 15 20 25
10
−9
10
−8
10
−7
10
−6
10
−5
10
−4
d (m)
path gain

NLOS
LS fit
LOS
LS fit
Figure 5.5: Distance dependency of the path gain in the LOS and NLOS scenarios.
A relation of local mean power to the distance at each shadowing point would lead the
extraction of the path gain component. Following the literature, we use a conventional power
law model [62, 83] (see eq. 6.14);
G
L
(d) =G
0
− 10·n·log
10

d
d
0
!
+S
σ
(5.5)
where, n is the path gain exponent, d
0
is the reference distance (1 m), G
0
is the path gain
(dB) at the reference distance and S
σ
is a lognormal distributed random variable describing
large-scale variations due to shadowing in the environment. Table 5.3 shows the path gain
exponent n obtained from LOS and NLOS measurement scenario, while the Fig. 5.5 shows
the scatter plot of the normalized path gain for all distances and shadowing point realization
measured. It can be observed that the a linear regression for the scatter plot does show a
monotonic dependence of path gain on distance with the slope of the fit corresponding to
the path gain exponent experienced in the channel.
Table 5.3: Extracted Large Scale Channel Parameters
n G
0
(dB) κ σ
s
(dB)
LOS 1.63 -38.26 1.46 2.10
NLOS 2.14 -49.06 1.46 3.16
114
Frequency-dependent path gain
The frequency-dependence of the path gain (G
L
(f)) primarily arises from the antenna
power area density, gain variations with frequency and additionally from frequency depen-
dence of physical propagation phenomena such as scattering and diffraction. In our model,
G
L
(f) is expressed as a power-law decay model [66] which in logarithmic form becomes
G
L
(f) =G
f
0
− 20·κ·log
10

f
f
Mc
!
. (5.6)
where κ is the frequency decay component. G
f
0
is the power in the lowest frequency sub-
band, normalized by the total power. f
Mc
is the center frequency of each selected sub-band
(each sub-band has a bandwidth of 500 MHz withf
Mc
= 2.25 GHz, 2.75 GHz, ... , 7.75 GHz).
Though [68] has shown that κ can be different for each MPC, we use a "bulk" model in our
analysis because we did not have sufficient number of measurement points to extract κ for
each path separately. The κ values obtained for LOS and NLOS scenarios are shown in
Table 5.3, while the linear regression fit for the frequency-dependent path gain (dB) as a
function of frequency (dB) is shown in Fig. 5.6. To test the accuracy of the extracted κ
value, the root-mean-square-error (RMSE) between the measured and the simulated (using
eq. 5.6) frequency-dependent path gain was estimated to be about−24 dB. Also, from our
calibration measurement in the anechoic chamber with Tx and Rx placed at 1 m separation,
κ = 1.1 was observed. This calibration measurement characterizes the antenna properties in
conjunction with the free-space path gain.
5.4.2 Shadowing
Shadowing typically denotes the large-scale fluctuations of the received power in a prop-
agation channel. The logarithmic values of this power deviation observed closely matches a
zero-mean Gaussian distribution N(0,σ
s
(dB)), which is standard model for shadowing and
has been reported in the literature [174, 72]. This parameter follows the same distribution
115
2.25 2.75 3.25 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75
10
−2
10
−1
10
0
f (GHz)
Normalized path gain

LOS
LS fit
NLOS
Figure 5.6: Frequency dependency of the path gain in the LOS and NLOS scenarios.
as well in our analysis and is represented asS
σ
in our modeling (see eq. 6.14). The standard
deviation (σ
s
(dB)) of this parameter for the LOS and NLOS scenarios are listed in Table 5.3.
5.5 Angular Analysis
Directionally resolved channel measurements, and models based on those measurements,
are important for the design and simulation of multiantenna systems. In this section, we
first extract the delay and direction parameters of the MPCs from the measured channel
transfer functions. We perform clustering of the MPCs with similar parameters and develop
the stochastic channel models for the LOS and NLOS environments using the intra-cluster
and inter-cluster propagation modeling.
5.5.1 MPC parameter extraction using CLEAN
CLEAN is an iterative deconvolution technique first introduced in [175] for the enhance-
ment of the radio astronomical maps of the sky and widely used in microwave and UWB
communities as an effective post-processing method for time-domain channel measurements.
However, the principle can also be used to extract the delay and direction information from
the channel transfer function measurements [163]. The details of the algorithm are available
in [176], and not included here for want of space.
116
Henceforth,

α
i
,τ
i
,φ
DoD
i
,φ
DoA
i

shall denote the extracted parameters for the i
th
MPC:
α
i
and τ
i
respectively denote the complex path gain and the delay experienced by the i
th
MPC; φ
DoD
i
and φ
DoA
i
respectively denote the azimuth direction of departure (DoD) and
azimuth direction of arrival (DoA) corresponding to the i
th
MPC.
5.5.2 Clustering of MPCs
The MPCs tend to be clustered and the clusters usually correspond to the physical
scattering objects in the environment. A cluster is defined as a group of MPCs with similar
delay, DoA and DoD. Multipath component distance (MCD) is a commonly used distance
metric for measuring the similarity of the MPCs. The MCD between the MPCs i and j is
defined as [177]
MCD
ij
=
q
MCD
2
τ
ij
+MCD
2
DoD
ij
+MCD
2
DoA
ij
(5.7)
where,
MCD
τij
=ξ
|τ
i
−τ
j
|
Δτ
max
τ
rms
Δτ
max
MCD
2
DoDij
=
1
4

cosφ
DoD
i
−cosφ
DoD
j

2
+
1
4

sinφ
DoD
i
−sinφ
DoD
j

2
MCD
2
DoAij
=
1
4

cosφ
DoA
i
−cosφ
DoA
j

2
+
1
4

sinφ
DoA
i
−sinφ
DoA
j

2
(5.8)
and where τ
rms
is the RMS delay spread and Δτ
max
is the delay difference between the
MPCs, maximized over all pairs of MPCs. ξ is the delay weighting factor, which is chosen
by inspection. For the measured data,ξ = 10 gave clusters consistent with the environment.
Because of the large bandwidth of the measurement setup, the delay information is more
accurate and hence more weight is given to the delay information in clustering.
We use the KPowerMeans clustering technique, which takes the MPC power into con-
sideration, to group the MPCs into clusters such that the total power weighted MCD of the
MPCs from their centroids is minimized [178]. The cluster centroid is defined as the power
weighted mean of the parameters of the MPCs in the cluster. For given cluster centroids,
117
−40
−20
0
20
40
−50
−30
−10
10
30
50
0
10
20
30
40
50
60

DoD (degrees)
Unclustered MPCs
DoA (degrees)

Distance (m)
−55
−50
−45
−40
−35
−30
−25
Figure 5.7: Scatter plot of the unclustered MPCs. (5 m LOS measurement.)
the algorithm assigns each MPC to the cluster centroid with the smallest MCD. The cluster
centroids are then updated based on the MPC grouping. The cluster centriod computation
and the MPC grouping is done iteratively until convergence. The initial cluster centroids
are chosen such that they are as far apart as possible.
The KPowerMeans algorithm requires as an input the number of clusters K. While
there are several metrics to find the optimal K based on the compactness of the clusters,
like the Calinski–Harabasz index and Davies–Bouldin index [179], they are very sensitive to
the outliers in the data. For this reason, we use visual inspection to determine the number
of clusters for each measurement point: we apply the KPowerMeans clustering for a given
number of clusters (2≤ K ≤ 14) and pick the value of K that gives the visually most
compact clusters.
We now present the clustering result for a sample measurement. Fig. 5.7 plots the delay,
DoD and DoA of the MPCs, for a 5 m LOS measurement. The corresponding measurement
Tx and Rx locations are shown as TXL3 and RXL3 in Fig. 5.2. The MPCs are color coded
with a scale indicating the path powers in dB scale. Fig. 5.8 shows the clustered MPCs,
obtained using the KPowerMeans algorithm. The cluster centroids are shown in the legend.
118
−40
−20
0
20
40
−50
−30
−10
10
30
50
0
10
20
30
40
50
60

DoD (degrees)
Clustered MPCs
DoA (degrees)

Distance (m)
C1 (6.3m, 13 deg, −10 deg)
C2 (5.3m, −2.1 deg, −3.8 deg)
C3 (5.4m, −14 deg, 15 deg)
C4 (5.7m, −49 deg, 5 deg)
C5 (6.3m, −31 deg, 34 deg)
C6 (6.3m, 29 deg, −33 deg)
C7 (29.7m, −1.3 deg, −0.3 deg)
Figure 5.8: Clustered MPCs with KPowerMeans algorithm. (5 m LOS measurement.)
Weobservedsevenclustersforthismeasurement. ClusterC2correspondstotheLOScluster.
We observe symmetric clusters with respect to Tx, consistent with the environment. Clusters
C1, C3, C5 and C6 corresponds to reflections from the concrete pillars and the metal racks
on either side of Tx and Rx. Cluster C4 corresponds to reflection from the concrete pillar
to the back and to the right of the Tx. Cluster C7 has similar DoD and DoA as that of
LOS cluster, but has an excess delay of 24 m compared to the LOS. This corresponds to the
reflection from metal racks exactly to the back of the Tx. Please note that for ULAs, the
LOS and the back wall reflections have similar DoA/DoD. In our measurements, we observed
a significant number of clusters from back wall reflections since the Tx/Rx was placed close
to the walls, metal doors etc.
We now develop the channel model for the LOS and NLOS environments separately.
5.5.3 LOS Environment
We first consider the intra-cluster properties of the MPCs, followed by the inter-cluster
properties. For all the statistical models developed in the paper, the goodness of the fit is
verified by applying the Kolmogorov-Smirnov (K-S) hypothesis test at 5% significance level.
119
Figure 5.9: Figure demonstrating that the intra-cluster DoD and DoA are independent, in
the LOS environment.
Intra-cluster modeling
We now develop the model for the ToA, DoD and DoA of the MPCs within each cluster,
with respect to the cluster center.
1
Dependency of MPC DoD, DoA and ToA: We first examine the dependency of the MPC
ToA, DoD and DoA. Fig. 5.9 plots the joint density of the MPC DoA and DoD (w.r.t. the
cluster center) and compares it with the product of corresponding marginal densities [83].
From visual inspection, we can see that both pdfs are similar and hence it can be concluded
that the intra-cluster DoD and DoA are independent. From Fig. 5.10, which similarly ana-
lyzes MPC DoD and ToA, it can be concluded that the intra-cluster ToA and DoD are
independent. Similar analysis showed that the intra-cluster DoA and ToA are also indepen-
dent.
Intra-cluster DoD and DoA (w.r.t. cluster center): The LOS cluster and the NLOS
clustersareobservedtohaveslightlydifferentstatistics. Figs.5.11and5.12plottheempirical
density of the MPC DoA and MPC DoD for the LOS and NLOS cluster respectively, and fit
them using a Laplace distribution (with parameters μ and b). It can be seen that the LOS
cluster has relatively smaller value ofb, and hence smaller angular spreads, compared to the
1
ToA of the cluster center is defined as the smallest ToA of all the MPCs within the cluster. DoD/DoA
of cluster center are defined as the power weighted mean DoD/DoA of MPCs within the cluster. The cluster
power is defined as the sum of the powers of MPCs within that cluster.
120
Figure 5.10: Figure demonstrating that the intra-cluster DoD and ToA are independent, in
the LOS environment.
NLOS clusters. It was observed that the goodness of the fit was better when the LOS and
NLOS clusters was treated separately, comapared to the case where both LOS and NLOS
clusters data was combined. Also, the angular spreads observed here are smaller than the
angular spread of 20
◦
− 25
◦
reported for indoor UWB channel in [163]. Unlike the MIMO
measurements in this paper, the indoor measurements in [163] were taken with a SIMO setup
and hence the clustering of MPCs was done in ToA and DoA domains only, thus resulting
in larger intra-cluster angular spreads.
Intra-cluster ToA (w.r.t. cluster center): The delay between the ToAs of successive
MPCs is modeled using an exponential mixture distribution. Fig. 5.13 plots the CCDF
for the LOS and NLOS clusters. The mixture probabilities (β) and the parameter (λ) of
the individual exponential distributions are determined using the expectation maximization
(EM) algorithm. It can be seen that the LOS cluster has higher arrival rates compared to
NLOS clusters.
Intra-cluster power decay (Normalized by cluster power): The power of the MPCs within
the cluster decays exponentially with the delay. However, the intra-cluster power decay
constant is a function of cluster delay as shown in Fig. 5.14. It can be seen that the LOS
121
−50 0 50
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Intra−cluster DoD (deg)
PDF

Measured
Laplace fit
μ = −0.25deg
b = 3.96deg
−50 0 50
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Intra−cluster DoA (deg)
PDF

Measured
Laplace fit
μ = −0.13deg
b = 4.17deg
Figure 5.11: Intra-cluster DoD and DoA for the LOS cluster, in the LOS environment.
−50 0 50
0
0.02
0.04
0.06
0.08
0.1
0.12
Intra−cluster DoD (deg)

PDF
Measured
Laplace fit
μ = −0.21deg
b = 5.95deg
−50 0 50
0
0.02
0.04
0.06
0.08
0.1
0.12
Intra−cluster DoA (deg)
PDF

Measured
Laplace fit
μ = −0.05deg
b = 6.06deg
Figure 5.12: Intra-cluster DoD and DoA for the NLOS clusters, in the LOS environment.
cluster has fast intra-cluster power decay and the far away clusters experience slower intra-
cluster power decay. The dependency of the intra-cluster power decay constant on the cluster
delay is modeled using a linear function.
Inter-cluster modeling
We now develop the model for the ToA, DoD and DoA of the cluster centers, with respect
to the LOS cluster. The ToA, DoD and DoA of the LOS cluster are completely deterministic:
the ToA is given by the Euclidean distance between the Tx and Rx arrays, while DoD and
DoA are determined by the relative orientation of Tx and Rx antenna arrays. For all the
122
0 5 10 15
10
−4
10
−3
10
−2
10
−1
10
0
Delay between ToA of successive MPCs (m)
CCDF
LOS cluster

Measured
Exponential mixture fit:
β = [0.021 0.979],
λ = [0.368 7.351]/m
0 10 20 30
10
−4
10
−3
10
−2
10
−1
10
0
Delay between ToA of successive MPCs (m)
CCDF
NLOS clusters

Measured
Exponential mixture fit:
β = [0.023 0.872 0.105],
λ = [0.170 5.690 0.820]/m
Figure 5.13: Intra-cluster ToA modeling for the LOS and NLOS clusters, in the LOS envi-
ronment.
0 10 20 30 40 50 60
−1.5
−1
−0.5
0
0.5
Excess Cluster ToA compared to the Tx−Rx separation distance (m)
Inra−cluster MPC power decay constant (/m)

Measured
Linear fit
Slope = 0.0035/m
2
Y−intercept = −0.2248/m
Figure 5.14: Intra-cluster power decay constant for different cluster ToA, in the LOS envi-
ronment.
measurements in the paper, the Tx and Rx arrays were aligned and hence the DoD and DoA
of the LOS cluster are close to zero degrees.
Dependency of cluster DoD, DoA and ToA: Fig. 5.15 plots the joint density of the cluster
DoAandDoD(w.r.t. theLOScluster)andcomparesitwiththeproductofthecorresponding
marginal densities. From visual inspection we can see that both pdfs are very different and
hence the cluster DoA and DoD are not independent. Similarly from Fig. 5.16, we can
see that the cluster ToA and DoD are also not independent. Similar observations about
dependency of cluster DoD, DoA and ToA were made in [164] for an indoor UWB channel.
123
Figure 5.15: Figure demonstrating that the cluster DoD and DoA are not independent, in
the LOS environment.
Figure 5.16: Figure demonstrating that the cluster DoD and ToA are not independent, in
the LOS environment.
Joint modeling of cluster ToA, DoD and DoA: The cluster DoD can be approximated
using a Laplace distribution as shown in Fig. 5.17. While both Normal distribution and
Laplace distribution were tried to fit the data, the Laplace distribution provided a bet-
ter fit, which was also verified using the K-S and Akaike’s Information Criterion (AIC)
hypothesis tests. The relatively large probability mass near zero can be attributed to the
backwall reflections. The empirical density function of the cluster DoA, conditioned on
the cluster DoD, is shown in Fig. 5.18. From the measured empirical density, it can be
124
−40 −20 0 20 40 60 80
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cluster DoD (deg)
CDF

Measured
Laplace fit
μ = 1.31 deg
b = 15.92 deg
Figure 5.17: Cluster DoD modeling in the LOS environment.
Figure 5.18: Figure comparing the measured and simulated conditional density DoA|DoD,
for the LOS environment.
seen that most of the probability mass is concentrated along the diagonals. This is con-
sistent with the propagation environment as we expect most of the propagation through
aisles–the principal diagonal represents the single bounce scattering along the aisle and the
antidiagonal represents the double bounce scattering along the aisle. To avoid overfitting
the data, we use a simple Gaussian mixture distribution to fit the conditional density, i.e.,
DoA|DoD∼ 0.8N(−DoD,
√
6
◦
) + 0.2N(DoD,
√
3
◦
), where N(μ,σ) denotes the standard
Normal density with mean μ and variance σ
2
. The simulated conditional density plot using
the Gaussian mixture model is shown on the right in Fig. 5.18. While the proposed model
may not be the most accurate representation of the measurements, it captures the depen-
dency of the cluster DoA and DoD with a small number of parameters.
125
We now model the cluster ToA conditioned on the cluster DoA and DoD. For this,
we consider different propagation scenarios. Because of the geometry of the setup and
the environment, we observed a significant number of clusters from back wall reflections.
For ULAs, the LOS cluster and the back wall refection clusters have very similar cluster
DoA and DoD (DoD and DoA are close to 0). For these clusters, the excess cluster ToA,
comparedtoLOS,wasobservedtobeuniformlydistributedasshowninFig.5.19(a). Among
the remaining clusters, we further differentiate between single bounce and double bounce
scattered clusters. Scattering with more than two bounces will have very weak power in our
scenario and hence we ignore them for modeling. For a single bounce scattering clusters,
the ToA is a deterministic function of DoA and DoD. If DoA and DoD have same sign
(both positive or both negative), we can only have double bounce scattering and the excess
cluster ToA, compared to LOS, is modeled using an exponential random variable as shown
in Fig. 5.19 (c); If DoA and DoD have opposite sign, both single bounce and double bounce
scattering are possible. For a single bounce, as mentioned earlier, the excess cluster ToA
compared to LOS is equal to the deterministic value of d
cos(0.5(DoD+DoA))
cos(0.5(DoD−DoA))
−d, where d is
the Tx-Rx Euclidean distance. For a double bounce scattering, we model the excess cluster
ToA as sum of the excess cluster ToA for a single bounce scattering plus an exponential
random variable (Fig. 5.19 (b)). From the measurements, we observed that 56% of clusters
correspond to single bounce scattering.
Hence the excess cluster ToA (w.r.t. LOS) conditioned on the cluster DoA and DoD can
be modeled as
126
0 20 40 60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Excess Cluster ToA (m)
CDF
(a) Backwall reflection

Measured
Uniform fit
U[1.77m, 53.21m]
0 5 10 15
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Excess Cluster ToA (m)
CDF
(b) DoD*DoA < 0 and
double bounce scattering

Measured
Exponential fit
(1/λ = 3.1074m)
0 10 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Excess Cluster ToA (m)
CDF
(c) DoD*DoA > 0

Measured
Exponential fit
(1/λ = 3.4067m)
Figure 5.19: Modeling the Excess cluster ToA for different propagation scenarios in the LOS
environment (a) Backwall reflection (b) Double bounce scattering with DoD∗DoA< 0 (c)
Double bounce scattering with DoD∗DoA> 0.
ToA|DoD,DoA
∼U[1.77 m, 53.21 m], if|DoA|< 10
◦
,|DoD|<10
◦
∼d
cos(
1
2
(DoD+DoA))
cos(
1
2
(DoD−DoA))
−d w.p. 0.56, elseif DoA∗DoD<0
∼d
cos(
1
2
(DoD+DoA))
cos(
1
2
(DoD−DoA))
−d+X
1
w.p. 0.44,elseif DoA∗DoD<0
∼X
2
,
elseif DoA∗DoD>0
(5.9)
whereX
1
andX
2
are exponen-
tial random variables with means 3.1 m and 3.41 m respectively.
2
Cluster power decay: It is observed that the cluster power decays exponentially with the
cluster ToA, and the decay constant is different for different propagation scenarios as shown
in Fig. 5.20. The backwall reflections has the smallest power decay constant.
Number of clusters: The average number of clusters increased with the measurement
distance as shown in Fig. 5.21. The distance dependency is captured by using a linear
function. While quadratic function might be a better fit to the data, it can result in over-
fitting the data. Since we did not have enough number of observations for each distance to
2
In both cases, the K-S test passed the exponential hypothesis test only at 1% significance level (fails at
standard 5% significance level). Because of the limited sample size and over-fitting issues, we still fit the
data with exponential distribution.
127
0 20 40 60
−35
−30
−25
−20
−15
−10
−5
0
Cluster ToA (m)
Normalized Power (dB)
(a) Backwall reflection

Measured
Exponential decay fit
(Λ = = 0.063993/m)
0 2 4 6
−30
−25
−20
−15
−10
−5
0
Cluster ToA (m)
Normalized Power (dB)
(b) DoD*DoA < 0

Measured
Exponential decay fit
(Λ = 0.55928/m)
0 2 4 6
−30
−25
−20
−15
−10
−5
0
Cluster ToA (m)
Normalized Power (dB)
(c) DoD*DoA > 0

Measured
Exponential decay fit
(Λ = 0.30855/m)
Figure 5.20: Inter-cluster power decay for different propagation scenarios in the LOS envi-
ronment (a) Backwall reflection (b) DoD∗DoA< 0 (c) DoD∗DoA> 0.
4 6 8 10 12 14 16 18 20 22 24 26
5
5.5
6
6.5
7
7.5
8
Measurement distance (m)
Average number of clusters

Measured
Linear fit
(5.34+0.06d)
Figure 5.21: Average number of clusters as a function of measurement distance in the LOS
environment.
extract the shape of the pdf, we model the number of clusters as a Poison random variable,
which is a common assumption in the literature.
128
LOS channel model
We now summarize the delay-double directional channel model for the LOS environment.
The channel impulse response for a Tx and Rx separated by distance d (in meters) is given
by
h(τ,θ,φ) =
K−1
X
k=0
L−1
X
l=0
|α
k,l
| exp (jθ
k,l
)δ(τ−ToA
k
−ToA
k,l
)
×δ(θ−DoD
k
−DoD
k,l
)δ(φ−DoA
k
−DoA
k,l
), (5.10)
where the number of clusters is modeled by K∼Poisson(5.34 + 0.06d).
For the LOS cluster, ToA
0
corresponds to the distance between Tx and Rx. DoD
0
and
DoA
0
are determined by the relative orientation of the Tx/Rx arrays. For all subsequent
clusters, the cluster centers relative to the LOS cluster (ToA
r
k
, ToA
k
−ToA
0
, DoD
r
k
,
DoD
k
−DoD
0
and DoA
r
k
,DoA
k
−DoA
0
) are modeled as
DoD
r
k
∼Laplace(μ = 1.31
◦
,b = 15.92
◦
),
DoA
r
k
|DoD
r
k
∼ 0.8N(−DoD
r
k
,
√
6
◦
)+0.2N(DoD
r
k
,
√
3
◦
) (5.11)
The conditional density of ToA
r
k
given DoD
r
k
and DoA
r
k
is given in eq. (5.9).
The intra-cluster ToA, DoA and DoD for the LOS cluster are modeled by:
P (ToA
0,l
−ToA
0,l−1
>τ)
= 0.02 exp(−0.37τ) + 0.98 exp(−7.35τ)
DoD
0,l
∼Laplace(μ =−0.25
◦
,b = 3.96
◦
)
DoA
0,l
∼Laplace(μ =−0.13
◦
,b = 4.17
◦
) (5.12)
129
The intra-cluster ToA, DoA and DoD for the NLOS clusters are modeled by:
P (ToA
k,l
−ToA
k,l−1
>τ)
= 0.02 exp(−0.17τ) + 0.11 exp(−0.82τ) + 0.87 exp(−5.69τ)
DoD
k,l
∼Laplace(μ =−0.21
◦
,b = 5.95
◦
)
DoA
k,l
∼Laplace(μ =−0.05
◦
,b = 6.06
◦
) (5.13)
The MPC power and the phase are modeled by (the small scale fading is not modeled,
as the MPCs are resolved in delay, transmit and receive azimuth domains and hence do not
expect several unresolvable MPCs in one bin):
|α
k,l
|
2
∝ exp (−ΛToA
r
k
) exp ((−0.22+0.0035ToA
r
k
)ToA
k,l
)
θ
k,l
∼U[0, 2π] (5.14)
where the inter-cluster exponential power decay constant (Λ) is given by
Λ = 0.064 m
−1
, if|DoA
r
k
|< 10
◦
and|DoD
r
k
|< 10
◦
= 0.56 m
−1
, else if DoA
r
k
∗DoD
r
k
< 0
= 0.31 m
−1
, else if DoA
r
k
∗DoD
r
k
> 0 (5.15)
5.5.4 NLOS Environment
We will now develop the stochastic channel model for the NLOS environment. Most of
the observations are very similar to the LOS environment, and hence we only emphasize the
key differences from the LOS environment.
130
−50 0 50
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Intra−cluster DoD (deg)
PDF

Measured
Laplace fit
μ = 0.113deg,
b= 9.71deg
−50 0 50
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Intra−cluster DoA (deg)
PDF

Measured
Laplace fit
μ = −0.19deg,
b = 10.82deg
Figure 5.22: Intra-cluster DoD and DoA modeling in the NLOS environment.
Intra-cluster modeling
As for the LOS environment, the MPC ToA, DoD and DoA are independent. The MPC
DoA and DoD are modeled using the Laplace distribution as shown in Fig. 5.22. The delay
between the ToAs of successive MPCs is modeled using exponential mixture distribution as
shown in Fig. 5.23. Unlike the LOS environment, we only have one type of clusters (NLOS
clusters) here. The intra-cluster angular spreads here are higher than the angular spreads
observed for the NLOS clusters in the LOS environment. It is observed that the MPC power
does not monotonically decay with the delay. Rather, it first slightly increases and then
decreases as shown in Fig. 5.24. This soft onset in the intra-cluster MPC power decay was
observed in industrial UWB environments as well, where it was modeled as [79].
P (τ)∝

1−χ exp

−
τ
γ
rise
!!
exp

−
τ
γ
fall
!
(5.16)
Inter-cluster modeling
As observed in LOS environment, the cluster ToA, DoD and DoA are dependent. The
dependency is again modeled using the conditional densities. Since there is no physical LOS
131
0 5 10 15 20 25
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
Delay between ToA of successive MPCs (m)
CCDF

Measured
Exponential Mixture fit:
β = [0.9716 0.0017 0.0267],
λ = [6.2242 0.1184 0.8131]/m
Figure 5.23: Intra-cluster ToA modeling in the NLOS environment.
cluster, we model the cluster DoD, DoA and ToA w.r.t. to the DoD, DoA and ToA cor-
responding to the geometrical LOS between the Tx and Rx arrays. The cluster DoD can
be modeled using the Laplace mixture distribution as shown in Fig. 5.25. Both Gaussian
mixture and Laplace mixture distributions were tried to fit the data and the latter distri-
bution provided a better fit. The conditional density of DoA given DoD is modeled using
a Gaussian mixture density, i.e., DoA|DoD∼ 0.5N(−DoD,
√
15
◦
) + 0.5N(DoD,
√
15
◦
) as
shown in Fig 5.26. As done for the LOS case, the conditional density of excess cluster ToA
given cluster DoD and DoA is modeled using Uniform distribution for backwall reflections
and Exponential distribution for double bounce scattering, as shown in Fig. 5.27. The cluster
power decays exponentially with the cluster ToA and the power decay constant for different
propagation scenarios is given in Fig. 5.28.
Number of clusters: Similar to LOS case, the average number of clusters increased with
measurement distance and is modeled using a linear function.
132
0 5 10 15 20
−35
−30
−25
−20
−15
−10
−5
0
5
Intra−cluster ToA (m)
Normalized power(dB)

Measured
Soft onset power decay fit
γ
rise
=5.66m, γ
fall
= 2.84m, χ =0.8
Figure 5.24: Intra-cluster power decay modeling in the NLOS environment.
−80 −60 −40 −20 0 20 40 60 80
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cluster DoD (deg)
CDF

Measured
Lalace mixture fit
β = [0.35 0.18 0.23 0.24]
μ = [−26.7 5.53 15.8 37.5] deg
b = [12.5 3.7 9.2 8.2] deg
Figure 5.25: Cluster DoD modeling in the NLOS environment.
Figure 5.26: Figure comparing the measured and simulated conditional density DoA|DoD,
for the NLOS environment.
133
NLOS channel model
We now summarize the delay-double directional channel model for the NLOS environ-
ment. The channel impulse response for a Tx and Rx separated by distance d is given
by
h(τ,θ,φ) =
K
X
k=1
L−1
X
l=0
|α
k,l
| exp (jθ
k,l
)δ(τ−ToA
k
−ToA
k,l
)
×δ(θ−DoD
k
−DoD
k,l
)δ(φ−DoA
k
−DoA
k,l
) (5.17)
where the number of clusters is modeled by K∼Poi(6.76 + 0.062d).
LetToA
0
=dbetheEuclideandistancebetweenTxandRx. DoD
0
andDoA
0
betheDoD
and DoA of the geometric LOS between Tx and Rx arrays. The cluster centers relative to the
geometric LOS (ToA
r
k
,ToA
k
−ToA
0
,DoD
r
k
,DoD
k
−DoD
0
andDoA
r
k
,DoA
k
−DoA
0
)
are modeled as
DoD
r
k
∼ 0.35Laplace(μ =−26.7
◦
,b = 12.5
◦
)
+ 0.18Laplace(μ = 5.53
◦
,b = 3.7
◦
)
+ 0.23Laplace(μ = 15.8
◦
,b = 9.2
◦
)
+ 0.24Laplace(μ = 37.5
◦
,b = 8.2
◦
)
DoA
r
k
|DoD
r
k
∼0.5N(−DoD
r
k
,
√
15
◦
)+0.5N(DoD
r
k
,
√
15
◦
) (5.18)
The conditional density of ToA
r
k
given DoD
r
k
and DoA
r
k
is given by
134
0 5 10 15 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Excess Cluster ToA (m)
CDF
(a) Backwall reflection

Measured
Uniform fit
U[0.68m, 18.32m]
0 5 10 15 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Excess Cluster ToA (m)
CDF
(b) DoD*DoA < 0 and
double bounce scattering

Measured
Exponential fit
(1/λ = 5.52m)
0 5 10 15 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Excess Cluster ToA (m)
CDF
(c) DoD*DoA>0

Measured
Exponential fit
(1/λ = 6.89m)
Figure5.27: ModelingtheexcessclusterToAfordifferentpropagationscenariosintheNLOS
environment (a) Backwall reflection (b) Double bounce scattering with DoD∗DoA< 0 (c)
Double bounce scattering with DoD∗DoA> 0.
ToA
r
k
|DoD
r
k
,DoA
r
k
∼U[0.68 m, 18.32 m], if|DoA
r
k
|<10
◦
,|DoD
r
k
|<10
◦
∼d
cos(
1
2
(DoD
r
k
+DoA
r
k
))
cos(
1
2
(DoD
r
k
−DoA
r
k
))
−d w.p. 0.21, elseif DoA
r
k
∗DoD
r
k
<0
∼d
cos(
1
2
(DoD
r
k
+DoA
r
k
))
cos(
1
2
(DoD
r
k
−DoA
r
k
))
−d+X
1
w.p. 0.79,elseif DoA
r
k
∗DoD
r
k
<0
∼X
2
,
elseif DoA
r
k
∗DoD
r
k
> 0
(5.19)
whereX
1
andX
2
are exponen-
tial random variables with mean 5.52 m and 6.89 m respectively.
3
The intra-cluster ToA, DoD and DoA are modeled by:
P (ToA
k,l
−ToA
k,l−1
>τ) = 0.9716 exp(−6.224τ)
+ 0.0267 exp(−0.8131τ) + 0.0017 exp(−0.1184τ)
DoD
k,l
∼Laplace(μ = 0.113
◦
,b = 9.71
◦
)
DoA
k,l
∼Laplace(μ =−0.19
◦
,b = 10.82
◦
) (5.20)
3
ForX
2
modeling, the K-S test passed the exponential hypothesis test only at 1% significance level (fails
at standard 5% significance level). Because of the limited sample size and over-fitting issue, we still fit the
data with an exponential distribution.
135
0 5 10 15 20
−25
−20
−15
−10
−5
0
Cluster ToA (m)
Normalized Power (dB)
(a) Backwall reflection

Measured
Exponential decay fit
(Λ = 0.15596/m)
0 5 10 15 20
−20
−18
−16
−14
−12
−10
−8
−6
−4
−2
0
Cluster ToA (m)
Normalized Power (dB)
(b) DoD*DoA<0

Measured
Exponential decay fit
(Λ = 0.066128/m)
0 10 20
−25
−20
−15
−10
−5
0
Cluster ToA (m)
Normalized Power (dB)
(c) DoD*DoA>0

Measured
Exponential decay fit
(Λ = 0.066914/m)
Figure 5.28: Inter-cluster power decay for different propagation scenarios in the NLOS envi-
ronment (a) Backwall reflection (b) DoD∗DoA< 0 (c) DoD∗DoA> 0.
The MPC power and the phase are modeled by:
|α
k,l
|
2
∝exp (−ΛToA
r
k
)

1−χ exp

−
ToA
k,l
γ
rise

exp

−
ToA
k,l
γ
fall

θ
k,l
∼U[0, 2π] (5.21)
whereχ = 0.8,γ
rise
= 5.66m,γ
fall
= 2.84m, and the inter-cluster exponential power decay
constant (Λ) is given by
Λ = 0.156 m
−1
, if|DoA
r
k
|< 10
◦
and|DoD
r
k
|< 10
◦
= 0.066 m
−1
, else if DoA
r
k
∗DoD
r
k
< 0
= 0.067 m
−1
, else if DoA
r
k
∗DoD
r
k
> 0 (5.22)
5.6 Model Validation
We validate the proposed channel models for the LOS and NLOS environment by com-
paring the capacity and the RMS delay spreads, from our model to that obtained from the
measurement data.
Synthetic data generation: For each measurement distance, we generate inter-cluster and
intra-cluster ToA, DoD and DoA, and the path weights as per the model given in Sec. 5.5.3
136
and 5.5.4, for the LOS and NLOS channels respectively. The N
T
×N
R
channel transfer
functions are generated as sum of discrete MPCs, as given below
H(f
k
)=
X
l
α
l
B
T
(f
k
,φ
l
)B
R
(f
k
,ψ
l
)
†
exp (−j2πf
k
τ
l
),1≤k≤N
F
(5.23)
where φ
l
, ψ
l
, τ
l
and α
l
respectively denote the DoD, DoA, delay and complex path gain
corresponding to the l
th
MPC. B
T
(f
k
,φ) and B
R
(f
k
,φ) are the beampatterns of the Tx and
Rx arrays used in the measurements.
Let H
syn
(f
k
) be the synthesized channel transfer function matrix. They are further
normalized such that E [
P
k
||H
syn
(f
k
)||
2
F
] = N
T
N
R
N
F
where the expectation is taken over
therealizationsofchannel. Thetransferfunctionsarefurther multipliedby

f
k
f
C

−κ
, tomodel
the frequency dependent path loss. (
˜
H
syn
(f
k
) =H
syn
(f
k
)

f
k
f
C

−κ
,f
C
is the center frequency.)
Capacity computation: The measured channel capacity (bits/sec/Hz) is given by
C
meas
=
1
N
F
X
k
log
2




I +
1
N
T
N
0
H
meas
(f
k
)H
meas
(f
k
)
†




(5.24)
where N
0
is the noise power per sub-carrier, measured from the noise-only region of the
channel impulse response, averaged over the measurements.
The synthesized channel capacity for a realization of the channel transfer function,
˜
H
syn
(f
k
), is given by
C
syn
=
1
N
F
X
k
log
2




I +
P
N
T
N
0
˜
H
syn
(f
k
)
˜
H
syn
(f
k
)
†




(5.25)
where P =
1
N
F
P
k
||H
meas
(f
k
)||
2
F
is the received power per sub-carrier for the corresponding
measurement. This is done to ensure that the synthetic data has the same wideband signal-
to-noise ratio (SNR) as the measured transfer functions.
RMS delay spread computation: RMS delay spread is defined as the second central
moment of the average power delay profile (APDP). For each measurement, the APDP
137
5 10 15 20 25
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Measurement distance (m)
Difference between measured and simulated values,
normalized by standard deviation
Capacity validation
5 10 15 20 25
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5
Measurement distance (m) Difference between measured and simulated values,
normalized by standard deviation
RMS delay spread validation
Figure 5.29: Capacity and RMS delay spread validation for the LOS channel model.
is obtained by averaging the absolute square magnitude of the channel impulse response
over the N
T
N
R
measurements.
APDP (τ) =
1
N
T
N
R
N
T
X
i=1
N
R
X
j=1
|h
ij
(τ)|
2
(5.26)
where h
ij
(τ) =IFFT{H
ij
(f)} is the channel impulse response between the i
th
Tx and the
j
th
Rx antenna elements of the array. The noise-threshold filter is applied to the APDP
obtained from the measured data, as described in Sec. 5.4. The RMS delay spread is given
by
τ
rms
=
v
u
u
t
R
τ
2
APDP (τ)dτ
R
APDP (τ)dτ
−
R
τAPDP (τ)dτ
R
APDP (τ)dτ
!
2
. (5.27)
Capacity and RMS delay spread validation: We now compare the delay spread and the
capacity values computed from the measurements with the synthetic data. For each mea-
surement distance and shadowing point, we have one realization of capacity/delay spread
from the measurement, and generate 300 realizations for the synthetic data. We compare the
measurement value with the mean value of the synthetic data, normalized by the standard
deviation of the synthetic data.
Fig. 5.29 plots the difference between the mean simulated RMS delay spread/capacity
and the measured RMS delay spread/capacity, normalized by the standard deviation of the
simulated RMS delay spread/capacity at the given distance, for the LOS environment. It
138
5 10 15 20 25
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Measurement distance (m)
Difference between measured and simulated values,
normalized by standard deviation
Capality validation
5 10 15 20 25
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Measurement distance (m)
Difference between measured and simulated values,
normalized by standard deviation
RMS delay spread validation
Figure 5.30: Capacity and RMS delay spread validation for the NLOS channel model.
can be seen that the synthetic data agrees reasonably well with the measurements both
in terms of capacity and the delay spread: the measured capacity is at-most one standard
deviation from the synthetic data and the measured delay spread is within 1.5 standard
deviation from the synthetic data, in most cases. The mean values of the channel capacity
varies from 80 bits/s/Hz (at Tx-Rx separation distance of 5 m) to 30 bits/s/Hz (at Tx-
Rx separation distance of 25 m). The standard deviation of the capacity varied from 10
bits/s/Hz at (at Tx-Rx separation distance of 5 m) to 5 bits/s/Hz (at Tx-Rx separation
distance of 25 m). The mean value of the RMS delay spread varied from 16.6 ns to 26.6 ns
and the standard deviation of RMS delay spread was around 4 ns. Similar observations hold
true even for the NLOS environment as can be seen from Fig. 5.30. For NLOS case, the
mean value of the channel capacity varies from 80 bits/s/Hz (at Tx-Rx separation distance
of 5 m) to 40 bits/s/Hz (at Tx-Rx separation distance of 25 m). The standard deviation of
the capacity was observed to be between 5-7 bits/s/Hz. The mean and standard deviation
values of the RMS delay spreads are 15 ns and 4.3 ns respectively. The capacity captures the
angular information and is an indirect validation of the channel model in terms of angular
characterization. Unlike the RMS delay spread and channel capacity, the angular spreads
cannot be computed directly from the raw channel transfer function measurements.
139
5.7 Summary and Conclusion
WeconductedameasurementcampaigninawarehouseenvironmentusingaUWBvirtual
MIMO (8 x 8) antenna array channel sounder setup for LOS and NLOS scenarios. From
these measurement data, we obtain a double-directional propagation channel model. The
main findings are as follows:
• The distance-dependent path gain coefficient in the LOS and NLOS environments is
n = 1.63 and n = 2.14 respectively.
• The extracted frequency decay components were similar (κ = 1.46) for both LOS and
NLOS scenarios.
• The shadowing was observed to be lognormal distributed with the standard deviation
σ(dB) = 2.10 for the LOS environment and σ(dB) = 3.16 for the NLOS environment.
• MPCs typically congregate into clusters.
• Intra-cluster analysis showed that the MPC ToA, DoD and DoA are independent. The
MPC DoD and DoA fit Laplace distributions and the MPC ToA fit an Exponential
mixture distribution. For the LOS environment, the NLOS clusters exhibited higher
angular spreads compared to the LOS cluster. The NLOS clusters in the NLOS envi-
ronment had higher angular spreads than the NLOS clusters in the LOS environment.
• Inter-cluster analysis showed that the cluster ToA, DoD and DoA are dependent. The
cluster DoD fits the Laplace distribution in the LOS environment and the Laplace
mixture distribution in the NLOS environment. The conditional DoA (DoA|DoD) can
be modeled using a Gaussian mixture distribution for both LOS and NLOS environ-
ments. The conditional ToA (ToA|DoD,DoA) fits a Uniform distribution (for backwall
reflections), deterministic (for single bounce scattering) and a random Exponential
distribution (for double bounce scattering).
140
• We also observed that the average number of clusters increased with distance. The
number of clusters in our measurement was modeled as a Poisson random variable.
From the results and statistics presented in this paper, it is clearly observable that the
propagation channel parameters of the warehouse environment are different from those of
other environments (indoor [163], industrial [79]) and a specific model, such as provided in
this paper, is needed for the system simulations in such an environment.
141
Chapter 6
Cluster Characterization of 3D
MIMO Propagation Channel in an
Urban Macrocellular Environment
6.1 Introduction
Increasing demand for higher data-rate services and the shortage of available spectrum
has resulted in the pursuit of new ways to improve wireless communications infrastructure.
To solve this challenge, a variety of techniques have been identified [180, 181], of which
Massive MIMO (Multiple-Input-Multiple-Output) is a prominent one. The use of Massive
MIMO [182], [183] in the form of Full-Dimensional MIMO (FD-MIMO) systems [184], [185],
[186] is pursued, inter alia, by the Third Generation Partnership Project (3GPP) [187].
These systems utilize a large number of antennas placed on 3D antenna array panels
1
for
realizing spatially distinct transmission links to a large number of mobile stations [182]. Due
to the 3D nature of these arrays, spatial separation of the links can be obtained in the
elevation domain as well as the azimuth domain. This leads to an increase in throughput
and system robustness; further advantages of FD-MIMO systems include simplified signal
processing and the reduction in energy consumption since the transmit energy can be focused
very precisely towards the intended receiver.
1
Most panel arrays, such as rectangular and cylindrical, are in fact 2D arrays, yet they are commonly
called 3D to indicate that the signal properties at their antenna elements are impacted by both elevation
and azimuth of the multipath components.
142
Figure 6.1: Map of measurement area in Cologne.
An essential step in the design of an FD-MIMO wireless system is the measurement
and modeling of the propagation channel in which this system is to operate. Hence, com-
prehensive and realistic characterization of multidimensional properties of the multipath
components (MPCs), in particular azimuth and elevation, is essential.
Massive MIMO systems will be deployed first in urban macrocells, since those require
the highest capacity. The current paper thus concentrates on this environment.
6.1.1 Related works
Several publications [188, 189, 190, 191, 192, 193, 194, 195, 196, 197] have investigated
the 3D characterization of urban macrocellular propagation channels. Some of these pub-
lications considered elevation parameters at one link-end only, i.e., either Multiple-Input-
Single-Output (MISO) [188], [191], [190] or Single-Input-Multiple-Output (SIMO) [192],
[194] setups. [193] conducted 3D MIMO measurements using a planar array at 2.6 GHz
and bandwidth of 65 MHz, however, the results presented were constrained to an angular
spread analysis at the Base Station (BS). Other publications [195], [196], [197] explored
143
3D Outdoor-to-Indoor (O2I) urban macro/microcellular environments, however, these were
done using ray-tracing simulations. Measurements were performed in an environment and
with a measurement setup similar to ours in [189], however this was done using a different
antenna array structure and not all parameters needed to fully characterize and develop a
double-directional polarimetric propagation channel model were provided. A 3D channel
model was developed in [198] using a geometry based stochastic model (GSCM) (following
the cluster-based approach common to COST 259, 273 and 2100 as well as SCM, WINNER
II models); however, the actual statistical values for channel parameters needed for a double-
directional model were not provided in the paper. Ref. [199] conducted 3D measurements in
an urban macrocell (with very large and regular high-rise buildings) environment, however,
this environment differs from ours which comprised of an irregularly built-up, Europe-style
old city. Also, the measurements were conducted on a dense grid in a wide street while our
measurements were conducted at isolated points, which are much more separated. Finally,
the sounder setup in [199] precluded 360 degree visibility of paths at the mobile station, as
is used in our paper. In our conference paper [200], we provided preliminary results for the
channel measurement campaign that underlies the current paper, in particular, path distri-
bution and MPC cluster parameters, however, we did not provide other channel parameters
(and their statistics) needed for modeling a 3D full-polarimetric urban macrocellular chan-
nel. For an overview of other related literature, we refer the interested reader to our recent
review [201] and [202].
6.1.2 Contribution
As seen from the literature review above, there is a dearth of investigations of 3D MIMO
propagationchannelmeasurementsandmodeling inurbanenvironments. Thecurrentpaper
aims to partly fill this gap. The contributions of this paper can be summarized as follows:
144
• We provide a detailed description of the measurement setup and procedure using an
advanced polarimetric wideband FD-MIMO channel sounder with massive number of
antenna elements.
• We extract MPCs through a high-resolution algorithm, group them into clusters and
derive both intra- and inter-cluster statistics.
• We provide a parameterization of the model for the Dense Multipath Components
(DMC) in the measured environment. Such an analysis of DMC in a 3D urban macro-
cellular environment has not been done before.
• We develop a double directional cluster-based channel model, which is validated by
comparing the resulting delay spread and direction spread to those obtained from the
raw data.
6.1.3 Organization
This paper is organized as follows. Section II describes the measurement environment
and the measurement setup. Section III describes the signal modeling procedure. Results for
the extracted MPCs are presented in Section IV. Section V describes the model validation
procedure. Summary and conclusions are provided in Section VI.
6.2 Measurement campaign
6.2.1 Measurement environment
We carried out the measurement campaign in Cologne (Germany). The structural layout
of the city has been discussed in [200], while Fig. 6.1 shows the map of the area covered
during our measurement campaign with the different receiver (RX) locations indicated as
well as BS position and its orientation. The transmitter (TX) was mounted on the rooftop
145
Figure 6.2: TX view of the urban macrocell in Cologne.
of a 30 m high-rise building just outside the old city center, see Fig. 6.2. The RX was
placed on the rooftop of a car at about 2.5 m height above ground. The measurements
were conducted at multiple RX positions in street canyons, alleys and open squares. The
measurements were done in the frequency band from 2.52-2.54 GHz, which the owner of the
band,DeutscheTelekom,madeavailableforourmeasurements. Thisalsoguaranteedabsence
of interference, and precisely limited the bandwidth we could use for the measurements.
6.2.2 Measurement setup
A key component of our measurement setup is the MEDAV RUSK sounder [203, 204]
– a wideband polarimetric MIMO channel sounder. This sounder is based on the switched
array principle: the transmit signal, which is a multi-carrier signal, is up-converted (via a
single RF chain) to passband and then is connected, via a fast electronic switch, to the
antenna elements of the transmit array one by one. Similarly, on the receive side, the
signals from the antenna elements are connected to the receive chain sequentially [205]. This
type of measurement provides a full channel characterization as long as all TX/RX antenna
combinations are measured within a time that is shorter than the coherence time of the
channel. Sounders based on this principle have been used extensively, e.g., [205], [203]. An
illustration of the sounder setup is shown in Fig. 6.3, while a system diagram is provided in
Fig. 6.5.
146
A cylindrical antenna array structure was used at both TX and RX. The TX array was
constructed from a synthetic aperture setup such that a switched 8-element (2 port per ele-
ment) polarimetric uniform linear patch array (PULPA, shown in Fig. 6.4(a)) was mechani-
cally rotated into different directions. To increase the gain of the PULPA in azimuth, a stack
of 4 horizontally placed antenna elements were connected by a pre-configured, controlled,
power divider (equal-split) array feeder network to form a narrow transmit beam in azimuth
(i.e., restricting azimuth opening angle). The PULPA was placed on a programmable posi-
tioner that was rotated in an azimuth angular range from−180
o
to 180
o
with a 6 degree
step-size to create 60 virtual positions, thereby imitating a cylindrical array structure. This
resulted in a virtual (16 x 60) TX antenna array (all ports considered). This TX structure
is referred to as vertical stacked polarimetric uniform circular patch array (VSPUCPA). The
antenna elements used in this setup have a 3 dB beamwidth of 100 degrees in elevation and
26 degrees in azimuth. Additional details on the TX array are provided in [200].
At the receiver, a purely switched approach (without positioner) was used: a stacked
polarimetricuniformcircularpatcharray(SPUCPA,showninFig. 6.4(b))with2(vertical)x
8 (circumference) x 2 (polarization) antenna ports was employed. The impact of the sounder
characteristics and the antenna arrays are measured and stored for post-processing (see
Sec. IV) during back-to-back calibration, and antenna calibration in an anechoic chamber,
respectively.
Rubidium (Rb) clocks are used at both TX and RX end for timing and frequency control
of the sounder. Also, the trigger signal between the TX and RX ends was sent over-the-air
using a cellular (Universal Mobile Telecommunications Service (UMTS)) connection.
Clock drifts of the local oscillators were observed in preliminary anechoic chamber mea-
surements. The clock drift can have a significant impact on the measurements results.
Details of the phase-drift correction techniques are given in [200], [206].
147
Figure 6.3: Illustration of channel measurement sounder.
(a) PULPA and reference antenna (b) RX-SPUCPA
Figure 6.4: TX antenna array (PULPA) and RX antenna array (SPUCPA)
Table 6.1: Channel sounder configuration.
Parameters Values
Bandwidth 2.52 GHz-2.54 GHz
No. of frequency points, M
f
257
Number of channels 900 x 32
Total time syn. aperture approx. 10mins
Tx ports, Rx ports 900 ports, 32 ports
Polarization H/V
Azimuth range [−180
◦
to 180
◦
]
Elevation range [90
◦
to−90
◦
]
6.3 Signal Model
This section presents the transfer function data structure, time domain representation
and parameter extraction procedure that form the basis of the post-processing of the data.
148
Figure 6.5: System diagram of the channel sounder setup and data processing.
6.3.1 Time-domain representation
Thetransferfunctionofthemeasuredpropagationchannelisa order-4tensorH(s,f,t,r)
fromwhichthespatio-temporalinformationoftheMIMOradiochannelcanbederived. Here
sdenotesthemeasuredsnapshotindex,f isthemeasuredfrequencyindexwithf = 1,...,M
f
,
where M
f
is the number of measured frequency points. t and r represent the TX and
RX antenna elements index respectively with t = 1,...,M
T
and r = 1,...,M
R
. M
T
, M
R
are the number of TX and RX elements. To improve the signal-to-noise ratio (SNR) of
the measurement, 10 snapshots were recorded for each TX/RX antenna pair and averaged
during post-processing. The channel impulse response h(s,τ,t,r), where τ indicates delay,
is obtained from the transfer function by inverse Fourier transform with Hanning window
to suppress aliasing. The local power-delay profile (PDP) is computed as PDP (s,τ,t,r) =
|h(s,τ,t,r)|
2
.
149
6.3.2 Parameter extraction
To obtain a channel characterization that is independent of the antenna structure, one
normally obtains a double-directional channel characterization that extracts the spatio-
temporal-polarimetric parameters of the MPCs from the transfer function through the use
of a high resolution parameter estimation (HRPE) algorithm. The HRPE algorithm that
was used in the work is RIMAX – an iterative maximum-likelihood estimator. An extensive
description of the parameter extraction procedure of RIMAX is provided in [157]. It differs
from other popular algorithms by modeling the propagation channel (h) as a superposition
of specular/deterministic paths (S(θ
sp
)), dense multipath components (DMC, D(θ
dmc
)) and
measurement noise (n):
h =S(θ
sp
) +D(θ
dmc
) +n ∈ C
M
T
M
R
M
f
× 1
, (6.1)
The DMC, which describes the stochastic part of the propagation channel, is assumed to
comprise of a large number of individually weak signal components that cannot be esti-
mated individually as plane waves, e.g., because of the underlying physical process (diffuse
scattering, wavefront curvature, etc.). Therefore, owing to the central limit theorem, D (to
simplify our notation, we will denote D(θ
dmc
) as D henceforth) is modeled as a zero-mean
complex circularly symmetric Gaussian distributed random vector with a covariance matrix
R
D
∈ C
M
T
M
R
M
f
×M
T
M
R
M
f
, i.e., D∼N
c
(0,R
D
). The measurement noise
2
is assumed to be
a white complex circularly symmetric Gaussian distributed random vector n∼N
c
(0,σ
2
N
I)
with variance σ
2
N
.
For simplicity, DMC and noise were modeled together to form a zero-mean complex
Gaussian process with covariance matrix:
R
dan
=R
D
+σ
2
n
I. (6.2)
2
The measurement noise results from both thermal noise from the electronics as well as ambient noise.
150
This implies that (6.1) can be written in a more compact form:
h =S(θ
sp
) +n
dan
∈ C
M
T
M
R
M
f
× 1
, (6.3)
where n
dan
∼N
c
(0,R
dan
).
In the estimator, specular components (S(θ
sp
)), or plane waves, are characterized by
the time-delay (τ), angle-of-arrival (azimuth (ϕ
R
) and elevation (ϑ
R
)), angle-of-departure
(azimuth (ϕ
T
) and elevation (ϑ
T
)) and the complex polarimetric path-weights (γ), i.e.,θ
sp
=
[ϕ
R
,ϑ
R
,ϕ
T
,ϑ
T
,γ,τ] such that
S(θ
sp
) =
L
X
l=1
B
T
R
(ϕ
R,l
,ϑ
R,l
)·




α
HH,l
α
HV,l
α
VH,l
α
VV,l




·B
T
(ϕ
T,l
,ϑ
T,l
)·e
−j2πf·τ
l
,
(6.4)
where the superscriptT denotes the transpose operator, B
R
and B
T
are the nonlinear map-
pings of the angles of arrival (ϕ
R
,ϑ
R
) and departure (ϕ
T
,ϑ
T
) to the antenna array responses
and are obtained from calibration measurements in an anechoic chamber. The parameters
α
HH,l
,α
HV,l
,α
VH,l
,α
VV,l
andτ
l
denote the radio wave polarization amplitudes (horizontal-to-
horizontal (HH), horizontal-to-vertical (HV), vertical-to-horizontal (VH), vertical-to-vertical
(VV)) and the time-delay of the l-th path respectively.
6.4 Results
We next discuss the path distribution in the environment, followed by a clustering anal-
ysis, and the intra- and inter-cluster statistics. Large scale parameters such as pathloss
and shadowing as well as the dense multipath components are also discussed in subsequent
subsections.
151
6.4.1 Path distribution in the environment
To provide insights into the propagation mechanisms in the environment, we first show
results from a sample NLOS location (position 47 indicated in Fig. 6.6). Fig. 6.6 shows
propagation paths and interacting objects (IOs) encountered along the paths by the MPCs;
in this and the subsequent plots not all extracted MPCs are shown to avoid congestion of
the figures. The arrows P1, P2 and P3 shown in Fig. 6.6 are in fact not representing a single
MPCbutgroupsofMPCs propagating alongtheseroutes. Asphericalcoordinatesystemhas
been used with orientation expressed such that the azimuth angle is defined clockwise from
−180
◦
to 0
◦
to 180
◦
(with 0
◦
indicating the PULPA orientation towards the LOS as shown
in Fig. 6.1), while the elevation angle is defined from 90
◦
to 0
◦
to−90
◦
, where 90
◦
indicates
the north pole, 0
◦
indicates the equatorial plane and−90
◦
indicates the south pole. Looking
at the direction-of-departure (DoD) azimuth - delay, DoD elevation - delay plots shown in
Figs. 6.7(a) and 6.7(b), it can be observed that MPCs having ϕ≈ 30
◦
, ϑ≈−6
◦
, and
τ≈ 245m/c
0
3
propagate via rooftop diffraction (Quasi-LOS, P2 on Fig. 6.7(a) and 6.7(b)),
while MPCs occurring in the range ϕ≈ 20
◦
− 26
◦
and ϑ≈−6
◦
were initially reflected off
the Galeria Kaufhof (P1, see Fig. 6.6, 6.7(a) and 6.7(b)) and then propagated through the
street canyon (SC 1 on Fig. 6.6) acting as a waveguide. MPCs with azimuth angles between
39
◦
− 40
◦
and elevation of about−5
◦
(P3, Fig. 6.6, 6.7(a) and 6.7(b)) are deemed to have
been reflected off the Inter-Continental building initially and then propagate through the
street canyon (SC 2, also in Fig. 6.6). Other observable MPCs with large delay (about 600
m) and elevation angle of about−1.5
◦
to−3
◦
are contributions from far-away scatterers.
A similar analysis was implemented on all other measurement points, and we determined
probable routes and IOs as well. This serves not only to gain insights into the propagation
mechanisms of MPCs in the urban macrocellular environment, but also to validate the high-
resolution parameter extraction procedure. Similar analyses were also performed in [190],
3
Note that c
0
≈ 3x 10
8
m/s denotes the speed of light in vacuum.
152
[191] and [207]. A detailed discussion of the propagation mechanisms of MPCs in this
environment is provided in [208].
As a further check for the validity of our high-resolution parameter extraction procedure,
we evaluated the relative residual power error (Δ
p
) between the power of the measured
transfer function and that of the reconstructed transfer function (obtained using RIMAX
results). The relative residual power error was calculated as: Δ
p
=
|P−
ˆ
P|
|P|
, where P denotes
the power of measured channel and
ˆ
P denotes the power
4
of the reconstructed channel (with
DMC power included). Δ
p
obtained in our analysis was 2.3%. Note that this is the power
not contained in either the discrete MPCs or the DMC, and thus different from the difference
between total power and specular MPC power that was used in other papers to assess the
importance of non-discrete MPCs.
Another observations is that the aforementioned MPCs naturally grouped into clusters.
This clustering phenomenon of MPCs is discussed subsequently.
Figure 6.6: Illustration of receiver position 47.
6.4.2 Clustering analysis
We define a cluster as a group of MPCs whose parameter values in all dimensions, i.e.,
delay, azimuth and elevation at TX and RX are very similar, while being notably different
4
Note that the power was averaged over all polarization.
153
(a) (b)
Figure 6.7: (a) DoD (az-delay) plot of extracted MPCs. (b) DoD (el-delay) plot of extracted
MPCs.
Figure 6.8: Clusters at RX position 47.
from those of other MPCs in at least one dimension. Clustering allows a more compact
channel description through the use of intra- and inter-cluster distributions, and thus has
been adopted in modern channel models such as COST 259 [209], [210], 3GPP SCM [187],
ITU-Winner [211], and COST 2100 [212].
In our work, we use the K-power means clustering algorithm [178], [213], [214], [215],
[216], along with visual inspection (as done in [217], [218], [219]) to obtain a reasonable
number of clusters. We then proceed to estimate cluster angular and delay statistics. Note
thattheclusterangularparametersincludeelevation-of-departure(EoD),elevation-of-arrival
(EoA), azimuth-of-departure (AoD) and azimuth-of-arrival (AoA).
154
Sample clustering results for RX position 47 are shown in Fig. 6.8. From this plot, it
is clearly observable that these clusters stem from the different IOs (shown in Fig. 6.6).
Similar clustering analyses were performed for all other measured locations. Statistics of
the aforementioned parameters inherent to the clusters can be used in our modeling process.
6.4.3 Clustering statistics
A statistical channel model is developed based on the results from the clustering analysis.
From [209], the generic form of the impulse response h
0
of the channel can be represented
as:
h
0
(τ, Ω
TX
, Ω
RX
) =
M
X
m=1
X
n∈Cm
h
0
n
(τ, Ω
TX
, Ω
RX
), (6.5)
where indices of the MPCs h
l
(τ, Ω
TX
, Ω
RX
), l = 1,...,L can be grouped into M≤L disjoint
clusters
C
1
,...,C
M
, (6.6)
with each cluster having N
m
≥ 1 elements, and
M
X
m=1
N
m
=L. (6.7)
Cluster-based channel models are characterized by two sets of parameters, namely intra-
and inter-cluster parameters. The inter-cluster parameters are cluster time-of-arrival (ToA,
T
m
), cluster DoD (Ω
TXm
), cluster direction-of-arrival (DoA) (Ω
RXm
), cluster power, and
number of clusters (M). The intra-cluster parameters include MPC ToA (τ
m,n
), MPC DoA
(ζ
m,n
), MPC DoD (ψ
m,n
), MPC complex amplitude (β
m,n
) and the number of MPCs (n) per
clusters. For ease of discussion and similarity to what is available in the literature, we will
henceforth refer to MPCs as rays.
Following the Saleh-Valenzuela model [220], the cluster and ray arrival time distributions
may be described by two Poisson processes, which implies that the cluster inter-arrival times
155
andrayintra-arrivaltimesaretypicallydescribedbytwoindependentexponentialprobability
density functions (PDFs) as follows:
p(T
m
|T
m−1
) = Λ·e
−Λ(Tm−T
m−1
)
, m> 0, (6.8)
p(τ
m,n
|τ
m,n−1
) =λ·e
−λ(τm,n−τ
m,n−1
)
, n> 0, (6.9)
where Λ is the mean cluster arrival rate and λ is the mean ray arrival rate.
Intra-cluster parameters
The intra-cluster parameter ToA of rays within each cluster is defined relative to the
smallest arrival time of all the rays within the cluster.
The cluster and ray power was modeled as
β
2
m,n
=β(0, 0)
2
·e
−
Tm
Γ
·e
−
τm,n
γ
·P
Ω
TXm
·P
Ω
RXm
, (6.10)
where Γ and γ are the cluster and ray decay constants, respectively, and β(0, 0)
2
is the
average power of the first ray in the first cluster [163]. P
Ω
TX
and P
Ω
RX
are intra-cluster
distribution in the angular domain (power angular spectra) and are modeled, both in the
azimuth and elevation domains, using the Laplacian distribution which is of the form:
P
Ω
(Ω) =
1
2σ
Ω
·e
−
|Ω−Ωn|
σ
Ω
. (6.11)
DoA/DoD are defined relative to the cluster center, which is computed as the power-
weighted mean of DoA/DoD of all rays within the cluster. The measured distributions of
the intra-cluster angular parameters at a sample location as well as their comparison to
the Laplacian fit is shown in Figs. 6.9(a) - 6.9(d). The distribution (using an ensemble of
all measured locations) of the spread of these angular parameters are modeled by lognormal
156
-60 -40 -20 0 20 40
Intra-cluster ray EoD
0
0.2
0.4
0.6
0.8
1
CDF
Laplacian Fit
Measured
(a) EoD.
-100 -50 0 50 100 150
Intra-cluster ray AoD
0
0.2
0.4
0.6
0.8
1
CDF
Laplacian Fit
Measured
(b) AoD.
-100 -50 0 50 100
Intra-cluster ray EoA
0
0.2
0.4
0.6
0.8
1
CDF
Laplacian Fit
Measured
(c) EoA.
-200 -100 0 100 200
Intra-cluster ray AoA
0
0.2
0.4
0.6
0.8
1
CDF
Laplacian Fit
Measured
(d) AoA.
Figure 6.9: Distribution of the intra-cluster angular (centered) parameters of rays for a
sample location.
distribution. The parameters of the lognormal distribution are shown in Table 6.4. Param-
eters λ, Λ, Γ and γ have been extracted as done in [163] and [12] with values also provided
in Table 6.4.
ThedelaybetweentheToAsofsucessiveraysismodeledusinganexponentialdistribution
as described in (6.9). The PDP of each cluster is a one-sided exponentially decaying function
as can be seen from (6.10). All cluster spreads (angular and delay) were found to be
lognormally distributed with the mean and variance provided in Table 6.4. Correlation
157
between cluster parameters
5
was explored in our work with correlation coefficient values
provided in Table 6.4. The ray arrival rate λ, and the inter-cluster parameters Γ and Λ are
modeled as constants. The number of rays per cluster were modeled with an exponential
distribution, where the average number of rays per cluster was approximately 16.
Inter-cluster parameters
In the inter-cluster case, we define the angular and delay parameters for each cluster
center relative to the geometric LOS connection (which is defined irrespective of whether
a LOS MPC exists or not). The ToA of this LOS connection is given by the Euclidean
distance between the TX and RX array at each measurement location, while the DoA and
DoD are determined by the orientation/alignment of the RX relative to LOS during the
channel measurement.
We found the relative cluster EoD and EoA to be Laplacian distributed, while the rel-
ative AoD follows a Gaussian distribution. Also, the relative AoA was found to follow a
uniform distribution in the range [−π,π). Figs. 6.10(a)-6.10(d) show the aforementioned
distribution fits while the parameters of these distributions are provided in Table 6.4. Note
that the selected distribution fits had the highest passing rates (at 5% signifcance level)
when compared to other candidate distributions in a Kolmogorov-Smirnov (K-S) hypothesis
test [221]. The K-S procedure is a standard nonparametric hypothesis test of the equality
of continuous, one dimensional probability distributions. It is based on the maximum dif-
ference between an empirical and a hypothetical cumulative distribution. The inter-cluster
parameters were found to be uncorrelated, which is understandable due to the NLOS nature
of the environment and the cluster-based modeling procedure. However, cluster parameters
might in fact be correlated when using a class-based modeling (i.e., grouping clusters into
classes) as in [208].
5
We used the logarithmic values of the parameters.
158
-20 -10 0 10
Relative EoD
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Laplacian Fit
Measured
(a) EoD.
-60 -40 -20 0 20 40 60 80
Relative AoD
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF

Measured
Gaussian Fit
(b) AoD.
-50 0 50
Relative EoA
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Laplacian Fit
Measured
(c) EoA.
-200 -100 0 100 200
Relative AoA
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Measured
Uniform Fit
(d) AoA.
Figure 6.10: Distribution of the inter-cluster angular parameters.
The cumulative distribution function (CDF) of the number of clusters from all measured
locations in the urban environment is shown in Fig. 6.11. Although some works have
reported smaller values in urban environments [210], others such as [190] show quite similar
results. The number of clusters N
k
can be modeled (similarly to the COST 259 model) as
N
k
= N
c
min
+X, where N
c
min
= 1 is the minimum number of clusters, while X is a Poisson
distributed random variable with an average rate (η
c
) of 2.18.
The cluster shadowing gain (SF) is defined as the deviation of the cluster power from its
expected value [222], which in turn can be derived from the estimation of the cluster power
decay constant (Γ, see (6.10)). In other words, when the cluster power decay constant is
159
1 2 3 4 5 6 7 8
Number of clusters
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Empirical
Poisson Fit
Figure 6.11: Distribution of the number of clusters.
estimated, the linear regression fit provides an expected cluster power for a certain relative
clusterdelay. Theclustershadowinginouranalysisis modeledtobelognormallydistributed,
i.e., its logarithmic value is approximated by a zero-mean Gaussian distribution (as shown in
Fig. 6.12) with standard deviation (σ
cl
) of 7.47 dB. We can see that the fit is somewhat loose;
however, since lognormal distribution of shadowing gains is widely used in the literature, we
adhere to this convention.
The lognormal distribution was confirmed by matching the empirical data to some typical
theoretical distribution such as lognormal, Nakagami, Rayleigh, Ricean, and Weibull. The
K-S hypothesis test was used to determine the goodness-of-fit (GOF) of these distribution
at 5% significance level. Results of the K-S test are shown in Table 6.2 below, it can be
seen that the lognormal distribution gives the highest passing rate.
-20 -10 0 10 20 30
Cluster shadowing (dB)
0
0.02
0.04
0.06
0.08
0.1
0.12
PDF
Measured
Gaussian fit
Figure 6.12: PDF of cluster shadowing gain.
160
Table 6.2: Passing rate of K-S test at 5% significance level.
.
Distribution K-S
Weibull 81.57
Rayleigh 65.87
Rician 65.87
Lognormal 92.36
Nakagami 66.36
6.4.4 Cluster polarization
A complete channel model requires the description of the polarization [223], [224] and
[225]. The cluster polarization can be described by a two-by-two polarimetric matrix A
pol
,
A
pol
[dB] =




CPR
HH
XPR
HV
XPR
VH
CPR
VV




, (6.12)
where the co- and cross-polarization ratios are represented as CPR and XPR while V and H
denote vertical and horizontal polarization respectively. The off-diagonal element, XPR
HV
(see (6.13)) describes the (total power) crosstalk from horizontal to vertical polarization of
MPCs within a cluster (and similarly for XPR
VH
(see (6.14))).
XPR
m
HV
(dB) = 10·log
10

P
Nm
n=1
|α
HH,m,n
|
2
P
Nm
n=1
|α
HV,m,n
|
2
!
(6.13)
XPR
m
VH
(dB) = 10·log
10

P
Nm
n=1
|α
VV,m,n
|
2
P
Nm
n=1
|α
VH,m,n
|
2
!
(6.14)
On-diagonal elements CPR
HH
and CPR
VV
represent the ratio of the co-polarized compo-
nent compared to the total power. From our analysis, XPR in dB is approximately Gaussian
distributed with a 6 dB average and a standard deviation of 1.5 dB. The occurrence of this
distribution for XPR had been reported in the literature [210], [226] and [227] for different
environments and is confirmed by Figs. 6.13(a) and 6.13(b). Parametric values for this
161
-5 0 5 10 15
XPR
HV
(dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Measured
Gaussian fit
(a) CDF of XPR
HV
.
-5 0 5 10 15 20
XPR
VH
(dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Measured
Gaussian fit
(b) CDF of XPR
VH
.
Figure 6.13: Distribution of the XPR.
distribution are provided in Table 6.4 below. Note that depending on the propagation con-
ditions, XPR
HV
can be different from XPR
VH
. Also, within each cluster, the XPR of rays
(
¯
XPR) can also be modeled as a Gaussian distributed variable with mean value as the cluster
XPR while the standard deviation values are 4.19 for
¯
XPR
HV
and 4.52 for
¯
XPR
VH
.
23 24 25 26 27 28 29
10Log
10
(distance (m))
105
110
115
120
125
130
135
Pathloss (dB)
Measured
Linear fit
Figure 6.14: Linear regression fit for pathloss and delay.
6.4.5 Pathloss and shadowing model
Pathloss model
Following the literature, we use a conventional power law equation [83], [62] to model the
distance-dependent pathloss P
L
in dB (also known as α−β model [228]):
P
L
(d) =P
0
+ 10·ξ·log
10

d
d
0
!
+χ
σ
, (6.15)
162
where d
0
is the reference distance namely 1 m, P
0
is the (fitted) pathloss at the reference
distance, ξ is the pathloss exponent and χ
σ
is a random variable describing large-scale
variations (in dB) due to shadowing; adhering to the literature [71] and [72], we model
the shadowing by a lognormal (i.e., Gaussian on a dB scale) distribution. Fig. 6.14 shows
the scatter plot of P
L
for all measurements conducted at different distances and a linear
regression fit. All parameters extracted are provided in Table 6.4. Of course, the fit is
only valid for the distance range of 200-728 m, namely the distances for which underlying
measurements exist.
Shadowing
Thebulk
6
shadowinggain(denotedasχ
σ
in(6.15))accountsforthelarge-scalefluctuation
of the received power. We see that, in agreement with the modeling assumption in (6.15),
the logarithmic value of the measured deviation closely matches a zero-mean Gaussian
distribution (N(0,σ
χ
[dB])) (see Fig. 6.15 and Table 6.4).
-20 -10 0 10 20
shadowing gain (χ
σ
)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Gaussian fit
Figure 6.15: CDF of the bulk shadowing gain.
The lognormal distribution was confirmed here as well by using a K-S hypothesis test to
determine the GOF of different candidate distributions at 5% significance level, see Table
6.3.
6
The term bulk denotes that we are analyzing the shadowing using the entire channel response.
163
Table 6.3: Passing rate of K-S test at 5% significance level.
Distribution K-S
Weibull 69.48
Rayleigh 15.39
Rician 15.38
Lognormal 95.41
Nakagami 22.68
Time delay τ (s)
Az_Tx (deg)

0 2 4 6
x 10
−6
−150
−100
−50
0
50
100
150
(a) Measured total.
Time delay τ (s)
Az_Tx (deg)

0 2 4 6
x 10
−6
−150
−100
−50
0
50
100
150
−130
−120
−110
−100
−90
(b) Residual.
Time delay τ (s)
Az_Tx (deg)

0 2 4 6
x 10
−6
−150
−100
−50
0
50
100
150
−130
−120
−110
−100
−90
(c) Modeled residual.
Figure 6.16: Comparison of (a) measured (h) (b) residual ( h− (S(θ
sp
))) and (c) modeled
DMC Power-azimuth-delay-profile (PADP) at Tx end for Rx Position 47.
6.4.6 Dense multipath component (DMC)
The DMC consists mainly of a large amount of weak MPCs originating from, e.g.,
scatteringfromobjectsthatareeithersmallinsizecomparedtothewavelengthorhaverough
surfaces [229], [230]. It is usually described as the residual after the specular component in
the channel response has been extracted.
Although more sophisticated techniques have been introduced in [231] and [232] to
advance the modeling of DMC, in our work we adhere to the DMC model as discussed
in [157], [233], [234]. The analysis in this work is done over an aggregate of the different
polarization components.
The DMC is described by its covariance matrix R
D
(see (6.2)) and can be decomposed
into the Kronecker-product of three matrices:
R
D
=R
R
⊗R
T
⊗R
F
, (6.16)
164
where R
F
is the covariance matrix in the frequency domain while R
R
and R
T
are the
covariance matrices of the antenna array elements at the TX and RX.
The frequency domain covariance matrices can be modeled by:
R
F
= toep(
¯
λ(θ
F
),
¯
λ(θ
F
)
†
), (6.17)
where the operator toep(·) denotes a Toeplitz matrix [235], [236] and
¯
λ is a sampled version
of the power spectral density, given by
¯
λ(θ
F
) =
˜ α
1
M
f


1
˜
β
d
,
e
−j2πτ
d
˜
β
d
+j2π
1
M
f
,··· ,
e
−j2π(M
f
−1)τ
d
˜
β
d
+j2π
M
f
−1
M
f


T
. (6.18)
The parameters of the frequency domain covariance matrix model are
θ
F
= [τ
d
,
˜
β
d
, ˜ α
1
]
T
, (6.19)
whereβ
d
is the normalized
7
coherence bandwidth of the channel, τ
d
and ˜ α
1
are the delay of
arrival and power of the first component in the time domain
8
equivalent of (6.17).
The spatial covariance matrices (R
T
and R
R
) can be modeled as:
R
R/T
=B
R/T
·K(θ
R/T
)·B
†
R/T
, (6.20)
whereB
R/T
denotes the antenna array responses at RX and TX, while K(θ
R/T
) is a diagonal
matrix whose entries are determined by the angular probability density distribution of the
7
Note that the normalization is done with the measurement bandwidth.
8
This is obtained by using an inverse Fourier transform.
165
DMC, which is modeled as a Von-Mises distribution (VMD) [233]. Superscript† denotes
Hermitian transpose. The PDF for the one-dimensional case is defined as:
f
ϕ
(ϕ,μ,κ) =
1
2π·I
0
(κ)
·e
κ·cos(ϕ−μ)
(6.21)
where μ is the mean angle, κ the concentration parameter, and I
0
the modified Bessel
function of the first kind of the order zero. A beamformer approach is discussed in [233]
where an additional uniform distribution (UD) with magnitude ¯ α is introduced such that
(6.21) is modified to:
f
ϕ,UD
(ϕ,μ,κ, ¯ α) =e
κ·cos(ϕ−μ)
·e
−κ

ˆ
A− ¯ α

+ ¯ α, (6.22)
where
ˆ
A is the maximum value of the beamformer output. In our work we assume that the
joint elevation-azimuth distribution can be factored into terms for elevation and azimuth
that each follow (6.21), i.e.,
f
ϕ,ϑ,UD
(ϕ,ϑ,μ
ϕ
,μ
ϑ
,κ
ϕ
,κ
ϑ
, ¯ α
ϕ
, ¯ α
ϑ
) =f
ϕ,UD
(ϕ,μ
ϕ
,κ
ϕ
, ¯ α
ϕ
)·
f
ϑ,UD
(ϑ,μ
ϑ
,κ
ϑ
, ¯ α
ϑ
)
(6.23)
Parameters of K(θ
T/R
) in the spatial domain are given by θ
T
=
[μ
ϕ,T
,μ
ϑ,T
,κ
ϕ,T
,κ
ϑ,T
, ¯ α
ϕ,T
, ¯ α
ϑ,T
] and θ
R
= [μ
ϕ,R
,μ
ϑ,R
,κ
ϕ,R
,κ
ϑ,R
, ¯ α
ϕ,R
, ¯ α
ϑ,R
].
Additional discussion on spatial modeling with the Von-Mises distribution is provided in
[231], [233], [237].
We extracted DMC spatial-temporal parameters at all measured locations. Statistical
distribution fits and corresponding moments for the extracted parameters are provided in
Table6.4whilesampleplotsoftheCDFforparameterssuchas ˜ α
1
andκ
ϕ,T
(bothlognormally
distributed) confirm a good fit of their logarithmic value to the Gaussian distribution as
shown in Figs. 6.18(a) and 6.18(b). To further validate the modeling of the DMC, we
166
synthesized the DMC by using (6.16) - (6.23). We then generated (i) the power-azimuth-
delay-profile (PADP) of the measurement data, which includes both specular and DMC
components, (ii) extracted residual components only (from the measurement data) and (ii)
the modeled residual at the TX end when taking position 47 as the measurement location.
The plots for the PADP are shown in Figs. 6.16(a) to 6.16(c). It can be clearly observed from
the aforementioned figures that the modeled residual does fit well to the residual obtained
from the actual measurement data.
The amount of power that the DMC (ˆ η
dmc
) contributes to the total channel power is
calculated from the R
D
as:
ˆ η
dmc
= Tr{R
D
}, (6.24)
where Tr{·} is the Trace of a matrix. The fractional DMC power
ˆ
f
dmc
, i.e., the percentage
the DMC contributes to the total channel power (P
Tot
) is derived as
ˆ
f
dmc
=
ˆ η
dmc
P
Tot
· 100%. (6.25)
0 10 20 30 40
ˆ
f
dmc
(%)
0
0.2
0.4
0.6
0.8
1
CDF
Figure 6.17: Empirical CDF of the fraction of power contained in the DMC.
The corresponding CDF of
ˆ
f
dmc
is provided below in Fig. 6.17. It can be observed that
the average value of
ˆ
f
dmc
is not too large meaning that the contribution of the DMC is rather
moderate in this scenario. Similar effects have also been observed in [233].
167
-160 -140 -120 -100 -80
˜ α
1
(dB)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Gaussian fit
(a)
5 10 15 20 25
κ
ϕ,T
(dB)
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Gaussian fit
(b)
Figure 6.18: Empirical CDF of DMC (a) delay parameter ˜ α
1
(dB) (b) spatial parameterκ
ϕ,T
(dB) with corresponding Gaussian fit.
6.5 Model validation
Verificationoftheresultsproceedsintwosteps. Inafirststep, weverifythemeasurement
setup; thishasbeendonein[203]andfurtherconfirmedbycomparisonoftheextractedMPCs
(and the resulting interactions with the IOs) with a geographical map of the environment
as described in Sec. IV-A. In a second step, we verify that the model derived in Sec. IV
reproduces channel characteristics in agreement with the underlying raw measurement data.
For this purpose, we use the rms delay and the directional spreads as validation metrics
by comparing results obtained from the overall channel model simulation to those obtained
directly from the measurement data.
We finally note that these steps are not a proof that the model holds for any arbitrary
urban environment, but rather that the model correctly reproduces the measurements in our
specific measured environment. A comparison of the results
9
obtained in our campaign with
those of measurements in different environments is given in Table 6.5.
Generally (from Table 6.5), we find that the qualitative behavior of "standard" channel
parameters (angular spreads, τ
rms
, pathloss coefficient and shadowing gain) extracted in
this paper is comparable to the measurements enumerated in Table 6.5 as well as to urban
9
To ease the comparison of our results with those in other papers, the angular spreads in Table 6.5 have
been computed using eq. (6.58) in [83] instead of the Fleury definition [238].
168
macrocellular models exisiting in the literature, such as the COST models [210], [239]. It is
important to note that the aggregate channel parameters from our work have been used for
comparison in Table 6.5 and not the cluster-based results as this affords us the opportunity
to compare with existing models since there is a dearth in cluster-based models. Disparity
between some parameters could stem from the difference in the environment as well as
differences in measurement setup, parameter extraction algorithms, etc.
6.5.1 RMS delay spread
The CDF plots of τ
rms
obtained from raw data and model results are provided in Fig.
6.19. It is clearly observable that the CDF of the τ
rms
values derived from the simulation
provides a close fit to that derived from the actual measurement data.
0 0.5 1 1.5 2 2.5
τ
rms
(s)
×10
-7
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Simulated
Figure 6.19: Empirical CDF of rms-delay spread computed from measurement and corre-
sponding simulated rms-delay spread obtained from the channel model.
6.5.2 Directional spread
The directional spread is used to compare the statistical angular properties of the channel
model to that of the measurement data. Figs. 6.20(a) and 6.20(b) compares DoD direction
spread in elevation (σ
el
) and azimuth (σ
az
) according to the definition of Fleury [238]. Again
169
simulated channel model results agree quite well with the measurement results, which implies
that our channel model is indeed appropriate to reproduce the measured data.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
σ
el
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Simulated
(a)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
σ
az
0
0.2
0.4
0.6
0.8
1
CDF
Measured
Simulated
(b)
Figure 6.20: Empirical CDF of the (a) DoD σ
el
(b) DoD σ
az
computed from measurement
data and corresponding simulation values obtained from the model.
In Table 6.4, it is important to note that the mean and std. of the rel. EoD are define
relative to the geometry of the LOS while the logarithmic values of the angular spreads
(ESD, ASD, ESA, ASA) and delay spread (τ
rms
) are computed as log
10
(·) (dB). Also, the rel.
μ
ϕ,T
(
◦
),μ
ϑ,T
(
◦
),μ
ϕ,R
(
◦
) andμ
ϑ,R
(
◦
) correspond to the relative (with respect to the geometric
LOS) values.
6.6 Summary and Conclusion
We conducted a 3D propagation channel measurement campaign in an urban macro-
cellular NLOS environment using an advanced MIMO antenna array setup. We extracted
parameters using RIMAX – a high-resolution parameter extraction algorithm. Our main
findings can be summarized as follows:
• The MPCs can be explained by physical propagation routes in the environment.
• MPCs are naturally grouped together into clusters in the propagation environment. A
detailed clustering analysis of the propagation channel was provided.
170
• In line with findings in previous papers, the intra-cluster DoD/DoA follows a Lapla-
cian distribution with the angular and delay spread parameters being lognormally
distributed and the inter-cluster parameters such as EoD and EoA follow Laplacian
distribution while AoD and AoA were Gaussian and uniformly distributed respectively.
The cluster relative delay is exponentially distributed.
• For the cluster polarization, the cross-polarization ratios (XPR) in dB are Gaussian
distributed with mean about 6 dB. The co-polarized values are equal. The XPR of
rays in dB are modeled as Gaussian distributed random variable with mean as the
cluster XPR value while standard deviation values are 4.2 (XPR
HV
) and 4.5 dB for
XPR
VH
.
• The pathloss can be modeled as a single-slope power law with pathloss exponent (ξ) 3.8
while the bulk shadowing is zero-mean lognormal distributed with standard deviation
of about 5.5 dB for the measured distance range of 200-730 m.
• We provide temporal and spatial parameters for the covariance matrices of the DMC
and their statistical distributions. The fractional power of the DMC is about 15% on
average. This implies that the DMC does contribute a moderate percentage of power
to the propagation channel being studied.
• By using two metrics, rms delay spread and directional spreads, we validated that the
model can provide a close fit in the CDF plot between the actual data measurement
results and that of the synthetic data generated using our developed channel model.
Theextractedparameters are(asfarascomparabledataexist)inreasonableagreement
with the existing literature. For parameters that were measured for the first time in
this paper, future measurements will be required to assess their sensitivity to the
environment.
Although a single 3D measurement campaign like this cannot provide a complete char-
acterization of the whole "urban macrocellular" environment, we however believe that these
171
results are useful for understanding and simulating 3D urban macrocellular propagation
channels. We also note that preliminary results from our measurements were used as an
input to the 3GPP standardization of 3D channel models [187].
172
Table 6.4: Extracted parameters.
Parameter Notation Values
Pathloss coefficient ξ 3.80
Pathloss at 1m (reference distance) P
0
(dB) 23.89
Bulk shadowing std. σ (dB) 5.50
Intra-cluster parameters
Parameters EoD AoD EoA AoA
Distribution Laplacian Laplacian Laplacian Laplacian
cluster angular spread ESD ASD ESA ASA
Distribution Lognormal Lognormal Lognormal Lognormal
mean (dB
◦
) 0.20 1.09 0.97 1.38
std. (dB
◦
) 0.05 0.23 0.24 0.25
Parameter γ
Distribution Lognormal
mean (dBns) 1.25
std. (dBns) 0.30
ray arrival rate (λ) (1/ns) 0.44
Distribution of the No. of rays per cluster Exponential
Average number of rays per cluster 16.0
Parameter cluster shadowing gain (SF)
Distribution Lognormal
mean (dB) 0.00
std. (dB) 7.47
Inter-cluster parameters
Parameter rel. AoD rel. EoD rel. EoA rel. AoA
Distribution Gaussian Laplacian Laplacian Uniform
Distribution Parameter
mean, std. mean, std. mean, std. min, max
6.5
◦
, 14.4
◦
1.0
◦
, 1.9
◦
5.1
◦
, 12.7
◦
-180.0
◦
, 180.0
◦
Distribution of the No. of cluster Poisson
Average number of clusters (
¯
N
k
) 3.18
cluster arrival rate (Λ) (1/ns) 0.015
cluster decay cnst. (Γ ) (ns) 71.23
cluster polarization
Pol. Parameters XPR
HV
XPR
VH
Distribution Gaussian Gaussian
mean (dB) 6.20 6.10
std. (dB) 1.59 1.26
ray polarization
Pol. Parameters XPR
HV
XPR
VH
Distribution Gaussian Gaussian
mean (dB) N(6.20, 1.59) N(6.10, 1.26)
std. (dB) 4.19 4.52
Cross-correlation
intra-cluster parameter 1 intra-cluster parameter 2 Coefficient
ESD ASD 0.51
ESA ASA 0.48
ESD ESA 0.13
ESD ASA 0.06
ESA ASD 0.01
ASD ASA -0.05
ESD SF -0.30
ASD SF -0.33
ESA SF -0.33
ASA SF -0.22
τrms SF 0.03
τrms ESD 0.25
τrms ESA -0.01
τrms ASD -0.01
τrms ASA -0.08
inter-cluster parameter 1 inter-cluster parameter 2 Coefficient
rel. AoD rel. EoD -0.12
rel. AoD rel. EoA -0.04
rel. AoD rel. AoA 0.01
rel. EoD rel. EoA 0.10
rel. EoD rel. AoA -0.11
rel. EoA rel. AoA -0.13
ToA rel. EoD 0.14
ToA rel. AoD -0.10
ToA rel. EoA -0.12
ToA rel. AoA 0.05
DMC parameters
Parameter mean std. distribution
˜ α
1
(dB) -117.12 9.09 Gaussian
˜
β
d
0.15 0.05 Gaussian
τ
d
(dBns) 1.40 0.60 Lognormal
rel. μ
ϕ,T
(
◦
) 13.5 9.2 Gaussian
κ
ϕ,T
(dB) 15.47 2.76 Lognormal
¯ α
ϕ,T
0.93 0.02 Gaussian
rel. μ
ϑ,T
(
◦
) 5.1 5.3 Gaussian
κ
ϑ,T
(dB) 17.15 6.21 Lognormal
¯ α
ϑ,T
0.94 0.02 Gaussian
rel. μ
ϕ,R
(
◦
) 26.8 23.1 Gaussian
κ
ϕ,R
(dB) 9.41 3.72 Lognormal
¯ α
ϕ,R
141.60 0.92 Gaussian
rel. μ
ϑ,R
(
◦
) 14.4 6.6 Gaussian
κ
ϑ,R
(dB) 13.98 4.16 Lognormal
¯ α
ϑ,R
141.63 0.55 Gaussian
173
Table 6.5: Comparing extracted channel parameters from different papers.
Papers Values ESD
log
10
([
◦
])
ASD
log
10
([
◦
])
ESA
log
10
([
◦
])
ASA
log
10
([
◦
])
τrms
log
10
([s])
ξ χσ
(dB)
measurement environment, setup, and
type of parameters
This paper
mean (dB) 0.52 1.09 1.29 1.83 -6.97
3.80 5.50
1) NLOS urban macrocellular European old-
town (mid-rise buildings), Cologne, Germany
2) 3D MIMO with 900 element TX array (cylin-
drical - with synthetic aperture configuration)
by 32 element RX array (cylindrical) using an
RF switch 3) Center frequency: 2.35 GHz,
bandwidth: 20 MHz 4) High-resolution param-
eter extraction (RIMAX) 4) Cluster-based mod-
eling, 5) Provides all parameters for 3D mod-
eling including DMC.
std. (dB) 0.15 0.23 0.13 0.25 0.36
Ref. [240] mean (dB) 0.83 1.05 1.26 1.87 -6.51
N/A N/A
1) LOS and NLOS urban macrocellular and
microcelluar environment with modern high-
rise buildings, Xian, China. Only results for
NLOS shown here 2) 3D MIMO with 32 ele-
ment TX array (dual polarized 8× 8 planar)
elements by 50 element RX array (arbitrary
– crown-shaped) using an RF switch 3) Cen-
ter frequency: 2.6 GHz, bandwidth: 35 MHz
4) High-resolution parameter extraction algo-
rithm (SAGE) 4) Models – angular and delay
statistics of rays, but not pathloss, shadowing,
polarization and DMC. Model is not cluster-
based.
std. (dB) 0.04 0.10 0.16 0.11 0.23
Ref. [189] mean (dB) 0.77 1.09 1.17 1.84 -6.44
N/A N/A
1) NLOS urban macrocellular European old-
town (mid-rise buildings), Cologne, Germany
2) 3D MIMO with 32 element TX array (cylin-
drical) by 32 element RX array (cylindrical)
using an RF switch 3) Center frequency: 2.35
GHz, bandwidth: 20 MHz 4) High-resolution
parameter extraction (RIMAX) 5) Models –
angular and delay spread statistics of rays,
but not pathloss, shadowing, polarization and
DMC. Model is not cluster-based.
std. (dB) 0.27 0.25 0.19 0.15 0.31
Ref. [194] mean (dB)
N/A N/A
1.09 1.85 -6.49
N/A N/A
1) Mostly NLOS urban macrocellular European
oldtown(mid-risebuildings), Mulhouse, France
2) 3D SIMO with a single element TX antenna
by 441 element RX array ( 21× 21 virtual uni-
formplanarconfiguration)3)Centerfrequency:
2.2 GHz, bandwidth: 62.5 MHz 4) Beamform-
ing parameter extraction algorithm 5) Models
– angular spread (at RX), delay spread and
polarization of rays, but not angular charac-
teristics at TX, pathloss, shadowing and DMC.
Model is not cluster-based.
std. (dB) only a single sample result was provided
Ref. [241] mean (dB) N/A 0.33 1.31 1.60 -7.15
N/A 8.30
1) LOS and NLOS urban macrocellular Euro-
pean oldtown (mid-rise buildings), Ilmenau,
Germany. Only results for NLOS shown here
2) 3D MIMO with 16 element TX array (uni-
form linear configuration) by 48 element RX
array (cylindrical ) + MIMO-Cube using an RF
switch 3) Center frequency: 2.53 GHz, band-
width: 2× 45 MHz 4) High-resolution param-
eter extraction (RIMAX) 5) Describes angular
spread (at the RX), delay spread, pathloss and
shadowing, but not elevation spread at TX,
polarization and DMC. Model is not cluster-
based.
std. (dB) 0.35 0.16 0.21 0.18
Note that the parameter values from Ref. [194] are from a single sample value (not over an ensemble). Also, the results are from the VV-polarization
measurements.
174
Chapter 7
Conclusion
In previous years, the concept of wireless system was limited to cellular communication
and local area networks. The acceptance and adoption and pervasiveness of wireless smart
devices in later years astounds and has been, in and of itself transformational. However,
the next generation (5G and beyond) aims to go further by embracing the higher data rate
and ubiquitous connectivity being proposed for many devices in form of Internet-of-things
(IoT), multidimensional high resolution video (3D Video, UHD Screens), augmented reality,
mission critical applications, self driving cars, industry automation and ofcourse high data
rate (Gbps) cellular communications. The development and simulating the performance of
these devices will require scenario-specific channel models since previous generation channel
models cannot be used for a next-generation model.
The intention of the work done in this thesis is to partly remedy this by providing
channel models catering to specific scenarios towards next-generation applications. These
channel models are multidimensional so as to include all possible parameters that could
lead into significant performance gain. For example, in massive MIMO cellular networks,
the introduction of elevation parameter at the Base-station (BS), which had otherwise not
be done in previous generation (3G & 4G) systems affords the opportunity to improve
spatial diversity gains, whereby beamforming is not only limited to users based on their
azimuth angle of departure but elevation can now be considered as well. The implication
of this being that users on different floors (elevation) and street level (azimuth) can now
be served individually as against the prior approach of just illuminating (i.e., transmission
the direction) the entire building and jointly serving all users all multiple floors in the most
wasteful/sub-optimal way.
175
The main achievement of this thesis are the following. Firstly, the impact of body
mass index on propagation channel parameters of wireless Body area network, Personal
area network and Body-to-Body networks was studied. Then a comprehensive channel
model, which factors in the dependencies exhibited by these channel parameters was cre-
ated. Thisisparticularlyusefulindevelopmentofwirelesshealthcareapplications. Secondly,
UWB MIMO propagation channel models have been provided for localization and ranging in
both warehouse and near-ground outdoor environments. Thirdly, a cluster-based 3D urban
macro/microcellularchannelmodelhasbeenprovidedinthisthesis. Thisisparticularuseful
for massive MIMO implementations in 5G cellular networks. Finally, a detailed description
of the channel measurement setup and results of the antenna array calibration to be used
for channel measurements in the public safety frequency bands has been provided.
All the proposed channel models were validated by considering different measures such
as parameter agreement between measurement data and synthetically generated data from
the channel model.
In the future, a novel modeling concept which uses a class-based approach as opposed to
the cluster-based approach to channel modeling done in this thesis will be explored. The idea
behind this is that MPCs in a clusters seem to have the same mode of propagation, i.e., they
either propagation through street canyons or above roof-tops of building or as a consequence
of far-scatterers (high-rises or mountains), clusters could also be grouped into their mode of
propagation thus simplifying the channel modeling procedure. A concept of "twin clusters"
(i.e., clusters as seen from the Base station will be paired with another virtual cluster as seen
from the mobile station) will also be introduced. Also, device-to-device channel modeling in
the public safety frequency band will also be considered.
176
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Abstract (if available)

Abstract Propagation channel measurement and modeling are essential for design, simulation and deployment of wireless systems for communication, localization and ranging. These channel models typically provide a closed-form description for complicated electromagnetic transmission process of reflection, scattering, diffraction and shadowing. Most channel models are empirically parameterized while the statistics of these parameters can be inferred as well. Since wireless systems are deployed in several scenarios and environments, designers of wireless systems/networks are typically interested in scenario-specific models, which allows the optimization of their system for that particular scenario or environment. These scenarios range from indoor to outdoor, human body and or even some with geographical variations at times. ❧ With the growing demand for higher data rate, improved precision in localization systems and reliable communication infrastructure in different applications, more advanced wireless architectures will be needed in the nearest future. The development of any such future wireless system will require new propagation channel models to either complement existing ones or as new stand-alone models. ❧ This thesis deals with measurement-based modeling of wireless propagation channels. Since channel measurement and modeling is a very broad field (albeit one in which few institutions or companies are working), I have concentrated on the following three areas: ❧ • Channels for “wireless healthcare” applications. It is expected that the human body tissues will have a significant effect on electromagnetic wave propagation around the human body especially when various body types with different dimensions and tissue properties are considered. Therefore, the impact of Body Mass Index (BMI) on ultrawideband multi-antenna Body Area Network (BAN), Personal Area Network (PAN) and Body-to-Body (B2B) network propagation channels was investigated in this thesis. A large number of human test subjects that is statistically sufficient for creating a comprehensive channel model, which had otherwise not been done in prior research in the literature were considered. The test subjects were divided into categories based on their BMI values. A comparison of statistics among the BMI categories reveals considerable differences emphasizing the fact that the classic propagation channel parameters are in fact BMI dependent. Parameters such as path gain showed a monotonic decrease across the BMI categories with values ranging from 1-2 dB to almost 13 dB in some channels. In this thesis, I have propose a propagation channel model for the BMI dependent parameters and validated that this model can reproduce the measured channel capacities. ❧ • Ultrawideband (UWB) and/or multiple-input-multiple output (MIMO) channels in the context of localization and ranging systems. A statistical channel model of UWB and/or MIMO in the context of localization and ranging systems is provided in this thesis by studying electromagnetic wave propagation when transceivers are i) near-ground i.e., in close proximity to the ground and ii) in a warehouse environment. ❧ – In the near-ground case, transceiver heights were varied from 200 cm to 10 cm with measurement conducted over distances ranging 10 m to 200 m. Distance- and frequency-dependent pathloss component and shadowing gain were found to increase with increasing antenna proximity to the ground with values ranging from 2.14 to 3.60 in distance-dependent pathloss component, 0.98 to 1.24 in the frequency-dependent pathloss exponent while shadowing gain varied 2.8 to 8.52 dB. Also, a 1 ns ranging accuracy was achieved from the measurement setup used for this work. ❧ – A UWB MIMO double-directional channel model was developed for the warehouse environment. The model is especially important for Radio Frequency Identification (RFID) tag localization in the warehouse environment. Multipath components were found to naturally grouped into clusters in the warehouse environment and as such the statistics of the cluster parameters observed has been provided. The cluster channel model proposed in this warehouse environment simplifies simulation and systems development. ❧ • Three-dimensional (3D) MIMO channels for urban macro/micro cellular networks. Using an advanced antenna array (3D massive MIMO) system, an extensive propagation channel measurement campaign in an urban macrocellular environment was conducted and a comprehensive channel model that includes both specular and diffuse contributions of multipath components in this type of environment has been provided in this thesis. A cluster-based approach was also implemented since multipath components were found to naturally grouped into clusters in type of urban environment. Cluster angular and delay spread parameters were modeled using a log-normal distribution while cluster angle-of-arrival and departure were modeled using a Laplacian distribution. The diffuse component were found to be a crucial part of the propagation channel with fraction power contribution of about 15%, therefore diffuse component modeling is essential in an urban macro/micro cellular environment. ❧ In all of these areas, there are very few (or none) existing measurement results. An extensive description of all measurement campaigns and relevant channel models inferred (with validation) has been provided in this thesis. Results of this work can be used for realistic system design in 4G LTE-Advanced and 5G networks and has also found its way into the 3GPP standardization work.

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Elements of next-generation wireless video systems: millimeter-wave and device-to-device algorithms

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Optimal resource allocation and cross-layer control in cognitive and cooperative wireless networks

Asset Metadata

Creator Sangodoyin, Oluwaseun (Seun) (author)

Core Title Multidimensional characterization of propagation channels for next-generation wireless and localization systems

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 08/02/2018

Defense Date 06/11/2018

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

Tag cellular communications,healthcare,localization,OAI-PMH Harvest,wireless propagation channel measurements and modeling

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Molisch, Andreas F. (committee chair), Golubchik, Leana (committee member), Moghaddam, Mahta (committee member)

Creator Email sangodoy@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-47088

Unique identifier UC11670339

Identifier etd-Sangodoyin-6602.pdf (filename),usctheses-c89-47088 (legacy record id)

Legacy Identifier etd-Sangodoyin-6602.pdf

Dmrecord 47088

Document Type Dissertation

Format application/pdf (imt)

Rights Sangodoyin, Oluwaseun (Seun)

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA