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Propagation channel characterization and interference mitigation strategies for ultrawideband systems

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Propagation channel characterization and interference mitigation strategies for ultrawideband systems

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Content PROPAGATION CHANNEL CHARACTERIZATION AND
INTERFERENCE MITIGATION STRATEGIES FOR
ULTRAWIDEBAND SYSTEMS
Author:
Vinod Kristem
A Dissertation Submitted to the
Faculty of the USC Graduate School
In Partial Fulfillment of the
Requirements for the Degree of
Doctor of Philosophy
Committee Members:
Prof. Andreas F. Molisch (Chair)
Prof. Hossein Hashemi
Prof. Leana Golubchik
Department of Electrical Engineering
University of Southern California
Los Angeles, CA 90089
August 2017
Abstract
Interference is a very common phenomenon in wireless communication systems. With the
Radio Frequency (RF) spectrum getting increasingly crowded due to the demand for high data
rates, and with the coexistence of the RF based radar, communication and navigation systems,
interference is often inevitable and often is the dominant effect limiting the performance. Radar
systems often suffer from malicious jammers. Communication and navigation systems suffer
from multiuser and multipath interference. Thus, wireless systems have to use smart signaling
schemes and post-processing techniques in order to mitigate interference.
Ultrawideband (UWB) technology is a good candidate to mitigate interference. The large
bandwidth helps in separating the closely spaced multipaths and thereby providing better rang-
ing accuracy for navigation systems. The large bandwidths can be used to achieve large data
rates in communication systems, and it can be used to combat the jammers in radar applications
using spread spectrum techniques. However, an efficient transceiver design requires the knowl-
edge of the propagation channel in which the system is deployed, as the propagation channel
plays a critical role in determining the performance of the wireless systems. Thus, propaga-
tion channel measurement and modeling are essential for design, simulation and deployment
of wireless systems. In my research work, I have addressed some of these issues related to
interference mitigation and propagation channel measurement for ultrawideband systems.
In my first work, I looked at propagation channel characterization for ultrawideband systems.
Two different scenarios were studied. The first scenario considered is an outdoor cellular envi-
ronment. We provide the results from a channel measurement campaign conducted in an urban
macro and micro-cellular environments, over the continuous frequency band of 3-18 GHz. For
an urban macro-cellular (UMa) environment, we characterize the wideband pathloss, shadow
fading, Root-Mean-Square (RMS) delay spreads and Ricean factor for different measurement
routes in line-of-sight (LOS) and non-line-of-sight (NLOS) scenarios; and for urban micro-
cellular (UMi) environments, we study these parameters as well as their dependence on the BS
height. By dividing the wideband channel transfer function into subbands of 1 GHz each, we
study the pathloss exponent, shadow fading, Ricean factor, RMS delay spreads and coherence
bandwidth dependence on frequency in UMa and UMi LOS/NLOS environments.
1
The second scenario considered a warehouse environment, in which we performed UWB
MIMO channel measurements and modeling. UWB systems have many envisioned applica-
tions including asset tracking in a warehouse environment. The measurement setup employs a
vector network analyzer (VNA) operating in the 2-8 GHz frequency band combined with an 8
x 8 virtual MIMO antenna array. We develop a comprehensive statistical propagation channel
model based on high-resolution extraction of MPCs, and subsequent spatio-temporal clustering
analysis. In particular we characterize the propagation of MPCs within the cluster and across
the clusters. The proposed stochastic channel model is further validated using the capacity and
RMS delay spread analysis.
My second work deals with the problem of interference mitigation for ultra-wideband (UWB)
based positioning systems. Accurate position information is of high importance in public safety
and military applications. While Global Positioning System (GPS) serves the purpose in out-
door environments, it is often unreliable in cluttered environments such as indoors, narrow
street canyons, caves, and dense forests. Time-of-arrival (ToA) measurements employing UWB
signals can provide high-precision ranging information. However, the accuracy is degraded by
multiuser interference (MUI), in particular in the presence of multipath propagation. While
the processing gain of time-hopping impulse radio (TH-IR) can be used to suppress the MUI,
this is often insufficient. We propose instead a non-linear processing scheme of TH-IR that
effectively suppresses MUI without requiring knowledge of the time-hopping sequences of the
interfering users. The principle is that multipath components (MPCs) of interferer’s do not
align closely, for the majority of transmission frames, with the MPCs of the desired signal.
Through a judicious choice of algorithm parameters we show that our algorithm is superior to
existing (realizable) thresholding and median filter algorithms, and in some cases can even beat
genie-aided thresholding algorithms. The performance is robust to both strength and number of
the interferers. The results are validated with both standardized 802.15.4a channel models and
measured outdoor UWB channels.
My last work deals with the problem of jammer sensing and interference mitigation for
spread spectrum systems. We consider an MC-CDMA transceiver that is being jammed by a
wideband non-stationary jammer. For a Rayleigh fading channel, we derive the symbol error
rate for the case that the jammer state information is available at the receiver. We derive the
2
Maximum-Likelihood based and Log-Likelihood Ratio based JSI estimators for both the case
where channel state information is available during jammer sensing and when it is not. The
performance of various jammer estimation schemes is studied using Monte Carlo simulations
and with the channel impulse responses collected from the wireless propagation measurements
conducted in the 10–12 GHz band.
3
Acknowledgments
Over the course of my PhD, I had the privilege of having the amazing support of many indi-
viduals, without which my thesis would not have materialized. First, I would like to thank my
advisor, Prof. Andreas F. Molisch. It has been an absolute honor to work with him. His support,
guidance and expertise knowledge in this field have paved the way toward the accomplishments
that I have had during the past years. The past few years under his guidance has been a great
learning experience.
I would also like to thank the members of my qualifying exam and dissertation committee
members, Prof. Hossein Hashemi, Prof. Leana Golubchik, Prof. Keith Chugg, and Prof.
Robert A. Scholtz whose insightful comments have greatly helped improve the quality of this
dissertation.
I would like to thank my amazing fellow research group members, Hao Feng, Seun San-
godoyin, Sundar Aditya, Daoud Burghal, Umit Bas, Rui Wang, Zheda Li, Vishnu Ratnam,
Junyang Shen, Joongheon Kim. They have all helped me in various stages of my research. It
has been a great experience to be part of this research group. Also, thanks to my CSI colleagues,
Navid Naderializadeh, Dilip Bethanabhotla, Sajjad Beygi, Arash Tehrani, Mingyue Ji, Hassan
Ghozlan for all the discussions.
I would like to extend my thanks to the CSI staff, Susan Wiedem, Gerrielyn Ramos and
Corine Wong, who have greatly helped me during my years at USC. I would like to thank
Diane Demetras, Jennifer Gerson, Tracy Charles for helping me out with the administrative
processing.
I would like to thank all my roommates Kiran, Sanjay and Aravind for all my friends for
making me feel home away from home. Lastly, I would like to express my deepest gratitude
to my amazing and loving family, my parents, my sister, my wife and my in-laws for their love
and support, even in toughest of times. This thesis would not have been possible without them.
4
Contents
Abstract 1
Acknowledgments 4
List of Tables 11
List of Figures 12
1 Introduction 18
1.1 Overview of UWB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.1.1 UWB Definition and Spectral Regulations . . . . . . . . . . . . . . . . 18
1.1.2 Background of UWB . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.1.3 Ultrawideband signalling methods . . . . . . . . . . . . . . . . . . . . 21
1.1.4 Standardization Activities . . . . . . . . . . . . . . . . . . . . . . . . 22
1.1.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2 Overview of UWB for Interference Suppression . . . . . . . . . . . . . . . . . 25
1.2.1 Multiuser Interference suppression in localization system . . . . . . . . 26
1.2.2 Jammer interference suppression in spread spectrum systems . . . . . . 27
1.3 Overview of UWB Channel Measurements . . . . . . . . . . . . . . . . . . . 28
5
1.4 Thesis Outline and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.4.1 Outdoor Wideband Channel Measurements and Modeling in the 3-18
GHz Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.4.2 Stochastic Double directional Channel modeling in Warehouse Envi-
ronment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.4.3 Ultrawideband Ranging with interference mitigation . . . . . . . . . . 34
1.4.4 Jammer Sensing and Performance Analysis of MC-CDMA Systems in
the Presence of Wideband Jammer . . . . . . . . . . . . . . . . . . . . 35
1.5 Other Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.6 Organization of the Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2 Outdoor Wideband Channel Measurements and Modeling in the 3-18 GHz Band 39
2.1 Measurement Setup and Environment . . . . . . . . . . . . . . . . . . . . . . 42
2.1.1 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.1.2 Measurement Environment . . . . . . . . . . . . . . . . . . . . . . . . 44
2.2 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.1 Noise averaging and Interference filtering . . . . . . . . . . . . . . . . 46
2.2.2 Small scale fading averaging . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.3 Wideband Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.4 Subband Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.3 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.3.1 Wideband Pathloss and Shadow fading . . . . . . . . . . . . . . . . . 52
2.3.2 Wideband RMS delay spread . . . . . . . . . . . . . . . . . . . . . . . 54
2.3.3 Subband Pathloss characterization . . . . . . . . . . . . . . . . . . . . 56
6
2.3.4 Subband shadow fading characterization . . . . . . . . . . . . . . . . . 60
2.3.5 Subband RMS delay spreads characterization . . . . . . . . . . . . . . 62
2.3.6 Subband Ricean factor characterization . . . . . . . . . . . . . . . . . 64
2.3.7 Subband Coherence Bandwidth characterization . . . . . . . . . . . . 64
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.5 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3 Stochastic Double directional Channel modeling in Warehouse Environment 70
3.0.1 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.0.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.0.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.1 Measurement Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3 Measurement Data processing and Results . . . . . . . . . . . . . . . . . . . 78
3.3.1 Pathloss Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3.2 Shadowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.4 Angular Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.4.1 MPC parameter extraction using CLEAN . . . . . . . . . . . . . . . . 82
3.4.2 Clustering of MPCs . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.4.3 LOS Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.4.4 NLOS Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.6 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7
3.7 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4 Ultrawideband Ranging with interference mitigation 110
4.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2 ToA estimation algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.2.1 Thresholding schemes . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.2.2 Proposed ToA estimation algorithm . . . . . . . . . . . . . . . . . . . 118
4.3 Proposed algorithm analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.1 False alarms from a noise peak . . . . . . . . . . . . . . . . . . . . . . 122
4.3.2 False alarms from an interference MPC . . . . . . . . . . . . . . . . . 123
4.3.3 Signal MPC detection . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.3.4 Choice of parameters

N,
, andW . . . . . . . . . . . . . . . . . . . 124
4.4 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.4.1 Measurement Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.4.2 Hardware and Post-processing . . . . . . . . . . . . . . . . . . . . . . 128
4.5 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.5.1 Synthetic channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.5.2 Measurement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5 Jammer Sensing and Performance Analysis of MC-CDMA Systems in the Presence
of Wideband Jammer 138
5.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8
5.2 SER analysis with JSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.2.1 Full JSI case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.2.2 With partial JSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.2.3 No JSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.3 JSI estimation and the symbol detection . . . . . . . . . . . . . . . . . . . . . 146
5.3.1 JSI estimation with perfect CSI . . . . . . . . . . . . . . . . . . . . . 147
5.3.2 JSI estimation with no CSI . . . . . . . . . . . . . . . . . . . . . . . . 152
5.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.4.1 Performance with synthetic channels . . . . . . . . . . . . . . . . . . . 156
5.4.2 Performance with measurement data . . . . . . . . . . . . . . . . . . . 160
5.4.3 Performance with mismatch in Jammer model . . . . . . . . . . . . . . 162
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
A Appendix: Ultrawideband Ranging with interference mitigation 167
A.0.1 False alarms from a noise peak . . . . . . . . . . . . . . . . . . . . . . 167
A.0.2 False alarms from an interference MPC . . . . . . . . . . . . . . . . . 168
A.0.3 Signal MPC detection . . . . . . . . . . . . . . . . . . . . . . . . . . 169
B Appendix: Jammer Sensing and Performance Analysis of MC-CDMA Systems in
the Presence of Wideband Jammer 172
B.0.4 SER with Full JSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
B.0.5 SER with partial JSI . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
B.0.6 LLR (
K;B
) derivation . . . . . . . . . . . . . . . . . . . . . . . . . . 174
9
B.0.7 LLR(k) derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Bibliography 176
10
List of Tables
1.1 FCC limits on the EIRP levels for UWB applications . . . . . . . . . . . . . . 19
2.1 Standard deviation of shadow fading in the UMa environment. . . . . . . . . . 53
2.2 Standard deviation of shadow fading in the UMi environment. . . . . . . . . . 54
3.1 Channel measurement parameters . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2 Hardware used in the UWB MIMO channel measurement . . . . . . . . . . . . 77
3.3 Extracted Large Scale Channel Parameters . . . . . . . . . . . . . . . . . . . 80
11
List of Figures
2.1 Transmitter and Receiver setups. . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.2 LOS measurement locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3 NLOS measurement locations. . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4 LOS and NLOS routes for the PSX measurements. . . . . . . . . . . . . . . . 47
2.5 Sample APDP plots for measurement taken along different routes in the LOS
and NLOS environments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.6 Distance dependent pathloss in the LOS and NLOS environments for the UMa
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.7 Distance dependent pathloss in the LOS and NLOS environments for the UMi
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.8 CDF of RMS delay spreads for different measurement routes in the UMa envi-
ronment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.9 CDF of the RMS delay spreads for different measurement routes in the UMi
environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.10 Pathloss exponents as a function of the frequency for different measurement
routes in the UMa LOS environment. . . . . . . . . . . . . . . . . . . . . . . 57
2.11 Pathloss exponents as a function of the frequency for different measurement
routes in the UMa NLOS environment. . . . . . . . . . . . . . . . . . . . . . 58
12
2.12 Pathloss exponents as a function of the frequency for different BS heights in the
UMi LOS/NLOS environments. . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.13 Shadow fading as a function of the frequency for different measurement routes
in the UMa LOS/NLOS environments. . . . . . . . . . . . . . . . . . . . . . 59
2.14 Shadow fading as a function of the frequency for different BS heights in the
UMi LOS/NLOS environments. . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.15 Correlation matrix of the shadow fading across different subbands in the UMa
LOS/NLOS environments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.16 Mean and standard deviation of the dB values of the RMS delay spreads, for
different subbands, in the UMa LOS environment. . . . . . . . . . . . . . . . 61
2.17 Mean and standard deviation of the dB values of the RMS delay spreads, for
different subbands, in the UMa NLOS environment. . . . . . . . . . . . . . . 62
2.18 Mean and standard deviation of the dB values of the RMS delay spreads, for
different subbands, in the UMi environment. . . . . . . . . . . . . . . . . . . 63
2.19 Mean and standard deviation of the Ricean factor (dB) for different subbands in
the UMa LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.20 Mean and standard deviation of the Ricean factor (dB) for different subbands in
the UMi LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.21 Mean and standard deviation of the Coherence bandwidth (dB values) for dif-
ferent subbands in the UMa LOS environments. . . . . . . . . . . . . . . . . 66
2.22 Mean and standard deviation of the Coherence bandwidth (dB values) for dif-
ferent subbands in the UMa NLOS environments. . . . . . . . . . . . . . . . . 67
2.23 Mean and standard deviation of the Coherence bandwidth (dB values) for dif-
ferent subbands in the UMi LOS and NLOS environments. . . . . . . . . . . . 68
3.1 USC Warehouse Facility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2 Floor map of the first floor of the warehouse. . . . . . . . . . . . . . . . . . . 75
13
3.3 Floor map of the basement of the warehouse. . . . . . . . . . . . . . . . . . . 75
3.4 Channel sounder measurement setup in the warehouse environment. . . . . . . 77
3.5 Distance dependency of the pathloss in the LOS and NLOS scenarios. . . . . . 80
3.6 Frequency dependency of the pathloss in the LOS and NLOS scenarios. . . . . 82
3.7 Scatter plot of the unclustered MPCs. (5 m LOS measurement.) . . . . . . . . 84
3.8 Clustered MPCs with KPowerMeans algorithm. (5 m LOS measurement.) . . . 85
3.9 Figure demonstrating that the intra-cluster DoD and DoA are independent, in
the LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.10 Figure demonstrating that the intra-cluster DoD and ToA are independent, in
the LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.11 Intra-cluster DoD and DoA for the LOS cluster, in the LOS environment. . . . 89
3.12 Intra-cluster DoD and DoA for the NLOS clusters, in the LOS environment. . 89
3.13 Intra-cluster ToA modeling for the LOS and NLOS clusters, in the LOS envi-
ronment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.14 Intra-cluster power decay constant for different cluster ToA, in the LOS envi-
ronment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.15 Figure demonstrating that the cluster DoD and DoA are not independent, in the
LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.16 Figure demonstrating that the cluster DoD and ToA are not independent, in the
LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.17 Cluster DoD modeling in the LOS environment. . . . . . . . . . . . . . . . . 93
3.18 Figure comparing the measured and simulated conditional densityDoAjDoD,
for the LOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
14
3.19 Modeling the Excess cluster ToA for different propagation scenarios in the LOS
environment (a) Backwall reflection (b) Double bounce scattering withDoD
DoA< 0 (c) Double bounce scattering withDoDDoA> 0. . . . . . . . . 95
3.20 Inter-cluster power decay for different propagation scenarios in the LOS envi-
ronment (a) Backwall reflection (b)DoDDoA< 0 (c)DoDDoA> 0. . . 95
3.21 Average number of clusters as a function of measurement distance in the LOS
environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.22 Intra-cluster DoD and DoA modeling in the NLOS environment. . . . . . . . . 99
3.23 Intra-cluster ToA modeling in the NLOS environment. . . . . . . . . . . . . . 100
3.24 Intra-cluster power decay modeling in the NLOS environment. . . . . . . . . . 100
3.25 Cluster DoD modeling in the NLOS environment. . . . . . . . . . . . . . . . 101
3.26 Figure comparing the measured and simulated conditional densityDoAjDoD,
for the NLOS environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.27 Modeling the excess cluster ToA for different propagation scenarios in the
NLOS environment (a) Backwall reflection (b) Double bounce scattering with
DoDDoA< 0 (c) Double bounce scattering withDoDDoA> 0. . . . . 103
3.28 Inter-cluster power decay for different propagation scenarios in the NLOS en-
vironment (a) Backwall reflection (b)DoDDoA< 0 (c)DoDDoA> 0. . 103
3.29 Capacity and RMS delay spread validation for the LOS channel model. . . . . 106
3.30 Capacity and RMS delay spread validation for the NLOS channel model. . . . 107
4.1 Effective impulse responses after de-hopping. (IEEE 802.15.4a CM1 channel
realization withN = 50 andI = 1.) . . . . . . . . . . . . . . . . . . . . . . . 114
4.2 Error in MPC location estimates obtained using CLEAN, for five strongest
MPCs. (IEEE 802.15.4a CM1 channel realization and second derivative of ba-
sic Gaussian pulse with pulse width of 1 ns are used. N = 50, SNR = 30 dB,
sampling time = 25 ps, andI = 0.) . . . . . . . . . . . . . . . . . . . . . . . . 119
15
4.3 Performance bounds with

W
opt
;
opt
;

N
opt

forN = 50. . . . . . . . . . . . . 127
4.4 Performance bounds with

W;
;

N

=

W
opt
3
;

opt
3
;

N
opt
3

and

W;
;

N

=

2W
opt
; 2
opt
; 2

N
opt

forN = 50 andI = 5. . . . . . . . . . . . . . . . . . . . 127
4.5 Performance evaluation of different ranging schemes, as a function of SIR (SNR
= 20 dB andN = 50). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.6 Performance evaluation of different ranging schemes, as a function of SNR, in
presence of one active interfering user (SIR = 0 dB,I = 1, andN = 50). . . . . 132
4.7 Performance evaluation of different ranging schemes, as a function of transmit
power, when SIR from different users is different (N = 50). . . . . . . . . . . 132
4.8 Ranging error comparison for different schemes, when both desired and inter-
fering users are in LOS scenario (N = 50). . . . . . . . . . . . . . . . . . . . 135
4.9 NLOS measurement floor map of USC VHE quad. . . . . . . . . . . . . . . . 135
4.10 Ranging error comparison for different schemes, when both desired and inter-
fering users are in NLOS scenario (N = 50). . . . . . . . . . . . . . . . . . . 137
5.1 MC-CDMA Transceiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.2 SER for different receivers when the JSI is available (N = 128, M = 16, L = 16,
D = 1, SNR = 21 dB). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.3 SER for different jammer estimation schemes, when the CSI is available (N =
128, M = 16, L = 16, = 0.9, SNR = 21 dB, ZC spreading sequence). . . . . . 157
5.4 SER for different jammer estimation schemes, when the CSI is available (N =
128, M = 16, L = 16, = 0.9, D = 10, JNR = 30 dB). . . . . . . . . . . . . . . 158
5.5 SER for different jammer estimation schemes, when the CSI is not available (N
= 128, M = 16, L = 16, = 0.9, SNR = 21 dB). . . . . . . . . . . . . . . . . . 159
5.6 SER for different jammer estimation schemes, when the CSI is not available (N
= 128, M = 16, L = 16, = 0.9, D = 10, JNR = 30 dB). . . . . . . . . . . . . . 160
16
5.7 The measurement locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5.8 SER for different jammer estimation schemes computed using the measured
impulse responses, when the CSI is available (System BW = 1.28 GHz and f
= 10 MHz (N = 128), Bcoh200 MHz, = 0.9, D = 100, SNR = 21 dB). . . . 161
5.9 SER for different jammer estimation schemes computed using the measured
impulse responses, when the CSI is not available (System BW = 1.28 GHz and
f = 10 MHz (N = 128), Bcoh200 MHz, = 0.9, D = 100, SNR = 21 dB). . 162
5.10 SER for different jammer estimation schemes for non-contiguous jammer, when
the CSI is available (N = 128, M = 16, L = 16, = 0.9, D = 100, SNR = 21 dB). 163
5.11 SER for different jammer estimation schemes for non-contiguous jammer, when
the CSI is not available (N = 128, M = 16, L = 16, = 0.9, D = 100, SNR =
21 dB). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.12 SER for different JSI estimation schemes when true jammer interference gen-
erated using uniform distribution. CSI is available for JSI estimation (N = 128,
M = 16, L = 16, = 0.9, D = 100, SNR = 21 dB). . . . . . . . . . . . . . . . . 164
5.13 SER for different JSI estimation schemes when true jammer interference gener-
ated using uniform distribution. CSI not available for JSI estimation (N = 128,
M = 16, L = 16, = 0.9, D = 100, SNR = 21 dB). . . . . . . . . . . . . . . . . 165
17
Chapter 1
Introduction
1.1 Overview of UWB
Ultrawideband (UWB) technology has emerged as one of the most promising candidates for
communication, radar and localization systems and has attracted great interest from the sci-
entific, military and industrial communities. It has number of attractive features such as the
possibility to provide extremely high data rates for short distance communications, efficient
use of radio spectrum through underlaying techniques, robustness to multipath propagation ef-
fects, precise ranging and localization, penetration through the materials, low cost transceiver
implementation.
1.1.1 UWB Definition and Spectral Regulations
The Federal communications commission (FCC) defines UWB signal as the signal that satisfies
either of the following: (i) fractional bandwidth of the signal more than 0.2; (ii) signal with
absolute bandwidth more than 500 MHz, irrespective of the fractional bandwidth.
The fractional bandwidth of the signal is defined as
2 (f
H
f
L
)
(f
H
+f
L
)
(1.1)
wheref
H
andf
L
are the highest and lowest frequency components in the transmitted signal.
18
Table 1.1: FCC limits on the EIRP levels for UWB applications
Frequency (GHz) Indoor (dBm/MHz) Outdoor (dBm/MHz)
0.96–1.61 -75.3 -75.3
1.61–1.99 -53.3 -63.3
1.99–3.10 -51.3 -61.3
3.10–10.6 -41.3 -41.3
Above 10.6 -51.3 -61.3
Because of the wide bandwidth associated with the UWB signals, they can overlap with
several existing radio technologies like TV Broadcast, Radio astronomy, Global Positioning
System (GPS) etc. To avoid disruption to the existing technologies in the 0–10 GHz band, the
FCC imposed stringent constraints on the UWB emissions. FCC regulations control the UWB
emissions through constraints on the Effective Isotropic Radiated Power (EIRP), measured in
dBm/MHz. The FCC radiation limits for UWB indoor and outdoor applications are given in
Tab. 1.1.
The UWB spectral masks are different for different countries. In the USA, FCC allows
emission in the 3:1–10:6 GHz band as long as the power spectral density (PSD) is less than -
41.3 dBm/MHz EIRP. In Europe, the Radio Spectrum Committee (RSC) of the European Com-
mission (EC) imposes a spectral mask of -41.3 dBm/MHz in the 4:2–4:8 GHz and 6–8:5 GHz
bands. In Japan, the UWB emissions are allowed in the 3:4–4:8 GHz and 7:25–10:25 GHz
bands.
1.1.2 Background of UWB
The origins of UWB dates back to the early 1900s, in particular the spark-gap transmission
experiments of Marconi and Hertz. The bandwidth associated with these experiments was large
and their approach can be considered as a crude form of impulse radio based ultrawideband
communications, and Marconi used this method to send Morse code across the Atlantic ocean.
Due to limitations in technology, ranging from electronic component design to antenna design,
UWB did not find widespread use in the subsequent decades. Instead, carrier modulated nar-
19
rowband communications was preferred.
Advancements in the measurement technology and the requirements for electronic warfare
helped in the evolution of UWB. For instance, circuits capable of generating sub-nanosecond
pulses were developed in the 1960s, enabling higher spatial resolution for radars. Ross and
Bennett [1] and Harmuth [2] made pioneering contributions to modern UWB radio, with the
first UWB patent filed by Ross in 1973. Yet, due to limitations in available electronic com-
ponents that can operate over large bandwidths, narrowband systems still dominated the wire-
less communication landscape until the beginning of the 1990s. UWB was mostly limited to
radar, sensing and military communications. A key step in making UWB viable for commu-
nications was the invention of impulse radio by Scholtz [3] and its detailed investigation in
the subsequent decade by Scholtz and Win [4–7]. A further milestone occured in February
2002, when the US Federal Communications Commission (FCC) issued the above-mentioned
ruling that UWB could be used for data communications subject to constraints on the spectral
mask. This triggered a lot of interest in academia and industry, as the wireless spectrum was
getting increasingly crowded in the 0–10 GHz band, and UWB can coexist with the existing
technologies. However, much of the action in the area reduced due to challenges in develop-
ing cost-effective UWB transceivers and mostly due to stringent requirements enforced by the
spectrum regulatory bodies.
With the advancements in the signal processing and the microwave technologies, today cost-
effective UWB radios can be designed that satisfy the spectrum regulations. Also, with the
availability of unlicensed mm-wave spectrum for UWB, there is a renewed interest in the UWB
technology. A lot of interest revolves around joint communication and localization technology,
as well as the capability of UWB systems to suppress interference through extremely large
spreading factors.
20
1.1.3 Ultrawideband signalling methods
Very large bandwidth signals can be generated in multiple ways.
Time-Hopping Impulse Radio (TH-IR)
Impulse radio UWB transmission is based on discontinuous emission of very short pulses. Each
pulse is typically of the order of nanoseconds and hence occupies several GHz of bandwidth in
the frequency domain. This type of transmission does not require additional carrier modulation
(though it can be included). Each information symbol is sent using N pulses, that are irregu-
larly spaced, thereby providing the processing gain required to combat noise and interference.
The pulse sequence is modulated either in amplitude–pulse amplitude modulation (PAM) or
position–pulse position modulation (PPM). The commonly used pulse shapes are Gaussian, or
derivatives of Gaussian pulses.
Frequency-Hopping (FH)
In FH UWB transmission, the carrier frequency is changed over time. The information signal
is transmitted over different carrier frequency in different time slots. Thus, the bandwidth of
the resulting signal depends on the range of the oscillator. The drawback of this method is
that at each point in time, the signal bandwidth is small, and the signal might thus induce
larger interference to victim receivers. For this reason, an FH signal might not be considered
“ultrawideband” by some frequency regulators.
Multicarrier schemes
OFDM based transmissions are based on sending information over a number of parallel subcar-
riers. OFDM has number of advantages such as high spectral efficiency, robustness to multipath
effects and ability to efficiently capture the energy in the multipaths. Ultrawideband transmis-
21
sion with OFDM can occur if the datarate is sufficiently high; or if further spreading of the
information signal is used. In multiband OFDM signals, a regular OFDM signal is transmitted
with frequency hopping [8]. In MC-CDMA, the data stream is spread over different subcarriers,
with each chip of pseudo-random code.
Direct sequence spread spectrum techniques
UWB signal can also be generated by extending the Direct-Sequence Spread-Spectrum (DSSS)
or Code-Division Multiple-Access (CDMA) techniques. Here each information symbol is mul-
tiplied by a (binary) chip sequence, where each chip has a short duration (on the order of ns
or less), leading to a large overall bandwidth of the signal. Such an approach is conceptu-
ally identical to code division multiple access (CDMA) that has been made popular by cellular
technology, though the chip duration in UWB systems is much shorter.
1.1.4 Standardization Activities
IEEE 802.15.3a
The main purpose of the 802.15.3a standard was to define a new physical layer for short-range,
high-data-rate applications. Data rates in excess of 110 Mbps were targeted for a communi-
cation distance of 10 m. The targeted applications include video, multimedia links, or cable
replacement. The primary goal of the standard is to provide high speed physical layer for exist-
ing 802.15.3 medium access standard. The standard was never approved by IEEE, though the
multiband-OFDM standard originally developed within IEEE 802.15.3a was later approved as
an ECMA standard. However, few products were ever developed using this standard.
IEEE 802.15.4
The main purpose of the 802.15.4 standard was to define a new physical layer for joint low-
data-rate communications and ranging [9]. This was targeted for very low power and very
22
low complexity systems. The targeted applications include sensors, remote controls, and home
automation.
1.1.5 Applications
The large bandwidth associated with UWB makes it an attractive candidate for several applica-
tions.
UWB for positioning
Accurate position information is of high importance in many commercial, public safety, and
military applications. While Global Positioning System (GPS) serves this purpose in outdoor
environments, it is often unreliable or inaccessible in cluttered environments such as indoors,
narrow street canyons, caves, and dense forests. Hence, alternative positioning techniques based
on ranging between ground-based devices were explored.
Ranging techniques are based on time-of-arrival (ToA) of the first path, using the assumption
that this ToA corresponds to the geometrical distance to be measured. Range estimates are
critical for localization, as the location information can be derived based on ranging with at
least three of the anchors and followed by triangulation.
ToA estimation is affected by receiver noise and multipath propagation. The mean square
error of any unbiased ToA estimator in an AWGN channel, is upper bounded by the cramer
rao lower bound (CRLB), which is inversely proportional to the bandwidth of the signal. Since
UWB signals has bandwidth of the order of GHz, it can separate multipaths spaced apart by few
centimeters and can achieve ranging accuracy of the order of few centimeters.
23
UWB for data communications
UWB can be used for the following two application scenarios (i) short range high data rate
applications and (ii) long range low data rate applications.
Based on Shannon’s channel capacity expression, C = B log(1 +SNR), the channel ca-
pacity increases with the bandwidth. Since UWB systems have large bandwidths, they can
support large data rates (several 100s Mbps). However spectral regulations impose a constraint
on the transmit power level, thereby limiting the communication distances to few 10s of me-
ters. Thus, UWB is attractive for short range high data rate applications such as wireless USB,
machine-to-machine communications, wireless personal area networks (WPAN) etc.
The long range low data rate applications include wireless sensor networks, RF tags etc.
Since the communication rate is low, a large spreading factor can be achieved, which in turn
allows a good “effective” SNR even over large distances. Furthermore, because of the large
bandwidth, UWB signal has better diversity compared to narrowband systems. It may even
provide better material penetration of some of its frequency components and hence makes it an
ideal candidate for search and rescue systems for first responders.
UWB for medical applications
The low transmit power, coupled with good material penetration capabilities and the good rang-
ing accuracy makes it an attractive candidate for medical imaging and medical sensing. UWB
radar is used for remote monitoring and tracking patients motion over a short distances. UWB
enabled sensors can detect micro movements in the body and hence be used for vital signs
monitoring like heartbeat.
24
UWB for Military Applications
Since the power spectral density of UWB signal can be close to, or even below, the level of
thermal noise, UWB signals are very hard to detect. UWB systems offer low probability of
interception/detection and hence makes it attractive to send secret messages. Furthermore, the
large bandwidth of the UWB signal provides very fine resolution of the multipath components
and thus lead to large frequency diversity. This makes UWB communications robust to multi-
path effects and interference. Apart from these, UWB radar can be used for intrusion detection,
collision avoidance, precision altimetry, precision geolocation etc.
1.2 Overview of UWB for Interference Suppression
Interference is a fundamental property of radio communication systems, in which multiple
transmissions take place over a common medium. Interference is often the limiting factor on
the performance of communication systems. Ultrawideband systems, along with smart signal-
ing and post-processing techniques, can mitigate the interference to a certain extent.
In wireless environment, the transmit signal undergoes multipath propagation (reflection,
diffraction, scattering etc) before reaching the receiver. Narrowband systems does not have
the ability to separate multipaths coming with different delays, and hence the multipaths will
add up (can be constructive/destructive) resulting in fading. UWB systems, equipped with large
bandwidth, helps in resolving the mutlipaths that are spaced apart by few centimeters, and hence
signal coming along different paths can be coherently combined at the receiver. Thus, UWB
can effectively manage the multipath interference and provide reduced symbol error rates for
data communications and better location accuracy for the positioning systems.
In multiuser environments, apart from multipath interference, one has to deal with mul-
tiuser interference. To overcome this, the desired information signal is spread over the available
bandwidth using the spread spectrum techniques and multiple users are accommodated using
25
multiple access techniques like CDMA. This approach helps in reducing the multiuser interfer-
ence by a factor of spreading gain. UWB systems, equipped with large bandwidth, provides
better processing gain and hence better suppression of multiuser interference.
The radar and military systems often suffer from malicious jammers. Jammer senses for any
ongoing transmissions and deliberately disturbs the ongoing communication by transmitting in
the same band of frequency thereby reducing the signal-to-noise ratio (SNR) of the ongoing
transmission. Spread spectrum techniques can be used in this scenario to mitigate the inter-
ference [77]. UWB is again a good candidate in this setting. The large bandwidth helps in
spreading the information signal thus making it undetectable.
In this thesis, I focus on multiuser and multipath interference suppression in UWB based
localization system and jammer interference suppression for UWB based spread spectrum sys-
tems.
1.2.1 Multiuser Interference suppression in localization system
As discussed above, location information is acquired by performing ranging with adjacent
nodes [76]. Since multiple nodes in the network can perform ranging with their neighbors
simultaneously, this results in multiuser interference which affects the ranging accuracy [105].
Since UWB systems has large bandwidth, it can effectively resolve the closely spaced MPCs
thus making it feasible to differentiate the multipath contributions from different users.
UWB ranging in the presence of noise and multipath propagation has been studied exten-
sively in the literature. For a single path additive white Gaussian noise (AWGN) channels, a
matched-filtering (MF) receiver is the maximum likelihood (ML) ToA estimator with theoret-
ical bounds on the ranging error given in [89–92]. For AWGN with multipath, [93] and [94]
respectively derived the Cramer-Rao bound (CRB) and Ziv-Zakai bound (ZZB) on the mean
square error (MSE) in ToA estimation. The ML estimators for the ToA estimation were pro-
posed in [95] and [96]; however, computational complexity of these estimators limits their
26
implementation. Practical sub-optimal ToA estimators were proposed in [97, 98, 100]. Several
low complexity, subsampling ToA estimators, based on the energy-detection (ED) have been
proposed in [99–103]. The performance of the MF and ED receivers has been summarized
in [104]. A two-step hybrid ToA estimator was proposed in [106]. In it, the coarse estimate is
obtained from energy detection and a fine estimate is obtained from matched-filtering.
Very few papers in literature addressed the issue of interference in UWB ranging. Ref. [107]
proposed non-linear filtering schemes like minimum filtering and median filtering to mitigate
the multiuser interference (MUI). Ref. [108] considered both MUI and narrowband interference
(NBI), and proposed differential filtering, to mitigate the interference. These papers considered
the ED receivers and studied the performance with only one interfering user. While the ED
receivers has low cost implementation, its performance is poor compared to matched-filtering
(coherent) receivers, especially when the signal-to-noise ratio (SNR) is small. Also, the energy
based non-linear filtering schemes cannot exploit noise averaging across frames, as the noise
becomes correlated after filtering. MUI mitigation in UWB ranging using coherent receivers
is considered in [109]. it was assumed that the receiver knows the TH sequences of all the
interfering users, and proposed an iterative successive interference cancellation technique for
ToA estimation. In a dense multipath channel, this approach becomes computationally intense.
More importantly, acquiring the TH sequences of all the interfering users is difficult especially
when the users are mobile. It can also happen that the interfering users are hostile and do not
share their TH sequences.
1.2.2 Jammer interference suppression in spread spectrum systems
Jamming, either intentional or unintentional, is a big, and increasingly prevalent, problem for
many wireless communications systems. A well-known countermeasure is the application of
spread spectrum techniques that distribute the information over a bandwidth larger than that of
the jammer.
27
Jammer estimation and suppression for spread spectrum applications have been well ex-
plored in the literature. The majority of the studies focused on DSSS, Frequency-Hopping SS
(FHSS), CDMA and OFDM systems. Refs. [115–119] provide jammer estimation techniques
and anti-jamming performance of DSSS systems. Performance of FHSS in the presence of
a jammer in additive white Gaussian noise (AWGN) and Rayleigh fading channels has been
given in [120–123]. Ref. [124–126] study the performance of CDMA systems in the presence
of jammer interference. Performance of OFDM system for different jammer models, and the
mitigation techniques, have been discussed in [127] and the references therein. Jammer esti-
mation and suppression for MC-CDMA systems has not been well explored in the literature.
Refs. [128] and [129] studied the performance of MC-CDMA system with jammer interference
and provided jammer estimation schemes; [128] provides a jammer estimation scheme for the
case when the receiver knows the channel state information (CSI), and derives the resulting
symbol error rate (SER) for an AWGN channel. The jammer state information (JSI) is obtained
using the data symbols alone. Ref [129] considers a Rayleigh fading channel, and using pi-
lot symbols, it provides an iterative JSI estimation, CSI estimation and data decoding approach.
Both these works assume a simplified jammer model–on each subcarrier, the jammer is modeled
to be either present or absent with a certain probability. The jammer contributions on different
subcarriers are assumed independent and identically distributed (i:i:d:).
1.3 Overview of UWB Channel Measurements
Design of sophisticated transmit signaling schemes and receive post-processing algorithms re-
quire the knowledge of the propagation environment in which the communication system is
deployed. For instance, a good OFDM system design requires the knowledge of the RMS delay
spread and coherence bandwidth of the channel. Characterization of the propagation environ-
ment requires the measurement and modeling of the channel.
There are two common ways to characterize the propagation environment: (i) Deterministic
28
approach and (ii) Stochastic modeling. The deterministic approach requires complete knowl-
edge of all the scatterers in the environment. This includes the material type, the geometry
and the electro-magnetic (EM) properties. Given these, the channel impulse responses can be
determined using EM simulation tools such as ray-tracing. While they provide an accurate de-
scription of that site, the problem with this approach is that acquiring the accurate and complete
knowledge of scatterers is difficult and if there are any changes in the environment, the collected
impulse responses will become irrelevant. The more popular approach of channel characteriza-
tion is through stochastic modeling. In this approach, the channel models are developed based
on measurement data. These stochastic models try to capture the typical properties of the envi-
ronment and they are not site specific, though they are distinct for different kind of environments
like indoor, outdoor, urban, rural, macrocell, microcell etc. Many popular UWB standards use
stochastic channel modeling.
One of the most popularly used stochastic channel model is the one developed by Saleh and
Valenzuela (SV). A generalization of this model has been adopted in IEEE 802.15.4a channel
model for system level simulations in office, residential, outdoor and industrial environments.
As per this model, the MPCs are grouped into clusters. The delays of MPCs within the cluster
as well as the delays of the cluster starting points follow a Poisson process; the power of the
MPCs within the cluster delay exponentially with the delay; the cluster power also decays
exponentially with the cluster delay. The IEEE 802.15.4a CM provides the stochastic channel
parameters for different measurement environments. Ref. [10–12] provides an overview of the
UWB channel models developed for various propagation environments ranging from indoor,
outdoor, industrial, office environments.
1.4 Thesis Outline and Contributions
I will now introduce the interference suppression problems and channel propagation aspects of
UWB addressed in this work one by one, and talk about the major contributions achieved in
29
each one of them, and list out the publications resulted from our work.
1.4.1 Outdoor Wideband Channel Measurements and Modeling in the 3-
18 GHz Band
Fifth generation cellular systems will operate in a wide range of frequencies, covering both
the traditional cellular bands, and mm-wave frequency bands, either selecting a specific band
or operating in multiple bands simultaneously. For the design of such systems, a detailed un-
derstanding of the frequency dependence of the propagation channel is essential. While many
channel measurements exist in either microwave bands (below 6 GHz) or mm-wave bands (in
excess of 20 GHz), the results are not easily comparable, and furthermore the transition between
these bands is not very well known.
In this work, we aim to bridge the gap by providing the results from a channel measurement
campaign conducted in an urban macro and micro-cellular environments, over the continuous
frequency band of 3-18 GHz. For an urban macro-cellular (UMa) environment, we character-
ize the wideband pathloss, shadow fading, Root-Mean-Square (RMS) delay spreads, coherence
bandwidth and Ricean factor for different measurement routes in line-of-sight (LOS) and non-
line-of-sight (NLOS) scenarios; and for urban micro-cellular (UMi) environments, we study
these parameters as well as their dependence on the BS height. By dividing the wideband chan-
nel transfer function into subbands of 1 GHz each, we study the pathloss exponent, shadow
fading, Ricean factor, RMS delay spreads and coherence bandwidth dependence on the fre-
quency in UMa and UMi LOS/NLOS environments.
Our Contributions
For a UMa environment, we provide the pathloss exponents, shadow fading, and RMS
delay spreads for the wideband channel, for different measurement routes in LOS and
NLOS environments.
30
For a UMi environment, we investigate the dependency of the pathloss exponent, shadow
fading and RMS delay spreads on the BS height.
By dividing the wideband channel frequency response into several non-overlapping sub-
bands of 1 GHz bandwidth each, we study the variation of the large scale channel param-
eters with the frequency over the 3–18 GHz band in the LOS and NLOS environments.
In particular,
– We provide the path loss exponents for different subbands in the UMa and UMi
LOS/NLOS environments.
– We study the shadow fading variation with frequency. We investigate the correlation
between the shadow fading in different subbands.
– We fit the RMS delay spreads, Ricean factor and coherence bandwidth in each sub-
band using log-normal distribution and study the variation of the parameters of the
distribution with the frequency. By pre-emphasis at the transmitter, we ensure (ap-
proximately) constant SNR over the measured frequency range, thus eliminating the
dynamic range effect from the frequency dependence of the delay spread.
Related Publications
V . Kristem, C. U. Bas, R. Wang, and A. F. Molisch, ”Outdoor Wideband Channel Mea-
surements and Modeling in the 3-18 GHz Band,” Submitted to IEEE Trans. on Wireless
Communications.
V . Kristem, C. U. Bas, R. Wang, and A. F. Molisch, ”Outdoor Macro-Cellular Channel
Measurements and Modeling in the 3-18 GHz Band,” Submitted to IEEE Globecom 2017.
C. U. Bas, V . Kristem, R. Wang, and A. F. Molisch, ” Real-time Ultra-Wideband fre-
quency sweeping channel sounder for 3-18 GHz,” Submitted to IEEE Milcom 2017.
31
My contributions in this work include measurement planning, conducting the measurements,
post-processing of data, and channel characterization in different propagation environments.
1.4.2 Stochastic Double directional Channel modeling in Warehouse En-
vironment
This work describes an extensive propagation channel measurement campaign in a warehouse
environment for Line-of-sight (LOS) and Non-Line-of-sight (NLOS) scenarios. The measure-
ment setup employs a vector network analyzer (VNA) operating in the 28 GHz frequency band
combined with an 8 x 8 virtual multiple-input-multiple-output (MIMO) antenna array. We
develop a comprehensive statistical propagation channel model based on high-resolution ex-
traction of multipath components (MPCs), and subsequent spatio-temporal clustering analysis.
The intra-cluster Direction of Departure (DoD), Direction of Arrival (DoA) and the Time of
Arrival (ToA) are independent, both for the LOS and NLOS scenarios. The intra-cluster DoD
and DoA can be approximated by the Laplace distribution, and the intra-cluster ToA approx-
imated by an exponential mixture distribution. The inter-cluster analysis however, shows a
dependency between the cluster DoD, DoA and ToA. To capture this dependency, we sepa-
rately model the clusters caused by single and multiple bounce scattering along the aisles in the
warehouse. The inter-cluster DoD distribution follows a Laplace distribution, while the cluster
DoA conditioned on the DoD is approximated by a Gaussian mixture distribution. The model
was validated using the capacity and delay-spread values. The developed model can be used for
realistic performance evaluations of UWB systems in warehouse environments.
Our Contributions
We report the details of a MIMO channel measurement campaign performed in a ware-
house environment for a LOS and NLOS scenario in the 2–8 GHz frequency range.
We extract the large scale propagation channel parameters such as distance-dependent
32
pathloss exponent (n), frequency-dependent pathloss coefficient () and shadowing vari-
ance (
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.
In light of the observation that MPCs typically can be grouped into clusters corresponding
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.
Related Publications
S. Sangodoyin, V . Kristem, A. F. Molisch, R. He, F. Tufvesson, and H. Behairy, ”Sta-
tistical Modeling of Ultrawideband MIMO Propagation Channel in a Warehouse Envi-
ronment,” IEEE Transactions on Antennas and Propagation, vol. 64, pp. 740751, Feb
2016.
S. Sangodoyin, R. He, A. F. Molisch, V . Kristem, F. Tufvesson, ”Ultrawideband mimo
channel measurements and modeling in a warehouse environment,” IEEE International
Conference on Communications (ICC), London, Jun. 2015.
My contributions in this work include MPC parameter extraction from transfer function mea-
surements, clustering techniques investigation, and developing the stochastic inter-cluster and
intra-cluster propagation models and their validation.
33
1.4.3 Ultrawideband Ranging with interference mitigation
Roundtrip Time-of-arrival (ToA) measurements employing ultra-wideband (UWB) signals can
provide high-precision ranging information. However, the accuracy is degraded by multiuser
interference (MUI), in particular in the presence of multipath propagation. While the processing
gain of timehopping impulse radio (TH-IR) can be used to suppress the MUI, this is often insuf-
ficient. We propose instead a nonlinear processing scheme of TH-IR that effectively suppresses
MUI without requiring knowledge of the time-hopping sequences of the interfering users. The
principle is that multipath components (MPCs) of interferers do not align closely, for the ma-
jority of transmission frames, with the MPCs of the desired signal. Through a judicious choice
of algorithm parameters we show that our algorithm is superior to existing (realizable) thresh-
olding and median filter algorithms, and in some cases can even beat genie-aided thresholding
algorithms. The performance is robust to both strength and number of the interferers. The
results are validated with both standardized 802.15.4a channel models and measured outdoor
UWB channels.
Our Contributions
We propose a novel coherent ranging algorithm that suppresses the MUI without having
to know the TH sequences of the interfering users. To the best of our knowledge, this is
the first work in the literature that considers MUI suppression for coherent UWB ranging,
without having to know the TH sequences of the interfering users.
By modeling the MPC delays as Poisson process, we derive the bounds on the false alarm
probability from the interference MPCs and detection probability of signal MPCs as a
function of algorithm parameters.
We provide a judicious choice of parameters and using the analytical expressions derived
earlier, we show that the proposed algorithm effectively suppresses the strong interference
34
MPCs.
Using the IEEE 802.15.4a channel models, we show that the proposed ranging scheme is
robust to the strength of interference and the number of interfering users in the system,
and is much better than the thresholding schemes and the non-linear filtering schemes
considered in the literature.
We also carried out an urban outdoor channel measurement campaign with UWB channel
sounder and tested the performance of our algorithm in both LOS and NLOS measured
scenarios. We again show that the proposed ranging scheme is robust to the interference
and the performance is much better than the thresholding schemes, and more so in NLOS
conditions.
Related Publications
V . Kristem, A. F. Molisch, S. Niranjayan, S. Sangodoyin, ”Coherent UWB Ranging in
the presence of Multiuser Interference,” IEEE Trans. on Wireless Communications, V ol.
13, Aug. 2014, pp. 4424-4439.
V . Kristem, S. Niranjayan, S. Sangodoyin, A. F. Molisch, ”Experimental Determination
of UWB Ranging Errors in an Outdoor Environment,” IEEE International Conference on
Communications (ICC), Sydney, Australia, Jun. 2014.
My contributions in this work include coming up with the problem statement, mathematical
modeling and analysis, performance simulations with synthetic and measurement data.
1.4.4 Jammer Sensing and Performance Analysis of MC-CDMA Systems
in the Presence of Wideband Jammer
Jamming, either intentional or unintentional, is a big, and increasingly prevalent, problem for
many wireless communications systems. A well-known countermeasure is the application of
35
spread spectrum techniques that distribute the information over a bandwidth larger than that of
the jammer; an especially attractive spreading technique is Multi-Carrier Code Division Mul-
tiple Access (MC-CDMA), due to its flexibility to shape transmit spectra, resilience to inter-
symbol interference, and ease of implementation. Such spreading needs to be combined with
spectral notching at the receiver RF frontend, to avoid saturation of the low-noise amplifiers.
Such notching in turn requires the receiver to sense the band over which the jammer is operat-
ing. In this work, we consider a MC-CDMA transceiver that is being jammed by a wideband
non-stationary jammer. For a Rayleigh fading channel, we derive the symbol error rate for the
case that the jammer state information is available at the receiver. We derive the Maximum-
Likelihood based and Log-Likelihood Ratio based JSI estimators for both the case where chan-
nel state information is available during jammer sensing and when it is not. The performance
of various jammer estimation schemes is studied using Monte Carlo simulations and with the
channel impulse responses collected from the wireless propagation measurements conducted in
the 10-12 GHz band.
Our Contributions
We derive the analytical expressions for the SER in a Rayleigh fading channel, for the
case when the receiver has a full knowledge of the JSI (the start frequency, bandwidth
and the covariance matrix) and for the case where receiver only has partial JSI (only the
start frequency and the bandwidth). They act as a reference to compare the JSI estimation
schemes. We further quantify the performance gap between the two cases and study the
impact of different spreading sequences on the performance.
We derive the ML based and LLR based JSI estimators for the case where CSI is available
during jammer sensing and for the case where CSI is not available for JSI estimation.
We compare the performance of various proposed JSI estimators, and their impact on
the data decoding. Performance is characterized both with synthetic channels and with
36
channel realizations obtained from the propagation channel measurements.
We investigate the impact of mismatch in the jammer model, on the performance of the
JSI estimators. The JSI estimators were derived for a Gaussian wideband jammer. Using
simulations, we study the performance of these estimators for a non-contiguous jammer
and for the case where the amplitude of jammer interference generated using uniform
distribution.
Related Publications
V . Kristem, A. F. Molisch, Louis Christen ”Jammer sensing and Performance analysis
of MC-CDMA systems in the presence of wideband tone Jammer,” Submitted to IEEE
Trans. on Wireless Communications.
My contributions in this work include problem formulaion, mathematical modeling and anal-
ysis, performance simulations with synthetic and measurement data.
1.5 Other Publications
Below listed are the publications, that are not related to the work listed in this report, but related
to the work done while at USC.
V . Kristem, S. Sangodoyin, C. U. Bas, M. Kaske, J. Lee, C. Schneider, G. Sommerkorn, J.
Zhang, R. Thoma, A. F. Molisch, ” Channel measurements and modeling for 3D-MIMO
outdoor to indoor propagation,” IEEE Trans. on Wireless Communications, 2017.
V . Kristem, N. B. Mehta, A. F. Molisch, ”Training for Antenna Selection in Time-varying
Channels: Optimal Selection, Energy Allocation, and Energy Efficiency Evaluation,”
IEEE Trans. on Communications, 61, 2295-2305 (2013).
37
V . Kristem, S. Sangodoyin, C. U. Bas, M. Kaske, J. Lee, C. Schneider, G. Sommerkorn,
J. Zhang, R. Thoma, A. F. Molisch, ”3D MIMO Outdoor to Indoor Macro/Micro-Cellular
Channel Measurements and Modeling,” IEEE Globecomm, San Diego, Dec. 2015.
V . Kristem, N. B. Mehta, A. F. Molisch, ”Energy-efficient training for antenna selec-
tion in time-varying channels, Asilomar Conference on Signals, Systems, and Computers,
Pacific Grove, CA, USA, Nov. 2011.
S. Sangodoyin, V . Kristem, C. U. Bas, M. Kaske, J. Lee, C. Schneider, G. Sommerkorn,
J. Zhang, R. Thoma, A. F. Molisch, ”Cluster characterization of 3D MIMO propagation
channel in an urban macro-cellular environment,” Submitted to IEEE Trans. on Wireless
Communications.
S. Sangodoyin, V . Kristem, C. U. Bas, M. Kaske, J. Lee, C. Schneider, G. Sommerkorn,
J. Zhang, R. Thoma, A. F. Molisch, ” Cluster-based Analysis of 3D MIMO Channel
Measurement in an Urban Environment,” IEEE Milcom, Tampa, Oct. 2015.
1.6 Organization of the Report
I now elaborate on each of these works in the subsequent chapters.
38
Chapter 2
Outdoor Wideband Channel
Measurements and Modeling in the 3-18
GHz Band
With the increasing number of wireless users and applications, mobile data traffic is expected
to grow exponentially over the next few years. It is anticipated that the fifth generation (5G)
wireless systems should be able to support data traffic 1000 times larger than the current, fourth
generation (4G), systems [13]. While the majority of the current fourth generation (4G) wireless
systems operate at frequencies below 6 GHz (henceforth called microwave in this chapter),
the high data needs motivate expansion to frequency bands above 6 GHz in 5G systems, as
they provide large bandwidth [14]. Furthermore, future systems might either adaptively select
frequency bands over a wide range, or perform carrier aggregation between the different bands.
The performance of any communication system depends on the propagation channel in
which it is deployed. Hence it is important to characterize the channel to get a more accu-
rate assessment of the performance of communication systems [130]. While the wireless signal
propagation characteristics for the sub 6 GHz frequencies have been well investigated in the
literature, and the majority of the channel measurements work for 5G systems have focused on
frequency bands of 20 GHz and above, only few papers have studied the intermediate frequency
bands. The propagation characteristics of ultrawideband systems, operating in 3–10 GHz have
39
been well studied in the literature [16, 17], but mostly for indoor channels. Ref. [18, 19] char-
acterizes the wireless propagation channel at 10 GHz in an urban micro cellular environment.
Ref. [20] characterizes the wireless propagation channel at 11 GHz in outdoor and indoor en-
vironments. Ref. [21] provides the results from indoor measurement campaign performed at
15 GHz. Thus, the outdoor propagation channel characteristics for the frequency band 10–
20 GHz are largely unknown.
Also, only few papers have studied the frequency dependence of the channel transition be-
tween microwave frequencies to mm-wave frequencies, which is essential for understanding
multi-band and carrier aggregation systems. Ref. [22–27] compare the channel propagation
characteristics like pathloss and delay spreads at the microwave and mm-wave bands, but they
measure only a small bandwidth in each band. Also, the majority of these works use different
measurement setups for microwave and mm-wave measurements, thereby making the com-
parison more difficult: For instance, [22] measures frequency bands 10 and 30 GHz; [23, 24]
measures frequency bands of 2-4 GHz, 14-16 GHz and 28-30 GHz; [25] measures frequency
bands 2.9, 18 and 28 GHz in macro cellular environment. They all use different channel sounder
setups for different subband measurements. [26] measures frequency bands 6.5, 10.5, 15 and
19 GHz in an indoor environment using the same setup, but the bandwidth is limited to 1 GHz.
Moreover, it uses horn antennas with limited azimuth opening and a small elevation beamwidth,
thereby limiting the number of interacting scatterers in the environment. The situation is even
more complicated for the dependence of the RMS delay spread on the carrier frequency. It
has been often conjectured that the delay spread decreases with increasing carrier frequency,
but few experimental proofs have been provided. The situation is compounded by the fact that
computation of the delay spread strongly depends on the dynamic range of the receiver. The
different measurement setups, and the different pathloss at the various carrier frequencies, make
such a comparison very difficult. Yet, this delay spread dependence is critical for the design of
5G cellular systems, as it determines the length of the cyclic prefix, and thus the spectral ef-
40
ficiency of OFDM systems. To the best of our knowledge, there are no continuous wideband
measurements that covers both microwave and mm-wave bands. Yet it would be essential since
wireless propagation characteristics can be considerably different for microwave and mm-wave
bands as the physical propagation mechanisms like reflection, diffraction and scattering varies
as the wavelength changes from cm to mm.
We partially fill these gaps by performing propagation channel measurements over the con-
tinuous frequency band from 3 to 18 GHz in an urban macro-cellular (UMa) and urban micro-
cellular (UMi) environments, using the same channel sounder setup. For a UMa case, measure-
ments were taken along different streets in line-of-sight (LOS) and non-line-of-sight (NLOS)
environments. For a UMi case, LOS and NLOS measurements were taken for different BS
heights. We report the pathloss, shadow fading, root-mean-square (RMS) delay spreads, Ricean
factor and coherence bandwidth results for different propagation scenarios and study the depen-
dency of these parameters on the frequency in the 3–18 GHz band.
The key contributions of this chapter are summarized below:
For a UMa environment, we provide the pathloss exponents, shadow fading, and RMS
delay spreads for the wideband channel, for different measurement routes in LOS and
NLOS environments.
For a UMi environment, we investigate the dependency of the pathloss exponent, shadow
fading and RMS delay spreads on the BS height.
By dividing the wideband channel frequency response into several non-overlapping sub-
bands of 1 GHz bandwidth each, we study the variation of the large scale channel param-
eters with the frequency over the 3–18 GHz band in the LOS and NLOS environments.
In particular,
– We provide the path loss exponents for different subbands in the UMa and UMi
LOS/NLOS environments.
41
– We study the shadow fading variation with frequency. We investigate the correlation
between the shadow fading in different subbands.
– We fit the RMS delay spreads, Ricean factor and coherence bandwidth in each sub-
band using log-normal distribution and study the variation of the parameters of the
distribution with the frequency. By pre-emphasis at the transmitter, we ensure (ap-
proximately) constant SNR over the measured frequency range, thus eliminating the
dynamic range effect from the frequency dependence of the delay spread.
These large scale channel parameters play an important role in the Orthogonal Frequency
Division Multiplexing (OFDM) system design [130], which is a key technology used in 4G and
5G communication systems. As a matter of fact, this work was partially motivated by intense
discussions in 3GPP about the frequency dependence of the delay spread.
The remainder of the chapter is organized the following way: The channel measurement
setup is described in Sec. 2.1.1. The measurement environment is described in Sec. 2.1.2. The
data post-processing is presented in Sec. 2.2: Wideband processing in Sec. 2.2.3 and subband
processing in Sec. 2.2.4. The wideband pathloss and delay spread results for different measure-
ment scenarios is presented in Sec. 2.3.1 and Sec. 2.3.2 respectively. Sec. 2.3.3 to 2.3.7 presents
the results on frequency dependency of various channel parameters: Pathloss in Sec. 2.3.3,
Shadow fading in Sec. 2.3.4, RMS delay spreads in Sec. 2.3.5, Ricean factor in Sec. 2.3.6,
and Coherence bandwidth in Sec. 2.3.7. A summary and conclusions wrap up the chapter in
Sec. 2.4.
2.1 Measurement Setup and Environment
2.1.1 Measurement Setup
Our measurement setup is based on a real time, frequency-hopped, multi-band channel sounder.
The transmitter (Tx) side comprises of an arbitrary waveform generator (AWG) that generates a
42
Figure 2.1: Transmitter and Receiver setups.
multitone baseband signal in the 0-1 GHz band with a sampling rate of 1.25 GSps. A subcarrier
spacing of 0.5 MHz was used, which corresponds to a measurable excess path length of 600 m.
Using an IQ mixer, the baseband signal is upconverted to radio frequency (RF) range, centered
around the carrier frequency. The RF signal is then amplified using a power amplifier and
transmitted from a biconical antenna.
At the receiver (Rx) end, the signal received by a biconical antenna is passed through a high
pass filter (with cutoff frequency at 3 GHz) and low-noise amplifier (LNA). This is done so as
to limit the interference from ongoing WiFi and cellular transmissions and to avoid the receiver
front end going into saturation. The IQ mixer downconverts the RF signal into baseband, which
is then digitized using an analog-to-digital converter (ADC). The transmitter and the receiver se-
tups can be seen in Fig. 2.1. The biconical antennas are isotropic in azimuth and their elevation
3 dB beamwidth varies from 45 to 65 deg in the 3–18 GHz band.
Using a combination of frequency synthesizer and frequency reference (one each at the Tx
and Rx), the carrier frequency was varied from 3 GHz to 18 GHz, in steps of 500 MHz. The
carrier frequency at the Tx and Rx are switched in a synchronized way using Labview scripts
43
running on real-time controllers. At any given time, our setup measures the channel frequency
response in a 1 GHz subband, centered around the carrier frequency and then switches to the
next 1 GHz subband. The successive subband measurements have an overlap of 500 MHz,
which is used to correct for the random phase shift in the channel transfer function measure-
ments, across the subbands. The phase corrected subband measurements are stitched together
to get the wideband channel frequency response in the 3–18 GHz band. The transmit signal is
pre-distorted such that the transmit signal-to-noise ratio (SNR) is the same across all subbands.
A more detailed description of the channel sounder setup can be found in [28].
The setup takes 100s to measure the frequency response in each 1 GHz subband. It takes
100s for the setup to switch to the next carrier frequency. Thus, it takes 6 ms to complete the
channel measurement in the 3-18 GHz band. We take five such snapshots of the wideband mea-
surements, which is used for noise averaging. The time gap between two successive wideband
measurement snapshots is 10 ms.
2.1.2 Measurement Environment
The measurements were taken near the Electrical Engineering Building (EEB) and the Parking
Structure X (PSX) on the USC campus. The density and height of buildings in this area is
typical for urban environments. For the EEB location, the transmitter was placed at on the
rooftop of the building (of height 29 m) and the receiver was placed on the street, thereby
representing a typical macro-cellular setup. For the PSX measurements, the transmitter was
placed at on different levels of the building (of height 12.5 m) and the receiver on the street,
thereby representing a typical micro-cellular setup.
UMa measurements: The transmitter was placed at two different locations on the rooftop of
EEB and the receiver setup was placed on a cart and moved along McClintock and 37th Street.
The measurement routes along with the Tx locations are shown in Fig. 2.2 and 2.3, respectively,
for the LOS and NLOS measurements. The lamp posts, parking meters, cars parked along the
44
Figure 2.2: LOS measurement locations.
sidewalks, and the buildings on either side of the measurement routes provide a rich scattering
environment. The Tx antenna was effectively 31 m above the ground and the Rx antenna was
1.5 m above the ground. For the LOS measurements, first the Tx was placed at the corner of
the rooftop and the Rx was moved along the perpendicular streets (route 1 and 2); the Tx was
then placed at the center of the building and the Rx moved along 37th street (route 3 and 4),
thereby generating 4 realizations of the LOS measurement routes. For the measurement route
1, the receiver was moved along the center of the street and there was clear LOS for all the
measurement locations along the route. For measurement routes 2, 3 and 4, the receiver was
moved along the sidewalk covered with trees and occasionally the LOS path was obstructed by
foliage.
A similar procedure was repeated for the NLOS measurements. The Tx was first placed at
the corner and the Rx was moved along the perpendicular streets (route 1 and 2); the Tx was
then placed at the center and the RX was moved along the McClintock street (route 3), thereby
generating 3 realizations of the NLOS measurement routes.
UMi measurements: The Tx was placed on three different levels of the parking structure,
very close to the outside wall; since the structure has large openings to the exterior, the TX
antenna was essentially at a location where a wall-mounted microcell antenna would be on a
45
Figure 2.3: NLOS measurement locations.
regular building. The Rx was moved along one LOS route and one NLOS route as shown in
Fig. 2.4. The Tx antenna was effectively 8.5 m, 11.5 m and 14 m for the BS on the level 1, 2,
and 3 respectively. The Rx antenna was 1.5 m above the ground.
2.2 Data processing
For each measurement route, the receiver cart was moved continuously along the street, roughly
at a speed of 0:2 m/s. Measurements were taken every 1 s and in each measurement, our setup
records five snapshots of the channel impulse response, with a time gap of 10 ms between
successive snapshots.
2.2.1 Noise averaging and Interference filtering
The multiple snapshots can be used for noise averaging and interference suppression. Since the
first and the last (fifth) snapshots have time gap of 40 ms, which corresponds to 0:8 cm spacing;
equivalent to 0:08 spacing at 3 GHz carrier frequency and 0:48 at 18 GHz carrier frequency.
46
Figure 2.4: LOS and NLOS routes for the PSX measurements.
Thus, the multiple snapshots will experience similar small scale fading and hence can be used
for noise averaging.
The multiple snapshots can also be used to suppress the bursty WiFi interference. Occasion-
ally, for some of the measurement routes, we noticed interference from the WiFi access points
operating in the 5 GHz band. Since the interference might be present only in a subset of the
snapshots, using a pair wise correlation of the snapshot channel impulse responses, followed by
median filtering, we can discard the snapshots corrupted by interference [29].
1
The remaining
snapshots are used for noise averaging.
1
This approach does not work if all the snapshots are corrupted by interference. In such a case, we use the
power variations in the subbands to detect and discard the measurements with interference. We divide the wideband
channel frequency response into subbands of 300 MHz and look at the power variations across the subbands. If
there is a large jump in the received power in adjacent subbands (in excess of 10 dB), it is probably because of the
interference and hence we discard such measurements for further processing.
47
2.2.2 Small scale fading averaging
Since the measurements were taken every 1 s along the route, this corresponds to 0:2 m spacing
between the successive measurements; equivalent to 2 spacing at 3 GHz carrier frequency and
12 at 18 GHz carrier frequency. Thus, the successive measurements along the route will expe-
rience independent small scale fading and hence can be used for spatial averaging to compute
the large scale channel parameters like pathloss, delay spreads, coherence bandwidth, etc.
2.2.3 Wideband Processing
APDP computation
LetfH
T
(f
k
);k = 1N
F
g be the wideband channel frequency response
2
measured at time T
seconds (time is measured relative to the first measurement in that route). For our measurement
setup, f
1
= 3 GHz, f = f
2
f
1
= 0:5 MHz and N
F
= 30000. The channel frequency
response is transformed to delay domain by taking an IFFT with a Hann window to suppress the
sidelobes. Leth
T
() denote the resulting channel impulse response. The magnitude squared
of the impulse response gives the instantaneous power delay profile,PDP
T
(). The influence
of the small scale fading is removed by averaging the consecutive instantaneous PDP measure-
ments within a window, to get the averaged power delay profile (APDP). Here the averaging
window is defined as the set of consecutive measurements where the multipath component
(MPC) path powers are similar, but the phases of the MPCs change across measurements. This
is characterized using the correlation between the instantaneous PDP and the variation in the
overall received power. To put it mathematically,
APDP () =
1
N
k+N
X
T=k
jh
T
()j
2
(2.1)
where N , min (N
1
;N
2
). Before averaging, the impulse responses are time adjusted such
that the strongest MPC are time-aligned. Due to the extremely high delay resolution, even
2
We treat the antennas as a part of the channel, as the antenna response cannot be clearly separated from the
overall response. Calibrated antenna arrays at Tx and Rx would be required to eliminate the impact of antennas.
48
Figure 2.5: Sample APDP plots for measurement taken along different routes in the LOS and
NLOS environments.
movement over short distances can lead to noticeable delay changes. Here N
1
denotes the
number of consecutive measurements over which the PDP’s are correlated andN
2
denotes the
number of consecutive measurements whose received power does not vary by more than 3 dB.
N
1
= minfn :Corr (PDP
k
();PDP
k+n
())< 0:5g (2.2)
N
2
= minfn :jP
k
P
k+n
j> 3dBg (2.3)
whereCorr(:;:) denotes the correlation coefficient andP
T
= 10 log
10

P
N
F
k=1
jH
T
(f
k
)j
2

de-
notes the power in the channel frequency response.
To reduce the effects of noise, a noise-thresholding filter is applied to the APDP, in which
the APDP samples whose magnitude is below a threshold is set to zero. The threshold is set to
be 6 dB above the noise floor. The noise floor is computed from the noise-only region of the
APDP (samples before the first MPC). This APDP is used to compute the RMS delay spread
and the coherence bandwidth of the channel.
49
Fig. 2.5 plots the sample APDP for the measurements taken along Routes 1 and 2 in LOS
and NLOS environments. For the LOS measurement routes, we typically observed 3-5 clusters,
depending on the measurement route. The maximum number of clusters was observed for
measurement route 1. For this route, apart from the LOS cluster, we observed far away clusters
resulting because of reflection from building P, located at the end of the measurement route.
For the NLOS measurement routes, there were typically 1-2 clusters. We conjecture that these
might be due to “merging” of different clusters, and resolution in directional domains would
give a higher number.
Wideband Pathloss and shadow fading characterization
The pathloss is obtained by averaging the absolute magnitude squared of the channel frequency
response over the small scale fading realizations and accumulating the power in the subcarriers.
We use the commonly used model
PL(d) =PL(d
0
) 10n log
10

d
d
0

+S

(2.4)
where PL(d) denotes the pathloss (measured in dB) at Tx-Rx separation distance d; d
0
is a
reference distance and n is referred as a pathloss exponent; S

is a shadow fading term that
captures the deviation of the measured pathloss from the linear model. This is typically modeled
using a zero-mean normal distribution with a standard deviation.
Wideband Delay spread
The RMS delay spreads are computed as the second central moment of the APDP [130].

RMS
=
s
R
1
0
( )
2
APDP ()d
R
1
0
APDP ()d
(2.5)
where is the mean delay, which is given by
=
R
1
0
APDP ()d
R
1
0
APDP ()d
(2.6)
50
2.2.4 Subband Processing
We now study the frequency dependency of the large scale channel parameters in the 3–18 GHz
band. We divide the measured wideband channel frequency response into 15 non-overlapping
subbands (3-4 GHz, 4-5 GHz, , 17-18 GHz) with each subband bandwidth equal to 1 GHz.
The APDP processing in Sec. 2.2 is repeated for each of the subbands and the pathloss expo-
nents, shadow fading and RMS delay spreads are independently computed for each of these
subbands.
3
Ricean factor
The Ricean factor is defined as the ratio of the power in the dominant MPC to all other MPCs.
It is an important parameter in characterizing the propagation channel in the LOS environ-
ments. For narrowband channel, it is computed using the classical method of moments [30].
This approach has been extended to wideband channels, by interpreting the signals on different
subcarriers as different narrowband fading realizations [31]. Thus, the Ricean factor in each
subband is computed as follows:
G
a
=
1
n
n
X
i=1
jH
i
j
2
(2.7)
G
v
=
1
n 1

n
X
i=1
jH
i
j
4
nG
2
a
!
(2.8)
K =
p
G
2
a
G
v
G
a

p
G
2
a
G
v
(2.9)
Since the number of spatial small scale fading realizations ofH in each averaging window
is small (typically 4 to 10), we pick the realizations ofH that are spaced apart by a coherence
bandwidth and combine them all into single bin for Ricean factor computation.
4
Note that pick-
3
For a fair comparison, we make sure that the number of realizations used for small scale fading averaging is
the same across all subbands. In theory, the value ofN can be different for different subbands. We computeN
for each of the 15 subbands and pick the minimum value across the subbands. Also, the APDP in each subband is
passed through a bandpass filter, so as to avoid any impact of different noise floor estimates in the subbands.
4
Based on the results in Sec. 2.3.7, the typical coherence bandwidth values are 200 MHz. Since each subband
51
ing uncorrelated values of fading realizations is important to avoid bias in the estimation of the
Rice factor [31].
Coherence Bandwidth
The channel coherence bandwidth for each subband is computed using the frequency correla-
tion function, which is obtained by taking the Fourier transform of the corresponding subband
APDP. The 3 dB coherence bandwidth is the smallest frequency at which the magnitude of the
correlation function becomes less than half of the maximum value.
BW
0:5
= min

f :

S (f)
S (0)

< 0:5

(2.10)
2.3 Measurement Results
2.3.1 Wideband Pathloss and Shadow fading
Fig. 2.6 plots the measured pathloss values along different measurement routes in the UMa
LOS/NLOS environments. In the LOS environment, the pathloss exponent was close to 2 for
the receiver in route 1, 2 and 4, and it was observed to be less than 2 for the receiver in route
3, indicating strong waveguiding. In the NLOS environment, the pathloss exponents were ob-
served to be significantly different for the Rx along different measurement routes (varies from
2.71 to 4.34), which is consistent with other recent results; compare [32], which also provides a
discussion of the reasons. The standard deviation of the shadow fading for various measurement
scenarios in the UMa environment is listed in Table 2.1. As expected, the shadowing values are
significantly higher for the NLOS environment.
Fig. 2.7 plots the measured pathloss values for different BS heights in the UMi LOS/NLOS
environments. In the LOS environment, there is no clear pattern in the pathloss exponent varia-
tion with the BS height. But in the NLOS environment, the pathloss exponents seem to increase
is 1 GHz wide, this approach increases the sample size by a factor of 5.
52
Figure 2.6: Distance dependent pathloss in the LOS and NLOS environments for the UMa
measurements.
Table 2.1: Standard deviation of shadow fading in the UMa environment.
Route 1 Route 2 Route 3 Route 4
LOS Environment 0.27 0.17 0.62 0.55
NLOS Environment 1.89 1.02 1.43 -
53
Figure 2.7: Distance dependent pathloss in the LOS and NLOS environments for the UMi
measurements.
Table 2.2: Standard deviation of shadow fading in the UMi environment.
Level 1 Level 2 Level 3
LOS Environment 1.27 1.10 0.61
NLOS Environment 0.83 1.03 1.90
as the BS height increases and the pathloss exponents are smaller than the ones in the UMa
environment. The standard deviation of the shadow fading for different BS heights in the UMi
environment is listed in Table 2.2. In the LOS environment, the shadowing values seem to de-
crease as the BS height increases. The shadowing increased with the BS height in the NLOS
environment.
2.3.2 Wideband RMS delay spread
Fig. 2.8 plots the CDF of the measured wideband RMS delay spread (dB ns values) for different
measurement routes in the LOS/NLOS UMa environments. The delay spreads are in the range
of 20–60 ns in the LOS environment and 60–300 ns in the NLOS environment. It can be seen
54
Figure 2.8: CDF of RMS delay spreads for different measurement routes in the UMa environ-
ment.
that the log values of the delay spreads fit well with a Normal distribution. The parameters of
the distribution (mean and standard deviation) are given in the legend. The CDF curves are
significantly different for different measurement routes both in LOS and NLOS environments,
except that for route 2 and 3 in the LOS environment, which are in the same street with only the
Tx location different.
Fig. 2.9 compares the CDF of the measured wideband RMS delay spread (dB values) for
different BS heights in the LOS/NLOS UMi environments. The delay spreads are in the range
of 25–50 ns in the LOS environment and 30–140 ns in the NLOS environment. While the delay
spreads are comparable to the UMa case in the LOS environment, they are significantly smaller
when compared to UMa case in the NLOS environment. This is again intuitive, as a UMi BS
cannot effectively illuminate far scatterers, so that long-delayed echoes carry less power than
in the UMa case. It can be seen that the log values of the delay spreads fit reasonably well to a
Normal distribution.
5
While the delay spreads did not change much with the BS height in the
5
While the Normal distribution is not so good fit for couple of the measurement routes in the NLOS scenario,
55
Figure 2.9: CDF of the RMS delay spreads for different measurement routes in the UMi envi-
ronment.
LOS environment, they increased with increasing BS height in the NLOS environment.
2.3.3 Subband Pathloss characterization
Fig. 2.10 plots the pathloss exponents as a function of the subband center frequency for the
UMa LOS environment. It can be seen that there are large variation in the pathloss exponents
over the subbands, which are more or less consistent across different measurement routes–
pathloss exponents are close to 2 in the 3–5 GHz band; decreases to 1 in the 5–8 GHz band;
vary between 2 and 3 in the 8-13 GHz band; and between 1 and 2 in the 13–18 GHz band.
We conjecture that a part of these variations were caused by the antennas. Specifically, while
the antennas are omni-directional in azimuth at all frequencies, and the maximum antenna gain
(in the horizontal plane) does not vary appreciably, the shape of the antenna pattern, including
the location of nulls and sidelobes, does vary with frequency. The elevation and azimuth gain
because of small sample size and for the sake of comparison with other routes, we still fit the data with the Normal
distribution.
56
Figure 2.10: Pathloss exponents as a function of the frequency for different measurement routes
in the UMa LOS environment.
patterns of the antennas, for different subbands, has been measured inside the anechoic chamber
at USC.
As the Rx moves along the street, the elevation angle corresponding to geometric LOS be-
tween the Tx and Rx decreases from 45 deg to 5 deg. Since the antennas are not isotropic in the
elevation domain as outlined above, the effective gain of the Tx and the Rx antennas changes
with the elevation angle, and equivalently with the Tx-Rx separation distance. Thus the antenna
response itself has an effective distance dependence, which is different for different frequency
bands as shown in Fig. 2.10, the frequency dependence induced on the pathloss coefficient by
the antenna response (black crosses). Note that while the general trend in the pathloss exponent
variation with frequency for the measured channel, follows the antenna response, the magni-
tude of the variation is increased for the measured channel, thereby indicating different pathloss
exponents for different subbands for the propagation channel alone.
Fig. 2.11 plots the pathloss exponents as a function of the subband center frequency for the
UMa NLOS environment. There is large variation in the pathloss exponents over the subbands
and it is different for different measurement routes, and also different from the antenna response.
57
Figure 2.11: Pathloss exponents as a function of the frequency for different measurement routes
in the UMa NLOS environment.
Figure 2.12: Pathloss exponents as a function of the frequency for different BS heights in the
UMi LOS/NLOS environments.
58
Figure 2.13: Shadow fading as a function of the frequency for different measurement routes in
the UMa LOS/NLOS environments.
In the NLOS environment, there is no dominant LOS component; MPCs incident at different
elevation angles will have comparable power and hence the impact of antenna response is more
likely to be averaged out.
Fig. 2.12 plots the pathloss exponents as a function of the subband center frequency for
the UMi LOS and NLOS environments. The observations are similar as in UMa case. For
the LOS environment, the pathloss exponents vary significantly across the subbands and it can
be explained by the variation in the antenna response. The pathloss exponents are similar for
different BS heights in the majority of the subbands. In the NLOS environment, it can be seen
that the subband pathloss exponents roughly increase with frequency and with increasing BS
height, which is in consistent with our earlier observations on the wideband pathloss exponents
variation with the BS height.
59
Figure 2.14: Shadow fading as a function of the frequency for different BS heights in the UMi
LOS/NLOS environments.
2.3.4 Subband shadow fading characterization
Fig. 2.13 and 2.14 respectively plot the shadow fading as a function of the subband center fre-
quency in the UMa and UMi environments. It can be seen that for both the UMa and UMi
scenarios, the shadow fading seems to increase with the frequency. We also investigate the
correlation of the shadow fading across different subbands. For this we combine the shadow
fading realizations across different measurement routes. Fig. 2.15 captures the pairwise corre-
lation of shadow fading across different subbands in the UMa LOS and NLOS environments.
It is interesting to see that at the higher ends of the 3–18 GHz bands, shadow fading is more
correlated with the adjacent bands. This behavior is more prominent in the NLOS environment.
This behavior is especially interesting in view of multi-band systems, which often rely on un-
correlated shadowing at different subbands. As a matter of fact the current 3GPP channel model
assumes completely independent shadowing in different frequency bands, an assumption that is
not supported by our measurements.
60
Figure 2.15: Correlation matrix of the shadow fading across different subbands in the UMa
LOS/NLOS environments.
Figure 2.16: Mean and standard deviation of the dB values of the RMS delay spreads, for
different subbands, in the UMa LOS environment.
61
Figure 2.17: Mean and standard deviation of the dB values of the RMS delay spreads, for
different subbands, in the UMa NLOS environment.
2.3.5 Subband RMS delay spreads characterization
We now study the frequency dependency of the RMS delay spreads in the 3–18 GHz band.
Since the wideband RMS delay spreads were observed to be significantly different for different
measurement routes, we do not combine the subband data across different measurement routes,
but rather analyze each measurement route separately.
In the LOS environment, it was observed that the delay spreads decreased from 3 GHz to
18 GHz. For instance, in measurement route 1, the mean delay spreads decreased from 46 ns
for 3–4 GHz band to 29 ns for 17–18 GHz band.
6
To capture this frequency dependency of the
subband RMS delay spreads, we fit the log
10
(delay spreads) in each subband with a Normal
distribution and study the variation of the parameters (mean and standard deviation) of the
distribution with the subband center frequency.
6
The RMS delay spreads of the antenna response varied from 2 ns to 8 ns across different subbands and
elevation angles. Since this is significantly smaller than the channel delay spreads, we can conclude that the
variation in the delay spreads here are purely because of the propagation channel.
62
Figure 2.18: Mean and standard deviation of the dB values of the RMS delay spreads, for
different subbands, in the UMi environment.
Fig. 2.16 plots the mean and standard deviation values as a function of the subband center
frequency for the measurement routes in the UMa LOS environments. It can be seen that the
mean roughly decreases (not monotonic) with frequency and the standard deviation is non-
decreasing with frequency. This behavior is consistent across all measurement routes. This
can be explained as follows: while the power in both the LOS and non-LOS MPCs decreases
with frequency, the decrease is stronger for the non-LOS MPCs, thereby resulting in decreasing
delay spreads with increasing frequency.
Fig. 2.17 plots the parameter (mean and standard deviation) values as a function of the sub-
band center frequency for the measurement routes in UMa NLOS environments. Unlike the
LOS case, here the mean does not change much with frequency and the standard deviation is
increasing with frequency. Since there is no strong LOS component, all non-LOS MPCs might
experience similar power decay with frequency and hence the RMS delay spreads does not
change significantly with frequency.
63
Fig. 2.18 plots the mean and standard deviation values as a function of the subband center
frequency for the measurements taken with different BS heights in the UMi LOS and NLOS
environments. In the LOS environment, it can be seen that the mean slightly decreases with
the frequency. The subband delay spreads does not change with the BS height. In the NLOS
environment, the mean and the standard deviation did not change with the frequency, but the
RMS delay spreads increased with the increase in the BS height. These subband delay spread
variations with the BS height are consistent with our earlier observations on the wideband delay
spread results.
2.3.6 Subband Ricean factor characterization
We now study the Ricean-K-factor dependency on the frequency. The K-factor in each 1 GHz
subband is computed as described in Sec. 2.2.4. In each subband, we fit the measured dB values
of the Ricean-K-factor using the Normal distribution. Fig. 2.19 plots the mean and standard
deviation of K-factor as a function of frequency, for different measurement routes in the UMa
LOS environment. It can be seen that the K-factor roughly increases with frequency in all the
measurement routes. This can be explained as follows: while the power in both the LOS and
non-LOS MPCs decreases with frequency, the decrease is stronger for the non-LOS MPCs,
thereby resulting in larger K values with increasing frequency.
Similar observations hold true even in the UMi LOS environment as can be seen from
Fig. 2.20. Mean and standard deviation values are given for different BS heights. The K-
factor roughly increased with frequency. There is no significant variation in the K-factor with
the BS height.
2.3.7 Subband Coherence Bandwidth characterization
We now investigate the coherence bandwidth dependency on the subband center frequency.
While there is a common misconception that the coherence bandwidth is simply the inverse of
64
Figure 2.19: Mean and standard deviation of the Ricean factor (dB) for different subbands in
the UMa LOS environment.
Figure 2.20: Mean and standard deviation of the Ricean factor (dB) for different subbands in
the UMi LOS environment.
65
Figure 2.21: Mean and standard deviation of the Coherence bandwidth (dB values) for different
subbands in the UMa LOS environments.
the RMS delay spread, this is not true–the two quantities are characterized by an uncertainty
(inequality) relationship [33], and thus their frequency dependence might be different. We com-
pute the coherence bandwidth in each 1 GHz subband, as described in Sec. 2.2.4. We investigate
the frequency dependency by first fitting the coherence bandwidth values in each subband using
a log normal distribution and study the variation of the parameters of the distribution with the
frequency.
7
Fig. 2.21 plots the mean and standard deviation of the log
10
(BW
0:5
(MHz)) as a function of
the subband center frequency, for different measurement routes in the UMa LOS environment.
In the LOS environment, the measured coherence bandwidth values are in the 200–250 MHz
range. It can be seen that both the mean and the standard deviation does not change much with
the frequency, even though the corresponding RMS delay spreads decreased with the frequency.
7
Both Gaussian and log normal distributions were tested on the data, and the log normal distribution provided
a better fit for the data.
66
Figure 2.22: Mean and standard deviation of the Coherence bandwidth (dB values) for different
subbands in the UMa NLOS environments.
Similar behavior is observed even in the NLOS environments. Fig. 2.22 plots the mean value
of the coherence bandwidth as a function of frequency in the UMa NLOS environment.
8
It can
be seen that the coherence bandwidth values does not vary much with frequency. The coherence
bandwidth values are observed to be< 10 MHz.
Fig. 2.23 plots the coherence bandwidth variation with frequency for different BS heights
in the UMi LOS and NLOS environments. The measured coherence bandwidth values are in
the 200–300 MHz range in the LOS environment and in the 5–50 MHz range in the NLOS
environment. In the LOS environment, we plot the mean and standard deviation of the dB
values of the coherence bandwidth for different subbands. It can be seen that these parameters
roughly do not change with frequency. It is interesting to note that the coherence bandwidth
values increased as the BS height increased, even though the RMS delay spreads did not show
8
For the NLOS scenario, we do not fit the data with any distribution because of the data quantization errors. The
coherence bandwidth is an integral multiple of the subcarrier spacing (0.5 MHz) and from the measured coherence
bandwidth values, the ratio is less than 20.
67
Figure 2.23: Mean and standard deviation of the Coherence bandwidth (dB values) for different
subbands in the UMi LOS and NLOS environments.
much height dependency in the UMi LOS environments. In the NLOS environment, we plot the
mean value of the coherence bandwidth as a function of the frequency, for different BS heights.
The coherence bandwidth decreased with increasing BS height, which is consistent with our
earlier observations that the subband RMS delay spreads increased with the BS height.
2.4 Conclusions
We presented wireless propagation channel measurement results in the 3-18 GHz band, con-
ducted in an urban macro and micro-cellular environments. The wideband measurements were
taken using a frequency-hopped multi-band channel sounder. We characterized the wideband
pathloss, shadow fading and RMS delay spreads in different measurement routes for UMa
LOS/NLOS environments. It has been observed that the propagation characteristics can be
significantly different in different routes–pathloss exponents varied from 1.8 to 2 in LOS envi-
ronments and from 2.71 to 4.34 in NLOS environments; RMS delay spread was observed to be
68
log normally distributed in all routes, but the parameters of the distribution were considerably
different in different routes. We investigated the dependency of the channel parameters on the
BS height in the UMi LOS/NLOS environments. The pathloss exponents and the RMS delay
spreads increased with the BS height in NLOS environment; not much dependency is observed
in the LOS environments.
Using 1 GHz subband evaluations, we characterized the dependency of the pathloss expo-
nents, shadow fading, RMS delay spreads, Ricean factor and the coherence bandwidth on the
frequency in the 3 18 GHz band. It has been observed that the RMS delay spreads roughly
decrease with frequency in the LOS environments, but the delay spreads did not change much
with frequency in the NLOS environments; the Ricean K-factor increased with frequency; the
shadow fading increased with frequency in both LOS and NLOS environments; the coherence
bandwidth values did not change much with frequency both in LOS and NLOS environments;
the pathloss exponents varied significantly with frequency, but there was no conclusive pattern
in the variation. The shadow fading is observed to be correlated with the adjacent subbands and
more so at the higher ends of the 3–18 GHz band.
2.5 Acknowledgments
We would like to thank Adolfo Corona, Niraj V . Nayak, and Louis Christen for the discussions
and for providing the initial equipment for the test measurements.
69
Chapter 3
Stochastic Double directional Channel
modeling in Warehouse Environment
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 scientific,
military and industrial communities [34–37]. UWB signals are defined as either having more
than 20% relative bandwidth or more than 500 MHz absolute bandwidth [38] and are permitted
to operate in the 3.1–10.6 GHz frequency band by the Federal Communication Commission
(FCC) [39] in the USA, while occupying 4.2–4.8 GHz and 6–8.5 GHz band in Europe, accord-
ing 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 signals show a number of important
and attractive qualities such as, accurate position location and ranging due to its fine time res-
olution [40,41], robustness to frequency-selective fading [34,42], possibility of extremely high
data rates for communications [43], efficient use of radio spectrum through underlaying tech-
niques [44] and easier material penetration due to the presence of energy at different frequen-
cies. Ultra-wideband systems have many envisioned applications 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-based wireless sensor networks, which could eventually find use in a warehouse-like
70
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.
3.0.1 Related work
UWB systems are being designed to operate in different environments and as such channel
models have been provided for several environments ranging from indoor–residential [45–48]
to offices [49], factories or industrial [50,51] and outdoor environment [52–55]. 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 [56], however, the results provided were only for a single-input-single-output (SISO) channel
model. Ref. [57], 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 [58] to enhance a ray-tracing tool, but the measurements was only performed
for 0.8–2.5 GHz.
3.0.2 Contributions
In this chapter, we remedy this gap by investigating the propagation channel parameters in
a typical warehouse environment. The contributions of this chapter can be summarized as
follows:
We report the details of a MIMO channel measurement campaign performed in a ware-
house environment for a LOS and NLOS scenario in the 2–8 GHz frequency range.
We extract the large scale propagation channel parameters such as distance-dependent
71
pathloss exponent (n), frequency-dependent pathloss coefficient () and shadowing vari-
ance (
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.
In light of the observation that MPCs typically can be grouped into clusters corresponding
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.
3.0.3 Organization
The rest of the chapter is organized as follows. Sec. 3.1 describes the measurement environment.
Sec. 3.2 describes the measurement setup. The large scale parameter extraction is described in
Sec. 3.3. The intra-cluster and inter-cluster channel models for LOS and NLOS environments
is developed in Sec. 3.4. The developed channel models are validated in Sec. 3.5.
3.1 Measurement Environment
Measurements were performed at the University of Southern California (USC) main warehouse
facility (shown in Fig. 3.1). The warehouse structure has four floors (including the basement)
72
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. 3.1) served as structural supports for the ceiling (and could also contribute to
shadowing effects in the propagation channel). Typically, the storage areas on each floor were
often demarcated into aisles, with each aisle containing rows of two layered metallic storage
racks (labeled B in Fig. 3.1). 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. 3.2
& 3.3 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 distances
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 campaign. The measured
positions are indicated in the Figs. 3.2 & 3.3. The Tx/Rx array locations for the LOS/NLOS
measurements are indicated on the floor maps with the abbreviations: TXL1 (Tx LOS posi-
tion 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
73
Figure 3.1: USC Warehouse Facility.
figures.
3.2 Measurement Setup
A frequency domain channel sounder setup with an 8 x 8 virtual MIMO antenna array configu-
ration (see Fig. 3.4) was used to perform the measurement campaign. At the heart of the channel
sounder setup is a vector network analyzer (VNA, HP 8720ET), 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 ends) rated at 0.37 dB/ft at 8
GHz and a 30 dB low noise amplifier (LNA) , 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 3.1 and a list of all equipment
used is given in Table 3.2.
The MIMO antenna array was implemented by using a virtual antenna array at both Tx and
74
Figure 3.2: Floor map of the first floor of the warehouse.
Figure 3.3: Floor map of the basement of the warehouse.
75
Rx. An omni-directional antenna [59] was attached to a 1.78 m high support pole and then
fastened to a stepper motor controlled by linear positioner. Using a linear positioner controlled
by LabView software, the single antenna was moved to different positions, thus creating a vir-
tual 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 distorted. Due to the building struc-
ture, 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 po-
sitioner 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 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.
Table 3.1: 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
76
Table 3.2: 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
Figure 3.4: Channel sounder measurement setup in the warehouse environment.
77
3.3 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
, where m = 1:::N
T
and n = 1:::N
R
re-
spectively denote the Tx and Rx antenna positions in the array,ff
k
;k = 1:::N
F
g 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
is 5 and 8 respectively for LOS and NLOS measurements, the set of distances measured are
d =f5; 10; 15; 20; 25gm. The transfer functionH
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;
, where 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;
=jh
d;s;m;n;
j
2
. The influence of small-scale fading is removed by averag-
ing the instantaneous PDPs over the 8 x 8 Tx/Rx positions, to obtain the average-power-delay-
profile (APDP,
^
P
d;s;
).
^
P
d;s;
=
1
N
T
N
R
N
T
X
m=1
N
R
X
n=1
P
d;s;m;n;
: (3.1)
Sample APDP plots for both LOS and NLOS measurements at 5 m and 25 m distances are
given in [56].
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. 3.5.
78
3.3.1 Pathloss Analysis
Pathloss is typically defined as the difference between the received and transmitted power [60].
It has been established through theoretical and practical investigation that the behavior of nar-
rowband and UWB pathlosses are remarkably different [45, 46, 61–65]. An example of this is
the fact that for frequency-independent receive antenna area, pathloss in narrowband channels
is only distance dependent [60], [65], [66]. A generic pathloss can be defined as
G
L
(f;d) =
1
f
E
8
>
<
>
:
f+f/2
Z
ff/2
jH(f;d)j
2
df
9
>
=
>
;
: (3.2)
whereH(f;d) is the channel transfer function. Efg is the expectation taken over the small-
scale and large-scale fading. In this case, the frequency range f 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 pathlossG
L
(d) to be independent of the frequency-dependent pathloss
G
L
(f), and hence the overall pathloss can be written as
G
L
(f;d) =G
L
(d)G
L
(f) : (3.3)
Distance-dependent pathloss
In order to obtain the distance-dependent pathloss, 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
=1
^
P
s;d;
(3.4)
A relation of local mean power to the distance at each shadowing point would lead the
extraction of the pathloss component. Following the literature, we use a conventional power
79
5 10 15 20 25
10
−9
10
−8
10
−7
10
−6
10
−5
10
−4
d (m)
pathloss

NLOS
LS fit
LOS
LS fit
Figure 3.5: Distance dependency of the pathloss in the LOS and NLOS scenarios.
law model [60, 66] (see eq. 3.5);
G
L
(d) =G
0
10nlog
10

d
d
0

+S

(3.5)
where, n is the pathloss exponent, d
0
is the reference distance (1 m), G
0
is the pathloss (dB)
at the reference distance and S

is a lognormal distributed random variable describing large-
scale variations due to shadowing in the environment. Table 3.3 shows the pathloss exponentn
obtained from LOS and NLOS measurement scenario, while the Fig. 3.5 shows the scatter plot
of the normalized pathloss 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
pathloss on distance with the slope of the fit corresponding to the pathloss exponent experienced
in the channel.
Table 3.3: Extracted Large Scale Channel Parameters
n G
0
(dB)
s
(dB)
LOS 1.63 -38.26 1.46 2.10
NLOS 2.14 -49.06 1.46 3.16
80
Frequency-dependent pathloss
The frequency-dependence of the pathloss (G
L
(f)) primarily arises from the antenna power
area density, gain variations with frequency and additionally from frequency dependence of
physical propagation phenomena such as scattering and diffraction. In our model, G
L
(f) is
expressed as a power-law decay model [67] which in logarithmic form becomes
G
L
(f) =G
f
0
20log
10

f
f
Mc

: (3.6)
where 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 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 for each path separately.
The values obtained for LOS and NLOS scenarios are shown in Table 3.3, while the linear
regression fit for the frequency-dependent pathloss (dB) as a function of frequency (dB) is
shown in Fig. 3.6. To test the accuracy of the extracted value, the root-mean-square-error
(RMSE) between the measured and the simulated (using eq. 3.6) frequency-dependent pathloss
was estimated to be about24 dB. Also, from our calibration measurement in the anechoic
chamber with Tx and Rx placed at 1 m separation, = 1:1 was observed. This calibration
measurement characterizes the antenna properties in conjunction with the free-space pathloss.
3.3.2 Shadowing
Shadowing typically denotes the large-scale fluctuations of the received power in a propagation
channel. The logarithmic values of this power deviation observed closely matches a zero-mean
Gaussian distributionN(0;
s
(dB)), which is standard model for shadowing and has been re-
ported in the literature [69, 70]. This parameter follows the same distribution as well in our
analysis and is represented asS

in our modeling (see eq. 3.5). The standard deviation (
s
(dB))
81
2.25e9 2.75e9 3.25e9 3.75e9 4.25e9 4.75e9 5.25e9 5.75e9 6.25e96.75e97.25e9 7.75e9
10
−2
10
−1
10
0
f(Hz)
Normalized pathloss

LOS
LS fit
NLOS
Figure 3.6: Frequency dependency of the pathloss in the LOS and NLOS scenarios.
of this parameter for the LOS and NLOS scenarios are listed in Table 3.3.
3.4 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 ex-
tract the delay and direction parameters of the MPCs from the measured channel transfer func-
tions. 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.
3.4.1 MPC parameter extraction using CLEAN
CLEAN is an iterative deconvolution technique first introduced in [71] for the enhancement of
the radio astronomical maps of the sky and widely used in microwave and UWB communi-
82
ties 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 [47]. The details of the algorithm are available in [72], and not
included here for want of space.
Henceforth,

i
;
i
;
DoD
i
;
DoA
i

shall denote the extracted parameters for thei
th
MPC:
i
and
i
respectively denote the complex path gain and the delay experienced by the i
th
MPC;

DoD
i
and
DoA
i
respectively denote the azimuth direction of departure (DoD) and azimuth di-
rection of arrival (DoA) corresponding to thei
th
MPC.
3.4.2 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 MPCsi andj is defined as [73]
MCD
ij
=
q
MCD
2

ij
+MCD
2
DoD
ij
+MCD
2
DoA
ij
(3.7)
where,
MCD

ij
=
j
i

j
j

max

rms

max
MCD
2
DoD
ij
=
1
4

cos
DoD
i
cos
DoD
j

2
+
1
4

sin
DoD
i
sin
DoD
j

2
MCD
2
DoA
ij
=
1
4

cos
DoA
i
cos
DoA
j

2
+
1
4

sin
DoA
i
sin
DoA
j

2
(3.8)
and where
rms
is the RMS delay spread and
max
is the delay difference between the MPCs,
maximized over all pairs of MPCs. is the delay weighting factor, which is chosen by inspec-
tion. For the measured data, = 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.
83
−50
0
50
−50
0
50
0
20
40
60

DoD (degrees)
Unclustered MPCs
DoA (degrees)

Delay (m)
−55
−50
−45
−40
−35
−30
−25
Figure 3.7: Scatter plot of the unclustered MPCs. (5 m LOS measurement.)
We use the KPowerMeans clustering technique, which takes the MPC power into consider-
ation, to group the MPCs into clusters such that the total power weighted MCD of the MPCs
from their centroids is minimized [74]. The cluster centroid is defined as the power weighted
mean of the parameters of the MPCs in the cluster. For given cluster centroids, 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 [75], 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
(2K 14) and pick the value ofK that gives the visually most compact clusters.
84
−50
0
50
−50
0
50
0
20
40
60

DoD (degrees)
Clustered MPCs (color coded). Number of clusters = 7
DoA (degrees)

Delay (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 3.8: Clustered MPCs with KPowerMeans algorithm. (5 m LOS measurement.)
We now present the clustering result for a sample measurement. Fig. 3.7 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. 3.2. The MPCs are color coded with
a scale indicating the path powers in dB scale. Fig. 3.8 shows the clustered MPCs, obtained
using the KPowerMeans algorithm. The cluster centroids are shown in the legend. We observed
seven clusters for this measurement. Cluster C2 corresponds to the LOS cluster. 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.
85
We now develop the channel model for the LOS and NLOS environments separately.
3.4.3 LOS Environment
We first consider the intra-cluster properties of the MPCs, followed by the inter-cluster proper-
ties. For all the statistical models developed in the chapter, the goodness of the fit is verified by
applying the Kolmogorov-Smirnov (K-S) hypothesis test at 5% significance level.
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. 3.9 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 [60]. 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. 3.10, which similarly analyzes 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 independent.
Intra-cluster DoD and DoA (w.r.t. cluster center): The LOS cluster and the NLOS clusters
are observed to have slightly different statistics. Figs. 3.11 and 3.12 plot the empirical density
of the MPC DoA and MPC DoD for the LOS and NLOS cluster respectively, and fit them
using a Laplace distribution (with parameters and b). It can be seen that the LOS cluster
has relatively smaller value of b, and hence smaller angular spreads, compared to the 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
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.
86
Figure 3.9: Figure demonstrating that the intra-cluster DoD and DoA are independent, in the
LOS environment.
Figure 3.10: Figure demonstrating that the intra-cluster DoD and ToA are independent, in the
LOS environment.
87
was combined. Also, the angular spreads observed here are smaller than the angular spread of
20 25

reported for indoor UWB channel in [47]. Unlike the MIMO measurements in this
chapter, the indoor measurements in [47] 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. 3.13 plots the CCDF for the LOS and
NLOS clusters. The mixture probabilities () and the parameter () of the individual exponen-
tial 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. 3.14. It can be seen that the LOS 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 measurements in
the chapter, 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. 3.15 plots the joint density of the cluster
DoA and DoD (w.r.t. the LOS cluster) and compares it with the product of the corresponding
88
−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 3.11: 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 3.12: Intra-cluster DoD and DoA for the NLOS clusters, in the LOS environment.
89
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 3.13: Intra-cluster ToA modeling for the LOS and NLOS clusters, in the LOS environ-
ment.
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 3.14: Intra-cluster power decay constant for different cluster ToA, in the LOS environ-
ment.
90
Figure 3.15: Figure demonstrating that the cluster DoD and DoA are not independent, in the
LOS environment.
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. 3.16, 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 [48] for an indoor UWB channel.
Joint modeling of cluster ToA, DoD and DoA: The cluster DoD can be approximated using
a Laplace distribution as shown in Fig. 3.17. While both Normal distribution and Laplace
distribution were tried to fit the data, the Laplace distribution provided a better 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. 3.18. From the measured empirical density, it can be seen that most of the probability mass
is concentrated along the diagonals. This is consistent 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
91
Figure 3.16: Figure demonstrating that the cluster DoD and ToA are not independent, in the
LOS environment.
along the aisle. To avoid overfitting the data, we use a simple Gaussian mixture distribution to
fit the conditional density, i:e:,DoAjDoD 0:8N(DoD;
p
6

) + 0:2N(DoD;
p
3

), where
N(;) denotes the standard Normal density with mean and variance
2
. The simulated
conditional density plot using the Gaussian mixture model is shown on the right in Fig. 3.18.
While the proposed model may not be the most accurate representation of the measurements, it
captures the dependency of the cluster DoA and DoD with a small number of parameters.
We now model the cluster ToA conditioned on the cluster DoA and DoD. For this, we con-
sider different propagation scenarios. Because of the geometry of the setup and the environ-
ment, 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, compared to LOS, was
observed to be uniformly distributed as shown in Fig. 3.19 (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
92
−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 3.17: Cluster DoD modeling in the LOS environment.
Figure 3.18: Figure comparing the measured and simulated conditional densityDoAjDoD, for
the LOS environment.
93
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. 3.19 (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
ofd
cos(0:5(DoD+DoA))
cos(0:5(DoDDoA))
d, whered is the Tx-Rx Euclidean distance. For a double bounce scat-
tering, we model the excess cluster ToA as sum of the excess cluster ToA for a single bounce
scattering plus an exponential random variable (Fig. 3.19 (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
ToAjDoD,DoA
U[1:77m; 53:21m]; ifjDoAj< 10

;jDoDj<10

d
cos(
1
2
(DoD+DoA))
cos(
1
2
(DoDDoA))
d w.p. 0:56; elseifDoADoD<0
d
cos(
1
2
(DoD+DoA))
cos(
1
2
(DoDDoA))
d+X
1
w.p. 0:44; elseifDoADoD<0
X
2
;
elseifDoADoD>0
(3.9)
whereX
1
andX
2
are exponential random variables with means 3:1 m and 3:41 m respec-
tively.
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. 3.20. The backwall reflections has the smallest power decay constant.
Number of clusters: The average number of clusters increased with the measurement dis-
tance as shown in Fig. 3.21. The distance dependency is captured by using a linear function.
2
In both cases, the K-S test passed the exponential hypothesis test only at 1% significance level (fails at stan-
dard 5% significance level). Because of the limited sample size and over-fitting issues, we still fit the data with
exponential distribution.
94
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 3.19: Modeling the Excess cluster ToA for different propagation scenarios in the LOS
environment (a) Backwall reflection (b) Double bounce scattering with DoDDoA < 0 (c)
Double bounce scattering withDoDDoA> 0.
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 3.20: Inter-cluster power decay for different propagation scenarios in the LOS environ-
ment (a) Backwall reflection (b)DoDDoA< 0 (c)DoDDoA> 0.
95
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 3.21: Average number of clusters as a function of measurement distance in the LOS
environment.
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 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.
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 distanced (in meters) is given by
h(;;) =
K1
X
k=0
L1
X
l=0
j
k;l
j exp (j
k;l
)(ToA
k
ToA
k;l
)
(DoD
k
DoD
k;l
)(DoA
k
DoA
k;l
); (3.10)
where the number of clusters is modeled byKPoisson(5:34 + 0:06d).
For the LOS cluster,ToA
0
corresponds to the distance between Tx and Rx.DoD
0
andDoA
0
are determined by the relative orientation of the Tx/Rx arrays. For all subsequent clusters, the
96
cluster centers relative to the LOS cluster (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
Laplace( = 1:31

;b = 15:92

);
DoA
r
k
jDoD
r
k
0:8N(DoD
r
k
;
p
6

)+0:2N(DoD
r
k
;
p
3

) (3.11)
The conditional density ofToA
r
k
givenDoD
r
k
andDoA
r
k
is given in eq. (3.9).
The intra-cluster ToA, DoA and DoD for the LOS cluster are modeled by:
P (ToA
0;l
ToA
0;l1
>) = 0:02 exp(0:37) + 0:98 exp(7:35) (3.12)
DoD
0;l
Laplace( =0:25

;b = 3:96

) (3.13)
DoA
0;l
Laplace( =0:13

;b = 4:17

) (3.14)
The intra-cluster ToA, DoA and DoD for the NLOS clusters are modeled by:
P (ToA
k;l
ToA
k;l1
>) = 0:02 exp(0:17) + 0:11 exp(0:82) + 0:87 exp(5:69)
(3.15)
DoD
k;l
Laplace( =0:21

;b = 5:95

) (3.16)
DoA
k;l
Laplace( =0:05

;b = 6:06

) (3.17)
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):
j
k;l
j
2
/ exp (ToA
r
k
) exp ((0:22+0:0035ToA
r
k
)ToA
k;l
)

k;l
U[0; 2] (3.18)
where the inter-cluster exponential power decay constant () is given by
= 0:064m
1
; ifjDoA
r
k
j< 10

andjDoD
r
k
j< 10

= 0:56m
1
; else ifDoA
r
k
DoD
r
k
< 0
= 0:31m
1
; else ifDoA
r
k
DoD
r
k
> 0 (3.19)
97
3.4.4 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.
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. 3.22. The delay between
the ToAs of successive MPCs is modeled using exponential mixture distribution as shown in
Fig. 3.23. 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 mono-
tonically decay with the delay. Rather, it first slightly increases and then decreases as shown
in Fig. 3.24. This soft onset in the intra-cluster MPC power decay was observed in industrial
UWB environments as well, where it was modeled as [51].
P ()/

1 exp

rise

exp

fall

(3.20)
Inter-cluster modeling
As observed in LOS environment, the cluster ToA, DoD and DoA are dependent. The depen-
dency is again modeled using the conditional densities. Since there is no physical LOS cluster,
we model the cluster DoD, DoA and ToA w.r.t. to the DoD, DoA and ToA corresponding 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. 3.25. Both Gaussian mixture and Laplace
mixture distributions were tried to fit the data and the latter distribution provided a better fit.
98
−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 3.22: Intra-cluster DoD and DoA modeling in the NLOS environment.
The conditional density of DoA given DoD is modeled using a Gaussian mixture density, i:e:,
DoAjDoD 0:5N(DoD;
p
15

) + 0:5N(DoD;
p
15

) as shown in Fig 3.26. 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. 3.27. The cluster power decays exponentially with
the cluster ToA and the power decay constant for different propagation scenarios is given in
Fig. 3.28.
Number of clusters: Similar to LOS case, the average number of clusters increased with
measurement distance and is modeled using a linear function.
99
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 3.23: Intra-cluster ToA modeling in the NLOS environment.
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 3.24: Intra-cluster power decay modeling in the NLOS environment.
100
−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 3.25: Cluster DoD modeling in the NLOS environment.
Figure 3.26: Figure comparing the measured and simulated conditional densityDoAjDoD, for
the NLOS environment.
101
NLOS channel model
We now summarize the delay-double directional channel model for the NLOS environment.
The channel impulse response for a Tx and Rx separated by distanced is given by
h(;;) =
K
X
k=1
L1
X
l=0
j
k;l
j exp (j
k;l
)(ToA
k
ToA
k;l
)
(DoD
k
DoD
k;l
)(DoA
k
DoA
k;l
) (3.21)
where the number of clusters is modeled byKPoi(6:76 + 0:062d).
LetToA
0
=d be the Euclidean distance between Tx and Rx. DoD
0
andDoA
0
be the DoD
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( =26:7

;b = 12:5

) + 0:18Laplace( = 5:53

;b = 3:7

)
+ 0:23Laplace( = 15:8

;b = 9:2

) + 0:24Laplace( = 37:5

;b = 8:2

)
DoA
r
k
jDoD
r
k
0:5N(DoD
r
k
;
p
15

)+0:5N(DoD
r
k
;
p
15

) (3.22)
The conditional density ofToA
r
k
givenDoD
r
k
andDoA
r
k
is given by
ToA
r
k
jDoD
r
k
;DoA
r
k
U[0:68m; 18:32m]; ifjDoA
r
k
j<10

;jDoD
r
k
j<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; elseifDoA
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; elseifDoA
r
k
DoD
r
k
<0
X
2
;
elseifDoA
r
k
DoD
r
k
> 0
(3.23)
whereX
1
andX
2
are exponential random variables with mean 5:52 m and 6:89 m respec-
tively.
3
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.
102
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)
Figure 3.27: Modeling the excess cluster ToA for different propagation scenarios in the NLOS
environment (a) Backwall reflection (b) Double bounce scattering with DoDDoA < 0 (c)
Double bounce scattering withDoDDoA> 0.
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 3.28: Inter-cluster power decay for different propagation scenarios in the NLOS envi-
ronment (a) Backwall reflection (b)DoDDoA< 0 (c)DoDDoA> 0.
103
The intra-cluster ToA, DoD and DoA are modeled by:
P (ToA
k;l
ToA
k;l1
>) = 0:9716 exp(6:224)
+ 0:0267 exp(0:8131) + 0:0017 exp(0:1184) (3.24)
DoD
k;l
Laplace( = 0:113

;b = 9:71

) (3.25)
DoA
k;l
Laplace( =0:19

;b = 10:82

) (3.26)
The MPC power and the phase are modeled by:
j
k;l
j
2
/exp (ToA
r
k
)

1 exp

ToA
k;l

rise

exp

ToA
k;l

fall

k;l
U[0; 2] (3.27)
where = 0:8,
rise
= 5:66m,
fall
= 2:84m, and the inter-cluster exponential power decay
constant () is given by
= 0:156m
1
; ifjDoA
r
k
j< 10

andjDoD
r
k
j< 10

= 0:066m
1
; else ifDoA
r
k
DoD
r
k
< 0
= 0:067m
1
; else ifDoA
r
k
DoD
r
k
> 0 (3.28)
3.5 Model Validation
We validate the proposed channel models for the LOS and NLOS environment by comparing
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. 3.4.3
and 3.4.4, for the LOS and NLOS channels respectively. TheN
T
N
R
channel transfer func-
tions are generated as sum of discrete MPCs, as given below
H(f
k
)=
X
l

l
B
T
(f
k
;
l
)B
R
(f
k
;
l
)
y
exp (j2f
k

l
);1kN
F
(3.29)
104
where
l
,
l
,
l
and
l
respectively denote the DoD, DoA, delay and complex path gain corre-
sponding to thel
th
MPC.B
T
(f
k
;) andB
R
(f
k
;) 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 nor-
malized such that E [
P
k
jjH
syn
(f
k
)jj
2
F
] = N
T
N
R
N
F
where the expectation is taken over the
realizations of channel. The transfer functions are further multiplied by

f
k
f
C

, to model the
frequency dependent path loss. (
~
H
syn
(f
k
) =H
syn
(f
k
)

f
k
f
C

,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
)
y
?
?
? (3.30)
whereN
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
)
y
?
?
? (3.31)
whereP =
1
N
F
P
k
jjH
meas
(f
k
)jj
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 mo-
ment of the average power delay profile (APDP). For each measurement, the APDP is obtained
by averaging the absolute square magnitude of the channel impulse response over the N
T
N
R
measurements.
APDP () =
1
N
T
N
R
N
T
X
i=1
N
R
X
j=1
jh
ij
()j
2
(3.32)
whereh
ij
() = IFFTfH
ij
(f)g is the channel impulse response between thei
th
Tx and the
j
th
Rx antenna elements of the array. The noise-threshold filter is applied to the APDP obtained
105
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 3.29: Capacity and RMS delay spread validation for the LOS channel model.
from the measured data, as described in Sec. 3.3. The RMS delay spread is given by

rms
=
s
R

2
APDP ()d
R
APDP ()d

R
APDP ()d
R
APDP ()d

2
: (3.33)
Capacity and RMS delay spread validation: We now compare the delay spread and the capac-
ity values computed from the measurements with the synthetic data. For each measurement
distance and shadowing point, we have one realization of capacity/delay spread from the mea-
surement, 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. 3.29 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 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,
106
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 3.30: Capacity and RMS delay spread validation for the NLOS channel model.
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. 3.30.
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.
107
3.6 Summary and Conclusion
We conducted a measurement campaign in a warehouse environment using a UWB virtual
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 find-
ings are as follows:
The distance-dependent pathloss coefficient in the LOS and NLOS environments isn =
1:63 andn = 2:14 respectively.
The extracted frequency decay components were similar ( = 1:46) for both LOS and
NLOS scenarios.
The shadowing was observed to be lognormal distributed with the standard deviation
(dB) = 2:10 for the LOS environment and(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 mix-
ture distribution. For the LOS environment, the NLOS clusters exhibited higher angular
spreads compared to the LOS cluster. The NLOS clusters in the NLOS environment 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 mix-
ture distribution in the NLOS environment. The conditional DoA (DoAjDoD) can be
modeled using a Gaussian mixture distribution for both LOS and NLOS environments.
The conditional ToA (ToAjDoD,DoA) fits a Uniform distribution (for backwall reflec-
tions), deterministic (for single bounce scattering) and a random Exponential distribution
(for double bounce scattering).
108
We also observed that the average number of clusters increased with distance. The num-
ber of clusters in our measurement was modeled as a Poisson random variable.
From the results and statistics presented in this chapter, it is clearly observable that the prop-
agation channel parameters of the warehouse environment are different from those of other en-
vironments (indoor [47], industrial [51]) and a specific model, such as provided in this chapter,
is needed for the system simulations in such an environment.
3.7 Acknowledgments
We would like to thank the USC office of Mailing and Material Management services for their
kind permission to measure at the Warehouse. We thank Prof. Xuesong Yang and Umit Bas for
their help with the measurement.
109
Chapter 4
Ultrawideband Ranging with interference
mitigation
Accurate position information is of high importance in many commercial, public safety, and
military applications. While Global Positioning System (GPS) serves this purpose in outdoor
environments, it is often unreliable or inaccessible in cluttered environments such as indoors,
narrow street canyons, caves, and dense forests. For this reason, alternative positioning tech-
niques based on ranging between ground-based devices need to be explored. While fingerprint-
ing of received signal strength (RSS) has received great attention [80–82], the ranging accuracy
depends on access to database of RSS. Ranging using the ultra-wideband (UWB) signals is
promising due to the good range resolution associated with large bandwidth.
Ranging techniques are based on time-of-arrival (ToA) of the first path. ToA estimation is
mainly effected by receiver noise, multipath propagation and interference. In a dense multi-
path channel, the first path is not always the strongest path thereby making ToA estimation
challenging.
UWB ranging in the presence of noise and multipath propagation has been studied exten-
sively in the literature. For a single path additive white Gaussian noise (AWGN) channels, a
matched-filtering (MF) receiver is the maximum likelihood (ML) ToA estimator with theoret-
ical bounds on the ranging error given in [89–92]. For AWGN with multipath, [93] and [94]
110
respectively derived the Cramer-Rao bound (CRB) and Ziv-Zakai bound (ZZB) on the mean
square error (MSE) in ToA estimation. The ML estimators for the ToA estimation were pro-
posed in [95] and [96]; however, computational complexity of these estimators limits their
implementation. Practical sub-optimal ToA estimators were proposed in [97, 98, 100]. Several
low complexity, subsampling ToA estimators, based on the energy-detection (ED) have been
proposed in [99–103]. The performance of the MF and ED receivers has been summarized
in [104]. A two-step hybrid ToA estimator was proposed in [106]. In it, the coarse estimate is
obtained from energy detection and a fine estimate is obtained from matched-filtering.
Very few papers in the literature addressed the issue of interference in UWB ranging. In
multiuser network, signals from multiple users can interfere with the desired signal thereby
deteriorating the ranging accuracy [105]. While using distinct time-hopping (TH) sequences
for different users, followed by coherent combining of signals can suppress the interference to
certain extent, the residual interference can be significant compared to the first arriving path
from the desired user, and hence can result in early false alarms. This is because the first
arriving path is not always the strongest path. In fact, it can have significantly lower energy
than the strongest path, especially in non-line of sight (NLOS) conditions. Thus this affect
might occur even in the absence of near=far effects that are the reason for significant MUI in TH
communication systems. Hence, finding a good threshold to separate the interference multipath
components (MPC) from the first MPC of the desired user is difficult or even impossible.
Ref. [107] proposed non-linear filtering schemes like minimum filtering and median filtering
to mitigate the multiuser interference (MUI). Ref. [108] considered both MUI and narrowband
interference (NBI), and proposed differential filtering, to mitigate the interference. These papers
considered the ED receivers and studied the performance with only one interfering user. While
the ED receivers has low cost implementation, its performance is poor compared to matched-
filtering (coherent) receivers, especially when the signal-to-noise ratio (SNR) is small. Also,
the energy based non-linear filtering schemes cannot exploit noise averaging across frames, as
111
the noise becomes correlated after filtering. MUI mitigation in UWB ranging using coherent
receivers is considered in [109]. However, it was assumed that the receiver knows the TH
sequences of all the interfering users, and proposed an iterative successive interference can-
cellation technique for ToA estimation. In a dense multipath channel, this approach becomes
computationally intense. More importantly, acquiring the TH sequences of all the interfering
users is difficult especially when the users are mobile. It can also happen that the interfering
users are hostile and do not share their TH sequences.
In this chapter, we propose a novel coherent ranging algorithm that suppresses the MUI
without having to know the TH sequences of the interfering users. Only the TH sequence of
the desired user is assumed known to the receiver. To the best of our knowledge, this is the
first work in the literature that talks about the MUI suppression for coherent UWB ranging,
without having to know the TH sequences of the interfering users. We make use of the fact
that after de-hopping the received signal, the receiver effectively has multiple waveforms, one
per every frame duration in the TH signal. While the signal MPCs in these waveforms are
time-aligned, because of the time-hopping nature, an interference MPC hops around the signal
MPCs across different waveforms, thereby making it feasible to separate the interference MPC
from the signal MPC. Using simulations, we show that the proposed ranging scheme is robust
to the strength of interference and the number of interfering users in the system, and is much
better than the thresholding schemes and the non-linear filtering schemes considered in the
literature. We also carried out an urban outdoor channel measurement campaign with UWB
channel sounder and tested the performance of our algorithm in both LOS and NLOS measured
scenarios. We compare the performance of our ranging scheme with some well-known coherent
and non-coherent thresholding schemes.
The chapter is organized as follows. The system model is developed in Sec. 4.1. The thresh-
olding schemes and the proposed ranging algorithm are described in Sec. 4.2.1 and 4.2.2 re-
spectively. The performance bounds for the proposed ranging scheme are developed in Sec. 4.3.
112
The measurements are described in Sec. 4.4. The performance evaluation is done with synthetic
channels and the measurement data in Sec. 4.5.1 and 4.5.2 respectively. Finally, the chapter is
concluded in Sec. 4.6. The mathematical details are moved to the Appendix.
4.1 System Model
We consider a multiuser network with (I + 1) users simultaneously transmitting at any given
time. Without loss of generality, we assume the first user as desired and the other I users as
interference. The users are assigned fixed and distinct TH sequences. The TH signal transmitted
by thei
th
user is given by [84]
s
i
(t) =
p
E
i
N
X
n=1
p(t (n 1)T
f
c
i
(n)T
c
); 0tNT
f
(4.1)
wherep(t) is the unit energy UWB pulse,E
i
is the signal energy per frame, andc
i
is the chip
sequence of thei
th
user withc
i
2f0; 1; ;N
c
1g
Nc
. T
c
is the chip duration,T
f
is the frame
duration, N
c
is the size of the code alphabet and the number of chips per frame (T
f
=N
c
T
c
),
andN is the number of frames per symbol. We assume that all users use the same pulse shape
p(t).
Leth
i
(t) denote the impulse response of the channel between thei
th
user and the receiver.
The received signal is given by
r(t) =
I+1
X
i=1
s
i
(t)h
i
(t) +n(t); (4.2)
where () is the convolution operation andn(t) is the zero-mean AWGN with varianceN
0
. The
model implicitly assumes that the channel is quasi-static during the transmission of the ranging
signals, given typical pedestrian coherence times ( 10 ms [78]), this is a realistic assumption.
We assume that NBI can be removed by notch filtering and hence do not model it.
The signal-to-noise ratio (SNR) and signal-to-interference ratio (SIR) are defined as follows
SNR,
E
1
N
0
; SIR(i),
E
1
E
i+1
; i = 1; 2; ;I: (4.3)
113
Figure 4.1: Effective impulse responses after de-hopping. (IEEE 802.15.4a CM1 channel real-
ization withN = 50 andI = 1.)
Notice that SIR in general is a function of user index as different interfering users can transmit
with different power and can be at different distances from the receiver. We assume that the
receiver only knows the TH sequence of the desired user and not of the interfering users. The
receiver can now perform the de-hopping process, by dividing the observation time into N
intervals,I
n
,[c
1
(n)T
c
+(n1)T
f
; c
1
(n)T
c
+(n1)T
f
+T ]; 1nN, each of lengthT (T<
T
f
). We assume that the delay spread of the channel is smaller than one frame duration. Without
loss of generality, we assume that the chip-sequence for the desired user is the all zero sequence.
The receiver effectively has the followingN waveforms
r
n
(t),r(t + (n 1)T
f
); 1nN; 0tT (4.4)
=S(t) +I
n
(t) +N
n
(t); (4.5)
114
where the signal, interference and the noise terms are defined as follows:
S(t),
p
E
1
p(t)h
1
(t) =p(t)h
S
(t); (4.6)
I
n
(t),
I+1
X
i=2
p
E
i
p(t)h
i
(tc
i
(n)T
c
) =p(t)h
(n)
I
(t); (4.7)
N
n
(t),n(t + (n 1)T
f
); (4.8)
where h
S
(t) ,
p
E
1
h
1
(t) is the effective impulse response between the desired user and the
receiver, h
(n)
I
(t) ,
P
I+1
i=2
p
E
i
h (tc
i
(n)T
c
) is the effective impulse response between the
interfering users and the receiver,N
n
(t) is the zero-mean AGWN with varianceN
0
.
Notice that while h
S
(t) is same for all the N waveforms, h
(n)
I
(t) is different for different
waveforms. This is because the chip sequence c
i
(n) is different for different n. Figure 4.1
compares the sample impulse responses h
S
(t) and h
(n)
I
(t) for different n. It can be seen that
the desired signal MPCs, across theN waveforms, are time aligned and have the same strength.
The interference MPCs appear to be time-hopping across the different waveforms. Hence, it is
possible to separate the signal MPC from the interference MPC without even knowing the TH
sequences of the interfering users.
4.2 ToA estimation algorithms
Our goal is to extract the ToA of the first path for the desired user, from the waveforms
fr
n
(t)g
N
n=1
. We first briefly discuss some ToA estimation schemes developed in the literature
for mitigating the MUI and then describe the proposed ToA estimation algorithm.
Since the high-resolution CLEAN algorithm is a base for these ranging schemes, we briefly
describe it below.
CLEAN algorithm: It is used to extract the MPCs from the received waveform. CLEAN is
an iterative deconvolution technique first introduced in [85] for the enhancement of the radio
astronomical maps of the sky and widely used in microwave and UWB communities as an
115
effective post-processing method for time-domain channel measurements [86, 87]. In it, the
received signal is correlated with the template signal, and the amplitude and location of the
correlation peak is determined, followed by a subtraction of the contribution of the thus-detected
MPC from the received signal.
For instance, ify(t) =
P
L
k=1

k
p(t
k
) +n(t) is the received signal withp(t) being the
template signal, the correlation is given by
() =
Z
p(t)

y(t)dt =
L
X
k=1

k
R
p
(
k
) +N() (4.9)
whereR
p
(:) is the auto-correlation of the template signal andN() ,
R
p(t)

n(t)dt is a
circular symmetric complex Gaussian random process with covariance functionK
N
(t
1
;t
2
) =
N
0
R
p
(t
1
t
2
).
The location of the strongest MPC is ^
1
= arg max

j()j and the corresponding strength is
^
1
=(^
1
). The contribution of the strongest MPC, ^
1
p (t ^
1
), is removed from the received
waveform. The residual signal is correlated with the template to determine the next strongest
MPC. This process repeats and by the end ofM iterations, we have the MPCs
n
f^
k
g
M
k=1
;f^
k
g
M
k=1
o
,
and the residual signal is
y
(M)
(t),y(t)
M
X
k=1
^
k
p(t ^
k
): (4.10)
The process stops when the peak correlation between the residual signal and the template falls
below a predetermined thresholdj
max
j (0 1 and
max
, ^
1
is the maximum correlation
between the received waveform and the template).
Notice that the estimated MPC location can be off from the true location. When the MPCs
are resolvable, the offset in the location estimate is bounded by [104]
P (j ^ jW ) =Q
0
@
s
jj
2
N
0
(1R
p
(2W ))
1
A
: (4.11)
whereQ(:) is the Q-function, is the strength of the MPC. Hence, the larger the strength of the
MPC and the faster the decay of the auto-correlation of the template signal, the smaller is the
116
offset.
4.2.1 Thresholding schemes
One simple and commonly used strategy for mitigating the MUI is to average theN waveforms,
extract the MPCs from the averaged waveform using CLEAN, use a good threshold to separate
the first arriving signal MPC from the interference MPCs and the noise peaks, and declare the
MPC with the smallest delay as the ToA estimate.
Notice that the ranging error is sensitive to the threshold. In the presence of noise and=or
MUI, finding a good threshold is challenging. Setting large can result in missing the weak
signal MPCs and a small can result in early false alarms from capturing interference MPCs or
noise peaks.
Averaging works well whenN is very large or SIR is high. But in reality,N is limited by the
coherence time of the channel. Since all users transmit with similar power level, SIR of 0 dB
is typical and it can even attain a large negative value due to near=far effects or LOS=NLOS
situations. For a finiteN and a reasonable SIR, the residual interference after averaging can be
comparable to or larger than the first arriving MPC from the desired user. Hence, this approach
can result in large miss-detection and early false alarms, thereby deteriorating the ranging ac-
curacy.
In the remainder of the chapter two different thresholds are considered as benchmarks:
Genie thresholding
For every channel realization, is chosen to minimize the instantaneous ranging error. This is
done by performing the brute-force Monte Carlo simulations-based search. Note that this is not
feasible in practice: in order to determine the instantaneous ranging error and hence the optimal
, we would have to know the instantaneous channel impulse response which is the quantity we
117
wish to measure.
Lookup table based thresholding
Here is chosen to minimize the mean-squared error (MSE) in the range estimates. This can
be realized in practice by forming a lookup table of optimal for different SNR, SIR,I andN.
The threshold is then picked based on the operating conditions.
4.2.2 Proposed ToA estimation algorithm
By averaging the waveforms, we lose the information about the location of the interference
MPCs. Instead, we can first determine the location of interference MPCs, remove their con-
tribution from each of the waveforms and then average the interference-free waveforms and
extract the ToA information. We now describe each of these steps in detail.
Impulse response extraction from the waveforms
We use CLEAN algorithm to extract the impulse responses from each of theN waveforms. We
use a fixed correlation threshold of , 2:12
p
N
0
, so that the false alarm probability due to
the noise peak is small. A noise peak occurs at if the correlation exceeds the threshold; the
probability of this event is
P (j()j>) =P (jN()j>) = exp

2
N
0

= 0:01: (4.12)
Let
n
^
(n)
k
; ^
(n)
k
; 1kL
n
o
be the location and the strength of the MPCs extracted from the
waveform r
n
(t). The impulse response is defined as
^
h
n
(t) ,
P
Ln
k=1
^
(n)
k
(t ^
(n)
k
). Since
r
n
(t) has contributions from desired user, interfering users, and noise, the MPC delay ^
(n)
k
can
correspond to desired user or the interfering users or the noise peak.
118
Figure 4.2: Error in MPC location estimates obtained using CLEAN, for five strongest MPCs.
(IEEE 802.15.4a CM1 channel realization and second derivative of basic Gaussian pulse with
pulse width of 1 ns are used.N = 50, SNR = 30 dB, sampling time = 25 ps, andI = 0.)
Separating the interference and signal MPCs
Consider the set
n
^
h
n
(); 1nN
o
. As seen from Figure 4.1, if corresponds to a signal
MPC location, most of the values in the set are similar. If corresponds to a noise peak in one
waveform, many of the values in the remainder of the set will be zero since the odds of noise
peaks happening at the same location in multiple waveforms are low. If corresponds to an
interference MPC location in one waveform, some of the values in the remainder of the set will
be zero and even the non-zero values in the set are distinct. This is because an interference MPC
time-hop across the different waveforms as explained earlier. However, as discussed earlier,
because of noise, the estimated MPC locations are off from the true locations. If is true signal
MPC location, because ofi:i:d: AWG noise in different waveforms, the offset in the location
estimate is alsoi:i:d: across the waveforms, but with high probability the estimates will all lie
in [W; +W ]. This can also be seen from Figure 4.2, which plots the offset in the signal
119
MPC location estimates for the strongest five MPCs. It can be seen that the amount of offset is
inversely proportional to the strength of the MPC.
Using the intuition presented above, we now propose the following heuristic rule to decide
if the MPC location ^
(n)
k
correspond to a signal MPC or an interference=noise MPC. We do not
distinguish between interference MPC and noise peak.
For 1nN and 1kL
n
,
Construct the setfX
n
; 1nNg, whereX
n
,
R
W
w=W
^
h
n
(^
(n)
k
w)dw. This is done
to compensate for the offset in the MPC location estimates. Let M be the number of
non-zero values in this set.
M <

N: Declare ^
(n)
k
as an interference MPC (A signal MPC will be detected in at least

N out ofN waveforms).

N is an algorithm parameter that will be discussed later.
M

N: If ^
(n)
k
is an interference MPC, theseM data points are distinct and far apart.
If it is a signal MPC, most of these data points are clustered. In some of the waveforms,
an interference MPC can overlap with the signal MPC thereby deteriorating the MPC
amplitude estimate. Since we do not assume the knowledge of strength of interference
MPCs, we simply identify such estimates and discard them as below.
– Construct a circle of radius
around every data point and count the number of data
points enclosed by the circle (including the center).
– If there is no such circle enclosing at least

N out ofM data points, declare ^
(n)
k
as
an interference MPC.
– If there is more than one circle enclosing

N or more data points, consider the circle
enclosing maximum number of data points. IfX
n
is outside the circle, declare ^
(n)
k
as an interference MPC and ifX
n
is inside, declare ^
(n)
k
as a signal MPC.
120
Interference suppression and noise averaging
Notice that we could have stopped once ^
(n)
k
is detected as signal MPC. But doing so, we
cannot take advantage of the increased SNR obtained from averaging the waveforms. Instead,
we detect the interference MPCs, remove their contribution from the waveforms, and average
them to increase the SNR.
Let
n
,
n
^
(n)
k
; 1kL
n
: ^
(n)
k
is interference MPC or noise peak
o
. The refined signal
is
~ r
n
(t) =r
n
(t)
X
2n
^
h
n
()p(t); 1nN (4.13)
Notice that the above steps remove strong interference and noise peaks. The waveforms are
now averaged to suppress any weak residual interference and noise.
r
avg
(t) =
1
N
N
X
n=1
~ r
n
(t) (4.14)
Range extraction
Assuming that the interference is effectively suppressed in the above steps,r
avg
(t) can be treated
as the received waveform in AWGN. We again use the CLEAN algorithm to extract the first
MPC. To be fair in comparison, we chose the correlation threshold from the lookup table that is
generated forI = 0 (No interference case). We furthermore require that the delay between the
first and second MPC is consistent with the statistics of the inter-arrival times of MPCs, which
is assumed to be known. When the MPC arrival times are modeled as Poisson process with
parameter, probability that the inter-arrival times exceed
5:3

is 0:5%.
Let the extracted MPCs location bef^
k
;k 1g. The ToA estimate is given by
d
ToA = min

^
k
:j^
k
^
k+1
j<
5:3

; (4.15)
121
4.3 Proposed algorithm analysis
We now analyze the performance of the proposed ranging scheme and study the impact of
parametersW ,
and

N. To make the analysis tractable we make the following modeling as-
sumptions. The channel impulse responses of the users,fh
i
(t)g
I+1
i=1
, are assumedi:i:d: random
processes. For thei
th
user, the arrival times of the MPCs are modeled as Poisson process with
rate and the strength of the MPCs are assumed to be independent Rayleigh RVs. The chip se-
quencec
i
(n) are assumedi:i:d: acrossn (waveform index) andi (user index), and independent
of the channel impulse responses.
Thus, the MPC arrival times corresponding to the delayed impulse responseh
i
(tc
i
(n)T
c
)
also follow a Poisson process with rate, for differenti andn. Hence, the MPC arrival times
corresponding to the sum interference, h
(n)
I
(t), follow a Poisson process with rate I, and is
i:i:d: acrossn.
Henceforth, we use the following notation: f
X
(x) shall denote the density function of RV
X.P(A) and E [A] shall denote the probability and expectation ofA respectively. Similarly
P(AjB) shall denote the conditional probability ofA givenB.
4.3.1 False alarms from a noise peak
We will now compute the probability that the algorithm falsely detects a noise peak from
CLEAN as a signal MPC. Let be a pure noise-only region. Without loss of generality, we
assume that a noise peak of strengthX
1
(jX
1
j>), occurs at, in the first waveform.
The algorithm makes false detection of as a signal MPC, if at least

N 1 of the remaining
N 1 waveforms have a noise peak in [W; +W ] and there exists a circle of radius
enclosing at least

N of these points, includingX
1
. The false alarm probability is upper bounded
122
by
P
f;N

N
X
m=

N
min

N 1
m 1

2W exp

2
N
0

m1

1 2W exp

2
N
0

Nm
;
m
X
k=

N
k

m1
k1
Z
1
0

1Q
1

r
2y
N
0
;
s
2
2
N
0
!!k1
Q
1

r
2y
N
0
;
s
2
2
N
0
!mk
1
N
0
exp

y
N
0

dy
!
;
whereQ
1
(:;:) is the Marcum Q-function. The details are given in Appendix A.0.1.
4.3.2 False alarms from an interference MPC
We will now compute the probability that the algorithm falsely detects an interference MPC as
a signal MPC. Without loss of generality, we assume that an interference MPC of strengthX
1
(jX
1
j>) occurs at, in the first waveform. LetE
I
be the average energy of the interference
MPCs.
The algorithm makes false detection of as a signal MPC if at least

N 1 of the remaining
N 1 waveforms have an interference MPC in [W; +W ] and there exists a circle of
radius
enclosing at least

N of these points, includingX
1
. The false alarm probability is upper
bounded by
P
f;I

N
X
m=

N
min

N 1
m 1

( 1exp (2WI) )
m1
exp (2WI(Nm));
m
X
k=

N
k

m1
k1
Z
1
0

1Q
1

r
2y
E
I
;
s
2
2
E
I
!!k1
Q
1

r
2y
E
I
;
s
2
2
E
I
!mk
1
E
I
exp

y
E
I

dy
!
:
The details are given in Appendix A.0.2.
4.3.3 Signal MPC detection
Consider a signal MPC with strength and at location. We will now compute the probability
that the algorithm detects as a signal MPC.
123
The algorithm correctly detects as a signal MPC, if in at least

N of theN waveforms is
detected as MPC and there exists a circle of radius
enclosing at least

N of these points. The
detection probability is lower bounded by
P
d

N
X
m=

N
Nm
X
k=0
m
X
l=

N

N
m+k

m+k
m

m 1
l 1

p()
m
(1p())
k
exp (2WI(m +k))
(1 exp (2WI))
Nmk
Z
1
max(jj;0)
q(;r)
l1
(1q(;r))
ml
r
N
0
exp

r
2
N
0

g(r)dr;
where p() and q(;r) are given in (A.8) and (A.13) respectively, g(r) is defined in Ap-
pendix A.0.3. The details are given in Appendix A.0.3.
4.3.4 Choice of parameters

N,
, andW
From the analysis presented in the earlier section, it can be seen that as

N increases, the false
alarm from noise and interference decreases, but the signal MPC detection probability also
decreases. Similarly as
orW increases, the detection probability increases but the false alarms
from noise and interference also increases. An optimized choice could be done based on the
bounds derived above; however this would require a 3-dimensional grid search. We instead use
a heuristic approach to find a good choice of parameters, and then use the bounds to demonstrate
the effectiveness of these choices.
Probability of a noise peak occurring in the interval [W; +W ], in any waveform is
upper bounded using (A.1). Since noise in different waveforms isi:i:d:, the expected number
of waveforms with a noise peak in the interval [W; +W ] is upper bounded by
E [Number of waveforms with a noise peak in [W; +W ]] 2WN exp

2
N
0

:
(4.16)
Hence, we chose

N 2WN exp

2
N
0

, so that the false alarms from noise peak is small.
Probability of an interference MPC in the interval [W; +W ], in any waveform is 1
exp (2WI). Since interference MPC arrival times in different waveforms is i:i:d:, the
124
expected number of waveforms with an interference MPC in the interval [W; +W ] is
given by
E [Number of waveforms with an interference MPC in [W; +W ]]=N ( 1exp (2WI ) )
(4.17)
Hence, we chose

N N (1 exp (2WI)), so that the false alarms from interference is
small.
Consider a signal MPC with strength and at location. The expected number of waveforms
in which an interference MPC also happens in [W; +W ] is given by (4.17). Hence, on
average onlyN exp (2WI) waveforms are free from interference at. For these waveforms
free from interference, the estimated strength of the signal MPC at is X
k
= +N
k
. The
radius of the circle,
, is chosen such that with high probability, circle centered around one
point encloses the other points. SincejX
i
X
j
j
2
=jN
i
N
j
j
2
is an exponential RV with
mean 2N
0
, for
opt
= 3
p
N
0
, we have
P (jX
i
X
j
j>
opt
) =P

jN
i
N
j
j
2
> 9N
0

= exp(4:5) = 0:01: (4.18)
Also, we chose

N N exp (2WI), so that the probability of detection of signal MPC is
high. Since the miss detection of signal MPC is more critical than the false alarms, as the false
alarms can be further suppressed by steps 3 and 4 of the algorithm, we chose

N
opt
= min

max

2WN exp

2
N
0

;N (1 exp (2WI))

;N exp (2WI)

:
(4.19)
The window size, W , should be small enough that the false alarms from a noise peak and an
interference MPC is small. On the other hand it must be large enough that signal MPC is
detected. We choseW such that any signal MPC location estimate, obtained from CLEAN, is
at mostW samples away from the true location. Setting 95% confidence interval for = ,
in (4.11), we have
P (j ^ jW
opt
) =Q

s

2
N
0
(1R
p
(2W
opt
))
!
= 0:05: (4.20)
125
Using = 2:12
p
N
0
, we haveW
opt
= 0:5R
1
p
(0:4).
We now study the bounds developed on the false alarm and detection probability for the
above choice of parameters. Figure 4.3 plots the false alarm probabilityP
f;N
andP
f;I
as a func-
tion ofE
I
and the signal MPC detection probabilityP
d
as a function ofjj
2
. Performance is
shown forI = 1, 5, and 10. It can be seen that the algorithm successfully rejects strong interfer-
ence MPCs and also rejects the noise peaks significantly. Weak residual interference MPCs can
be further suppressed by averaging the waveforms. The signal MPC detection probability in-
creases withjj
2
. When the number of interfering users are large, an interference MPC overlaps
with the signal MPC in several of the waveforms, and if the interference is strong, it makes the
desired signal unrecognizable and hence the algorithm misses the signal MPCs. ForI = 10, the
signal MPC detection probability is only 0:55. In Figure 4.4, we justify the choice of parameters

W
opt
;
opt
;

N
opt

. ForI = 5, we plot the performance with significantly different choice of pa-
rameters. The solid lines is the performance with

W;
;

N

=

W
opt
3
;

opt
3
;

N
opt
3

. It has higher
false alarms from noise and lower signal MPC detection probability than

W
opt
;
opt
;

N
opt

. The
dotted lines is the performance with

W;
;

N

=

2W
opt
; 2
opt
; 2

N
opt

. It has very poor signal
MPC detection probability.
4.4 Measurement Setup
4.4.1 Measurement Site
The measurements were performed for both line-of-sight (LOS) and non-line-of-sight (NLOS)
scenarios in an outdoor campus environment, namely the Vivian Hall of Engineering (VHE)
building at USC. The LOS measurements were performed in the quad area, which is an open
space enclosed by tall buildings and trees on all the four sides, making it a multipath rich
environment. The terrain is a flat field mainly made up of 5 cm high grass. The transmitter
was fixed and the receiver was moved around. Measurements were carried out with 3 sets of
126
Figure 4.3: Performance bounds with

W
opt
;
opt
;

N
opt

forN = 50.
Figure 4.4: Performance bounds with

W;
;

N

=

W
opt
3
;

opt
3
;

N
opt
3

and

W;
;

N

=

2W
opt
; 2
opt
; 2

N
opt

forN = 50 andI = 5.
127
distances between Tx and Rx (20 m, 30 m, and 40 m). For each distance, the receiver was
placed at 3 different positions (far apart) along the circumference of the circle with transmitter
as the center. At every position, a virtual 1x4 SIMO antenna array, with horizontal separation
of 10 cm was used at the receiver. The Tx=Rx antenna heights was set to 100 cm. The same
procedure was repeated for the 8 NLOS receiver positions shown in Figure 4.9.
4.4.2 Hardware and Post-processing
The channel measurements were performed with a UWB channel sounder. An arbitrary wave-
form generator (AWG) that can generate signals up to 12 GHz with a sampling rate of 24 GS=s
is used at transmitter. A digital sampling scope (DSO) operating at 40 GS=s is used at receiver
for data acquisition. The transmitter and receiver were synchronized using a trigger signal. A
pair of UWB Skycross Omni-directional antennas were used at transmitter and receiver. The
transmitter sends a periodic multitone OFDM-like waveform, with frequency range of 3 GHz
– 10 GHz. It has a center frequency of 6.5 GHz and 9559 sub carriers with a uniform spacing
of 732.42 KHz. Each waveform is 1.36s long and we store 50 such waveforms at the DSO
for every measurement. We also record 3.45 s of receiver noise (transmitter off) for every
measurement. This is used to compute the noise power,N
0
, and to set the parameters during the
post processing. More details about the hardware and the excitation signal can be found in [88].
Since the measurements were conducted close to campus buildings with WiFi access points
and devices, there was significant interference. The received signal is thus first passed through
a band pass filter to remove the out of band interference. The template signal for the CLEAN
algorithm was obtained from a measurement taken with the setup in the anechoic chamber at
USC, with a known distance between transmitter and receiver and thus includes the distortions
by the antennas.
The periodic signal is converted into a time-hopping signal by artificially introducing a shift
to each of the N waveforms and adding them back together. Since only one AWG and one
128
DSO was used in the measurements, the MUI is simulated by adding the measurements taken
at different receiver positions. Since the transmitter location is same for all the measurements,
assuming that the channel is reciprocal, this has the same effect as if multiple users were trans-
mitting at the same time. For instance,I = 3 level MUI can be simulated by adding the received
waveforms at positions 5, 6 and 7 as interference to the received waveform at position 1.
4.5 Performance Evaluation
We now evaluate the performance of the proposed ranging scheme and compare it with some
of the well-studied schemes in the literature. We first present the results with the synthetic
channels and then with the measurement data. RMSE in the distance,
s
E

^
dd

2

, is used
as the performance metric. Hered is the true distance between the desired user and the receiver,
and
^
d =c
d
ToA is the estimated distance withc = 3 10
8
being the speed of light.
4.5.1 Synthetic channels
The following parameter settings were used. For the transmit pulse, the second derivative of
the basic Gaussian pulse,p(t)/

1 4

t
Tp

2

exp

2

t
Tp

2

is used withT
p
= 1 ns.
The parameters of the time-hopping signal areT
c
= 4 ns andN
c
= 60 (T
f
=N
c
T
p
= 240 ns).
The chip sequencesc
i
(n) are generatedi:i:d: from the setf0; 1; ;N
c
1g with equal prob-
ability. The performance was evaluated with 10
3
channel realizations of the IEEE 802.15.4a
CM1 (residential line-of-sight) channel model [79]. Three different values ofI (I = 1,I = 5
andI = 10) and two different values ofN (N = 50 andN = 15) were considered; = 6 ns
was used. The window size using (4.20) wasW = 0:25 ns (10 samples).

N and
are chosen
as per the discussion in Sec. 4.3.4. The performance of the proposed ranging scheme is com-
pared with the thresholding schemes described in Sec. 4.2.1 and the non-linear filtering based
energy detection schemes in [107]: for the minimum and median filtering, the performance is
optimized over the block energy threshold and the length of the filter; the search back window
129
Figure 4.5: Performance evaluation of different ranging schemes, as a function of SIR (SNR =
20 dB andN = 50).
size is fixed to 60 ns. We first present the results with interference from different users being the
same. For the later part of simulations, we also model the path loss and shadowing and hence
different SIR from different interfering users.
Figure 4.5 compares the RMSE of different ranging schemes, as a function of SIR, for a
fixed SNR of 20 dB andN = 50 waveforms. Performance was shown forI = 1,I = 5 and
I = 10. From (4.19), the corresponding

N are 12, 17, and 22. As mentioned earlier, we assume
E
2
= E
3
= = E
I+1
. As expected, for the thresholding schemes, the RMSE decreases
with SIR. Also, for these schemes, RMSE significantly increases with I in the interference
limited regime. In the interference limited regime, the residual interference after averaging is
comparable to the strength of the LOS component from the desired user and hence even a genie
thresholding scheme has a large RMSE. The proposed ranging scheme effectively suppresses
the strong interference MPCs (can also be seen from Figure 4.3), and hence reduces the RMSE
significantly, and performs equally well at all SIR.
130
Notice that the proposed ranging scheme is always better than the minimum and median
filtering schemes, is better than the lookup table thresholding scheme for SIR 8 dB, and is
even better than the genie thresholding scheme for SIR8dB. In the noise limited regime,
averaging is the best thing to do and hence the lookup table thresholding scheme is slightly
better than the proposed ranging scheme. While the proposed ranging scheme can eliminate
noise peaks, it also misses weak signal MPCs resulting in increased RMSE. Also evident is the
robustness of the proposed ranging scheme to the strength of the interference and the number
of interfering users. While the RMSE is very similar forI = 1 andI = 5 in the interference
limited regime, it slightly increases forI = 10. For largeI, the proposed ranging scheme has a
lower signal MPC detection probability as discussed in Figure 4.3, and hence increased RMSE.
Similar observations hold even for other values ofN. For example, withN = 15 waveforms,
the proposed ranging scheme is better than the lookup table thresholding scheme for SIR
10 dB, it is better than even the genie thresholding scheme for SIR4 dB and is better than
median and minimum filtering schemes at all SIR. The corresponding figure is not shown for
lack of space. In general, smaller the N, better is the performance of the proposed ranging
scheme relative to the thresholding schemes.
Figure 4.6 plots the RMSE of different ranging schemes as a function of SNR, for SIR = 0 dB
andI = 1. As expected, the RMSE decreases with SNR for all the ranging schemes in the noise
limited regime. When SNR is low (noise limited regime), averaging is better than any non-linear
filtering and hence both the thresholding schemes outperform the proposed ranging scheme.
Beyond 16 dB SNR, interference is comparable to noise and hence the proposed ranging scheme
perform better than the lookup table based thresholding scheme. However, it is still inferior to
the genie scheme, which can change threshold every channel realization. Please note that the
genie scheme is unrealistic and is only used as a benchmark.
So far we had implicitly assumed that all the interfering users are at same distance from
the receiver and hence cause same interference. We now model the user locations using Pois-
131
Figure 4.6: Performance evaluation of different ranging schemes, as a function of SNR, in
presence of one active interfering user (SIR = 0 dB,I = 1, andN = 50).
Figure 4.7: Performance evaluation of different ranging schemes, as a function of transmit
power, when SIR from different users is different (N = 50).
132
son point process in two dimensional plane. The path loss and shadowing are modeled as
per the specifications in IEEE 802.15.4a CM1 channel model. We assume all the users (both
desired and interfering) transmit with the same power level P
tx
. Since different interfering
users are at different distance from the receiver, the received power from the interfering users

E
k
/P
tx
d
n
k

is different for differentk.
Figure 4.7 compares the RMSE with different ranging schemes as a function of SIR and for
different I. Notice that as P
tx
increases, the SNR increases but SIR remains the same. For
smallP
tx
, the system is in noise limited regime and hence the ranging error decreases withP
tx
.
As mentioned earlier, in noise dominated regime, averaging is better than non-linear filtering
and hence the thresholding schemes perform better than the proposed ranging scheme. Beyond
certain P
tx
, the system is in the interference limited regime and hence the performance does
not change with P
tx
for the thresholding schemes. However for the proposed scheme, which
can suppress the interference, the ranging error decreases with P
tx
. Notice that the proposed
scheme is better than lookup table thresholding scheme beyondP
tx
= 5 dBm, is also better than
the genie thresholding scheme forP
tx
15 dBm, and is always better than the minimum and
median filtering schemes. For largeP
tx
, the RMSE with the proposed ranging scheme slightly
increases and this is more significant forI = 10. This can be explained as follows: For large
I and largeP
tx
, the strength of interference is large. Hence, as discussed earlier, interference
MPC overlaps with signal MPC in most of the waveforms, and since interference is strong, it
makes the desired signal unrecognizable and hence the algorithm misses the signal MPCs. Also
the behavior of the minimum and median filtering are consistent with the earlier work in the
literature. At low SNR, median filtering is better and at high SNR, minimum filtering is better
which is also reflected in the figure. Minimum filtering works well at high SNR and hence for
largeP
tx
, it has lower RMSE than the lookup table thresholding scheme.
133
4.5.2 Measurement data
We now evaluate the performance of the proposed ranging scheme with the measurement data,
and compare it with the two thresholding schemes. For the performance evaluation with the
proposed scheme, a fixed

N of
N
2
is used as no knowledge aboutI was assumed.
opt
andW
opt
are chosen according to the discussion in Sec. 4.3.4. For the lookup table thresholding scheme,
the optimal threshold for LOS/NLOS scenarios is computed as follows: For every receiver
position, the SNR and SIR are computed by averaging over the small scale fading and the
Monte Carlo simulations were performed for these parameter settings and with CM5 (outdoor
LOS)=CM6 (outdoor NLOS) channel models. The correlation threshold,, with the minimum
MSE is picked. Since the transmitted pulsep(t) is a long multi-tone waveform, energy based
non-coherent schemes suffer from poor SNR and hence the corresponding performance curves
are not shown. The channel impulse response can also be computed from the channel transfer
function and by applying a threshold, the noise and interference can be separated from the ToA
of the desired user. The performance with this approach is not included as it is inferior to the
thresholding schemes.
Figure 4.8 compares the CDF of the ranging error, (
^
dd), for different ranging schemes,
when both the desired user and interfering users are in LOS scenario. Results are shown for
I = 0 (No MUI), 1, 5, and 8. While the proposed ranging scheme has slightly more RMSE
than the lookup table thresholding scheme forI = 0, it gives significantly lower RMSE than
the lookup table thresholding scheme in the presence of MUI. While the ranging error with
the proposed scheme is always less than 0:5 m, it is more than 20 m for 10% of times with
the lookup table thresholding scheme. While the proposed scheme is robust to the number of
interfering users, the performance with the thresholding scheme degrades asI increases. Genie
thresholding outperforms the other two ranging schemes in this case.
Figure 4.9 gives the floor map of the NLOS measurement site with its dimensions. For
these receiver locations, the direct path is completely blocked by the buildings. The signal gets
134
Figure 4.8: Ranging error comparison for different schemes, when both desired and interfering
users are in LOS scenario (N = 50).
Figure 4.9: NLOS measurement floor map of USC VHE quad.
135
diffracted around the corners of the buildings and reaches the receiver as shown. In the ab-
sence of MUI, the ranging errors (with both the proposed ranging scheme and the thresholding
schemes) for measurements taken at receiver positions 1–6 was less than 5 m. But for the mea-
surements taken at receiver positions 7 and 8, it was 18–20 m. As shown in the figure, for the
receiver positions 7 and 8, the shortest measurable signal path is the reflection from building 4,
diffraction at building 3. This path length is 12 m more than the Euclidean distance between
transmitter and receiver. However, the diffraction angle at building 3 is 60 degrees. Hence, the
ray undergoes significant loss from diffraction and the corresponding MPC is not detectable.
The next shortest path is from double reflection at buildings 4 and 5 as shown in Figure 4.9.
This path length is 18 m more than the Euclidean distance. Since the average RMSE is dom-
inated by these two receiver positions, we exclude them for the performance comparison of
different ranging schemes. Results including these receiver positions are given in [83].
Figure 4.10 compares the CDF of the ranging error for different ranging schemes, when both
the desired user and interfering users are in the NLOS scenario. In the absence of interference
the proposed ranging scheme is as good as the lookup table thresholding scheme. Even with just
one interfering user, the proposed scheme gives considerably lower RMSE than the thresholding
schemes. While the ranging error with the proposed scheme is always less than 5 m, it can
be more than 15 m with the thresholding schemes. While the proposed scheme is robust to
the number of interfering users, the performance with the thresholding schemes degrades as
I increases. The impact of MUI is more significant in NLOS scenarios and even the genie
thresholding scheme cannot suppress the MUI effectively.
4.6 Conclusions
In this chapter, we proposed a novel coherent ranging algorithm to mitigate the MUI. We con-
sidered time-hopping impulse radio. We observed that after de-hopping the received signal,
receiver effectively sees multiple waveforms in which signal MPC occurs at same location, but
136
Figure 4.10: Ranging error comparison for different schemes, when both desired and interfering
users are in NLOS scenario (N = 50).
interference MPC location for different waveforms is different. Using this observation, we were
able to separate the interference MPCs and hence remove their contribution from the received
signal. We also derived the performance bounds with the proposed ranging scheme. Using the
IEEE 802.15.4a CM1 channel model as well as measured data, we showed the robustness of the
proposed ranging scheme to the strength of interference and the number of interfering users.
4.7 Acknowledgements
This work is partially supported by the Office of Naval Research (ONR) and Defense University
Research Instrumentation Program (DURIP). We thank Hao Feng, Sundar Aditya and Rui Wang
for their help with the measurements, Dr. Alan Willner for providing test and measurement
equipment for initial measurements, Asher V oskoboinik, Salman Khaleghi, and Hao Huang for
their help with the hardware components.
137
Chapter 5
Jammer Sensing and Performance
Analysis of MC-CDMA Systems in the
Presence of Wideband Jammer
The Radio Frequency (RF) spectrum is getting increasingly crowded with communication, nav-
igation, control and radar applications. As a result, the military has to deal unintentional jam-
ming, as well as malicious jamming. Spread spectrum (SS) techniques are well known for
their ability to combat the interference from jammer, and have been in use for more than 70
years. [110, 111]. In SS, the information signal is spread over a large bandwidth, that is larger
than the jammer bandwidth, thus making jammer suppression feasible.
While Direct-sequence spread spectrum (DSSS), where a low rate data sequence is multi-
plied by a pseudo noise (PN) sequence and subsequently despread at the receiver, is a popular
choice for SS, requires a rake receiver to combat the effects of multipath propagation, thus
making the receiver design complex. Multicarrier-code division multiple access (MC-CDMA),
a SS technique that combines code division multiple access (CDMA) and orthogonal frequency
division multiplexing (OFDM) was proposed in [112, 113]. It is robust against inter-symbol-
interference (ISI) and inter-carrier-interference (ICI), and does not require a rake receiver. Fur-
thermore, it allows an easy shaping of the transmit spectrum, allowing to adapt to both imperfec-
tions of hardware, and possible spectral regulations. For these reasons, it has been considered
138
for future communication systems [114, 132].
While the spreading and despreading of the information signal provides some processing
gain to mitigate the jammer interference, it is often insufficient when the jammer power is
large. Furthermore, if the received jammer power is large, it can drive the receiver front end into
saturation thereby making the desired transmitted signal detection infeasible. To avoid this, it is
desirable to do spectral notching at the receiver frontend, to suppress the jammer interference at
least partially. In order to achieve a good cancellation in the analog domain, the receiver needs
to have the capability to sense the band over which the jammer is operating. This becomes more
challenging when the jammer changes its frequency band of transmission over time. Overall,
a good receiver requires a joint design of notch filter, jammer estimator, and data demodulator.
The strength of the jammer impacts both how much residual interference is present (impacting
the optimum demodulator) and the estimator for the jammer state information (JSI).
While jammer estimation and suppression for spread spectrum applications have been well
explored in the literature, the majority of the studies focused on DSSS, Frequency-Hopping SS
(FHSS), CDMA and OFDM systems. Refs. [115–119] provide jammer estimation techniques
and anti-jamming performance of DSSS systems. Performance of FHSS in the presence of
a jammer in additive white Gaussian noise (AWGN) and Rayleigh fading channels has been
given in [120–123]. Ref. [124–126] study the performance of CDMA systems in the presence
of jammer interference. Performance of OFDM system for different jammer models, and the
mitigation techniques, have been discussed in [127] and the references therein. Jammer esti-
mation and suppression for MC-CDMA systems has not been well explored in the literature.
Refs. [128] and [129] studied the performance of MC-CDMA system with jammer interference
and provided jammer estimation schemes; [128] provides a jammer estimation scheme for the
case when the receiver knows the channel state information (CSI), and derives the resulting
symbol error rate (SER) for an AWGN channel. The jammer state information (JSI) is obtained
using the data symbols alone. Ref [129] considers a Rayleigh fading channel, and using pi-
139
lot symbols, it provides an iterative JSI estimation, CSI estimation and data decoding approach.
Both these works assume a simplified jammer model–on each subcarrier, the jammer is modeled
to be either present or absent with a certain probability. The jammer contributions on different
subcarriers are assumed independent and identically distributed (i:i:d:).
In this chapter, we consider a more realistic model for the jammer–the jammer is assumed
to be wideband in nature with a certain start frequency and bandwidth, and thus the jammer
contributions on different subcarriers (in the band of operation) are correlated. We derive the
performance of MC-CDMA systems with this realistic jammer model and derive the Maximum
Likelihood (ML) and Log-Likelihood Ratio (LLR) based JSI estimators. The main contribu-
tions of this chapter are summarized below:
We derive the analytical expressions for the SER in a Rayleigh fading channel, for the
case when the receiver has a full knowledge of the JSI (the start frequency, bandwidth
and the covariance matrix) and for the case where receiver only has partial JSI (only the
start frequency and the bandwidth). They act as a reference to compare the JSI estimation
schemes. We further quantify the performance gap between the two cases and study the
impact of different spreading sequences on the performance.
We derive the ML based and LLR based JSI estimators for the case where CSI is available
during jammer sensing and for the case where CSI is not available for JSI estimation.
We compare the performance of various proposed JSI estimators, and their impact on
the data decoding. Performance is characterized both with synthetic channels and with
channel realizations obtained from the propagation channel measurements.
The remainder of the chapter is organized the following way: The system model is described
in Sec. 5.1. The analytical expressions for the SER with known JSI is derived in Sec.5.2. Several
JSI estimation schemes when the CSI is available at the receiver are discussed in Sec. 5.3.1–the
ML based JSI estimator in Sec. 5.3.1 and the LLR based JSI estimators in Sec. 5.3.1 and 5.3.1.
140
JSI estimation schemes when the CSI is not available at the receiver is discussed in Sec. 5.3.2–
the ML based JSI estimator in Sec. 5.3.2 and the LLR based JSI estimators in Sec. 5.3.2. The
simulation results are given in Sec. 5.4. A summary and conclusions wrap up the chapter in
Sec. 5.5. Several mathematical derivations are moved to the Appendix.
Notation: Boldface lowercase and uppercase letters respectively denote a column vector and
a matrix, e.g., y is a vector and Y is a matrix. y
T
and y
y
respectively denote the transpose
and conjugate transpose of vector y;jjyjj shall denote the standard l
2
vector norm; x y
denotes element by element multiplication. y(k) denotes thek
th
element of the vector;jy(k)j
and (y(k))

shall denote the magnitude and conjugate of a complex number.jYj shall denote
the determinant of a matrix; I
N
shall denote the NxN identity matrix. P (X) and P (XjZ)
respectively denotes the marginal and conditional probability density function (pdf) of random
variable (RV)X; E [X] and var [X] shall denote the expectation and variance of RVX;X
CN(;
2
) shall denote thatX is a Complex Normal RV with mean and variance
2
.
5.1 System Model
We consider an MC-CDMA system with a transmitter and receiver block structure as shown
in Fig. 5.1. At the transmitter side, a data symbol s
d
is spread onto the N subcarriers using
a spreading sequencefc(k); 1kNg, i:e:, the complex transmission symbol at timed on
thek
th
subcarrier isc(k)s
d
. The resulting multicarrier signal then undergoes an IFFT, Parallel-
to-Serial (P/S) conversion, and addition of a cyclic prefix, just like an OFDM signal (com-
pare [130], Chapter 19); we will henceforth refer to the signal in time intervald as an “OFDM
symbol”. The resulting signal is then upconverted to bandpass domain, centered around car-
rier frequencyf
c
. Both the transmitter and the receiver are assumed to have a single antenna
element. The signal goes through a frequency-selective propagation channel, whose transfer
functions at the subcarrier frequencies are written into a vector h. At the receiver end, the RF
signal is down converted to baseband, and the OFDM symbol is demodulated (serial-to-parallel
141
Figure 5.1: MC-CDMA Transceiver.
conversion, elimination of the cyclic prefix, and Fourier transform); the signal on the N sub-
carriers is combined using the weightsfw
k
; 1kNg and the resulting complex symbol is
decoded to obtain an estimate of the transmitted data symbol.
We assume that the ongoing transmission is corrupted by a wideband jammer, centered at
frequency f
0
and with bandwidth B (expressed in units of subcarrier spacings, for notational
convenience). The band of frequencies in which the jammer is operating is not known to the
receiver and needs to be estimated. A notch filter at the receiver front end is used to partially
suppress the jammer interference so that the receiver does not go into saturation. The notch
frequency, the width and the depth will be determined in the digital domain and is fed back to
the analog front end.
Thus, for MC-CDMA transceiver, the received signal at the output of the FFT block, in the
presence of a wideband tone jammer (with start indexK and bandwidthB), is modeled as
y(k) =h(k)c(k)s +n(k);k2 [1;K 1][ [K +B;N] (5.1)
y(k) =h(k)c(k)s +n(k) +j(k);k2 [K;K +B 1] (5.2)
Let y
J
denote the vector of observations corresponding to subcarriers with Jammer and y
NJ
denote the vector of observations corresponding to subcarriers with no Jammer. Rewriting the
142
above equations in vector notation, separating the subcarriers into two sets–with and without
jammer, we get
y
NJ
=
~
h
NJ
s + n
NJ
(5.3)
y
J
=
~
h
J
s + j + n
NJ
(5.4)
where
~
h(k) , h(k)c(k). Here h is the true channel between the transmitter (Tx) and re-
ceiver (Rx). It is assumed to be a complex Gaussian vector with zero mean and covariance
matrix R
h
; c is the frequency domain spreading sequence

jc(k)j
2
=
1
N

; n is the additive
white Gaussian (AWG) noise vector with zero mean and covariance matrixN
0
I;s is the trans-
mitted data symbol that takes values from M-ary Phase Shift Keying (MPSK) constellation set
S,
p
E
S
exp (j2m=M); 0mM 1

; whereM denotes the modulation order andE
S
is the symbol energy; j is the jammer signal vector, which is assumed to be complex Gaussian
with zero mean and covariance matrix R. The interference from jammer and the AWG noise
are assumed to be independent.
Let E
J
be the overall jammer power, which is assumed to be known at the receiver. It is
assumed that the jammer has a flat power-spectral density (PSD) in the band of operation.
Hence, the jammer power per subcarrier is
E
J
B
. While the jammer start index and the bandwidth
can vary over time, the overall jammer power is assumed to be fixed. Hence, the jammer power
per subcarrier,
E
J
B
, can vary over time.
We first consider the case where the receiver has the knowledge of the jammer state infor-
mation (JSI) and derive the performance of MC-CDMA system. We later look into schemes to
estimate the jammer state information.
5.2 SER analysis with JSI
We consider two scenarios here–(i) a receiver that knows complete JSI, i:e:, jammer start index,
bandwidth and the complete jammer covariance matrix R; (ii) the receiver only knows partial
143
jammer information, i:e:, the jammer start index and the bandwidth but not the covariance
matrix. For both cases, we assume that the instantaneous channel, h, is known to the receiver,
which can be acquired by data pilots.
5.2.1 Full JSI case
The ML decoder is given by
^ s = arg max
s2S
P (y
J
; y
NJ
?
?
?h
J
; h
NJ
;s) (5.5)
= arg min
s2S
jjy
NJ

~
h
NJ
sjj
2
N
0
+

y
J

~
h
J
s

y
(R +N
0
I
B
)
1

y
J

~
h
J
s

(5.6)
= arg max
s2S
Re
(
y
NJ
y
~
h
NJ
s
N
0
+ y
J
y
(R +N
0
I
B
)
1
~
h
J
s
)
(5.7)
whereP (:) denotes the probability density function andRef:g denotes taking the real part.
Thus, the decision variable for the optimum combining is given by
D =
y
NJ
y
~
h
NJ
N
0
+ y
J
y
(R +N
0
I
B
)
1
~
h
J
(5.8)
Note thatD
?
?
?h
J
; h
NJ
is a complex Gaussian RV with mean and variance given by
E
h
D
?
?
?h
J
; h
NJ
i
=
jj
~
h
NJ
jj
2
s
N
0
+
~
h
y
J
(R +N
0
I
B
)
1
~
h
J
s (5.9)
var
h
D
?
?
?h
J
; h
NJ
i
=
jj
~
h
NJ
jj
2
E
S
N
0
+
~
h
y
J
(R +N
0
I
B
)
1
~
h
J
E
S
(5.10)
Thus, the instantaneous signal-to-interference-plus-noise ratio (SINR) for the data decoding is
given by
SINR =
jjh
NJ
jj
2
E
S
N
0
+ h
J
y
(R +N
0
I
B
)
1
h
J
E
S
(5.11)
The SER for the MPSK, conditioned on the channel, is
P

Err
?
?
?h
J
; h
NJ

=
1

Z M1
M

0
exp

jjh
NJ
jj
2
E
S
N
0
sin
2

M

sin
2

h
J
y
(R +N
0
I
B
)
1
h
J
E
S
sin
2

M

sin
2

!
d (5.12)
144
Averaging over the channel h
NJ
and h
J
, the SER expression simplifies to
P (Err) =
1

Z M1
M

0
N
Y
i=1

1 +

i
E
S
sin
2

M

sin
2

!
1
d (5.13)
wheref
i
g
N
i=1
are the eigen values of the matrix L
y
~
RL;
~
R,Block

1
N
0
I
NB
; (R +N
0
I
B
)
1

;
matrix L is the square-root of matrix R
~
h
0
or equivalently LL
y
= R
~
h
0
; R
~
h
0
is the covariance ma-
trix of
~
h
0
with
~
h
0
,
h
~
h
T
NJ
;
~
h
T
J
i
T
.
The detailed derivation is given in Appendix B.0.4.
5.2.2 With partial JSI
Since estimating the jammer covariance matrix is difficult and might not be easily available,
in this section we compute the SER for a case where the receiver only knows the jammer start
frequency and bandwidth, but not the covariance matrix R. The receiver assumesi:i:d: jammer
contributions across the subcarriers with powerE
J
=B on each subcarrier. In other words, the
receiver ignores the jammer correlation across subcarriers.
The ML decoder for this case is given by
^ s = arg max
s2S
P (y
NJ
; y
J
?
?
?h
NJ
; h
J
;s) (5.14)
= arg min
s2S
jjy
NJ

~
h
NJ
sjj
2
N
0
+
jjy
J

~
h
J
sjj
2
E
J
=B +N
0
(5.15)
= arg max
s2S
Re
(
y
NJ
y
~
h
NJ
s
N
0
+
y
J
y
~
h
J
s
E
J
=B +N
0
)
(5.16)
The decision variable for the optimum combining is given by
D =
y
NJ
y
~
h
NJ
N
0
+
y
J
y
~
h
J
E
J
=B +N
0
(5.17)
D
?
?
?h
NJ
; h
J
is a complex Gaussian RV with mean and variance given by
E
h
D
?
?
?h
NJ
; h
J
i
=
jj
~
h
NJ
jj
2
s
N
0
+
jj
~
h
J
jj
2
s
E
J
=B +N
0
(5.18)
var
h
D
?
?
?h
NJ
; h
J
i
=
jj
~
h
NJ
jj
2
E
S
N
0
+
~
h
y
J
(R +N
0
I
B
)
~
h
J
E
S
(E
J
=B +N
0
)
2
(5.19)
145
Thus, the SER of MPSK averaged over the channel fading is given by
P (Err)
1

Z M1
M

0
N
Y
i=1

1 +

i
E
S
sin
2

M

sin
2

!
1
d (5.20)
wheref
i
g
N
i=1
are the eigen values of the matrix L
y
~
R
2
L;
~
R
2
, Block

1
N
0
I
NB
; R
2

; R
2
,
2
E
J
=B+N
0
I
B

R+N
0
I
B
(E
J
=B+N
0
)
2
; matrix L is the square-root of matrix R
~
h
0
or equivalently LL
y
= R
~
h
0
;
R
~
h
0
is the covariance matrix of
~
h
0
with
~
h
0
,
h
~
h
T
NJ
;
~
h
T
J
i
T
.
The detailed derivation is given in Appendix B.0.5.
5.2.3 No JSI
When the receiver does not know the jammer subcarrier locations, the ML decoder is given by
^ s = arg min
s2S
jjy
NJ

~
h
NJ
sjj
2
N
0
+
jjy
J

~
h
J
sjj
2
N
0
(5.21)
= arg min
s2S
Re
(
y
NJ
y
~
h
NJ
s
N
0
+
y
J
y
~
h
J
s
N
0
)
(5.22)
5.3 JSI estimation and the symbol detection
In this section, we will estimate the JSI, i.e., the start index, the bandwidth and the covariance
matrix of the jammer. We assume that the jammer characteristics change relatively faster than
the channel. Hence we cannot use dedicated pilots to estimate the jammer but instead esti-
mate the jammer characteristics using the data symbols alone. We propose joint and sequential
jammer sensing and data decoding approaches.
We consider two scenarios, (i) the scenario where the CSI between the Tx and Rx is available
during jammer detection and (ii) the scenario where this is not the case. However, in both
scenarios we assume that perfect CSI is available for data decoding. This can be obtained in
practise using dedicated pilots to sense the channel for data decoding.
146
5.3.1 JSI estimation with perfect CSI
We assume that the jammer changes its characteristics within the coherence time of the channel
and we denote byD the number of realizations of the MC-CDMA symbols during which the
jammer characteristics remains the same. While the instantaneous jammer signal is different
in theseD data symbols, the higher order statistics like the location, bandwidth and covariance
matrix remain the same for theseD symbols.
Let K denote the true jammer start index and B denote the true jammer bandwidth. Let

K;B
,fK;K + 1; ;K +B 1g denote the set of subcarriers with jammer and let
K;B
,
f1;K 1;K +B; ;Ng denote the set of subcarriers without jammer.
The received signal after the IFFT of thed
th
MC-CDMA symbol is given by
y
(d)

K;B
=
~
h
(d)

K;B
s
(d)
+ n
(d)

K;B
+ j
(d)
; 1dD (5.23)
y
(d)

K;B
=
~
h
(d)

K;B
s
(d)
+ n
(d)

K;B
; 1dD (5.24)
where
~
h
(d)

K;B
, h

K;B
c
(d)

K;B
,
~
h
(d)

K;B
, h

K;B
c
(d)

K;B
The AWG noise is assumed to bei:i:d: across subcarriers and data symbols. The interfer-
ence from jammer j
(d)
is assumed to be circularly symmetric complex Normal with covariance
matrix R, and it is assumed to bei:i:d: across the data symbols.
Since the CSI is assumed to be known during jammer estimation, we have
y
(d)

K;B
CN

~
h
(d)

K;B
s
(d)
; R +N
0
I
B

(5.25)
y
(d)

K;B
CN

~
h
(d)

K;B
s
(d)
;N
0
I
NB

(5.26)
147
Joint ML estimation of jammer and the data symbols
The joint probability of jammer start indexK, the bandwidthB, the covariance matrix R, and
thed transmitted MPSK symbols, conditioned on the observations is given by
P

K;B; R;

s
(d)

D
d=1

n
y
(d)

K;B
; y
(d)

K;B
;
~
h
(d)

K;B
;
~
h
(d)

K;B
o
D
d=1

/N
0

D(NB)
2
jR +N
0
I
B
j

D
2
exp
0
B
@

1
2
D
X
d=1

y
(d)

K;B

~
h
(d)

K;B
s
(d)

2
N
0

1
2
D
X
d=1

y
(d)

K;B

~
h
(d)

K;B
s
(d)

y
(R+N
0
I
B
)
1

y
(d)

K;B

~
h
(d)

K;B
s
(d)

1
C
A
(5.27)
The joint ML estimator of the jammer start index, bandwidth, covariance matrix and the
D MPSK data symbols maximizes the above joint probability. Simplifying further, the joint
estimate of the jammer parameters and the MPSK data symbols is given by

^ s
(d)

D
d=1
;
^
K;
^
B;
^
R

= arg min
s
(d)
2S;1KN;0BNK;R

D(NB) log (N
0
)+D logjR+N
0
I
B
j
+
D
X
d=1

y
(d)

K;B

~
h
(d)

K;B
s
(d)

2
N
0
+
D
X
d=1

y
(d)

K;B

~
h
(d)

K;B
s
(d)

y
(R+N
0
I
B
)
1

y
(d)

K;B

~
h
(d)

K;B
s
(d)

!
(5.28)
whereS is the set of MPSK constellation symbols.
It can be seen that while the search over the jammer start index, bandwidth and the MPSK
data symbols is discrete, the elements of matrix R are continuous, thus making the above ex-
pression difficult to evaluate. For this reason, we use a sequential search instead of joint search.
MPSK symbol detection: Given the estimate of jammer parameters

^
K;
^
B;
^
R

, the ML esti-
mate of theD data symbols reduces to a one dimensional grid search as given below
^ s
(d)
= arg max
s2S
Re
0
B
@

y
(d)

^
K;
^
B

y
~
h
(d)

^
K;
^
B
s
N
0
+

y
(d)

^
K;
^
B

y

^
R +N
0
I
^
B

1
~
h
(d)

^
K;
^
B
s
1
C
A
; 1dD
(5.29)
Jammer covariance matrix estimation: Given the estimates of theD data symbols and the
jammer start index and bandwidth

^
K;
^
B

, the ML estimator of the covariance matrix reduces
148
to a sample covariance matrix
^
R =
1
D
D
X
d=1

y
(d)

^
K;
^
B

~
h
(d)

^
K;
^
B
^ s
(d)

y
(d)

^
K;
^
B

~
h
(d)

^
K;
^
B
^ s
(d)

y

N
0
I
^
B
(5.30)
Jammer start index and bandwidth estimation: The estimate of jammer start index and band-
width cannot be simplified further than (5.28) as each of the terms in the expression depend on
eitherK orB. Thus, we need to evaluate (5.28) for each (K;B) pair and find the one that min-
imizes the expression. More importantly, this requires the knowledge of R and the data symbol
estimates. Thus, the estimation of the jammer parameters and data symbols are coupled, i:e:,
estimation of one parameter requires the knowledge of the other.
To remove this coupling in the estimation of the parameters, we make a simplifying as-
sumption that R is a diagonal matrix, i:e:, we ignore the jammer correlation across subcarriers,
and evaluate (5.28) for each data symbol. The joint ML estimate of the jammer start index,
bandwidth and the data symbol then reduces to the three dimensional grid search given below

^ s;
^
K
d
;
^
B
d

= arg min
s2S;1KN;0BNK

(NB) log (N
0
) +B log

N
0
+
E
J
B

+

y
(d)

K;B

~
h
(d)

K;B
s

2
N
0
+

y
(d)

K;B

~
h
(d)

K;B
s

2
E
J
B
+N
0
!
(5.31)
Note that the estimate of the jammer start index and bandwidth can be different for different
symbols. Hence we take the highest frequency value of
n
^
K
d
;
^
B
d
o
D
d=1
to get the final estimate
ofK andB.
Sequence of evaluations: We first evaluate (5.31) to get the initial estimate of the D data
symbols, the jammer start index and the jammer bandwidth. With these estimates, we compute
the jammer covariance matrix estimate using (5.30), which is further used in (5.29) to get the
refined estimates of theD data symbols.
149
Block LLR based jammer detection and data decoding
We can see that the ML approach is computationally intense because of the three-dimensional
grid search with search space complexity ofO(MN
2
); M being the MPSK constellation size
andN being the FFT size. To reduce the search space complexity, we use the LLR approach.
We compute the LLR of the jammer occupying a certain set of subcarriers, and then determine
the jammer start index and the jammer bandwidth that maximizes the LLR. For this, we assume
that the covariance matrix R is diagonal

R =

E
J
B
+N
0

I
B

, i:e:, the jammer contribution on
each subcarrier isi:i:d: within the band of transmission.
We rewrite the system model in a simplified way. The received signal on thek
th
subcarrier
of thed
th
MC-CDMA symbol can be written as
y
(d)
(k) =
~
h
(d)
(k)s
(d)
+n
(d)
(k) +(k)j(k); 1kN; 1dD: (5.32)
where(k) is 1, if jammer is present on thek
th
subcarrier and 0 otherwise.
The LLR of the jammer being present on the subcarrier set
K;B
,fK; ;K+B1g is
given by
LLR (
K;B
) =
DB
2
log (N
0
)
K+B1
X
k=K
D
X
d=1
log
0
B
@
M
X
m=1
exp
0
B
@

y
(d)
(k)
~
h
(d)
(k)s
(d)
m

2
2N
0
1
C
A
1
C
A

DB
2
log

N
0
+
E
J
B

+
K+B1
X
k=K
D
X
d=1
log
0
B
@
M
X
m=1
exp
0
B
@

y
(d)
(k)
~
h
(d)
(k)s
(d)
m

2
2

N
0
+
E
J
B

1
C
A
1
C
A
(5.33)
The detailed derivation is given in Appendix B.0.6.
Thus, the joint estimate of the jammer start index and the jammer bandwidth is given by

^
K;
^
B

= arg max
1KN;0BNK
LLR (
K;B
) (5.34)
The search space complexity in this case isO(N
2
).
150
The ML estimate of thed
th
data symbol is
^ s
d
= arg max
s2S
Re

1
N
0
^
K
X
k=1
y
(d)
(k)

~
h
(d)
(k)s +
1

E
J
^
B
+N
0

^
K+
^
B1
X
k=
^
K+1
y
(d)
(k)

~
h
(d)
(k)s
+
1
N
0
N
X
k=
^
K+
^
B
y
(d)
(k)

~
h
(d)
(k)s

(5.35)
LLR based subcarrier level jammer sensing
While the block LLR approach reduces the search space complexity, it can still be considerably
high when the FFT size is large. In this section, we do jammer sensing on each subcarrier
independently, thereby reducing the search space further.
The LLR of the jammer being present on thek
th
subcarrier is given by
LLR(k) =
D
2
log (N
0
)
D
X
d=1
log
0
B
@
M
X
m=1
exp
0
B
@

y
(d)
(k)
~
h
(d)
(k)s
(d)
m

2
2N
0
1
C
A
1
C
A

D
2
log

N
0
+
E
J
B

+
D
X
d=1
log
0
B
@
max
B
M
X
m=1
exp
0
B
@

y
(d)
(k)
~
h
(d)
(k)s
(d)
m

2
2

N
0
+
E
J
B

1
C
A
1
C
A
(5.36)
The details are given in Appendix B.0.7
SinceLLR(k) = log

P (Jammer on subcarrierk)
1P (Jammer on subcarrierk)

, we can compute the probability of subcarrier
k corrupted by Jammer which is equal to 1= (1 + exp (LLR(k))).
Thus, we can do the soft combining of the LLRs for data detection. The ML estimate of the
data symbol is given by
^ s
d
= arg max
s2S
Re

N
X
k=1
y
(d)
(k)

~
h
(d)
(k)w
k
s
!
(5.37)
where the weightw
k
for thek
th
subcarrier is given by
w
k
=
E
S

E
J
^
B
+N
0

1
1 + exp (LLR(k))

+
E
S
N
0

1
1 + exp (LLR(k))

(5.38)
151
In order to evaluate the above expression, we need to estimateB. The jammer bandwidth
can be approximated by the sum of probabilities of subcarrier corrupted by jammer
^
B =
N
X
k=1
1
1 + exp (LLR(k))
(5.39)
5.3.2 JSI estimation with no CSI
It can be seen that all the above approaches for jammer estimation require the knowledge of
the channel h between Tx and Rx . In some scenarios, it is possible that the instantaneous CSI
might not be available during jammer estimation.
ML estimation of the JSI
LetK andB respectively be the jammer start index and bandwidth;
K;B
,fK; ;K+B1g
denote the subcarriers with jammer and
K;B
, f1;K 1;K +B; ;Ng denote the
subcarriers without jammer. The received signal after the IFFT of thed
th
MC-CDMA symbol
is given by
y
(d)

K;B
=
~
h
(d)

K;B
s
(d)
+ n
(d)

K;B
+ j
(d)
; 1dD (5.40)
y
(d)

K;B
=
~
h
(d)

K;B
s
(d)
+ n
(d)

K;B
; 1dD (5.41)
Since the CSI is not known during the jammer detection, we have
y
(d)

K;B
CN

0; R
~
h
(d)

K;B
E
S
+ R +N
0
I
B

(5.42)
y
(d)

K;B
CN

0; R
~
h
(d)

K;B
E
S
+N
0
I
NB

(5.43)
where R
~
h
(d)

K;B
, E

~
h
(d)

K;B

~
h
(d)

K;B

y

and R
~
h
(d)

K;B
, E

~
h
(d)

K;B

~
h
(d)

K;B

y

which are com-
pletely known.
We now derive the ML estimate of the jammer start index and the jammer bandwidth. For
this, we first assume that the jammer covariance matrix is diagonal

R =

E
J
B
+N
0

I
B

. The
152
joint probability of jammer start index and the bandwidth, conditioned on thed
th
MC-CDMA
symbol is given by
P

K;B

y

(d)
K;B
; y

(d)
K;B

/

R
~
h
(d)

K;B
E
S
+

E
J
B
+N
0

I
B

1
2

R
~
h
(d)

K;B
E
S
+N
0
I
NB

1
2
exp

1
2
y
(d)

K;B
y

R
~
h
(d)

K;B
E
S
+

E
J
B
+N
0

I
B

1
y
(d)

K;B

1
2
y
(d)

K;B
y

R
~
h
(d)

K;B
E
S
+N
0
I
NB

1
y
(d)

K;B
!
The joint ML estimator of the jammer start index and the bandwidth maximizes the above
joint probability. Simplifying further, the joint estimate of the jammer start index and the band-
width is given by

^
K
d
;
^
B
d

=arg min
1KN;0BNK
log

R
~
h
(d)

K;B
E
S
+

E
J
B
+N
0

I
B

+ log

R
~
h
(d)

K;B
E
S
+N
0
I
NB

+ y
(d)

K;B
y

R
~
h
(d)

K;B
E
S
+

E
J
B
+N
0

I
B

1
y
(d)

K;B
+ y
(d)

K;B
y

R
~
h
(d)

K;B
E
S
+N
0
I
NB

1
y
(d)

K;B
(5.44)
Note that the estimate of the jammer start index and bandwidth can be different for different
symbols. Hence we take the highest frequency value of
n
^
K
d
;
^
B
d
o
D
d=1
to get the final estimate
ofK andB.
Given the estimate of the jammer start index and the jammer bandwidth, the ML estimate of
theD data symbols is given by (5.29), with
^
R replaced by
E
J
^
B
I
^
B
. Once, the data symbols are
decoded, the ML estimate of the jammer covariance matrix is computed using (5.30). We can
further use the estimated R to refine the data symbol estimates using (5.29).
LLR based Jammer estimation
As we can see, the ML estimator is computationally very intense as it has a search space com-
plexity of O(N
2
). For each grid point, evaluating (5.44) involves matrix inverse operations,
which are computationally intense. To reduce this computational complexity, we use the LLR
based jammer estimation on each subcarrier.
Rewriting the system model in a simplified way, the received signal on thek
th
subcarrier of
153
thed
th
MC-CDMA symbol can be written as
y
(d)
(k) =
~
h
(d)
(k)s
(d)
+n
(d)
(k) +(k)j(k); 1kN; 1dD: (5.45)
where(k) is 1, if jammer is present on thek
th
subcarrier and 0 otherwise.
Thus, the LLR of the jammer being present on thek
th
subcarrier is given by
LLR(k) = log

P

(k) = 1jy
(d)
(k)

P ((k) = 0jy
(d)
(k))
!
(5.46)
= log

max
0BN
P

y
(d)
(k)j(k) = 1;B

P (y
(d)
(k)j(k) = 0)
!
(5.47)
Substituting the corresponding conditional probabilities, the above expression simplifies to
LLR(k) =
1
2
log (E
S
+N
0
) +
1
2

y
(d)
(k)

2
(E
S
+N
0
)
+ log
0
@
max
0BN
1
q
E
S
+
E
J
B
+N
0
exp

y
(d)
(k)

2
2

E
S
+
E
J
B
+N
0

!
1
A
(5.48)
The resulting LLRs are soft combined to detect the MPSK symbol as done in Sec. 5.3.1.
Clustering approach
For the estimation of the jammer start index and the bandwidth, the ML approach requires the
knowledge of the channel covariance matrix R
h
and the LLR approach requires the knowledge
of the overall jammer powerE
J
. Moreover, both these approaches require the knowledge that
the channel h and interference from jammer j are complex Normal distributed.
We now present a simple heuristic algorithm, that detects which of the subcarriers are cor-
rupted by jammer. This approach only requires the knowledge of the coherence bandwidth of
the channel, which is environment specific and fairly easy to obtain relative to R
h
.
Let L be the number of subcarriers in each coherence bandwidth. After the IFFT of the
MC-CDMA symbol, letfy(k)g
L
k=1
be the observations in one coherence bandwidth. It can
be seen that, in the absence of jammer interference, the observations
n
~ y(k),
y(k)
c(k)
o
L
k=1
are all
154
(a) = 0:6 (b) = 0:9
Figure 5.2: SER for different receivers when the JSI is available (N = 128, M = 16, L = 16, D =
1, SNR = 21 dB).
clustered around the signal term, hs, and with high probability, these observations are inside
a circle of radius
p
3N
0
. In the presence of strong jammer interference (jammer power larger
than the noise power), the subcarriers corrupted by jammer lie outside this circle. Hence, using
a clustering approach we can detect the subcarriers affected by jammer. Since we do not have
knowledge ofh ands, the cluster center is determined as the observation that has the smallest
sum distance to all other observations. The index of the cluster center is mathematically given
by
^ o = arg min
1kL
L
X
i=1
j~ y(k) ~ y(i)j
2
(5.49)
We use the following decision rule to determine the subcarriers with jammer interference:
^
k
, 1

j~ y(^ o) ~ y(k)j
2
> 6N
0

(5.50)
where 1f:g is the indicator function.
The MPSK symbol estimate is given by
^ s = arg max
s2S
Re
8
<
:
X
fk:^
k
=0g
y(k)

h(k)s
N
0
+
X
fk:^
k
=1g
y(k)

h(k)s
N
0
+
E
J
^
B
9
=
;
(5.51)
where
^
B =
P
N
k=1
^
k
.
155
5.4 Simulation Results
5.4.1 Performance with synthetic channels
We now compare the performance of different jammer estimation schemes developed in our
work. We consider a block fading channel in which the channel is completely correlated across
subcarriers within a block of L subcarriers, and is i:i:d: across the blocks. When not stated
otherwise, N = 128, L = 16, M = 16, and the signal-to-noise-ratio (SNR) =
E
S
N
0
is 21 dB.
For the jammer modeling, we generate the Jammer start index K to be uniformly distributed
in [0;N] and jammer bandwidth is uniformly distributed in [0;NK]. An exponential jam-
mer correlation model is assumed, i:e:, the i;j
th
entry of the covariance matrix is given by
R(i;j) =
E
J
B

jijj
. The Monte Carlo simulations are performed with 1000 realizations of the
fading channel and 100 realizations of the Jammer start and bandwidth.
We first investigate the impact of the JSI on the performance. Fig. 5.2 compares the per-
formance of different receiver schemes covered in Sec. 5.3, when = 0:6 and = 0:9. It
plots the SER as a function of Jammer-to-Noise Ratio (JNR,
E
J
N
0
). Specifically, we compare
the case where the receiver has the complete JSI–the start index, bandwidth and the covariance
matrix, with partial JSI, namely the case where the receiver only knows the start index and the
bandwidth. It can be seen that as increases (from Fig. 5.2a to Fig. 5.2b), i:e:, the jammer
correlation between the subcarriers increases, the gap between the Perfect JSI and the Partial
JSI receivers increases as expected. For a given, the performance gap between the two curves
first increases with the Jammer power and then reduces. When the jammer power per subcarrier
is really large, the receiver just ignores these subcarriers with jammer in both cases and hence
the jammer correlation across the subcarriers does not matter much.
These figures also serve to demonstrate the impact of different spreading sequences. We
investigate specifically Walsh-Hadamard (WH) sequences, which have been widely used in 3G
cellular systems for spreading in the time domain, and Zadoff-Chu (ZC) sequences, which are
156
(a)D = 100 (b)D = 10
Figure 5.3: SER for different jammer estimation schemes, when the CSI is available (N = 128,
M = 16, L = 16, = 0.9, SNR = 21 dB, ZC spreading sequence).
used for various purposes (such as channel sounding) in Long Term Evolution (LTE) cellu-
lar systems in the frequency domain. Fig. 5.2 shows the SER as a function of JNR for both
sequences. The ZC sequences perform almost universally better. It can be seen that when in-
creases (from Fig. 5.2a to Fig. 5.2b), the performance gap between the two spreading sequences
increases. When the jammer contribution isi:i:d: across subcarriers, all spreading sequences
will give similar performance, as long asjc(k)j =c (constant value); the SER expressions only
depend on c(k) in the form ofjc(k)j
2
. When the jammer is correlated, SER is different for
different spreading sequences. Fig. 5.2b validates the analytical expressions developed for SER
with Monte Carlo simulations; good agreement can be observed.
We next turn to the different jammer estimation techniques and their impact on the perfor-
mance. Hereon, we use the ZC spreading sequence for all our simulations. Fig. 5.3 plots the
SER as a function of JNR forD = 100 andD = 10, for the case where CSI is available dur-
ing jammer estimation.
1
The figure compare the performance of different jammer estimation
schemes: two ML based estimators – Type 1 ML estimator that estimates just the jammer start
and the jammer bandwidth and Type 2 ML estimator that estimates the jammer start, bandwidth
and covariance matrix; two LLR based approaches–Block LLR and subcarrier level LLR. It can
1
Remember thatD is the number of data symbols during which the jammer characteristics remain the same.
157
Figure 5.4: SER for different jammer estimation schemes, when the CSI is available (N = 128,
M = 16, L = 16, = 0.9, D = 10, JNR = 30 dB).
be seen that the type 1 ML estimator and Block LLR estimators are as good as the case where
the Rx knows the jammer start index and the jammer bandwidth exactly (Partial JSI case). In
the interference dominated regime (JNR > 25 dB), the subcarrier level LLR estimator is as
good as the block LLR estimator. As the jammer power per subcarrier increases, it is easier to
distinguish jammer from noise and hence both LLR approaches and ML estimator perform as
well as receiver having perfect knowledge of the jammer locations.
For theD = 100 case (Fig. 5.3a), as expected, the type 2 ML estimator is better than the type
1 ML estimator and the performance is slightly worse when compared with the perfect JSI case.
Interestingly, as can be seen from Fig. 5.3b, the performance of the type 2 ML estimator, which
estimates the jammer covariance matrix, is very bad for theD = 10 case. Since the sample size
to estimate R is very small, the estimate is unreliable and hence using the estimated R for data
decoding resulted in large errors.
We next analyze the effect of varying the desired signal power. Fig. 5.4 plots the SER as
a function of SNR, for different jammer estimation schemes, when D = 10 and 30 dB JNR.
Again, the performance of the Type 1 ML estimator, the block LLR approach and the subcarrier
level LLR approach are very similar to the partial JSI case, for moderate values of SNR.
158
(a)D = 100 (b)D = 10
Figure 5.5: SER for different jammer estimation schemes, when the CSI is not available (N =
128, M = 16, L = 16, = 0.9, SNR = 21 dB).
An additional complication arises when the CSI is not available during jammer estimation,
as described in Sec. 5.3.2. Fig. 5.5 plots the SER as a function of JNR for D = 100 and 10
respectively, for this case. The figures compare the performance of ML based estimators, the
LLR approach and the clustering approach. As anticipated, the ML estimators are better than
the LLR approach, which is again better than the clustering approach. The performance gap
between these schemes decreases as the JNR increases. Again, whenD is small, estimating the
jammer covariance matrix and subsequently using it for data decoding will result in large errors
as can be seen from Fig. 5.5b.
Fig. 5.6 plots the SER as a function of SNR, for different jammer estimation schemes, when
D = 10 and 30 dB JNR. For small values of the SNR, the performance of Type 1 ML estimator
and the LLR approach are very similar to the partial JSI case. In this regime, interference dom-
inates the signal and hence jammer subcarriers can be easily identified. As the SNR increases,
it is difficult to distinguish jammer and signal as the receiver does not have CSI. Hence, the
performance gap between the curves increases as the SNR increases.
159
Figure 5.6: SER for different jammer estimation schemes, when the CSI is not available (N =
128, M = 16, L = 16, = 0.9, D = 10, JNR = 30 dB).
Figure 5.7: The measurement locations.
5.4.2 Performance with measurement data
The performance of different jammer estimation algorithms has been tested using the mea-
surement data as well. We conducted a channel measurement campaign on the campus of the
University of Southern California (USC), which is a typical urban environment. The transmit-
ter was placed on the rooftop of the electrical engineering building (EEB) and the receiver was
moved continuously along the street. The measurement locations can be seen in Fig. 5.7. The
channel frequency responses were recorded in the 10-12 GHz band. A subcarrier spacing of
10 MHz was used. 300 independent channel realizations were collected. More details about the
measurement setup and campaign can be found in [131].
160
Figure 5.8: SER for different jammer estimation schemes computed using the measured impulse
responses, when the CSI is available (System BW = 1.28 GHz and f = 10 MHz (N = 128),
Bcoh200 MHz, = 0.9, D = 100, SNR = 21 dB).
The performance of the jammer estimation algorithms was tested using the collected channel
frequency responses, with jammer signals added in the postprocessing. Fig. 5.8 plots the SER
as a function of JNR, for different jammer estimation schemes, when the CSI is available for
jammer estimation. The observations are similar as in synthetic data. The ML estimators and
the Block LLR approach are as good as the partial JSI case. The subcarrier based LLR approach
works well for JNR above 30 dB. For these JNR values, we are in interference dominated regime
and hence jammer can be easily distinguished from noise.
Fig. 5.9 compares the SER for different jammer sensing schemes when the CSI is not avail-
able. Unlike the previous case, there is a noticeable performance gap between the LLR ap-
proach, ML approach and perfect JSI case even at high JNR values. Please note that, when the
CSI is not available, we need to differentiate Jammer from the signal plus noise term which is
more challenging than differentiating jammer from noise alone.
161
Figure 5.9: SER for different jammer estimation schemes computed using the measured impulse
responses, when the CSI is not available (System BW = 1.28 GHz and f = 10 MHz (N = 128),
Bcoh200 MHz, = 0.9, D = 100, SNR = 21 dB).
5.4.3 Performance with mismatch in Jammer model
So far we assumed that the jammer transmits in a single contiguous band and the interference
is complex Gaussian in distribution. The JSI estimators and the mathematical analysis was
developed for this jammer model. We now investigate the degradation in the performance of
the JSI estimators when some of these modeling assumptions about the jammer does not hold.
Non-contiguous jammer: So far we considered a case where the jammer transmits in one
contiguous frequency band with certain start index and bandwidth. The ML and block LLR
approaches estimate these parameters of the jammer. We now let jammer transmit in non-
contiguous frequency bands. This is also equivalent to having multiple band jammers, simul-
taneously interfering with the desired transmission. For the performance study, we simulate
a jammer transmitting in two non-contiguous bands, first subband randomly and uniform dis-
tributed in lower half of the system bandwidth and the second subband in the upper half of the
system bandwidth.
Fig. 5.10 compares the SER for different jammer sensing schemes when the CSI is available.
It can be seen that the mismatch in the jammer model resulted in increased SER for the ML and
162
Figure 5.10: SER for different jammer estimation schemes for non-contiguous jammer, when
the CSI is available (N = 128, M = 16, L = 16, = 0.9, D = 100, SNR = 21 dB).
Block LLR approaches. Since the subcarrier level LLR based JSI estimation approach does not
assume band structure, the performance is much better than the ML and Block LLR approach,
and for large JNR values, it is close to the performance of Rx with perfect knowledge of jammer
start index and bandwidth. Fig. 5.11 compares the SER for different jammer sensing schemes
when the CSI is not available. Again, because of mismatch in the jammer band of operation,
the performance of the ML approaches degrades for large JNR values. In the interference dom-
inated regime, the subcarrier level LLR based JSI estimation approach and clustering approach
provide better performance than the ML approach.
Non-Gaussian jammer interference: So far we assumed that the jammer interference on
each subcarrier is complex Gaussian in distribution. The ML and the LLR JSI estimators were
derived based on this assumption. We now investigate the performance degradation when this
assumption does not hold. For the study, we generate the jammer interference on each subcarrier
to be uniformly distributed (both real and imaginary part). We keep the Jammer covariance
matrix the same.
Fig. 5.10 compares the SER for different jammer sensing schemes when the CSI is avail-
able. It is interesting to note that there is not much degradation in the performance. The ML
163
Figure 5.11: SER for different jammer estimation schemes for non-contiguous jammer, when
the CSI is not available (N = 128, M = 16, L = 16, = 0.9, D = 100, SNR = 21 dB).
Figure 5.12: SER for different JSI estimation schemes when true jammer interference generated
using uniform distribution. CSI is available for JSI estimation (N = 128, M = 16, L = 16, =
0.9, D = 100, SNR = 21 dB).
164
Figure 5.13: SER for different JSI estimation schemes when true jammer interference generated
using uniform distribution. CSI not available for JSI estimation (N = 128, M = 16, L = 16, =
0.9, D = 100, SNR = 21 dB).
and the LLR based estimators developed under the assumption of Gaussian interference works
fairly well even when the true jammer interference is taken from uniformly distribution. These
estimators are not very sensitive to the true distribution of the jammer interference, but only
sensitive to the actual jammer power in the subcarriers. Similar observations hold true even
for the case where CSI is available during JSI estimation, as can be seen from Fig. 5.11. In
this case, there is a considerable gap between the ML approaches and the perfect JSI case at
moderate values of JNR. But the gap closes as the jammer power increases.
5.5 Conclusions
In this paper, we considered a MC-CDMA transceiver, jammed by wideband interference, in a
Rayleigh fading channel. For a non-stationary jammer, we derived the SER of MPSK constel-
lations for the case where the receiver knows the complete JSI (start index, bandwidth and the
jammer covariance matrix) and for the case where receiver only knows partial JSI (start index
and bandwidth). It has been observed that the performance gap between these two cases is
sensitive to the type of spreading sequences used and the correlation of the jammer interference
165
between adjacent subcarriers–the loss in performance by not knowing the jammer covariance
matrix is maximum for Zadoff-Chu sequences and when the adjacent subcarriers are perfectly
correlated.
We developed the ML based and LLR based JSI estimators for the case where CSI is avail-
able for JSI estimation and for the case CSI not available for JSI estimation. When CSI is
available for JSI estimation, the performance of Block LLR estimator is as good as the ML esti-
mator that estimates the start index and bandwidth, and partial JSI receiver. The subcarrier LLR
based JSI estimation works well when the JNR is large. The ML based estimation of jammer
covariance matrix works well when the number of data symbols is large (D > 100). When the
CSI is not available for JSI estimation, there is a noticeable performance gap between the partial
JSI receiver and ML based estimators and the LLR based JSI estimators.
5.6 Acknowledgments
We would like to thank Adolfo Corona and Niraj V . Nayak for the discussions and for providing
the initial equipment for the test measurements. We would like to thank Umit Bas and Rui Wang
for the help in the measurement setup and the propagation channel measurements.
166
Appendix A
Appendix: Ultrawideband Ranging with
interference mitigation
A.0.1 False alarms from a noise peak
A noise peak occurs in the interval [W; +W ], in thek
th
waveform (k> 1), ifjN
k
(t)j>
for somet2 [W; +W ]. It can be upper bounded as
P

Noise peak in [W; +W ] ink
th
waveform

=P (9t2 [W; +W ];jN
k
(t)j>)
2WP

jN
k
(t)j
2
>
2

= 2W exp

2
N
0

: (A.1)
Since it is assumed that the noise peak happens in the first waveform, the algorithm makes false
detection of as a signal MPC, if at least

N 1 of theN 1 waveforms have a noise peak in
[W; +W ] and there exists a circle of radius
enclosing at least

N of these points, includ-
ingX
1
. Let Event 1,fm 1 out ofN 1 waveforms have a noise peak in [W; +W ]g
and Event 2,f9 circle enclosing at least

N of m points, including X
1
g. The false alarm
probability can be upper bounded by
P
f;N

N
X
m=

N
P (Event 1; Event 2)
N
X
m=

N
min(P (Event 1);P (Event 2)): (A.2)
167
Using (A.1), we haveP (Event 1)

N 1
m 1

2W exp

2
N
0

m1

1 2W exp

2
N
0

Nm
:
LetX
1
;X
2
; ;X
m
be the strength of them noise peaks (jX
i
j>). Using union bound,
P(Event 2)
m
X
l=1
P

at least

N ofm points, includingX
1
; enclosed by circle aroundX
l

=(m1 )P

at least

N ofm points, includingX
1
; enclosed by circle aroundX
2

+P

at least

N ofm points are enclosed by circle aroundX
1

(A.3)
We will now evaluate each of the above two terms. The first term is given by
P

at least

N ofm points, includingX
1
; enclosed by circle with centerX
2
and radius

=
m
X
k=

N

m2
k2

P

jX
1
X
2
j<
;
k
Y
j=3
jX
j
X
2
j<
;
m
Y
j=k+1
jX
j
X
2
j>
!
=
m
X
k=

N

m2
k2
Z
P (jX
1
x
2
j<
)
k
Y
j=3
P (jX
j
x
2
j<
)
m
Y
j=k+1
P (jX
j
x
2
j>
)f
X
2
(x
2
)dx
2
=
m
X
k=

N

m2
k2
Z
1
0

1Q
1

r
2y
N
0
;
s
2
2
N
0
!!k1
Q
1

r
2y
N
0
;
s
2
2
N
0
!mk
1
N
0
exp

y
N
0

dy;
(A.4)
where Q
1
(:;:) is the Marcum Q-function. We have used the fact that

jX
i
j
2

m
i=1
are i:i:d:
Exponential RVs with meanN
0
andfjX
i
x
2
jg
m
i=3
arei:i:d: Rice RVs with parametersjx
2
j
and
q
N
0
2
[78]. The second term in (A.3) can similarly be shown to be
P

at least

N ofm points are enclosed by circle with centerX
1
and radius

=
m
X
k=

N

m1
k1
Z
1
0

1Q
1

r
2y
N
0
;
s
2
2
N
0
!!k1
Q
1

r
2y
N
0
;
s
2
2
N
0
!mk
1
N
0
exp

y
N
0

dy:
(A.5)
Using (A.4) and (A.5) in (A.3) and further using it in (A.2), the false alarm probability from a
noise peak follows after some simplification.
A.0.2 False alarms from an interference MPC
Interference peak occurs in the interval [W; +W ], in thek
th
waveform (k> 1), if at least
one interference MPC arrives in the interval [W; +W ], and the strength of the interfer-
168
ence exceeds the threshold . Since is small, we assume that the strength of interference
always exceeds threshold, whenever an interference MPC arrives in [W; +W ]. Hence,
the probability of an interference peak is upper bounded by
P

Interference peak in [W; +W ]; in thek
th
waveform

P (at least one interference MPC arrives in [W; +W ])
= 1 exp (2WI): (A.6)
We have used the fact that interference MPC arrivals are Poisson with parameter I. Since
it is assumed that an interference peak happens in the first waveform, the algorithm makes
false detection of as a signal MPC, if at least

N 1 of theN 1 waveforms has interfer-
ence peak in [W; +W ] and there exists a circle of radius
enclosing at least

N of these
points, includingX
1
. Let Event 1,fm 1 out ofN 1 waveforms has interference peak in
[W; +W ]g and Event 2,f9 circle enclosing at least

N ofm points, includingX
1
g. The
false alarm probability is upper bounded by
P
f;I

N
X
m=

N
P (Event 1; Event 2)
N
X
m=

N
min(P (Event 1);P (Event 2)): (A.7)
Using (A.6), we haveP (Event 1)

N 1
m 1

( 1 exp (2WI) )
m1
exp (2WI(Nm)):
Event 2 is very similar to the noise case, except that

jX
i
j
2

m
i=1
are nowi:i:d: Exponential RVs
with meanE
I
. Hence, replacingN
0
withE
I
in (A.4) and (A.5), and further using it in (A.7),
the false alarm probability from an interference peak follows.
A.0.3 Signal MPC detection
A signal MPC is detected in the interval [W; +W ], in thek
th
waveform, if the offset in
the location estimate by CLEAN is less thanW and the strength of the estimate,X
k
= +N
k
,
169
exceeds the threshold. The detection probability is given by
p(),P

signal MPC is detected in [W; +W ]; in thek
th
waveform

P(j^ jW)P(jX
k
j> )=
0
@
1Q
0
@
s
jj
2
N
0
( 1R
p
(2W ) )
1
A
1
A
Q
1
0
@
s
2jj
2
N
0
;
s
2
2
N
0
1
A
: (A.8)
For some of the waveforms, an interference MPC can overlap with the signal MPC at. Let
Event 1,fNo interference in [W; +W ]; in m +k out of N waveformsg, Event 2,
fSignal MPC detected in [W; +W ]; inm out ofm +k waveformsg, and Event 3,f9
circle enclosing at least

N out ofm pointsg. We assume that interference is strong enough that
the resulting MPC estimates at in these waveforms are far away from true value,, and hence
will be outside the circle. Hence the detection probability is lower bounded by
P
d

N
X
m=

N
Nm
X
k=0
P (Event 1,Event 2,Event 3)
=
N
X
m=

N
Nm
X
k=0
P (Event 1)P (Event 2jEvent 1)P (Event 3jEvent 1; Event 2) (A.9)
Using (A.6), we have
P (Event 1) =

N
m +k

exp (2WI(m +k)) (1 exp (2WI))
Nmk
: (A.10)
Using (A.8), we have
P (Event 2jEvent 1) =

m +k
m

p()
m
(1p())
k
: (A.11)
We will now evaluate the conditional probability term. Let
n
X
i
, +N
i
; 1im
o
be the
strength of them detected MPCs that are free from interference. The conditional probability
170
can be lower bounded as
P (Event 3jEvent 2; Event 1)
P

circle centered atX
1
with radius
encloses at least

N points
?
?
?Event 1; Event 2

=
m
X
l=

N

m1
l1

P

l
Y
j=2
jN
j
N
1
j<
;
m
Y
j=l+1
jN
j
N
1
j>
?
?
?j+N
1
j>; ;j+N
m
j>
!
=
m
X
l=

N

m1
l1
Z
n
1
:j+n
1
j>
P

jNn
1
j<
?
?
?j+Nj>

l1
P

jNn
1
j>
?
?
?j+Nj>

ml
f
N
1
(n
1
)dn
1
:
(A.12)
The conditional probability term in (A.12) can be written asP

jNn
1
j<
?
?
?j+Nj>

=
P(jNn
1
j<
;j+Nj>)P (j +Nj>)
1
. SinceN is a complex Gaussian RV with vari-
anceN
0
, we haveP (j +Nj>) = Q
1

q
2jj
2
N
0
;
q
2
2
N
0

. Since, 2:12
p
N
0
is small, for
jj
2
>>N
0
, we haveP(jNn
1
j<
;j+Nj>)P(jNn
1
j<
)=1Q
1

q
2jn
1
j
2
N
0
;
q
2
2
N
0

.
Hence we have
q(;jn
1
j),P

jNn
1
j<
?
?
?j+Nj>

0
@
1Q
1
0
@
s
2jn
1
j
2
N
0
;
s
2
2
N
0
1
A
1
A
Q
1
0
@
s
2jj
2
N
0
;
s
2
2
N
0
1
A
1
: (A.13)
Note thatjN
1
j is a Rayleigh RV and\N
1
is a uniform RV .
Rewriting the integral in (A.12) in polar coordinates and evaluating it over\N
1
, we get
x
r;:cos(\)>

2
jj
2
r
2
2rjj
q(;r)
l1
(1q(;r))
ml
r
N
0
exp

r
2
N
0

drd
=
Z
1
max(jj;0)
q(;r)
l1
(1q(;r))
ml
r
N
0
exp

r
2
N
0

g(r)dr; (A.14)
whereg(r) = 2 cos
1

2
jj
2
r
2
2rjj

forr2 (jjjj;jj +) and is 2 otherwise.
Hence the detection probability follows.
171
Appendix B
Appendix: Jammer Sensing and
Performance Analysis of MC-CDMA
Systems in the Presence of Wideband
Jammer
B.0.4 SER with Full JSI
The SER for the MPSK, conditioned on the channel, is
P

Err
?
?
?h
NJ
; h
J

=
1

Z M1
M

0
exp

jj
~
h
NJ
jj
2
N
0
E
S
sin
2

M

sin
2

~
h
y
J
(R +N
0
I
B
)
1
~
h
J
E
S
sin
2

M

sin
2

!
d
This can be rewritten in the form as given below
P

Err
?
?
?h

=
1

Z M1
M

0
exp

h
0
y
~
Rh
0
E
S
sin
2

M

sin
2

!
d (B.1)
where
~
h
0
=
h
~
h
T
NJ
;
~
h
T
J
i
T
and
~
R =Block

1
N
0
I
NB
; (R +N
0
I
B
)
1

.
Notice that
~
h
0
can be written as
~
h
0
= Lg with g as ani:i:d: standard Normal vector and
LL
y
= R
~
h
0
. We thus have,
~
h
0
y
~
R
~
h
0
= g
y
L
y
~
RLg (B.2)
Please note that L
y
~
RL is also a hermitian symmetric non-negative definite matrix. Hence
172
we can write L
y
~
RL = U
y
1
U
1
, where U
1
is a unitary matrix and is a diagonal matrix with
real, non-negative entries.
The SER expression, conditioned on the channel h, can thus be rewritten as
P

Err
?
?
?h

=
1

Z M1
M

0
exp

(U
1
g)
y
(U
1
g)
E
S
sin
2

M

sin
2

!
d (B.3)
=
1

Z M1
M

0
exp

N
X
i=1

i
j~ g(i)j
2
E
S
sin
2

M

sin
2

!
d (B.4)
where ~ g , U
1
g is also standard a normal random vector. Thus

j~ g(i)j
2

N
i=1
arei:i:d: expo-
nential RVs with mean 1.
Thus, averaging the above expression over ~ g gives (5.13).
B.0.5 SER with partial JSI
The instantaneous SINR for the data decoding is given by
SINR =

jj
~
h
NJ
jj
2
N
0
+
jj
~
h
J
jj
2
E
J
=B+N
0

2
jj
~
h
NJ
jj
2
N
0
+
~
h
y
J
(R+N
0
I
B
)
~
h
J
(E
J
=B+N
0
)
2
E
S
(B.5)

jj
~
h
NJ
jj
2
N
0
+ 2
jj
~
h
J
jj
2
E
J
=B +N
0

~
h
y
J
(R +N
0
I
B
)
~
h
J
(E
J
=B +N
0
)
2
!
E
S
(B.6)
where the approximation follows from
E
J
B
>> N
0
and
(a+b)
2
a+c
=
a(1+
b
a
)
2
1+
c
a
a + 2bc, when
a>>b anda>>c.
Using the above approximation, the SER for the MPSK, conditioned on the channel, is given
by
P

Err
?
?
?
~
h
NJ
;
~
h
J

1

Z M1
M

0
exp

jj
~
h
NJ
jj
2
1
N
0
E
S
sin
2

M

sin
2

~
h
y
J
R
2
~
h
J
E
S
sin
2

M

sin
2

!
d
where R
2
,
2
E
J
=B+N
0
I
B

R+N
0
I
B
(E
J
=B+N
0
)
2
.
Similar to the SER analysis for the full JSI case, the above expression when averaged over
173
the channel reduces to
P (Err)
1

Z M1
M

0
N
Y
i=1

1 +

i
E
S
sin
2

M

sin
2

!
1
d (B.7)
wheref
i
g
N
i=1
are the eigen values of the matrix L
y
~
R
2
L; LL
y
= R
~
h
0
and the matrix
~
R
2
is
defined as
~
R
2
,Block

1
N
0
I
NB
; R
2

: (B.8)
B.0.6 LLR (
K;B
) derivation
The LLR of the jammer being present on the k
th
subcarrier, conditioned on the observations

y
(d)
(k)

D
d=1
and the jammer bandwidth beingB is given by
LLR(k) = log
0
B
B
@
P

(k) = 1

y
(d)
(k)

D
d=1
;
n
~
h
(d)
(k)
o
D
d=1
;B

P

(k) = 0

fy
(d)
(k)g
D
d=1
;
n
~
h
(d)
(k)
o
D
d=1
;B

1
C
C
A
(B.9)
= log
0
@
Q
D
d=1
P

y
(d)
(k)

(k) = 1;
~
h
(d)
(k);B

Q
D
d=1
P

y
(d)
(k)

(k) = 0;
~
h
(d)
(k);B

1
A
(B.10)
= log
0
@
Q
D
d=1

1
M
P
M
m=1
P

y
(d)
(k)

(k) = 1;
~
h
(d)
(k);B;s
(d)
m

Q
D
d=1

1
M
P
M
m=1
P

y
(d)
(k)

(k) = 0;
~
h
(d)
(k);B;s
(d)
m

1
A
(B.11)
Substituting the corresponding conditional distributions fory
(d)
(k), the above equation simpli-
fies
LLR(k) =
D
2
log (N
0
)
D
X
d=1
log
0
B
@
M
X
m=1
exp
0
B
@

y
(d)
(k)
~
h
(d)
(k)s
(d)
m

2
2N
0
1
C
A
1
C
A

D
2
log

N
0
+
E
J
B

+
D
X
d=1
log
0
B
@
M
X
m=1
exp
0
B
@

y
(d)
(k)
~
h
(d)
(k)s
(d)
m

2
2

N
0
+
E
J
B

1
C
A
1
C
A
(B.12)
Since the jammer contributions on different subcarriers is assumedi:i:d: in the band of trans-
mission, the LLR of jammer occupying the subcarrier set
K;B
=fK; ;K+B1g is given
174
by
LLR (
K;B
) =
K+B1
X
k=K
LLR(k) (B.13)
B.0.7 LLR(k) derivation
The LLR of jammer being present on thek
th
subcarrier is given by
LLR(k) = log
0
B
B
@
P

(k) = 1

y
(d)
(k)

D
d=1
;
n
~
h
(d)
(k)
o
D
d=1

P

(k) = 0

fy
(d)
(k)g
D
d=1
;
n
~
h
(d)
(k)
o
D
d=1

1
C
C
A
(B.14)
= log
0
@
max
1BN
Q
D
d=1

P

y
(d)
(k)

(k) = 1;
~
h
(d)
(k);B

Q
D
d=1

P

y
(d)
(k)

(k) = 0;
~
h
(d)
(k)

1
A
(B.15)
= log
0
@
max
1BN
Q
D
d=1

1
M
P
M
m=1
P

y
(d)
(k)

(k) = 1;
~
h
(d)
(k);B;s
(d)
m

Q
D
d=1

1
M
P
M
m=1
P

y
(d)
(k)

(k) = 0;
~
h
(d)
(k);s
(d)
m

1
A
(B.16)
Substituting the corresponding conditional distributions for y
(d)
(k), The above expression
simplifies to
LLR(k) =
D
2
log (N
0
)
D
X
d=1
log
0
B
@
M
X
m=1
exp
0
B
@

y
(d)
(k)
~
h
(d)
(k)s
(d)
m

2
2N
0
1
C
A
1
C
A

D
2
log

N
0
+
E
J
B

+
D
X
d=1
log
0
B
@
max
B
M
X
m=1
exp
0
B
@

y
(d)
(k)
~
h
(d)
(k)s
(d)
m

2
2

N
0
+
E
J
B

1
C
A
1
C
A
(B.17)
175
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Abstract (if available)

Abstract Interference is a very common phenomenon in wireless communication systems. With the Radio Frequency (RF) spectrum getting increasingly crowded due to the demand for high data rates, and with the coexistence of the RF based radar, communication and navigation systems, interference is often inevitable and often is the dominant effect limiting the performance. Radar systems often suffer from malicious jammers. Communication and navigation systems suffer from multiuser and multipath interference. Thus, wireless systems have to use smart signaling schemes and post-processing techniques in order to mitigate interference. ❧ Ultrawideband (UWB) technology is a good candidate to mitigate interference. The large bandwidth helps in separating the closely spaced multipaths and thereby providing better ranging accuracy for navigation systems. The large bandwidths can be used to achieve large data rates in communication systems, and it can be used to combat the jammers in radar applications using spread spectrum techniques. However, an efficient transceiver design requires the knowledge of the propagation channel in which the system is deployed, as the propagation channel plays a critical role in determining the performance of the wireless systems. Thus, propagation channel measurement and modeling are essential for design, simulation and deployment of wireless systems. In my research work, I have addressed some of these issues related to interference mitigation and propagation channel measurement for ultrawideband systems. ❧ In my first work, I looked at propagation channel characterization for ultrawideband systems. Two different scenarios were studied. The first scenario considered is an outdoor cellular environment. We provide the results from a channel measurement campaign conducted in an urban macro and micro-cellular environments, over the continuous frequency band of 3–18 GHz. For an urban macro-cellular (UMa) environment, we characterize the wideband pathloss, shadow fading, Root-Mean-Square (RMS) delay spreads and Ricean factor for different measurement routes in line-of-sight (LOS) and non-line-of-sight (NLOS) scenarios

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Asset Metadata

Creator Kristem, Vinod (author)

Core Title Propagation channel characterization and interference mitigation strategies for ultrawideband systems

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 07/21/2017

Defense Date 05/30/2017

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

Tag channel measurements,channel modeling,interference mitigation,localization,OAI-PMH Harvest,ultrawideband,wireless communications

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Molisch, Andreas F. (committee chair), Golubchik, Leana (committee member), Hashemi, Hossein (committee member)

Creator Email kristem@usc.edu,vinod.kristem@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-408703

Unique identifier UC11264509

Identifier etd-KristemVin-5579.pdf (filename),usctheses-c40-408703 (legacy record id)

Legacy Identifier etd-KristemVin-5579.pdf

Dmrecord 408703

Document Type Dissertation

Rights Kristem, Vinod

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

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