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Gains of Mobility for Communication and Sensing in Vehicular SensorNetworks
by
Waleed Saeed Alasmary
A thesis submitted in conformity with the requirementsfor the degree of Doctor of Philosophy
Graduate Department of Electrical and Computer EngineeringUniversity of Toronto
c© Copyright 2015 by Waleed Saeed Alasmary
Abstract
Gains of Mobility for Communication and Sensing in Vehicular Sensor Networks
Waleed Saeed Alasmary
Doctor of Philosophy
Graduate Department of Electrical and Computer Engineering
University of Toronto
2015
In this thesis, mobility information exchanged among vehicles devices is utilized to improve the
communication and sensing in vehicular networks. Mobility usually causes a loss in communications,
and can add an additional load in sensing. There have been research attempts to handle such challenges
in vehicular networks by addressing them after realizing the mobility impact, or adaptively addressing
the problem as the mobility changes. This thesis takes a different approach to enhance communication,
and sensing in vehicular networks. The first objective of this thesis is to utilize mobility information in
order to enhance communication in vehicular networks by reducing the excessive load on the channel,
while preserving the communicated information. The second objective of this thesis is to utilize predicted
mobility information in order to enhance sensing in vehicular sensor networks by efficiently providing
the sensing metric, with a minimal load on the communication channel. In order to have mobility
information, vehicles has to communicate that information.
The first part of this thesis examines location awareness in vehicular networks via sparse recovery:
that is, how vehicles would know the locations of each other in the vicinity in order to provide the
optimized mobile sensing of the first part of the thesis. Locations of vehicles are exchanged periodically
via beaconing to make each vehicle aware of the location of nearby vehicles for improved safety, and to
provide non-safety services. The amount of data exchanged via periodical beacon broadcast can be ex-
tremely large, and the channel can become congested in dense scenarios. We proposed a novel congestion
control scheme that minimizes the amount of broadcast data while preserving the location information
for each vehicle using compressive sensing. This novel scheme is designed for two different modes that
ii
are suitable for two different applications. The first approach is a super-frame scheme that is designed
for delay-tolerant applications, such as updating traffic maps (e.g., Google maps). The second approach
is a sliding window scheme that is designed for real-time applications, such as safety packet exchange in
vehicular networks. The proposed congestion control scheme was implemented on a smartphone-based
testbed and shown to minimize the amount of data exchange while successfully preserving beaconing
information with high accuracy in both delay-tolerant and real-time modes. Experimental tests were
conducted in the highways and downtown streets of the city of Toronto. The proposed scheme is shown to
reduce the number of exchanged packets while preserving the communicated information with excellent
accuracy.
The second part of this thesis examines the gain of predicted mobility in enhancing the coverage of
targets. Herein, the sensors can be cameras, and sensing becomes the coverage of targets. Moreover,
targets becomes the specific areas of the road that are of interest for coverage. Due to the limited com-
munication channel capacity in the vehicular network, the main objective is to minimize the amount of
sensed and transmitted data while preserving the coverage of all target areas. Specifically, we utilize pre-
dicted car mobility in order to provide the required coverage of target areas with less sensor activations.
Activations in this context means that a sensor is selected for covering a target area, and the captured
image is transmitted over the communication channel to a fusion centre. First, we formulate mathe-
matical optimization models for the proposed mobile sensing scheme and the existing stationary sensing
scheme. Then, by using probability analysis, we demonstrate that the proposed scheme outperforms the
existing stationary solution in terms of sensing cost and size of the feasibility region of the optimization
problem. After that, we propose two approximation algorithms that allow practical implementation of
the novel coverage scheme in the centralized and distributed modes. In this part, we assume that the
mobility information is known.
The mobile sensing scheme is also studied when the predicted mobility information is noisy. We
show that the mobile sensing scheme outperforms the stationary sensing scheme when the noise level in
mobility information is small. Increasing the noise level in mobility information results in an increased
sensing cost for the mobile sensing scheme. Then a breaking point exists in which the noise level in
iii
mobility information results in larger sensing cost for the mobile sensing scheme compared to that of
the stationary sensing scheme. The mobile sensing scheme breaking point is found via analysis and
simulation.
iv
Dedication
This thesis is dedicated to the person who changed my perspective of the world—my daughter, Leen!
v
Acknowledgements
This thesis would not have been completed without the help of many people. Herein, I will express my
gratitude to them.
First, I would like to express my deepest appreciation and gratitude to my Ph.D. supervisor Professor
Shahrokh Valaee for his constant guidance, support, and patience during the course of my Ph.D. research.
Professor Valaee succeeded in preparing me to be an excellent researcher with a long-term vision and to
be an independent researcher. Truly, without his guidance and valuable suggestions, this thesis would
not be in its existing state.
I would like to thank Professor Baochun Li, Professor Deepa Kundur, Professor Dimitrios Hatzinakos
and Professor Elvino Sousa for serving as members of my thesis defense committee.
I would like to thank my colleagues at the WIRLab group. Special thanks to Hamed Sadeghi for his
help in co-authoring two of my research papers. I would like to also thank the members of the ITS lab
at the University of Toronto, especially Dr. Samah El-Tantawy and Professor Baher Abdulhai for their
collaboration in one of my research papers.
Special thanks to Umm Al-Qura University for providing me a scholarship to pursue my Ph.D. degree.
I would like to thank the Ministry of Higher Education at Saudi Arabia and the Saudi Arabian Cultural
Bureau in Canada for their efforts and support.
I would like to thank all my friends at the University and the city of Toronto, who helped me through
the course of my studies, and made my life enjoyable. Special thanks to my friend Ahmad Al-Sohaily.
We shared unforgettable moments!
I am truly thankful for my parents, my siblings Hassan, May, and Badr for their unconditional and
endless support and encouragement.
I cannot express enough gratitude to my wife, Rabab, for living the journey of my studies, starting
from the moment I decided to study at the University of Toronto until the last moment of my Ph.D.
defense. I will always remember that we experienced each moment together.
Finally, I would like to express my feelings to the one person who was my daily inspiration to seek
perfection through hard work. Everyday when I come home from my office in Bahen Building, I see
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my daughter, and she refuels me with energy, passion, and motivation to continue my research until the
end. Leen, you are my true inspiration in life.
vii
Contents
1 Introduction 1
1.1 Vehicular Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 A VSN Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Prediction of Mobility Information in a VSN . . . . . . . . . . . . . . . . . . . . . 4
1.1.3 Network Congestion in a VSN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.4 A New Perspective for Addressing Network Congestion in a VSN . . . . . . . . . . 6
1.2 Gain of Mobility for Communication in VSNs . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Research Scope and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Gain of Mobility for Sensing in VSNs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Research Scope and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Interconnection between Communication and Sensing in VSNs . . . . . . . . . . . . . . . 15
1.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 Background and Related Works on Communication and Sensing in VSNs 18
2.1 Communications in VSNs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.1 Congestion Control in VSNs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.2 Compressive Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Sensing in Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Coverage Problems in Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Mobility and Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
viii
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 Location Awareness via Sparse Recovery in VSNs 30
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.1 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.2 Velocity Correction Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.3 Sliding Window CS Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.4 Delay of the Sliding Window CS Scheme . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Performance Evaluation of The Location Awareness Scheme . . . . . . . . . . . . . . . . . 41
3.3.1 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Super-frame Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.3 Sliding Window Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.4 Sliding Window Edge Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Gain of Mobility for Sensing in VSNs 56
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 System Model and Sensing Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.1 Stationary Sensing Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.2 Mobile Sensing Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.3 Interconnection of Mobile and Stationary Problems . . . . . . . . . . . . . . . . . . 63
4.2.4 Mobility and Coverage Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Mobility Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3.1 Feasibility Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.2 Sensing Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4 Approximation Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.1 Centralized Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
ix
4.4.2 Distributed Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5.1 Feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5.2 Sensing Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.5.3 Approximation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.6 Evaluation of the Mobile Scheduler with a Markovian Mobility Model . . . . . . . . . . . 87
4.6.1 Markovian Mobility Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.6.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5 Noisy Mobility Impact on Sensing 90
5.1 Dissection of the Mobile Scheduler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.1.1 Better Sensing Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.1.2 Better Coverage Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.1.3 Better Coverage Delay and Sensing Cost . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 Analytical Study of Noise Impact on Sensing Cost . . . . . . . . . . . . . . . . . . . . . . 94
5.2.1 Sensing Cost Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2.2 Noise in Coverage Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2.3 Interpretation of the Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2.4 Mask Noise Impact on Sensing Cost . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6 Conclusions and Future Works 104
6.1 Gain of Mobility for Communication in VSNs . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.2 Gain of Mobility for Sensing in VSNs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.3 Application to Future Cars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.4 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
x
6.4.1 Integration with a Distributed Congestion Controller . . . . . . . . . . . . . . . . . 108
6.4.2 Impact of the CS-based Congestion Controller on Safety Metrics . . . . . . . . . . 108
6.4.3 Distributed Compressive Sensing Location Awareness . . . . . . . . . . . . . . . . 108
6.4.4 Applications of Location Awareness in Heterogenous Networks . . . . . . . . . . . 109
6.4.5 Time-to-Space Conversion of the Mobile Scheduler . . . . . . . . . . . . . . . . . . 109
Bibliography 110
xi
List of Figures
1.1 Illustration of a VSN architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Example of beaconing according to the WAVE standard. . . . . . . . . . . . . . . . . . . . 9
1.3 Illustration of how the sparse recovery location awareness results in congestion avoidance. 10
2.1 Performance degradation of SPR beaconing in vehicular networks. . . . . . . . . . . . . . 19
2.2 A sample velocity trajectory based on the traffic flow theory [55]. . . . . . . . . . . . . . . 27
3.1 Illustration of the measurements at the MAC layer. . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Illustration of measurements collection by the CS scheme. . . . . . . . . . . . . . . . . . . 35
3.3 Illustration measurements collection in the CS scheme. . . . . . . . . . . . . . . . . . . . . 39
3.4 The SWE estimation algorithm for enhancing the accuracy of x(Q)i . . . . . . . . . . . . . . 41
3.5 Location of the data collected on Toronto map . . . . . . . . . . . . . . . . . . . . . . . . 43
3.6 Example of velocity estimation using CS scheme and interpolation using city data. . . . . 44
3.7 Example of velocity estimation using CS scheme and interpolation using city data. . . . . 44
3.8 Example of edge error using the last two measurements only at location n = i and n− 1
(i.e., the transmission time of (M−1) measurements) for the CS scheme and interpolation
using one velocity vector. M = 10 is the total number of super-frame sampling times. For
example, for the values the horizontal axis of 200, the immediate sample before the last
one is transmitted at that time, and the estimation errors is computed over the interval
[200, 328]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
xii
3.9 Average and maximum errors in velocity estimation using the CS scheme and interpolation
versus α for the city data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.10 Average and maximum errors in velocity estimation using the CS scheme and interpolation
versus α for the highway data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.11 Average and maximum errors in velocity estimation using the CS scheme and interpolation
versus α for the city data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.12 Example of velocity estimation using the CS scheme with a sliding window using the city
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.13 Example of velocity estimation using the CS scheme with a sliding window using the city
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.14 Estimation errors for a fixed R versus L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.15 Estimation errors for a fixed L versus R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.16 Estimation of the location information using the CS sliding window scheme. . . . . . . . . 51
3.17 Estimation error with and without considering x(Q)i versus R. . . . . . . . . . . . . . . . . 52
3.18 Estimation error with and without considering x(Q)i versus α. . . . . . . . . . . . . . . . . 53
3.19 Estimation error of x(Q)i versus the sliding index. . . . . . . . . . . . . . . . . . . . . . . . 53
3.20 Estimation error of x(Q)i using the SWE algorithm versus the sliding index. . . . . . . . . 54
3.21 Estimation error of the sliding window CS scheme and interpolation versus R. . . . . . . . 55
4.1 Illustration of the system model practical scenario. . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Theoretical feasibility gain Γ, based on (4.18), versus p for different values of K. . . . . . 70
4.3 Q(zs) versus p for different values of K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4 Theoretical feasibility gain Γ, based on (4.18), versus p for different values of N , M , and q. 71
4.5 Illustration of how the stationary and mobile schedulers satisfy coverage qualities on average. 73
4.6 Ks and Km based on Theorems 3 and 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.7 Ks
Kmbased on Theorems 3 and 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.8 Approximations of Ks and Km based on (4.33) and (4.35). . . . . . . . . . . . . . . . . . 78
4.9 f(N) =(εs − εm√
N
)versus N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
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4.10 Ks −Km versus M based on Theorems 3 and 4, and equations (4.33), (4.35), and (5.5). . 80
4.11 The CGA algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.12 The DGA algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.13 The probability of feasibility based on Theorem 1 and Theorem 2 for the mobile scheduler,
and stationary one [25]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.14 The probability of feasibility for the mobile and stationary schedulers for different values
of λ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.15 Sensing cost based on Theorem 3 and Theorem 4 for the mobile scheduler, and stationary
one [25]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.16 Sensing cost for centralized and distributed greedy algorithms with the BB solution for
the stationary approach [25] as the benchmark for comparison. . . . . . . . . . . . . . . . 86
4.17 Illustration of temporal dependence in availability for coverage for a sensor-target pair. . . 87
4.18 Markov chain for sensor-target coverage model. . . . . . . . . . . . . . . . . . . . . . . . . 88
4.19 Sensing cost for the mobile and stationary schedulers using the Markovian mobility model. 88
5.1 Microscopic view of the stationary and mobile schedulers results. Mobile scheduler shows
better sensing cost compared to the stationary one. K = 3, M = 2, N = 4, and q = 1. . . 92
5.2 Microscopic view of the stationary and mobile schedulers results. Mobile scheduler shows
faster coverage of targets compared to the stationary one. K = 3, M = 2, N = 4, and
q = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3 Microscopic view of the stationary and mobile schedulers results. Mobile scheduler shows
better sensing cost and faster coverage of targets compared to the stationary one. K = 3,
M = 2, N = 4, and q = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.4 Microscopic view of the stationary and mobile schedulers results. Mobile scheduler shows
better sensing cost and faster coverage of targets compared to the stationary one. K = 6,
M = 3, N = 4, and q = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
xiv
5.5 Microscopic view of the stationary and mobile schedulers results. Mobile scheduler shows
better sensing cost and faster coverage of targets compared to the stationary one. K = 6,
M = 3, N = 4, and q = 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.6 The effective sensing cost versus p. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.7 The effective sensing cost for the stationary and the mobile schedulers with noise-free
mobility information, and the mobile scheduler with noisy mobility information versus β.
Breaking point is at β = 0.36. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.8 The breaking point of the mobile scheduler β∗ for different values of M , N and q versus p. 102
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List of Abbreviations
BB Branch and bound approximation algorithm
CCH Control channel
CGA Centralized greedy algorithm
CS Compressive sensing
DCS-SOMP Distributed compressed sensing SOMP
DGA Distributed greedy algorithm
ETSI European Telecommunications Standards Institute
ITS Intelligent transportation systems
MAC Medium access control
MSN Mobile sensor networks
OMP Orthogonal matching pursuit
PSN Pedestrian smartphone network
QoS Quality-of-service
RIP Restricted isometry property
RSU Road-side unit
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SOMP Simultaneous orthogonal matching pursuit
SPR Synchronous p-persistent repetition
V2P Vehicle-to-pedestrian
VSN Vehicular sensor network
WAVE Wireless access in vehicular environments
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Chapter 1
Introduction
1.1 Vehicular Sensor Networks
In addition to smartphone-based mobile sensor networks, vehicular sensor networks (VSN) are consid-
ered one of the most promising mobile sensor networks (MSNs) that will become reality in the near
future. Interest in the design of vehicular communication [1–4] and sensing [5] has grown in recent
years. There are several projects that are focused on transferring the technology into the market. For
instance, Qualcomm Research is currently implementing a vehicle-to-pedestrian (V2P) safety commu-
nication systems on smartphones and vehicles as an example of vehicular networks [6]. The vehicular
communication technology has established a foundation for diverse types of applications, including en-
hancing road safety, traffic monitoring, transportation management, multimedia streaming, and data
collection [5, 7]. The majority of these applications requires the vehicle to act as a sensor—hence the
name VSN. A VSN is a vehicular network where sensors attached to the vehicles sense the environment,
and transmit the sensed data to a fusion centre or to a destination vehicle for processing.
A VSN relies primarily on the sensing capabilities of the vehicles and the reliability of the commu-
nication channel. For example, a vehicle equipped with a camera can perform traffic monitoring and/or
video streaming and, subject to the availability of the communication channel, transmit the captured
data to a fusion centre. In a VSN, a sensor vehicle that is willing to perform sensing might not provide
1
Chapter 1. Introduction 2
a good communication channel for data transmission due to the nature of the vehicular communication
channel (e.g., due to the distance between source and destination [11]). Hence, the communication chan-
nel is a bottleneck in VSNs. A vehicle can be equipped with different sensors including GPS, radars,
vehicle or wheel speed sensors, etc. These sensors can be used to collect data or monitor the streets,
and this type of sensing is the focus of this thesis. Any sensor that collects data can be considered in
this context, but we focus on cameras to convey the concepts of this thesis contribution.
Similar to MSNs, mobility is considered one of the main issues in VSNs. Mobility represents the
physical availability for sensing and/or communication, which significantly impacts the communication
channel and network protocol performance [11, 12]. Although the mobility impact on sensing and com-
munication is known to some extent, using mobility to improve sensing and communication in mobile
networks is still an open research area. This thesis attempts to utilize mobility information in order to
improve sensing and communications in VSNs. The focus of this thesis research is twofold: utilizing
mobility for communication, and sensing1. Although the next section provides a unified architecture
in which both communication and sensing exists, this thesis address each focus separately. This is due
to the fact that we address two different applications, a sensing application and a communication ap-
plication, and the success of the sensing application is dependent on the successful execution of the
communication application2.
1.1.1 A VSN Architecture
Let us consider a generic VSN as in Figure 1.1. The figure shows a number of vehicles that are moving on
the road. Each vehicle is equipped with a number of sensors (e.g., cameras, radars, temperature sensors,
etc.). Vehicles communicate with each other, and to an infrastructure. The infrastructure consists of
road-side units (RSUs) that can communicate with vehicles via a single-hope communication link. The
information at an RSU can be communicated to another RSUs via a second communication link.
The network in Figure 1.1 can be used for different vehicular applications. First, safety awareness
of the vehicular environment is considered an important application where vehicles exchange messages
1A specific definition of sensing and communication in VSNs will be provided in the next sections.2The details of each focus of this thesis will be explained shortly.
Chapter 1. Introduction 3
Figure 1.1: Illustration of a VSN architecture.
(i.e., beacons) at a high rate to ensure awareness of the vehicles mobility. Beacons contain mobility
information of the vehicles that is used for safety awareness, and the mobility information can also
be used to maintain the network topology information to guarantee the quality-of-service for the non-
safety applications. In addition to beacons, vehicles disseminate event-based messages on the same
communication channel. Event-based messages are released to broadcast information of specific safety
events such as sudden-braking. These two types of safety messages are considered the main messages
that are transmitted on the vehicular communication channel. We refer to this application throughout
the thesis as communication in VSNs.
Second, the network in Figure 1.1 can provide a platform for several sensing applications [5]. Define
a target as an area of interest on the road. Moreover, define a sensor as an equipment mounted on the
vehicle that has a specific sensing range (e.g., camera, temperature sensor, radar, etc). Based on the
Chapter 1. Introduction 4
scenario in Figure 1.1, vehicles can sense the environment, and transmit the sensed data to a fusion
centre (a specific RSU). In some cases, this information can be of a significant size (e.g., cameras sensing
the road for surveillance). This application is considered one of the most promising applications of a
VSN. We refer to this application throughout the thesis as sensing in VSNs.
The sensed information can be used for safety and non-safety applications. For safety, sensing
pedestrian and cyclist lanes could provide additional information in the vehicular environment that
can increase awareness. Covering danger zones such as icy roads that can not be sensed by some
vehicles approaching the area is another application. For non-safety applications, surveillance is a typical
application.
1.1.2 Prediction of Mobility Information in a VSN
In Figure 1.1, each group of vehicles communicates to an RSU within its proximity. An RSU can listen
to the beacons broadcasted by vehicles. Moreover, an RSU can communicate the mobility information
of vehicles to another RSU. Once the mobility information arrives at the receiver RSU, prediction of
the arriving time of the group of vehicles in the proximity of receiver RSU can be made. This is
how mobility information can be predicted in such a scenario. We assume that prediction of vehicles
mobility information is doable with acceptable accuracy for the purpose of the proposed system model
[8–10]. Prediction of mobility depends on the accuracy of prediction and the usefulness of the predicted
mobility information for the application. In this thesis, we separately consider the two components,
namely, usefulness and predictability of mobility information in the system models, in Chapters 4 and
5, respectively.
In this thesis, prediction of mobility information is not the focus; rather, how mobility information
is utilized. In vehicular networks, vehicle mobility can be predicted due to the road geometry, speeding
rules, or using of GPS navigation when an origin and destination are known. The accuracy of prediction
of mobility information can be related to the prediction time frame. However, in this thesis we do not
study this problem. This thesis assumes that predicted mobility information is known in order to study
the usefulness of predicted mobility information in scheduling of sensors as in Chapter 4. Specifically,
Chapter 1. Introduction 5
we show that the more the time frame of prediction, the more the usefulness of mobility information is
given the fact prediction is accurate. We also consider the impact of accuracy in prediction of mobility
information by assuming erroneous mobility information in Chapter 5, and we show the level of usefulness
of mobility information, given the fact prediction is erroneous.
1.1.3 Network Congestion in a VSN
In a VSN, vehicles communicate according to the vehicular communication standards [1–3]. That is,
vehicles broadcast their mobility information in packets that are called beacons every 100ms. Beacons
contain several mobility information including the location, speed, acceleration, etc. The broadcast of
beacons is essential for safety awareness of the vehicular environment, and to enhance the non-safety
application performance by providing better tracking of the network topology. It has been shown in the
literature that a VSN communication channel capacity is limited, and that the number of successfully
communicating vehicles is very small for some specific scenarios [11, 12]. This is due to several reasons
including the large transmission rate of beacons, the mechanisms of the IEEE 802.11p protocol, and the
large number of communicating vehicles in some scenarios. Similar studies has been performed in the
literature for different number of communicating vehicles, different settings of medium access control
(MAC) protocol (e.g., packet size and transmission rate), and different settings of the communication
channel reliability. The results of different performance evaluations showed that the vehicular commu-
nication channel capacity is limited, and some of the communicated information is lost. That is, to the
best of our knowledge, network congestion in a VSN is inevitable. This problem is referred to throughout
the thesis as the channel or network congestion problem.
Given the fact that the IEEE 802.11p standard is approved, and that the wireless access in vehicular
environments (WAVE) protocol stack is the current candidate for practical implementation, the network
congestion problem is inevitable in the VSN implementation. Having said that, several attempts have
been made in the literature to address such a problem by understating the MAC protocol performance3,
and accordingly alleviate the network congestion. This thesis takes a different approach to address the
network congestion problem in VSNs as we explain in the next section.
3We discuss some of these attempts in Chapter 2.
Chapter 1. Introduction 6
1.1.4 A New Perspective for Addressing Network Congestion in a VSN
Network congestion in a VSN in inevitable based on the current vehicular communications standards.
Therefore, instead of studying the IEEE 802.11p protocol performance, which is significantly investigated
in the literature, we attempt to understand the sources of the congestion in a VSN. After that, we
carefully attempt to find a special characteristic about the source of the problem in order to resolve or
at least alleviate the problem.
To address the network congestion due to beacons, we perform a careful analysis of the content of
mobility information that is broadcasted in beacons, which is mobility information of vehicles. Then, we
approach the problem of channel congestion by finding a special characteristic about this information;
that is the sparsity of a vehicle mobility trajectory. The sparsity of a vehicle mobility allows the use of
sparse recovery techniques, which should result in a significant reduction in the sampling of the vehicular
mobility trace. Therefore, we aim at reducing the number of packets that are transmitted in a VSN,
while preserving the communicated information through sparse recovery algorithms. This is the new
aspect of addressing the network congestion problem due to beaconing in a VSN.
This part of this thesis is designed for enhancing communications in VSNs. Specifically, a novel
vehicular location awareness scheme is studied that preserves the velocity trajectories of the vehicles and
reduces the load on the communication channel. That is, we address the network congestion problem
due to beaconing by designing a broadcast scheme that allows a significant reduction in the transmission
rate of beacons, while preserving the communicated velocity information. The novel scheme is based on
exploiting the sparsity of mobility trajectory, which we refer to as the gain of mobility in communications.
To address the network congestion due to sensory data collection, we take advantage of another special
characteristic that a VSN has. That is, the fact that vehicles mobility information can be predicted with
an acceptable accuracy. We use this information to reduce the size of the collected sensory data to be
transmitted over the VSN communication channel, which alleviate the network congestion. That is the
aspect of addressing the network congestion problem due to sensing in a VSN.
This part of this thesis is designed for enhancing sensing in VSNs. Herein, a novel sensing scheme
is studied that preserves the sensed data of the environment with a minimum sensing load on the
Chapter 1. Introduction 7
communication channel. The novel scheme utilizes predicted mobility information to reduce the cost of
target sensing, which is referred to as the gain of mobility in sensing. Any type of sensor that senses
the environment can be used in this context, but we focus on cameras as using them as sensors can
be tangible. The novel sensing scheme is studied and analyzed using an independent random coverage
model, and a Markovian coverage model4. We show in the next chapters that it is doable to reduce the
sensing load on the communication channel by utilizing predicted mobility information. The analysis
in Chapter 4 demonstrates that regardless of the mobility model used, the same conclusion is reached:
mobility helps in sensing targets by minimizing the sensing load on the communication channel. Hence,
the network congestion problem is alleviated.
In the following two sections, the two main foci of the thesis are discussed in further details. Section
1.2 describes the location awareness problem in VSN, and Section 1.3 describes the gain of mobility for
sensing. Each section outlines the methodology of the previously proposed solutions in the literature,
describes the approach of this thesis in addressing the problem, specifies the context and the type of
network within which the problem is studied, and defines the research scope and contribution of this
thesis.
1.2 Gain of Mobility for Communication in VSNs
In vehicular communications, vehicles transmit beacons to make each other aware of the location of
nearby vehicles in order to improve safety on the roads. Beacons are packets that are periodically
broadcasted to share information about the network statistics and mobility information without the
driver’s involvement. The mobility information includes data about position, speed, heading, and ac-
celeration [13]. These packets are transmitted at the maximum rate of 10Hz (i.e., every 100ms) to all
neighbours in the vicinity of the transmitting vehicle [12,13]. It is shown that using the vehicular com-
munications standard and wireless access in vehicular environments (WAVE) protocol stack [1, 2], the
channel can become congested when the number of communicating vehicles is large [11].
To avoid channel congestion due to the large number of transmitted beacons, it has been suggested
4Coverage models are directly related to mobility models.
Chapter 1. Introduction 8
that in the lower layers of the WAVE protocol stack or the European Telecommunications Standards
Institute (ETSI) [14], the transmission rate adapts to the channel occupancy [15,16] or to the number of
neighbours and to the distance between vehicles [16], or that the number of vehicles in the transmission
range decreases via power control [11,17]. The adaptation of the transmission rate or range is shown to
alleviate the congestion in vehicular communications.
Because the previously used methodologies to address the channel congestion problem share a com-
mon perspective of the problem (i.e., transmission rate/range adaptation), we ask certain questions in
an attempt to look at the problem from a different perspective. That is, does the problem change if
vehicles are aware of the fact that they do not have to transmit at the maximum rate? The answer is
yes. In this case, congestion would not be as severe as in the case of transmitting with the maximum
rate. Moreover, what if the communicating vehicles know that despite the decrease in the number of
exchanged packets, they would still be able to recover all the data that would have been transmitted
with the maximum rate? The answer is that the channel congestion would be relieved, and the network
applications would guarantee QoS due to the knowledge of location of vehicles. Therefore, we approach
the problem of congestion control and location awareness in vehicular communications from this perspec-
tive. Specifically, we propose a novel location awareness scheme that allow vehicles to transmit beacons
at a low rate and preserve the presumably communicated information (at the maximum rate) with high
accuracy using the mechanisms of sparse recovery. This is different from the literature in the sense that
the previous works on congestion control in vehicular networks address the problem with respect to
the network parameters (such as channel busy time or estimated number of communicating vehicles),
whereas this thesis addresses the problem with respect to the content of the exchanged information (i.e.,
mobility traces).
Figure 1.2 provides an example of three vehicles exchanging beacons according to the WAVE protocol
stack. Each vehicle transmits a beacon at every frame. The shaded frames are supposed to be transmitted
using the IEEE 802.11p standard. All other vehicles in the vicinity of the transmitting vehicle should
repeat the same procedure. Ideally, a collision-free scenario would result in receiving all the packets,
which occurred to vehicle C in the figure. However, vehicles A and B lost some packets due to collisions.
Chapter 1. Introduction 9
Tx
Rx Rx
Tx
Rx Rx
Tx
Rx Rx
Time
A
B
C
Figure 1.2: Example of beaconing according to the WAVE standard.
Interpolation is suggested to recover the data contained in the missing packets. Instead, we use the
theory of compressive sensing to transmit the encoded packets prior to each transmission, and estimate
the original velocity vector with excellent accuracy upon reception of the encoded packets. This is
illustrated in Figure 1.3, where each vehicle transmits three packets at random locations and is able
to estimate the data contained in the missing packets. This new aspect of addressing the networks
congestion problem in vehicular network can be integrated into the current vehicular communications
standards. Figures 1.2 and 1.3 are meant to illustrate the general concept of the location awareness
scheme; however, congestion occurs for a larger number of communicating vehicles.
1.2.1 Research Scope and Contributions
The location awareness for congestion control in vehicular communication networks is studied in Chapter
3. The vehicular network model used in Chapter 3 is meant to address the channel congestion problem
in delay-tolerant and real-time scenarios. Hence, there are two different designs for the proposed solu-
tion. The super-frame scheme is designed to enhance location awareness in the vehicle-to-infrastructure
communications scenario where vehicles transmit their mobility packets to a fusion centre. An example
of a delay-tolerant application where the super-frame scheme can be used is the updating of traffic maps
Chapter 1. Introduction 10
Figure 1.3: Illustration of how the sparse recovery location awareness results in congestion avoidance.
(such as Google maps). The sliding window scheme is specifically designed to enhance location aware-
ness in inter-vehicle communications where there is no infrastructure involved in the communications
scenario. An example of a sliding window application is beaconing. For both types of applications, the
concept of sparse recovery is applied to address the congestion problem in vehicular networks. Specif-
ically, compressive sensing estimation is integrated into the vehicular communications standards as a
congestion-avoidance mechanism.
We would like to emphasize that the proposed novel scheme is not a traditional congestion control
algorithm, and it does not compete with existing solutions; rather, the proposed solution treats the
problem differently and can easily integrate into any existing congestion avoidance/control schemes for
vehicular networks. This is due to the fact that the proposed scheme addresses the issue from a different
perspective, as discussed in Section 1.2. In addition, the proposed solution does not require any hardware
modifications and can be implemented as a software patch to any vehicular congestion controller.
The problem of beaconing congestion control is specific to vehicular communications. This is due to
the fact that, to the best of our knowledge, there is no standard that transmits beacons at such a large
transmission rate for a large number of communicating nodes. However, the recently released iBeacon
technology might be of interest to study because there are large number of nodes (i.e., smartphones)
Chapter 1. Introduction 11
that are communicating. Having said that, the network congestion issue is not considered as significant
as in vehicular networks because the topology of a PSN does not change as fast as in a VSN, and the
transmission rate would not be as large as in a VSN. In a PSN, each node can transmit its mobility
information within a couple of seconds, and the network topology would not change significantly within
that time. The scope of this thesis does not consider iBeacon.
The main contributions of this thesis to location awareness in VSNs are:
• To the best of our knowledge, we are the first to use compressive sensing velocity estimation in
vehicular networks.
• We proposed a super-frame velocity estimation scheme and a sliding window broadcast scheme that
are compatible with vehicular communications standards and require only minor modifications,
which are allowed by the standard operation modes.
• We evaluated the novel super-frame and sliding window schemes with real data collected while
driving on Toronto highways and city streets.
• We propose an algorithm to enhance the accuracy of the non-overlapped measurements of the
sliding window scheme.
Part of the results of the above contributions of the thesis are submitted for publication in [18,19].
1.3 Gain of Mobility for Sensing in VSNs
Consider a street surveillance system where stationary cameras on the streets provide limited coverage
areas. Moreover, assume vehicles have cameras and communication capabilities. If these cameras were
used to collect data and transfer them to a fusion centre, then surveillance of the roads would be
significantly improved. The use of cameras in vehicles for surveillance has been an active area of research
in order to monitor and manage traffic [20], to detect dangerous traffic [21], to transmit hidden road
information to blind vehicles [22], or to transmit road information to a fusion centre [23]. However,
different applications require coverage data, which would result in a large amount of data to be stored
Chapter 1. Introduction 12
and analyzed for the covered areas. Sensing can be considered as acquiring the data, or can be as
acquiring the data that can be transmitted over the communication channel. Throughout the thesis,
we consider sensing as acquiring data that can be transmitted over the communication channel. Hence,
the first part of this thesis objective is to optimize the amount of sensed and transmitted data while
preserving the coverage of all target areas in the VSN.
The system we study is the same as in Figure 1.1, and it is similar to the system used by Google to
build traffic intensity on roads, except that our model extends it to sensors with high volume of data.
In this context, a scheduler of the sensors minimizes the number of the activated sensors, whenever
there exists sufficient communication channel capacity. Sensor activation here means that the sensors
are activated and their channel allows transmission of the captured images data.
It is obvious that the surveillance can be improved by using mobile cameras on vehicles as sensors.
The contribution of this thesis is not this, though; the improved surveillance can be efficiently provided
by vehicles if they incorporate their predicted mobility trajectories in the surveillance procedure. In
other words, the surveillance system utilizes space and time information of the vehicles instead of space
information only. The above are examples of a sensing vehicular system that uses cameras as sensors. A
similar approach can be used for different kind of sensors that sense the environment. It is obvious that
other sensors can be used by considering their coverage area that are different from the coverage area
of cameras. The main objective of this part of the thesis is to design sensing algorithms that utilizes
predicted mobility information, which can be estimated with acceptable accuracy in VSNs.
There has been research that studies mobility and sensing5 in MSNs [24–26]. It has been shown that
mobility results in a larger coverage area where nodes can keep sensing the environment at each time
instant, and mobility helps in minimizing the detection time of targets [24]. Moreover, mobility is is
shown to improve the connectivity of mobile nodes. Understanding and utilizing the mobility impact on
coverage has been the focus of recent research [25,26]. In [25], the authors formulate a coverage problem
in a time domain, and transfer the formulation to an equivalent stationary one in the space domain.
Both formulations are shown to have the same solutions under some conditions. In [26], the authors
5Sensing and coverage represents the acquiring of data throughout the thesis.
Chapter 1. Introduction 13
study the spatial-temporal coverage of a wireless sensor network with the objective of maximizing the
network lifetime and present a centralized heuristic.
Unlike previous works, this thesis uses predicted space and time information (i.e., mobility) in the
coverage process. Coverage is considered to be the sensing metric for the problem. To provide the
required coverage of targets, sensors activation sequence should be scheduled. A novel mobile scheduler
of sensor activation is proposed where sensors provide the required coverage of targets with a minimum
load on the communication channel by utilizing the predicted mobility information. The results detailed
in Chapter 4 demonstrate that the more predicted mobility information is incorporated into enhancing
scheduling of sensors, the more the mobility gain over the stationary sensing scheduler is (i.e., the
stationary scheduler is a tailored version of [25], which considers only space information in enhancing
coverage). To the best of our knowledge, we are the first to utilize such an approach in VSNs.
The objective of this part of the thesis is to design sensing algorithms that utilizes predicted mobility
information as opposed to the literature. By optimizing the amount of sensed and transmitted data, the
number of unnecessary and redundant data that might cause network congestion can be significantly
reduced, yet would provide the required coverage. In this context, the nature of the mobile sensing
problem can be theoretically studied, and the objective of this research is to minimize the amount
of sensed data, regardless of the implementation. The problem is based on the mobility model of the
sensor vehicles and the behaviour of the communication channel. Hence, the problem can be theoretically
studied by modelling the mobile sensing scheduler as an optimization problem based on a specific mobility
model, and the gain of mobility in sensing can be quantified using probability analysis. The problem can
be adapted to VSNs by the integration of the proposed optimization model, the specific mobility model
of the network, and the characterization of the communication channel of the network. Conceptually,
the proposed approach can be applied to any mobility model that represents a mobile network; however,
we focus on VSNs. Therefore, we theoretically study the mobile sensing problem in the context of VSNs
in Chapter 4. First, we define a VSN scenario where a vehicular coverage of targets can be modelled by
an independent random coverage model, which allows us to find closed-form analytical results. Second,
we perform simulations for the study of the problem in the context of another VSN scenario using a
Chapter 1. Introduction 14
Markovian mobility model.
1.3.1 Research Scope and Contributions
The gain of mobility for sensing in VSNs is studied in Chapter 4. We consider a mobility model
and a communication channel availability of a VSN as an input to an optimization framework. The
framework is based on two optimization problems: the mobile sensing scheduler and the stationary
sensing scheduler. The objective of the mobile scheduler is to minimize the sensing cost of the VSN by
utilizing the predicted mobility of the sensor vehicles, whereas the stationary scheduler does not utilize
the predicted mobility information. The approach taken to address the problem is to incorporate the
predicted mobility information in the optimization model, and then quantify the mobility gain in sensing
by probability analysis. We define a scenario where an independent random coverage model can be used
and closed-form expression can be found. Despite the simplicity of the coverage model, it will be shown
in Chapter 4 that the analysis provides a good understanding of the proposed mobile scheduler. We focus
on one type of sensor in this part, which is cameras. However, the proposed mobile sensing scheduler
can be used in different contexts where sensors are not cameras.
The study in Chapter 4 considers perfect knowledge of mobility information. We relax this assump-
tion in Chapter 5, and assume that the predicted mobility information is erroneous. This can be a result
of the limited vehicular communication channel capacity, where initial mobility mobility information
is not received, and hence prediction is not available for some vehicles. This type of noise is due to
the uncertainty in receiving the mobility information. We focus on the impact of erroneous mobility
information on the sensing cost of the mobile scheduler. We model the noise in a parameter that cap-
tures the uncertainty in knowing the mobility information. Moreover, the concept of a breaking point
is defined, at which the sensing cost of the mobile scheduler with uncertainty in mobility information is
larger than that of the stationary scheduler. In this case, utilizing mobility information in scheduling
sensors does not reduce the sensing cost. The main message of studying the mobile scheduler with noisy
mobility information is to reach a decision whether to use the mobile scheduler or not. The uncertainty
in knowing mobility information can be due to the limitation of the vehicular communication channel
Chapter 1. Introduction 15
capacity or the accuracy of the future mobility prediction.
The main contributions of this thesis to the gain of mobility for sensing in VSNs are as follows:
• We proposed a novel mobile scheduler to incorporate the predicted mobility in scheduling of sensors
activity while providing the required coverage of targets within the limitations of the communica-
tion channel.
• We studied the stationary and the proposed mobile schedulers using an independent mobility
model and derive expressions for the sensing cost and the probability of feasibility. We show that
the mobile scheduler outperforms the stationary one in terms of sensing cost and probability of
feasibility.
• We proposed practical algorithms to approximate the mobile scheduler. Specifically, we proposed
a centralized greedy algorithm to approximate the centralized version of the mobile scheduling
problem and a distributed greedy one to approximate the distributed version.
• We extended our study to include noisy mobility information in the proposed mobile scheduler
and compare it to the stationary one with perfect mobility information. We find expressions for
the sensing cost for the mobile scheduler, and we study the breaking point where the noise in the
mobility information results in a sensing cost of the stationary scheduler that is smaller than that
of the noisy mobile scheduler.
Part of the results of the above contributions of the thesis are published in [27,28].
1.4 Interconnection between Communication and Sensing in
VSNs
Although there are two foci of this thesis that address two different problems, an interconnection between
the two contribution streams exists given a specific network model and an application. In this section,
a scenario is discussed where there is an interconnection between the location awareness and sensing in
VSNs.
Chapter 1. Introduction 16
Consider a vehicular network where vehicles are equipped with cameras to provide surveillance of
the streets where the coverage data should be transmitted to a fusion centre as in Figure 1.1. We focus
on a group of vehicles that perform sensing in a certain proximity. For example the group of vehicles
that are sensing the target area. To optimize sensing using the proposed mobile scheduling scheme, both
the mobility information of each vehicle and the predicted mobility information for the whole group
of vehicles for a period of time in the future are required. There can be two methods to acquire the
mobility information during first exchange before prediction: using either the standard WAVE protocol
stack or the proposed location awareness scheme to communicate the mobility information contained
in beaconing. This information must be received at an RSU, and then transmitted to another RSU
that performs prediction of future mobility and scheduling of sensors activation. In the case of a large
number of vehicles in the same vicinity, congestion would occur when using the WAVE protocol stack and
several mobility information packets will be lost. However, the proposed location awareness scheme can
be used to exchange the location information with excellent accuracy. Once initial vehicles information
are received at the fusion centre, prediction of future mobility can be performed using different methods,
with acceptable accuracy. At the same time, sensing of the environment can be minimized to reduce the
load on the communication channel. This is accomplished via the proposed mobile sensing approach.
The above scenario is an example of the interconnection between mobility gains for communications
and sensing in VSNs. The interconnection between the two contributions of this thesis is the mobility
information. Vehicles are supposed to exchange their mobility information via beaconing. And, Bea-
coning can be enhanced by the proposed location awareness scheme of this thesis. After that, having
that mobility information, sensing can be enhanced using the proposed mobile sensing scheduler. Any
scenario that uses such an exchange of beaconing messages and sensing information can be used as an
interconnection example between the two contributions. The remainder of the thesis discusses the gains
of communications and sensing separately.
1.5 Thesis Organization
The rest of the thesis is organized as follows:
Chapter 1. Introduction 17
• Chapter 2 provides the literature review and related works to the contributions of this thesis. It
provides a background on the coverage problem of mobile networks, research on mobility-based
coverage, and the related works on the gain of mobility in coverage. Moreover, it provides back-
ground on compressive sensing theory, the channel congestion problem in vehicular networks, and
the related works on streaming compressive sensing.
• Chapter 3 discusses the proposed compressive sensing location awareness schemes in VSNs. The
chapter describes the novel velocity estimation scheme and its super-frame and sliding window
variants. In addition, a thorough discussion of the experimental testing is also provided.
• Chapter 4 discusses the proposed mobile sensing scheme in MSNs. It describes the formulations
of the stationary and mobile sensing problems, the analysis framework, the heuristic algorithm to
solve the problem in a distributed fashion, and simulation results for different VSN scenarios.
• Chapter 5 describes the methodology of examining the mobile scheduler performance with noisy
mobility information. It provides analytical and simulation results for the comparison of the noisy
mobile scheduler and the noise-free stationary scheduler.
• Chapter 6 provides conclusions and final remarks, the limitations of the proposed solutions, and
an outline for the future work of this thesis.
Chapter 2
Background and Related Works on
Communication and Sensing in
VSNs
2.1 Communications in VSNs
In this section, we discuss the recent related works that studied the congestion problem from a traditional
perspective, that inspired our work, or can be integrated to provide congestion control. First, we discuss
the congestion control problem in vehicular networks in Section 2.1.1. Then, we introduce compressive
sensing concept and discuss the related works streaming compressive sensing 2.1.2.
2.1.1 Congestion Control in VSNs
In vehicular networks, vehicles operate according to the WAVE protocol stack of standards [2]. In
addition to several network management and security layers, WAVE includes the IEEE 802.11p in the
MAC layer [1] and the 1609.4 multichannel coordination layer [2] which assumes that vehicles broadcast
beacons on the dedicated control channel (CCH) every 100ms [12, 13]. It is evident that vehicular
18
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 19
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Transmission Rate
Pro
babili
ty o
f F
ailu
re in a
ll T
imeslo
ts
10 vehicles
20 vehicles
30 vehicles
50 vehicles
100 vehicles
Number of vehicles increasing
Figure 2.1: Performance degradation of SPR beaconing in vehicular networks.
broadcast is inefficient in the case of large number of communicating nodes but some schemes are
proposed to alleviate congestion [29]. In the case of repetition-based schemes that increase reliability
of the broadcast [30], congestion can be severe. For example, we plot the probability of failure in
beacon reception in all time slots versus the transmission rate1 for different number of vehicles, based
on Synchronous p-persistent Repetition (SPR) beaconing in Figure 2.1. The figure is a replication of
the results of [30]. We can see that the probability of failure increases drastically when the number
of communicating vehicles or the beaconing rate, p, increases. The lower the rate is, the better the
probability of successful reception would be. Hence, researchers have been studying the problem of
adaptive rate congestion control in vehicular networks [11,15,16,31]. The majority of the related works
focus was to enhance channel utilization given a measured information such as channel occupancy,
distance between nodes, or network utility parameters.
In the case of network congestion, several packets are lost, and hence interpolation is suggested
to reconstruct the missing values. Using interpolation makes sense, since vehicles mobility traces are
linear, and there exists an implied assumption that vehicles might lose a small percentage of the mobility
1The transmission rate represents the number of transmissions per MAC frame normalized by the frame size.
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 20
information that can be recovered via interpolation. However, Figure 2.1 shows that several packets
might be lost due to the high density of vehicles. Unlike the above works, this thesis proposes a novel
scheme that allows recovery of missing value by encoding them into current transmission, and at the
same time reduces the number of beacons to a level where channel congestion can be avoided while
preserving the exchanged information. It is clear that mobility information is the objective of beaconing
in the WAVE protocol stack, and preserving the mobility information while reducing the transmission
rate aligns with the standard goals.
Vehicular networks establish a ground for diversity of applications [5,32,33]. Each application tolerate
some delay. The rate can be adjusted to the minimum requirement of the highest priority application. In
Chapter 3, we illustrate an information exchange scheme that can operate in two modes. The first mode
is designed to tolerate some delay and is suitable for transportation management, traffic monitoring,
and crowd sourcing, while the second is designed to align with delay-sensitive applications such as
safety applications. This proposed congestion control scheme in Chapter 3 is meant to integrate with a
distributed congestion controller to enhance the location awareness in vehicular networks.
2.1.2 Compressive Sensing
Compressive Sensing Theory
Compressive sensing or CS was introduced as a useful scheme to reduce the sampling rate of a signal
that is sparse or compressible. CS provides a perfect reconstruction of the original signal under some
conditions [34–36]. The sensing matrix that reduces the dimensionality of the signal should satisfy the
Restricted Isometry Property (RIP) condition. RIP sensing matrices provide the ability to reverse the
sampling process and estimate the original data from the reduced one via Convex optimization [35, 36]
or greedy algorithms such as Orthogonal Matching Pursuit (OMP) [37]. Collaborative reconstruction of
multiple signals can be achieved using simultaneous OMP (SOMP) [38] or distributed compressed sensing
SOMP (DCS-SOMP) [39].
CS works as follows. Consider x to be a vector of length N . x is sparse if it can be represented as a
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 21
linear combination of vectors in a sparse domain. Let Ψ be the sparse domain. Hence, we have
x = Ψα.
For x to be K-sparse, α has K nonzero coefficients. CS suggests that x can be efficiently sampled as
follows y = Ax, where y is the measurement vector and A is an M ×N sampling matrix with M � N .
For such a system, x can be recovered from y given that the reduction size is M , and the matrix A
satisfy certain conditions. The conditions are the incoherence and restricted isometry property. The
matrix A must satisfy the Restricted Isometry Property (RIP) where there is a constant δ such that
(1− δ)||x||2 ≤ ||Ax||2 ≤ (1 + δ)||x||2
The value of M depends on the signal length N , the sparsity level K and a measure of coherence between
the sparse domain Ψ and the sampling matrix A. That is, the number of measurements should satisfy
M > cKlogN
where c is a constant. Recovery of x can be achieved by solving an `1 norm minimization problem as
arg minα
||α||1
subject to y = AΨα.
Streaming Compressive Sensing
Streaming measurements has been considered for compressive sensing over video frames [40–42]. Stream-
ing measurements is suitable for video since frames might be highly correlated and compressible in the
wavelet domain. In [40–42], the authors propose a streaming measurement mechanism and then they
perform the recovery based on CoSAMP algorithm [44] with a proposed refinement procedure. Their
streaming algorithm assumes an initial solution as a start and then the algorithm finds a new solutions
iteratively over the streamed measurements. The work assumes that a solution can be obtained as long
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 22
as the sensing matrix is within the RIP region. Moreover, the work solved the leftmost edge estimation,
and waits until the end of he sensing matrix to register the value of the estimation. In [43], the au-
thors proposed an L1-homotopy algorithm to estimate the signal from few measurements. The method
in [43] is suitable for frame-based streaming which streams blocks of data. Frame-Based streaming is
not realtime and the work of [43] is designed for block streaming systems where each block is an offline
compressive sensing problem, where the measurements are taken over the complete vector of input data.
The results of [43] is not suitable for beaconing in vehicular networks. This is due to the fact that it
will result in reducing the size of the beaconing vector and transmitting the compressed size at the end
of the frame. In this case, all the vehicles will transmit their compressed beaconing vectors at the same
time.
Compressive Sensing Applications in Vehicular Networks
This have been a new direction of research by applying CS techniques in vehicular communication
environments [45–48]. Motivated by the scarcity of inter-vehicle contact, a CS scheme is used to enhance
monitoring in vehicular networks [45]. Moreover, CS was used with clustering to improve data collection
in a vehicular network [46]. A hybrid of time-of-arrival and direction-of-arrival positioning method
based on Bayesian compressive sensing is proposed in [47] to enhance localization of vehicles. In [48], a
compressive sensing approach to estimate urban traffic by using probe vehicles is proposed. A different
approach to effective monitoring using vehicular sensor networks and probe vehicles that exploits the
average entropy of the sampling process is presented in [49].
Unlike the above works, the present thesis address the problem of congestion control from a different
perspective. This thesis aims at streaming measurements for vehicular networks without having any
initial solution, with a continuously sliding window, and by considering a real experiment on collected
data from vehicles. This thesis proposes the scheme to work in two modes, a super-frame mode that
can tolerate delay, and a streaming one that is delay sensitive. Both schemes are designed specifically
to address the communication channel congestion problem in vehicular networks.
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 23
2.2 Sensing in Sensor Networks
In this Section, we will discuss the background and related works to the sensing and coverage problems
in mobile sensor networks. First, we will discuss the coverage problems in sensor networks in Section
2.2.1. Then, we will discuss the mobility based enhancement in mobile sensor networks in Section 2.2.2.
2.2.1 Coverage Problems in Sensor Networks
Coverage is an important performance metric in sensor networks that quantifies the quality of monitoring
in a specific area [50]. Sensor networks coverage has been extensively studied in the literature [50, 51]
from various perspectives (e.g., placement, selection, and detection). Several works have investigated
the placement of sensors to enhance coverage [52]; however, such methods deal with stationary sensors
or the initial placement of mobile sensors. Although a stationary sensor network is simpler than the
mobile version, a significant amount of complexity exists depending on how the coverage problem is
modeled. Sensor coverage can be modeled as the capability of a sensor to cover a target point (area)
located within its geometrical coverage range. Coverage range can be generally omnidirectional (e.g.,
microphone sensor) or directional (e.g., camera).
Optimal Node Placement for Coverage
Node placement for coverage aims to identify the optimal locations for sensors among all available
possibilities. The problem can be viewed as a search problem. In [50], the author thoroughly discussed
the node placement in terms of coverage problems. The most general case of the problem is when each
target should be covered by at least one sensor until the whole field is covered. The problem can be
written as [50]
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 24
Minimize
I∑i=1
xi (2.1)
subject to
I∑i=1
yij > 0, j = 1, . . . , J (2.2)
xi ∈ {0, 1}, yij ∈ {0, 1}, i = 1, . . . , I (2.3)
where xi is an indicator function denoting the placement of a sensor at location i, and yij is another
indicator function denoting the coverage of target j by sensor i. This formulation is an integer linear
program. The problem minimizes the number of deployed sensors (2.1) under the condition that each
target is covered by at least one sensor (2.2) while (2.3) ensures that all variables are binaries.
Several variants of problem (2.1)-(2.3) are discussed in [50]. For example, the constraint set can
be modified to contain additional metrics, such as pairwise distance, node classification, or orientation
(angle of coverage). Although it is easy to modify the original problem, doing so usually creates greater
complexity. Including directional sensors is one example [53]. Another approach is to modify the problem
to use a different cost function instead of minimizing the number of sensors, such as maximizing the
lifetime of sensors. A well-known variant of this problem is the K-coverage problem where each target
should be covered by at least K sensors.
Node placement can be perceived as static or dynamic [52]. Static nodes initial optimal placement is
maintained over time. Dynamic nodes are repositioned over time to find their future optimal placement.
Actually, a dynamic network can be decomposed into a multiple of static networks. Both static and
dynamic nodes solve a similar problem-the former once and for good and the latter several times. For
the mobile network, the coverage over all time instants should be considered as a performance metric.
In [25], the authors formulated a mobile coverage problem to maximize the the lifetime of the network
(T ) while providing the K-coverage of the targets. For the sake of brevity, without considering energy
constraint, their problem can be written as [25]
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 25
Minimize T (2.4)
subject to
I∑i=1
yij(t) ≥ qj , j = 1, . . . , J (2.5)
yij(t) ∈ {0, 1}, i = 1, . . . , I (2.6)
where qj is the number of sensors that should cover target j. This formulation is time dependent.
In particular, time dependence is captured in the indexing parameter t, which indicates the coverage
constraint for each time instant.
Although nonlinear programs exist for coverage problems, generally coverage problems are modeled
as linear programs. Such problems are generally NP-hard. Generally speaking, greedy algorithms that
are proposed for set covering are used for the solving node placement [50]. The most general form of
the algorithm selects the sensors to be placed at a location that covers the largest number of uncovered
targets [50]. A simple variant for the general greedy algorithm for directional sensors selects the sensor
orientation covering the largest number of uncovered targets [54].
Scheduling for Coverage
In node placement for coverage, coverage area of sensors might overlap, thereby creating coverage re-
dundancy. Hence, scheduling the activity of the sensors to reduce (or eliminate) redundancy is often
desirable. Scheduling here refers to the order and timing of turning a sensor on at a time slot. Schedul-
ing implies that the network time is greater than a time slot. Therefore, scheduling should incorporate
sensor placement to provide enhanced redundancy reduction.
Scheduling is usually performed by identifying any coverage area overlap, followed by the scheduling
of sensor activity [50]. This approach is based on a redundancy check. In mobile sensor networks, the
problem is viewed from two different angles: space and time [25] [26]. In [25], the authors demonstrated
that, for certain objective functions such as network lifetime, the formulation of the problem in the
time domain can be transferred to an equivalent one in the space domain by investigating the different
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 26
available connectivity patterns. This can help in scheduling by finding the optimal schedule for each
pattern a priori and then applying the schedule when the pattern exists. In [26], the authors examined
the spatial-temporal coverage of a wireless sensor network and presented a centralized heuristic. Their
focus was on eliminating redundancy and enhancing target coverage.
Greedy algorithm was shown to be very close to optimal for sensor selection in both of its centralized
and distributed forms [54]. The greedy algorithm was shown to be an upper bound for the optimal
solution by O(K|C|), where K denotes K-coverage and |C| is the maximum benefit of an unselected
sensor [54]. Greedy scheduling algorithm has the advantage of distributed implementation in practical
systems. In [54], the authors found that the distributed version of the greedy algorithm is very close
to the centralized one in directional sensor selection. Their algorithm works as follows. First, each
target point is owned by a sensor (sensors can be identified by their MAC addresses). Then, each owner
requests the benefits of each sensor able to cover its target. Each sensor receiving that enquiry sends its
benefit of best orientation to the owner, and each owner of a target subsequently decides which selection
is to be made to acquire the maximum coverage by selecting the corresponding sensor and orientation.
This process continues until no targets remain to be covered.
2.2.2 Mobility and Coverage
Mobility Pattern
Mobility is a space-time description of the physical availability of the node. In vehicular networks,
roads restrict the mobility of the nodes; hence, some type of knowledge exists about how vehicles move
according to the mobility constraints. Moreover, different roads with different directions, traffic lanes,
and turns result in different mobility parameters. However, the mobility behavior is modeled in the
literature in terms of these parameters and the notion of a constrained environment. Regardless of the
values of the mobility parameters, mobility trajectories have some specific characteristics.
It is important to note that vehicles usually change their behaviors smoothly (i.e., there is no sudden
change in the velocity). In other words, a vehicle might change its speed by adding (reducing) a few
kilometers per second. Based on the traffic flow theory [55], we plotted a velocity trajectory of a vehicle
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 27
approaching a general intersection while decreasing its speed to zero and then increasing its speed in two
cases: normal acceleration and deceleration versus maximum acceleration. In other words, the vehicle
reduces its speed when approaching the intersection from 1000 feet and then starts increasing its speed.
Acceleration parameters are based on [55]. Figure 2.2 shows the example velocity trajectory. It is clear
from the figure that changing the acceleration to the maximum case does not change the fact that the
velocity trajectory is smooth and predictable. Therefore, acceleration and deceleration imply the same
idea of smooth change (except in the case of sudden braking or significant unusual acceleration, which
is not usual in traffic although it exists). This smooth change is beneficial for estimating the mobility
of nodes in VSNs. Moreover, the linearity in the mobility trajectory exists over different scales, which
is also beneficial as mobility components can be studied over different time scales for different layers of
the vehicular network. For example, the impact of mobility on communication and scheduling can be
studied using a milliseconds timescale while connectivity can be studied using a seconds time scale. The
linearity property holds for both situations.
0 5 10 15 20 25 30 35−1000
−800
−600
−400
−200
0
200
400
600
800
1000
Time (second)
Dis
tan
ce (
feet)
60
50
40
30
150
15
30
40
50
60
1530
40
50
60
Normal Acceleration and Decleration
Maximum Acceleration
Speed (miles/hour)
Figure 2.2: A sample velocity trajectory based on the traffic flow theory [55].
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 28
Coverage Enhancement
Existing literature examining coverage and mobility has shown that mobility enhances coverage and
reduces detection time in sensor networks [24] [56]. In [24], mobility was shown to result in a larger
coverage area. Using stochastic geometry, the authors demonstrated that the fraction of area covered by
a sensor at a time instant is equal to 1− e−λπr2 and during a time interval [0, t) is 1− e−λ(πr2+2rE[Vs]t)
(where r is the radius of nodes coverage disk and Vs is the node speed). In addition, moving sensors in
a straight line was found to be the optimal strategy for maximum coverage. Interestingly, the optimal
moving direction is uniform between [0, 2π) while the optimal intruder mobility strategy for minimal
detection delay should be to remain stationary. In [56], the authors showed that controlling the mobility
of sensors forced to move on the sea surface results in enhanced coverage and sensors lifetime. Their
approach to relocate (control) sensors sought to increase the lifetime of the network.
In [25], the authors formulated the coverage problem in the time domain and derived an upper bound
for that formulation. In addition, they transferred the formulation from the time domain to the space
domain and proved that the problem has the same optimal solution with the same network lifetime.
They concluded that the time formulation results in different graph patterns, which can be formulated
to result in the same optimal network lifetime.
It has been widely discussed that mobile nodes could improve coverage in a hybrid of mobile and
static sensors network. In [57], the authors aimed to minimize movement in order to enhance target
coverage. The majority of such approaches consider limited mobility patterns. A probabilistic approach
to studying the impact of mobility and cooperation on data collection was presented in [58].
Coverage and connectivity are highly related areas in mobile sensor networks. Coverage is a measure
of sensing quality whereas connectivity is a measure of network quality. In other words, covered areas
are better sensed-and sensed data better transmitted-if the network has high connectivity. Furthermore,
increasing mobility could help improve connectivity [59]. In [60], the authors demonstrated that net-
working performance metrics such as delay can be traded off for coverage. In [61], a target coverage
problem that guarantees service delay was proposed. Similar efforts are proposed in [62] to minimize
the service delay of such formulation.
Chapter 2. Background and Related Works on Communication and Sensing in VSNs 29
Although mobility directly impacts coverage and connectivity, it also affects the delay of coverage
and the delay of data collection. As previously discussed, scheduling sensors activity results in different
coverage times. Moreover, connectivity directly impacts networking performance (i.e., MAC and rout-
ing). Therefore, we can use two delay components to acquire the data from a source node: mobility
delay in terms of coverage or connectivity and networking delay in terms of scheduling, MAC, or routing.
Unlike the previous works, this thesis contributes to the scheduling of mobile sensor networks to
provide coverage by incorporating the predicted mobility of the mobile nodes in the scheduling procedure.
Chapter 4 will show that the more predicted mobility information is incorporated in the scheduling
process, the smaller the number of activated sensor would be.
2.3 Summary
In this chapter, we provided the necessary background knowledge and related works to the contribu-
tions of this thesis. First, we focused on the background and related works to the location awareness
contribution in vehicular networks. Specifically, we discussed the congestion control problem in vehicu-
lar networks, the background on compressive sensing, and the related works to streaming compressive
sensing in vehicular networks. Second, we discussed coverage problems in mobile sensing networks, the
optimal placement of both static sensors and mobile sensors, and how scheduling was used to improve
sensing. Then, we discussed the recent related works on how mobility can be used to enhance sensing
in mobile sensing networks. We discussed the linearity of the mobility trajectories in VSNs. After that,
we discussed the research efforts on how mobility can enhance coverage of sensors.
Chapter 3
Location Awareness via Sparse
Recovery in VSNs
In this chapter, we study the gain of mobility for communications in vehicular sensor networks. We
explain how we use compressive sensing to estimate the velocity trajectories and reduce the network
congestion. The material of this chapter has been published in the International Wireless Communi-
cations and Mobile Computing Conference [18] and the IEEE International Symposium on Wireless
Vehicular Communications [19].
3.1 Introduction
In vehicular networks, location of vehicles is considered an essential information for different applications.
In safety applications, each vehicle should be aware of the location of immediate neighbours with an
update rate of 10Hz via beaconing. This information is used for the cooperative collision avoidance (CCA)
application. For non-safety applications, location of vehicles is also required but at a lower rate, and is
used for traffic light management [33], efficient routing of vehicles, and vehicle speed management [32].
The transmission rate of the location of vehicles varies, but a minimum requirement is set to guarantee
the application robustness. In the lower layers of the wireless access in vehicular environment (WAVE)
30
Chapter 3. Location Awareness via Sparse Recovery in VSNs 31
protocol stack, the transmission rate is suggested to adapt to the channel occupancy [15] [16], to the
number of neighbours, and to the distance between vehicles [16], or via power control [11]. The proposed
approaches for congestion control demonstrate a good adaptation to the mobile environment based on
certain network measures.
In this chapter, we study the problem of channel congestion in vehicular networks from a different
perspective. We use the mobility information included in the transmitted packets as a key to reduce
the number of exchanged packets in the network. We show that vehicular mobility traces (i.e. location
and speed traces) are sparse in the Fourier [18] and the Cosine [19] transform domains. Moreover, we
demonstrate that sparsity of vehicle kinematic signals is a key for velocity estimation and congestion
avoidance in vehicular networks. By exploiting sparsity in communicating velocity traces, we achieve
information exchange among vehicles with a small number of transmissions to avoid channel congestion
while preserving the mobility information with a certain level of accuracy. This is achieved by utilizing
compressive sensing (CS) to broadcast location and velocity packets. The CS theory suggests that a
vector, which is sparse in a specific domain, can be estimated with a small number of samples given
certain conditions [35,36]; mainly, the sparsity of signal and the incoherence of measurements.
Unlike the previous work in the literature, this thesis presents a system evaluation that utilizes
compressive sensing for velocity estimation in vehicular networks. We presents a novel scheme to reduce
the number of packets transmitted to obtain the neighbourhood velocity information by leveraging CS
for velocity estimation. The proposed scheme suggests the following procedure; in each transmission
epoch, the vehicle transmits both the current value of the kinematic measurements and a random linear
combination of the past values. At the reception of each packet, the receiver would be able to learn the
recent velocity and possibly reconstruct the past values.
The proposed information exchange scheme is tailored to vehicular networks where past measure-
ments are used within a super-frame for crowd sourcing applications. The super-frame reduces the
number of transmissions. The proposed scheme is robust to the loss of few samples as long as the sparse
recovery conditions hold. We evaluate the proposed schemes with real-data collected while driving in
the major highways and downtown streets in Toronto.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 32
The main contributions of the chapter are as follows. We propose a novel super-frame velocity
estimation scheme that works on top of the MAC layer. At each transmission epoch in the super-
frame, the packet is repeated α times at the MAC layer to enhance reliability of transmission. The α
transmissions at the MAC layer will also contribute to enhancing velocity estimation at the receiver due
to the fact they contain encoded information. Moreover, we propose a streaming scheme via a sliding
window. The receiver would be able to learn the recent velocity of the transmitter after sliding the
window for a specific number of times. After that, at each sliding epoch, the receiver would be able to
make a new estimation. We evaluate the super-frame scheme and the streaming scheme with real-data
collected while driving in Toronto highways and city streets. The experiments show that the proposed
schemes provide estimation of the velocity with excellent accuracy.
In this chapter, we perform estimation using the two proposed schemes, and show the resulting
estimation accuracy. On one hand, it is important to note that different applications in vehicular
networks tolerate different estimation accuracy. The tolerable estimation accuracy on the other hand
depends on multiple factors including the vehicular scenario, the car model and specifications, the
efficiency of the car in reacting to the received estimation, and to the location of the transmitter.
An estimation error of location/speed represents an inaccurate realization of the vehicular environ-
ment. This inaccurate representation of the vehicular environment must allow the vehicle to properly
react to the application request. Otherwise, the estimation error is intolerable.
For a safety application, an example is receiving the velocity/location of vehicles in an danger zone.
Assume that there are two vehicles approaching the danger zone. The two vehicles have different safety
distances. The estimation error translates into an error in the braking time given the safety distance for
each vehicle. If the estimation error does not guarantee each vehicle to brake within the safety distance,
then it is intolerable. This also depends on other factors such as the car size, quality of braking for each
car, speed, etc. For delay-tolerant applications such as optimized navigation and routing of vehicles on
the roads, the same factors hold for the tolerable estimation given the fact that the applications are
different.
We would like to emphasize that this novel scheme is not a traditional congestion control algorithm,
Chapter 3. Location Awareness via Sparse Recovery in VSNs 33
and it is not competing with the existing solutions; rather, our proposed solution treats the problem
differently and can easily integrate to or be used to enhance any existing congestion avoidance/control
scheme for vehicular networks. This is due to the fact that the parameters of the proposed scheme
can be integrated to any other congestion control scheme. A congestion control scheme would reduce
the packet transmission rate according to a network measure, whereas our proposed scheme enables the
vehicular network to transmit a few packets due to the sparsity of the vehicle velocity vector.
Finally, mobility information of vehicles consist of multiple components, namely, location, speed,
acceleration, etc. In this chapter, we focus on velocity estimation. Velocity information can be used to
estimate the displacement of initial location if estimated with excellent accuracy. In addition to velocity
estimation, we provide an example of location estimation to demonstrate the feasibility of the proposed
scheme to enhance location awareness.
The rest of the chapter is organized as follows. Section 3.2 describes the network transmission model.
Section 3.3 explains the data collection and experiment setup, and discusses the experimental results.
Finally, Section 3.4 summarizes the chapter.
3.2 System Model
We consider vehicles to operate according to a repetition-based MAC protocol. Each vehicle identifies
its location with a GPS device. Vehicles are assumed to have this information every 100ms. We consider
a sublayer on top of the MAC layer, that coordinates the transmission of packets among a super-frame.
The super-frame length is N , and the sublayer randomly chooses M samples from N to be transmitted to
the MAC layer. The last sample (i.e., M th one) is forced to be at the end of the super-frame. Generally,
we reduce the frequency of transmission and send a small number of samples of the velocity vector1. In
addition to the transmission of the actual velocity value at each sample, each packet contains a randomly
encoded value of that sample with recent previous samples of the velocity vector (the number of the
encoded samples depends on the transmission scheme).
1Location vector can also be used, but we choose not to use it to focus on estimation error, but not the GPS localizationerror.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 34
3.2.1 Network Model
Let xi be the N × 1 actual velocity measurement vector at time i, which can be considered over the
interval of interest. We use time notation to indicate that xi represents a small part of an infinite
streaming velocity vector. Let us assume that zi is the corresponding sparse vector of xi in the discrete
cosine transform (DCT) domain. Therefore, the vector xi can be represented as xi = Ψzi, where Ψ is
the basis at which xi is sparse. In the IEEE 802.11p standard, sampling is ideally performed as
yi = Λxi (3.1)
where Λ is a N×N identity sampling matrix. The identity matrix results in transmission of all elements
of the velocity vector, and reflects periodic transmission where the transmitted vector in this case is
yi = xi.
In our proposed CS sub-layer, instead of transmitting samples periodically, each vehicle transmits
its current velocity and a linear combination of the past measurements in the observation window.
Therefore, at each transmission we send
ui = [vn, ynj ]T ,
where vn is the current actual velocity at time n, and ynj is a random combination of the previous
measurements at the super-frame time n and the MAC frame jth time slot.
Let the length of the MAC frame be F , and the number of repetitions at a MAC frame be α. That
is, there would be α transmissions at the MAC frame as [yn1, · · · , ynα] with the actual velocity value,
vn, where we assume that vn does not change significantly within the MAC time frame (e.g., 100ms).
Figure 3.1 illustrates the top down view for the measurements from the super-frame to the MAC frame.
For such a MAC, w = αF is the retransmission rate. For each sample ynj , we have
ynj =
n∑t=1
φtjxt,
Chapter 3. Location Awareness via Sparse Recovery in VSNs 35
Figure 3.1: Illustration of the measurements at the MAC layer.
Figure 3.2: Illustration of measurements collection by the CS scheme.
where φtj is the weight for the linear combination, and xt is the actual velocity value at time t. Figure
3.2 illustrates the transmissions of the actual measurements at the super-frame level.
To design a sampling matrix, we should consider three parameters of the system, namely, the length
of the observation window, the number of sampled packets, and the estimation time at the receiver.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 36
Given the above three design parameters, each vehicle should transmit a vector yi of length αMas
yi = Φixi (3.2)
where Φi is an αM × N (where αM � N) sampling matrix, and subscript i indicates the vector of
αM linearly combined measurements at time i corresponding to the vector xi. The sampling matrix,
Φi, defines the transmission strategy and reduces the dimensionality of the transmitted velocity vector.
From the theory of CS, if αM ≈ c log(N), where c is a constant, then the whole velocity vector can be
thoroughly reconstructed [35,36]. The transmitted vector can also be written as
yi = ΦiΨzi (3.3)
In the sequel we will focus on how we construct yi which is a linear combination of samples from the
transmitter velocity values up to time i. For such a system, xi can be recovered from yi given that αM ,
and the matrix Φi satisfy certain conditions. The conditions are the incoherence of measurements and
restricted isometry property (RIP). The matrix Φi satisfies the (RIP) where there is a constant δ such
that
(1− δ)||x||2 ≤ ||Φix||2 ≤ (1 + δ)||x||2
The value of αM depends on the signal lengthN , the sparsity levelK and a measure of coherence between
the sparse domain basis matrix Ψ and the sampling matrix Φi. That is, the number of measurements
should satisfy
αM > cKlogN
where c is a constant [35,36].
Note that the M th transmission toward the end of the super-frame is prone to estimation error due to
the fact that there are only α measurements at that time instant. It is doable to increase the reliability
of the M th transmission by increasing the rate at that time instant from α to αN , where αN denotes the
transmissions at the end of the super-frame. Increasing the repetition rate will results in packet loss on
Chapter 3. Location Awareness via Sparse Recovery in VSNs 37
the MAC frame as shown in Chapter 2 in Figure 2.1. Therefore, we use another approach in the next
section, which is a velocity correction scheme that can help with increasing the accuracy at the end of
the frame for a small α.
For estimation of the original velocity trajectory, the receiver collects the αM packets, and then can
use `1 norm minimization. That is, zi can be recovered with a very high probability by
zi = argmin ‖zi‖1
subject to yi = ΦiΨzi
(3.4)
Finally, we can recover the time domain vector xi from the corresponding recovered vector in the discrete
cosine domain via the inverse cosine transform. Alternatively, a greedy algorithm such as OMP [37] can
be used instead of the `1 minimization to recover the velocity vector.
Denote the number of vehicles by V , and the number of retransmissions for each packet by α.
Compared to the IEEE 802.11p standard, which requires periodic transmissions of packets, the number
of messages to be transmitted is reduced from α× V ×N to α× V ×M , where M � N . This is a very
significant reduction in the number of transmitted packets while preserving the information of the whole
traffic scenario via compressive sensing. Moreover, our approach does not require hardware changes and
can be implemented as a software patch to the system.
3.2.2 Velocity Correction Scheme
In the proposed CS scheme, the transmitted packets contain the actual velocity sample vi = xi and
the randomly encoded measurements in yij at each transmission time i. Therefore, the receiver would
have M of the actual velocity values and αM encoded values to which it will apply CS estimation. We
note that the sampling matrix Φi is a lower block triangular matrix. That is the velocity vector values
towards the end of the super-frame are only mixed in a small number of samples. In some scenarios,
this might create error on the estimated values of these velocity values. Here, we propose a solution to
reduce such errors. LetM be the set of received velocity actual values, vn, n = 1, · · · ,M , at the receiver.
Consider xc[n,n+1] be the corrected part of the estimated velocity vector between the two sampling times
Chapter 3. Location Awareness via Sparse Recovery in VSNs 38
n and n+ 1. Then, for (n < M), the velocity correction is performed by
xc[n,n+1] =
x[n,n+1] |vi − xi| ≤ EThresh
f(vn, vn+1, t) |vi − xi| > EThresh
, (3.5)
where EThresh is the threshold for the estimation error set by each receiver, and f(vn, vn+1, t) =
vn+(vn+1−vn) t−(n)(n+1)−(n) , that represents the linear interpolation between the two known actual velocity
values (vn, vn+1). That is, the velocity correction scheme suggests to use interpolation where the CS
theory does not provide accurate estimation of the velocity vector.
3.2.3 Sliding Window CS Estimation
The CS estimation scheme in the previous section has two properties that is acceptable for delay-tolerant
applications, but not real-time applications. First, each vehicle has to wait until the end of the super-
frame to perform the CS estimation. Second, the measurements at the end of the super-frame are
prone to errors due to the small number of measurements at the end of the super-frame. Hence, we
propose a sliding window CS estimation scheme where a window of measurements is shifted after each
CS transmission2. The sliding window scheme has two advantages over the CS super-frame estimation
scheme. First, the sliding window keeps a limited number of measurements to be used for estimation,
which reduces the storage size and the complexity of the CS estimation. Second, the receivers do not
have to wait until the end of the super-frame to perform estimation of samples; rather, they can perform
estimation after collecting αM measurements. After that, at the reception of new measurements, there
will be always α(M−1) measurements that have been collected in the past. This sliding window scheme
is different from [40–42] because of the integration of the MAC transmissions, which enhance the CS
estimation, and the design of the CS streaming estimation scheme. Figure 3.3 illustrates the streaming
CS scheme.
Denote the shift of the sliding window by R, and the length of the sliding window by L3. R can be
variable, but for simplicity we use a fixed value for it. Let Q = NR be an integer and also K = L
R is an
2The sliding window scheme is the only part of the chapter that does not use the super-frame.3The parameters M , N , R, L are integers that are multiple of the MAC frame length, F = 100ms.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 39
Figure 3.3: Illustration measurements collection in the CS scheme.
integer. We can decompose xi into
xi = [x(1)i ,x
(2)i , · · · ,x(Q)
i ]T .
We can also decompose Φi into
Φi =
Φ(1,1)i · · · Φ
(1,K)i 0 · · ·
0 Φ(2,2)i · · · Φ
(2,K+1)i · · ·
.... . .
. . .. . .
. . .
0 · · · Φ(M,Q−K+1)i · · · Φ
(M,Q)i
From this structure, we can also decompose yi into
yi =
∑Kr=1 Φ
(1,r)i x
(r)i∑K+1
r=2 Φ(2,r)i x
(r)i
...∑Qr=Q−K+1 Φ
(M,r)i x
(r)i
.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 40
As time increases, and the sliding window shifts, x(Q)i is estimated M times. Therefore, we propose an
algorithm to find the best estimation of x(q)i . Before we discuss the details of the algorithm, let us focus
on the rightmost edge of the velocity vector x(Q)i and Φ
(M,Q)i after each shift of the sliding window. At
time i, x(Q)i is has α measurements to perform the CS estimation using Φ
(M,Q)i . At time i+ 1, x
(Q)i has
approximately 2α measurements to perform the CS estimation using Φ(M,Q−1)i+1 and Φ
(M,Q−1)i , which
increases accuracy. The sliding process continues and each time the number of measurements increases
until the x(Q)i becomes on the leftmost edge of the used sampling matrix Φi+M . After M shifts of the
sliding window, x(Q)i will not be used for sampling anymore.
We claim that the CS estimation error of x(Q)i will decrease as the sliding window shifts when x
(Q)i
moves towards the centre of the estimated velocity vector, and then starts increasing again as x(Q)i
moves aways from the centre of the estimated velocity vector. Therefore we propose the following sliding
window edge (SWE) estimation algorithm in Figure 3.4 to record the best estimation accuracy of the
velocity values of x(Q)i at each sliding window shift. In the algorithm, we use the index r to denote
the location of x(Q)i inside the sampling matrix (i.e. r = 1 corresponds to x
(Q)i being in the rightmost
edge of the estimated vector, whereas r = M corresponds to x(Q)i being in the leftmost edge). The
algorithm keeps estimating x(Q)i , and records the edge estimation with the least error compared to the
actual velocity values vi and vi−1 corresponding to the head and tail of that edge. Define T(r)i as the
computed estimates of x(Q)i at each sliding window shift time r, and let g be the index of the registered
estimate of x(Q)i .
3.2.4 Delay of the Sliding Window CS Scheme
The delay of the sliding window scheme can be divided into two components; (1) the delay of the first
estimation of the complete velocity vector, and (2) the delay of receiving vn. The delay of receiving vn
is equal to L. This is due to the fact that vn is transmitted at the end of each sliding window (along
with other mobility and MAC information such as location and ID). The delay for preforming the first
estimation is
DSW = MR+ L,
Chapter 3. Location Awareness via Sparse Recovery in VSNs 41
Ti = {}, v0 is already receivedfor i = 1, 2, · · · do
Perform the CS estimation using (3.4)
Compute w(1)i = |xi − vi|+ |xi−1 − vi−1|, T (1)
i = {x(Q)i }
g = 1
x(Q)i = T
(1)i
for r = 2, · · · ,M doSliding window shifts by RPerform the CS estimation using (3.4)
Compute w(r)i = |xi − vi|+ |xi−1 − vi−1|, T (r)
i = {x(Q)i }
g = arg min wix(Q)i = T
(g)i
end forend for
Figure 3.4: The SWE estimation algorithm for enhancing the accuracy of x(Q)i .
where MR denotes M shifts of the sliding window before collecting M samples, and L is the length of
the last sliding window. After the first estimation, the estimation can be performed after each shift of
the sliding window, which is of length L.
3.3 Performance Evaluation of The Location Awareness Scheme
In this section, we describe the data collection experiment used for the evaluation of the proposed CS
schemes, and then we discuss the results.
3.3.1 Experiment Setup
To evaluate the proposed schemes, we perform a real experiment that reflects a realistic scenario. We
developed an App on Android smart-phone that collects the GPS sensor data from the device and
transmits them to a laptop via a TCP connection. The data collected from the GPS sensor are the
location (longitude and latitude), speed, accuracy, and acceleration. We collect the data from the App
with the highest possible frequency, which is 1Hz. We use linear interpolation to up-sample the data
to a frequency of 10Hz that is compatible with the vehicular communications standard. The data is
collected in two different experiments. The first one is in major highways in the city of Toronto, and
Chapter 3. Location Awareness via Sparse Recovery in VSNs 42
the second one is in Toronto downtown. We made sure that the data is collected during both rush and
normal not congested hours. In Figure 3.5, we show the locations of the data collected on Toronto map.
Since we have two sets of data, and to avoid repartition for the same discussion over the two sets of
data, we generally focus on the city data in this section. This is due to the fact that highway velocity
traces are smoother than those of the city, and consequently, have a smaller estimation error in general.
Showing the results for the city data proves the same concept with larger estimation errors. We use
interpolation as a benchmark for comparison similar to the comparison performed recently in [49] for
traffic estimation. In fact, the comparison to linear interpolation is biased towards linear interrelation.
We up-sample the data using linear interpolation to be compatible with the vehicular communications
standard. So recovery with linear interpolation makes sense after losing some of samples due to the
linearity in short intervals. However, we will show that by losing a significant number of samples, the
CS scheme outperforms interpolation.
In the experiment, we use only one vehicle velocity trace. In the case of multiple vehicles, each
vehicle has to transmit αM packets. The number of transmitted packets will represent multiple vehicles.
However, each vehicle would estimate the velocity of each vehicle separately using its representative αM
packets.
In the experiment, we transmit packets to the laptop via a TCP connection. This connection guar-
antees the reception of the packets. This setup does not consider the loss of packet due to the channel
congestion (or density of vehicles). However, packet loss is implied in the parameters α and M of the
experiment. For all the figure in the next sections, on one hand, the larger the value of α or M or
α ×M , the smaller the packet loss (or density of vehicles) is, and the smaller the estimation error is.
That means that a large number of packets were successfully received. On the other hand, the smaller
the values of α or M or α ×M , the larger is the packet loss (or density of vehicles), and therefore the
estimation error is large. That is, a small number of packets were successfully received.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 43
−79.6 −79.55 −79.5 −79.45 −79.4 −79.35 −79.343.6
43.62
43.64
43.66
43.68
43.7
43.72
43.74
43.76
43.78
Longitude
La
titu
de
Locations of the data collected over Toronto highways
(a) Highways data collection
−79.41 −79.4 −79.39 −79.38 −79.37 −79.3643.645
43.65
43.655
43.66
43.665
43.67
43.675
43.68
Longitude
La
titu
de
Locations of the data collected in Toronto downtown
(b) City data collection.
Figure 3.5: Location of the data collected on Toronto map
3.3.2 Super-frame Estimation
We plot estimation for a single trace in Figure 3.6 using the CS scheme. The figure shows that velocity
estimation via `1 minimization is very good given the fact that a few measurements are transmitted
(M = 10). The figure shows that interpolation actually missed a large part of the velocity vector where
there is large change in the velocity values. That is, the CS scheme gains from the encoded measurements
at each sampling time although the super-frame transmissions are the same for interpolation and the
CS scheme. In this figure, the CS scheme outperforms interpolation in terms of average and maximum
estimation errors.
In Figure 3.7, we plot another example of estimation where there is a larger estimation error at
the rightmost edge for the CS scheme. This occurs due to having a long distance between the last
two samples at the rightmost edge part of the velocity vector due to random sampling (i.e., the length
between the last sampling time n = i and the previous one (i.e., M − 1) transmitted at time n − 1 is
large). We apply the velocity correction scheme and we plot the estimation error on the same figure.
There are two parts of the velocity vector that are corrected, where velocity correction reduced the
estimation error. However, that depends on the linearity of the estimated part of the velocity vector,
and the distance between the last two measurements. If the estimated part of the vector is so linear,
then interpolation could provide a very good estimation.
Although velocity correction is useful, it might not be accurate for correcting every part of the
velocity vector, and may result in a worse estimation compared to the CS scheme. The correction based
Chapter 3. Location Awareness via Sparse Recovery in VSNs 44
0 50 100 150 200 250 300
4
6
8
10
12
14
Velocity vector of the Vehicle, M=10, N=328, α=4
Vel
oci
ty (
m/s
)
Original Signal
CS Scheme
Interp.
0 50 100 150 200 250 300 3500
2
4
6CS Scheme Error=0.15, Interp. Error=1.21
Time of Sample
Est
imat
ion E
rror
(m/s
)
Figure 3.6: Example of velocity estimation using CS scheme and interpolation using city data.
0 50 100 150 200 250 300 3500
5
10
15
Velocity vector of the Vehicle, M=10, N=328, α=4, EThresh=0.4
Vel
oci
ty (
m/s
)
Original Signal
CS Scheme
CS Scheme+Interp
0 50 100 150 200 250 300 3500
0.5
1
1.5
2CS Scheme Error=0.2, CS Scheme+Interp Error=0.14
Time of Sample
Est
imat
ion E
rror
(m/s
)
Figure 3.7: Example of velocity estimation using CS scheme and interpolation using city data.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 45
on interpolation is directly related to the distance between the two sampling locations at the super-
frame, and the linearity of their corresponding part of the velocity vector. The shorter the distance
between the two sampling locations, the better is the linearity of the velocity vector, and the better
is the interpolation accuracy. Moreover, the CS scheme requires a certain number of α rows at each
super-frame transmission time to perform accurate estimation. The longer the edge of the velocity vector
(i.e., the distance between the two samples n = i and its predecessor (i.e., M − 1) transmitted at time
n− 1), the more α rows are required to perform accurate estimation of the edge. In Figures 3.8 (a), (b)
and (c), we study the estimation errors for the edge for interpolation and the CS scheme. We repeated
estimation 50, 000 times for the same vector. Figure 3.8 (a) shows the velocity vector of interest. Figure
3.8 (b) and (c) show the average and maximum error versus the location of the (M − 1) super-frame
sample, respectively. The figures show that interpolation outperforms the CS scheme over very short
intervals of estimation (i.e., n − 1 > 310) due to the linearity of the velocity over these intervals. For
n−1 < 310, the CS scheme outperforms interpolation in terms on average and maximum errors (for small
parts, the maximum errors for both schemes are equal). Hence, we suggest the use of velocity correction
if the distance between the two super-frame velocity samples is short to avoid erroneous interpolation
estimations.
We plot the average and maximum errors versus α for the super-frame CS scheme using the city data
in Figures 3.9 (a) and (b), and using the highway data in Figures 3.10 (a) and (b). In these figures,
we fix αM and we change α. Figure 3.9 (a) shows that the CS scheme outperforms interpolation in
terms of the average error in velocity estimation. As α increases, M decreases because αM is fixed,
and hence the estimation error increases for both the CS scheme and interpolation. However, the CS
scheme benefits from α because as α increases, the number of transmissions of encoded measurements
at each super-frame time i increases. Therefore, the error does not increase for the CS scheme as fast
as for interpolation. However, it slightly increases due to the having a smaller overlap region between
the measurements at the edge4. This is due the fact that as α increases for a fixed αM , M decreases,
and the distance between the last two sampling times increases with respect to a larger M . Similar
4We use the term edge to refer to the rightmost edge of the velocity vector throughout the rest of the chapter.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 46
0 50 100 150 200 250 300 3502
4
6
8
10
12
14
N=328, α=10, M=10O
rigin
al v
eloci
ty v
ecto
r (m
/s)
Time of sample
(a) Vector of interest.
0 50 100 150 200 250 300 3500
0.5
1
1.5
2
2.5
3
3.5
4
4.5
N=328, α=10, M=10
Err
or
in v
elco
ity
est
imat
ion
(m
/s)
Position of the (M−1) sample on the super−frame
CS Scheme
Interp.
(b) Error versus position of (M − 1) sample.
0 50 100 150 200 250 300 3500
1
2
3
4
5
6
7
8
9
N=328, α=10, M=10
Max
. er
ror
in v
elco
ity e
stim
atio
n (
m/s
)
Position of the (M−1) sample on the super−frame
CS Scheme
Interp.
(c) Max. error versus position of (M − 1) sample.
Figure 3.8: Example of edge error using the last two measurements only at location n = i and n − 1(i.e., the transmission time of (M − 1) measurements) for the CS scheme and interpolation using onevelocity vector. M = 10 is the total number of super-frame sampling times. For example, for the valuesthe horizontal axis of 200, the immediate sample before the last one is transmitted at that time, and theestimation errors is computed over the interval [200, 328].
observations can be made for the maximum error in Figure 3.9 (b). For the highway data in Figures
3.10 (a) and (b), we can make similar observations regarding the average and maximum errors, but we
notice that the values of both errors are smaller compared to the city data. This is due to the fact that
the collected highway data is smoother than the collected city data. In the city data, there exists more
frequent and fast changes compared to the highway data. We generally noticed that the estimation of
the city data reveals higher average and maximum errors. Hence, in the sequel we will focus on the city
Chapter 3. Location Awareness via Sparse Recovery in VSNs 47
1 2 3 4 5 6 7 8 9 10 11−0.2
0
0.2
0.4
0.6
0.8
1
1.2
α
Err
or
in v
elo
city
(m
/s)
N=328, αM=120
CS Scheme
Interp.
(a) Error in velocity estimation.
2 3 4 5 6 7 8 9 100
0.5
1
1.5
2
2.5
α
Max
. er
ror
in v
eloci
ty (
m/s
)
N=328, αM=120
CS Scheme
Interp.
(b) Max. error in velocity estimation.
Figure 3.9: Average and maximum errors in velocity estimation using the CS scheme and interpolationversus α for the city data.
1 2 3 4 5 6 7 8 9 10 11−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
α
Err
or
in v
elo
city
(m
/s)
N=328, αM=120
CS Scheme
Interp.
(a) Error in velocity estimation.
2 3 4 5 6 7 8 9 100
0.5
1
1.5
α
Max
. er
ror
in v
eloci
ty (
m/s
)
N=328, αM=120
CS Scheme
Interp.
(b) Max. error in velocity estimation.
Figure 3.10: Average and maximum errors in velocity estimation using the CS scheme and interpolationversus α for the highway data.
data results since it shows larger estimation errors compared to those of the highway data.
In Figures 3.11 (a) and (b), we fix α and we plot the average and maximum estimation errors versus
αM , respectively. The figures show that the errors increases as αM increases. Moreover, the CS scheme
outperforms interpolation in both of the figures.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 48
0 20 40 60 80 100 120 140−0.5
0
0.5
1
1.5
2
2.5
αM
Err
or
in v
elo
city
(m
/s)
N=328, α=4
CS Scheme
Interp.
(a) Error in velocity estimation.
20 30 40 50 60 70 80 90 100 110 1200
0.5
1
1.5
2
2.5
3
3.5
4
αM
Max
. er
ror
in v
elo
city
(m
/s)
N=328, α=4
CS Scheme
Interp.
(b) Max. error in velocity estimation.
Figure 3.11: Average and maximum errors in velocity estimation using the CS scheme and interpolationversus α for the city data.
3.3.3 Sliding Window Estimation
For the sliding window estimation, we do not have a super-frame, however, measurements are streamed
over time. In this part, we define the estimation error as
Error = |xi − xi| .
We plot a snapshot for the sliding window estimation in Figure 3.12. The figure shows that the velocity
vector was thoroughly estimated with an average error of 0.002m/s using the CS scheme. The figure
shows that the estimation error is slightly larger at the edges of the velocity vector. Both edges have
a smaller number of overlapped measurements compared to the middle of the velocity vector. Hence,
estimation is less accurate. The reason that the CS scheme works with velocity estimation with such a
very good accuracy is the fact that the velocity vector is smooth and linear over short intervals of time.
Hence, α = 4 or α = 5 is sufficient for CS theory to estimate the velocity vector.
We plot the sliding window estimation snapshot for R = 10 > L = 5 in Figure 3.13. As expected,
the un-sampled parts of the velocity vector are not estimated correctly, whereas the sampled parts have
been estimated accurately. In fact, the figure shows that after each sliding window shift, 5 samples are
Chapter 3. Location Awareness via Sparse Recovery in VSNs 49
0 20 40 60 80 100 12010
10.5
11
11.5
Velocity vector, M=20, N=124, α=4, R=6, L=10
Vel
oci
ty (
m/s
)
Original Signal
CS Scheme
0 20 40 60 80 100 1200
0.05
0.1
CS Scheme Error=0.002
Time of Sample
Est
imat
ion E
rror
(m/s
)
Figure 3.12: Example of velocity estimation using the CS scheme with a sliding window using the citydata.
missed.
We plot the average and maximum errors for a fixed window shift size R = 6 versus the sliding
window size L in Figures 3.14 (a) and (b). The figures show that for a L = 2, the errors are large. As
L increases, the errors decreases. This is due to the fact that the number of missed samples decrease
which results in decreasing the average and maximum estimation errors. When L increases in Figure
3.14 (a) and (b), there might be a slight increase in the estimation errors due to the need of estimating
more variables, which can be improved by increasing α as will will show later on.
We plot the estimation errors in Figures 3.15 (a) and (b) for a fixed L versus R. Again, as R increases,
the estimation errors increase. Based on these results, we can strongly recommend to set R ≤ L so that
at most the measurements are back to back in order for each vehicle to obtain accurate estimation of
the neighbourhood during the recent past time.
Finally, we show an example of location estimation using highway data in Figure 3.16. The figure
shows the displacement of one vehicle in meters, and it shows that CS sliding window scheme performs
Chapter 3. Location Awareness via Sparse Recovery in VSNs 50
0 10 20 30 40 50 60 70 80 9011.5
12
12.5
13
Velocity vector, M=10, N=95, α=4, R=10, L=5
Vel
oci
ty (
m/s
)
Original Signal
CS Scheme
0 10 20 30 40 50 60 70 80 900
0.1
0.2
0.3
0.4
0.5
CS Scheme Error=0.051
Time of Sample
Est
imat
ion E
rror
(m/s
)
Figure 3.13: Example of velocity estimation using the CS scheme with a sliding window using the citydata.
1 2 3 4 5 6 7 8 9 10 11−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
L
Err
or
in v
elo
city
(m
/s)
N=488, M=10, α=4, R=6
CS Scheme
(a) Error in velocity estimation.
2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
1.2
1.4
L
Max
. er
ror
in v
eloci
ty (
m/s
)
N=488, M=10, α=4, R=6
CS Scheme
(b) Max. error in velocity estimation.
Figure 3.14: Estimation errors for a fixed R versus L.
estimation up to 1m accuracy.
Chapter 3. Location Awareness via Sparse Recovery in VSNs 51
0 5 10 15 20 25−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
R
Err
or
in v
elo
city
(m
/s)
M=10, α=4, L=10
CS Scheme
(a) Error in velocity estimation.
0 2 4 6 8 10 12 14 16 18 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
R
Max
. er
ror
in v
eloci
ty (
m/s
)
M=10, α=4, L=10
CS Scheme
(b) Max. error in velocity estimation.
Figure 3.15: Estimation errors for a fixed L versus R.
0 10 20 30 40 50 60 70 80
1850
1900
1950
2000
Displacement vector, M=10, N=82, α=4, R=8, L=10
Dis
pla
cem
ent
(m)
Original Signal
CS Scheme
0 10 20 30 40 50 60 70 800
0.5
1
1.5
CS Scheme Error=0.115
Time of Sample
Est
imat
ion E
rror
(m)
Figure 3.16: Estimation of the location information using the CS sliding window scheme.
3.3.4 Sliding Window Edge Estimation
In this part, we focus on the rightmost edge of the velocity vector at time i and the estimation error in
the interval [n− 1, n = i] where the values of x(Q)i are the focus of interest. Over the [n− 1, n = i], xQi
Chapter 3. Location Awareness via Sparse Recovery in VSNs 52
2 4 6 8 10 12 1410
−6
10−5
10−4
10−3
10−2
10−1
100
R
Err
or
in v
elo
city
, lo
g(m
/s)
M=10, α=4, L=5
Complete vector
Vector without edge
Figure 3.17: Estimation error with and without considering x(Q)i versus R.
will be placed differently in Φi until n = m. Outside [n−1, n = i], x(Q)i won’t be included in Φi. We find
the estimation error for the complete estimated vector xi and for the estimated vector xi,{1,··· ,(N−R)}
without considering x(Q)i estimation error. We plot the results in Figure 3.17 for a fixed L = 5. The
figure shows that as R increases, both estimation errors becomes closer to each others until R equals 7,
which means that there is not more overlap between the M measurements, and every measurement has
the same effect as the edge. Moreover, the estimation error increases as R increases.
We also plot the estimation error for an overlapped measurements with L = 10 > R = 5 in Figure
3.18 versus α. As α increases, the estimation error decreases, and the edge error becomes more negligible.
This is because having a larger α allows accurate estimation of the edge without the need of overlap
between the measurements.
We plot the edge error for different time shifts i in Figure 3.19. For the sliding index of 1, we are
estimating x(Q)i which shows a larger error due to the location at the rightmost edge. As the sliding
index increases to i+ 1 = 2, the edge x(Q)i is placed at a better position in the sensing matrix with more
overlapped measurements. For i + 1 the estimation error decreases. As we further increase the sliding
index, the x(Q)i is estimated with a better accuracy until the corresponding measurements are placed
near the leftmost edge of the sensing matrix, which results in slightly increasing the estimation error.
We plot the estimation error for in Figure 3.20 for the proposed SWE estimation algorithm. We
compare the algorithm to the error of averaging the estimation after each sliding window shift. Let
Chapter 3. Location Awareness via Sparse Recovery in VSNs 53
4 5 6 7 8 9 100
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
−3
α
Err
or
in v
eloci
ty, (m
/s)
M=10, R=5, L=10
Complete vector
Vector without edge
Figure 3.18: Estimation error with and without considering x(Q)i versus α.
0 2 4 6 8 10 120
1
2
3
4
5
6x 10
−3
i
Err
or
in v
eloci
ty e
stim
atio
n o
f x
i(Q) ,
(m/s
)
M=12, α=6, L=10, R=4
Figure 3.19: Estimation error of x(Q)i versus the sliding index.
r = 1, · · · ,M be the index of shift, and T(r)i = x
(Q)i at shift r. Then we have
A(r)i =
1
r
r∑j=1
T(j)i ,
where A(r)i is the average of the estimations for x
(Q)j up to shift r. And the estimation error becomes
Error = |x(Q)i −A(r)
i |.
Figure 3.20 shows that at i = 1, both SWE algorithm and averaging results in the same estimation
Chapter 3. Location Awareness via Sparse Recovery in VSNs 54
0 2 4 6 8 10 120
1
2
3
4
5
6
7
8x 10
−3
i
Err
or
in v
elo
city
est
imat
ion
of
xi(Q
) , (m
/s)
M=12, α=6, L=10, R=6
Averaging
SWE
Figure 3.20: Estimation error of x(Q)i using the SWE algorithm versus the sliding index.
error, which is correct due to having a single estimate of x(Q)i at that time. However, for i > 1, SWE
results in a better estimation compared to averaging of CS estimations. This is due to the fact that
SWE algorithm always selects the estimation with the minimum error compared to the actual velocity
valuea vi and vi−1.
Finally, we compare the errors of the CS sliding window scheme with interpolation for different
values of R and L = 40 in Figures 3.21 (a) and (b). The figures show that as R increases, the errors
for interpolation is increasing faster than the CS scheme, and the CS scheme outperforms interpolation
for all values of R. In fact, as R increases, the distance between the every two sampling times i and
i+ 1 increases, and the overlap between the samples decrease resulting in higher errors. The CS scheme
though shows higher estimation accuracy by encoding L samples in each observation window.
3.4 Summary
This chapter proposed a system level design for a congestion avoidance scheme that utilizes compressive
sensing to estimate velocity in vehicular networks. The key concept is that we approached the congestion
control problem from a different perspective. That is, instead of designing a rate controller, we propose
to investigate the sparsity of velocity information contained in transmitted packets. Furthermore, we
use sparse recovery concepts to estimate the original velocity information for each vehicle. We propose
Chapter 3. Location Awareness via Sparse Recovery in VSNs 55
0 5 10 15 20 25 30 35 40 45−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
R
Err
or
in v
elo
city
(m
/s)
M=10, α=10, L=40
CS Scheme
Interp.
(a) Error in velocity estimation.
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
R
Max
. er
ror
in v
eloci
ty (
m/s
)
M=10, α=10, L=40
CS Scheme
Interp.
(b) Max. error in velocity estimation.
Figure 3.21: Estimation error of the sliding window CS scheme and interpolation versus R.
two velocity estimation schemes, namely, a super-frame CS scheme that is suitable for delay-tolerant
applications, and an sliding window CS scheme that is suitable for delay-sensitive applications. The
former CS scheme performs estimation at the end of the super-frame and reduces the burden on the
communication channel while preserving the information. In fact, the proposed scheme provides more
information compared to the suggested sampling scheme for vehicular velocity trajectory estimation. The
siding window scheme uses a sliding window and encodes samples over a limited window of observation.
We evaluated the proposed CS schemes by performing an experimental study in highways and downtown
of the city of Toronto. Our results show that the proposed CS scheme outperforms interpolation in both
highway and city experiments. Moreover, we found by further study of the sliding window scheme that
the edge error can be mitigated after a small number of sliding window shifts.
Chapter 4
Gain of Mobility for Sensing in
VSNs
In this chapter, we focus on the gain of mobility for sensing in vehicular sensor networks. First, we start
by introducing the problem, define the used terminologies in this chapter, and state the benchmark for
comparison. Then, we quantify the mobility gain for sensing in VSNs. The material of this chapter has
been published in the IEEE International Conference on Communications [27].
4.1 Introduction
An MSN is composed of a number of mobile nodes that sense the environment. In a typical coverage
problem, these sensors attempt to cover targets several times. In some applications, the number of times
targets are required to be covered is referred to as the “coverage quality”. The problem of activating
sensors to provide coverage has been an active area of research for energy-saving [68]. This problem
discusses how to design a scheduler to assign sensor activations based on certain constraints. However,
there is a recent interest in studying the relation between mobility and sensing for coverage [24], and
mobility is shown to help in coverage in mobile sensor networks [24]. It has been shown in [24] that
with a fixed number of mobile sensors, detection time of a target is optimized when sensors choose their
56
Chapter 4. Gain of Mobility for Sensing in VSNs 57
direction of movement uniformly at random.
In this chapter, we discuss the following question: How much predicted mobility can help in reducing
the number of sensors that are activated to cover a number of targets? We show in this chapter that for
a certain mobility model, the incorporation of predicted mobility (i.e. space and time) information in
scheduling reduces the number of activated sensors significantly compared to the stationary scheduler,
which considers time or space information in scheduling as in [25]. We focus on a specific category
of mobile sensor networks in which energy is not limited such as vehicular sensor networks. In such
a sensor network, the bottleneck is the communication channel capacity, where the channel can be
congested [11,15, 16,18, 19,29,66, 67]. Hence, reducing the amount of sensed and communicated data is
essential to providing reliable coverage for targets.
This part of the thesis is different from the mobility-based coverage studies in the literature that
consider initial deployment of sensors and mobilize them to optimize coverage [68]. The proposed
scheme assumes that mobile nodes’ behaviour is predictable, and then it activates sensors accordingly
to provide the required coverage. In this chapter, we quantify the mobility gain in terms of sensing cost,
probability of feasibility, and then present practical heuristics to approximate the mobile scheduler in
centralized and distributed communication environments.
To investigate the possibility of reducing sensor activity, while providing the required coverage of
targets, we start by tailoring the stationary sensor scheduling problem in [25] to our wireless network
model, by removing the energy constraints, and adding the wireless channel constraints. The formulation
of this problem is called the stationary scheduler throughout the thesis and considered as the benchmark
for comparison. After that, we introduce an independent mobility model that describes the availability
of sensors to cover targets over a time interval. This mobility model is then incorporated and utilized
in a novel mobile scheduler in order to reduce the number of activated sensors while providing the same
required coverage as the stationary scheduler. We study both schedulers by comparing the number of
activated sensors, and the probability of feasibility.
We study the stationary scheduler and the novel mobile one via analysis and extensive simulations.
Simulation results show that the mobile sensing scheduler outperforms the stationary one in a number
Chapter 4. Gain of Mobility for Sensing in VSNs 58
of performance metrics; e.g., it shows a higher probability of feasibility, and a lower sensing cost.
The rest of the chapter is organized as follows. Section 4.2 describes the system model and the
sensing-coverage problem formulations for both the stationary and mobile approaches. In Section 4.3,
we illustrate the analysis framework for both approaches. Section 4.4 describes the proposed practical
algorithms. Section 4.5 discusses the numerical results. Section 4.6.1 discusses the results for the
Markovian mobility model. Finally, Section 4.7 summarizes the chapter.
4.2 System Model and Sensing Problem Formulation
The system model considers autonomous mobile sensor networks that are mobile themselves without
energy-constraints such as vehicular sensor networks. We consider a communication channel between
each mobile node and a roadside unit. The communication channel is known to be limited in such a
highly mobile network [11, 15, 16, 29, 67]. Each vehicle is equipped with a number of cameras. When
activated, each camera captures a frame at each time instant. This frame is transmitted to the fusion
centre via standard IEEE 802.11p protocol vehicle-to-infrastructure (V2I) to be processed for safety
and non-safety applications. The more the number of communicating vehicles in the area, the larger the
volume of data transmitted to the fusion centre, and the lower the ratio of successful packet reception due
to possible large number of packet collisions in vehicular communications [67]. Hence, we consider that
the maximum number of sensors per vehicle that can communicate to the fusion centre in a parameter in
our system model, λ. In our system model, we attempt to reduce this load on the channel by activating
a small number of sensors while the coverage of targets is provided. In the sequel, sensor activation
means that the sensors are activated and their channel can transmit the captured images.
Consider a segment of the road, where vehicles are moving according to a realistic mobility model as
in Figure 4.1. There exists a target and each camera in the vicinity of the target takes images of that
target. We assume that sensing of the target at the road side is required at N epochs of time. A target
can be a building, a segment of sidewalk, a stalled vehicle, etc. The application of our system model is
similar to the one in [63], where an image capture service is provided by vehicles.
Our system model uses the clustering concept. Clustering of vehicles is based on sensing range and
Chapter 4. Gain of Mobility for Sensing in VSNs 59
Figure 4.1: Illustration of the system model practical scenario.
the location of target. Vehicles that are in the vicinity of a target form a cluster that we refer to as the
currently covering vehicles or currently covering cluster. Each cluster is assumed to be far apart from
other clusters, which results in inter-cluster independence. This is a valid assumption, and has been
used to model vehicles mobility visiting certain vicinity on the road [64]. The currently covering cluster
of K vehicles is available to sense the target at one time instant. Those vehicles are able to sense and
communicate the captured images to the fusion centre via a single-hop communication. K represents
the maximum number of vehicles available in a cluster. We also assume that there are M targets that
should be covered by sensors, and sensors are mobile while targets are fixed.
Location information of each mobile node is assumed to be known via a GPS device. We assume
that the fusion centre has the location information of the vehicles at time 1, and is able to predict their
mobility with high accuracy [8–10], hence coverage availability over the entire period of scheduling [1, N ]
with acceptable accuracy.
There are three assumptions for sensing availability in our system model. First, a sensor is available
for capturing the target if it is physically available to cover the target based on its relative location
with respect to the target, and there exists no blocking vehicles between the sensor and the target (e.g.
cameras on top of the cars, transparent vehicles by vehicle-to-vehicle communications on a different
Chapter 4. Gain of Mobility for Sensing in VSNs 60
channel, and image processing techniques, or covering large targets). Second, the driver of the vehicle is
willing to participate in sensing the target. Third, the communication channel availability to the fusion
centre allows the sensor to transmit the captured image. That is, a limited number of sensors per vehicle
can communicate to the fusion centre in the cluster. That number is λi, for the ith vehicle.
As we will see later on, mobility causes diversity of sensing availability, which can lead to improvement
in capturing a target with certain coverage. The quality of coverage is defined as the number of times a
target is covered.
Assume that a vehicle can have more than one cameras. Let B be a K × L matrix that defines the
sensor node association (i.e. which sensor belongs to which node). That is, a sensor k belongs to node i
if its corresponding position (k, i) in matrix B is 1; otherwise its corresponding value is set to zero.
Finally, define λ = [λ1, . . . , λL]T to be the vector of normalized channels for nodes representing the
maximum number of allowed sensors to be active. In the sequel, the channel is captured in λ, which is
the result of the channel behaviour in restricting the number of allowed sensor data to be transmitted
through the channel.
In short, the system model consists of three components; the sensor scheduler, the mobility model,
and communication channel. The mobility model, which reflects the topology of the network, and the
capacity of the communication channel are input parameters to the schedulers that follow.
4.2.1 Stationary Sensing Network
In this section, we formulate the sensing-coverage scheduler as an integer linear program (ILP) by tailor-
ing the stationery scheduler of [25] to our network model, which is used as a benchmark for comparison.
Let ak denote the activity of a sensor. That is
ak =
1 if sensor k is active
0 otherwise
,
and a = [a1, . . . , aK ]T to be the sensor activity vector of size K × 1. The objective is to optimize the
number of active sensors while satisfying the communication constraints and the quality of coverage.
Chapter 4. Gain of Mobility for Sensing in VSNs 61
In order to perform sensor selection, we need to identify which sensor has the ability to cover a target.
Let U[n] be a K ×M matrix that describes the availability of each sensor to cover the targets at time
n. That is, a sensor k covers target j if its corresponding position (k, j) in matrix U[n] is 1; otherwise
its corresponding value is set to zero. Let us stack the mobility matrixes U[n] to build a tensor block of
U. Since U has a 3-D structure, we can consider independence along three dimensions. As mentioned
earlier, clustering of vehicles is based on sensing range and the location of target. The currently covering
cluster represents a column in our U[n] matrix. Each cluster is assumed to be far apart from other
clusters, which results in inter-cluster independence. Furthermore, we assume that targets are covered
independently (this independence is along the rows in our U[n] matrix). For example, targets can be
far apart or can be on different sides of the road. Finally, the third dimension of independence is among
the cars within a cluster that are covering the same target. This is due to the fact vehicles may opt-in
to participate on sensing the target or not. This independence is called intra-cluster independence.
We assume that each target should be covered qj times at each time instant. Let q = [q1, . . . , qM ]T
be the vector of the number of required coverage times for targets (i.e. quality of coverage). The sensor
selection problem for a stationary sensor network can be formulated as follows
Minimizea
K∑k=1
ak = aT1 (4.1)
subject to a ∈ S (4.2)
where 1 is the K × 1 vector of all 1’s, and
S = {a | aTB � λT (4.3)
aTU � qT (4.4)
ak ∈ {0, 1}, bki ∈ {0, 1}, ukj ∈ {0, 1}}, (4.5)
and the notation � (similarly �) indicates element-wise inequality. Constraint (4.3) limits the com-
munication channel usage, (4.4) enforces the required coverage for each target, and (4.5) assures that
Chapter 4. Gain of Mobility for Sensing in VSNs 62
all variables are binary. The above minimization problem is an integer program, which is NP-hard in
general. It represents a tailored version of the stationary coverage problem in [25], where the energy
constraints are removed. In this particular formulation, (4.3) is not an active constraint, but it affects
the feasibility of the problem as will be shown in Section 4.3.1. However, it can become active in a
different context with a different objective function such as a utility maximization function [27].
In this optimization problem, we will minimize the number of active sensors while providing the
required coverage. That is, if the problem is feasible, then the data of the captured images is transmitted
to the fusion centre. This formulation represents the case where we want to provide a minimum sensor
activations while guaranteeing the required coverage quality within the limitation of the communication
channel. The provided coverage quality assures coverage of targets (i.e. detection) while relieving the
network from unnecessary load. This particular formulation helps in understanding how mobility can
help in scheduling sensors later on in Section 4.3.
4.2.2 Mobile Sensing Network
For the mobile case, we need to include the notion of time in sensor activity. That is, the kth sensor
might be active at one time slot, n (e.g. ak[n = 1] = 1), and inactive in the following slot, n + 1 (e.g.
ak[n = 2] = 0). Let a[n] = [a1[n], . . . , aK [n]]T be the sensor activity vector of size K × 1, at each time
instant n (i.e. the total number of selections in time is composed of n vectors, each of size K × 1).
And define A = [a[1], . . . ,a[N ]]. Now, B is a K × L matrix that defines the sensor-node association
for vehicle i over N time slots. Note that sensor-node association does not change over time, hence
B is independent of time. We assume that sensors are always offering their channel for sensing. That
is, whenever a sensors is scheduled for sensing, it can transmit its sensed data over the communication
channel
The mobility is captured in the K×M availability matrix1 U[n], n ∈ {1, . . . , N}, where it depicts the
ability of a sensor to cover a target during each time instant n based on its mobility. The channel rate
vector also changes over time, λ[n] = [λ1[n], . . . , λL[n]]T . This is due to the fact that the communication
channel changes in the highly dynamic vehicular environment, and the fact that the number of vehicles
1We use the words availability and mobility matrix interchangeably throughout the thesis.
Chapter 4. Gain of Mobility for Sensing in VSNs 63
contending over the communication channel in a cluster changes. The mobile sensing-coverage problem
can hence be formulated as
MinimizeA
K∑k=1
N∑n=1
ak[n] (4.6)
subject to A ∈M (4.7)
where
M = {A | aT [n]B � λT [n], n = 1, . . . , N (4.8)
N∑n=1
aT [n]U[n] � qTm (4.9)
ak[n] ∈ {0, 1}, bki ∈ {0, 1}, ukj [n] ∈ {0, 1}}, (4.10)
where qm is the vector of required coverage of targets in the mobile scenario.
The objective function (4.6) minimizes the number of active sensors, during the whole time interval
[1, N ]. Constraints (4.8) and (4.9) enforce the maximum transmission rate and the required target
coverage over the whole time interval, respectively. The above formulation particularly captures the
mobility of sensors and their availability in the coverage problem. In the stationary formulation, the
activity vector “a” represents one epoch (time slot) of K sensors, while here∑Kk=1
∑Nn=1 ak[n] represents
N epochs of K sensors activities. To obtain the stationary problem formulation, one can set n = 1 (i.e.
one time instant).
4.2.3 Interconnection of Mobile and Stationary Problems
In order to compare the mobile and stationary schedulers throughout the thesis, we identify the input
parameters, and the resulting scheduling cost for each scheduler. In the sequel, we refer to the mobility
matrix at one time instant as U[n], and over the whole interval [1, N ] as U. Denote the stationary
approach2 sensing cost at one time instant as Cs(U[n]) =∑Kk=1 ak[n]. As a benchmark, the stationary
2We use the words ”approach”, ”problem”, and ”scheduler” interchangeably throughout the thesis.
Chapter 4. Gain of Mobility for Sensing in VSNs 64
problem can be solved for each time instant of the whole system time, N , independently. We call this
method N -fold stationary approach, which gives a total cost of CNs (U) =∑Nn=1 Cs(U[n]). Moreover,
we define the cost of the mobile approach to be Cm(U) =∑Nn=1
∑Kk=1 ak[n].
It is important to note that the stationary sensing-coverage problem enforces q coverage at each epoch
of time as it solves a time-independent coverage problem. For each epoch of time, such an approach for
coverage is useful for continuous coverage applications with specific sensing rate but places an overload
on the communication channel. The mobile approach enforces Nq coverage over the total system time.
We claim that in a fair comparison between the mobile and stationary scenarios, where the channel
capacities, and coverage qualities are assigned fairly, the mobile scenario outperforms the stationary case
in terms of the number of active sensors (i.e. CNs (U) ≥ Cm(U)). To be able to have a fair comparison
between the two scenarios, we assume λ[n] = λ for all n = 1, . . . , N , and that qm is N times of that of
the static case, qm = Nq.
Although the objective functions of the stationary and mobile schedulers are the same, the constraints
of the two problems are different (i.e. constraints (4) and (9) in the stationary and mobile schedulers
respectively), and we claim that the mobile scheduler outperforms the stationary one in terms of sensing
cost and probability of feasibility. The stationary scheduler is restricted to provide the coverage of targets
at each time instant without utilizing predicted mobility. Whereas, the predicted mobility information
in the mobile scheduler provides more flexibility for sensor activation through utilization of the future
mobility information.
4.2.4 Mobility and Coverage Model
In mobile sensor networks, the mobility models describe the availability of a sensor to cover a target. In
our coverage model, we assume that inter-node and sensor-target temporal dependence are negligible.
Inter-node dependance is for different sensors covering one target. This assumption is valid for group
of vehicles covering targets on different sides of the road. Sensor-target temporal dependence is for one
mobile sensor covering one target over time. This is not a limiting assumption for our model because
our goal is to use the same coverage model to study the performance metrics for both stationary and
Chapter 4. Gain of Mobility for Sensing in VSNs 65
mobile approaches. In Figure 4.1, as the covering clusters are far enough, the two covering clusters
become independent in covering the same target. Moreover, we assume that the coverage of each sensor
is independent of all the other sensors in its cluster. Furthermore, sensors in a cluster might to choose
to opt-in for sensing or not. Hence, the actual availability for coverage of the target can be random
and modelled by an independent coverage model. This independent model is represented by U, which
is assumed to be known at the fusion centre. Therefore, we use the independent coverage model for
the availability of sensors to cover targets. Moreover, the independent model allows analyzing and
understanding the mobility impact on feasibility and scheduling performance metrics (e.g. number of
active sensors). In this model, a sensor, k, is available to cover a target, j, with probability p. The
availability of a sensor to cover a target is a Bernoulli random variable
P (ukj [n] = 1) = 1− P (ukj [n] = 0) = p ∀k, j, n.
The resulting cost of this coverage model is a function of p; hence Cm(U) = Cm(p), for the mobile
approach, and similarly CNs (U) = CNs (p), for the N -fold stationary approach. The effective number of
sensors in each epoch of time is pK on average.
It is obvious that the extension of these assumptions to mobile targets is straightforward. In our
model, at each time instant, a cluster of sensors in the vicinity of a target can participate in sensing. If
the target is mobile, the same assumption is applied as the time is discrete. At any sampling instant, all
sensors in the neighbourhood of a moving target will be considered as potential sensors. From among
these sensors, only the ones that opted-in to participate in sensing are the ones that will be available for
coverage.
4.3 Mobility Gain
In this section, we compare the average sensing cost, and the average feasibility of the mobile approach,
with the N -fold stationary one. In our analysis, sensing cost depends on the feasibility of the problem.
Hence, we start by finding the feasibility of the stationary and mobile schedulers, and then we find the
Chapter 4. Gain of Mobility for Sensing in VSNs 66
sensing costs. The study is based on an independent coverage model defined next.
4.3.1 Feasibility Analysis
We study the probability of feasibility (probability of satisfying the coverage constraints) using the
random coverage model defined in Section 4.2.4. Using that model, we can compute the probability of
feasibility for the N -fold stationary approach P (A ∈ SN ), (SN = S × . . .×S, where × is the Cartesian
product, and that S has been multiplied N times by itself), and for the mobile approach P (A ∈ M).
Based on the frequentist definition, the probability of feasibility is equal to the size of the feasibility
set (i.e. number of feasible scenarios) normalized by 2KN , which is the size of the possible binary
matrices of size K × N . Since it is impossible to count the number of feasible scenarios directly, we
consider an average scenario instead and calculate its probability of feasibility. The feasibility analysis
considers the impact of the random mobility on feasibility because sensing cost is dependent on the
mobility model. Let qj = q, ∀j. Here, the number of available sensors for coverage is restricted by
the communication channel constraint. However, since sensing cost analysis in the next section depends
only in the coverage constraint and mobility information, we consider λ to allow feasibility of problem,
and study the impact of mobility information on feasibility. That is, we assume λ ≥ KL in this analysis.
We found by simulations that our scheduler is not significantly affected by λ < KL since our scheduler is
minimizing the number of active sensors, and is not selecting all the sensors within each vehicles.
Theorem 1. Probability of Feasibility for the N-fold Stationary Problem: The probability that
the N -fold stationary problem is feasible is
P (A ∈ SN ) = (P (xs ≥ q))MN (4.11)
where xs ∼ B(K, p).
Proof. The probability that we have xs sensors covering a target, Is(xs) = P (∑Kk=1 ak[n]ukj [n] = xs),
Chapter 4. Gain of Mobility for Sensing in VSNs 67
follows a Binomial distribution as
Is(xs) =
(K
xs
)pxs(1− p)(K−xs).
The probability of satisfying the coverage for target j at that time instant is
T s(j) = P
(K∑k=1
ak[n]ukj [n] ≥ q
)=
K∑xs=q
Is(xs).
The probability of satisfying coverage qualities for all the targets on that time epoch (or equivalently
satisfying constraint (4.4) at a time epoch) becomes
P(aT [n]U[n] � qT
)=
M∏j=1
T s(j).
This approach can be applied to the whole system time to get
P (A ∈ SN ) =
N∏n=1
M∏j=1
T s(j) = (P (xs ≥ q))MN (4.12)
Theorem 2. Probability of Feasibility for the Mobile Problem: The probability that the mobile
problem is feasible is
P (A ∈M) = (P (xm ≥ q))M (4.13)
where xm ∼ B(K, p).
Proof. In the average scenario, the probability that we have xm sensors available to cover a target
(Im(xm) = P (∑Kk=1
∑Nn=1 ak[n]ukj [n] = xm) follows a Binomial distribution as
Im(xm) =
(KN
xm
)pxm(1− p)(K−xm).
Chapter 4. Gain of Mobility for Sensing in VSNs 68
The probability of satisfying the coverage for target j over the whole system time is
Tm(j) = P
(K∑k=1
N∑n=1
ak[n]ukj [n] ≥ Nq
)=
KN∑xm=Nq
Im(xm).
Hence, the probability of satisfying the qualities for M targets becomes
P (A ∈M) = P
(N∑n=1
aT [n]U[n] � qTm
)=
M∏j=1
Tm(j) = (P (xm ≥ q))M . (4.14)
As we mentioned, both Is(xs) and Im(xm) follow Binomial distributions, and can be approximated
by Normal distributions. Hence, T s(j) and Tm(j) can be approximated by Q functions as follows (using
Q(−x) = 1−Q(x))
P (A ∈ SN ) ≈ QNM(
q − pK√pK(1− p)
)= QNM (−zs) ,
P (A ∈M) ≈ QM(
Nq − pK√pK(1− p)
)= QM (−zm) ,
where we have defined
zs = − −q + pK√pK(1− p)
, (4.15)
and
zm = − −Nq + pK√pK(1− p)
, (4.16)
because the arguments of the Q functions are negative. This is due to the fact that in practical scenarios
K � q, which results in a negative argument. Let us define the feasibility gain as
Γ =P (A ∈M)
P (A ∈ SN ). (4.17)
Chapter 4. Gain of Mobility for Sensing in VSNs 69
Γ can be represented in terms of approximated probabilities as
Γ ≈
(1−Q(zm)
(1−Q(zs))N
)M. (4.18)
We can use Taylor series to approximate the denominator of (4.18) because in practice the argument of
the Q function is negative enough to make the function value small. Hence,
Γ ≈ (1 +NQ(zS)−Q(zm))M
(4.19)
Figure 4.2 illustrates the feasibility gain Γ as a function of p for different values of p. The feasibility gain
occurs when Γ > 1 or equivalently NQ(zS)−Q(zm) > 0. We can study the behaviour of the Q(zS) and
Q(zm) using their upper bounds. For example, the Chernoff bound suggests
Nexp
(−z2s
2
)> exp
(−z2m
2
), (4.20)
and by taking the log of both sides, we have
log(N)− z2s2
+z2m2> 0 (4.21)
From (4.21), as p→ 1,z2s2 →∞ because of (1−p) in the denominator of zs, and (4.21) becomes negative
which represents no gain. This is illustrated in Figure 4.3, which shows that as p → 1, Q(zs) → 1
regardless of other parameters (e.g. K). Figure 4.2 also confirms that Γ→ 1 as p→ 1, regardless of K.
Figures 4.4 shows Γ increases as M , N or q are increased. In the figure, we change fix two parameters
and change the third one from 1 to 5. This is expected because increasing M (similarly N) increases
the number of elements in U. As q increases, the number of sensors used in the stationary and mobile
schedulers increases. However, the feasibility gain increases due to the fact that zm is greater than zs as
can be seen in (4.18) and (4.21).
Chapter 4. Gain of Mobility for Sensing in VSNs 70
0.4 0.5 0.6 0.7 0.8 0.9 10
2
4
6
8
10
12
14
16
p
Γ
N=4, M=4, q=2
K=10
K=20
K=50
Figure 4.2: Theoretical feasibility gain Γ, based on (4.18), versus p for different values of K.
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
p
Q(z
s)
q=1
K=10
K=20
K=50
Figure 4.3: Q(zs) versus p for different values of K.
4.3.2 Sensing Cost
To quantify the sensing cost, we compute the average number of active sensors. As we discussed in
the feasibility analysis section, in a practical scenario, the limiting constraint for the sensing-coverage
Chapter 4. Gain of Mobility for Sensing in VSNs 71
0.4 0.5 0.6 0.7 0.8 0.9 11
1.5
2
2.5
3
3.5
4
4.5
5
5.5
p
Γ
K=10
N=4 , q=2, M=1
N=4 , q=2, M=5
N=4 , q=1, M=5
N=4 , q=5, M=5
N=1 , q=2, M=5
N=5 , q=2, M=5
Figure 4.4: Theoretical feasibility gain Γ, based on (4.18), versus p for different values of N , M , and q.
minimization problem is usually the required coverage constraint. The sensing cost is computed for the
feasible scenarios.
To find the minimum number of sensors, we should calculate how many sensors are activated while
satisfying constraints (4.4) and (4.9) for the stationary and mobile approaches, respectively.
Let qj be the required coverage for target j at any time instant in the stationery problem. We assume
that qj is constant over the interval [1, N ]. Let us also define qmj = Nqj to be the required coverage for
target j over the interval [1, N ] for the mobile case.
Lemma 1. Minimum Sensing Cost: Over an interval [1, N ], the minimum number of active sensors
for both mobile and stationery problems is Nmaxj
qj.
Proof. Let as[n] be the solution of (4.1)-(4.5) and am[n] be the solution of (4.6)-(4.10)3. We have
Cs(U[n]) =∑Kk=1 a
sk[n] and Cm(U) =
∑Nn=1
∑Kk=1 a
mk [n]. The minimum number of sensors is achieved
when ukj [n] = 1, ∀k, j, n. Using constraint (4.9), we have
N∑n=1
K∑k=1
amk [n] ≥ qmj ∀j,
3Superscripts s and m in ask and amk denote the stationary and mobile problems solutions, respectively.
Chapter 4. Gain of Mobility for Sensing in VSNs 72
where qmj = Nqj . Hence,
Cm(U) =
N∑n=1
K∑k=1
amk [n] ≥ maxj
qmj = Nmaxj
qj .
Similarly, we can prove that for the stationary case, Cs(U[n]) =∑Kk=1 a
sk ≥ max
jqj , and this results in
CNs (U) =∑Nn=1
∑Kk=1 a
sk[n] ≥ Nmax
jqj .
This lemma determines the minimum cost for both approaches. The following lemma determines the
sensing cost as p→ 1.
Lemma 2. Sensing Cost when p → 1: Over an interval [1, N ], as p → 1, the minimum number of
active sensors in the mobile and stationary problems satisfy Cm(U) = NCs(U[n]).
Proof. When p→ 1, we get U[n] = 11T . Then from (4.4), we get
aTU = (aT1)1T = Cs(U[n])1T ≥ qT ,
which gives limp→1
Cs(U[n]) = maxj
qj . From (4.9), we have
N∑n=1
aT [n]U[n] =
N∑n=1
aT [n]11T =
N∑n=1
(aT [n]1)1T (4.22)
= Cm(U)1T ≥ qTm,
which gives limp→1
Cm(U) = maxj
qmj . Hence, limp→1
Cm(U) = N limp→1
Cs(U[n]).
As explained before, U is a cube of binary elements (i.e. ukj [n] ∈ {0, 1}), where U[n] is a K ×
M matrix that represents one epoch of sensor availability to cover targets at time n. Based on the
independent coverage model, each element of U is a Bernoulli random variable with parameter p. We
can visualize that each scheduler selects a subset of the U tensor to satisfy the coverage constraint as
depicted in Figure 4.5. As seen in Figure 4.5 (a), the stationary scheduler satisfies the quality constraint
for all the targets at each time instant independently. Hence, it gains from target overlap between
sensors, but not from temporal overlap. Each depicted subframe (i.e. a frame with a height less than
Chapter 4. Gain of Mobility for Sensing in VSNs 73
(a)
(b)
Figure 4.5: Illustration of how the stationary and mobile schedulers satisfy coverage qualities on average.
K) in the figure shows the provided coverage by sensors at each time instant. On the other hand, the
mobile scheduler gains not only from the target overlap, but also from the temporal overlap by selecting
a subcube instead of multiple subframes as depicted in Figure 4.5 (b). The provided coverage quality is
equal to the number of 1’s in the shaded areas. Based on the independent coverage model, this number
follows a Binomial distribution.
Chapter 4. Gain of Mobility for Sensing in VSNs 74
Let Ks be the average number of sensors activated by the stationary scheduler at each time instant
(i.e. average effective height of the shown frames in Figure 4.5 (a)). Similarly, let Km be that of mobile
scheduler at each time instant (i.e. the height of the selected subcube in Figure 4.5 (b)). Moreover,
define δNs and δm to be the thresholds of satisfying the probability of coverage for all targets for the
N -fold stationary and mobile schedulers, respectively. Furthermore, let us define σ = Mp(1−p), which is
indeed the variance of the Binomial distribution B(M,p). The sensing cost of each scheduler represents
the average of the minimum number of activated sensors that satisfies the coverage qualities.
Theorem 3. Average Sensing Cost for the Stationary Approach: Over an interval [1, N ], the
mean number of active sensors (i.e. average area of the shaded face) can be expressed as CNs (U) = Ks×N
for the stationary approach, where
Ks =q
p+σε2s + εs
√σ2ε2s + 4M2pqσ
2M2p2, (4.23)
Proof. As discussed above, in order to find the average sensing cost, we need to compute the average
effective height (Ks). One approach to find the average Ks is to calculate it based on the coverage
quality constraint (4.4). In order to do this, we assume that at the minimum Ks, the probability of
covering each target q times is greater than a large threshold δNs
P
(KsM∑i=1
Xi ≥Mq
)≥ δNs . (4.24)
where Xi’s are Bernoulli random variables. This inequality states that the stationary scheduler should
provide a quality of q for each target (i.e. a total of Mq qualities) at each time instant inside a frame.
Moreover, in each frame, the average number of selected ones is KsM to satisfy the qualities.
The minimum Ks will satisfy the above equation with equality. Furthermore, the probability has a
Binomial distribution form and the above inequality can be approximated by Q function as
QN
(Mq −KsMp√KsMp(1− p)
)= δNs . (4.25)
Chapter 4. Gain of Mobility for Sensing in VSNs 75
which results in solving the following equation for Ks
Mq −KsMp = Q−1(δNs)√
Ksσ. (4.26)
Let εs = Q−1(δNs). Finally, by solving (4.26) we arrive at (4.23).
Ks is the effective height selected by the stationary scheduler for a threshold δs at each epoch of
time. Note that our model represents the average case where Ks is the same for all time instants within
a feasible scenario. That is, we can solve the problem for a single time instant to find Ks, and then
multiply by N to find CNs (U). Ks × N represents the average sensing cost for the N -fold stationary
scheduler. So, we solve the stationery problem at one time instant as
P (Cs(U[n]) = x) =δNsN
= δs, (4.27)
to find the minimum Ks as shown in the above theorem.
Theorem 4. Average Sensing Cost for the Mobile Approach: Over an interval [1, N ], the mean
number of active sensors can be expressed as Cm(U) = Km ×N for the mobile approach, where
Km =q
p+Nσε2m + εm
√Nσ(Nσε2m + 4N2M2pq)
2N2M2p2. (4.28)
Proof. Similar to the previous proof, we can form an inequality for satisfying the coverage qualities for
all the targets over the total system time in the mobile scenario as
P
(KmNM∑i=1
Xi ≥ NMq
)≥ δm, (4.29)
where we present the volume of the subcube as KmNM with an effective height of Km. Furthermore,
the required coverage quality for all the targets and over the total period of time is NMq.
Chapter 4. Gain of Mobility for Sensing in VSNs 76
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
p
N=4, M=4, q=2
Km
Ks
Figure 4.6: Ks and Km based on Theorems 3 and 4.
Again the above probability expression can be approximated by a Q function as
Q
(NMq −KmNMp√KmNMp(1− p)
)= δm. (4.30)
To find Km, we have to solve the following equation
NMq −KmNMp = Q−1 (δm)√KmNσ. (4.31)
Let εm = Q−1 (δm). Similar to the stationary case, the above equation can be solved with equality to
find Km, which will result in (4.28).
The above theorems quantify the sensing cost (effective height ×N) for both schedulers and can
describe the mobility gain in terms of different parameters. We plot Ks and Km in Figure 4.6. We can
see that Ks < Km for p 6= 1. Otherwise Ks = Km. Moreover, Figure 4.7 shows that the mobility gain
(i.e. Ks
Km) for the same network can be as large as 1.87 for such a small scale network.
We will attempt to simplify the results of the two Theorems 3 and 4. We will start by simplifying
Chapter 4. Gain of Mobility for Sensing in VSNs 77
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
N=4, M=4, q=2
p
Ks/K
m
Figure 4.7: Ks
Kmbased on Theorems 3 and 4.
Ks for the stationery scheduler. (4.23) has two dominating terms in the numerator, which are 4M2pq
and 2εs√σ(4M2pq). These two terms in the numerator can approximate (4.23) very closely as
Ks ≈q
p+
2εs√
4M2p2(1− p)q4M2p2
, (4.32)
and we get
Ks ≈q
p+εs√
(1− p)q√Mp
. (4.33)
Similarly, we can consider only 4NM2pq and 2εm√Nσ(4N2M2pq) in the numerator to approximate
(4.28) very closely as
Km ≈q
p+
2εm√
4N3M3p2(1− p)q4N2M2p2
, (4.34)
Chapter 4. Gain of Mobility for Sensing in VSNs 78
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
p
N=6, M=6, q=1
Km
−Analysis
Ks−Analysis
Km
−Simplified
Ks−Simplified
Figure 4.8: Approximations of Ks and Km based on (4.33) and (4.35).
which can be simplified to
Km ≈q
p+εm√
(1− p)q√NMp
. (4.35)
The approximations are found to be numerically close to the exact expressions as Figure 4.8 shows,
and therefore can be used to study the mobility gain. To compare Ks and Km, we find the difference,
and substitute εs and εm by their values to get
Ks −Km ≈√q(1− p)√Mp
(εs −
εm√N
)(4.36)
=
√q(1− p)√Mp
εs
(1− 1√
N
Q−1 (δm)
Q−1 (δs)
)
In Figure 4.9, we fix δm and δNs to a large value (close to 1) and plot f(N) =(εs − εm√
N
), which
shows that the gain increases with N as expected. From (5.5), for N = 1, we get Ks = Km which shows
that would be no difference between the mobile and stationery cases as expected. However, for N > 1
Chapter 4. Gain of Mobility for Sensing in VSNs 79
0 10 20 30 40 50 60 70 80 90 1000
0.5
1
1.5
2
2.5
N
f(N
)
Figure 4.9: f(N) =(εs − εm√
N
)versus N .
the mobility gain decreases as p increases. We also plot (5.5) versus M in Figure 4.10. Figure 4.10 shows
that as M increases, the Ks decreases while Km increases. This can be seen in (5.5) since M is in the
denominator of the right hand side. This is due to εs being positive while εm is negative. The figure
also shows that the approximations of the equations (4.33) and (4.35) closely follow the exact results of
Theorems 3 and 4. Finally, the figure shows Ks −Km decreases as M increases.
4.4 Approximation Algorithms
In this section, we propose a greedy algorithm to utilize mobility information in sensing that is inspired
by concepts in [54] for stationary networks. The ILP problem that we proposed for the scheduling is
NP-hard. This motivates us to propose heuristic algorithms to solve it. However, the main motivation
for the greedy algorithm is that it can be extended to a distributed algorithm by exchanging local
information. In the algorithm description, we use the subscript i to denote an iteration.
Define the benefit of a sensor as the number of targets that can be covered by activating that sensor.
Let Ti be the set of targets that require q coverage at iteration i. Initially, T0 = {t1, · · · , tM}. Let bki [n]
Chapter 4. Gain of Mobility for Sensing in VSNs 80
2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
M
N=4, p=0.5, q=1
Km
−Exact
Ks−Exact
(Ks−K
m)−Exact
Km
−Simplified
Ks−Simplified
(Ks−K
m)−Simplified
Figure 4.10: Ks −Km versus M based on Theorems 3 and 4, and equations (4.33), (4.35), and (5.5).
be the coverage benefit of sensor k at time n and iteration i of the algorithm. Then, we have
bki [n] =∑j
ukj [n], ∀j ∈ Ti.
bki [n] is important for the design of the greedy algorithm where the scheduler makes decisions by com-
paring bki [n] of different sensors in the network. Moreover, bki [n] depends on iteration via Ti.
4.4.1 Centralized Algorithm
In the centralized case, it is assumed that a controller knows all parameters of the system. The key idea
of the algorithm is as follows. At each iteration, it selects the sensor that covers the largest possible
number of targets that have not been covered by q sensors yet (i.e. have not received their desired
coverage). The algorithm knows which sensor covers the largest possible targets via bki [n], and knows
the targets that are not covered q times yet via Ti.
Let Si be the set of activated sensors up to iteration i. Initially, S0 = {φ}. At i = 1, a sensor k is
Chapter 4. Gain of Mobility for Sensing in VSNs 81
activated (i.e. ak[n] = 1) where
k1 = arg maxk
bk1 [n], ∀j ∈ T1,
where k1 is the sensor to be activated at the 1st iteration. The set of activated sensors is updated by
adding that sensor S1 = S0 ∪ {k1}. Moreover, the set of required coverage is updated by removing any
target with satisfied coverage as follows. Let Qi be the set of targets that are cumulatively covered by
at least q times at iteration i. Define cji as follows
cji =
1 if target j is cumulatively covered
q times at iteration i
0 otherwise
.
Initially, Q0 = {φ}. At iteration i, Qi is updated by adding the targets with satisfied quality of coverage
Qi = {tj | cji = 1}. Then, the set of required coverage is updated by T1 = T0 − Q1 The procedure
continues until Ti = {φ}, and there are no more targets to be covered. The iterative greedy algorithm
running time is upper bounded by O(ln q|∑n Max
kbk[n]|) [54].
The greedy algorithm can be applied to both the N -fold stationary and mobile approaches as follows.
For the N -fold stationary case, the inputs for the algorithm are given every epoch of time, which include
U[n], λ[n], and q. The cost computed by the algorithm in this case at each time instant is Cs(U[n]),
and the total cost is Cs(U). Furthermore, the output of the algorithm is a[1], · · · ,a[n]. For the mobile
approach, the inputs to the algorithm are U, λ[n], and qm. The output cost is Cm(U) and the vectors are
a[1], · · · ,a[N ]. This means that the greedy version of the mobile scheduler activates sensors by knowing
the predicted mobility in U. The algorithm treats each sensor at different times as an independent sensor
in computing the cost and bki [n]. Figure 4.11 describes the steps of the centralized greedy algorithm
(CGA).
Chapter 4. Gain of Mobility for Sensing in VSNs 82
Require: Initialize ak[n] = 0,∀k, n, S0 = {φ}, T0 = {t1, · · · , tM}, Q0 = {φ}while Ti 6= {φ} do
Activate sensor k, k = arg maxk
bki [n], ∀j ∈ Ti.
Si = Si−1 ∪ {k}Qi = {tj | cji = 1}Ti = Ti−1 −Qi
end while
Figure 4.11: The CGA algorithm.
4.4.2 Distributed Algorithm
The distributed algorithm is an extended version of the centralized algorithm designed to work with
local information of subgroup of nodes. It is also inspired by the one proposed in [54]. However, our
proposed algorithm is specifically tailored to solve our proposed mobile approach. In our network, we
consider that the communication range is at least twice the sensing range. Hence, every two nodes that
cover the same target can communicate. In the distributed greedy algorithm, we use the concept of
target ownership. That is, each target is assumed to be owned by a mobile node. This mobile node can
be considered as a scheduler (or cluster controller) in the distributed case. Each owner communicates
with its neighbors. The neighbors of an owner are all nodes that are able to cover the owned target j.
Whenever the owner is required to exchange messages with its neighbors, only nodes within the cluster
receive those messages. However, neighbors might sense different targets but we assume that they stay
within the sensing range of the owned target j.4
Let Oj be the owner of a target. If target j is owned by a sensor k, the neighbors of that nodes
includes all nodes that are able to cover target j having ukj [n] = 1. Let Nj be the set of neighbors of the
owner Oj . Then k ∈ Nj if and only if ukj [n] = 1. For each Oj , it communicates with its neighbors Nj ,
and requests Uk[n]5 and bki [n] of each sensor k ∈ Nj . The decision of sensing is done accordingly. The
main difference between the distributed and centralized algorithms is that decision of sensing is made
locally by each owner Oj . This decision making process depends on local mobility information and hence
results in a fully distributed algorithm. To refer to a cluster (group of neighbors of target j), we use the
4This is necessary or we need to exchange messages between different clusters and reschedule at every time instantwhich contradicts the goal of the mobile approach.
5Uk[n] includes the availability information of sensor k with respect to all targets.
Chapter 4. Gain of Mobility for Sensing in VSNs 83
Require: Initialize ak[n] = 0,∀k, n, Sj0 = {φ}, T j0 = {tj | j ∈ Nj}, Q0 = {φ}1: while T ji 6= {φ} do2: for every Oj do3: Oj requests Uk[n] and bki [n],∀k ∈ Nj4: Activate sensor k, k = arg max
k,nbki [n]
5: k ∈ Nj ,∀j ∈ Ti6: Sji = Sji−1 ∪ {ki}7: Qji = {tj | cji = 1}8: T ji = T ji−1 −Q
ji
9: end for10: end while
Figure 4.12: The DGA algorithm.
superscript j in defining the distributed parameters such as Sji , Qji , and T ji . We apply the distributed
algorithm to the mobile approach since we are interested in comparing it with the stationary approach.
An activated sensor informs its neighbors about its activation by not responding to the new requests of
bki [n] in the next iterations (this can be also done by sending an activation notice to the nodes around
the activated-sensor node). Figure 4.12 describes the steps of the distributed greedy algorithm (DGA).
4.5 Simulation Results
Location of targets is assumed to be known. Then, we solve the ILP problem via the branch and bound
approximation algorithm (BB) [69] and greedy algorithms, CGA and DGA. The benchmark for our
comparison is the N -fold stationary sensing-coverage scheduling of sensors, which can be considered as
an extended version of [25] tailored to our problem. We call it “stationary” approach in our simulations.
In this stationary approach, the scheduling problem is solved at each time instant without taking the
predication of mobility into consideration. In contrast, in the mobile approach, an accurate prediction
of the mobility information is assumed based on the knowledge of mobility model.
4.5.1 Feasibility
We use BB to check the feasibility of the stationary and mobile schedulers based on Theorems 1 and 2.
Figure 4.13 shows the probability of feasibility for both approaches based on Theorem 1 and Theorem
Chapter 4. Gain of Mobility for Sensing in VSNs 84
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
1.2
1.4N=4, M=10, q=1
p
Pro
babili
ty o
f fe
asib
ility
Mobile−Simulation
Stationary−Simulation
Mobile−Analysis
Stationary−Analysis
K=15
K=10
Figure 4.13: The probability of feasibility based on Theorem 1 and Theorem 2 for the mobile scheduler,and stationary one [25].
2. The figure shows that the probability of feasibility of the mobile approach is higher than or at least
equal to that of the stationary one for different number of sensors. It also shows that our analysis and
simulations match. A higher probability of feasibility leads to a lower sensing cost. K = 10 shows a
larger feasibility gap between mobile and stationary approaches since the number of sensors is small,
whereas for K = 20, the number of sensors is large and the feasibility gap is less.
We also plot the feasibility for different values of λ in Figure 4.14. The figure shows that as λ
increases, the feasibility of both the stationary and mobile schedulers increases; however, the feasibility
of the mobile scheduler is always larger than (or equal to) that of the stationary one. This is the gain
in feasibility, which allows the proposed mobile scheduler to actually provide the required coverage and
adapt itself to the communication channel availability changes.
4.5.2 Sensing Cost
We compare the mobile and stationary sensing approaches in terms of normalized sensing cost (i.e. Ks
and Km). That is, for a random U, we solve both the stationary and mobile schedulers using BB
algorithm. In Figure 4.15, we show the sensing cost for different values of the network parameters based
Chapter 4. Gain of Mobility for Sensing in VSNs 85
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1K=10, N=4, M=10, q=2
p
Pro
babili
ty o
f fe
asib
ility
Mobile−λ=1
Stationary−λ=1
Mobile−λ=2
Stationary−λ=2
Mobile−λ=5
Stationary−λ=5
λ=2
λ=1
λ=5
Figure 4.14: The probability of feasibility for the mobile and stationary schedulers for different valuesof λ.
on Theorems 3 and 4. The figure shows that on average the mobile approach results in a smaller number
of active sensors compared to the stationary one while providing the same required coverage quality. This
is one of the strongest motivations of using such a sensing scheme for large scale mobile networks. In the
figure, the mobile approach reduced the number of active sensors by 1 sensor at each time instant for a
small scale network. Moreover, the analysis results follow the simulation results very closely, and we can
see that as the probability of availability increases (i.e. p → 1), the mobile and stationary approaches
activate the same number of sensors as expected (i.e. no mobility gain as stated in Lemma 2). Hence,
the mobile approach is very useful in scenarios with low to medium density of available sensors. This is
due to the fact that dense scenarios do not benefit from mobility prediction.
4.5.3 Approximation Methods
In Figure 4.16, we study the sensing cost of the greedy algorithms. The figure shows that CGA closely ap-
proximates the BB solution. In addition, the distributed algorithm, DGA, at its farthest approximation
to the BB solution outperforms the stationary network BB solution. Hence, both greedy algorithms, es-
pecially the distributed one, can be adopted for practical implementation of the mobile sensing-coverage
Chapter 4. Gain of Mobility for Sensing in VSNs 86
0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 13
4
5
6
7
8
9
10
p
K=10, N=4, M=10, q=4
Km
−Simulation
Ks−Simulation
Km
−Analysis
Ks−Analysis
Figure 4.15: Sensing cost based on Theorem 3 and Theorem 4 for the mobile scheduler, and stationaryone [25].
approach.
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.912
14
16
18
20
22
24
p
Sen
sin
g C
ost
K=10, N=6, M=8, q=2
BB−Mobile Network
CGA−Mobile Network
DGA−Mobile Network
BB−Stationary Network
Figure 4.16: Sensing cost for centralized and distributed greedy algorithms with the BB solution for thestationary approach [25] as the benchmark for comparison.
Chapter 4. Gain of Mobility for Sensing in VSNs 87
Time1 3 7... ... ...
0 10 1 1 1 1 0 0 0
10
u
Coverage area of the sensor
Target to be covered
Figure 4.17: Illustration of temporal dependence in availability for coverage for a sensor-target pair.
4.6 Evaluation of the Mobile Scheduler with a Markovian Mo-
bility Model
4.6.1 Markovian Mobility Model
So far, we have used an independent coverage model in the previous sections. In this section, we
consider a different coverage model, where we consider temporal dependence in coverage. Consider a
vehicle equipped with a sensor moving along the road. The goal is to cover a target on one side of
the road as shown in Figure 4.17. At time n = 1, the target might be in the vicinity of the sensor
(i.e. ukj [1] = 1) or not (i.e. ukj [1] = 0). Beyond time n = 1, the availability of the sensor to cover
that target depends on the availability in the past, sensing range and the speed of the vehicle. Hence,
temporal dependence in availability for coverage represents a realistic case for coverage in a vehicular
sensor network.
To capture the sensor-target location dependence in coverage, we use the following Phase-type dis-
tribution, with three transient states and an absorbing one. This model is represented by the Markov
chain (MC) in Figure 4.18. πs (similarly 1 − πs) are the initial transition probabilities. States 0 and 1
represents absence and availability of a sensor to cover a target, respectively. π0 (π1) is the transition
probability of continuing not to cover (cover) a target. State A is the state when the vehicle passes the
target and will not cover it in the future.
Markovian coverage is suitable for modeling vehicular sensor coverage. In fact, the parameters πs, π0
and π1 should be related to the speed and location of the vehicle, the location of target, and the sensing
Chapter 4. Gain of Mobility for Sensing in VSNs 88
0
Sstart
1 A
πs
1− πs
1− π1
π1
1− π0
π0 1
Figure 4.18: Markov chain for sensor-target coverage model.
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 14
4.5
5
5.5
6
6.5
7
π1
Num
ber
of
sele
cted
sen
sors
π0=0.6, K=10, M=3, N=4, q=1
BB−Mobile Network
BB−Stationary Network
Figure 4.19: Sensing cost for the mobile and stationary schedulers using the Markovian mobility model.
range of the sensor.
4.6.2 Simulation Results
We simulated the stationary and mobile schedulers using the Markovian mobility model, and we plot the
sensing cost in Figure 4.19. Figure 4.19 shows that as the probability of a staying at covering state, π1
decreases (i.e. 1 in U), the mobile scheduler results in a smaller sensing cost compared to the stationary
scheduler. The figure shows that our approach can work with different mobility models.
Chapter 4. Gain of Mobility for Sensing in VSNs 89
4.7 Summary
This chapter studies the problem of scheduling sensors for coverage in VSNs. The goal is to provide
the required quality of coverage with the minimum number of sensors to cope with the limitation of
channel capacity and voucher constraints in the communications. First, we formulated the stationary
sensing-coverage problem. Then, we extended the formulation to the mobile sensing-coverage network
and included the predicted mobility information of mobile nodes in the scheduling of sensors. Sensing is
performed via an N -fold stationary approach, and a mobile one using the predicted mobility information.
Using an independent mobility model, we analyzed both N -fold stationary and mobile schedulers in
terms of sensing cost, and probability of feasibility. Closed form expressions for minimum sensing cost,
average sensing cost, and probability of feasibility are found. Extensive simulations of the proposed
mobile sensing-coverage approach demonstrated the benefits of utilizing mobility information in sensing.
Simulations results matched our analysis, and they showed that the mobile approach outperforms the
stationary network in terms of average sensing cost and probability of feasibility. We also proposed
a centralized greedy algorithm to approximate the optimal method (branch and bound) very well and
extended it to a distributed version. Finally, we studied the problem in the context of participatory
sensing VSNs. Simulations showed that the proposed mobile sensing approach provides a smaller sensing
cost compared to the stationary one as the mobility parameters increase. Hence, mobility helps when
the mobility model is random, Markovian or a car following vehicular mobility model
Chapter 5
Noisy Mobility Impact on Sensing
In Chapter 4, we discussed the mobile sensing scheduler that demonstrated better performance than the
stationary scheduler. In this Chapter, we further investigate the mobile scheduler. Specifically, we want
to answer this question, what is the level of uncertainty for which the mobility information does not
enhance sensing in mobile sensor networks due to noise in prediction.
First, we study the performance of the mobile scheduler by understanding the mobility gain in sensing
over the stationary scheduler at a microscopic level. Then, we analyze the performance of a noisy version
of the mobile scheduler. The results of this Chapter are published in the IEEE Vehicular Technology
Conference [28].
The organization of this chapter is as follows. First, we discuss the mobile scheduler activation
procedure at a microscopic level in Section 5.1. After that, we define the uncertainty model in the
mobility information in Section 5.2.2, and study its impact on the sensing cost of the mobile sensing
scheduler in Section 5.2. Section 5.4 summarizes this Chapter.
5.1 Dissection of the Mobile Scheduler
Now we have established an understanding on the gain of mobility for coverage in terms of feasibility
and sensing cost in Chapter 4, we will try to investigate the performance of the mobile scheduler at a
microscopic level in order to find other advantages of the mobile scheduler over that of the stationary
90
Chapter 5. Noisy Mobility Impact on Sensing 91
one. The results of the previous Chapter 4 were on the average sensing cost and average feasibility of
the scheduler. In the sequel, we study of the mobile scheduler at the sensor level, which we refer to as
the microscopic level. This level of study shows the gain in terms of each sensor activity in the network.
The objective of this study is to better understand the mobile scheduler performance with noisy mobility
information. Throughout this chapter, we consider noise-free stationary and mobile schedulers.
5.1.1 Better Sensing Cost
Consider a network where the number of sensors K = 3, the number of targets M = 2, the probability
of availability p = 0.4, and the system time N = 4. Moreover, we want each target to be covered
q = 1 time. We solve the mobile and stationary schedulers for the network via the Branch and Bound
algorithm, and we plot the dissection of the results on Figures 5.1 (a) and (b). First, let us look at the
checkerboards as blackbox objects. Figure 5.1 (a) is divided into three columns that represent (from
left) the mobility matrix U, the coverage based on the stationary scheduler, and the coverage based
on the mobile scheduler. The figure also divided into four rows, which represents the information over
different epochs of time. Then, each of the checkerboard consists of K rows and M columns. Within a
checkerboard, rows represent sensors, and columns represent targets.
For the first column of checkerboards (i.e., to the left), the white colour indicates sensor availability
for covering target (i.e. 1 in the mobility matrix), and the black colour indicates the sensor unavailability
for coverage. For the other two columns of checkerboards, each white square indicates a covered target
due to an activated sensor (i.e. akj [n] = 1). That is, each checkerboard illustrates the projection of
sensors activation on the coverage of targets. The black colour indicates the inactivity of a sensor,
whereas the grey colour indicates the inactivity of all sensors at that time instant.
From Figure 5.1 (a), it can be seen in the third column that the mobile scheduler did not activate
any sensor during time n = 3. In fact, the mobile scheduler utilized the predicted mobility information
at time n = 3, whereas the stationary scheduler activated two sensors at time n = 3 due to the lack of
predicted mobility information of time n = 4. That follows our intuition where the stationary scheduler
deals with each time instant as an independent problem, whereas the mobile scheduler benefits from
Chapter 5. Noisy Mobility Impact on Sensing 92
(a)
(b)
Figure 5.1: Microscopic view of the stationary and mobile schedulers results. Mobile scheduler showsbetter sensing cost compared to the stationary one. K = 3, M = 2, N = 4, and q = 1.
combining different stationary availability into a single mobile problem (i.e. the mobile scheduler utilized
the predicted mobility information at n = 4).
Let us focus on the third column and third row. The mobile scheduler did not activate any sensor
within that time instant, whereas the stationary one activated two sensors and provided two coverage
instants to two targets. What if at time instant was n = 4, the mobile scheduler did not activate any
sensors? The mobile scheduler would have completed all the coverage requirements in the third time
instant. In fact, in this case the mobile scheduler actually would minimize the sensing cost and provide
Chapter 5. Noisy Mobility Impact on Sensing 93
the coverage within a shorter time compared to the stationary scheduler. In Figure 5.1 (b), we can see
the activity of the sensors via the stationary (top) and mobile (bottom) scheduling. The Figure shows
clearly that the mobile scheduler activated less sensors. Cs(U) and Cm(U) are the sensing costs for the
stationary and mobile scheduler over N time instants. For the above case, Cs(U) > Cm(u).
5.1.2 Better Coverage Delay
For the same network parameters, another run of scheduling results in the inactivation of all sensors at
the fourth time instant n = 4 = N for the mobile scheduler, as shown in Figure 5.2 (a). The mobile
scheduler actually provides all the required coverage of targets within three time instants (i.e. faster
than the stationary scheduler). However Figure 5.2 (b) shows that both schedulers provided the same
sensing costs (i.e. Cs(U) = Cm(u)). That is, the gain in this case is in terms of delay in providing
coverage, which is important in delay-sensitive coverage applications.
5.1.3 Better Coverage Delay and Sensing Cost
Figure 5.3 shows a case where the mobile scheduler actually outperforms the stationary one in terms of
sensing cost as well as the delay of providing coverage of targets.
We set the parameter K = 6, while all other network parameters are the same and q = 1. Figure 5.4
shows that the mobile scheduler provides a smaller sensing cost by utilizing the first two time instances.
That is, the mobile scheduler utilized all possible coverage possibilities and in this case the optimal
solution is obtained within a smaller time than that of the stationary scheduler.
We increase the coverage requirements to q = 2, and plot the microscopic view of the sensor activities
in Figure 5.5. The mobile scheduler provides better sensing cost compared to the the stationary one. It
again provides the coverage requirement faster than the stationary scheduler. The main conclusion here
is that there exists a gain in target coverage for different combinations of network parameters.
Chapter 5. Noisy Mobility Impact on Sensing 94
(a)
(b)
Figure 5.2: Microscopic view of the stationary and mobile schedulers results. Mobile scheduler showsfaster coverage of targets compared to the stationary one. K = 3, M = 2, N = 4, and q = 1.
5.2 Analytical Study of Noise Impact on Sensing Cost
In this section, we study the noise in mobility information impact on the mobile scheduler and compare
it to the noise-free stationary scheduler.
Chapter 5. Noisy Mobility Impact on Sensing 95
Figure 5.3: Microscopic view of the stationary and mobile schedulers results. Mobile scheduler showsbetter sensing cost and faster coverage of targets compared to the stationary one. K = 3, M = 2, N = 4,and q = 1.
Figure 5.4: Microscopic view of the stationary and mobile schedulers results. Mobile scheduler showsbetter sensing cost and faster coverage of targets compared to the stationary one. K = 6, M = 3, N = 4,and q = 1.
Chapter 5. Noisy Mobility Impact on Sensing 96
Figure 5.5: Microscopic view of the stationary and mobile schedulers results. Mobile scheduler showsbetter sensing cost and faster coverage of targets compared to the stationary one. K = 6, M = 3, N = 4,and q = 2.
5.2.1 Sensing Cost Analysis
To quantify the mobility gain in sensing we follow the same approach as in Chapter 4. That is, we find
the number of activated sensors by studying the random availability of sensors at the coverage quality
constraints. Based on Chapter 4, the effective number of activated sensors (i.e. sensing cost) 1 can be
very closely approximated by
Ks ≈q
p+εs√
(1− p)q√Mp
, (5.1)
Km ≈q
p+εm√
(1− p)q√NMp
, (5.2)
for the noise-free stationary and mobile schedulers, respectively, where εs = Q−1 (δs), εm = Q−1 (δm),
δs and δm are thresholds that are very close to 1.
1The effective number of activated sensors is the actual number of activated sensors divided by the system time, N .
Chapter 5. Noisy Mobility Impact on Sensing 97
5.2.2 Noise in Coverage Models
Coverage information could be noisy. We assume each sensor-target coverage information is indepen-
dently corrupted with noise. That is, a sensor coverage information might be noisy while another sensor
information is not.
Mask Noise
Define β as the probability that mobility information (i.e. ukj [n]) is not correctly known. This probability
determines whether noise exists or not at each element of U. Let ε[n] be the noise matrix and
P (εkj [n] = 0) = 1− P (εkj [n] = 1) = β.
For the first type of noise, noise contaminates the mobility information by masking each sensor availability
with probability β as
ukj [n] = ukj [n]� εkj [n],
where ukj [n] is the noisy mobility information, and � denotes binary multiplication. This type of
noise (i.e. mask noise) falsely removes some available sensors from the scheduling problem, and hence
decreases the mobility information gain in sensing. Here, mobility information is masked and there is no
false coverage of targets. We refer to this type of noise as mask error. Mask error revokes the privileges
of knowing sensors availability, and hence, restricts the mobile sensing approach from its future mobility
knowledge.
5.2.3 Interpretation of the Noise Model
The noise model proposed here is selected because it has an interpretation in mobile networks. The mask
noise model is chosen to represent the limitations in the communication channel in reception of mobility
information. In mobile networks, there is uncertainty in receiving information over the communication
channel. Hence, this uncertainty in the reception of the mobility information contained in the matrix
U would occur in such networks. Therefore, we introduced this uncertainty in a parameter β that we
Chapter 5. Noisy Mobility Impact on Sensing 98
would explain later that would affect the reception of U. We chose the uncertainty to reflect the number
of vehicles that we receive information from due to the limitation of the communication channel. That
is, out of K sensors at time n, we receive the mobility information of at most K depending on the
uncertainty parameter β Therefore, some of the information will be missing or masked; hence the name
mask noise.
5.2.4 Mask Noise Impact on Sensing Cost
A highly masked U has a smaller number of available sensors. That is reflected in the effective number
of active sensors in the analysis. Denote the effective number of active sensors in the noisy case of the
mobile scheduler by KNm . The probability of availability is reduced from p to
pNm = p(1− β).
Accordingly, the effective number of active sensors can be approximated based on (5.2) as
KNm ≈q
p(1− β)+εm√
(1− p(1− β))q√NMp(1− β)
. (5.3)
Mobile Scheduler Breaking Point with Mask Noise
The noise-free mobile scheduler normally outperforms the stationary scheduler for p < 1. However, as
noise increases, the sensing cost of the mobile scheduler becomes closer to the stationery one until they
become equal. Therefore, we define the breaking point of the mobile scheduler as follows.
Definition 1. Mobile Scheduler Breaking Point. For a stationary schooled with noise-free mobility
information, the mobile scheduler contaminated with mask noise breaking point is at β that makes the
following equation holds KNm = Ks.
Based on the above definition, we study the difference between the two quantities KNm and Ks, which
Chapter 5. Noisy Mobility Impact on Sensing 99
is
Ks −KNm =q
p− q
p(1− β)(5.4)
+εs√
(1− p)q√Mp
−εm√
(1− p(1− β))q√NMp(1− β)
= f(β)
(5.4) shows that for β = 0 there is a mobility gain in sensing which is equal to
f(β = 0) = Ks −KNm = Ks −Km (5.5)
≈√q(1− p)√Mp
(εs −
εm√N
)=
√q(1− p)√Mp
εs
(1− 1√
N
Q−1 (δm)
Q−1 (δs)
),
whereas for β > 0, the mobility gain is reduced due to β being in the denominators of the negative terms
of (5.4).
Proposition 1. Breaking Point of the Mobile Scheduler with a Mask Noise: The breaking
point of the mobile scheduler with a mask noise β∗ is at
β∗ =(x∗)2 + p− 1
p,
where x∗ is a constant, and p is the probability of availability in the independent coverage model.
Proof. For f(β) = Ks −KNm , the breaking point is at f(β) = 0. Therefore, we set f(β) = 0, and solve
for the β∗. Let x =√
1− p(1− β). Then, we need to solve the following equation for x∗, and then find
β∗
−x2√qNM
(√q + εs
√1− pM
)− xpεm
√q + q
√NM
(1− p+ εs
√1− pqM
)= 0, (5.6)
where β at the root corresponds to the breaking point of the mobile scheduler. After finding x∗, The
Chapter 5. Noisy Mobility Impact on Sensing 100
breaking point becomes
β∗ =(x∗)2 + p− 1
p.
5.3 Numerical Results
The ILP optimization problems are solved via the Branch and Bound algorithm. We run each scenario
several times, and show the average results. We find the mobile scheduler breaking point via exhaustive
search and by finding the roots of (5.6). We compare the normalized cost which is the total cost over the
system time divided by N , or Ks, Km, and KNm for the stationary, noise-free mobile, and noisy mobile
schedulers, respectively. We study the three schedulers for different value of β and p, and we find the
mobile scheduler breaking points β∗.
We plot the noisy and noise-free normalized sensing costs versus p for the mobile scheduler in Figure
5.6. The figure shows that simulations closely match our analysis. It also shows that as noise increases,
the mobile scheduler normalized cost increases. That is, the utilization of mobility information decreases.
Therefore, we should check how much noise affects sensing and compare it to the stationary scheduler.
Figure 5.7 shows the noise impact on the mobile scheduler versus the probability of availability β
via simulation and analysis. We can see for β ≤ 0.36, the mobile scheduler outperforms the stationary
one. However, at β = 0.36, both mobile and stationary schedulers provide the same number of activated
sensors. The breaking point at this figure is β∗ = 0.36, where increasing β will increase the sensing
cost of the mobile scheduler and the stationary one outperforms it. We show the figure for β = [0, 0.5]
because for β > 0.5 the feasibility of solving the problem becomes very small due to the smaller number
of available sensors for coverage. The figure shows simulations matches analysis very closely.
Figure 5.8 shows the breaking point for the different network parameters versus p. We fix two
parameters and change one to study its impact on the braking point. We can see that as M changes
from 4 to 8, the mobile scheduler breaks at a smaller β. This is due to the fact that the mobile scheduler
needs more available sensors to satisfy the larger number of targets (similarly larger coverage quality).
Chapter 5. Noisy Mobility Impact on Sensing 101
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10
0.5
1
1.5
2
2.5
3
3.5
4
p
Kx
M=5, N=4, q=2
Km
, β=0−Analysis
Km
, β=0−Simulation
Km
N, β=0.2−Analysis
Km
N, β=0.2−Simulation
Km
N, β=0.3−Analysis
Km
N, β=0.3−Simulation
Figure 5.6: The effective sensing cost versus p.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.51
1.5
2
2.5
3
3.5
4
β
Kx
M=5, N=4, q=2, p=0.8
Ks−Analysis
Km
−Analysis
Km
N−Analysis
Km
N−Simulation
Figure 5.7: The effective sensing cost for the stationary and the mobile schedulers with noise-free mobilityinformation, and the mobile scheduler with noisy mobility information versus β. Breaking point is atβ = 0.36.
After that, we change N from 2 to 6 and the breaking point gets smaller, but with a lower gap. That
means that the impact of the system time (N) is not as significant as the number of targets (M). Similar
observation is seen for changing the required coverage (q) from 2 to 4, but with a significant gap. That
Chapter 5. Noisy Mobility Impact on Sensing 102
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
β*
M=4, N=2, q=2−Analysis
M=4, N=2, q=2−Simulation
M=8, N=2, q=2−Analysis
M=8, N=2, q=2−Simulation
M=8, N=6, q=2−Analysis
M=8, N=6, q=2−Simulation
M=8, N=6, q=4−Analysis
M=8, N=6, q=4−Simulation
Figure 5.8: The breaking point of the mobile scheduler β∗ for different values of M , N and q versus p.
is, β is more susceptible to M and q than to N .
5.4 Summary
This chapter studied the impact of noisy mobility information on sensing in vehicular sensor networks.
We studied the microscopic performance of the mobile scheduler that utilizes predicted mobility infor-
mation, and compared it to the stationary scheduler. We found by our microscopic analysis that the
mobile scheduler not only outperforms the stationary scheduler in terms of sensing cost, but also it terms
of delay of covering targets.
After that, we proposed a noise model that affects the exchange of predicted mobility information.
That is, the mask noise represents channel in wireless communication channel. We analyzed the sens-
ing cost of the mobile scheduler under noisy mobility information, and compared it to the stationary
scheduler with noise-free mobility information. We found the breaking point of the mobile scheduler,
which indicates the usefulness of the mobile scheduler under utilization of noisy mobility information up
to the breaking point. We performed simulations and showed that they closely match our analysis. In
conclusion, the mobile scheduler can tolerate noisy mobility information and outperform the stationary
Chapter 5. Noisy Mobility Impact on Sensing 103
networks up to a certain threshold, which is called the breaking point of the mobile scheduler. When-
ever prediction of mobility information is below the breaking point, the mobile scheduler provides better
sensing cost compared to the stationary scheduler.
Chapter 6
Conclusions and Future Works
This thesis examined communications and sensing in mobile sensor networks. We showed that location
awareness communications can be enhanced by exploiting the sparsity of exchanged information. In
addition, we showed that predicted mobility information can significantly enhance sensing (i.e., coverage
of targets) in vehicular sensor networks.
Although this thesis addresses each subject separately, the proposed enhancement approaches for
communications and sensing can be integrated into a single system that performs both functionalities—
in fact, this is the case in VSNs. For example, in VSNs, vehicles will be communicating for safety
applications, and they are equipped with sensors at the same time to sense the environment and trans-
mit sensed data. This thesis proposed specific approaches for addressing the problems, yet there are
other methodologies that may obtain similar results. In this chapter, we focus on discussing the main
contributions and methodologies used in this thesis, the main results achieved, the impact of the achieved
results, the limitations of the used schemes, and possible directions for future research.
6.1 Gain of Mobility for Communication in VSNs
The location of a vehicle is crucial information for supporting safety applications on the roads, main-
taining information of the network topology, and estimating the traffic information on maps. This thesis
contributed a novel method of location broadcast in vehicular networks where vehicles do not have to
104
Chapter 6. Conclusions and Future Works 105
transmit location packets at the maximum rate of 100ms; instead, a few encoded packets can be trans-
mitted at random times. The transmission scheme is simple and relieves the communication channel
from unnecessary congestion. Receivers can then estimate the velocity information of the source by
solving a compressive sensing estimation problem.
We have shown in Chapter 3 that compressive sensing information exchange can significantly reduce
the amount of data transmitted to make every node aware of the location of other nodes in the network.
Results were validated by real experiments using data collected from highways and city streets. The
outcome of this experiment can be generalized for different ITS applications, where the complete map
of traffic can be dealt with as sparse information. Compressive sensing would enable the construction of
the complete picture of the data with fewer transmissions.
There are two main concerns regarding the proposed approach. First, the number of packets trans-
mitted must satisfy the RIP condition. Satisfying the RIP condition guarantees the prefect recovery
using compressive sensing. Moreover, satisfying the RIP condition guarantees a small estimation error
using the proposed streaming information exchange scheme. Otherwise, using a number of measure-
ments below the RIP condition would results in a significant estimation error. Second, for the sliding
window scheme, we concluded that the measurements should be overlapped to perform good estimation
of the velocity vector. In the case of no overlap, the proposed sliding window scheme is not guaranteed
to perform an estimation of the velocity vector, and the estimation error might be large. We have shown
that the SWE algorithm enhances the accuracy of the edge of the velocity vector as the sliding window
shifts. It is possible for each vehicle to improve the accuracy as the sliding window shifts and records
the best estimate.
Finally, the proposed CS scheme is scalable. This is due to the fact that it reduces the number
of transmitted packets over the channel. Moreover, a VSN transmits packets over a short-range of
communication. Having said that, the more the number of vehicles on the road, the more the segments
of short-range communication zones exist. Therefore, each zone can apply the CS scheme without a
scalability issue.
Chapter 6. Conclusions and Future Works 106
6.2 Gain of Mobility for Sensing in VSNs
Sensing data might interfere with high-priority data. In Chapter 4, we demonstrated how this data
can be minimized in order to relieve the channel from unnecessary load. Predictable mobility informa-
tion was used in the scheduling process of sensors that are covering targets. Mobility information is
predictable with acceptable accuracy, and target coverage is an important problem in surveillance. We
incorporated predicted mobility information in the activation process of sensors and showed that the
number of activated sensors is reduced compared to the stationary scheduling model, which does not
utilize predicted mobility information. The proposed model was studied with a random independent
mobility model, the Markovian mobility model, and a realistic mobility model that represents the vehi-
cles moving on a highway. The results of this research can be used to efficiently reduce the redundancy
in coverage of real-time events, improve surveillance of the vehicular environments, and enhance traffic
safety by exchanging the messages between vehicles.
We noticed that predicted mobility information might be noisy. In this case, the mobile scheduler
indeed might not be performing as required. The scheduling outcome of the mobile scheduler depends on
the type of noise in the predicted mobility information. We have studied a noise model in Chapter 5, and
showed that the mobile scheduler actually results in a smaller number of activated sensors compared to
the stationary scheduler, until the noise level exceeds a certain level. At this level, the mobile scheduler
reaches a breaking point and it no longer results in a smaller number of activated sensors compared to
the stationary scheduler. Chapter 5 demonstrated that the mobile scheduler outperforms the stationary
scheduler when the noise level in the mobility information is acceptable.
A remark on the mobile scheduler: it does not guarantee coverage at each time instant; rather, it
guarantees coverage of targets at the total time interval. Therefore, if coverage is intended over each
time instant, then the stationary scheduler should serve the purpose. The mobile scheduler searches for
optimality in sensor activation by observing the availability of sensors to cover targets over an interval
of time. Such a limitation depends on the application requirements of coverage.
Finally, the mobile scheduler is scalable in a centralized and distributed fashions. In the centralized
version, this is due to the fact that the fusion centre is considered a powerful centre of computation.
Chapter 6. Conclusions and Future Works 107
Therefore, it can solve the mobile scheduling problem for a large number of vehicles. In the distributed
fashion, the DGA (i.e. distributed greedy) algorithm can be solved at each vehicle. And, each vehicle
has the mobility information of a limited number of neighbours within its short-range of communication.
Therefore, the mobile scholar is scalable.
6.3 Application to Future Cars
This thesis discussed the sensing and communication aspects of a VSN as it is described by the available
standards. However, the contributions of this thesis can be applied to future cars as well. For example,
autonomous cars, such as Google car, are considered a potential platform for the research contributions of
this thesis. Consider a network of Google cars. This group of vehicles must communicate their mobility
information for safety. Hence, a broadcast scheme that guarantees the reception of safety messages is
desired for such a system. Moreover, Google cars are equipped with a significant number of sensors that
are collecting a significant volume of data. It is obvious that some of these data should be communicated
to a fusion centre. This can be performed by transferring all the information that are collected by
each vehicle sensors. This can be successful only with an ideal communication channel. However,
the vehicular communication channel capacity is limited as we discussed in the thesis. Therefore, a
scheduler for selecting the transmitted collected data is required. This scheduler should capture the
minimum required sensors data that can be accommodated by the available communication channel.
Finally, prediction of mobility information would be excellent for autonomous cars due to the excellent
a prior knowledge of mobility ahead of time.
6.4 Future Works
The work presented in this thesis can serve in different applications, and can be extended in different
directions. In this section, we discuss possible future research directions from the contributions of this
thesis.
Chapter 6. Conclusions and Future Works 108
6.4.1 Integration with a Distributed Congestion Controller
The proposed solution to the congestion control problem in Chapter 3 is studied thoroughly by sim-
ulations and experiments. Integrating of the proposed solution solution with a distributed congestion
controller for vehicular networks would demonstrate how the controller reacts to the channel congestion
and adjusts the compressive sensing broadcast scheme transmission parameters. Such a study would
show the realistic changes in packet transmission and drop rates, the delay of packet reception, and the
accuracy of compressive sensing estimation.
6.4.2 Impact of the CS-based Congestion Controller on Safety Metrics
Reducing the congestion on the communication channel and delivering more safety packets are crucial for
vehicular networks. The reason is that vehicles become more alert of the fast changes in the environment.
The CS-based scheme proposed in Chapter 3 shows the estimation of the velocity trajectory using a small
number of packets, with a trade-off between the number of exchanged packets and the accuracy. A third
metric that could be taken into consideration is a safety metric. One possible metric is the awareness
range of the network. It would be interesting to study the impact of the CS-based scheme on the
awareness range of the vehicular network.
6.4.3 Distributed Compressive Sensing Location Awareness
The recovery in the compressive sensing broadcast scheme in Chapter 3 is performed disjointly. That
is, a receiver reconstructs the original velocity vector of its neighbour vehicle by the packets received
from that neighbour only. Joint recovery of correlated samples is shown to require a fewer number of
samples compared to the disjoint recovery [38, 39]. Using distributed compressive sensing would results
in a different accuracy of estimation, and a different number of measurements that would satisfy the
RIP condition.
Chapter 6. Conclusions and Future Works 109
6.4.4 Applications of Location Awareness in Heterogenous Networks
We have studied the location awareness problem in the context of vehicular networks. The same concept
can be applied to different future networks. An example is an MVN that would include vehicles, pedestri-
ans, cyclists, smart stationary sensors, and so forth. For such a network, location awareness is necessary,
and the amount of data exchanged could be significantly large, but the applications are different from
the vehicular networks. The applications in such a network would have different QoS requirements in
terms of delay and transmission frequency requirements. Extending the location awareness scheme in
Chapter 3 to work in such a network would require a different design of the transmission and recovery
schemes.
6.4.5 Time-to-Space Conversion of the Mobile Scheduler
The mobile scheduler demonstrated superior performance in reducing the number of active sensors
compared to the stationary scheduler (discussed in chapters 4 and 5). There is an interesting fact that
in the problem setting, both stationary and mobile schedulers share the space-time information, but the
mobile scheduler utilizes the predicted space-time information ahead of time via prediction. It would
be interesting to use the same concepts of mobility gain when the sensor nodes are stationary and the
operation pattern of these sensors is predictable. That is, a stationary scheduler in this case would not
utilize the patterns of sensing for other sensors, while the mobile scheduler would use that information
in scheduling the sensors.
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