gains of mobility for communication and sensing …...gains of mobility for communication and...

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

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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

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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.

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Dedication

This thesis is dedicated to the person who changed my perspective of the world—my daughter, Leen!

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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.

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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

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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

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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

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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

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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

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3.9 Average and maximum errors in velocity estimation using the CS scheme and interpolation

versus α for the city data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47


versus α for the highway data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47


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


faster coverage of targets compared to the stationary one. K = 3, M = 2, N = 4, and

q = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94


better sensing cost and faster coverage of targets compared to the stationary one. K = 3,

M = 2, N = 4, and q = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95



M = 3, N = 4, and q = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

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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.


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


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,


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.


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


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.


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.


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


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)


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


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.


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


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


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.


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 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.


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


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


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.


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]


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]


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


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


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].


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.


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.


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,


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.


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,


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.


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


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


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.


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

.


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,


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


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.


−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


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.


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.


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


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.


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.


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.


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.


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.


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


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


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


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


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


Figure 3.14: Estimation errors for a fixed R versus L.

estimation up to 1m accuracy.


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


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


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


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


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


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


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


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.


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.


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


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


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


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.


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


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.


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.


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


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


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),


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).


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)


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).


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


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.


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


(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.


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)


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.


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


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)


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


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]


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


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).


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.


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


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


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


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.


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


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.


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


(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


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.


(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.


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.




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 .


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


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


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


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).


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


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







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


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.


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.


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.


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.


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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