Optimal Networking in Wirelessly Powered Sensor Networks

Optimal Networking in Wirelessly Powered Sensor Networks

RONG DU

Doctoral Thesis

Stockholm, Sweden 2018

TRITA-EECS-AVL-2018:64 ISSN 1653-5146

ISBN 978-91-7729-934-9

KTH Royal Institute of Technology School of EECS SE-100 44 Stockholm SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska h¨ogskolan framl¨agges till offentlig granskning f¨or avl¨aggande av teknologie doktorsexamen i n¨atverk och systemteknik den 19 oktober, 2018 klockan 10:15 i sal D3, KTH Campus, Lindstedtsv¨agen 5, Stockholm.

© 2018 Rong Du, unless otherwise stated.

Tryck: Universitetsservice US AB

Abstract

Wireless sensor networks (WSNs) are nowadays widely used for the long- term monitoring of small or large regions, such as lakes, forests, cities, and industrial areas. The performance of a WSN typically consists of two aspects: i) the monitoring performance, e.g., the accuracy and the timeliness of the measurements or estimations produced by the sensor nodes of the WSN; and ii) the lifetime, i.e., how long the WSN can sustain such a performance. Naturally, we would like to have the monitoring performance as good as possible, and the lifetime as long as possible. However, in traditional WSNs, the sensor nodes generally have limited resources, especially in terms of battery capacity. If the nodes make measurements and report them frequently for a good monitoring performance, they drain their batteries and this leads to a severely shortened network lifetime. Conversely, the sensors can have a longer lifetime by sacrificing the monitoring performance. It shows the inherent trade-off between the monitoring performance and the lifetime in WSNs.

We can overcome the limitations of the trade-off described above by wireless energy transfer (WET), where we can provide the sensor nodes with additional energy remotely. The WSNs with WET are called wirelessly powered sensor networks (WPSNs). In a WPSN, dedicated energy sources, e.g., static base stations or mobile chargers, transmit energy via radio frequency (RF) waves to the sensor nodes. The nodes can store the energy in their rechargeable batteries and use it later when it is needed. In so doing, they can use more energy to perform the sensing tasks. Thus, WET is a solution to improve the monitoring performance and lifetime at the same time. As long as the nodes receive more energy than they consume, it is possible that the WSN be immortal, which is impossible in traditional WSNs.

Although WPSNs can potentially break the trade-off between monitoring per- formance and lifetime, they also bring many fundamental design and performance analysis challenges. Due to the safety issues, the power that the dedicated energy sources can use is limited. The propagation of the RF waves suffers high path losses. Therefore, the energy received by the sensor nodes is much less than the energy transmitted from the sources. As a result, to have a good WSN performance, we should optimize the energy transmission on the energy source side and the energy consumption on the nodes side. Compared to the traditional WSN scenarios where we can only optimize the sensing and data communication strategies, in WPSNs, we have an additional degree of freedom, i.e., the optimization of the energy transmission strategies. This aspect brings new technical challenges and problems that have not been studied in the traditional WSNs. Several novel research questions arise, such as when and how to transmit the energy, and which energy source should transmit. Such questions are not trivial especially when we jointly consider the energy consumption part.

This thesis contributes to answer the questions above. It consists of three

contributions as follows.

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In the first contribution, we consider a WPSN with single energy base stations (eBS) and multiple sensor nodes to monitor several separated areas of interest. The eBS has multiple antennas, and it uses energy beamforming to transmit energy to the nodes. Notice that, if we deploy multiple sensor nodes at the same area, these nodes may receive the energy from the eBS at the same time and they can reduce the energy consumption by applying sleep/awake mechanism. Therefore, we jointly study the deployment of the nodes, the energy transmission of the eBS, and the node activation. The problem is an integer optimization, and we decouple the problem into a node deployment problem and a scheduling problem. We provide a greedy-based algorithm to solve the problem, and show its performance in terms of optimality.

The second contribution of the thesis starts by noticing that wireless channel state information (CSI) is important for energy beamforming. The more energy that an eBS spends in channel acquisition, the more accurate CSI it will have, thus improving the energy beamforming performance. However, if the eBS spends too much energy on channel acquisition, it will have less energy for WET, which might reduce the energy that is received by the sensor nodes. We thus investigate how much energy the eBS should spend in channel acquisition, i.e., we study the power allocation problem in channel acquisition and energy beamforming for WPSNs.

We consider the general optimal channel acquisition and show that the problem is non-convex. Based on the idea of bisection search, we provide an algorithm to find the optimal solution for the single eBS cases, and a closed-form solution for the case where the eBS uses orthogonal pilot transmission, least-square channel estimation, and maximum ratio transmission for WET. The simulations show that the algorithm converges fast, and the performance is close to the theoretical upper bound.

In the third contribution, we consider a joint energy beamforming and data routing problem for WPSNs. More specifically, we investigate the WPSNs consisting of multiple eBSs, multiple sensor nodes, and a sink node. Based on the received energy, the sensor nodes need to decide how to route their data. The problem aims at maximizing the minimum sensing rate of the sensor nodes while guaranteeing that the received energy of each node is no less than that is consumed. Such a problem is non-convex, and we provide a centralized solution algorithm based on a semi-definite programming transformation. We extend this approach with a distributed algorithm using alternating direction method of multipliers (ADMM).

We prove that the centralized algorithm achieves the optimal energy beamforming and routing, and we show by simulation that the distributed one converges to the optimal solution. Additionally, for the cases where the energy beamforming options are pre-determined, we study the problem of finding the energy that should be spent on each vector. We observe that, if the pre-determined beamforming options are chosen wisely, their performance is close to the optimal.

The results of the thesis show that WET can prolong the lifetime of WSNs, and even make them work sufficiently long for general monitoring applications.

More importantly, we should optimize the WPSN by considering both the energy

v

provision and the energy consumption part. The studies of the thesis have the potential to be used in many Internet of Things (IoT) systems in smart cities, such as water distribution lines and building monitoring.

Keywords : Wireless energy transfer, network lifetime, energy beamforming,

IoT, smart cities, sensor networks, scheduling, optimization

Sammanfattning

Trådl¨osa sensorn¨atverk (TSN) anv¨ands i stor utstr¨ackning f¨or långtids¨over- vakning av små och stora regioner, såsom sj¨oar, skogar, st¨ader och industriella anl¨aggningar. Prestandan hos ett TSN m¨ats huvudsakligen via två aspekter: i) dess

¨overvakningsprestanda, d.v.s. hur noggranna dess m¨atningar och de skattningar dess sensornoder producerar ¨ar; samt, ii) dess livsl¨angd, d.v.s. hur l¨ange n¨atverket kan bibehålla funktionsduglighet. Det ¨ar naturligtvis ¨onskv¨art att ha så h¨og

¨overvakningsprestanda samt så lång livsl¨angd som m¨ojligt. Dessa två mål ¨ar dock motstridiga i traditionella TSN eftersom sensornoderna har begr¨ansade resurser, speciellt i termer av batterikapacitet. Om noderna kontinuerligt anv¨ander sina sensorer och rapporterar m¨atningarna, f¨or att uppnå en h¨og ¨overvakningsprestanda, så dr¨aneras snabbt deras batterier och n¨atverkets livstid kommer drastiskt att reduceras. Omv¨ant så kan en lång livstid uppnås på bekostnad av n¨atverkets

¨overvakningsprestanda, om endast sporadiska m¨atningar g¨ors. Detta påvisar den naturliga avv¨agningen mellan ¨overvakningsprestanda och livsl¨angd som måste g¨oras i TSN.

Det ¨ar m¨ojligt att kringgå denna avv¨agning genom att anv¨anda trådl¨os energi¨overf¨oring (TE ¨O) till sensornoderna. TSN med TE ¨O kallas trådl¨ost drivna sensorn¨atverk (TDSN). I ett TDSN f¨orser externa energik¨allor (t.ex. statiska basstationer och/eller mobila laddare) sensornoderna med energi trådl¨ost via radiovågor. Noderna kan lagra denna energi i uppladdningsbara batterier och anv¨anda den senare vid behov. Detta betyder att TE ¨O kan f¨orb¨attra både n¨atverkets ¨overvakningsprestanda och dess livsl¨angd. I teorin ¨ar det m¨ojligt f¨or ett TDSN att ha en o¨andlig livsl¨angd (om noderna f¨orbrukar mindre energi ¨an de tar emot), vilket inte ¨ar m¨ojligt i traditionella TSN.

De f¨ordelar som TDSN ger upphov till i prestandaavv¨agningen f¨or sensorn¨atverk f¨or ¨aven med sig fundamentala frågor och utmaningar i termer av deras design och prestandaanalys. Av s¨akerhetssk¨al ¨ar effekten på de externa energik¨allorna begr¨ansad. Vidare går mycket energi till spillo vid trådl¨os energi¨overf¨oring med hj¨alp av radiovågor. Detta betyder att energin som kan tas upp av sensornoderna

¨ar mycket mindre ¨an den som uts¨ands vid k¨allan, och att man d¨arf¨or b¨or optimera både energitransmission från de externa energik¨allorna, samt energikonsumtion hos sensornoderna, f¨or att åstadkomma en bra prestanda hos ett TDSN. Detta står i kontrast till vanliga TSN i vilka man bara kan optimera sensor- och kommunikationsprotokollen hos noderna. Man har alltså tillgång till en extra frihetsgrad i TDSN: optimering av energi¨overf¨oringsprotokollet. Denna aspekt medf¨or nya tekniska utmaningar och problem som inte tidigare har studerats. Ett flertal forskningsfrågor kan formuleras, såsom: n¨ar och hur ska energi ¨overf¨oras, och vilken eller vilka energik¨allor ska utf¨ora ¨overf¨oringen? Dessa frågor ¨ar inte triviala att besvara n¨ar man gemensamt b¨or optimera energikonsumtionen hos sensornoderna.

Den h¨ar avhandlingen avser besvara ovann¨amnda frågor.

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I den f¨orsta delen av avhandlingen behandlar vi ett TDSN med en ensam energibasstation (eBS) och ett flertal sensornoder. N¨atverkets eBS har multipla antenner och anv¨ander strålformning f¨or att ¨overf¨ora energi till noderna. Notera att om vi placerar flera sensornoder i n¨arheten av varandra så kan dessa ta emot energi samtidigt från n¨atverkets eBS, vilket kan reducera n¨atverkets energikonsumtion genom ett synkroniserat standby- och uppvakningsprotokoll. Vi studerar d¨arf¨or det gemensamma optimeringsproblemet f¨or nodplacering, energi¨overf¨oring från n¨atver- kets eBS samt nodaktivering. Mer specifikt så erhålls ett heltalsoptimeringsproblem som vi frikopplar till ett nodplaceringsproblem samt ett schemal¨aggningsproblem.

Vi f¨oreslår en girig algoritm f¨or att l¨osa problemet, och demonstrerar dess prestanda.

I den andra delen av avhandlingen noterar vi f¨orst att den trådl¨osa kanaltill- ståndsinformationen (KTI, eng: channel state information) ¨ar viktig f¨or ener- gistrålformning. Desto mer energi som en eBS l¨agger på kanalanskaffning, desto exaktare KTI kommer den att ha, vilket medf¨or en b¨attre strålformningsprestanda.

Dock, om en eBS l¨agger f¨or mycket energi på kanalanskaffning så kommer energin den har tillg¨anglig f¨or TE ¨O bli lidande, vilket kan reducera energin som noderna kan ta emot. D¨arf¨or unders¨oker vi hur mycket energi en eBS b¨or l¨agga på kanalanskaffning, d.v.s. vi studerar energiallokeringsproblemet mellan kanalanskaffning och energistrålformning i TDSN. F¨orst betraktar vi det allm¨anna optimala allokeringsproblemet och visar att det ¨ar icke-konvext. Vi f¨oreslår en algoritm f¨or att ber¨akna den optimala l¨osningen n¨ar en ensam eBS anv¨ands (baserad på bisektionss¨okning), samt en l¨osning på sluten form f¨or fallet då n¨atverkets eBS anv¨ander ortogonal pilottransmission, kanalestimering via minsta-kvadratmetoden, eller maximum-ratio transmission f¨or TE ¨O. Simuleringar visar att algoritmen konvergerar snabbt, och att dess prestanda ¨ar n¨ara den teoretiska ¨ovre gr¨ansen.

I den tredje delen av avhandlingen behandlar vi det gemensamma energistrålform- nings- och datadirigeringsproblemet f¨or TDSN. Mer specifikt så betraktar vi TDSN som består av ett flertal eBS och sensorer, samt en s¨anknod. Baserat på energin sensornoderna mottar beh¨over de best¨amma hur deras data ska dirigeras.

Problemet avser att maximera den minimala sensoruppdateringsfrekvensen hos noderna, medan energin som tas emot av varje nod garanteras vara st¨orre ¨an den m¨angd som konsumeras. Vi f¨oreslår en centraliserad algoritm f¨or att l¨osa detta icke-konvexa problem, baserad på semidefinit optimering. Vi generaliserar vår metod till en distribuerad algoritm som anv¨ander alternating direction method of multipliers-metoden(ADMM). Vi visar teoretiskt att den centraliserade algoritmen uppnår optimal energistrålformning och datadirigering, och, via simuleringar, att den distribuerade algoritmen konvergerar till den optimala l¨osningen. Vidare, f¨or fallet då energistrålformningen ¨ar f¨orbest¨amd, studerar vi problemet att best¨amma den energim¨angd som ska allokeras i varje riktning. Vi observerar att om energistrålformningen ¨ar v¨al vald så kan en n¨ara optimal prestanda uppnås.

Sammantaget visar resultaten i den h¨ar avhandlingen att TE ¨O kan f¨orl¨anga

livsl¨angden hos TSN, och till och med ge dem en tillr¨ackligt lång livsl¨angd f¨or

allm¨anna långtids¨overvakningstill¨ampningar. Våra resultat grundar sig i att vi

optimerar TDSN med avseende på energis¨andning och -mottagning gemensamt.

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Vi ser m¨ojliga framtida till¨ampningar av våra resultat inom många IoT-system f¨or

smarta st¨ader (t.ex., vattendistribuering och byggnads¨overvakning).

Acknowledgments

First of all, I would like to express my sincere appreciation towards my supervisor Associate Professor Carlo Fischione for his constructive support, guidance, and encouragement. I would like to thank Associate Professor Ming Xiao for being my co-advisor, and also Dr. Lazaros Gkatzikis and Dr. Ay¸ca ¨Oz¸celikkale for their patient guidance and fruitful discussions. Working with them has allowed me to develop me knowledge substantially.

I would thanks to the people of Network Systems and Engineering department and Automatic Control department for building a harmonic and funny environment.

Especially, I thank Riccardo Sven Risuleo, Miguel Ramos Galrinho, and Sebastian Hendrik van de Hoef for providing help in courses, especially in the first few months when I started my PhD in KTH; Alexandros Nikou, Robert Mattila, Pedro Miguel Otao Pereira, Xinlei Yi, Christos Verginis, Manne Henriksson, Peiyue Zhao, Sladana Josilo, Seyed Mohammad Khodaei, Dan Pettersson, Ming Zenng, Kewei Zhang, Wenjun Xiong, and Hongyu Jin for interesting discussions; Dr. Yuzhe Xu, Dr.

Hossein Shokri Ghadikolaei, Dr. Sindri Magn´usson, Dr. Hadi Ghauch, Jos´e Mairton Barros da Silva Jr., and Xiaolin Jiang for supportive comments, suggestions, and helps. I would like to thank Robert Mattila and Dan Pettersson again for their translation and double check of the thesis abstract in Swedish. I am also grateful for the assistance and support from the administrators: Connie Linell, Eleni Nyl´en, Anneli Str¨om, Hanna Holmqvist, Karin K. Eklund, Gerd Franzon, and Silvia Cardenas Svensson.

Finally, I also want to thank my parents and grandparents for their love and encouragements. I am deeply grateful to the most important one in my life, Yuanying, for her understanding, support and love.

Rong Du

Stockholm, August 2018

Contents

Contents xiii

List of Figures xvii

List of Tables xxi

List of Acronyms xxiii

I Thesis Overview 1

1 Introduction 3

1.1 Wirelessly Powered Sensor Networks: Background . . . . 3

1.1.1 Example: Lakes or coastal regions . . . . 5

1.1.2 Example: Warehouses . . . . 5

1.2 Challenges . . . . 6

1.3 Problem Formulation . . . . 7

1.3.1 Example 1: WET and sleep/awake activation . . . . 7

1.3.2 Example 2: Energy beamforming and data routing . . . . 8

1.4 Thesis Contribution . . . . 9

1.4.1 Node placement and energy provision . . . . 10

1.4.2 Power allocation for channel acquisition and energy trans- mission . . . . 11

1.4.3 Energy beamforming and data routing . . . . 13

1.5 Contributions not Covered in This Thesis . . . . 14

1.6 Summary and Future Work . . . . 15

2 Preliminaries 17 2.1 Wireless Energy Transmission . . . . 17

2.2 ADMM . . . . 18

xiii

xiv Contents

II Included Papers 21

A Optimal Node Deployment and Energy Provision for Wire-

lessly Powered Sensor Networks 23

A.1 Introduction . . . . 25

A.2 Related Works . . . . 27

A.3 System model and Problem Formulation . . . . 30

A.4 Node Deployment for Immortal WSN . . . . 34

A.4.1 Node deployment sub-problem . . . . 34

A.4.2 Problem Solution . . . . 36

A.4.3 Performance Analysis and Discussions . . . . 38

A.5 WET Scheduling and Node Activation . . . . 41

A.6 Simulations . . . . 43

A.7 Conclusions and Future works . . . . 48

A.8 Appendix: Discussion on g(x) . . . . 48

A.9 Appendix: Proofs . . . . 52

B Wirelessly-powered Sensor Networks: Joint Channel Estima- tion and Energy Beamforming 59 B.1 Introduction . . . . 61

B.1.1 Related Works and Motivations . . . . 61

B.1.2 Contributions . . . . 64

B.2 Modelling and Problem Formulation . . . . 65

B.2.1 Network Model . . . . 65

B.2.2 Channel Estimation and Beamforming . . . . 65

B.2.3 Energy Consumption Model . . . . 68

B.2.4 Power Allocation Problem . . . . 68

B.2.5 Complexity Analysis . . . . 69

B.3 Solution Method . . . . 69

B.3.1 Algorithm Development . . . . 70

B.3.2 Performance Analysis . . . . 71

B.3.3 Illustrative Example . . . . 73

B.3.4 Solution for Linear Energy Harvesting Model . . . . 75

B.3.5 Asymptotic Case . . . . 76

B.4 Numerical Results . . . . 77

B.4.1 Simulation Set-ups . . . . 78

B.4.2 Convergence Tests . . . . 78

B.4.3 Comparing Non-linear and Linear Models . . . . 79

B.4.4 Performance Tests . . . . 80

B.5 Conclusions and Future Works . . . . 84

B.6 Appendix: Proofs . . . . 85 C Towards Immortal Wireless Sensor Networks by Optimal

Energy Beamforming and Data Routing 89

Contents xv

C.1 Introduction . . . . 91

C.2 Related Work . . . . 94

C.3 System Model and Problem Formulation . . . . 96

C.4 Centralized Solution Approach . . . . 98

C.4.1 Algorithm based on SDP . . . . 99

C.4.2 Pre-determined beamforming vectors . . . . 104

C.5 Distributed Approach . . . . 106

C.5.1 Distributed solution for optimal beamforming . . . . 106

C.5.2 Distributed solution for pre-determined beamforming . . . 109

C.6 Numerical Results . . . . 111

C.6.1 Centralized case . . . . 112

C.6.2 Distributed approach . . . . 119

C.7 Conclusions and Future Work . . . . 121

Bibliography 123

List of Figures

1.1 An example of coverting electromagnetic energy into direct current

electricity by rectenna. . . . 4 1.2 An example of the wirelessly powered sensor network with multiple

energy base stations, sensor nodes, and a sink. . . . 5 1.3 A possible solution of using wirelessly powered sensor network for

lake monitoring. . . . 6 1.4 The comparison of our scheme with non optimal deployment and non

optimal energy transmission. . . . 11 1.5 Comparison of our algorithm (Algorithm 4 in Chapter B) to other

approaches (fixed power allocation, random power allocation) and

an upper bound with different noise level. . . . 12 1.6 Comparison of minimum sampling rate with varying number of sen-

sors, achieved by our optimal energy beamforming, pre-determined

beamforming, no beamforming, and the cases without routing. . . . 14 A.1 A wirelessly powered sensor network with one energy base station

and multiple sensors. The sensors in a region take turn to make

measurements and transmit the data. . . . 26 A.2 The probability of wirelessly powered sensor networks to be immortal

with different field size N and sampling rates λ. . . . 43 A.3 Comparison of the required number of sensor nodes achieved by

different algorithms. . . . 44 A.4 The dynamic of the minimum percentage of residual energy. . . . . 45 A.5 The comparison of our scheme with non optimal deployment and non

optimal energy transmission. . . . 46 A.6 The dynamic of the minimum percentage of residual energy with

different standard deviation of the harvested power. . . . 47 A.7 The comparison of the minimum percentage of residual energy with

additional sensor nodes. . . . 47 A.8 The difference of g(x) with respect to x under the model of the first

motivating example. . . . 50

xvii

xviii List of Figures

A.9 The second motivating example, with the consideration of shadowing

of nodes. . . . 51 A.10 The difference of g(n) with respect to n under the model of the second

motivating example. . . . 51 B.1 The wirelessly powered sensor network considered in Chapter B. . . 62 B.2 Power allocation of channel estimation, energy transmission, and

data transmission . . . . 67 B.3 The PEB gain and its approximation at different pilot power P

. . 74 B.4 Convergence of Algorithm 4 (non-linear energy harvesting case). . . 78 B.5 Convergence of Algorithm 4 (linear energy harvesting case). . . . 79 B.6 The network sensing rates achieved by Algorithm 4, and the relative

difference between the non-linear and linear model. . . . 80 B.7 Comparison of Algorithm 4 to other approaches with different radius

R . . . . 82 B.8 Comparison of Algorithm 4 to other approaches with different

numbers of nodes N. . . . 83 B.9 Comparison of Algorithm 4 to other approaches with different noise

level. . . . 84 B.10 Comparison of Algorithm 4 to other approaches with different static

power consumption c. . . . 85 C.1 A wireless sensor network with dedicated wireless energy chargers

(base stations) . . . . 92 C.2 Operations of the distributed approach for Problem (C.3) . . . . 109 C.3 Comparison of minimum sampling rate with varying number of

antennas, achieved by optimal energy beamforming, pre-determined

beamforming, and no beamforming, with N = 15, K = 100 . . . . . 112 C.4 Comparison of minimum sampling rate with varying number of

antennas, achieved by optimal energy beamforming, pre-determined

beamforming, and no beamforming, with N = 15, K = 2.8 . . . . 113 C.5 Comparison of minimum sampling rate with varying number of

sensors, achieved by optimal energy beamforming, pre-determined

beamforming, and no beamforming, with M = 100, K = 100 . . . . . 114 C.6 Comparison of minimum sampling rate with varying number of

sensors, achieved by optimal energy beamforming, pre-determined

beamforming, and no beamforming, with M = 100, K = 2.8 . . . . . 115 C.7 Comparison of the minimum sampling rates with varying number

of sensors, achieved by optimal energy beamforming, pre-determined beamforming, and no beamforming from four chargers, with M=100,

K =100 . . . . 116 C.8 Comparison of the minimum sampling rates with varying number of

sensors, achieved by optimal energy beamforming, pre-determined beamforming, and no beamforming from four chargers, with M=10,

K =100 . . . . 117

List of Figures xix

C.9 Comparison of the minimum sampling rates with varying number of chargers and antennas achieved by optimal energy beamforming and

no beamforming. . . . 118 C.10 The relative difference of the minimum sampling rate achieved by

the distributed approach (Algorithm 7) . . . . 120 C.11 The relative difference of the minimum sampling rate achieved by

the distributed approach (Algorithm 7 adopted for Problem (C.8))

with the optimum in each iteration. . . . 121

C.12 Comparison of the convergence of different distributed approaches. . 122

List of Tables

1.1 Contribution of the chapters. . . . 10

A.1 Comparisons of the literature on WET for WSN. . . . 30

A.2 Major notations used in Chapter A. . . . 31

B.3 Major notations used in Chapter B. . . . 66

C.4 Major notations used in Chapter C. . . . 98

C.5 Simulation parameters. . . . 111

xxi

List of Acronyms

ADMM Alternating Direction Method of Multipliers BS Base Station

CSI Channel State Information DC Direct Current

eBS energy base station EH Energy Harvesting IoT Internet of Thingss

MIMO Multiple-input and Multiple-output

PEB Pilot, Estimation, and Beamforming Scheme RF Radio Frequency

SDP Semi-definite Programming WET Wireless Energy Transfer

WPCN Wirelessly Powered Communication Network WPSN Wirelessly Powered Sensor Network

WSN Wireless Sensor Network

xxiii

Part I

Thesis Overview

1

Chapter 1

Introduction

Wireless networks are an important part of our daily life, with applications including the use of mobile phones to convey and retrieve messages and information, the use of blue-tooth networks for short range personal network communication, the use of WiFi to connect our laptop to Internet, the use of wireless sensor networks (WSNs) to monitor the living environment or the industrial process. With the growing demand in terms of higher rate, smaller delay, more reliable transmission, etc., considerable research and development is underway.

In general, the more power that a wireless device can use, the better performance (such as throughput, delay, bit error rate) it can achieve. However, for the low power devices, such as sensor nodes and some Internet of Things (IoT) devices, their power consumption has to be modest. This is because it drains the battery of the devices, and significantly degrades the performance in terms of lifetime. Fortunately, the idea of energy harvesting [1,2] and wireless energy (or power) transfer (WET) [3–5] gives us a way to remotely provide additional energy to the devices, and thus they can have a higher data rate or smaller transmission delay without the losing of lifetime.

In such cases, the networks are called wirelessly powered communication networks (WPCNs) [6,7]. For such networks, an essential question is how to efficiently provide more energy to the wireless devices and how the devices use the energy to improve the network performance. In this thesis, we focus on such a question in the network instance of WSN, which is called wirelessly powered sensor networks (WPSNs) [8].

1.1 Wirelessly Powered Sensor Networks: Background

WSNs are widely used to monitor the areas or process of interests, such as the humidity, temperature, and luminance of the rooms in smart buildings [9, 10], the road traffic of smart cities [11, 12], the structural-health condition of tunnels, bridges, and towers [13–15], the contaminations in air and water [16], the growth of the crops in smart agriculture [17], and the production line in Industry 4.0 (smart industry) [18]. In most of such applications, the WSNs are designed for long term monitoring. Therefore, the lifetime is one of the most important metrics of WSNs

3

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Figure 1.1: An example of coverting electromagnetic energy into direct current electricity by rectenna.

to be considered. Therefore, to prolong network lifetime of the traditional WSNs without the capability of battery recharging, the key method is to reduce the energy consumptions of nodes, such as by forming clusters [19, 20], data routing [21, 22], data compression [22,23], and duty-cycling [16,21]. However, as long as the sensor nodes cannot recharge their battery, the energy will run out and the network will eventually expire.

To address such a problem of energy depletion, we can use the idea of energy harvesting. In an energy harvesting sensor network, the nodes harvest ambient energy, such as solar [24], wind [25], vibrations [26], and radio frequency (RF) waves [27]. For example, the nodes can harvest energy from the RF waves that are broadcasted from TV towers [28] or different wireless devices. The nodes can save the energy into their rechargeable battery, and use the energy later. Then, as long as the nodes harvest enough energy, the sensor network will not expire.

One advantage of energy harvesting is that the energy in environment usually is sustainable and green. However, due to that the source of ambient energy is hard to control or even not controllable [29], the prediction of the arrival of the energy is important for the scheduling the sensor nodes. If we had the knowledge of the energy arrivals, the scheduling is off-line [30,31]. However, in practice, we only have partial information of the arriving energy, and the scheduling is on-line [32, 33].

Therefore, the performance of the scheduling is usually sub-optimal compared to the off-line one. We can observe that, the major limitation of energy harvesting is that the arriving of the energy is inconsistent and thus the performance of the WSN is inconsistent.

To have a more consistent network performance, we should try to control the energy source. Among the different types of energy, RF wave is the easiest to generate and control. This gives us the motivation to charge the nodes with RF waves remotely. More specifically, we use base stations (BSs) to generate RF waves. The BSs transmit the RF waves to the nodes. To harvest the RF energy, the sensor nodes use rectifying antenna [34, 35], namely rectenna, to convert the electromagnetic energy into direct current (DC) electricity, as shown in Figure 1.1.

The nodes store the energy into their capacitor or rechargeable battery. The process

of transmitting RF energy wirelessly is called wireless energy transmission (WET)

1.1. Wirelessly Powered Sensor Networks: Background 5

energy base station energy transmission

data transmission

sensor node

sink

Figure 1.2: An example of the wirelessly powered sensor network with multiple energy base stations, sensor nodes, and a sink.

or wireless power transmission (WPT) [3, 5], and such a kind of sensor network is called WPSN. To increase the energy that is received by the nodes, we can for example schedule energy transmission time, the energy transmission targets, and the power to transmit.

Different to the traditional WSNs and the energy harvesting sensor networks, where we can only reduce the energy consumption of sensor nodes, in a WPSN, we can reduce the energy consumption of the nodes and also improve the energy received by the nodes. It means that we have an additional degree of freedom to control and to improve the performance of the network. Therefore, we should optimize the WPSN performance by jointly consider energy consumption and energy provision. However, this additional degree of freedom also makes the problems more challenging than the cases where we only consider energy consumption. The methods to solve such problems are not trivial, and this thesis presents our study on these problems and the corresponding contributions. In the following, we provide some examples of WPSN.

1.1.1 Example: Monitoring of lakes or coastal regions

To monitor the water quality and the fluid dynamic of a lake or a coastal region, we can put sensor nodes inside the waterproof capsules and put them in the lake water.

In such a case, it is hard to recharge the sensor nodes with cables. Therefore, we can build eBSs at the coasts/shores, as shown in Figure 1.3. The eBSs charge the sensor nodes such that the nodes always have sufficient energy to perform sensing.

1.1.2 Example: Monitoring of warehouses

In a smart warehouse, sensors and radio-frequency identification tags can provide

the information of the exact locations of any products. With small energy base

stations deployed in the warehouse, the sensor nodes can be charged wirelessly,

meanwhile the tags can transmit the information by reflecting the energy sent from

the eBSs.

6 Introduction

Figure 1.3: A possible solution of using wirelessly powered sensor network to monitor the water quality of Lake M¨alaren, Sweden, for the Vinnova iWater project.

1.2 Challenges

WPSN can be considered as a special case of WPCSs. They share some similarities.

For example, the major problem of WET is that the RF waves are transmitted from the BSs to the devices are through air. Thus, the strength of the RF waves decay greatly due to path losses, or shadowing. Notice that the transmitting power of the BSs cannot be arbitrarily high due to the safety issues [36, 37]. As a result, the energy received by the devices may be very limited. Recall that the received RF waves are converted into DC electricity through rectenna circuit, whose conversion rate is small when the input power is small. Therefore, the harvested energy is even less, and it is one challenge to overcome, such that more energy can be harvested by the devices.

One possible method to overcome the problem is to use multiple antennas at the BSs. It allows the BSs to form energy beams [38,39] towards the target devices such that the energy is more concentrated. In this way, less energy will be wasted on the other directions where there are no target devices. This process is called energy beamforming, and it determines how much power can be received at the devices. Therefore, it is a vital process for WPCNs, and it is challenging to perform a good energy beamforming. One reason is that, to perform beamforming, we should have the information of the channel from each BS to each device [39–41]. Thus, one interesting problem is to design the channel acquisition, such as who should transmit pilots, how much power it should spend, how to perform channel estimation. This thesis provides our contributions on this issue.

Recall that, in WPSNs, we can control not only the energy provision process,

but also the energy consumption. Therefore, even when the energy transmission

process is optimal, if the energy consumption is not, the harvested energy might

be wasted and thus the WPSNs performance will be suboptimal. Therefore, to

optimize the WPSNs performance, one should jointly consider both processes. It

naturally introduces new variables and constraints, and thus makes the problems

more challenging. Therefore, we also jointly consider the energy beamforming and

1.3. Problem Formulation 7

data routing of the WPSNs, and provide the results in the thesis.

Different to the WPCNs, the sensor nodes in WPSNs are usually low power devices. Therefore, rather than optimizing the performance such as delay [42], throughput [43], and achievable rate [44], as they do in WPCNs, in WPSNs we want to optimize the performance such as the sensing accuracy [45], the amount of measured data [46], and the lifetime of the network [47]. As a result, there are some minor differences in problem formulations and models. Some results for WPCNs may not be applied in WPSNs directly. This also leads to some challenges.

In addition, there are other challenges, such as designing the circuit of rectennas and the MAC protocols of the network. However, due to the limited time and the knowledge, we have not investigated these problems, and we believe these problems are also worth to study.

1.3 Problem Formulation

The problems that are investigated in this thesis can be generalized in the following form:

max

F (x) (1.1a)

s.t. E

= G

(y) , ∀i ∈ N (1.1b) E

= H

(x) , ∀i ∈ N (1.1c)

E

≤ E

, ∀i ∈ N (1.1d)

x ∈ X , y ∈ Y , (1.1e)

where N is the index set of the sensor nodes, x corresponds to the energy consumption of the nodes, y corresponds to the energy provision of the eBSs, the objective function F (x) corresponds to the performance of the WPSN, Constraint (1.1b) denotes the energy received by each node, Constraint (1.1c) denotes the energy consumption of each node, Constraint (1.1d) means that the energy consumed by each node should be no larger than the energy they harvest, and Constraint (1.1e) denotes the feasible region of the energy consumption and the energy provision. We provide two examples in the following.

1.3.1 Example 1: WET and sleep/awake activation

Consider a case where we have N regions of interest to monitor. In each region i, i = 1, . . . N, there are n

number of sensor nodes monitoring the same phenomena, therefore, the nodes in the same region can take turns to sense and to transmit the measurement. In such a way, the energy consumption of the sensor nodes is reduced.

The time is divided into timeslots. We denote binary variable x

(t) the activation

of the j-th node (we denote it by v

) in region i in timeslot t, i.e., x

(t) = 1 if it is

awake in timeslot t. For the monitoring purpose, each region should have at least

one active node. Suppose that the monitoring of region i requires a sensing rate w

8 Introduction

(bits/s), and the energy consumption to transmit one bit of measurement to the sink from region i as a

. Besides transmitting the measurement, the static energy consumption of the nodes are c. Then, the energy consumption of an active node v

is a

w

+ c. Thus, Constraint (1.1c) becomes E

(T ) = P

[a

w

x

(t) + c].

We use one eBS to transmit energy to the nodes. Suppose that the eBS uses a WET scheme that it transmits energy to one region in a timeslot. Then, we use binary variable y

(t) to denote the transmission of energy, i.e., y

(t) = 1 if and only if the eBS transmits energy to the nodes in region i, and all the nodes in that region can harvest the energy. For simplicity, we normalize the transmission power of the eBS to be 1. Then, Constraint (1.1b) is E

= P

α

y

(t), where α

corresponds to the path loss and energy conversion rate. Let E

(0) be the initial energy of v

. Then, Constraint (1.1d) becomes E

(0) + E

(T ) ≤ E

(T ), ∀T . Recall that, for any region i, at least one node should be active. In additional, the eBS transmits energy to a region in a timeslot. Then, Constraint (1.1e) becomes P

j=1

x

(t) ≥ 1, ∀i, ∀1 ≤ t ≤ T , and P

y

(t) = 1, ∀1 ≤ t ≤ T . The objective is to maximize the lifetime of the WPSN, and thus the objective function is max T . We study a similar problem with additional decision variables on the deployment of the sensor nodes. Therefore, the problem becomes more challenging. We present the result in Chapter A.

1.3.2 Example 2: Energy beamforming and data routing

In this example, the eBSs form energy beams to charge the sensor nodes. Based on the received energy, the sensor nodes determine the sensing rate and the routing of the measurements. Therefore, the variable x consists of two parts, i.e., the sensing rate of each node w = [w

, . . . , w

] and the routing q. y = [U

, . . . , U

ET

]

is the energy beamforming covariance matrix of the nodes, where y

is the conjugate transpose of y

, and N

is the number of eBSs. Then, we can formulate Constraint (1.1c) as E

= B

q , where B

corresponds to the energy consumption of node i to transmit a bit of data to its neighboring nodes. We formulate Constraint (1.1b) as E

= η P

tr [K

U

], where K

is the covariance matrix of the channel from BS j to node i, and tr is the trace operation. We have additional constraint on x from the flow conservation of the routing, and we can formulate it as Aq + w = 0. The constraint on y is the power constraint of the energy beamforming, and it is tr[U

] ≤ P , where P is the power that each eBS has. We want to maximize the minimum sensing rate of the nodes. Then the objective function is F (x) = min{w

, . . . , w

} . We study such a problem in the first contribution.

We propose a centralized algorithm and also a distributed algorithm to achieve the

optimal solution. More details of the results can be found in Chapter C.

1.4. Thesis Contribution 9

1.4 Thesis Contribution

This thesis mainly focuses on optimizing the WPSN monitoring performance from the networking point of view. It consists of three chapters, each of which studies a specific instance of Problem (1.1), i.e., (i) energy beamforming and data routing, (ii) power allocation for channel acquisition and energy transmission, and (iii) node placement and energy provision. The chapters are based on the following papers or submitted manuscripts

:

[J1]Rong Du, Ming Xiao, and Carlo Fischione, “Optimal Node Deployment and Energy Provision for Wirelessly Powered Sensor Networks,” accepted by IEEE Journal on Selected Areas in Communications (IEEE JSAC), 2018.

[C1]Rong Du, Carlo Fischione, and Ming Xiao, “Lifetime Maximization for Sensor Networks with Wireless Energy Transfer,” in Proceedings of IEEE International Conference on Communications (IEEE ICC), 2016.

[C2]Rong Du, Carlo Fischione, and Ming Xiao, “Joint Node Deployment and Wireless Energy Transfer Scheduling for Immortal Sensor Networks,” in Proceedings of International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt), 2017.

[J2]Rong Du, Hossein S Ghadikolaei, and Carlo Fischione, “Wirelessly-powered Sensor Networks: Power Allocation for Channel Estimation and Energy Beam- forming,” submitted to IEEE Transactions on Wireless Communications (IEEE TWC), 2018.

[C3]Rong Du and Carlo Fischione, “Power Allocation for Channel Estimation and Energy Beamforming in Wirelessly Powered Sensor Networks,” in Proceedings of IEEE International Conference on Communications (IEEE ICC) (IEEE Workshop on Energy Harvesting Wireless Communications), 2018.

[J3]Rong Du, Ay¸ca ¨Oz¸celikkale, Carlo Fischione, and Ming Xiao, “Towards Immortal Wireless Sensor Networks by Optimal Energy Beamforming and Data Routing,” IEEE Transactions on Wireless Communications, vol. 17, no. 8, pp. 5338–5352, 2018.

[C4]Rong Du, Ay¸ca ¨Oz¸celikkale, Carlo Fischione, and Ming Xiao, “Optimal Energy Beamforming and Data Routing for Immortal Wireless Sensor Networks,” in Proceedings of IEEE International Conference on Communications (IEEE ICC), 2017.

The contribution of our work is summarized in Table 1.1.

1

B: Book chapter; C: Conference; J: Journal;

10 Introduction

Table 1.1: Contribution of the chapters.

WET Sensor nodes Method Optimality

Chapter A Energy scheduling Node deployment,

Activation Greedy Global Chapter B Channel

acquisition − Bisection Global

Chapter C Beamforming Routing SDP Global

1.4.1 Node placement and energy provision

We first considered a case where we have requirements on the sensing rate of the nodes in Chapter A. This chapter is based on the work in J1, C1, and C2. The eBS in the WPSN forms energy beams to charge the sensor nodes, and the nodes use the received energy for sensing and data transmission. When the eBS does not have enough power to charge the network, the WPSN may not be able to monitor as long as possible. In such a case, we need to reduce the energy consumption of the nodes and increase the harvest energy of the nodes. This can be fulfilled by deploying additional sensor nodes to monitor the same target. More specifically, the nodes that monitor the same target can take turns to measure and transmit the information. Therefore, the actual sensing rate of each node is reduced, and thus their energy consumption rate is reduced. Since the nodes that monitor the same target are close to each other, they can harvest the energy from the eBS at the same time. Consequently, the total harvested power increases. Based on this observation, we want to know how many nodes we should deploy, and where to deploy them.

Besides node deployment, the scheduling of the wireless transmission and the node activation are also important factors in terms of WPSN lifetime. Therefore, we investigated a joint node deployment and energy provision scheduling problem in the chapter. We minimized the nodes to deploy whilst ensuring that the WPSN always has enough energy to perform the monitoring application. The formulated problem is an integer programming with non-linear constraints, which makes the problem challenging. To solve the problem, we first analyzed the necessary condition on the node deployment, such that the WPSN be immortal. Based on this necessary condition, we decoupled the original problem into a node deployment problem and a scheduling problem. For the node deployment problem, we developed a greedy based algorithm and showed that it achieves the optimal solution of the deployment problem. Based on the solution of the deployment problem, we proposed a simple scheduling algorithm for energy transmission and node activation. We proved that with the proposed deployment and scheduling, the WPSN always has enough energy for the monitoring requirement.

In the simulation, we show by Figure 1.4 that, if the WET is not optimized, the

lifetime of the WPSN may be very limited. Also, even when the WET is optimized,

1.4. Thesis Contribution 11

1 10 100 1000 10000 100000

0 0.2 0.4 0.6 0.8 1

timeslots

percentage of residual energy

our scheme non opt. deploy non opt. WET

Figure 1.4: The comparison of our scheme with non optimal deployment and non- optimal energy transmission in terms of the residual energy of a sensor nodes at different time slots. It shows that with our scheme the sensor nodes always have enough energy to perform the monitoring tasks, whereas under other non optimal scheme, the energy of the sensor nodes eventually runs out.

if we do not place enough sensor nodes, the energy of the network will also run out eventually. Besides, we showed that the number of nodes to be deployed according to our algorithm is close to the lower bound. The number of nodes achieved by our algorithm is approximately 10% less than the one achieved by an algorithm based on relaxation.

My Contribution: As the first author, I formulated and solved the studied problems. In addition, I run the simulations and wrote the manuscript. The other authors contributed through serving the roles of supervision of the first author, by detailed discussions on the technical issues. They also contributed in the structure of the papers.

1.4.2 Power allocation for channel acquisition and energy transmission

To perform energy beamforming, the eBS needs the channel state information (CSI).

However, to acquire the CSI, the eBS should spend some power. The more power it

spends, the better CSI it can achieve, which makes the energy beamforming more

efficient. However, if the eBS spends too much energy in channel acquisition, it

can transmit less energy to the nodes. Therefore, there is a trade-off in spending

energy for channel acquisition and energy transmission. Based on this observation,

12 Introduction

−90 0 −85 −80 −75 −70 −65 −60 −55 −50 −45 10

20 30 40 50

noise level (dBm)

network sensing rate (bits/s)

Alg. 4 Fixed PA Random PA Upper bound

Figure 1.5: Comparison of our algorithm (Algorithm 4 in Chapter B) to other approaches (fixed power allocation, random power allocation) and an upper bound with different noise level. It shows that our algorithms outperform the benchmark algorithms, and the results are close to the upper bound when the noise level in the channel acquisition is low.

we studied the power allocation for channel acquisition and energy transmission in Chapter B. It is based on the work J2 and C3. Noticing that there are many different way for channel acquisition, we tried to not limit our study to a specific channel acquisition. Therefore, we generalized the gain of channel acquisition as a concave and monotone increasing function of power. We also generalize the energy harvesting model by a monotone increasing function, such that our results are valid for non-linear energy harvesting models. We formulated the optimization problem and showed that it is non-convex. We provided a bisection searching based algorithm that finds the optimal solution. For a special case where the eBS uses an orthogonal piloting, least square estimation, and maximum ratio transmission, we provide a closed-form optimal solution. To show the performance of our algorithms, we also provided an upper bound of the sensing rate.

The simulation results in Figure 1.5 show that our algorithms outperform the case where the power for channel acquisition is a fixed value. Also, the performance is close to the upper bound when the noise level is low. In addition, we observe that, when the noise level is high, the eBS needs to spend more energy in channel acquisition. Therefore, the energy that the eBS can transmit is less than the case where the noise level is low. As a result, the nodes receive less energy such that the sensing rate reduces.

My Contribution: As the first author, I formulated and solved the studied

1.4. Thesis Contribution 13

problems. In addition, I run the simulations and wrote the manuscript. The other authors contributed through serving the roles of supervision of the first author, by detailed discussions on the technical issues. They also contributed in the structure of the papers.

1.4.3 Energy beamforming and data routing

Chapter C is based on the work J3 and C4. In this chapter, we investigated a joint energy beamforming and data routing problem. More specifically, the multiple eBSs form energy beams to charge the sensor nodes, and the nodes consume the received energy in sensing and data transmission. Instead of direct data transmission, the sensor nodes relay the data to save power. We need to find the maximum sensing rate of the nodes by controlling the energy beamforming of the eBSs and the data routing of the sensor nodes, whilst ensuring that the WPSN be immortal, which means that the average consumed energy of each node should be no more than the average harvested energy. Such a requirement gives a non-convex constraint, which makes the optimization problem challenging. To solve the problem, we turned it into a semi-definite programming (SDP) problem [48]. We proved the strong duality of the problem, which means that the optimal solution of the SDP is achievable.

Then, we transformed the optimal solution of the SDP back to the solution of the original problem. To further reduce the computational complexity of the problem, we also considered the distributed solution based on Alternating Direction Method of Multipliers (ADMM) [49]. We also considered the cases where the beamforming vectors are pre-determined, but the power and time duration of these beamforming vectors are to be optimized. We called it pre-determined beamforming. For such cases, we also proposed a centralized algorithm and a distributed algorithm to solve the problem.

From the simulation results as shown in Figure 1.6, we observed that, the performance in terms of sensing rate first decreases with the number of sensor nodes, and then increase. The reason is that, with more sensor nodes that need to charge, each node in average harvest less energy from the eBS. It makes the sensing rate decreasing in the beginning. However, when the network is dense enough, each node has more choices in the routing to save more energy. Therefore, the reduction in energy consumption becomes the major factor and it allows the nodes sense with a high rate. Therefore, when the nodes do not apply routing, i.e., they transmit the data directly to the sink, the sensing rate is always decreasing with the number of nodes. In addition, if the eBS just broadcasts the energy, rather than forming energy beams, the network performance is much worse than the case when it uses energy beamforming.

My Contribution: As the first author, I formulated and solved the studied

problems. In addition, I run the simulations and wrote the manuscript. The other

authors contributed through serving the roles of supervision of the first author by

detailed discussions on the technical issues. They also contributed in the structure

of the papers.

14 Introduction

5 10 15 20 25

0 5 10 15 20 25 30 35

Number of sensors

Average minimum sampling rate (kbits/s)

Opt. BF Pre. BF No BF

Opt. BF No Rout.

Pre. BF No Rout No BF No Rout.

Figure 1.6: Comparison of minimum sampling rate with varying number of sensors, achieved by our optimal energy beamforming, pre-determined beamforming, no beamforming, and the cases without routing. It shows that the performance of the pre-determined beamforming is close to the optimal beamforming, and they are much better than the case with no energy beamforming. In addition, the routing also improves the network performance by allowing the nodes to save energy by relaying data.

1.5 Contributions not Covered in This Thesis

Besides the seven papers or manuscripts listed above, I have worked on some other topics during my PhD study, as shown in the following publications. These papers are not included in the thesis for the consistency of the thesis. In each of the following paper, the order of the authors reflects the contribution of the authors.

[J4]Rong Du, Lazaros Gkatzikis, Carlo Fischione, and Ming Xiao, “Energy Efficient Sensor Activation for Water Distribution Networks Based on Com- pressive Sensing,” IEEE Journal on Selected Areas in Communications (IEEE JSAC), Vol. 33, No. 12, pp.2997-3010, 2015.

[J5]Rong Du, Lazaros Gkatzikis, Carlo Fischione, and Ming Xiao, “On Maximiz- ing Sensor Network Lifetime by Energy Balancing,” IEEE Transactions on Control of Network Systems, Vol. 5, No. 3, pp. 1206-1218, 2018.

[C5]Rong Du, Lazaros Gkatzikis, Carlo Fischione, and Ming Xiao, “Energy Effi-

cient Monitoring of Water Distribution Networks via Compressive Sensing,”

1.6. Summary and Future Work 15

in Proceedings of IEEE International Conference on Communications (IEEE ICC), 2015.

[C6]Rong Du, Carlo Fischione, and Ming Xiao, “Flowing with the Water: On Optimal Monitoring of Water Distribution Networks by Mobile Sensors,”in Proceedings of IEEE International Conference on Computer Communications (IEEE INFOCOM), 2016.

[B1]Rong Du, Carlo Fischione, “Deployment and Scheduling of Wireless Sensor Networks for Monitoring Water Grids,” Smart Water Grids: A Cyber-Physical Systems Approach, CRC Press, 2018.

1.6 Summary and Future Work

In this thesis, we considered the optimization of WPSNs in terms of monitoring from the networking perspective. With the WET technology, we are able to provide energy to the sensor nodes remotely, such that the network lifetime is sufficiently long. While WET can provide more energy to the sensor nodes such that the monitoring performance of the network can be improved, it also brings challenges, such as how to get the CSI, how to transmit energy to the nodes, how the nodes consume energy based on the received energy from the eBSs. Compared to the traditional WSN without WET, the problems in WPSNs are more difficult due to the additional variables to optimize, and the additional constraints. We investigated a joint node deployment and energy transmission scheduling problem, a power allocation problem for channel acquisition and energy beamforming, and a joint routing and energy beamforming problem.

In our first work, we provided a solution on deploying additional nodes to make the WPSN immortal in the cases that the power of the eBS is limited. In our second work, we investigated the trade off of using more energy in channel acquisition and in energy transmission. In our third work, we showed the benefits of jointly optimizing the data routing and energy beamforming of the WPSN. In addition, we found out that our pre-determined energy beamforming scheme is a good approach with low complexity to achieve a performance that is close to the optimal.

The major novelty and contribution of the thesis is the idea of improving the WPSN performance by the joint consideration of improving energy transmission and reducing energy consumption. For different problems, we have different solution approaches, which might bring some insights when one study the optimization of WPSN from other perspectives. The approaches are not complex and are easy to implement.

1.6.1 Future Work

There are many interesting ideas, problems, and challenges that are left for future

investigations. Some important ones are listed in the following.

16 Introduction

Design of the WPSNs

To improve the performance of the WPSNs, we can have a better design of the energy receiving circuits, to enable the nodes harvest more energy from the eBSs.

Also, we can find a better location of the BSs such that the nodes can harvest more energy. On the other hand, we can reduce the energy consumption of the nodes.

Besides routing, and sleep/awake scheduling, there are other ways, such as using data compression, MAC protocols. Therefore, we can consider these factors with energy transmission. For example, the nodes can decide whether they should stay silent to harvest energy, or to sleep, or to transmit data according to the WET scheduling and the remaining battery they have. Such a problem can be formulated as a MAC problem for WPSN. The problem will be more challenging when multiple energy saving approaches are jointly considered with WET. Besides, for different objectives, such as the lifetime of the WPSN and the estimation accuracy of the WPSN, the corresponding solution approaches may be different and worth to study.

Channel acquisition

To perform energy beamforming, CSI is required in practice. For traditional WPCN systems, there are several ways to get the CSI. In the thesis, we consider the case where the eBS transmits pilots to the sensor nodes, and the sensor nodes provide feedback to the eBSs. We have a closed-form solution for a special case, where the eBS uses orthogonal pilot transmission and least-square channel estimation on the channel. It is interesting to study the closed-form solution of other channel acquisition schemes. Besides, the other way of channel acquisition is that the nodes transmit pilots and the eBSs estimate the channel [40]. In this case, the sensor nodes need to allocate the power for pilot transmission and data transmission. Thus, the problem would be a little bit different to the case studied in the thesis. It is worth investigating which scheme is more reasonable for the WPSNs, and optimize the system parameters.

WPSN with energy harvesting

Recall that the sensor nodes can also harvest ambient energy. Thus, the nodes

in a WPSN can also harvest the ambient energy. In this case, the nodes can

schedule their consumptions based on the WET transmission, and also the expected

energy that they can harvest from the environment. Then, there will be some

randomness in the optimization problem. Additionally, the new idea of black-

scattering communication [50,51] could also be used in a WPSN. More specifically,

when the received power is too low to be harvested by the nodes, they can choose

to use black-scattering communication to transmit their data. This is also an

interesting direction to study.

Chapter 2

Preliminaries

This chapter gives some essential elements of the background theory used in the thesis. Section 2.1 briefly describes how a base station forms energy beams to transmit energy to a node. Since we used ADMM in Chapter A, we also summaris the basics steps of the ADMM method in Section 2.2.

2.1 Wireless Energy Transmission

Let us consider a WET network with one eBS and one energy receiver. The eBS has M

antennas, and the receiver has M

antennas. Let the channel from the eBS to the receiver be H

. When the eBS transmit the energy with power P

with signal s

, then the receiver receives signal

y

= H

s + n,

where n is the noise. Assuming that the noise part are too weak to be harvested, the harvested power of the receiver will be

P

= η|y|

≈ ηs

HH

s ,

where η is the RF-DC conversion rate. In practice, the relationship is non-linear, i.e., the RF-DC conversion rate is not a constant especially when the received power is low, and it may have an saturation effect when the received power is larger than a certain threshold [52]. However, in the thesis, we adopt such a linear model on the energy harvesting module, i.e., the harvested power is proportional to the received power, due to its simplicity and popularity.

To maximize the harvested energy of the receiver, we can solve the following problem:

max

ηs

HH

s (2.1a)

s.t. s

s ≤ P

. (2.1b)

17

18 Preliminaries

It is easy to show that the solution of Problem (2.1) is s = √

P

v

(HH

) [5], where v

(X) denotes the eigenvector corresponds to the dominant (largest) eigenvalue of matrix X.

If we have K energy receivers, and the weight for the harvested energy of the receivers are µ = [µ

, . . . , µ

]

, then the problem to maximize the weighted harvested energy of the nodes is as follows:

max

X

i=1

ηµ

s

H

H

s (2.2a)

s.t. s

s ≤ P

. (2.2b)

The objective function of Problem (2.2) can be turned to that of Problem (2.1) with an equivalent channel ¯H that satisfies ¯H ¯H

= P

µ

H

H

. Therefore, it is straightforward to achieve that the solution is s = √

P

v

( ¯H ¯H

).

2.2 ADMM

ADMM method is widely used to solve a complex convex optimization in a distributed way. Consider a convex optimization in the following form:

min

f (x) + g(z) (2.3a)

s.t. Ax + Bz = c , (2.3b)

where x and z are variables, A, B, c are inputs. Assume that function f and g are convex. The augmented Lagrangian function is

L

(x, z, y) = f(x) + g(z) + y

(Ax + Bz − z) + ρ

2 k Ax + Bz − ck

, with ρ > 0. Then, the ADMM consists of the iterations [49]:

x

= arg min

x

L

(x, z

, y

) z

= arg min

z

L

(x

, z, y

)

y

= y

+ ρ(Ax

+ Bz

− c ) . This form is called unscaled form.

The ADMM method can also be written in a more convenient form by defining a scaled dual variable u = (1/ρ)y. With this scaled dual variable, the iterations of the scaled form become [49]:

x

= arg min

x

f (x) + (ρ/2)kAx + Bz

− c + u

k

z

= arg min

z

g (z) + (ρ/2)kAx

+ Bz − c + u

k

u

= u

+ Ax

+ Bz

− c .

2.2. ADMM 19

There are many nice propositions for the ADMM methods. One basic and general result is provided here. Assume that function f and g are closed, proper, and convex. Also, assume that the unaugmented Lagrangian function

L (x, z, y) = f(x) + g(z) + y

(Ax + Bz − c) has a saddle point. Then, the ADMM iterations satisfy [49]:

• Residual convergence. r

→ 0 as k → +∞, where r

= Ax

+ Bz

− c , i.e., the iterations approach feasible solution.

• Objective convergence. f(x

) + g(z

) → p

as k → +∞, where p

is the optimal value of Problem (2.3), i.e., the objective function of the iterations approach the optimal value.

• Dual variable convergence. y

→ y

as k → +∞, where y

is a dual optimal point.

The ADMM iteration listed above divided the decision variables into two groups,

i.e., x and z. In practice, we can use it to separate the decision variables into multiple

groups. Thus, it has been widely used in distributed model fitting, consensus, and

sharing.

Part II

Included Papers

21