Optimal Networking in Wirelessly Powered Sensor Networkskth.diva-portal.org/smash/get/diva2:1250045/FULLTEXT01.pdf · TRITA-EECS-AVL-2018:64 ISSN 1653-5146 ISBN 978-91-7729-934-9

Optimal Networking in Wirelessly Powered SensorNetworks

RONG DU

Doctoral ThesisStockholm, Sweden 2018

TRITA-EECS-AVL-2018:64ISSN 1653-5146ISBN 978-91-7729-934-9

KTH Royal Institute of TechnologySchool of EECS

SE-100 44 StockholmSWEDEN

Akademisk avhandling som med tillstånd av Kungl Tekniska hogskolan framlaggestill offentlig granskning for avlaggande av teknologie doktorsexamen i natverkoch systemteknik den 19 oktober, 2018 klockan 10:15 i sal D3, KTH Campus,Lindstedtsvagen 5, Stockholm.

© 2018 Rong Du, unless otherwise stated.

Tryck: Universitetsservice US AB

AbstractWireless sensor networks (WSNs) are nowadays widely used for the long-

term monitoring of small or large regions, such as lakes, forests, cities, andindustrial areas. The performance of a WSN typically consists of two aspects: i) themonitoring performance, e.g., the accuracy and the timeliness of the measurementsor 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 tohave the monitoring performance as good as possible, and the lifetime as long aspossible. However, in traditional WSNs, the sensor nodes generally have limitedresources, especially in terms of battery capacity. If the nodes make measurementsand report them frequently for a good monitoring performance, they drain theirbatteries and this leads to a severely shortened network lifetime. Conversely, thesensors can have a longer lifetime by sacrificing the monitoring performance. Itshows the inherent trade-off between the monitoring performance and the lifetimein WSNs.

We can overcome the limitations of the trade-off described above by wirelessenergy transfer (WET), where we can provide the sensor nodes with additionalenergy remotely. The WSNs with WET are called wirelessly powered sensornetworks (WPSNs). In a WPSN, dedicated energy sources, e.g., static base stationsor mobile chargers, transmit energy via radio frequency (RF) waves to the sensornodes. The nodes can store the energy in their rechargeable batteries and use itlater when it is needed. In so doing, they can use more energy to perform the sensingtasks. Thus, WET is a solution to improve the monitoring performance and lifetimeat the same time. As long as the nodes receive more energy than they consume, itis 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 performanceanalysis challenges. Due to the safety issues, the power that the dedicated energysources can use is limited. The propagation of the RF waves suffers high pathlosses. Therefore, the energy received by the sensor nodes is much less than theenergy 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 theenergy consumption on the nodes side. Compared to the traditional WSN scenarioswhere we can only optimize the sensing and data communication strategies, inWPSNs, we have an additional degree of freedom, i.e., the optimization of theenergy transmission strategies. This aspect brings new technical challenges andproblems that have not been studied in the traditional WSNs. Several novel researchquestions arise, such as when and how to transmit the energy, and which energysource should transmit. Such questions are not trivial especially when we jointlyconsider the energy consumption part.

This thesis contributes to answer the questions above. It consists of threecontributions 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. TheeBS has multiple antennas, and it uses energy beamforming to transmit energyto 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 canreduce the energy consumption by applying sleep/awake mechanism. Therefore, wejointly study the deployment of the nodes, the energy transmission of the eBS, andthe node activation. The problem is an integer optimization, and we decouple theproblem into a node deployment problem and a scheduling problem. We provide agreedy-based algorithm to solve the problem, and show its performance in terms ofoptimality.

The second contribution of the thesis starts by noticing that wireless channelstate information (CSI) is important for energy beamforming. The more energythat an eBS spends in channel acquisition, the more accurate CSI it will have, thusimproving the energy beamforming performance. However, if the eBS spends toomuch energy on channel acquisition, it will have less energy for WET, which mightreduce the energy that is received by the sensor nodes. We thus investigate howmuch energy the eBS should spend in channel acquisition, i.e., we study the powerallocation problem in channel acquisition and energy beamforming for WPSNs.We consider the general optimal channel acquisition and show that the problemis non-convex. Based on the idea of bisection search, we provide an algorithm tofind the optimal solution for the single eBS cases, and a closed-form solution forthe case where the eBS uses orthogonal pilot transmission, least-square channelestimation, and maximum ratio transmission for WET. The simulations show thatthe algorithm converges fast, and the performance is close to the theoretical upperbound.

In the third contribution, we consider a joint energy beamforming and datarouting problem for WPSNs. More specifically, we investigate the WPSNs consistingof multiple eBSs, multiple sensor nodes, and a sink node. Based on the receivedenergy, the sensor nodes need to decide how to route their data. The problem aimsat maximizing the minimum sensing rate of the sensor nodes while guaranteeingthat the received energy of each node is no less than that is consumed. Sucha problem is non-convex, and we provide a centralized solution algorithm basedon a semi-definite programming transformation. We extend this approach with adistributed algorithm using alternating direction method of multipliers (ADMM).We prove that the centralized algorithm achieves the optimal energy beamformingand routing, and we show by simulation that the distributed one converges to theoptimal solution. Additionally, for the cases where the energy beamforming optionsare pre-determined, we study the problem of finding the energy that should bespent on each vector. We observe that, if the pre-determined beamforming optionsare 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

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

Keywords: Wireless energy transfer, network lifetime, energy beamforming,IoT, smart cities, sensor networks, scheduling, optimization

SammanfattningTrådlosa sensornatverk (TSN) anvands i stor utstrackning for långtidsover-

vakning av små och stora regioner, såsom sjoar, skogar, stader och industriellaanlaggningar. Prestandan hos ett TSN mats huvudsakligen via två aspekter: i) dessovervakningsprestanda, d.v.s. hur noggranna dess matningar och de skattningardess sensornoder producerar ar; samt, ii) dess livslangd, d.v.s. hur lange natverketkan bibehålla funktionsduglighet. Det ar naturligtvis onskvart att ha så hogovervakningsprestanda samt så lång livslangd som mojligt. Dessa två mål ar dockmotstridiga i traditionella TSN eftersom sensornoderna har begransade resurser,speciellt i termer av batterikapacitet. Om noderna kontinuerligt anvander sinasensorer och rapporterar matningarna, for att uppnå en hog overvakningsprestanda,så draneras snabbt deras batterier och natverkets livstid kommer drastiskt attreduceras. Omvant så kan en lång livstid uppnås på bekostnad av natverketsovervakningsprestanda, om endast sporadiska matningar gors. Detta påvisar dennaturliga avvagningen mellan overvakningsprestanda och livslangd som måste gorasi TSN.

Det ar mojligt att kringgå denna avvagning genom att anvanda trådlosenergioverforing (TEO) till sensornoderna. TSN med TEO kallas trådlost drivnasensornatverk (TDSN). I ett TDSN forser externa energikallor (t.ex. statiskabasstationer och/eller mobila laddare) sensornoderna med energi trådlost viaradiovågor. Noderna kan lagra denna energi i uppladdningsbara batterier ochanvanda den senare vid behov. Detta betyder att TEO kan forbattra bådenatverkets overvakningsprestanda och dess livslangd. I teorin ar det mojligt forett TDSN att ha en oandlig livslangd (om noderna forbrukar mindre energi an detar emot), vilket inte ar mojligt i traditionella TSN.

De fordelar som TDSN ger upphov till i prestandaavvagningen for sensornatverkfor aven med sig fundamentala frågor och utmaningar i termer av deras designoch prestandaanalys. Av sakerhetsskal ar effekten på de externa energikallornabegransad. Vidare går mycket energi till spillo vid trådlos energioverforing medhjalp av radiovågor. Detta betyder att energin som kan tas upp av sensornodernaar mycket mindre an den som utsands vid kallan, och att man darfor bor optimerabåde energitransmission från de externa energikallorna, samt energikonsumtionhos sensornoderna, for att åstadkomma en bra prestanda hos ett TDSN. Dettastår i kontrast till vanliga TSN i vilka man bara kan optimera sensor- ochkommunikationsprotokollen hos noderna. Man har alltså tillgång till en extrafrihetsgrad i TDSN: optimering av energioverforingsprotokollet. Denna aspektmedfor nya tekniska utmaningar och problem som inte tidigare har studerats. Ettflertal forskningsfrågor kan formuleras, såsom: nar och hur ska energi overforas,och vilken eller vilka energikallor ska utfora overforingen? Dessa frågor ar intetriviala att besvara nar man gemensamt bor optimera energikonsumtionen hossensornoderna.

Den har avhandlingen avser besvara ovannamnda frågor.

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I den forsta delen av avhandlingen behandlar vi ett TDSN med en ensamenergibasstation (eBS) och ett flertal sensornoder. Natverkets eBS har multiplaantenner och anvander strålformning for att overfora energi till noderna. Notera attom vi placerar flera sensornoder i narheten av varandra så kan dessa ta emot energisamtidigt från natverkets eBS, vilket kan reducera natverkets energikonsumtiongenom ett synkroniserat standby- och uppvakningsprotokoll. Vi studerar darfor detgemensamma optimeringsproblemet for nodplacering, energioverforing från natver-kets eBS samt nodaktivering. Mer specifikt så erhålls ett heltalsoptimeringsproblemsom vi frikopplar till ett nodplaceringsproblem samt ett schemalaggningsproblem.Vi foreslår en girig algoritm for att losa problemet, och demonstrerar dess prestanda.

I den andra delen av avhandlingen noterar vi forst att den trådlosa kanaltill-ståndsinformationen (KTI, eng: channel state information) ar viktig for ener-gistrålformning. Desto mer energi som en eBS lagger på kanalanskaffning, destoexaktare KTI kommer den att ha, vilket medfor en battre strålformningsprestanda.Dock, om en eBS lagger for mycket energi på kanalanskaffning så kommerenergin den har tillganglig for TEO bli lidande, vilket kan reducera energinsom noderna kan ta emot. Darfor undersoker vi hur mycket energi en eBS borlagga på kanalanskaffning, d.v.s. vi studerar energiallokeringsproblemet mellankanalanskaffning och energistrålformning i TDSN. Forst betraktar vi det allmannaoptimala allokeringsproblemet och visar att det ar icke-konvext. Vi foreslår enalgoritm for att berakna den optimala losningen nar en ensam eBS anvands (baseradpå bisektionssokning), samt en losning på sluten form for fallet då natverkets eBSanvander ortogonal pilottransmission, kanalestimering via minsta-kvadratmetoden,eller maximum-ratio transmission for TEO. Simuleringar visar att algoritmenkonvergerar snabbt, och att dess prestanda ar nara den teoretiska ovre gransen.

I den tredje delen av avhandlingen behandlar vi det gemensamma energistrålform-nings- och datadirigeringsproblemet for TDSN. Mer specifikt så betraktar viTDSN som består av ett flertal eBS och sensorer, samt en sanknod. Baserat påenergin sensornoderna mottar behover de bestamma hur deras data ska dirigeras.Problemet avser att maximera den minimala sensoruppdateringsfrekvensen hosnoderna, medan energin som tas emot av varje nod garanteras vara storre anden mangd som konsumeras. Vi foreslår en centraliserad algoritm for att losadetta icke-konvexa problem, baserad på semidefinit optimering. Vi generaliserar vårmetod till en distribuerad algoritm som anvander alternating direction method ofmultipliers-metoden(ADMM). Vi visar teoretiskt att den centraliserade algoritmenuppnår optimal energistrålformning och datadirigering, och, via simuleringar, attden distribuerade algoritmen konvergerar till den optimala losningen. Vidare,for fallet då energistrålformningen ar forbestamd, studerar vi problemet attbestamma den energimangd som ska allokeras i varje riktning. Vi observerar attom energistrålformningen ar val vald så kan en nara optimal prestanda uppnås.

Sammantaget visar resultaten i den har avhandlingen att TEO kan forlangalivslangden hos TSN, och till och med ge dem en tillrackligt lång livslangd forallmanna långtidsovervakningstillampningar. Våra resultat grundar sig i att vioptimerar TDSN med avseende på energisandning och -mottagning gemensamt.

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Vi ser mojliga framtida tillampningar av våra resultat inom många IoT-system forsmarta stader (t.ex., vattendistribuering och byggnadsovervakning).

AcknowledgmentsFirst of all, I would like to express my sincere appreciation towards my supervisor

Associate Professor Carlo Fischione for his constructive support, guidance, andencouragement. I would like to thank Associate Professor Ming Xiao for beingmy co-advisor, and also Dr. Lazaros Gkatzikis and Dr. Ayca Ozcelikkale for theirpatient guidance and fruitful discussions. Working with them has allowed me todevelop me knowledge substantially.

I would thanks to the people of Network Systems and Engineering departmentand Automatic Control department for building a harmonic and funny environment.Especially, I thank Riccardo Sven Risuleo, Miguel Ramos Galrinho, and SebastianHendrik van de Hoef for providing help in courses, especially in the first few monthswhen I started my PhD in KTH; Alexandros Nikou, Robert Mattila, Pedro MiguelOtao Pereira, Xinlei Yi, Christos Verginis, Manne Henriksson, Peiyue Zhao, SladanaJosilo, 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 Magnusson, Dr. Hadi Ghauch, Jose MairtonBarros da Silva Jr., and Xiaolin Jiang for supportive comments, suggestions, andhelps. I would like to thank Robert Mattila and Dan Pettersson again for theirtranslation and double check of the thesis abstract in Swedish. I am also gratefulfor the assistance and support from the administrators: Connie Linell, Eleni Nylen,Anneli Strom, Hanna Holmqvist, Karin K. Eklund, Gerd Franzon, and SilviaCardenas Svensson.

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

Rong DuStockholm, August 2018

Contents

Contents xiii

List of Figures xvii

List of Tables xxi

List of Acronyms xxiii

I Thesis Overview 1

1 Introduction 31.1 Wirelessly Powered Sensor Networks: Background . . . . . . . . 3

1.1.1 Example: Lakes or coastal regions . . . . . . . . . . . . . 51.1.2 Example: Warehouses . . . . . . . . . . . . . . . . . . . . 5

1.2 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.1 Example 1: WET and sleep/awake activation . . . . . . . 71.3.2 Example 2: Energy beamforming and data routing . . . . 8

1.4 Thesis Contribution . . . . . . . . . . . . . . . . . . . . . . . . . 91.4.1 Node placement and energy provision . . . . . . . . . . . 101.4.2 Power allocation for channel acquisition and energy trans-

mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.4.3 Energy beamforming and data routing . . . . . . . . . . . 13

1.5 Contributions not Covered in This Thesis . . . . . . . . . . . . . 141.6 Summary and Future Work . . . . . . . . . . . . . . . . . . . . . 15

2 Preliminaries 172.1 Wireless Energy Transmission . . . . . . . . . . . . . . . . . . . . 172.2 ADMM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

xiii

xiv Contents

II Included Papers 21

A Optimal Node Deployment and Energy Provision for Wire-lessly Powered Sensor Networks 23A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25A.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27A.3 System model and Problem Formulation . . . . . . . . . . . . . . 30A.4 Node Deployment for Immortal WSN . . . . . . . . . . . . . . . 34

A.4.1 Node deployment sub-problem . . . . . . . . . . . . . . . 34A.4.2 Problem Solution . . . . . . . . . . . . . . . . . . . . . . . 36A.4.3 Performance Analysis and Discussions . . . . . . . . . . . 38

A.5 WET Scheduling and Node Activation . . . . . . . . . . . . . . . 41A.6 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43A.7 Conclusions and Future works . . . . . . . . . . . . . . . . . . . . 48A.8 Appendix: Discussion on g(x) . . . . . . . . . . . . . . . . . . . . 48A.9 Appendix: Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

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

B.1.1 Related Works and Motivations . . . . . . . . . . . . . . . 61B.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 64

B.2 Modelling and Problem Formulation . . . . . . . . . . . . . . . . 65B.2.1 Network Model . . . . . . . . . . . . . . . . . . . . . . . . 65B.2.2 Channel Estimation and Beamforming . . . . . . . . . . . 65B.2.3 Energy Consumption Model . . . . . . . . . . . . . . . . . 68B.2.4 Power Allocation Problem . . . . . . . . . . . . . . . . . . 68B.2.5 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . 69

B.3 Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 69B.3.1 Algorithm Development . . . . . . . . . . . . . . . . . . . 70B.3.2 Performance Analysis . . . . . . . . . . . . . . . . . . . . 71B.3.3 Illustrative Example . . . . . . . . . . . . . . . . . . . . . 73B.3.4 Solution for Linear Energy Harvesting Model . . . . . . . 75B.3.5 Asymptotic Case . . . . . . . . . . . . . . . . . . . . . . . 76

B.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . 77B.4.1 Simulation Set-ups . . . . . . . . . . . . . . . . . . . . . . 78B.4.2 Convergence Tests . . . . . . . . . . . . . . . . . . . . . . 78B.4.3 Comparing Non-linear and Linear Models . . . . . . . . . 79B.4.4 Performance Tests . . . . . . . . . . . . . . . . . . . . . . 80

B.5 Conclusions and Future Works . . . . . . . . . . . . . . . . . . . 84B.6 Appendix: Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

C Towards Immortal Wireless Sensor Networks by OptimalEnergy Beamforming and Data Routing 89

Contents xv

C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91C.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94C.3 System Model and Problem Formulation . . . . . . . . . . . . . . 96C.4 Centralized Solution Approach . . . . . . . . . . . . . . . . . . . 98

C.4.1 Algorithm based on SDP . . . . . . . . . . . . . . . . . . 99C.4.2 Pre-determined beamforming vectors . . . . . . . . . . . . 104

C.5 Distributed Approach . . . . . . . . . . . . . . . . . . . . . . . . 106C.5.1 Distributed solution for optimal beamforming . . . . . . . 106C.5.2 Distributed solution for pre-determined beamforming . . . 109

C.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . 111C.6.1 Centralized case . . . . . . . . . . . . . . . . . . . . . . . 112C.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 currentelectricity by rectenna. . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 An example of the wirelessly powered sensor network with multipleenergy base stations, sensor nodes, and a sink. . . . . . . . . . . . . 5

1.3 A possible solution of using wirelessly powered sensor network forlake monitoring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 The comparison of our scheme with non optimal deployment and nonoptimal energy transmission. . . . . . . . . . . . . . . . . . . . . . . 11

1.5 Comparison of our algorithm (Algorithm 4 in Chapter B) to otherapproaches (fixed power allocation, random power allocation) andan 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-determinedbeamforming, no beamforming, and the cases without routing. . . . 14

A.1 A wirelessly powered sensor network with one energy base stationand multiple sensors. The sensors in a region take turn to makemeasurements and transmit the data. . . . . . . . . . . . . . . . . . 26

A.2 The probability of wirelessly powered sensor networks to be immortalwith different field size N and sampling rates λ. . . . . . . . . . . . . 43

A.3 Comparison of the required number of sensor nodes achieved bydifferent algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

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

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

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

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

motivating example. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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xviii List of Figures

A.9 The second motivating example, with the consideration of shadowingof nodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

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

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

data transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67B.3 The PEB gain and its approximation at different pilot power P p. . 74B.4 Convergence of Algorithm 4 (non-linear energy harvesting case). . . 78B.5 Convergence of Algorithm 4 (linear energy harvesting case). . . . . . 79B.6 The network sensing rates achieved by Algorithm 4, and the relative

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

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

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

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

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

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

antennas, achieved by optimal energy beamforming, pre-determinedbeamforming, and no beamforming, with N = 15,K = 100 . . . . . 112

C.4 Comparison of minimum sampling rate with varying number ofantennas, achieved by optimal energy beamforming, pre-determinedbeamforming, and no beamforming, with N = 15,K = 2.8 . . . . . . 113

C.5 Comparison of minimum sampling rate with varying number ofsensors, achieved by optimal energy beamforming, pre-determinedbeamforming, and no beamforming, with M = 100,K = 100 . . . . . 114

C.6 Comparison of minimum sampling rate with varying number ofsensors, achieved by optimal energy beamforming, pre-determinedbeamforming, and no beamforming, with M = 100,K = 2.8 . . . . . 115

C.7 Comparison of the minimum sampling rates with varying numberof sensors, achieved by optimal energy beamforming, pre-determinedbeamforming, and no beamforming from four chargers, with M=100,K=100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

C.8 Comparison of the minimum sampling rates with varying number ofsensors, achieved by optimal energy beamforming, pre-determinedbeamforming, 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 ofchargers and antennas achieved by optimal energy beamforming andno beamforming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

C.10 The relative difference of the minimum sampling rate achieved bythe distributed approach (Algorithm 7) . . . . . . . . . . . . . . . . 120

C.11 The relative difference of the minimum sampling rate achieved bythe 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. . . . . . . . . . . . 30A.2 Major notations used in Chapter A. . . . . . . . . . . . . . . . . . . 31B.3 Major notations used in Chapter B. . . . . . . . . . . . . . . . . . . 66C.4 Major notations used in Chapter C. . . . . . . . . . . . . . . . . . . 98C.5 Simulation parameters. . . . . . . . . . . . . . . . . . . . . . . . . . 111

xxi

List of Acronyms

ADMM Alternating Direction Method of MultipliersBS Base StationCSI Channel State InformationDC Direct CurrenteBS energy base stationEH Energy HarvestingIoT Internet of ThingssMIMO Multiple-input and Multiple-outputPEB Pilot, Estimation, and Beamforming SchemeRF Radio FrequencySDP Semi-definite ProgrammingWET Wireless Energy TransferWPCN Wirelessly Powered Communication NetworkWPSN Wirelessly Powered Sensor NetworkWSN Wireless Sensor Network

xxiii

Part I

Thesis Overview

1

Chapter 1

Introduction

Wireless networks are an important part of our daily life, with applications includingthe use of mobile phones to convey and retrieve messages and information, the useof blue-tooth networks for short range personal network communication, the use ofWiFi to connect our laptop to Internet, the use of wireless sensor networks (WSNs)to monitor the living environment or the industrial process. With the growingdemand 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 powerdevices, such as sensor nodes and some Internet of Things (IoT) devices, their powerconsumption 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 ideaof energy harvesting [1,2] and wireless energy (or power) transfer (WET) [3–5] givesus a way to remotely provide additional energy to the devices, and thus they canhave 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 providemore energy to the wireless devices and how the devices use the energy to improvethe network performance. In this thesis, we focus on such a question in the networkinstance 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 thehumidity, 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 ofthe crops in smart agriculture [17], and the production line in Industry 4.0 (smartindustry) [18]. In most of such applications, the WSNs are designed for long termmonitoring. Therefore, the lifetime is one of the most important metrics of WSNs

3

4 Introduction

!"#$ %&' ()**$+, -

.$/*$00)10$+2,3

*+)045!**$+

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

to be considered. Therefore, to prolong network lifetime of the traditional WSNswithout the capability of battery recharging, the key method is to reduce the energyconsumptions 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 sensornodes cannot recharge their battery, the energy will run out and the network willeventually expire.

To address such a problem of energy depletion, we can use the idea of energyharvesting. In an energy harvesting sensor network, the nodes harvest ambientenergy, 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 thatare broadcasted from TV towers [28] or different wireless devices. The nodes cansave 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 issustainable and green. However, due to that the source of ambient energy is hardto control or even not controllable [29], the prediction of the arrival of the energyis important for the scheduling the sensor nodes. If we had the knowledge of theenergy arrivals, the scheduling is off-line [30,31]. However, in practice, we only havepartial information of the arriving energy, and the scheduling is on-line [32, 33].Therefore, the performance of the scheduling is usually sub-optimal compared tothe off-line one. We can observe that, the major limitation of energy harvestingis that the arriving of the energy is inconsistent and thus the performance of theWSN is inconsistent.

To have a more consistent network performance, we should try to controlthe energy source. Among the different types of energy, RF wave is the easiestto generate and control. This gives us the motivation to charge the nodes withRF waves remotely. More specifically, we use base stations (BSs) to generate RFwaves. 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 theelectromagnetic energy into direct current (DC) electricity, as shown in Figure 1.1.The nodes store the energy into their capacitor or rechargeable battery. The processof 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 multipleenergy base stations, sensor nodes, and a sink.

or wireless power transmission (WPT) [3, 5], and such a kind of sensor networkis called WPSN. To increase the energy that is received by the nodes, we can forexample schedule energy transmission time, the energy transmission targets, andthe 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 theenergy received by the nodes. It means that we have an additional degree offreedom to control and to improve the performance of the network. Therefore, weshould optimize the WPSN performance by jointly consider energy consumptionand energy provision. However, this additional degree of freedom also makesthe problems more challenging than the cases where we only consider energyconsumption. The methods to solve such problems are not trivial, and this thesispresents our study on these problems and the corresponding contributions. In thefollowing, we provide some examples of WPSN.

1.1.1 Example: Monitoring of lakes or coastal regionsTo monitor the water quality and the fluid dynamic of a lake or a coastal region, wecan 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, wecan build eBSs at the coasts/shores, as shown in Figure 1.3. The eBSs charge thesensor nodes such that the nodes always have sufficient energy to perform sensing.

1.1.2 Example: Monitoring of warehousesIn a smart warehouse, sensors and radio-frequency identification tags can providethe information of the exact locations of any products. With small energy basestations deployed in the warehouse, the sensor nodes can be charged wirelessly,meanwhile the tags can transmit the information by reflecting the energy sent fromthe eBSs.

6 Introduction

Figure 1.3: A possible solution of using wirelessly powered sensor network tomonitor the water quality of Lake Malaren, 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 fromthe BSs to the devices are through air. Thus, the strength of the RF waves decaygreatly due to path losses, or shadowing. Notice that the transmitting power of theBSs cannot be arbitrarily high due to the safety issues [36, 37]. As a result, theenergy received by the devices may be very limited. Recall that the received RFwaves are converted into DC electricity through rectenna circuit, whose conversionrate is small when the input power is small. Therefore, the harvested energy is evenless, and it is one challenge to overcome, such that more energy can be harvestedby the devices.

One possible method to overcome the problem is to use multiple antennas atthe BSs. It allows the BSs to form energy beams [38,39] towards the target devicessuch that the energy is more concentrated. In this way, less energy will be wastedon the other directions where there are no target devices. This process is calledenergy beamforming, and it determines how much power can be received at thedevices. Therefore, it is a vital process for WPCNs, and it is challenging to performa good energy beamforming. One reason is that, to perform beamforming, we shouldhave the information of the channel from each BS to each device [39–41]. Thus, oneinteresting problem is to design the channel acquisition, such as who should transmitpilots, how much power it should spend, how to perform channel estimation. Thisthesis 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 transmissionprocess is optimal, if the energy consumption is not, the harvested energy mightbe wasted and thus the WPSNs performance will be suboptimal. Therefore, tooptimize the WPSNs performance, one should jointly consider both processes. Itnaturally introduces new variables and constraints, and thus makes the problemsmore 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 wewant to optimize the performance such as the sensing accuracy [45], the amount ofmeasured data [46], and the lifetime of the network [47]. As a result, there are someminor differences in problem formulations and models. Some results for WPCNsmay not be applied in WPSNs directly. This also leads to some challenges.

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

1.3 Problem Formulation

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

maxx,y

F (x) (1.1a)

s.t. Eri = Gi(y) ,∀i ∈ N (1.1b)

Eci = Hi(x) ,∀i ∈ N (1.1c)

Eci ≤ Er

i ,∀i ∈ N (1.1d)x ∈ X , y ∈ Y , (1.1e)

where N is the index set of the sensor nodes, x corresponds to the energyconsumption 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 theenergy 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 andthe energy provision. We provide two examples in the following.

1.3.1 Example 1: WET and sleep/awake activationConsider a case where we have N regions of interest to monitor. In each region i,i = 1, . . . N , there are ni number of sensor nodes monitoring the same phenomena,therefore, the nodes in the same region can take turns to sense and to transmit themeasurement. In such a way, the energy consumption of the sensor nodes is reduced.The time is divided into timeslots. We denote binary variable xij(t) the activationof the j-th node (we denote it by vij) in region i in timeslot t, i.e., xij(t) = 1 if it isawake in timeslot t. For the monitoring purpose, each region should have at leastone active node. Suppose that the monitoring of region i requires a sensing rate wi

8 Introduction

(bits/s), and the energy consumption to transmit one bit of measurement to thesink from region i as ai. Besides transmitting the measurement, the static energyconsumption of the nodes are c. Then, the energy consumption of an active nodevij is aiwi + c. Thus, Constraint (1.1c) becomes Ec

ij(T ) =∑Tt=1[aiwixij(t) + c].

We use one eBS to transmit energy to the nodes. Suppose that the eBS uses aWET scheme that it transmits energy to one region in a timeslot. Then, we usebinary variable yi(t) to denote the transmission of energy, i.e., yi(t) = 1 if andonly if the eBS transmits energy to the nodes in region i, and all the nodes inthat region can harvest the energy. For simplicity, we normalize the transmissionpower of the eBS to be 1. Then, Constraint (1.1b) is Er

ij =∑Ti=1 αiyi(t), where αi

corresponds to the path loss and energy conversion rate. Let Eij(0) be the initialenergy of vij . Then, Constraint (1.1d) becomes Eij(0) + Ec

ij(T ) ≤ Erij(T ),∀T .

Recall that, for any region i, at least one node should be active. In additional, theeBS transmits energy to a region in a timeslot. Then, Constraint (1.1e) becomes∑ni

j=1 xij(t) ≥ 1,∀i,∀1 ≤ t ≤ T , and∑Ni=1 yi(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 deploymentof the sensor nodes. Therefore, the problem becomes more challenging. We presentthe 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 onthe received energy, the sensor nodes determine the sensing rate and the routing ofthe measurements. Therefore, the variable x consists of two parts, i.e., the sensingrate of each node w = [w1, . . . , wN ] and the routing q. y = [UH

1 , . . . ,UHNET

]His the energy beamforming covariance matrix of the nodes, where yH1 is theconjugate transpose of y1, and NET is the number of eBSs. Then, we can formulateConstraint (1.1c) as Ec

i = Biq, where Bi corresponds to the energy consumptionof node i to transmit a bit of data to its neighboring nodes. We formulateConstraint (1.1b) as Er

i = η∑NETj tr [KjiUi], where Kji is the covariance matrix of

the channel from BS j to node i, and tr is the trace operation. We have additionalconstraint on x from the flow conservation of the routing, and we can formulateit as Aq + w = 0. The constraint on y is the power constraint of the energybeamforming, and it is tr[Ui] ≤ P , where P is the power that each eBS has. We wantto maximize the minimum sensing rate of the nodes. Then the objective functionis F (x) = min{w1, . . . , wN}. We study such a problem in the first contribution.We propose a centralized algorithm and also a distributed algorithm to achieve theoptimal 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 fromthe networking point of view. It consists of three chapters, each of which studies aspecific instance of Problem (1.1), i.e., (i) energy beamforming and data routing,(ii) power allocation for channel acquisition and energy transmission, and (iii) nodeplacement and energy provision. The chapters are based on the following papers orsubmitted manuscripts1:

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

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

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

[J2]Rong Du, Hossein S Ghadikolaei, and Carlo Fischione, “Wirelessly-poweredSensor 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 andEnergy Beamforming in Wirelessly Powered Sensor Networks,” in Proceedingsof IEEE International Conference on Communications (IEEE ICC) (IEEEWorkshop on Energy Harvesting Wireless Communications), 2018.

[J3]Rong Du, Ayca Ozcelikkale, Carlo Fischione, and Ming Xiao, “TowardsImmortal Wireless Sensor Networks by Optimal Energy Beamforming andData Routing,” IEEE Transactions on Wireless Communications, vol. 17,no. 8, pp. 5338–5352, 2018.

[C4]Rong Du, Ayca Ozcelikkale, Carlo Fischione, and Ming Xiao, “Optimal EnergyBeamforming and Data Routing for Immortal Wireless Sensor Networks,” inProceedings of IEEE International Conference on Communications (IEEEICC), 2017.

The contribution of our work is summarized in Table 1.1.

1B: Book chapter; C: Conference; J: Journal;

10 Introduction

Table 1.1: Contribution of the chapters.

WET Sensor nodes Method Optimality

Chapter A Energy schedulingNode deployment,Activation

Greedy Global

Chapter BChannelacquisition

− 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 thenodes in Chapter A. This chapter is based on the work in J1, C1, and C2. TheeBS in the WPSN forms energy beams to charge the sensor nodes, and the nodesuse the received energy for sensing and data transmission. When the eBS does nothave enough power to charge the network, the WPSN may not be able to monitoras long as possible. In such a case, we need to reduce the energy consumption ofthe nodes and increase the harvest energy of the nodes. This can be fulfilled bydeploying additional sensor nodes to monitor the same target. More specifically,the nodes that monitor the same target can take turns to measure and transmitthe information. Therefore, the actual sensing rate of each node is reduced, and thustheir energy consumption rate is reduced. Since the nodes that monitor the sametarget are close to each other, they can harvest the energy from the eBS at the sametime. 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 nodeactivation are also important factors in terms of WPSN lifetime. Therefore, weinvestigated a joint node deployment and energy provision scheduling problem inthe chapter. We minimized the nodes to deploy whilst ensuring that the WPSNalways has enough energy to perform the monitoring application. The formulatedproblem is an integer programming with non-linear constraints, which makes theproblem challenging. To solve the problem, we first analyzed the necessary conditionon the node deployment, such that the WPSN be immortal. Based on this necessarycondition, we decoupled the original problem into a node deployment problem anda scheduling problem. For the node deployment problem, we developed a greedybased algorithm and showed that it achieves the optimal solution of the deploymentproblem. Based on the solution of the deployment problem, we proposed a simplescheduling algorithm for energy transmission and node activation. We proved thatwith the proposed deployment and scheduling, the WPSN always has enough energyfor the monitoring requirement.

In the simulation, we show by Figure 1.4 that, if the WET is not optimized, thelifetime of the WPSN may be very limited. Also, even when the WET is optimized,

1.4. Thesis Contribution 11

1 10 100 1000 10000 1000000

0.2

0.4

0.6

0.8

1

timeslots

per

cen

tag

e o

f re

sid

ual

en

erg

y

our schemenon opt. deploynon 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 atdifferent time slots. It shows that with our scheme the sensor nodes always haveenough energy to perform the monitoring tasks, whereas under other non optimalscheme, 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 outeventually. Besides, we showed that the number of nodes to be deployed accordingto our algorithm is close to the lower bound. The number of nodes achieved by ouralgorithm is approximately 10% less than the one achieved by an algorithm basedon relaxation.

My Contribution: As the first author, I formulated and solved the studiedproblems. In addition, I run the simulations and wrote the manuscript. The otherauthors contributed through serving the roles of supervision of the first author, bydetailed discussions on the technical issues. They also contributed in the structureof the papers.

1.4.2 Power allocation for channel acquisition and energytransmission

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 itspends, the better CSI it can achieve, which makes the energy beamforming moreefficient. However, if the eBS spends too much energy in channel acquisition, itcan transmit less energy to the nodes. Therefore, there is a trade-off in spendingenergy for channel acquisition and energy transmission. Based on this observation,

12 Introduction

−90 −85 −80 −75 −70 −65 −60 −55 −50 −450

10

20

30

40

50

noise level (dBm)

netw

ork

sens

ing

rate

(bi

ts/s

)

Alg. 4Fixed PARandom PAUpper bound

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

we studied the power allocation for channel acquisition and energy transmissionin Chapter B. It is based on the work J2 and C3. Noticing that there are manydifferent way for channel acquisition, we tried to not limit our study to a specificchannel acquisition. Therefore, we generalized the gain of channel acquisition as aconcave and monotone increasing function of power. We also generalize the energyharvesting model by a monotone increasing function, such that our results are validfor non-linear energy harvesting models. We formulated the optimization problemand showed that it is non-convex. We provided a bisection searching based algorithmthat finds the optimal solution. For a special case where the eBS uses an orthogonalpiloting, least square estimation, and maximum ratio transmission, we provide aclosed-form optimal solution. To show the performance of our algorithms, we alsoprovided an upper bound of the sensing rate.

The simulation results in Figure 1.5 show that our algorithms outperform thecase where the power for channel acquisition is a fixed value. Also, the performanceis close to the upper bound when the noise level is low. In addition, we observethat, when the noise level is high, the eBS needs to spend more energy in channelacquisition. Therefore, the energy that the eBS can transmit is less than the casewhere the noise level is low. As a result, the nodes receive less energy such that thesensing 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 otherauthors contributed through serving the roles of supervision of the first author, bydetailed discussions on the technical issues. They also contributed in the structureof 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 jointenergy beamforming and data routing problem. More specifically, the multiple eBSsform energy beams to charge the sensor nodes, and the nodes consume the receivedenergy in sensing and data transmission. Instead of direct data transmission, thesensor nodes relay the data to save power. We need to find the maximum sensingrate of the nodes by controlling the energy beamforming of the eBSs and the datarouting of the sensor nodes, whilst ensuring that the WPSN be immortal, whichmeans that the average consumed energy of each node should be no more than theaverage harvested energy. Such a requirement gives a non-convex constraint, whichmakes the optimization problem challenging. To solve the problem, we turned itinto a semi-definite programming (SDP) problem [48]. We proved the strong dualityof 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 theoriginal problem. To further reduce the computational complexity of the problem,we also considered the distributed solution based on Alternating Direction Methodof Multipliers (ADMM) [49]. We also considered the cases where the beamformingvectors are pre-determined, but the power and time duration of these beamformingvectors are to be optimized. We called it pre-determined beamforming. For suchcases, we also proposed a centralized algorithm and a distributed algorithm to solvethe problem.

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

My Contribution: As the first author, I formulated and solved the studiedproblems. In addition, I run the simulations and wrote the manuscript. The otherauthors contributed through serving the roles of supervision of the first author bydetailed discussions on the technical issues. They also contributed in the structureof the papers.

14 Introduction

5 10 15 20 250

5

10

15

20

25

30

35

Number of sensors

Ave

rag

e m

inim

um

sam

plin

g r

ate

(kb

its/

s)

Opt. BFPre. BFNo BFOpt. BF No Rout.Pre. BF No RoutNo BF No Rout.

Figure 1.6: Comparison of minimum sampling rate with varying number ofsensors, achieved by our optimal energy beamforming, pre-determined beamforming,no beamforming, and the cases without routing. It shows that the performance ofthe pre-determined beamforming is close to the optimal beamforming, and they aremuch better than the case with no energy beamforming. In addition, the routing alsoimproves the network performance by allowing the nodes to save energy by relayingdata.

1.5 Contributions not Covered in This Thesis

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

[J4]Rong Du, Lazaros Gkatzikis, Carlo Fischione, and Ming Xiao, “EnergyEfficient Sensor Activation for Water Distribution Networks Based on Com-pressive Sensing,” IEEE Journal on Selected Areas in Communications (IEEEJSAC), 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 onControl 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 (IEEEICC), 2015.

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

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

1.6 Summary and Future Work

In this thesis, we considered the optimization of WPSNs in terms of monitoringfrom the networking perspective. With the WET technology, we are able to provideenergy to the sensor nodes remotely, such that the network lifetime is sufficientlylong. While WET can provide more energy to the sensor nodes such that themonitoring 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 nodesconsume energy based on the received energy from the eBSs. Compared to thetraditional WSN without WET, the problems in WPSNs are more difficult due tothe additional variables to optimize, and the additional constraints. We investigateda joint node deployment and energy transmission scheduling problem, a powerallocation problem for channel acquisition and energy beamforming, and a jointrouting and energy beamforming problem.

In our first work, we provided a solution on deploying additional nodes to makethe WPSN immortal in the cases that the power of the eBS is limited. In our secondwork, we investigated the trade off of using more energy in channel acquisitionand in energy transmission. In our third work, we showed the benefits of jointlyoptimizing the data routing and energy beamforming of the WPSN. In addition, wefound out that our pre-determined energy beamforming scheme is a good approachwith 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 theWPSN performance by the joint consideration of improving energy transmissionand reducing energy consumption. For different problems, we have different solutionapproaches, which might bring some insights when one study the optimization ofWPSN from other perspectives. The approaches are not complex and are easy toimplement.

1.6.1 Future WorkThere are many interesting ideas, problems, and challenges that are left for futureinvestigations. 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 theenergy 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 moreenergy. 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 usingdata compression, MAC protocols. Therefore, we can consider these factors withenergy transmission. For example, the nodes can decide whether they should staysilent to harvest energy, or to sleep, or to transmit data according to the WETscheduling and the remaining battery they have. Such a problem can be formulatedas a MAC problem for WPSN. The problem will be more challenging when multipleenergy saving approaches are jointly considered with WET. Besides, for differentobjectives, such as the lifetime of the WPSN and the estimation accuracy of theWPSN, the corresponding solution approaches may be different and worth to study.

Channel acquisition

To perform energy beamforming, CSI is required in practice. For traditional WPCNsystems, there are several ways to get the CSI. In the thesis, we consider the casewhere the eBS transmits pilots to the sensor nodes, and the sensor nodes providefeedback to the eBSs. We have a closed-form solution for a special case, wherethe eBS uses orthogonal pilot transmission and least-square channel estimation onthe channel. It is interesting to study the closed-form solution of other channelacquisition schemes. Besides, the other way of channel acquisition is that the nodestransmit pilots and the eBSs estimate the channel [40]. In this case, the sensor nodesneed to allocate the power for pilot transmission and data transmission. Thus, theproblem would be a little bit different to the case studied in the thesis. It is worthinvestigating which scheme is more reasonable for the WPSNs, and optimize thesystem parameters.

WPSN with energy harvesting

Recall that the sensor nodes can also harvest ambient energy. Thus, the nodesin a WPSN can also harvest the ambient energy. In this case, the nodes canschedule their consumptions based on the WET transmission, and also the expectedenergy that they can harvest from the environment. Then, there will be somerandomness 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 chooseto use black-scattering communication to transmit their data. This is also aninteresting direction to study.

Chapter 2

Preliminaries

This chapter gives some essential elements of the background theory used in thethesis. Section 2.1 briefly describes how a base station forms energy beams totransmit energy to a node. Since we used ADMM in Chapter A, we also summaristhe 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 eBShas Mt antennas, and the receiver has Mr antennas. Let the channel from the eBSto the receiver be HMt×Mr . When the eBS transmit the energy with power P t withsignal sMt×1, then the receiver receives signal

yMr×1 = HH 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 r = η|y|2 ≈ ηsHHHH 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 poweris low, and it may have an saturation effect when the received power is larger thana certain threshold [52]. However, in the thesis, we adopt such a linear model on theenergy harvesting module, i.e., the harvested power is proportional to the receivedpower, due to its simplicity and popularity.

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

maxs

ηsHHHH s (2.1a)

s.t. sH s ≤ P t . (2.1b)

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18 Preliminaries

It is easy to show that the solution of Problem (2.1) is s =√P tvmax(HHH) [5],

where vmax(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 ofthe receivers are µ = [µ1, . . . , µK ]T , then the problem to maximize the weightedharvested energy of the nodes is as follows:

maxs

K∑i=1

ηµisHHiHHi s (2.2a)

s.t. sH s ≤ P t . (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 HHH =

∑Ki=1 µiHiHH

i . Therefore, it isstraightforward to achieve that the solution is s =

√P tvmax(HHH).

2.2 ADMM

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

minx,z

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 areconvex. The augmented Lagrangian function is

Lρ(x, z, y) = f(x) + g(z) + yT (Ax + Bz− z) + ρ

2‖Ax + Bz− c‖22 ,

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

xk+1 = arg minxLρ(x, zk, yk)

zk+1 = arg minzLρ(xk, z, yk)

yk+1 = yk + ρ(Axk+1 + Bzk+1 − 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 ofthe scaled form become [49]:

xk+1 = arg minx

(f(x) + (ρ/2)‖Ax + Bzk − c + uk‖2

2)

zk+1 = arg minz

(g(z) + (ρ/2)‖Axk+1 + Bz− c + uk‖2

2)

uk+1 = uk + Axk+1 + Bzk+1 − c .

2.2. ADMM 19

There are many nice propositions for the ADMM methods. One basic andgeneral 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) + yT (Ax + Bz− c)

has a saddle point. Then, the ADMM iterations satisfy [49]:

• Residual convergence. rk → 0 as k → +∞, where rk = Axk + Bzk − c, i.e.,the iterations approach feasible solution.

• Objective convergence. f(xk) + g(zk) → p∗ as k → +∞, where p∗ is theoptimal value of Problem (2.3), i.e., the objective function of the iterationsapproach the optimal value.

• Dual variable convergence. yk → y∗ as k → +∞, where y∗ is a dual optimalpoint.

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 multiplegroups. Thus, it has been widely used in distributed model fitting, consensus, andsharing.

Part II

Included Papers

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