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Time synchronization and scheduling in underwater wireless networks

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Time synchronization and scheduling in underwater wireless networks

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Content TIME SYNCHRONIZATION AND SCHEDULING IN UNDERWATER WIRELESS NETWORKS by Pai-Han Huang A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements of the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) August 2010 Copyright 2010 Pai-Han Huang Dedication Dedicated to my father. Thank you for giving me the condence and courage to pursue my dream, and the fascinating experience I can cherish through my life| thank you. Also dedicated to my wife. This dissertation cannot be done without your unselsh support, and thank you for the commitment to live and love with me. ii Acknowledgments The path to pursue a doctorate degree is never at to me. It requires so much knowledge and so many skills that I was not equipped with when rst I stepped into USC. The frustration of progress, and the astonishment brought by other re- searchers' achievements, ever made me lose my faith, and I hesitated to continue my study. I am so fortunate to have my advisor, Bhaskar Krishnamachari, who guided me through the darkness on my path of research. I greatly appreciate his generous support. His wisdom of life not just warms my heart, but also becomes the bedrock for my exploration ahead. I'd like to thank Prof. Michael Neely for his feedback as a committee, and time to meet with me during my course of PhD. Thanks to Prof. David Kempe, who provided me guidance and direction of my research. I'd also like to thank Prof. Anil Kumar, who took time and guided m research. Thanks also to Prof. Jay Kuo and Prof. Cauligi Raghavendra, for their comments to my work and as the committee members of my dissertation proposal. I'd like to appreciate Ashwin Sridharan for his valuable comments, which greatly improve the quality of my submitted work. Thanks to Ying Chen and Yi Gai, for their contribution on our work and comments to the writing. I extend a special thank you to Chih-Ping Li. He helped me to rene my research direction, and encouraged me during my research at USC. I owe gratitude to ANRG members; Scott Moeller, Amitabha Ghosh, Joon Ahn, Hua Liu, Yi Wang, Sundeep Pattem, iii and Maheswaran Sathiamoorthy. They have taught me a great deal and brought me so much fun during our work together. I also like to thank my sisters, Wen-Hsin Huang and Chia-Wen Huang. Their encouragement, prayer, and care for my father has been a strong support for me to continue my study in the US. I appreciate my in-laws in Taiwan. Thank you for letting your precious daughter, Shu-Ling, to stay with me. Finally, I'd like to acknowledge my daughter, Emma, and my son, Ethan. Their smiles and cheer make me forget all unhappiness and sustain me to the end of this happy journey! iv Table of Contents Dedication ii Ackowledgments iii List of Tables vii List of Figures x Abstract xi Chapter 1: Introduction 1 1.1 Overview of UWASN . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Characteristics of Wireless Sensor Networks . . . . . . . . . 2 1.1.2 Characteristics of Acoustic Channel . . . . . . . . . . . . . . 4 1.1.3 UWASN Architecture . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Time Synchronization Support for UWASN . . . . . . . . . . . . . . 9 1.4 Link Scheduling in a Single Broadcast Domain UWASN . . . . . . . 12 1.5 Random Access Scheme for UWASN . . . . . . . . . . . . . . . . . 15 1.6 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Chapter 2: Related Work 18 2.1 Time Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Link Scheduling and Medium Access for UWASN . . . . . . . . . . 25 Chapter 3: Time Synchronization for UWASN 31 3.1 Pair-wise Synchronization Error Analysis . . . . . . . . . . . . . . . 36 3.1.1 Analysis of One-way Dissemination Scheme . . . . . . . . . 36 3.1.2 Analysis of Two-way Exchange Scheme . . . . . . . . . . . . 40 3.1.3 Analysis of Hybrid Scheme . . . . . . . . . . . . . . . . . . . 41 3.1.4 Analysis of Receiver-Receiver Scheme . . . . . . . . . . . . . 46 3.1.5 Analysis of Multiple Two-way Exchange Scheme . . . . . . . 47 3.2 Analysis of Synchronization Error under Multi-hop Situations . . . 49 3.2.1 Denitions and Assumptions of Analysis . . . . . . . . . . . 49 3.2.2 Propagation Error Without Relative Oset Compensation . 50 3.2.3 Propagation Error With Relative Oset Compensation . . . 56 v 3.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3.1 Experimental Setup for Collection of Time-Stamp Traces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3.2 Multi-hop Error Calculation . . . . . . . . . . . . . . . . . . 63 3.3.3 Illustrations of Multi-hop Error Calculation . . . . . . . . . 64 3.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.4.1 Predicted outcomes . . . . . . . . . . . . . . . . . . . . . . . 66 3.4.2 Experiment Results and Discussion . . . . . . . . . . . . . . 66 3.4.3 Variance Comparison Between Hybrid and Two-way Scheme 72 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Chapter 4: Link Scheduling in UWASN 77 4.1 Algorithmic Complexity . . . . . . . . . . . . . . . . . . . . . . . . 78 4.1.1 NP-Hardness Proof . . . . . . . . . . . . . . . . . . . . . . . 79 4.1.2 Approximability Result . . . . . . . . . . . . . . . . . . . . . 83 4.2 Findings from Applying a Complete SAT Solver . . . . . . . . . . . 85 4.2.1 SAT Problem Transformation of Time-Slotted Transmission Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.2.2 Results of Equivalent SAT Problems . . . . . . . . . . . . . 87 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Chapter 5: Random Access in UWASN 89 5.1 Performance Analysis of Uniform DRT Scheduler . . . . . . . . . . 90 5.1.1 System Modeling . . . . . . . . . . . . . . . . . . . . . . . . 90 5.1.2 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . 92 5.1.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.2 Optimal DRT Scheduler . . . . . . . . . . . . . . . . . . . . . . . . 97 5.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 97 5.2.2 Characteristics of Optimal DRT Scheduler . . . . . . . . . . 98 5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Chapter 6: Conclusions and Future Work 107 Bibliography 110 vi List of Tables 3.1 Propagation error under dierent synchronization schemes with rel- ative oset error compensation . . . . . . . . . . . . . . . . . . . . . 67 3.2 Propagation error under dierent synchronization schemes without relative oset error compensation . . . . . . . . . . . . . . . . . . . 67 vii List of Figures 1.1 An example UWASN consisted of two acoustic links. In this net- work, due to the high propagation delay of acoustic communica- tions, we can schedule both links simultaneously without incurring collision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2 An example UWASN consisted of three acoustic links. Because of the high propagation delay, we need at least four time slots in order to schedule each link once. . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Message timelines for one-way synchronization scheme. The in- tersection of a horizontal line and an arrow represents the time instance of the corresponding transmission taking place. The left most and right most end of the horizontal line represents the earliest and latest time instance, respectively. . . . . . . . . . . . . . . . . 36 3.4 Message timelines for two-way synchronization schemes . . . . . . 40 3.5 Illustration of synchronization errors with (a) one-way and (b) two- way schemes. The dotted and solid line represents the relation of estimated and actual clock readings between reference node and un-sync node, respectively. . . . . . . . . . . . . . . . . . . . . . 43 3.6 Message timelines for hybrid synchronization schemes. . . . . . . 43 3.7 Message timelines for receiver-receiver (RBS) synchronization schemes 46 3.8 Message timelines for multiple two-way synchronization schemes . 48 3.9 An example scenario for doing synchronization in a multihop net- work using one-way scheme. . . . . . . . . . . . . . . . . . . . . . 51 3.10 An example scenario for doing synchronization in a multihop net- work using two-way scheme. . . . . . . . . . . . . . . . . . . . . . 53 3.11 An example scenario for doing synchronization in a multihop net- work using hybrid scheme. . . . . . . . . . . . . . . . . . . . . . . 55 viii 3.12 Trace based simulation results showing multi-hop error propaga- tion for one-way, two-way and hybrid schemes with inter-sync error compensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.13 Trace based simulation results showing multi-hop error propagation for one-way, two-way and hybrid schemes without inter-sync error compensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.14 Variance comparison between two-way and hybrid scheme in a 19- hop network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.15 Variance comparison between two-way and hybrid scheme in a 5- hop network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.16 Construction of a gadget, such that each node in graphG is mapped to a pair of nodes in the new graph H, with an edge of length a between them. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.17 In G = (V;E), if there exists an edge uv2 E, then we create two edges with length of a in H. . . . . . . . . . . . . . . . . . . . . . 82 4.18 In G = (V;E), if there exists no edge between node u and v, then we create two edges with length of 2a in H. . . . . . . . . . . . . 82 4.19 Probability of infeasibility when schedule length is xed. . . . . . 88 5.20 Comparison of PDF between random variableA and normal distri- bution (small K value) . . . . . . . . . . . . . . . . . . . . . . . . 94 5.21 Probability density function of random variable A (large K value) 94 5.22 PMF of optimal random policy with K = 0:5;N = 5;P = 0:1 and P = 0:5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.23 PMF of optimal random policy with K = 2;N = 5;P = 0:1 and P = 0:5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.24 Distribution of rst bit arrival time: A*(optimal) vs. A(uniform) . 100 5.25 Throughput comparison between uniform and throughput-optimal policy. N = 2;P = 0:5 and P = 1:5 . . . . . . . . . . . . . . . . . 101 ix 5.26 Throughput comparison between uniform and throughput-optimal policy. N = 7;P = 0:1 and P = 1 . . . . . . . . . . . . . . . . . . 101 5.27 Throughput comparison between uniform and throughput-optimal policy. K = 0:5;P = 0:5 and P = 1 . . . . . . . . . . . . . . . . . 102 5.28 Throughput comparison between uniform and throughput-optimal policy. K = 2;P = 0:5 and P = 1:5 . . . . . . . . . . . . . . . . . 102 5.29 Throughput comparison between uniform and throughput-optimal policy. K = 0:5;N = 2 and N = 6 . . . . . . . . . . . . . . . . . . 103 5.30 Throughput comparison between uniform and throughput-optimal policy. N = 2;K = 0:5 and K = 2 . . . . . . . . . . . . . . . . . . 103 5.31 Throughput improvement ratio vs. packet length P . . . . . . . . 106 x Abstract Because of our limited knowledge of the huge water body that covers 70% of Earth's surface, Underwater Acoustic Sensor Network (UWASN) is an emerging topic in the research society. However, the unique properties of acoustic com- munication systems, such as high propagation delay, high communication power consumption, low transmission rate, distance dependent bandwidth, all make the networking issues of UWASN very challenging. In this thesis, we study three dier- ent topics that can be applied in UWASN, with a focus on addressing the challenge of high propagation delay. One is time synchronization, another one is link schedul- ing, and the last one is random access. Because of high propagation delay, time synchronization protocols which are designed for terrestrial-RF networks may not be suitable for UWASN. We perform extensive analysis of existing solutions, and conclude their pros and cons. Based on our ndings, we propose a hybrid synchronization scheme, which outperforms exist- ing solutions in terms of precision, has bounded multi-hop error, and low variance. In addition, we also analyze the proposed solution with other schemes in multi-hop settings. The performance of hybrid scheme is not only analyzed theoretically, but also veried by traced-based simulations. In the second topic, we formally prove the NP-hardness and best possible ap- proximation ratio for Metric Underwater Scheduling problem. We then use a com- plete SAT solver to study the feasibility of a given scheduling length, regarding a xi network under consideration. We notice that UWASN has good throughput when the deployment density is low, but deteriorates when density goes up. Due to the in exibility and high communication power consumption of central- ized schedulers, we nally study the performance of a ALOHA-like random access scheme. We use non-linear programming to improve its throughput by modify- ing the channel access distribution. Based on our ndings, the improvement can be several orders compared to primitive solutions. While packet length increases, schedule length decreases, and deployment density increases, the improvement ratio also goes up accordingly. xii Chapter 1: Introduction Water is one fundamental element required by all life forms. The circulation of water nourishes numerous plants and animals; water raises plants, thus supporting the life of animals which rely on them. Because of the dependency on water, most habitat of living creatures is within the proximity of some form of water. In addition, nearly 71% of Earth's surface area is covered by water. After a water body absorbs heat emitted by the sun, the process of transformation itself not only provides lots of energy, changes our climate, but also plays a critical role in maintaining a hospitable environment for all species on Earth. Water is one of the most important factors that support our ecological system. Although the importance of water is unquestionable, our understanding of water bodies is limited. Most of our knowledge is constrained to the area that is close to land. The water body beneath hundreds of meters of surface, which is hard to access and observe for the last generation of technology, is completely under- explored. On one hand, extreme and destructive climate situation have become a repeated and frequent phenomenon in the past decades, and recent evidence implies the close relation between abrupt climate changes and ocean conditions. On the other hand, applications, such as ecology system monitoring, emergency rescue, and tsunami precaution alarm, all depend on the existence of a reliable ocean monitoring mechanism. Due to the need for these applications, exploring complex ocean processes and their interactions is becoming an emerging topic in 1 the research society. The advancement of under-water acoustic sensor networks (UWASN) opens a door for us to investigate this unknown part of our planet. 1.1 Overview of UWASN In this section, we brie y summarize the unique features of UWASN in the following contents, including characteristics of acoustic communication and applications. 1.1.1 Characteristics of Wireless Sensor Networks UWASN is one kind of sensor networks that are deployed in underwater environ- ments. Thus, it inherits many features from wireless sensor networks (WSN). A WSN consists of many autonomous nodes, such that each node can pro- vide some straightforward functions and has wireless communication capability [44]. Each node may equip with some sensors, thus may provide readings about, but not limited to, temperature, sound, vibration, pressure, motion or pollutants, etc. Be- cause most nodes are spatially distributed in a deployed area, readings from a single node is locally meaningful only. However, through the collaboration of many nodes, we can do a lot more sophisticated tasks by using WSN. Some common applica- tions include ecology system monitoring [88] [38], mechanical structure monitoring [42], object tracking [45], etc. In addition, since the operation of WSN does not require frequent human labor involvement, it not only largely reduces the cost of 2 applications, but also provides ne grained observations and enables applications, which may not be possible for human execution. Unique characteristics of a WSN include: Limited power supply: Most sensor nodes are only equipped with a small capacity power source, such as batteries. In order to sustain a long network lifespan, WSN imposes a strict power consumption constraint. Ability to cope with node failures: WSN can achieve a specic task through the collaboration of nodes that are spatially distributed. However, due to the low cost hardware adopted, and the possibility that nodes may run out of power, WSN has to deal with the situation when the availability of nodes change, in order to maintain its functionality. Dynamic network topology: In many cases, sensors are not deployed in a structured way, thus the designer may not have good control of the network topology. In this scenario, deployments need to be capable of dealing with dynamic network topology, such that the tasks can still be fullled. Communication failures: Because of the low manufacturing cost, or drained out batteries, or system malfunction, sensor nodes may lose their communi- cation capability. How to cope with the situations when these failures occur is also a critical issue during deployment. Heterogeneity of nodes: Due to the cost consideration, or application require- ments, some WSN are composed of sensor nodes with dierent capability, in 3 terms of power supply, processing power, transmission, etc. In such scenario, it is necessary to consider how to make these heterogeneous sensor nodes collaborate eciently. Large scale of deployment: Because WSN can achieve a specic task through the collaboration of sensor nodes, the more sensor nodes available, the more functionality the designer can realize. However, getting a large number of nodes to collaborate is very challenging. Thus, the scalability issue is also critical during deployment. Unattended operation: Beyond harvesting data, one would like a WSN to be properly functioning with minimum labor involvement. Thus, how to design a WSN that requires infrequent maintenance and human operations is also interesting to the research community. Limited transmission range and rate: Again, because of the low cost hardware adopted and limited power supply, most sensor nodes have limited transmis- sion range (up to hundreds of feet) and rate (up to hundreds of kbps). 1.1.2 Characteristics of Acoustic Channel Although most WSN communications are based on terrestrial-RF technology, this solution is not suitable for underwater deployment. This is because of the rapidly decaying signal strength of electro-magnetic waves while propagate in water [29]. Researchers at University of Southern California have done experiments and show 4 that, Mica 2, one of the most popular sensor network solution, can only communi- cate within the distance of 120cm. Acoustic communication, on the hand, experiences far less path loss than radio waves in water. However, there are several fundamental dierences between these communication systems. Speed of propagation: The speed of sound underwater is around 1500m=s, which is ve orders slower than 310 8 m=s (the speed of light), the propagation speed of radio waves. High bit error rate: Because of the long propagation delay of acoustic waves, acoustic communications suer from relatively large Doppler eect and severe inter-symbol interference, which leads to high bit error probability [73]. Limited bandwidth: Due to the high strong attenuation in high frequency band, low carrier frequency is preferred in acoustic communication systems, which limits the available bandwidth. In addition, shorter distance enjoys larger bandwidth. Thus, if bandwidth is major concern, then placing relay nodes can help improve system throughput. Existing of shadow zone: In longer links, because of frequency dependent attenuation, dierence of pressure, temperature and refraction, some spatial regions may not have available accoustic channel [8], thus losing connectivity. These regions are referred to as \shadow zone". 5 Even severe power restriction: Existing underwater modems generally cost power in the scale of tens of watts and couple watts in transmit and receive mode, respectively, which implies a higher power consumption comparing with terrestrial-RF based WSN (It takes hundreds of milli-watts for both transmit and receive mode.). 1.1.3 UWASN Architecture There are several dierent devices involved in the structure of UWASN. There can be 2D deployments, which are constituted by sensor nodes anchored to the seabed, and 3D deployments, such that sensor nodes are placed in dierent depth. In general, a UWASN may include sensor nodes, surface stations, and underwa- ter vehicles. Sensor nodes are used to generating readings. They can be either anchored on the bottom of water body, or oat in the water. In order to collect sensing data from sensor nodes, we usually use a surface station, which oats on the surface of water. Sensor nodes then use vertical acoustic channel to communicate and send the sensing data to it. Thereafter, the surface station can use RF communication system to transmit collected data back to the sink. Sometimes, a underwater vehicle, e.g. a submarine, is also used in the deploy- ment, and it can perform dierent functionality. An underwater vehicle can equip with several sensors. Because of its mobility, this vehicle can be used to enhance 6 system coverage or increase sensing resolution. An underwater vehicle can also be used a data collection device. Sensor nodes can transmit their sensing data to it, when they are close. Underwater vehicles can be used to update or recongure system and sensor nodes. For example, the deployment location of sensor nodes may change over time, and we can use a submarine to update or calibrate the loca- tion of these drifted sensor nodes. In sum, the usage of an underwater vehicle can substantially increase the exibility of UWASN. 1.2 Motivation In order to help us understand the under-explored water body, continuous obser- vation and monitoring data collection is essential. Because most of these area are inhospitable, and because of the limitation of technology developed in the last century, most data acquisition is done by human workforce, which is expensive, inaccurate, and limited. This trend has been changed since the emergence of wire- less sensor networks (WSN). Through the deployment of WSN, we not only can study the area which is not accessible by human being, but also can construct a observation system which is continuous, ne-grained and low cost. However, the uniqueness of underwater monitoring tasks also introduces new challenges to the applicability of existing WSN technology. First, because electro-magnetic waves can only propagate distance in the scale of hundreds of meters in the medium of water under a reasonable transmitting power [2][3][4], it becomes extremely expensive for WSN to cover a large area in 7 underwater environment using radio frequency (RF) technology. Therefore, acoustic communications, which are capable to communicate in the range of miles of distance, become the most popular alternative for underwater networks [2][3][4]. Although acoustic communications give an answer to the issue of communication distance of RF systems, it raises other issues which require further investigation. Because the propagation speed of acoustic waves in the medium of water is around 1500m/s, which is ve order of magnitude slower than light of speed [2][3][4], the propagation delay of transmissions is in the scale of seconds. On the contrary, prop- agation delay for RF systems is usually a negligible term. Thus, the applicability of protocols, which are designed based on the assumption of insignicant propagation latency, becomes questionable. On one hand, the communication power consumption of exiting underwater modems is signicantly dierent in terms of the operation modes; while the power overhead in transmit mode is in the scale of tens of watts, the overhead of receive mode is only in the scale of watts [2][3][4]. On the other hand, the power overhead for RF modules used in RF-based WSN is almost the same, and is in the scale of milli-watts [2][3][4]. These features suggest a more stringent energy constraint, and a very dierent random access strategy from RF-based systems. In terms of transmission rate, existing underwater modems, which are at most hundreds of kbps, are also signicantly lower than most RF-based WSN, which can go up to the scale of Mbps [2][3][4]. 8 In addition, the available bandwidth, carrier frequency, and noise level all depend on communication distance, which is also very dierent from RF-based systems [2][3][4]. In light of these unique features of underwater acoustic communication systems, it is necessary to study the networking issues of underwater acoustic sensor networks (UWASN), such that the deployment is capable of providing satisfying performance as in terrestrial-RF WSN. We study three issues for UWASN, time synchronization, scheduling, and random access, in the following contents. 1.3 Time Synchronization Support for UWASN Many applications in sensor networks have to be accomplished through collabora- tion between several nodes. Accurately synchronized clocks are important for many other mechanisms, e.g. TDMA-based medium access protocols, sleep scheduling techniques, and object tracking. Because every node in a sensor network operates independently, the clocks of each node may not be synchronous with one another. First, since two dierent clocks may start ticking at dierent time instances, the dierence between the readings of these two clocks may be signicant. We refer to this value of clock reading dierence as \clock oset", and estimation of the oset thus helps to reset the clocks for resynchronization. In addition, given each clock may tick in a rate that is dierent from its nominal rate, the dierence of actual ticking rate between dierent clocks may incur signicant reading dierence over some period time, and we refer 9 to the value of ticking rate dierence as \clock skew". Estimating the rate of this change can be useful in mitigating further clock drift between synchronization events, especially in a sensor network adopting low duty cycle. Packets that are used for synchronization purpose are referred to as \synchro- nization packets". In general, time synchronization tasks are done by exchanging synchronization packets between a node, that provide reference clock readings, and a node, that requests time synchronization support. While the former are referred to as \reference nodes", the later ones are referred to as \un-sync nodes". Syn- chronization protocols embed readings, with respect to individual clocks, into these synchronization packets, and utilize acquired packets to estimate clock oset and skew between the nodes involved in this process. However, due to the various sources of jitters taking place during synchronization processes, synchronization protocols suer from error. Typical sources of jitter include send time, access time, propagation time, and receive time. A more detailed explanation can be found in [49]. Because of the common properties shard by WSN and UWASN, i.e. stringent power consumption constraint and inconsistent clock readings caused by low cost oscillators, understanding time synchronization protocols which aim at terrestrial- RF WSN provides guidance for the design in even more challenging environments. Depending on the synchronization packets exchange strategies, existing works can be categorized into two major types. One is the \sender-receiver" scheme, which involves direct communication between two devices in order to synchronize 10 one to the other. The other one is the \receiver-receiver" scheme, which will syn- chronize clocks between nodes receiving the same reference broadcast. The existing works that involve sender-receiver synchronization can be further categorized into two types. One can be called \one-way dissemination" and the other is \two-way exchange". While the former needs a synchronized node to disseminate packets to unsynchronized nodes, the latter achieves synchronization by exchanging packets between synchronized and unsynchronized nodes. Flooding Time Synchronization Protocol (FTSP) [49] and Timing-sync Protocol for Sensor Network (TPSN) [23] are representative works which utilize one-way packet dissemination scheme and two-way packet exchange scheme, respectively, and Reference Broadcast Synchro- nization (RBS) [16] is a representative work of receiver-receiver scheme. One common problem of the above works is the assumption of ignorable prop- agation delay, which may not be true in underwater acoustic sensor networks [77]. Existing protocols which designed specically for radio-based sensor networks may produce signicant synchronization error due to the high propagation latency. Ac- cording to our analysis, in high propagation delay environments, RBS-like receiver- receiver schemes show poor performance. Among the sender-receiver schemes, the one-way packet dissemination does better on estimating clock skew, while the two- way exchange does better on estimating clock oset. However, in high propagation delay environments, the one-way scheme shows high average synchronization error while the two-way scheme shows high variance. Although NTP [50] can tolerate 11 high propagation latency, it does not bear power conservation in mind, thus not suitable in this power scarcity environment either. We use our insights from the analysis to propose a hybrid one-way/two-way mechanism that is shown theoretically to perform more gracefully in multihop net- works with high propagation delay, while incurring mild additional communication overhead. We validate our analysis through experimental trace-based simulations on a line network of terrestrial RF-based sensor nodes where we use application-layer time stamping to mimic conditions of high propagation delay with high variance. The results of these simulations conrm that the hybrid scheme not only provides bounded error propagation over multiple hops in average but also produces low variance of propagation error. 1.4 Link Scheduling in a Single Broadcast Do- main UWASN For underwater networks, since radio waves fade rapidly in water, acoustic com- munications becomes an attractive alternative. Dierent from radio, acoustic com- munication has its own characteristics, such as low bandwidth, long delay, high error rate, distance-dependent bandwidth, etc. These features make the scheduling for underwater acoustic sensor network fundamentally dierent from radio-based communication systems. 12 We use the two networks plotted in Figure 1.1 and 1.2 to illustrate the dierence between scheduling terrestrial-RF WSN and UWASN. In these gures, each circle and square represents a receiver and a transmitter, respectively. If nodes are lled with the same color, they belong to the same transmission session. For example, the intended receiver of transmitter 1 in Figure 1.1 is receiver 1. The number besides an arrow describes the distance, in units of time, between the two end points attached to this arrow. Thus, after transmitter 1 in Figure 1.1 sends out a packet, this packet will arrive receiver 1 at exactly 1 unit of time later. Every packet takes exactly 1 unit of time to transmit, and every transmission can only take place at the boundary of a time slot. When another transmission arrive the same receiver at an overlap period of time, then an \collision" happens and none of the transmissions involved in an collision can go through. There are two kinds of receptions in the viewpoint of a receiver; one is intended transmission and the other one is interference. An intended transmission is the data sent by the corresponding sender of this receiver, and interference is data sent by nodes other than its corresponding sender. Further, we assume that all links, which can be uniquely identied by a pair of nodes lled with the same color, are located in the same broadcast domain. Therefore, a transmitter can be interfered with any other transmission in the same network. A transmission fails if and only if it is corrupted by interference. Our goal is to schedule every link once in minimum time, such that no transmission is corrupted Consider these networks in terrestrial-RF setting rst. Because the propagation delay is negligible, comparing with the transmission time, we can schedule at most 13 Figure 1.1: An example UWASN consisted of two acoustic links. In this network, due to the high propagation delay of acoustic communications, we can schedule both links simultaneously without incurring collision. 1 link at any time. Thus, we need at least two and three slots to schedule every link once in Figure 1.1 and 1.2, respectively. In other words, the number of time slots we need to schedule every link once for terrestrial-RF WSN equals the number of links located in the same broadcast domain. The situation is very dierent when we consider the case of UWASN. In some cases, because propagation latency is signicant, it is possible to schedule two or more links at the same time slot without causing any interference. Thus, we only need one time slot to schedule both links once in Figure 1.1. In some other cases, because propagation delay may cause interference at a signicant time, the required number of time slots may be larger than the number of links located in the same broadcast domain. Take Figure 1.2 for example, we need at least 4 time slots to schedule all 3 links in this network. Although we notice that propagation delay plays an important role of making scheduling decisions in UWASN from the above example, the algorithmic complexity of devising an optimal scheduler has never been formally studied. 14 Figure 1.2: An example UWASN consisted of three acoustic links. Because of the high propagation delay, we need at least four time slots in order to schedule each link once. 1.5 Random Access Scheme for UWASN Besides being computationally hard, centralized scheduling has other limitations. First, in order to apply a centralized scheduling protocol, complete knowledge of network topology and links that requested for service is required. While it is only a one time eort for a scheduler to learn about the topology in a statically deployed network, frequent update of link requests can cause signicant power consumption, which is unacceptable for a power scarce environment like UWASN. Second, when- ever a change of topology takes place, or nodes lose synchronization, centralized algorithms have to spend energy to update this information, and repeat scheduling decision making processes again, thus becoming in exible in a dynamic environ- ment. Hence, a distributed medium access scheme, which is exible to changes of network states and low on energy overhead, is preferable in this scenario. 15 There are many dierent avors of distributed medium access protocols. Carrier- sensing is one popular medium access scheme in both wired and terrestrial-RF environments. However, it does not necessarily imply a failure if a node starts a transmission while it detects a busy channel. In addition, it cannot guarantee a success, if a node starts a transmission when it detects an idle channel, either. The property of high propagation delay limits the applicability of carrier-sensing based medium access scheme. In reservation based schemes, a node has to send out packets to reserve the channel before it can access to it. A consistent acknowledgement of which node has right to access the medium is crucial for this strategy to work properly. However, because of the high propagation delay, it may take a long period of time for a reservation packet to travel between nodes which are far away from each other, which implies low utilization of medium. Due to these unwanted properties, we are interested in a light energy overhead, low deployment eort, and versatile to network dynamics medium access protocol. An answer to our needs can be a Distributed, Randomized and Topology-unaware (DRT) medium access strategy. Given that optimal scheduling is hard even to approximate well, and DRT solutions are preferable, we focus on analyzing and optimizing a ALOHA-like, distributed, random access protocol for UWASN in this thesis. Unlike in terrestrial RF networks, we show that a DRT scheme with uniformly distributed channel access distribution is not optimal. We formulate and solve a 16 novel non-linear optimization problem to nd the optimal channel access distribu- tion, which is demonstrated to give enormous improvements in throughput. For brevity, we refer to a DRT scheme that picks the transmission times uniformly from a given period as a uniform DRT scheme, and the DRT scheme obtained by us- ing nonlinear programming as an optimal DRT scheme. We present the achievable throughput by using DRT strategy, and compare the performance of uniform DRT scheme with the optimal DRT one. Based on our ndings, optimal DRT scheme pre- vails in low density and long packet length setting. Compared with uniform DRT scheme, the throughput improvement ratio keeps increasing while packet length goes up. 1.6 Thesis Organization The rest of the thesis is organized as follows: In Chapter 2 we discuss the background and existing work on time synchronization, scheduling, and random access protocols for UWASN. In Chapter 3 we address the problem of accurate time synchronization. In Chapter 4 we deal with the scheduling problem for UWASN and study a random access scheme in Chapter 5. We discuss our future work and conclude this thesis in Chapter 6. 17 Chapter 2: Related Work In this chapter, some prior work and existing solutions related to this thesis are presented. Particularly, we summarize these eorts into two categories. One is time synchronization for communication systems in Section 2.1, and the other one is wireless medium access control and scheduling techniques in Section 2.2. 2.1 Time Synchronization Several issues make time synchronization challenging in high propagation delay en- vironment, such as UWASN. First, because the propagation distance of radio signal in water is limited, acoustic communication becomes a popular alternative [82]. However, the speed of underwater sound is ve orders slower than radio signal, propagation latency becomes a non-negligible source of delay. Therefore, alleviat- ing the impact of high propagation delay plays a major role in devising an ecient time synchronization protocol for such challenging environment. Because of low cost hardware adopted in sensor networks, clock generators perform dierently from each other. Thus, eliminating the uncertainty is also an important and challenging issue. Some existing literatures [77] [3] have more detailed descriptions about underwater acoustic sensor networks. Reference Broadcast Synchronization (RBS) [16] is an representative protocol of receiver-receiver scheme. In RBS, a reference beacon is broadcasted by a reference 18 node. Nodes which receive the broadcasted beacon will record its time of arrival and exchange this information with others. Because synchronization packets are only exchanged among reference beacon receivers, one advantage of RBS is able to get rid of sender side jitter terms [16] [23]. The average error of RBS is 1.851.28s in 802.11 wireless Ethernet with kernel timestamping [16]. However, as shown in following contents, RBS is not suitable for high propagation delay environments due to the dierent distance between the reference node and other receivers. Karp et al. [40] propose an variation of RBS, which is applicable to a network with a loop. The authors use resistive networks to derive a synchronization algo- rithm which provides global consistency and low variance. The trade-o between energy consumption and synchronization precision is also studied. Because we fo- cus on tree-structured networks, this type of implementation is out of extent of our work. In the two-way exchange scheme, synchronization packets are sent back and forth between reference and unsyn nodes. Timing-sync Protocol for Sensor Networks (TPSN) [23] is one implementations of two-way exchange scheme. For a multi- hop network, TPSN rst builds up a tree, assign each node to a specic level, and doing synchronization from level to level sequentially. The average error of TPSN is 16.9s [23]. In addition, TPSN is the rst protocol to use MAC layer time stamping, which is able to reduce medium access time eciently. Lightweight Time Synchronization (LTS) [28] also adopts two-way exchange scheme and is a similar tree-style, sender-receiver implementation as TPSN. 19 Gridhar et al. [24] and Solis et al. [70] use two-way exchange scheme, and take advantage of loops existing in networks to smoothen their synchronization estima- tion. The key idea of these papers is the sum of oset along a loop should be zero, and imposing these constraints to each loop can provide a smooth and accurate value. The authors also mention that if the graph is a tree, the variance of error will grow linearly with hop distance from the root, which is consonant with our results. Graham et al. [27] and Sichitiu et al. [68] propose synchronization protocols which use two-way exchange scheme. CTP [27] uses a similar equation as TPSN to estimate oset, and then further renes the estimation with linear regression. While Tiny-sync and Mini-sync [68] uses multiple time stamps collected from bi- directional synchronization packets to form constraints of clock oset and skew estimations, this algorithm has similar precision as CTP [27] when the number of time stamps is large. In one-way dissemination scheme, synchronization packets are only transmitted by reference nodes and received by unsynchronized nodes. The Flooding Time Syn- chronization Protocol (FTSP) [49] utilizes one-way dissemination scheme. Maroti et al. propose a sophisticated time stamping technique, which is able to reduce various kinds of jitter terms signicantly [49]. The performance of FTSP is mainly veried by experiments, and the average error of FTSP is 1.5s pair-wise and 0.5s per hop [49](Note: by \pair-wise" and \per hop", we are referring to single-hop 20 and multi-hop network setting, respectively. The \per-hop" error, is calculated by dividing the error at n-hop clock by n). RITS and RATS [46] [64] both utilize one-way scheme. While the former is a reactive protocol, the later is proactive. One important conclusion is that if the non-determinism is minimal, even a simple implementation of one-way scheme can provide high synchronization precision. The average error of RATS and RITS is in the scale of s [46]. Bychkovskiy et al. [6] propose another one-way scheme implementation. For pair-wise synchronization, the authors use linear regression on collected uni-directional time stamps to compute oset. For multi-hop calibration, they take advantage of existing loops to maximize consistency. There is a recent version of IEEE 1588 [37], or Precision Time Protocol (PTP), which targets at providing networks with clock precision in sub-microsecond. Dier- ent from prior time synchronization standards, IEEE 1588 also applies to networks composed of devices embedded with low-cost clock oscillators, such as sensor net- works. There are two fundamental assumptions that dierentiate our works and this eort. First, PTP assume synchronization messages can be exchanged in a short period of time, such that no relative oset occurs during the exchange pro- cess. Second, PTP also assumes that the transmit time of synchronization messages between two clocks is a constant. In our works, we do not make these assumptions, thus making our conclusions more versatile and applicable to UWASN. 21 Paxson [55] collected time stamps information from hosts connected by Internet. Due to the high-variance and long latency nature of Internet routing, we can expect their results also apply to the UWASN environment. The author propose to use only one-way messages to predict the relative skew, and two-way messages to estimate relative oset between two hosts. The author also propose an algorithm to detect clock adjustment, and verify it eectiveness by the time stamp traces they collected. Although they have similar solution as ours, detailed theoretical analysis, especially variance analysis and multi-hop performance evaluation, is lacking in this paper. Besides statistically verifying their conclusions, they do not have variance analysis, nor multi-hop performance evaluation. Ellingson et al.'s work [14] is the closest one to our studies. The authors analyze one-way and two-way and propose variance analysis of one-way pair-wise error under the case of dynamic network setting. In addition, the authors propose a recursive algorithm to lter out measurement error. Again, the multi-hop, variance, and the impact of message number analysis for pair-wise two-way is lacking. On the hand, we focus more on the precision with the existence of non-ltered measurement error. An excellent survey [76] reviews some of the state of the art in time synchro- nization, that are not mentioned here. Some synchronization works are designed for networks using strategies other than sender-receiver and receiver-receiver schemes, as well as objective other than precision or power consumption. Some synchronization works focus on objectives other than precision or power consumption. Cristian [11] proposes a probabilistic 22 method to alleviate the clock reading error. The authors assume the duration of synchronization process can be arbitrarily long, which is the same as we do in our works. Their solution is using a probabilistic method to determine a clock reading is valid or not, according to the knowledge of the distribution of network delay. In our works, we don't discard clock readings, and use all collected time-stamps for average performance analysis. Clearly, combining Cristian's technique can improve the results presented in our works. Lamport [47] propose an algorithm to reconstruct the complete ordering of all events taking place in the system, by using knowledge of partial ordering of a subset of events. They apply this concept to do time synchronization, and bound the synchronization error. One of the main assumption of this paper is, if a message is sent earlier than another message, then it will also be received earlier. This assumption does not apply to acoustic communication system, due to the slow propagation speed of acoustic waves. Some existing works deal with the synchronization tasks with special assump- tions. Lamport et al. [48] propose an algorithm that can provide bounded error, in the existence of \two-faced clock". A two-faced clock provide inconsistent clock readings to dierent users, thus making many synchronization protocols fail. In this thesis, we assume no two-faced clocks exist in our system. Although the satisfying precision and moderate power consumption provided by existing works designed for radio-based sensor networks, the common assumption 23 of these protocols, ignorable propagation delay, makes their applicability to under- water acoustic sensor networks doubtful [77][34]. TSHL [77] is an implementation specically designed for high propagation delay networks, which was done in par- allel with our work. Basically, TSHL operates in two stages. In the rst stage, the reference node keeps transmitting several packets to the un-synchronized node. The un-synchronized node uses these uni-directional packets to compute the clock skew between itself and the reference node, and calibrate its clock accordingly. In the second stage, these two nodes start exchanging synchronization packets back and forth. Then, the un-synchronized node uses these bi-directional packets and the oset equation from TPSN to compute oset estimation. However, there are some pieces missing in that work [77]. First, the authors only address the propa- gation delay in their computation, and assume all other jitter terms are negligible. This assumption may not be true when the acoustic traveling distance is not long enough, and application layer time stamping is adopted, thus making the appli- cability limited. In addition, the analysis of their TSHL protocol, and multi-hop setting are also lacking. To summarize, synchronization protocols designed for wired environment do not take energy overhead into account explicitly. Although protocols designed for RF-based sensor networks do bear power consumption in mind, they suer from long propagation delay. Although a few works are capable of providing precise and energy ecient protocols for the challenging UWASN environment, comprehensive comparison and performance analysis under multi-hop network setting are lacking. 24 2.2 Link Scheduling and Medium Access for UWASN In order to design a high performance MAC protocol for UWASN, it s necessary to understand the features underwater acoustic channels. Stojanovic is the rst one to propose a comprehensive and systematic study about this problem [73]. The author reveals several unique features of underwater acoustic channel. These features in- clude transmission distance and frequency dependent path loss, distance dependent bandwidth, and frequency dependent noise, etc. Some closed form approximation equations are also proposed in this paper. Preisig [59] studies the propagation properties of acoustic waves through sea- water. The author discusses seawater absorption, surface scattering, bubbles and noise issues for underwater acoustic communication channels. Due to the unique features of acoustic communication, some existing work fo- cuses on designing new MAC protocols, and some of them modify existing solutions designed for terrestrial-RF or wired environments. Syed et al. [79] study the performance of traditional slotted and non-slotted ALOHA performance for underwater networks and show that they can have the same throughput due to variations in latency. In order to improve the throughput, the authors propose a guard-band scheme, such that a node cannot transmit in consecutive time slots. This scheme is mathematically analyzed and optimized by Ahn et al. in [1]. 25 Syed et al. [78] propose a tone-based protocol called T-Lohi [78]. In T-Lohi, there exists a specially designed circuitry, which can transmit/receive a tone signal with low power consumption. Whenever a data is ready for transmission, the trans- mitter sends a tone through this hardware to compete for channel access right. If no other tone is overheard during a certain period of time, then this transmitter starts transmitting its own data. Although the adoption of special hardware improves energy overhead, the long channel competing process undermines the utilization. Chirdchoo et al. [9] propose Two ALOHA based MAC, namely ALOHA-CA and ALOHA-AN. The complete knowledge of network topology is necessary for both protocols to work. Whenever a node overhears a transmission, it immediately knows when this packet will in uence its neighbor, thus it can determine whether its transmission will be corrupted by overheard signal or not. In addition, each node also maintains a table of all possible arrivals of its neighbors such that it can help improve the transmission decision. Although both solution can help improve throughput by reducing possible collisions, it achieves this goal by extensive chan- nel monitoring and bookkeeping trac conditions, thus leading to excessive power consumption. Molins et al. use ideas similar to slotted-CSMA/CA to design a reservation based MAC protocol, Slotted-FAMA[56], which uses RTS/CTS mechanism to avoid colli- sion. However, because of the high propagation delay, the time spent on completing RTS/CTS exchange becomes signicant, thus leading to low channel utilization. In 26 addition, the power consumption incurred by this handshake process, which in- cludes packet transmitting, channel monitoring, and packet receiving, also raises the communication energy overhead. In Slotted-FAMA, it is necessary to maintain a common agreement about the channel access right throughout the whole network. Although this strategy guar- anteed the absence of interference, the long handshake process becomes the major issue that deteriorates utilization. In light of this observation, Peleato et al. [56] improve the low utilization issue of Slotted-FAMA by shortening the handshake process. The tradeo of this solution is the risk of potential interference. However, when the trac is light, it is possible to enjoy higher throughput, and limited level of interference simultaneously. Rodoplu et al. [61] propose a CSMA based MAC which aims to save energy overhead by using sleep period. Unlike T-Lohi that uses specially designed tone device, a transmitter broadcasts a packet to reserve the channel usage through its modem. Because its neighbors can overhear this broadcast, they know when the channel will be this transmitter, thus back-o while it is using the channel. Because it requires a common agreement of channel access right, the long handshake process implies low channel utilization. In addition, when contention is heavy, it may be possible that some transmitters cannot retrieve the channel. A similar solution can also be found in [84]. Because CDMA is robust to frequency selective fading, and serious multipath issue in UWASN due to high propagation delay, it becomes a popular MAC design 27 strategy [4]. In [74], Stojanovic et al. disclose their deployment based on CDMA, and shows promising performance. Pompili et al. [57] propose a CDMA based MAC for UWASN, which is called UW-MAC. In UW-MAC, the authors propose a distributed close-loop algorithm to set transmit power and code length, which can deal with the common near far eect of CDMA systems. Salva-Garau et al. [65] propose a TDMA-CDMA mixed MAC for UWASN. In this paper, the authors rst clustering nodes into clusters, while inter-cluster medium access is done by CDMA, intra-cluster is done by TDMA. FDMA has been deployed in Seaweb. However, due to the constraints of fre- quency selective channel and limited bandwidth, Seaweb abandon this solution in recent experiments. Nguyen et al. [52], Casari et al. [7] and Doukkali et al. [13] compare the existing MAC protocols, and review the pros and cons of various underwater medium access techniques under dierent network setting. Preisig et al. [59] focus on acoustic channel property descriptions and provide propagation phenomena that can in u- ence network performance in a quantitative way. Other tutorials which have broad coverage about UWASN can be found in [54][12][2][4]. In addition to pure medium access solutions, Badia et al. [5] propose a cross-layer optimization framework, which utilizes integer programming, that can determine link scheduling and packet routing. Unlike the channel exclusive model, such that interference necessarily implies failure of delivery, the authors consider SINR model. In this model, every receiver has a certain SINR ratio, such that when signal strength 28 of the intended transmission is higher than this predened threshold at receiver end, this receiver can correctly decode the transmission that is destined to itself. Although this model is closer to practical situations, but the high computing cost of this solution largely limited the applicability, especially for online implementation. According to the authors' observation, it takes a Xeon workstation 3 hours to nd the optimal solution for a network with 20 nodes. Pompili et al. [58] have a cross layer solution for multimedia support in UWASN. Because some applications are delay sensitive, e.g. video surveillance, some are delay tolerant, e.g. le transfer, the authors argue that networking solutions has to adapt to it for better end to end performance. They propose a solution, which determines modulation, forward error correction, MAC and routing, to accommodate dierent needs for dierent applications. interactions To the best of our knowledge, our work is the rst to formally prove the NP- completeness of UWASN link scheduling problem. In addition to the algorithmic complexity discussion, our work is also the rst one to investigate the tightest possible approximation ratio for this problem. The paper that's closest to our work in spirit is the work by Ahn et al. [1] in that both focus on an analysis of randomized access in underwater networks. However, while that work focuses on the improvement of throughput for a single receiver using guard-bands, our focus is on maximizing the sum-throughput of multiple links in the same broadcast domain by optimizing the access time distribution. This is more 29 challenging because in underwater networks, the same transmission may appear as interference at signicantly dierent times at dierent receivers. 30 Chapter 3: Time Synchronization for UWASN We rst explain some terminology that will be used in the following contents. By \ideal clock", we are referring to a clock that is capable of measuring time consistently, and \ideal clock reading" is a clock reading given by an ideal clock. By \clock oset", we are referring to the reading dierence between two clocks at the same instance. The rate of one clock \drifting away" from an ideal clock or another non-ideal clock is dened as \clock bias", and \relative clock skew", respectively. In this chapter, we assume every node is equipped with an ane clock. In other words, if the clock reading from the ideal clock ist, then the reading of clockj at the same This chapter is based on our prior published work: [34] P. Huang and B. Krishnamachari, \Analysis of existing approaches and a new hybrid strategy for synchronization in sensor networks", in Proceedings of the Fifth (EmNets 2006), Boston, MA, May 2006. [35] P. Huang, M. Desai, X. Qiu, B. Krishnamachari, \On the Multi-Hop Performance of Various Synchronization Mechanisms," USC technical report, 2008. [36] P. Huang, M. Desai, X. Qiu, B. Krishnamachari, \On the Multihop Performance of Synchronization Mechanisms in High Propagation Delay Networks", IEEE Transactions on Computers, P577-590, Vol. 58, No. 5, May 2009. 31 instance can be represented as t j (t) = S j t +b j , whereas S j and b j represents the clock skew and oset between clock j and the ideal clock at time 0, respectively. This assumption has been veried to be accurate in [21]. We assume clock biasfS i g are not functions of time and iid (identically, independently distributed), and every node is equipped with identical hardware and software settings. In the following, we use a random variable i to denote the total delay/jitter taken for packet i, transmitted from one node to another and is measured by an ideal clock. When a time stamp is generated, because it requires certain processing, including both hardware and software mechanisms, the clock reading information stored in it becomes obsolete at the time when a time synchronization protocol can actually utilize this reading. Suppose we denote the time, with respect to an ideal clock, a time stamp is generated and it is ready to be utilized by synchronization protocols as t i and t j , respectively. Because synchronization protocols \assume" that t i and t j are the same instance of time, the larger the dierence between these two values, the higher the synchronization error will be. The latency contributed byt j t i is the reason why synchronization protocols cannot guarantee perfect synchronous clocks. Some possible source that can introduce delays during synchronization process, include send-receive times for communication layering purpose, channel access time, link layer transmission and reception time, propagation time, interrupt handling time, encoding and decoding time, and byte alignment time [49]. A brief explanation of these terms is given as follows, and more detailed descriptions can be found in [49] and [26]: 32 Communication Protocol Layering Delay: Because of the layering structure of communication protocol stack, and protocols for dierent lay- ers may perform various kind of processing before a piece of information can pass through it, the time spent on layering processing task causes error to the synchronization procedure. This term has high variance, and depends on system loading. While loading increases, this term goes up accordingly. Channel Access Time: In a shared communication medium, a transmitter has to wait for its right to access the channel. When the contention on the medium is high, channel access time becomes un-negligible. This term has high variance. When the contention on the medium becomes higher, this term also increases. Transmission and Reception Time: This term refers to the latency contributed by communication cie send the data out of transmitters. The higher the transmission rate is, the lower this delay will be. This term has low variance. Propagation Time: This term refers to the time of transmitted signals propagate from the transmitter to the intended receiver. This term has low variance when the network deployment is static. Interrupt Handling Time: In general, processor is shared by many tasks. Thus, when data used for synchronization arrive at an instance, that the processor is taking care of other tasks, an interrupt will be triggered. This 33 term refers to the delay introduced by interrupt handler, and has high variance in general. Encoding and Decoding Time: Encoding time refers to the time, such that circuitry converts data ready for transmission, to data actually be trans- mitted, by using various channel coding techniques. Byte Alignment Time: When the communication circuitry receives data from medium, it needs to determine the alignment such that it can correctly decode the received signal. This term refers to this delay and has low variance. In addition, we assumef i g are iid , andf i g andfS i g are independent with each other. Note that, even after some delay sources are mitigated through sophis- ticated time stamping techniques such as those proposed in FTSP [49], the value of i ;8i, is always positive. The symbols used in the following contents are summarized as follows: T i : A clock reading (time stamp) generated by a node involved in a synchro- nization process. t i : The time measured by the ideal clock corresponding to the clock reading T i . i : Total delay/jitter corresponding to packeti as measured by the ideal clock. S i : Bias of clock i (clock skew between clock i and the ideal clock). 34 b i : Intercept of clock i (clock reading dierence between clock i and the ideal clock at time 0). O a t i : Actual oset between reference and unsynchronized node at instance t i . O e t i : Estimated value of O a t i . RO a t i !t j : Actual oset dierence between reference and unsynchronized node contributed by period t i to t j . RO a t i !t j =O a t i O a t j RO e t i !t j : Estimated value of RO a t i !t j . " j t i : Overall error at time t i , up to level j. For convenience, we list the assumptions as follows: f i g are random variables, such that for dierent value of i, they are iid. fS i g andfb i g are random variables, and iid among dierent value of i. f i g andfS i g are independent with each other. We will present the analysis of existing synchronization schemes and the pro- posed hybrid scheme under the pair-wise and multi-hop setting in Section 3.1 and 3.2.2, respectively. We then present the experiment results in Section 3.3, and related discussion in Section 3.4. Finally, we make a brief summary in Section 3.5. 35 Figure 3.3: Message timelines for one-way synchronization scheme. The intersection of a horizontal line and an arrow represents the time instance of the corresponding transmission taking place. The left most and right most end of the horizontal line represents the earliest and latest time instance, respectively. 3.1 Pair-wise Synchronization Error Analysis 3.1.1 Analysis of One-way Dissemination Scheme An example of one-way scheme is plotted in Figure 3.3. The arrows in the gure represent directions of transmitted packets for synchronization purposes. The time relations of packet I can be written as T 2 = T 1 +O A!B t 1 +S A I , and similarly for other packets. We rst dene the following matrix: A M = 0 B B B B B @ 1 T 1 1 T 3 . . . . . . 1 C C C C C A ;B M = 0 B B B B B @ T 2 T 4 . . . 1 C C C C C A ;X M = 0 B @ C M D M 1 C A (3.1) 36 Where matrixX M represents the two unknown parameters of doing linear regression on these time stamps. By using linear algebra [75], we can computeX M by solving A T M A M X M =A T M B M . Therefore, X M = 0 B @ C M D M 1 C A = (A T M A M ) 1 A T M B M (3.2) However, if all uncertainties can be magically eliminated, matrix X I becomes: X I = 0 B @ C I D I 1 C A = (A T A) 1 A T B I where, A =A M ;B I =B M N;N = 0 B B B B B @ S A I S A II . . . 1 C C C C C A (3.3) Thus, X error =X M X I = (A T A) 1 A T N. Because: A T A = 0 B @ m P m i=1 T 2i1 P m i=1 T 2i1 P m i=1 T 2 2i1 1 C A A T N = 0 B @ S A P m i=1 i S A ( P m i=1 T 2i1 i ) 1 C A m: number of packets (3.4) 37 X error can be calculated as (for brevity purpose, we omit the superscript m and subscript i = 1 of summation in the following derivation): X error =X M X I = 0 B @ C error D error 1 C A = S A m( P T 2 2i1 ) ( P T 2i1 ) 2 0 B @ ( P T 2 2i1 )( P i ) ( P T 2i1 )( P T 2i1 i ) ( P T 2i1 )( P i ) +m( P T 2i1 i ) 1 C A (3.5) Because of independency off i g andfS i g, one important observation of equa- tion (3.5) is that the expected value of D error equals 0, even the value of m is the minimal 2. That means, one-way dissemination scheme is capable of estimating clock skew accurately in average, and this result is consonant with Freris et al's conclusion [20]. On the other hand, becausef i g are iid, the expected value of C error becomes S, given Exp[ i ] = and Exp[S i ] =S. Since the value off i g andfS i g are pos- itive, doing linear regression on time stamps collected from uni-directional packets will over-estimate oset in average, and this conclusion holds no matter how large the value of m is. From equation (3.5), because the variance of D error is a decreasing function of m, it would be helpful to use more packets if an accurate and low variance skew estimation is desired. 38 An Explanation of FTSP's Performance In FTSP [49], RITS [64] and RATS [46] we notice the average error of these protocols may uctuate with respect to the hop distance, i.e. using one-way sometimes may under-estimate oset. One possible reason for this contradiction is the high variance of C error and D error . Because of the adoption of sophisticated time stamping techniques, e.g. FTSP [49], the value of is very small in practice. However, from equation (3.5), we notice the standard deviation of C error and D error is so large comparing with . Thus, it is possible to see the situation of under-estimate for one-way scheme if the number of iteration is not large enough. In addition, because the variance increases with respect to hop distance in multi-hop scenario, this phenomenon becomes even more likely when the un-synchronized node is far from the root node. Even though we do not explicitly model the mechanism of ltering out extreme sample points while doing linear regression in FTSP, this strategy has equivalent eect of using smaller variance of in our analysis. Because we do not make assumption about the variance of , the conclusion of over-estimate clock oset in average still subsists. 39 Figure 3.4: Message timelines for two-way synchronization schemes 3.1.2 Analysis of Two-way Exchange Scheme Figure 3.4 is an example of two-way scheme. Similar as prior analysis, we can write: T 2 =T 1 O a t1 +S ref I T 4 =T 3 +O a t3 +S A II (3.6) From TPSN [23], LTS [28] and Paxson et al.[55], the oset estimation is (T 4 T 3 )+(T 1 T 2 ) 2 . Because O a t 1 =O a t 3 + (S ref S A )(t 3 t 1 ), from equation (3.6): O e t 4 = (T 4 T 3 ) + (T 1 T 2 ) 2 = 1 2 [(O a t 3 +S A II ) + (O a t 1 S ref I )] =O a t 3 + 1 2 [(S ref S A )(t 3 t 1 ) + (S A II S ref I )] (3.7) 40 However, O a t 4 =O a t 3 (S ref S A )(t 4 t 3 ) =O a t 3 (S ref S A ) II . Thus, Error = (T 4 O e t 4 ) (T 4 O a t 4 ) =O a t 4 O e t 4 = 1 2 (S ref S A )(t 4 t 1 ) S ref 2 ( II I ) (3.8) Because the clock skew is dierence, the rst term in equation (3.8) represents the relative oset contributed by the period of synchronization process, which we call it \actual relative oset from t 1 to t 4 " and is denoted by RO a t 1 !t 4 . Sincef i g are iid, andfS i g are iid, the expected error is 0. Therefore, two-way is capable of estimating oset precisely in average. One potential problem of two-way scheme is the high variance of precision. From equation (3.8), the rst term is a function of t 4 t 1 . Because the variance of this error can be computed as: Variance of error = (t 4 t 1 ) 2 2 var[S] + 1 2 var[S] (3.9) If (t 4 t 1 ) is large, then the variance of synchronization precision can be poten- tially high. Therefore, using two-way scheme in a low-duty, high propagation delay environment may not be able to provide satisfying synchronization precision. 3.1.3 Analysis of Hybrid Scheme Figure 3.5 illustrates the error incurred by one-way dissemination and two-way exchange scheme. In Figure 3.5(a), we plot the scenario for one-way dissemination scheme. Because the un-sync node A always use obsolete clock readings,A andB, to 41 represent later time instances,A 0 andB 0 , one-way dissemination un-avoidably over- estimates the clock oset. Using sophisticated time-stamping techniques indeed helps to reduce the distance between A and A 0 , B and B 0 . In Figure 3.5(b), we plot the scenario for two-way exchange scheme. Unlike one-way dissemination scheme, two-way uses two packets that are transmitted back and forth between a reference node and a un-sync node. Because of the reverse of packet transmission direction, two-way scheme uses an obsolete clock reading in one packet, but an futuristic reading in the other packet. Therefore, two-way performs disgracefully on estimating clock skew. In average, using one-way can give us precise estimation of skew, while using two-way can provide accurate estimation of oset. On the other hand, one-way may over-estimates clock oset in average, and the variance of using two-way is potentially high. Therefore, we try to combine the goods, and alleviate the weakness from both schemes by proposing hybrid scheme. The basic idea of hybrid is: using two-way scheme to estimate oset, and then using the skew estimation calculated from one-way scheme to further rene the oset estimation. y y TSHL uses one-way skew estimation to calibrate time stamps of un-synchronized node before it proceeds to use two-way scheme to estimate oset. In hybrid scheme, we ONLY use the skew estimation to compensate the relative oset taking place during the synchronization process. Therefore, hybrid scheme can operate with only 3 synchronization packets, while TSHL needs at least 4. In addition, hybrid scheme is lighter in terms of computation demand. 42 (a) (b) Figure 3.5: Illustration of synchronization errors with (a) one-way and (b) two-way schemes. The dotted and solid line represents the relation of estimated and actual clock readings between reference node and un-sync node, respectively. Figure 3.6: Message timelines for hybrid synchronization schemes. 43 An example of simplest 3-packet exchange scenario of hybrid scheme is shown in Figure 3.6. First, we can write: T 2 =T 1 O a t1 +S A I T 4 =T 3 +O a t3 +S ref II T 6 =T 5 O a t5 +S A III (3.10) From packetII andIII we can computeO e t 6 = (T 6 T 5 )+(T 3 T 4 ) 2 . From equation (3.8), we know the error of O e t 6 is 1 2 (S ref S A )(t 6 t 3 ) + S ref 2 ( III II ). To reduce the variance contributed byRO a t 3 !t 6 = 1 2 (S ref S A )(t 6 t 3 ), we use the skew estimation calculated from packet I and III to compensate it. Because the skew estimation is T 5 T 1 T 6 T 2 , the estimation of RO a t 3 !t 6 becomes: RO e t 3 !t 6 = T 6 T 3 T 6 T 2 (T 5 T 1 ) (T 6 T 3 ) (3.11) According to the ane clock model assumption, equation (3.11) can be re-written as: RO e t 3 !t 6 = T 6 T 3 T 6 T 2 (T 5 T 1 ) (T 6 T 3 ) = S ref (t 5 t 1 ) T 6 T 3 T 6 T 2 S A (t 6 t 3 ) (3.12) 44 Thus, the error of hybrid can be calculated as: O e t 6 O a t 6 = error of RO e t 3 !t 6 + S ref 2 ( II I ) = S ref 2 [ T 6 T 3 T 6 T 2 ( III I ) + ( II I )] (3.13) Becausef i g are iid, the mean error of hybrid equals to 0. In addition, the variance of hybrid scheme is: Variance of error =var[S] ( 1 4 ( T 6 T 3 T 6 T 2 ) 2 + 1 4 ( T 6 T 3 T 6 T 2 + 1) 2 + 1 4 ) (3.14) Because T 6 T 3 T 6 T 2 < 1 , we notice the high variance problem of two-way has been mitigated by compensating the relative oset. Thus, hybrid scheme not only has 0 mean error, its variance is also signicantly smaller than two-way scheme. Although the hybrid scheme we analyze here is the case with least packet exchange, it is possible to use more uni-directional packets from reference to A, to improve the precision of clock skew estimation. Note that, more uni-directional packets can produce higher skew estimation precision in the expense of higher energy overhead. On the other hand, higher clock skew estimation in a single synchronization instance leads to less frequent re-synch process, given a desired error requirement. Thus, one of our future work is to study the trade-o between number of uni-directional packets involved in a single synchronization process and synchronization precision. 45 Figure 3.7: Message timelines for receiver-receiver (RBS) synchronization schemes We also have interest in nding the optimal number of packets used in hybrid scheme, in terms of network lifespan. 3.1.4 Analysis of Receiver-Receiver Scheme An example of synchronization packet exchange scenario by using receiver-receiver scheme is shown in Figure 3.7. Similarly, we can write: T 2 =T 1 +O a;ref!A t 1 +S A I T 3 =T 1 +O a;ref!B t 1 +S B II (3.15) 46 For clarication, we useO a;ref!A t 1 to denote the actual oset between reference and A at instancet 1 , and similarly forO a;ref!A t 1 . Because the estimated oset isT 3 T 2 , the error of this oset estimation becomes: Error = (T 3 T 2 ) (O a;ref!B t 1 O a;ref!A t 1 ) = S B II S A I (3.16) One potential problem of receiver-receiver scheme is the dierence of acoustic trav- eling distance between reference to A and reference to B. If the dierence of trav- eling distance for A and B are signicant, then the error of oset estimation using receiver-receiver scheme can be non-negligible. In addition, receiver-receiver scheme requires A and B to be located within the broadcast region of reference. However, we focus on a tree-structured network with only one node in each level. Thus, receiver-receiver scheme does not t into our need. 3.1.5 Analysis of Multiple Two-way Exchange Scheme CTP [27], Tiny-sync, and Mini-Sync [68] are representative works of this scheme. Basically, multiple two-way exchange requires multiple rounds of two-way packet exchange, and then using linear regression to estimate clock oset and skew. An 47 Figure 3.8: Message timelines for multiple two-way synchronization schemes example of multiple two-way exchange scheme is shown in Figure 3.8. We can write: A M = 0 B B B B B B B B B B B B @ 1 T 2 1 T 3 1 T 6 1 T 7 . . . . . . 1 C C C C C C C C C C C C A ;B M = 0 B B B B B B B B B B B B @ T 1 T 4 T 5 T 8 . . . 1 C C C C C C C C C C C C A ;X M = 0 B @ C M D M 1 C A (3.17) Similarly as one-way, we can calculate the error as: Error =X I X M = S A m( P r 2 i ) ( P r i ) 2 0 B @ ( P r 2 i )( P (1) i+1 i ) ( P r i )( P r i (1) i+1 i ) ( P r i )( P (1) i+1 i ) +m( P r i (1) i+1 i ) 1 C A (3.18) Wherefr i g represents the time stamps generated by reference, i.e. T 2 ;T 3 ;T 6 ;T 7 ... etc. One observation is that the expected value of C error is strictly larger than 0 , 48 and the mean value of D error is strictly less than 0. Obviously, this is not an ideal solution comparing with hybrid scheme. 3.2 Analysis of Synchronization Error under Multi- hop Situations 3.2.1 Denitions and Assumptions of Analysis Because of the existence of clock skew, a synchronized clock, say A, may already signicantly drift away from the reference clock before another clock, say B, tries to synchronize with it. If clock A uses skew estimation to calibrate itself before providing readings to other clocks, the inaccuracy of clock skew estimation still de- teriorates the synchronization precision. Therefore, the relative oset taking place during the synchronization process is not a negligible error source when synchro- nization process is long. In multi-hop networks with sleep-scheduling, which can increase the intervals between two consecutive synchronization process, this source of error is signicant. We call this error as \relative oset error". Intuitively, if precise clock skew estimation is possible, then we can benet from compensating relative oset error; otherwise, it may further deteriorate synchronization precision. We analyze both cases separately in the following sections. In this section, we make the following assumptions on top of prior ones: 49 (i). We assume a tree-structured network, and every node is assigned to a specic level, determined by its hop distance to the root/reference node. The root node is assigned to level 0, and synchronization takes place sequentially from the root to higher level node. (ii). Every synchronization instance is independent with each other. (iii). By \overall error up to level i", we refer to the clock reading dierence between calibrated level i clock and the root clock, at the instance when level i node completes its synchronization with level i 1 node. 3.2.2 Propagation Error Without Relative Oset Compen- sation One-way Dissemination Scheme An example scenario is plotted in Figure 3.9. Similarly, we can compute X M;i+2 = (C M;i+2 ;D M;i+2 ) T = [(A i+2 +P i+2 ) T (A i+2 +P i+2 )] 1 (A i+2 +P i+2 ) T B M;i+2 , where: A i+2 = 0 B B B B B @ 1 T 7 1 T 9 . . . . . . 1 C C C C C A ;P i+2 = 0 B B B B B @ 0 O e t 6 ;i+1 0 O e t 6 ;i+1 . . . . . . 1 C C C C C A ;B M;i+2 = 0 B B B B B @ T 8 T 10 . . . 1 C C C C C A (3.19) For clarication, we add the subscripts i + 2 to A i+2 , P i+2 and B M;i+2 to identify these matrixes/vlaues are computed between level i + 2 and i + 1 clock, and add 50 Figure 3.9: An example scenario for doing synchronization in a multihop network using one-way scheme. the subscript i + 1 in O e t 6 ;i+1 represent this oset estimation is computed between level i + 1 and i clocks. If we re-write the matrix A M;i+2 =A i+2 +P i+2 , where A i+2 = 0 B B B B B B B B @ 1 T 7 1 T 9 1 T 11 . . . . . . 1 C C C C C C C C A ;P i+2 = 0 B B B B B B B B @ 0 O e t 6 ;i+1 0 O e t 6 ;i+1 0 O e t 6 ;i+1 . . . . . . 1 C C C C C C C C A (3.20) Then, the error matrix X error;i+2 can be computed as: X error;i+2 = S i+2 m P (T e 2i1 ) 2 ( P T e 2i1 ) 2 0 B @ ( P (T e 2i1 ) 2 )( P i ) ( P T e 2i1 )( P (T e 2i1 i )) ( P T e 2i1 )( P i ) +m( P (T e 2i1 i )) 1 C A (3.21) 51 For brevity, we useT e 2i1 =T 2i1 O e t 6 ;i+1 to represent the clock readingT 2i1 from leveli+1, such that it has been calibrated by using oset estimations between level i + 1 and i. Becausef i g are iid, we can compute the expected value of X error;i+2 as: Exp[X error;i+2 ] = S i+2 m P (T e 2i1 ) 2 ( P T e 2i1 ) 2 0 B @ m( P (T e 2i1 ) 2 ) ( P T e 2i1 ) 2 m( P T e 2i1 ) +m( P T e 2i1 ) 1 C A (3.22) Two conclusions can be made by observing equation (3.22). First, the mean error of D M;i+2 is 0. That means, one-way can provide precise clock skew estimation between i + 1 and i + 2 in average, without using clock skew estimation. The other observation is that mean error of C M;i+2 equals S. Therefore, using one- way without compensating relative oset error will produce excess S amounts of intercept estimation error in average. Because the intercept estimation error in level i + 2 is on top of prior errors, using one-way without relative oset compensation will lead to unbounded error under multi-hop scenario in average. By induction, we can write: Exp[Overall Error up to level j] =jS (3.23) 52 Figure 3.10: An example scenario for doing synchronization in a multihop network using two-way scheme. Two-way Exchange Scheme An example scenario is plotted in Figure 3.10. For convenience, we denote the reference clock reading at instance t i as T a i , i.e. T a i = S 0 t i +b 0 . By denition, we can write " i+1 t 4 =T e 4 T a 4 . Because: T e 6 =T 6 O e t 4 ;i+1 T e 7 =T 7 O e t 4 ;i+1 O e t 8 ;i+2 = (T 8 T e 7 ) + (T 5 T e 6 ) 2 (3.24) 53 Using the ane clock model, e.g. T 6 =S i+1 t 6 +b i+1 , we can thus compute " i+2 t 8 as: " i+2 t 8 =T e 8 T a 8 = (T 8 O e t 8 ;i+2 )T a 8 =" i+1 t 4 +S 0 (t 4 t 7 IV ) +S i+1 t 6 +t 7 2t 4 2 +S i+2 t 7 t 6 + III + IV 2 (3.25) BecausefS i g andf i g are iid, the mean value of " i+2 t 8 equals " i+1 t 4 . From section 3.1.2 we know the average error up to level 1 is 0. By induction, we can have: Exp[overall error at level j] = 0 (3.26) However, one potential problem of using two-way without relative oset compen- sation is the high variance of error. By observing equation 3.25, because every synchronization task introduces a constant error on top of prior hop's overall error in average, it can be expected using two-way without relative oset error compensa- tion demonstrates linear increasing variance with respect to hop count distance. In addition, if the length of synchronization process and inter-synchronization period are large, we may end up with huge propagation error in some instances. If we denote the variance up to level i + 1 at instance t 4 as V i+1 , then the variance at instance t 8 up to level i + 2 can be calculated as: V i+2 =V i+1 +var[S]( 3 2 ) +var[S][(t 4 t 7 ) 2 + ( t 6 +t 7 2t 4 2 ) 2 + ( t 7 t 6 2 ) 2 ] (3.27) 54 Figure 3.11: An example scenario for doing synchronization in a multihop network using hybrid scheme. If the value of (t 7 t 6 ) and (t 6 t 4 ), i.e. the length of synchronization process and inter-synchronization period, are large, we may end up with huge propagation error in some instances. In addition, because the value ofvar[S] andvar[S] are xed, the variance of using two-way without compensating relative oset error demonstrates a linearly increasing trend with respect to hop count distance to the root clock. This result is also consonant with Giridhar and Kumar's result[24]. Hybrid Scheme An example scenario is plotted in Figure 3.11. Overall error at t 6 up to level i + 1 as " i+1 t 6 =T e 6 T a 6 , and the oset estimation at t 1 2 can be computed as: O e t 12 ;i+2 = (T 12 T e 11 ) + (T 9 T e 10 ) 2 RO e t 9 !t 12 (3.28) 55 Using the ane clock assumption, and the clock skew estimation D M;i+2 derived from doing linear regression on packets sent by level i + 1 and received byi + 2, we can compute overall error at t 12 up to level i + 2 as: " i+2 t 12 =" i+1 t 6 +S i+2 t 12 t 9 2 +S i+1 t 10 +t 11 2t 6 2 S 0 (t 12 t 6 ) + (D M;i+2 1)(t 12 t 9 ) (3.29) SincefS i g are iid, the expected value of " i+2 t 12 equals " i+1 t 6 . From section 3.1.3, we know the mean value of overall error up to level 1 is 0. By induction, we know the mean overall error at any level j;8j 1 is still 0. Therefore, using hybrid without compensating relative oset error can produce good synchronization precision under multi-hop scenario in average. However, the trade-o of not compensating relative oset error is high variance of precision, and this eect will be re ected by large value and high variance of D M;i+2 . Because hybrid can produce accurate clock skew estimation, using hybrid without compensating relative oset error is clearly a sub-optimal strategy. 3.2.3 Propagation Error With Relative Oset Compensa- tion One-way Dissemination Scheme Consider Figure 3.9 again. The eect of compensating relative oset error makes the matrix P i+2 dierent from equation (3.20), thus changing the value offT e 2i1 g 56 in equation (3.21) and (3.22). However, this eect will be canceled out because they both appear in the numerator and denominator of equation (3.22). Therefore, no matter we compensate relative oset error or not, using one-way will lead to unbounded multi-hop error in average. SincefS i g andfig are both iid and in- dependent with each other, by induction, we know the expected overall error up to level of using one-way with relative oset error is the same as equation (3.23). Although the mean error is the same as not compensating inter-sync error, com- pensating relative oset error does provide lower variance, due to the fact one-way is capable of estimating clock skew precisely. Two-way Exchange Scheme Consider Figure 3.10 again. Because both TPSN[23] and LTS[28] do not provide skew estimation, we assume its skew estimation by doing linear regression on col- lected time stamps. Thus, the clock skew estimation can be computed as T 4 T 1 T e 3 T e 2 , whereT e 2 andT e 3 represent the relative oset calibrated time stamps corresponding to T 2 and T 3 , respectively. For convenience, we denote the clock skew estimation between levelj andj + 1 as e j+1 . By using ane clock model, we can compute the error of skew estimation between level i and i + 1 as: Error of e i+1 = S i+1 (t 3 t 2 + I + II ) S i (t 3 t 2 ) +RO e t 2 !t 3 (3.30) 57 Because RO e t 2 !t 3 = e i (t 3 t 2 ), the error of clock skew estimation in one level will further deteriorate clock skew estimation in its next level. By changing the value of T e 6 andT e 7 in equation (3.24), we can calculate the overall error up to level at t 8 as: " i+2 t 8 =T e 8 T a 8 =" i+1 t 4 +S i+1 t 7 +t 6 2t 4 2 e i+1 + S 0 2 [(1 1 e i+1 )(t 6 +t 7 ) 2t 4 e i+1 2t 8 ] +S i+2 t 7 t 6 + III + IV 2 (3.31) SincefS i g andf i g are both iid and independent with each other, the expected overall error becomes: Exp[" i+2 t 8 ] =" i+2 t 4 S 2t 4 e i+1 (3.32) We rst notice, oset estimation error in current hop will be carried to the next hop. Second, the skew estimation keeps adding error in every hop and also deteriorates the oset estimation in next hop. Therefore, the overall error of using two-way with compensating relative oset error under multi-hop scenario will keep accumulating quadratically. 58 Hybrid Scheme Consider Figure 3.11 again. Due to the ane clock model assumption, the overall error up to level i + 2 at time t 12 can thus be calculated as: " i+2 t 12 =" i+1 t 6 + (S i+1 +D M;i+1 1) t 10 +t 11 2t 6 2 S 0 (t 12 t 6 ) +S i+2 t 12 t 9 2 + (D M;i+2 1)(t 12 t 9 ) (3.33) SincefS i g andf i g are both iid and independent with each other, the expected value of " i+2 t 12 becomes " i+1 t 6 . In addition, because we know the average overall error up to level 1 is 0 from Section 3.1.3, by induction, we can write: Exp[overall error up to level j] = 0;8j (3.34) Although using hybrid with compensating relative oset error seems to have the same precision as not compensating relative oset error in average, their variance of precision can be very dierent. Because we already know that doing linear regression on uni-directional packets can produce precise clock skew estimation, it can be expected using hybrid with relative oset compensation can give us lower variance, comparing with not compensating relative oset error. Again, since every synchronization task adds in a constant error on top of prior hop's propagation error in average, it can be expected the variance of using hybrid with relative oset compensation increases linearly with respect to level number. 59 3.3 Experiments Our focus in this chapter is on evaluating dierent schemes for high propagation delay environments, such as underwater acoustic sensor networks. However, we are not aware of any acoustic underwater testbeds that would be suitable for experimen- tal evaluations. Instead, we use traces collected from experiments with RF-based sensor nodes (specically the Moteiv Tmote Sky platform [81]). State of the art RF-based time synchronization mechanisms such as FTSP and TPSN advocate the use of MAC-layer time stamping to reduce communication jitter. However, our testbed uses application-layer time-stamping, which incurs a higher latency and variance from sender to receiver. This suciently mimics the high high propaga- tion delay and high variance characteristics of interest to us. Although underwater acoustic sensor networks can see propagation delays on the order of hundreds of mil- liseconds, while the application layer time stamping on our testbed gives per-hop latencies of around ten milliseconds, it still suces to show the relative strengths and weaknesses of the various techniques. We have chosen to evaluate various schemes by rst collecting time-stamp data traces from a common set of experiments and then undertaking oine simulations, instead of directly implementing these schemes on the motes and running them sep- arately online. There are several good reasons for adopting this approach. First, the oine method will yield essentially the same performance as an online implemen- tation as the only key dierence is in where the computations take place (on-mote 60 versus o-board on a PC). Since the calculations involved in the dierent schemes that we evaluate (one-way, two-way, and hybrid) are extremely lightweight, the ef- fect of additional hardware capability on performance is negligible. We instead gain several benets from this approach. The testbed experiments we use are set up in such a way (all nodes can hear packets from each other) that they can be easily used to generate simulations of n! permutations of multihop chains. This allows us to average results over a thousand runs trivially, to generate results with high statistical signicance. By contrast, if the algorithms were to be run online, we would have to manually change the topology a thousand times while doing the ex- periments, which would make it prohibitively time-consuming to achieve the same signicance. Further, this approach is inherently fair to the various schemes, as they are each evaluated over the same set of time-stamp data. Finally, the traces from the experiments that we undertook in order to obtain these simulations can be reused in the future as a benchmark for other techniques and mechanisms. We now detail the experiments, and then present and comment on the results obtained. 3.3.1 Experimental Setup for Collection of Time-Stamp Traces We use 20 motes and mark each of them with a unique physical ID number, from 1 to 20. Every mote is placed within the transmission range of others, thus, each mote is capable of communicating directly with any other one in our experiment. 61 A synchronization packet includes the following information: Round Number, Sender Time Stamp, and Receiver Time Stamp, which are explained as follows: (i). Round Number: A round is consisted of a sequential synchronization packets sent through Node ID 1 to Node ID 20. Each round consists of 20 sending cycles. (Detailed in following contents.) (ii). Time Stamp: The clock readings when a synchronization packet is con- structed. Our data collection experiment proceeds as follows: (i). Exactly one node is scheduled to transmit packets in any instance, and all the others are considered as receivers. At time 0, ID 1 node starts broadcasting ten synchronization packets at an interval of 10ms. Once it nishes transmitting 10 packets, a sending cycle is complete. (ii). Whenever a receiver hears a synchronization packet, it records the sending time stamp, sender ID, and the corresponding local receive time stamp for that packet. Only the rst packet, which is commonly received by all receivers, is kept for future use and the remaining packets within the same sending cycle are discarded. Because we need to guarantee the existence of such packet in one sending cycle despite possible transmission errors, we make each sender broadcast 10 packets within its sending cycle. (iii). Nodes in the network initiate their own sending cycle in sequence of their physical ID. Because every sending cycle takes roughly 100 ms, we make the 62 node with physical ID i + 1 start its cycle after 150 ms of the rst received packet from ID i node to avoid overlapping prior sending cycle. (iv). When the node with ID 20 nishes its sending cycle, one sending round com- pletes. To avoid overlapping of two sending rounds, ID 1 node waits one minute and start a new sending round, after it receives packets sent by ID 20 node. (v). Repeat the above steps. In our experiments, we have collected 80 sending rounds of data. 3.3.2 Multi-hop Error Calculation The scheme of data collection makes it possible to manipulate the data to simulate various combinations of real-world time synchronization. We used a Matlab pro- gram to simulate all three synchronization schemes based on the traces we acquired. By choosing a permutation of the 20 nodes in our experiments, we obtain a virtual 19-hop line network with exactly one node in each level. The node which provides the reference clock for other nodes is located in level 0. The sequence of time-stamped message exchanges for each scheme are obtained by using the packet from each round of the experimental trace. To simulate a dierent network instance, we simply pick a dierent permutation of the 20 nodes. This allows us to obtain statistically meaningful results by averaging over dierent independent random network. 63 For each permutation, we apply the dierent synchronization schemes (one-way, two-way and hybrid; with and without relative oset compensation) oine using Matlab and compute the error at each level as follows. Synchronization is conducted by calibrating the clocks sequentially level-by-level from 0 to 19, with each scheme. Error at leveli is computed by obtaining the clock dierence between \calibrated level i clock reading" and \the corresponding level 0 clock reading at the same instance". By \level 0 clock reading at the same instance", we are referring to the receive time of the last packet involved in level i's synchronization process, measured by the node assigned to level 0 in the same permutation z . Presented results for each technique are average of error at each level across 1000 permutations. 3.3.3 Illustrations of Multi-hop Error Calculation For clarication, consider a simple scenario as follows. Suppose we want to simulate a 3-node, two-level network, and using one-way scheme z In other words, we use a receiver-receiver scheme to determine the error. It is for sure this method may introduce some \noise" into the actual error. However, the average error introduced by this mechanism is insignicant. According to our analysis in section 3.1.4, the major problem of using receiver-receiver scheme is the dierence of I and II . Because every T-mote in our experiment is congured identically, and physically located nearby, it can be expected I and II has approximately the same distribution. Thus, the average error introduced by this method is negligible. 64 We rst randomly select three nodes from the collected trace to form a 3-node, two-level network. Assume the node with physical ID 5, 11, and 8 are assigned to the level 0, 1, and 2 of the resulting network, respectively. Assume we use three synchronization packets to proceed one-way calculation. First, we choose the time stamp, which includes the send time of ID 5 node and receive time of ID 11 node, from sending round 1 to be the rst packet we need in the synchronization task between level 0 and level 1 in this iteration. Similarly, we can determine the time stamps from sending round 2 and 3 for the rest two packets in this synchronization iteration. Thereafter, we use linear regression on these time stamps to estimate the clock skew and oset between these two nodes, and calibrate level 1 (which is also ID 11 node in this example) clock reading accordingly. We use Figure 3.9 to illustrate the clock readings we get from the above process, and the level i in the gure corresponds to level 0 in this example. If we denote the calibrated value of a clock reading with a comma on it, then the calibrated value of T 6 is represented by T 0 6 . The synchronization error at level 1 is thus computed as the clock reading dierence between T 0 6 and T 5 . Before computing propagation error at level 2, we use the skew and oset esti- mation between level 1 and 0 to calibrate receive time of packet IV , V , and VI. Then, we do linear regression on the following data points: (T 0 7 ,T 8 ), (T 0 9 ,T 10 ), and (T 0 11 ,T 12 ). If the receive time of packetVI at ID 5 node is denoted byT 13 , then the synchronization error at level 2 is thus computed as the dierence of T 0 12 and T 13 . 65 3.4 Results and Discussion 3.4.1 Predicted outcomes In the trace based simulations, we have the following conditions which are relevant to our analysis models: The time periods between two consecutive packets, within the same synchro- nization process, are approximately the same. The time periods between two consecutive synchronization process, i.e. the duration between the end of a synchronization process and the beginning of the next immediate process, are approximately the same. The above two values are approximately the same. By applying above conditions, the predicted outcomes of our experiments are listed in Table 3.1 and 3.2. The former adopts skew estimation to compensate for relative oset error, whereas the later does not. 3.4.2 Experiment Results and Discussion The average 19-hop propagation error of all three synchronization schemes with and without inter-sync error compensation are listed in Table 3.1 and Table 3.2, 66 One-Way Two-Way Hybrid Measured Mean Overall 176 ms 4535 ms -0.18 ms Propagation Error Predicted Mean Overall 19 (E[]) 510 (E[]) 0 Propagation Error (" 19 ) Measured Mean Per-hop 9.26 ms 238.7 ms -0.0.095 ms Propagation Error Estimated Mean Per-hop E[] 26:8 (E[]) 0 Propagation Error (" 19 =19) Table 3.1: Propagation error under dierent synchronization schemes with relative oset error compensation One-Way Two-Way Hybrid Measured Mean Overall 167.4 ms - 0.2 ms 0.38 ms Propagation Error Predicted Mean Overall 19 (E[]) 0 0 Propagation Error (" 19 ) Measured Mean Per-hop 8.8 ms - 0.0105 ms 0.02 ms Propagation Error Predicted Mean Per-hop E[] 0 0 Propagation Error (" 19 =19) Table 3.2: Propagation error under dierent synchronization schemes without rela- tive oset error compensation 67 (a) One-way (b) Two-way (c) Hybrid Figure 3.12: Trace based simulation results showing multi-hop error propagation for one-way, two-way and hybrid schemes with inter-sync error compensation. 68 (a) One-way (b) Two-way (c) Hybrid Figure 3.13: Trace based simulation results showing multi-hop error propagation for one-way, two-way and hybrid schemes without inter-sync error compensation. 69 respectively, and are plotted in Figure 3.12 and Figure 3.13, respectively. The out- comes presented are averaged over 1000 synchronization iterations. For comparison purpose, we list the results side by side to the predicted outcomes. As listed in Table 3.1, the hybrid scheme performs the lowest average error, while two-way scheme performs the highest. A more interesting conclusion can be made by observing Figure 3.12. One-way scheme maintains a linearly increasing trend with respect to the hop distance to the root node, and two-way scheme raises quadratically. Both schemes suer from unbounded error. On the other hand, hybrid scheme not only performs signicantly better precision comparing to the other two schemes under the same settings, most importantly, hybrid scheme is capable of providing bounded average propagation error. By comparing the one-way scheme with our predicted value, the mean value of thus can be computed as 167ms=19 8:8ms. Similarly, the average value of calculated from two-way scheme can be computed as 4535ms=510 8:9ms, which is very close to what we get from one-way calculation. For the hybrid case, while the predicted value is 0, our experiment outcomes show uctuated propagation error at dierent hop distance. The reason of this unmatched results is caused by the high jitter nature of . From the traces, we can calculate the mean of is around 8.9 ms, the standard deviation is 2.3, and, in addition, the distribution of is very close to normal distribution. In both one-way and two-way scheme, since the mean propagation error is large, the uctuation caused by the variance is not obvious at all. However, the hybrid scheme is very precise such that little uctuations will be 70 easily observed. Based on the above discussions, all these experiment outcomes are consistent with our analysis conclusions. In Table 3.2, although one-way and hybrid scheme still performs similarly as they do in previous setting, two-way scheme possesses considerably lower propaga- tion error comparing with the prior settings. Especially, two-way scheme, as hybrid scheme, shows no obvious trend of increasing propagation while hop distance goes up in Figure 3.13, and the synchronization precision of both two-way and hybrid schemes are comparable. These results also match our prediction. From the one- way side, because of the precise clock skew estimation, most of the relative oset error can be mitigated eciently. Thus only the oset estimation error will prop- agate hop by hop. By calculating the average value of E[] from the experiment outcomes, we get 171ms=19 8:9ms, which is the same as prior value. For the hy- brid scheme, because it is capable of providing accurate oset and skew estimations simultaneously, the results presented also match our expectation. For the two-way scheme, due to the precise oset estimation we can get from it, the dominant error source is the relative oset taken place during inter and intra synchronization pe- riod. However, because of the equal probability that the clock bias of one node is faster or slower than the other clock that intends to synchronize with itself, it can be expected that the relative oset are equally likely to get positive and negative values. In addition, the value of T inter and T intra is a constant in our trace based simulations, it is also reasonable to expect the relative oset will cancel each other 71 throughout dierent synchronization iterations. A more detailed descriptions can be found in Section 3.2. From the above results, we notice while the average propagation error of one- way increases without bounded, two-way without inter-sync error compensation and our hybrid scheme (no matter compensating inter-sync error or not) perform comparably. In addition, both the later two strategies provide bounded propagation error in average. To further address the benets of hybrid scheme, we compare the variance of these two strategies in the following section. 3.4.3 Variance Comparison Between Hybrid and Two-way Scheme For comparison purpose, we compare the variance of precision between hybrid and two-way scheme under two dierent strategies: with or without relative oset error compensation. The results are plotted in Figure 3.14(a) and 3.14(b). In sum, both hybrid and two-way schemes perform linearly increasing trend with respect to hop distance to the root node. This conclusion is also consonant with Giridhar and Kumar's work [24]. By comparing 3.14(a) and 3.14(b) we notice that, hybrid does benet from compensating relative oset error. However, the variance performance of hybrid is not impressive, considering the extra packets exchange it costs. One possible reason is, the relative oset error is not signicant. In our time stamps collecting experiment, since all motes are placed near to each other, the environment may not cause high enough skew between dierent clocks. In addition, the length of 72 a synchronization process and the inter-synchronization period are not long enough, either. Therefore, the relative oset is not a signicant source of error. Instead, the high variance off i g plays the major role on determining the variance of both schemes. In order to verify our speculation, we intentionally increase the inter- synchronization period to around 12 minutes and re-do the trace-based simulation to simulate a 6-node, 5-hop line network. The variance comparison are plotted in Figure 3.15(a) and 3.15(b). One interesting observation is, variance of two-way without relative oset com- pensation increases much faster than prior setting. Even the 5-hop variance is higher than prior result of 20-hop. Although the variance of hybrid also increases with longer inter-synchronization period, the rate is much slower. By comparing Figure 3.15(a) and 3.15(b), we also notice that hybrid does benet from compensating relative oset error. From above results, hybrid with relative oset compensation does perform more gracefully than other existing strategies in a high propagation delay and low-duty cycle network. 3.5 Summary The major contributions of this work are as follows. First, we have presented a thorough comparison of two-way packet exchange, one-way dissemination schemes, 73 (a) Two-way without compensation vs. hybrid with compensation (19-hop) (b) Two-way without compensation vs. hybrid without compensation (19-hop) Figure 3.14: Variance comparison between two-way and hybrid scheme in a 19-hop network. 74 (a) Two-way without compensation vs. hybrid with compensation (5-hop) (b) Two-way without compensation vs. hybrid without compensation (5-hop) Figure 3.15: Variance comparison between two-way and hybrid scheme in a 5-hop network. 75 receiver-receiver scheme, and multiple two-way scheme. We nd that, one-way dis- semination performs worse in estimating clock oset, two-way dissemination per- forms worse while relative oset error is signicant, receiver-receiver scheme per- forms worse when propagation delay is substantially dierent, and multiple two-way performs biased oset and skew estimation. Second, we have proposed a hybrid one-way dissemination/two-way exchange synchronization scheme that can provide substantially better accuracy, bounded error propagation over multiple hops in aver- age, and low variance of propagation error. Such a strategy would be most useful for a challenging environment, characterized by high propagation delay, low-duty cycle, and highly skewed clocks, such as underwater acoustic sensor networks. Third, we implement a series of experiments to collect time stamps from real Tmotes. From the trace-based simulation results, we get the same conclusions as we make in our analysis. 76 Chapter 4: Link Scheduling in UWASN x In this chapter, we consider the problem of scheduling acoustic links in a single broadcast domain. We rst formally formulate the problem and prove its NP- completeness in Section 4.1, and propose the tightest possible approximation ratio in Section 4.1.2. In order to understand the relation between schedule length and network topology, we propose the SAT conversion of underwater scheduling prob- lem, and use a complete SAT solver for this purpose in Section 4.2. Finally, we make a brief summary of this chapter in Section 4.3. x This chapter is based on our prior published work: [32] Huang, P., and Chen, Y., and Kumar, A., and Krishnamachari, B., "Link Scheduling in a Single Broadcast Domain Underwater Networks", USC Engineering School Technical Report, No. 2009-3, 2009. [33] Huang, P., and Chen, Y., and Kumar, A., and Krishnamachari, B., "Link Scheduling in a Single Broadcast Domain Underwater Networks", Proceedings of the Third IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing (SUTC2010) June 7-9, 2010. 77 4.1 Algorithmic Complexity We consider a time-slotted, single carrier frequency and single communication power setting system. Each node we considered is located in the same broadcast domain, i.e. each transmission can be overheard by all nodes. There are two kinds of receptions in the viewpoint of a receiver; one is intended transmission and the other one is interference. An intended transmission is the data sent by the corresponding sender of this receiver, and an interference is data sent by nodes other than its corresponding sender. We assume a transmission has high enough power to corrupt an intended transmission, even it has propagated the longest distance within the deployed area. Every transmission can only take place at the beginning of a time slot, and spans exactly one time slot. We assume no coding protection for all transmissions. Therefore, an intended transmission fails, if and only if a collision happens. By collision, we refer to the condition that an intended transmission is corrupted by interferences. Our interest is, \given a set of transmitter-receiver pairs P , and pair-wise delay between any two nodes, which satisfy a metric { , is it possible to schedule all trans- missions within a schedule period with lengthK, such that no collision will corrupt intended communications?" We call this problem \Metric Underwater Scheduling", and claim that it is NP-complete. { A valid metric satises the following properties: (1) non-negativity , (2) identity of indis- cernible, (3) symmetry, and (4) triangle inequality. 78 4.1.1 NP-Hardness Proof We rst brie y explain a concept that will be used in the proof. K-Coloringproblem: Given a graphG = (V;E), such thatV andE represent the set of vertexes and edges in this graph, respectively, and K dierent colors. we are interested in nding the way to color all vertexes v2 V in this graph with a color, such that no two vertexes, which share a common edgee2E, be painted the same color. It has been shown that K-Coloring problem is NP-hard [43]. Theorem 1. Metric Underwater Scheduling is NP-complete. Proof. A schedule with lengthK is a certicate of the Metric Underwater Schedul- ing. We could check this schedule, in polynomial time, whether every transmitter is scheduled withinK and no intended communication is corrupted by interference. Therefore, Metric Underwater Scheduling is in NP. To prove the NP-hardness, we do the polynomial reduction from K-Coloring. Consider an arbitrary instance with graph G = (V;E) of K-Coloring, we build a corresponding graph H = (V 0 ;E 0 ) as follows. For every node v 2 V , we build a gadget consisting of two nodes v 0 1 2 V 0 and v 0 2 2 V 0 , such that v 0 1 and v 0 2 can be considered as a transmitter and a receiver in Metric Underwater Scheduling, respectively. Note that, if the highest degree of G is4, K must be no less than4 to be feasible. Connect every transmitter and receiver pair inH with an edge, which has length a > K. The length of an edge in H represents the propagation delay 79 between the pair of nodes connected by this edge. For every edge (u;v)2E, we add two edges, (u 0 1 ;v 0 2 ) and (v 0 1 ;u 0 2 ), with lengtha inH. If two nodes, sayx andy, are not connected by an edge inG, then we add two edges, (x 0 1 ;y 0 2 ) and (y 0 1 ;x 0 2 ), with length 2a in H. In this construction, the exhaustive combination of edges which form a triangle can be listed as:fa;a;ag;fa; 2a;ag;f2a; 2a;ag. Obviously, they satisfy triangular inequality. In addition, distances are non-negative and symmetry, thus, H is in a metric space. We rst prove that, if vertexes of G are K colorable, then we can construct a solution of Metric Underwater Scheduling as follows: for each color used in K- Coloring, we map it to a unique time slot within K. If we denote the color of node v2 V as c(v), then we assign its corresponding time slot, t(v), to the transmitter v 0 1 2H. Because G is K colorable, two vertexes, say u and v in G, which are joint by a edge, say (u;v) inG, can not have the same color. In other words, transmitter u 0 1 and v 0 1 in H can not transmit at the same time slot because of interference. On the other hand, if two vertexes, say x and y in G, are not connected by an edge, then they can be assigned either the same color , i.e., t(x) =t(y), or dierent, i.e., t(x)6=t(y), and both corresponding assignments are feasible in H. First, consider t(x) = t(y). Since the packets of both x 0 1 and y 0 1 will arrive at their intended receivers and other's intended receivers at timet(x) +a andt(x) + 2a, respectively, no collision occurs under this schedule. If t(x)6=t(y), then transmission of x 0 1 will arrive y 0 2 at time (t(x) + 2a)> 2a. However, y 0 2 already receives its packet at time (t(y) +a) (2a 1). Similarly, we can verify that y 0 1 will not interfere with x 0 2 80 Figure 4.16: Construction of a gadget, such that each node in graph G is mapped to a pair of nodes in the new graph H, with an edge of length a between them. intended communication. Thus K-colorable implies a feasible solution of Metric Metric Underwater Scheduling. Conversely, we will prove that if Metric Underwater Scheduling has a satisfying solution, then G is also K-colorable. For a transmission schedule, say t(u) for transmitteru 0 1 , we map it to a unique color within the K choices. If a receiver, say v 0 2 , is connected with another transmitter, say u 0 1 , with a length a edge in H, then we know u 0 1 and v 0 1 will interfere with each other, thus will not be scheduled in the same slot. By the above mapping, u andv inG are also colored in dierent colors. However, we know that (u;v)2 E. Therefore, this color assignment is feasible in G. If a receiver, sayy 0 2 , is connected with another transmitter, sayx 0 1 , with a length 2a edge in H, then we know there does not exist an edge (x;y)2 G. Therefore, there is no direct con ict on color choices between node x and y in G. Thus, we construct a viable K-Coloring solution from Metric Underwater Scheduling. 81 Figure 4.17: InG = (V;E), if there exists an edgeuv2E, then we create two edges with length of a in H. Figure 4.18: In G = (V;E), if there exists no edge between node u and v, then we create two edges with length of 2a in H. 82 4.1.2 Approximability Result In addition to NP-completeness, we next present the tightest possible approxima- tion ratio of Metric Underwater Scheduling. For convenience, we explain some terminology used in the following contents before preceding to the proof. More detailed descriptions can be found in [83]. Turing Machine: A Turing machine is one kind of state machine. At an instance, the machine can be in any one of a nite number of states. Instructions for a Turing machine consist in specied conditions under which the machine will transition from one state to another. Probabilistic Turing Machine: A probabilistic Turing Machine is a non- deterministic Turing Machine, such that it randomly determines the transition from available states according to some probability distribution. ZPP (Zero-error Probabilistic Polynomial time): ZPP can be dened as the class of problems for which a probabilistic Turing machine exists with the following properties: { It always runs in polynomial time. { Returned answers can only be YES, NO or DO NOT KNOW. { Returned answers can either be the correct answer or DO NOT KNOW. { If the correct answer is YES, then it returns YES with probability at least 1/2 (and DO NOT KNOW otherwise). 83 { If the correct answer is NO, then it returns NO with probability at least 1/2 (and DO NOT KNOW otherwise). Theorem 2. If we denote the number of nodes in Metric Underwater Scheduling as n, then it is not possible to approximate Metric Underwater Scheduling within ( n 2 ) 1 ;8> 0, unless NP = ZPP. Proof. Suppose the original K-coloring instance hasK nodes, then the correspond- ing Metric Underwater Scheduling instance has 2K nodes. According to the above proof, we notice that the number of minimum chromatic number equals to the min- imum schedule length. If we have n 2 1 = K 1 ;8 > 0 approximation for Metric Underwater Scheduling, then it implies that we can approximate Minimum Chro- matic Number within K 1 ;8 > 0, which contradicts to the conclusion proposed by Feige and Kilian [19]. The most challenging issue of dealing with underwater scheduling problem is the non-negligible propagation delay: the same transmission may be considered as interference by dierent nodes at signicantly dierent times. Therefore, the interference pattern not just depends on the time the packet has been sent, but also relates to the network topology. In short-ranged terrestrial RF networks, because propagation delay is negligible, once a packet is transmitted, it arrives every node in the same broadcast domain immediately. Therefore, the minimum number of 84 time slots we need to time schedule every link once within a given period, equals to the number of links in the same broadcast domain. On the contrary, UWASN allows concurrent transmission without incurring colli- sion due to the fact of high propagation latency. Therefore, it is possible to schedule multiple, sayX, transmission pairs with scheduling length less thanX slots. An ex- ample of this scenario is depicted in Figure 1.1. However, when a network has high density, it is more likely that we may need a scheduling period with length larger than the number of transmission pairs. An example of this situation is plotted in Figure 1.2. 4.2 Findings from Applying a Complete SAT Solver Besides to be algorithmically complex, we are interested in studying the relation between a feasible schedule length and the number of nodes. To achieve this goal, we plan to transform our problem into an equivalent SAT instance, and determine the satisability of transformed problem by using a complete SAT solver, zcha [85]. 4.2.1 SAT Problem Transformation of Time-Slotted Trans- mission Model We rst demonstrate the transformation of an arbitrary instance to a SAT prob- lem. For example, we are given a set of transmission pairsfT;Rg, K consecutive transmission slots, and a pair-wise delay matrixD. We introduce a set of indicator 85 variablesft ij j8i2 T;j2 Kg, such that t ij = 1 means transmitter i is allowed to transmit at slot j, or t ij = 0 otherwise. Thus, we havejTj clauses which have the following form: (t i1 _t i2 _:::_t iK );8i2T . For convenience, we call these clauses as \feasibility clauses". In order to nd out which schedule may cause interference, thus corrupting intended communication, we adopt the following algorithm: 8i2T;j2K, if t ij +D(i;i)<t kl +D(k;i) + 1; for any k2T;k6=i;l2K, or, t kl +D(k;i)<t ij +D(i;i) + 1; for any k2T;k6=i;l2K, then we know, if transmitter i transmits at slot j, it will cause interference, if transmitter k transmits at slot l. Keep iterating until all possible con ict schedules are found. For every con ict schedulet ij ;t kl , we dene a clause (t ij _t kl ). For convenience, we call these clauses as \con ict clauses". Lemma 1. We can nd a feasible schedule from the truth assignment of a trans- formed SAT problem. Proof. Suppose we cannot nd a viable schedule from the truth assignment. With- out loss of generality, we assume the truth assignment isft ij ji2T;j2Kg. There are only two conditions such that we cannot nd a viable schedule from the truth assignment. One is that some transmitter are not assigned any slots to transmit, and the other one is the occurrence of interference. 86 Due to the the existence of feasibility clauses, every feasibility clause has at least one indicator variable that is one. We can always choose one indicator variable in each feasibility clause accordingly. Thus, it is not possible that a transmitter is not assigned any slot in the truth assignment. On the other hand, the existence of con ict clauses also guarantees that, at most one of the indicator variable involved in a con ict clause can be assigned to 1. Therefore, interference will not take place in a truth assignment, thus proving our claim. 4.2.2 Results of Equivalent SAT Problems We choose two variables in our simulations. One is the number of available slots, and the other one is node density. All the results are the mean of 100 randomly formed networks with given parameters. In Figure 4.19, we notice two dierent scenarios. While for the case of K = 5, every instance with number of pairs less 8 can be satised. On the other hand, a certain percentage of 10-pair instances is not satisable when K = 10. In other words, the minimum schedule length that guarantees satisability can be more or less than the number of pairs located in the same broadcast domain, depending on dierent network density. An example of the later case is plotted in Figure 1.2. While there are only 3 transmission pairs in this network, the minimum schedule length is 4 time slots in this case (with assumption that packet length is 1 time slot). 87 Figure 4.19: Probability of infeasibility when schedule length is xed. Another observation is the existence of a transition region between feasible and infeasible instances. Take K = 5 for instance, it is highly likely that we can nd a feasible schedule when there are no more than 7 pairs. On the contrary, it is almost impossible to satisfy more than 8 pairs under the same setting. In addition, the transition region, which located between feasible and infeasible cases, becomes wider when the schedule length K increases. 4.3 Summary In this chapter, we rst formally prove the NP-completeness and the tightest approx- imation ratio for Metric Underwater Scheduling problem. We then use a complete SAT solver to study the feasibility of Underwater Scheduling problem We notice that, while the node deployment is sparse, it is likely that UWASN can be sched- uled eciently; while the node density increases, UWASN becomes inecient due to the high propagation latency and complicated delayed interference. 88 Chapter 5: Random Access in UWASN k Because of the high computing cost, high energy overhead, and in exibility, we focus on a Distributed, Randomized, and Topology-unaware (DRT) medium access scheme for UWASN in this chapter. We start from analyzing a DRT scheduler, that a nodes determines its channel access time by using uniform distribution, in Section 5.1. Thereafter, we nd the highest possible throughput of DRT scheme by modifying channel access PMF, and compare the throughput of optimal DRT with uniform one in Section 5.2. Finally, we present a short summary of this chapter in Section 5.4. k This chapter is based on our prior published work: [32] Huang, P., and Chen, Y., and Kumar, A., and Krishnamachari, B., "Link Scheduling in a Single Broadcast Domain Underwater Networks", USC Engineering School Technical Report, No. 2009-3, 2009. [33] Huang, P., and Chen, Y., and Kumar, A., and Krishnamachari, B., "Link Schedul- ing in a Single Broadcast Domain Underwater Networks", Proceeding of the Third IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing (SUTC2010) June 7-9, 2010. 89 5.1 Performance Analysis of Uniform DRT Sched- uler As mentioned in the introduction, because of several undesired features of central- ized schedulers, reservation-based protocols and carrier-sensing protocols, we are interested in the performance that DRT strategy can achieve in UWASN. Due to its throughput superiority and simplicity for terrestrial RF networks, uniform DRT scheduler, which picks the transmission times uniformly from a given period, is an- alyzed in this section as a starting point to help us understand the applicability and limitations of DRT strategy. 5.1.1 System Modeling For the sake of generality, we use \normalized distance unit" and \normalized time unit" in the following context. For example, if a network of interest has dimension 1000m 1000m, then we will denote the area as 1 1. In addition, \1 unit of normalized time" in this example represents the actual time, in unit of second, for the sound wave to travel 1000m. Consider the following settings. In a 1 1 square area, a network is indepen- dently, uniformly and randomly deployed with 2N nodes. Exactly N of them are transmitters, and the remaining nodes are receivers. Each transmitter is uniquely and exclusively coupled with a receiver, and can transmit one packet in one schedule 90 period. In other words, there are exactlyN links located in this broadcast domain. The length of a schedule period isK units of normalized time, and each transmitter independently chooses an instance within this period to start transmitting a packet according to a continuous uniform distribution. Moreover, every packet takes ex- actly P units of normalized time to transmit, and a transmission fails if and only if collision takes place. The assumptions about transmission power, coding and transmission bands are the same as in Section 4.1. We are interested in the proba- bility of a successful transmission, system throughput (dened later), and per user throughput using this random scheduler. The symbols we use are listed as follows. X i : A random variable representing the X-axis coordinate of node i. Y i : Aa random variable representing the Y-axis coordinate of node i. K: The schedule length. N: Number of transmission pairs in the same broadcast domain. A ij : A random variable representing the 1st bit transmitted by nodei, arriving time at node j. Z ij : A random variable representing the Euclidean distance between node i and j. F I (i): The cumulative mass function (CMF) of random variable I. f I (i): The probability mass function (PMF) of random variable I. 91 P : The packet length. 5.1.2 Theoretical Analysis We start by calculating the probability distribution function (PDF) of the distance between any two nodes deployed in this network. Lemma 2. S is dened as the square of horizontal distance between any two nodes, that is S = (X i X j ) 2 . The CDF of S is as follows: F S (s) =Pr[Ss] = 8 > > > > > < > > > > > : 2 p ss if 0s 1 1 if s 1 0 if s 0 Similarly, we can get S 0 , square of the vertical distance between two nodes. Hence, the distance between two nodes Z = p S +S 0 . By applying Lemma 2, we can calculate the CDF of random variable Z as: Lemma 3. The CDF of random variable Z, F Z , is: F Z (z) = 8 > < > : 1 3 + 2 p z 2 1 2z 2 z 4 2 1 6 [ 16z 4 +20z 2 4 p z 2 1 + 12z 2 tan 1 ( z 2 2 2 p z 2 1 )] if z 1 z 2 8 3 z 3 + z 4 2 if z > 1 By applying elementary probability techniques, we can nd the exact PDF of random variable A ij (the rst bit, transmitted by node i, arrival time at node 92 j). Since every node is independently deployed, and transmission times are also independently determined, we abbreviate Z ij and A ij to Z and A, respectively. Pr[Aa] = 8 > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > : 1 K (a p 2 + R p 2 aK F Z1 dz) 8a>K + 1;a> p 2 a2 K + 1 K ( R 1 aK F Z1 dz + R p 2 1 F Z2 dz) 8K <aK + 1;a> p 2 1 K R a aK F Z1 dz 8K <aK + 1;a 1 1 K ( R 1 aK F Z1 dz + R a 1 F Z2 dz) 8K <aK + 1; 1<a p 2 1 K R a aK F Z2 dz 8 p 2a>K + 1 1 K R a 0 F Z1 dz 8amin(1;K) 1 K ( R 1 0 F Z1 dz + R a 1 F Z2 dz) 81<amin(K; p 2) When K > p 2, the CDF of random variable A is: Pr[Aa] = 8 > > > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > > > : 1 K (a p 2 + R 1 aK F Z1 dz + R p 2 1 F Z2 dz); 8K + 1a>K 1 K (a p 2 + R p 2 aK F Z2 dz); 8 p 2 +Ka>K + 1 1 K (a p 2 + R 1 0 F Z1 dz + R p 2 1 F Z2 dz); 8Ka> p 2 1 K R a 0 F Z1 dz; 8a 1 1 K ( R 1 0 F Z1 dz + R a 1 F Z2 dz); 81<a p 2 93 Figure 5.20: Comparison of PDF between random variable A and normal distribu- tion (small K value) Figure 5.21: Probability density function of random variable A (large K value) A good approximation of A can be stated as follows: when K 1:3, PDF of A can be approximated as a normal distribution; when K >> 1:3, PDF of A can be approximated as a uniform distribution within the range (0;K + p 2). Examples of the distribution of A for small K and large K are plotted in Figure 5.20 and 5.21, respectively. When K > 1:3, the PDF of A always has a at region as plotted in Figure 5.21, and the width of this region becomes wider, as K increases. 94 Note that, although the scenario we discuss so far is for \one" scheduling period only, independently iterating this random access process can be a viable MAC protocol. However, in order to prevent transmissions taking place in prior schedule periods from interfering with consequent ones, using \guard time" between two consecutive schedule periods is necessary. In our case, the longest propagation delay is p 2 unit of normalized time and the packet length is P , thus p 2 +P is proper for our purpose. Because decisions of transmission time are made independently across dierent users and dierent schedule periods, the above iterating scheme can be considered as a renewal process. Therefore, the throughput can be calculated as: throughput = average amount of delivered data in one schedule period length of one schedule period (5.35) Because of independency, the numerator of Equation 5.35 can be computed as: (average amount of delivered data in one schedule period) = N (probability a transmission succeeds) (packet length) (5.36) If we denote the PDF and CDF (Cumulative Density Function) ofA asf A andF A , respectively, then a transmission will be corrupted by interferences with probability: Pr(collision) = Z K 0 f A (j) Z min(K;j+P) max(0;jP) f A (k)dkdj (5.37) 95 Therefore, the probability a transmission succeeds is 1Pr(collision). For the sake of space restriction, the exact expressions of the probability that a packet can be successfully delivered are listed in our technical report [32]. We will present plots showing the throughput of this uniform scheme with respect to various parameters in the next section, after describing the optimal DRT scheduler. 5.1.3 Observations One of the main dierence between the PDF ofA plotted in Figure 5.20 and 5.21 is the shape: while K is small, the PDF has an obvious peak, whereas the other one has at top. In Figure 5.20, around 80% of transmissions start arriving a receiver within time 0.516 to 1.528, which represents only 41% of total possible arrival period. On the contrary, in Figure 5.21, around 80% of transmissions arrive within time 1.522 to 9.521, which is over 70% of total possible arrival period. Therefore, when schedule length K is small, using uniform DRT scheduler will lead to high collision probability, due to the concentration of transmission arrival pattern. The throughput of using uniform DRT scheduler is even more problematic when longer packets are used. On the other hand, although the rst bit arrival time for the case of long schedule length distributes more evenly across whole possible arrival period, as we will see in Section 5.3, uniform DRT scheduler still suers from long transmission packets, thus leading to low throughput. 96 5.2 Optimal DRT Scheduler In light of our ndings, we seek for the throughput-optimal scheduler, which uses DRT strategy, in this section. Because of the consideration of computation complex- ity, we approximate PDF with PMF (Probability Mass Function), which is derived from discretizing PDF, in this section. 5.2.1 Problem Formulation System throughput is determined by Equation 5.35 and 5.36. If packet length P , schedule length K, and number of transmission pairs N are constants, then maximizing throughput is equivalent to minimizing collision probability. We denote the transmission time generated by optimal DRT scheduler and its corresponding rst bit arrival time as T and A , respectively. Because DRT strategy does not utilize the knowledge of network topology, f A (a), PMF of A , can be calculated as: f A (a) = X i2f0;1;:::;ag f T (i)f Z (ai) (5.38) The collision probability becomes: Pr(collision) = X j2f0;1;:::;Kg (f A (j) X jjmj<P;m2f0;1;:::;Kg f A (m)) (5.39) 97 Therefore, our goal can be achieved by solving the following optimization problem: minimize : X j2f0;1;:::;Kg (f A (j) X jjmj<P;m2f0;1;:::;Kg f A (m)) subject to : f T (t) 0;8t2f0; 1;:::;Kg X t2f0;1;:::;Kg f T (t) = 1 (5.40) 5.2.2 Characteristics of Optimal DRT Scheduler We use Matlab optimization toolbox to solve the above problem, and 1 unit of time is divided into 100 segments in our PMF computation. In general, we have the following observations: When K < 1, the optimal DRT scheduler only picks the rst and the last available transmission instances. In this case, if K >> P , then these two instances have equal probability to transmit; ifKP , then the last available instance has higher probability. An example PMF of optimal DRT scheduler is plotted in Figure 5.22. When K 1, the optimal DRT scheduler may use some instances in the middle of the schedule period. If K >> P , then the PMF of optimal DRT scheduler may look like the circle/red set of points in Figure 5.23; if K >P , then the PMF of optimal DRT scheduler may look like the plus/blue set of points in Figure 5.23; ifKP , then the PMF of optimal DRT scheduler has the shape of the circle/red set of points in Figure 5.22. 98 Figure 5.22: PMF of optimal random policy with K = 0:5;N = 5;P = 0:1 and P = 0:5. When K >> 1 and K >> P , then the uniform DRT scheduler is close to optimal. As plotted in Figure 5.24, compared with uniform DRT scheduler, optimal DRT scheduler tends to distribute the transmission arrival time more evenly, so as to avoid the trac concentration issue. 5.3 Discussion In Figure 5.25, we varyK and setN = 2 andP =f0:5; 1:5g. Because there are only two pairs, contention is light, thus leading to low collision probability when packet is short. WhenP = 0:5, the improvement of using optimal DRT scheduler, compared with uniform DRT scheduler, is 22%. However, when longer packet P = 1:5 is used, collision probability raises signicantly for uniform DRT scheduler. On the contrary, collision probability of optimal DRT scheduler degrades more gracefully, 99 Figure 5.23: PMF of optimal random policy with K = 2;N = 5;P = 0:1 and P = 0:5. Figure 5.24: Distribution of rst bit arrival time: A*(optimal) vs. A(uniform) 100 Figure 5.25: Throughput comparison between uniform and throughput-optimal pol- icy. N = 2;P = 0:5 and P = 1:5 Figure 5.26: Throughput comparison between uniform and throughput-optimal pol- icy. N = 7;P = 0:1 and P = 1 101 Figure 5.27: Throughput comparison between uniform and throughput-optimal pol- icy. K = 0:5;P = 0:5 and P = 1 Figure 5.28: Throughput comparison between uniform and throughput-optimal pol- icy. K = 2;P = 0:5 and P = 1:5 102 Figure 5.29: Throughput comparison between uniform and throughput-optimal pol- icy. K = 0:5;N = 2 and N = 6 Figure 5.30: Throughput comparison between uniform and throughput-optimal pol- icy. N = 2;K = 0:5 and K = 2 103 thus beneting from using longer packets. When P = 1:5, optimal DRT scheduler has around 4 times of throughput than uniform DRT scheduler, and this ratio keeps increasing when P goes up as plotted in Figure 5.31. More importantly, the maximum throughput of optimal DRT scheduler is even higher than P = 0:5. In general, optimal DRT scheduler prevails under long packet settings. The major dierence between Figure 5.26 and 5.25 is the increase of network density from N = 2 to N = 7. When N = 7, because contention is high, both schedulers suer in this setting. Although the improvement ratio of using opti- mal DRT scheduler is even higher (around 9 times) when P = 1, the achievable throughput is still low and may not be an ideal operational choice. In Figure 5.27, we vary N and set K = 0:5 and P =f0:5; 1g. For both sched- ulers, the throughput optimal density is N = 2, and experience low throughput in this short schedule length K = 0:5 setting. While we increase K to 2 in Figure 5.28, both schedulers still prefer low network density. Therefore, it is not suitable to deploy DRT strategy-based schedulers in heavy contention environments. In Figure 5.29, we vary P and set K = 0:5 and N =f2; 6g. While N = 2, both schedulers can benet from using longer packet. As contention raises (N increases to 6), no one can take advantage of long packet, and need to use the shortest packet to maximize throughput. The throughput gain of using optimal DRT scheduler also shrinks, as the network density goes up. To understand how the throughput optimal packet length varies with schedule length K, we compare both schedulers in Figure 5.30. It is noticeable that both 104 schedulers choose to use longer packets, while schedule length increases. In addi- tion, the throughput gain of optimal DRT scheduler, compared with uniform DRT scheduler, also increases with schedule length. We summarize our ndings as follows: When schedule length and density are xed, the throughput improvement ratio of using optimal DRT scheduler, compared with uniform DRT scheduler, increases as packet length goes up as plotted in Figure 5.31. For optimal DRT scheduler, there exists an throughput optimal packet length and network density, when schedule length is xed. In general, optimal DRT scheduler achieves higher throughput when densityN is low and packet length P is long. Both policies benet from low network density. In other words, DRT strategy- based schedulers are suitable for low contention environments. 5.4 Summary Having seen that collision-free scheduling is intractable, we have focused on low- complexity distributed, randomized, topology-independent (DRT) schemes. In light of our analysis results, we nd that uniform DRT scheduler, which is the throughput- optimal DRT strategy-based scheduler for terrestrial RF networks, performs poorly in UWASN. We nd the optimal DRT scheduler by using nonlinear programming, 105 Figure 5.31: Throughput improvement ratio vs. packet length P and characterize its properties. The performance comparison of optimal DRT sched- uler and uniform DRT scheduler is also presented. Although the propagation delay is the major issue in uencing the throughput of UWASN, it is possible to signi- cantly improve throughput without the knowledge of network topology. In general, optimal DRT scheduler provides highest throughput in low contention environments and prefers long packet. 106 Chapter 6: Conclusions and Future Work In this thesis, we have investigated time synchronization, link scheduling and random access problems for underwater acoustic sensor networks. In the time syn- chronization part, we performed extensive performance analysis of existing solu- tions, and conclude that, receiver-receiver scheme can be largely biased by high propagation delay, one-way dissemination is good at estimating clock skew but poor at clock oset, and two-way exchange scheme provides accurate clock oset but low precision clock skew. Based on these ndings, we proposed a hybrid time synchronization scheme, which can produce both precise clock skew and oset pre- diction. We also analyzed the precision variance under multi-hop scenario and show that our hybrid scheme has bounded average multi-hop error and low variance. In link scheduling part, we formally proved the NP-completeness and proposed the best approximation ratio for Metric Underwater Scheduling problem. We then used a complete SAT solver to study the feasibility issue of a given network and scheduling length. On one hand, we concluded that underwater acoustic networks can benet from spatial multiplexing and have better eciency in sparse deployed networks. On the other hand, throughput of underwater acoustic networks can be seriously harmed by high deployment density, due to the complicated delayed interference pattern. 107 In random access part, we rst analyzed the throughput of randomly deployed networks using ALOHA-like access scheme. We then used non-linear programming to optimize this distributed, randomized medium access scheme, by tuning the chan- nel access probability mass function. Although an ALOHA-like scheme with uni- formly distributed channel access pattern is the optimal solution for terrestrial-RF networks, it suers from high propagation delay environments, such as underwater acoustic networks. Based on our simulation results, the throughput of ALOHA- like random access scheme with uniformly distributed channel access pattern can be improved by several orders while packet length increases, deployment density increases, and/or scheduling length decreases. We believe that extending this work by doing ne-grained time stamping in practical experiments, and developing a time synchronization protocol based on the hybrid scheme will be a promising future direction, especially for multi-hop networks. It would then be of great value to compare the dierent approaches in detail through real implementations on wireless devices. In addition, nding out the optimal number of packets used in hybrid scheme, in terms of maximum network lifespan, is also a worthy extension. 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Abstract (if available)

Abstract Because of our limited knowledge of the huge water body that covers 70% of Earth's surface, Underwater Acoustic Sensor Network (UWASN) is an emerging topic in the research society. However, the unique properties of acoustic communication systems, such as high propagation delay, high communication power consumption, low transmission rate, distance dependent bandwidth, all make the networking issues of UWASN very challenging. In this thesis, we study three different topics that can be applied in UWASN, with a focus on addressing the challenge of high propagation delay. One is time synchronization, another one is link scheduling, and the last one is random access.

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Asset Metadata

Creator Huang, Pai-Han (author)

Core Title Time synchronization and scheduling in underwater wireless networks

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2010-08

Publication Date 08/06/2010

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

Tag OAI-PMH Harvest,scheduling,time synchronization,underwater,wireless

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Krishnamachari, Bhaskar (committee chair), Kempe, David (committee member), Kuo, C.-C. Jay (committee member), Neely, Michael J. (committee member), Raghavendra, Cauligi S. (committee member), Sukhatme, Gaurav S. (committee member)

Creator Email paihanhu@usc.edu,paihanhuang@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3325

Unique identifier UC1183288

Identifier etd-Huang-3905 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-370515 (legacy record id),usctheses-m3325 (legacy record id)

Legacy Identifier etd-Huang-3905.pdf

Dmrecord 370515

Document Type Dissertation

Rights Huang, Pai-Han

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu