Synchronization in Wireless Sensor Networks by Erchin Serpedin

5158302a926b88e-261x361.jpg Author Erchin Serpedin
Isbn 9780521764421
File size 2MB
Year 2009
Pages 244
Language English
File format PDF
Category information technologies


This page intentionally left blank Synchronization in Wireless Sensor Networks: Parameter Estimation, Performance Benchmarks and Protocols Wireless sensor networks are set to play a key role in a wide range of civilian and military applications, with tiny sensors connected through wireless links performing various sensing, computing, communication, and control tasks in highly distributed systems. This book presents a critical element in the deployment of wireless sensor networks: the process of synchronization. It summarizes the most important clock synchronization protocols proposed for wireless sensor networks, with special emphasis placed on deriving efficient clock offset estimation schemes and performance benchmarks. Graduate students of electrical and computer engineering and computer science will find this a valuable resource, as will engineers who are interested in designing efficient clock synchronization algorithms and improving the performance of existing synchronization protocols. E RCHIN SERPEDIN is currently an Associate Professor in the Wireless Communications Laboratory at Texas A&M University, where he joined after receiving his Ph.D. in Electrical Engineering from the University of Virginia, Charlottesville, in 1999. His research interests lie in the areas of statistical signal processing and wireless communications. Dr. Serpedin has served as Associate Editor for numerous journals including IEEE Transactions on Wireless Communications, IEEE Transactions on Signal Processing, IEEE Transactions on Communications, IEEE Signal Processing Letters, and IEEE Communications Letters. Q ASIM M. CHAUDHARI was awarded his Ph.D. in Electrical Engineering from Texas A&M University in 2008 and is currently an Assistant Professor at Iqra University, Islamabad, Pakistan. Before entering academia, he worked with the SoC Tools Group of Communications Enabling Technologies, Islamabad, and later with the HSDPA performance test team of Qualcomm Inc., San Diego. His research interests include digital communications, estimation and detection theory in general and channel estimation and synchronization in wireless sensor networks in particular. Synchronization in Wireless Sensor Networks: Parameter Estimation, Performance Benchmarks and Protocols Erchin SERPEDIN Texas A&M University and Qasim M. CHAUDHARI Iqra University CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York Information on this title: © Cambridge University Press 2009 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2009 ISBN-13 978-0-511-65149-6 eBook (NetLibrary) ISBN-13 978-0-521-76442-1 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. To our parents and families, Zara, Nisa, Aisha, Nesrin and Maryam. CONTENTS Preface · page xi 1 Introduction · page 1 §1.1 Wireless Sensor Networks · 1 §1.2 Time Synchronization · 2 §1.3 Importance of Time Synchronization · 3 §1.4 History of Clock Synchronization · 4 §1.5 Outline · 6 2 Signal Models for Time Synchronization · page 10 §2.1 Definition of Clock · 10 §2.2 Design Considerations · 11 §2.3 Delay Components in Timing Message Delivery · 13 3 Time Synchronization Protocols · page 15 §3.1 Pairwise Synchronization · 16 §3.1.1 Timing-Sync Protocol for Sensor Networks (TPSN) · 16 §3.1.2 Tiny-Sync and Mini-Sync · 18 §3.1.3 Reference Broadcast Synchronization (RBS) · 19 §3.1.4 Flooding Time Synchronization Protocol (FTSP) · 21 §3.2 Network-Wide Synchronization · 21 §3.2.1 Extension of TPSN · 22 §3.2.2 Lightweight Time Synchronization (LTS) · 22 §3.2.3 Extension of RBS · 23 §3.2.4 Extension of FTSP · 23 §3.2.5 Pairwise Broadcast Synchronization (PBS) · 24 §3.2.6 Time Diffusion Protocol (TDP) · 24 §3.2.7 Synchronous and Asynchronous Diffusion Algorithms · 26 vii Contents viii §3.2.8 Protocols Based on Pulse Transmissions · 27 §3.3 Adaptive Time Synchronization · 28 §3.3.1 Rate-Adaptive Time Synchronization (RATS) · 28 §3.3.2 RBS-based Adaptive Clock Synchronization · 29 §3.3.3 Adaptive Multi-Hop Time Synchronization (AMTS) · 30 4 Fundamental Approaches to Time Synchronization · page 32 §4.1 Sender–Receiver Synchronization (SRS) · 33 §4.2 Receiver-Only Synchronization (ROS) · 36 §4.3 Receiver–Receiver Synchronization (RRS) · 39 §4.4 Comparisons · 41 5 Minimum Variance Unbiased Estimation (MVUE) of Clock Offset · page 42 §5.1 The System Architecture · 43 §5.2 Best Linear Unbiased Estimation Using Order Statistics (BLUE-OS) · 45 §5.2.1 Symmetric Link Delays · 47 §5.2.2 Asymmetric Link Delays · 48 §5.3 Minimum Variance Unbiased Estimation (MVUE) · 51 §5.3.1 Asymmetric Link Delays · 51 §5.3.2 Symmetric Link Delays · 55 §5.4 Explanatory Remarks · 57 6 Clock Offset and Skew Estimation · page 62 §6.1 Gaussian Delay Model · 63 §6.1.1 Maximum Likelihood (ML) Clock Offset Estimation · 63 §6.1.2 Cramer–Rao Lower Bound (CRLB) for Clock Offset · 64 §6.1.3 Joint Maximum Likelihood Estimation (JMLE) of Clock Offset and Skew · 64 §6.1.4 Cramer–Rao Lower Bound (CRLB) for Clock Offset and Skew · 67 §6.2 Exponential Delay Model · 69 §6.2.1 Cramer–Rao Lower Bound (CRLB) for Clock Offset · 70 §6.2.2 Joint Maximum Likelihood Estimation (JMLE) of Clock Offset and Skew · 73 Contents 7 Computationally Simplified Schemes for Estimation of Clock Offset and Skew · page 90 §7.1 Using the First and the Last Data Sample · 91 §7.1.1 Gaussian Delay Model · 91 §7.1.2 Exponential Delay Model · 92 §7.1.3 Combination of Clock Offset and Skew Estimation · 95 §7.1.4 Simulation Results · 96 §7.2 Fitting the Line Between Two Points at Minimum Distance Apart · 99 §7.2.1 Simulation Results · 101 §7.2.2 Computational Complexity Comparison · 102 8 Pairwise Broadcast Synchronization (PBS) · page 104 §8.1 Synchronization for Single-Cluster Networks · 105 §8.2 Comparisons and Analysis · 105 §8.3 Synchronization for Multi-Cluster Networks · 107 §8.3.1 Network-Wide Pair Selection Algorithm (NPA) · 108 §8.3.2 Group-Wise Pair Selection Algorithm (GPA) · 110 §8.4 Comparisons and Analysis · 114 9 Energy-Efficient Estimation of Clock Offset for Inactive Nodes · page 118 §9.1 Problem Formulation · 119 §9.2 Maximum Likelihood Estimation (MLE) · 121 §9.3 Cramer–Rao Lower Bound (CRLB) · 132 §9.3.1 CRLB for the Clock Offset of Inactive Node φˆ q · 133 §9.3.2 CRLB for the Clock Offset of Active Node φˆ p · 137 §9.4 Simulation Results · 138 10 Some Improved and Generalized Estimation Schemes for Clock Synchronization of Inactive Nodes · page 140 §10.1 Asymmetric Exponential Link Delays · 141 §10.1.1 Best Linear Unbiased Estimation Using Order Statistics (BLUE-OS) · 142 §10.1.2 Minimum Variance Unbiased Estimation (MVUE) · 145 §10.1.3 Minimum Mean Square Error (MMSE) Estimation · 149 §10.2 Symmetric Exponential Link Delays · 151 §10.2.1 Best Linear Unbiased Estimation Using Order Statistics (BLUE-OS) · 151 §10.2.2 Minimum Variance Unbiased Estimation (MVUE) · 153 §10.2.3 Minimum Mean Square Error (MMSE) Estimation · 155 ix Contents x 11 Adaptive Multi-hop Time Synchronization (AMTS) · page 157 §11.1 Main Ideas · 158 §11.2 Level Discovery Phase · 159 §11.3 Synchronization Phase · 159 §11.4 Network Evaluation Phase · 160 §11.4.1 Synchronization Mode Selection · 160 §11.4.2 Determination of Synchronization Period · 162 §11.4.3 Determination of the Number of Beacons · 164 §11.4.4 Sequential Multi-Hop Synchronization Algorithm (SMA) · 164 §11.5 Simulation Results · 167 12 Clock Drift Estimation for Achieving Long-Term Synchronization · page 169 §12.1 Problem Formulation · 170 §12.2 The Estimation Procedure · 171 13 Joint Synchronization of Clock Offset and Skew in a Receiver–Receiver Protocol · page 177 §13.1 Modeling Assumptions · 177 §13.2 Joint Maximum Likelihood Estimation (JMLE) of the Offset and Skew · 178 §13.3 Application of the Gibbs Sampler · 179 §13.4 Performance Bounds and Simulations · 181 14 Robust Estimation of Clock Offset · page 185 §14.1 Problem Modeling and Objectives · 187 §14.2 Gaussian Mixture Kalman Particle Filter (GMKPF) · 189 §14.3 Testing the Performance of GMKPF · 192 §14.4 Composite Particle Filtering (CPF) with Bootstrap Sampling (BS) · 196 §14.5 Testing the Performance of CPF and CPF with BS · 204 15 Conclusions and Future Directions · page 211 Acronyms · page 214 References · page 218 Index · page 227 PREFACE The clock or time synchronization problem in wireless sensor networks (WSNs) requires a procedure for providing a common notion of time across the nodes of WSNs. In general, clock synchronization is viewed as a critical factor in maintaining the good functioning of WSNs due mainly to their decentralized organization and timing uncertainties caused by the imperfections in hardware oscillators and message delays at the physical and medium access control (MAC) layers. In addition, synchronization of the nodes of wireless sensor networks is crucial for implementing fundamental operations such as power management, transmission scheduling, data fusion, localization and tracking, and security protocols to name only a few applications. The aim of this book is to provide an introduction to the clock synchronization problem of WSNs from a statistical signal processing viewpoint. Therefore, most of the topics presented in this book deal with building efficient clock offset estimation algorithms and performance benchmarks for general synchronization approaches that rely on sender–receiver and receiver–receiver timing packet exchange mechanisms. A summary of the key features of the most representative protocols proposed for clock synchronization of WSNs is also presented, together with some interesting open research problems. Synchronization of WSNs is currently a very active research field with a large number of results and very diverse contributions coming from an equally diverse body of researchers: computer scientists, electrical engineers, mathematicians, statisticians, etc. Despite the deployed efforts, the general problem of building efficient global synchronization protocols for large-scale wireless sensor networks is still open and the proposed results are still introduced in a quite ad-hoc manner, lacking comprehensive design and optimization studies to assess and improve their performance in a systematic fashion. Although herein we will not solve these general and very important problems, this book assumes the modest task of building efficient synchronization algorithms and performance benchmarks for simple sender–receiver and receiver–receiver timing packet exchange based xi xii Preface synchronization protocols. Despite its unambitious goal, this book will be of interest to all practitioners who are looking for techniques to improve the performance of existing protocols such as network time protocol (NTP), time protocol for synchronization of sensor networks (TPSN), reference broadcast synchronization (RBS), pairwise broadcast synchronization (PBS), etc., and to develop novel synchronization protocols. This book consists of 15 chapters. Chapter 1 is a short introduction to the time synchronization problem, its history, and importance. Chapter 2 presents the main constraints that must be taken into account when designing time synchronization protocols for WSNs. Chapter 3 focuses on the most representative synchronization protocols for wireless sensor networks by outlining their main features, while Chapter 4 discusses three general packet-based synchronization approaches for WSNs. Chapters 5–14 propose a variety of statistical signal processing algorithms for improved estimation of clock phase offsets and assessing performance benchmarks. A series of novel results, extensions, and interesting relationships between different estimation schemes are reported. At first, the emphasis is put on developing efficient clock offset estimators for the general scenarios when the network delays are normally or exponentially distributed. However, observing the facts that the distribution of network delays in general cannot be predicted accurately, and that the estimators reported in the literature are not robust with respect to the unknown possibly time-varying distribution of network delays, we address in Chapter 14 the problem of building clock offset estimators that are robust to the distribution of network delays. Finally, Chapter 15 concludes this book with some open research problems. This work would have not been possible without the support and encouragement of Dr. Bruce Suter from Air Force Research Laboratory (AFRL), Rome, NY, and the help of our students. Our heartfelt thanks go to Bruce, and to our families and students (Dr. Kyoung-Lae Noh, Dr. Jangsub Kim, Dr. Yik-Chung Wu, Mr. Ilkay Sari, Mr. Jaehan Lee, and Mr. Sabit Ekin). Despite our efforts to contain all sources of errors and misunderstandings, we believe that inconsistencies and errors might show up. Therefore, we are asking our readers kindly to email us their feedback to: [email protected] Any feedback is welcome to improve this work. This book webpage will be maintained at∼serpedin/. Chapter 1 INTRODUCTION 1.1 Wireless Sensor Networks With the help of technological advances in micro-electro-mechanical systems (MEMS) and wireless communications, low-cost, low-power, and multi-functional wireless sensing devices have been developed. When these devices are deployed over a wide geographical region, they can collect information about the environment and efficiently collaborate to process such information by forming a distributed communication network, called a wireless sensor network (WSN), as illustrated in Figure 1.1. A WSN is a special case of an ad-hoc wireless network, and assumes a multi-hop communication framework with no common infrastructure, where the sensors spontaneously cooperate to deliver information by forwarding packets from a source to a destination. The number of practical applications involving WSNs keeps growing rapidly, and WSNs have been regarded as providing the fundamental infrastructure for future communications due to a variety of promising potential applications: monitoring the health status of humans, animals, plants, and the environment; control and instrumentation of industrial machines and home appliances; homeland security; detection of chemical and biological threats and leaks, etc. [2], [14], [75], [100]. When designing sensor networks, there are a number of important factors to be considered such as tolerance to node failures, scalability, dynamic network topology, hardware constraints, production cost, and power consumption [2]. In general, the lifetime of a sensor network is proportional to that of a battery since the sensor nodes are usually inaccessible after deployment. Moreover, due to the space limitations and other practical constraints in sensor nodes, power is a scarce resource for practical WSNs. For these reasons, energy efficiency in general has top priority when designing WSNs out of all the above mentioned design considerations. Data 1 2 Introduction Sensor node Mesh sensor node Figure 1.1: A wireless sensor network. communication is one of the most significant operations in WSNs and requires a huge portion of the overall energy consumption. Indeed, the energy required for data communication is far greater than the energy required for data processing in a sensor node [75]. 1.2 Time Synchronization In distributed systems, maintaining the logical clocks of the computers in such a way that they are never too far apart is one of the most complex problems of computer engineering. Whether disciplining computer clocks with the devices synchronized to a global positioning system (GPS) satellite or a network time protocol (NTP) [62] time server over the Internet, it is possible to equip some primary time servers to synchronize a much larger number of secondary servers and clients connected through a common infrastructure. In order to do this, a distributed network clock synchronization protocol is required through which a server clock can be read, the readings to other clients can be transmitted, and each client clock can be adjusted as required. In such a distributed synchronization approach, the participating devices exchange timing information with their chosen reference at regular intervals and adjust their logical clocks accordingly. A computer clock in general has two components, namely a frequency source and a means of accumulating timing events (consisting of a clock interrupt Importance of Time Synchronization 3 mechanism and a counter implemented in software). The implementation of the computer clock in the operating system and the programming interface differ between operating systems and hardware platforms. However, the basic sources of timing errors are an uncompensated quartz crystal oscillator and the clock interrupts it generates. Theoretically, two clocks would remain synchronized if their offsets were set equal and their frequency sources run at the same rate. However, in practice clocks are set with limited precision and the frequency sources run at slightly different rates. In addition, the frequency of a crystal oscillator varies due to the initial manufacturing tolerance, aging, temperature, pressure, and other factors. Because of these inherent instabilities, distributed clocks must regularly be synchronized. 1.3 Importance of Time Synchronization Time synchronization is a procedure for providing a common notion of time across a distributed system. It is crucial for WSNs when performing a number of fundamental operations, such as: • Data fusion Data merging is a major operation in all distributed networks for processing and integrating the collected data in a meaningful way, and it requires some or all nodes in the network to share a common timescale. • Power management Energy efficiency is a key factor when designing WSNs since sensors are usually left unattended without maintenance and battery replacement for their lifetimes after deployment. Most energy-saving operations strongly depend on time synchronization. For instance, duty cycling (sleep and wake-up modes control) helps the nodes to save huge energy resources by spending minimal power during the sleep mode. Thus, networkwide synchronization is essential for efficient duty cycling and its performance is proportional to the synchronization accuracy. • Transmission scheduling Many scheduling protocols require time synchronization. For example, the time division multiple access (TDMA) scheme, one of the most popular communications schemes for distributed networks, is only applicable to a synchronized network. • Miscellaneous Many localization, security, and tracking protocols also demand the nodes to timestamp their messages and sensing events. Therefore, time synchronization is one of the most important research challenges in the design of energy-efficient WSNs. 4 Introduction 1.4 History of Clock Synchronization Many time synchronization protocols for maintaining synchronization of physical clocks over computer networks have been designed over the past few decades. The pioneering work in this area was the remote clock reading method proposed by Cristian, which handles unbounded message delays between processes [16]. In this algorithm, a time request is sent to the remote process and after receiving the response, the host process calculates the round-trip time as the difference between the transmission and reception times. The main feature of this algorithm relies on the fact that performing a large number of request/response experiments will make it more likely that at least one trial will not encounter random delays. Logically, the chosen trial is the one with the least round-trip delay. The standard for time synchronization in the Internet, the network time protocol (NTP), was developed by Mills [62] (also see [61]). NTP is a protocol for synchronizing the clocks of computer systems over packet-switched, variable-latency data networks. It is a layered client–server architecture based on user datagram protocol (UDP) message passing, which synchronizes computer clocks in a hierarchical way. The main attractive features of NTP are its scalability, robustness to failure, self-configuration in large multi-hop networks, and ubiquitous deployment. NTP’s sender–receiver synchronization architecture is now widely accepted in designing time synchronization algorithms and relies on the same two-way timing message exchange mechanism targeted in most of this book. The time transmission protocol (TTP), which is used by a node to communicate the time of its clock to a target node, was introduced in [7]. The target node estimates the time in the source node by using the message timestamps and message delay statistics without any feedback response or pairwise synchronization. The exploitation of the inherent properties of the broadcast media, where a node sends timing beacons to all the nodes within a single broadcast domain, was first introduced in the CesiumSpray system [97]. Later, one of the most popular clock synchronization protocols in wireless sensor networks, the reference broadcast synchronization (RBS) [22], was proposed based on the same idea, but allowing an extension of the protocol to multiple domains. The RBS protocol will be discussed in detail in Chapter 3. For ad-hoc communication networks, the time synchronization protocol [79] is one of the pioneering contributions. This protocol is based on generating timestamps to record the time at which an event of interest occurred. The timestamps are updated by each node using its local clock and the time transformation method, in which the final timestamp is expressed in terms of an interval with a lower bound and an upper bound. Clock synchronization in WSNs is an entirely new area of research due to the fact that the above general synchronization History of Clock Synchronization 5 protocols present a number of challenges when applied to WSNs. This is because of the unique nature of sensor networks: limited power resources, wireless channel conditions, and dynamic topology caused by node mobility and failure. Therefore, different types of synchronization schemes have to be designed explicitly for WSN applications to cope with these challenges. References [23], [24], [80], [81], [82], [84], [88], [89], [91] are excellent surveys of research in this area. The main protocols put forward for clock synchronization to cope with the above mentioned requirements in WSNs are described next. RBS [22] is based on the postfacto receiver–receiver synchronization approach. In RBS, a reference broadcast message is sent by a node to two or more neighboring nodes which record their own local clocks at the reception of broadcasted message. After collecting a few readings, the nodes exchange their observations and a linear regression approach is used to estimate their relative clock offset and skew. The timing synch protocol for sensor networks (TPSN) [29] is a conventional sender–receiver protocol which assumes two operational stages: the level discovery phase followed by the synchronization phase. During the level discovery phase, the WSN is organized in the form of a spanning tree, and global synchronization is achieved by enabling each node to be synchronized with its parent (the node located in the adjacent upper level) by means of a two-way message exchange mechanism through adjusting only its clock offset. Because TPSN and NTP share the same signaling mechanism, one might interpret TPSN as an extension of NTP to WSNs. The timing synchronization protocol for high latency acoustic networks (TSHL) [93] combines both of these approaches, namely the receiver–receiver (RBS) and sender–receiver (TPSN), in two stages. The first stage in TSHL is similar to RBS while the second stage is similar to TPSN. TSHL is particularly suitable for networks involving large message delays, e.g., underwater acoustic networks. The flooding time synchronization protocol (FTSP) [58] also combines the two approaches in the sense that the beacon node sends its timestamps within the reference broadcast messages. The delay measurement time synchronization (DMTS) protocol for WSNs [74] is an energy-efficient protocol which avoids estimating the round-trip time unlike NTP or TPSN, synchronizes the sender and multiple receivers at the same time, and requires a smaller number of message transfers than RBS. Among other nonprobabilistic approaches, the tiny–mini-synchronization protocols [86] provide good synchronization accuracy in WSNs while using a deterministic protocol with minimal computational and storage complexity. The Time Diffusion Protocol (TDP) proposed in [90] achieves a network-wide time equilibrium by using an iterative, weighted averaging technique based on a diffusion of messages involving all the nodes in the synchronization process. Also, 6 Introduction the asynchronous diffusion protocol (ADP) [53] uses a diffusion strategy similar to TDP, but the network nodes execute the protocol and correct their clocks asynchronously with respect to each other. Suggesting a probabilistic approach to tackle the clock synchronization problem in WSNs, PalChaudhuri et al. [69] extended the results from RBS by providing probabilistic bounds on the accuracy of clock synchronization. Valuable research was carried out by Abdel-Ghaffar [1] who adopted the probabilistic approach. He presented a detailed analysis of clock offset estimation assuming a symmetric exponential model for network delays. It was implicitly argued in [1] that for known fixed delay and exponential delay parameters, the maximum likelihood estimator of the clock offset does not exist because the likelihood function does not possess a unique maximum with respect to the clock offset. However, it was proved by Jeske in [41] that for an unknown fixed delay, irrespective of the exponential delay parameter being known or unknown, the MLE of the clock offset does exist and coincides with a previously proposed estimator by Paxson in [71] and [72]. The research presented in this book advances the results for the clock synchronization problem for WSNs by adopting a probabilistic approach and applying techniques from statistical signal processing and estimation theory. The next section lists the major topics in the book. Some very interesting results for this problem were derived in [27], which showed that for the synchronization problem consisting of estimating all the unknown parameters, i.e., skews and offsets of all the clocks as well as the delays of all the communication links, even in the presence of noiseless communication of messages, the estimation of all the unknown parameters is impossible. 1.5 Outline The topics covered in this book are summarized as follows. In Chapter 2, the general clock model for time synchronization is first introduced and analyzed. The most important features that have to be considered when designing time synchronization protocols for WSNs are presented. In addition, the different delay components that are present in the timing message delivery are categorized. In Chapter 3 we categorize and survey the existing time synchronization protocols for WSNs, focusing mainly on the signal processing aspects. In addition, in Chapter 3 we describe the importance and effectiveness of adaptive time synchronization schemes, and introduce some important adaptive synchronization protocols as well. In Chapter 4 three general and fundamentally different time synchronization approaches are presented, based on packet synchronization, namely,

Author Erchin Serpedin Isbn 9780521764421 File size 2MB Year 2009 Pages 244 Language English File format PDF Category Information Technologies Book Description: FacebookTwitterGoogle+TumblrDiggMySpaceShare Wireless sensor networks are set to play a key role in a wide range of civilian and military applications, with tiny sensors connected through wireless links performing various sensing, computing, communication, and control tasks in highly distributed systems. This book presents a critical element in the deployment of wireless sensor networks: the process of synchronization. It summarizes the most important clock synchronization protocols proposed for wireless sensor networks with special emphasis placed on deriving efficient clock offset estimation schemes and performance benchmarks. Graduate students of electrical and computer engineering and computer science will find this a valuable resource, as will engineers who are interested in designing efficient clock synchronization algorithms and improving the performance of existing synchronization protocols.     Download (2MB) Probability and Statistics with Reliability, Queuing, and Computer Science Applications, Second Edition Wireless Ad hoc and Sensor Networks Introduction To Computer Networks And Cybersecurity Wireless Sensor Networks: A Networking Perspective Security in Wireless Ad Hoc and Sensor Networks Load more posts

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