In [30], a systems solution, UDAAN, based on combination of directional and om- ...... has a non-binary nature, multiple levels of trust can be used in the claimed ...
Information Propagation in Wireless Sensor Networks Using Directional Antennas DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Serdar Vural, M.S., B.S. ***** The Ohio State University 2007
Dissertation Committee:
Approved by
Prof. Eylem Ekici, Adviser ¨ uner Prof. F¨usun Ozg¨ Prof. Andrea Serrani
Adviser Graduate Program in Electrical and Computer Engineering
ABSTRACT
The information propagation capability of Wireless Sensor Networks (WSN) is directly related with the properties of multihop paths. Two main measures of the multihop data propagation capability are the maximum Euclidean distance that can be covered in a multihop path and the effectiveness of the medium access control (MAC) protocol. To achieve high propagation capacity, MAC protocols should enhance the channel use by maximizing simultaneous traffics and reducing end-to-end delay in high data load scenarios often encountered in WSN data collection applications. In this regards, directional antennas offer various benefits such as the extended communication ranges, spatial reuse capability, and reduced interference patterns that enable higher network performance compared to omnidirectional antennas. In this thesis, the maximum multihop Euclidean distance covered by directional packet transmissions is evaluated for both linear and planar WSNs using analytical modeling of distance distributions. Expressions for calculating the distribution parameters are derived and provided. Comparison of experimental and analytical results demonstrate the high accuracy of the proposed models in estimating distance distributions. Furthermore, a WSN security application which utilizes the derived models for verifying sensor locations is presented. The second contribution of this thesis is the Smart AntennaBased MAC (SAMAC) protocol designed for multihop data collection applications for WSNs with sectored antennas. A detailed protocol description as well as performance evaluation results are provided. Simulation results demonstrate that SAMAC with sectored ii
antennas improves end-to-end delay, data throughput, and data delivery ratio under high data generation rates and highly loaded traffic conditions compared to IEEE 802.11 with omnidirectional antennas.
iii
Dedicated to my family. . .
iv
ACKNOWLEDGMENTS
I wish to express my sincere gratitude to my advisor, Prof. Eylem Ekici, who guided me throughout my graduate study at the Ohio State University. Without his sincere help and attention to my studies, this work would not come to reality. Especially, I appreciate his assistance and motivation whenever I was in need for suggestions and directions to ¨ uner for her valuable comments and follow. I also would like to thank Prof. F¨usun Ozg¨ guidance throughout my graduate study. I would like to also express my sincere gratitude to Prof. Andrea Serrani and Prof. Can Emre K¨oksal for accepting to be a member of my candidacy examination and PhD Oral examination. Furthermore, I would like to thank all my examination committee members for their valuable comments about my research and future study directions. Many people supported me during the completion of this thesis with criticism and helpful assistance. I would like to thank all those people who made this work possible and an enjoyable experience for me. In particular, I would like to express my sincere gratitude to my lab colleague and friend, Emad Felemban, for the nice work we accomplished together during the last year of my graduate study. My sincere and foremost gratitude goes to my fellow friend, Tan Apaydın, for his best wishes, support, and help, not to mention the enjoyable conversations we had during my graduate study in Columbus. I would like to express my sincere gratitude to my dearest friends Doruk Bozda˘g, Onur Cant¨urk Hamsici, ˙Ilter Sever, and Onur Ozan K¨oyl¨uo˘glu, v
not to mention all my friends in Columbus Ohio, for all the fun and good time we had. Furthermore, I would like to thank Dr. G¨okhan Korkmaz, my former lab colleague and friend, for his valuable guidance, suggestions, and his hints about graduate life. My deepest gratitude goes to my parents and my brother, who have been generous with their encouragement throughout my educational life. This thesis is dedicated to them.
vi
VITA
March 16, 1980 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Born - Eskisehir, Turkey July 2003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B.S. in Electrical and Electronics Engineering, Bo˘gazic¸i University, Istanbul, Turkey March 2005 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M.S. in Electrical and Computer Engineering, The Ohio State University, Columbus, Ohio, USA
PUBLICATIONS 1. S. Vural and E. Ekici. Probability Distribution of Multihop Distance in One Dimensional Sensor Networks. Computer Networks Journal, Elsevier Science, volume 1, pages 3727-3749, September 2007. 2. S. Vural and E. Ekici. Hop-Distance Based Addressing and Routing for Dense Sensor Networks without Location Information. Ad Hoc Networks Journal, Elsevier Science, volume 5, pages 486-503, May 2007. 3. E. Ekici, S. Vural, J. McNair, and D. Al-Abri. Secure Probabilistic Location Verification in Randomly Deployed Wireless Sensor Networks. To appear in Ad Hoc Networks Journal, Elsevier Science, January 2007. 4. S. Vural and E. Ekici. Analysis of Hop-Distance Relationship in Spatially Random Sensor Networks. In ACM Mobihoc, pages 320-331, 2005. 5. E. Felemban, C-G. Lee, E. Ekici, R. Boder, and S. Vural. Probabilistic QoS Guarantee in Reliability and Timeliness Domains in Wireless Sensor Networks. In IEEE Infocom, volume 4, pages 2646-2657, March 2005. 6. S. Vural and E. Ekici. Wave Addressing for Dense Sensor Networks. In Proceedings of Second International Workshop on Sensor and Actor Network Protocols and Applications (SANPA), August 2004. vii
7. S. Vural, Y. Tian, and E. Ekici. QoS-Based Communication Protocols in Sensor Networks. In Algorithms and Protocols for Wireless Ad Hoc and Sensor Networks, ed: Azzedine Boukerche, Wiley & Sons, 2006.
FIELDS OF STUDY Major Field: Electrical and Computer Engineering Studies in Wireless Sensor Networks: Prof. Eylem Ekici
viii
TABLE OF CONTENTS
Page Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Chapters: 1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2.
Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.1 2.2
8
Distance Distributions in Wireless Sensor Networks . . . . . . . . . . . Medium Access Control Protocols in Wireless Ad hoc and Sensor Networks with Directional Antennas . . . . . . . . . . . . . . . . . . . . . 2.2.1 CSMA/CA-Based MAC Protocols . . . . . . . . . . . . . . . . 2.2.2 The Deafness and Directional Hidden Terminal Problems . . . . 2.2.3 Power Consumption in Directional Antenna-Based MAC Protocols 2.2.4 Mobility and User-Identification in Ad hoc Networks with Directional Antennas . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 Directional Antenna-Based MAC Protocols in Sensor Networks . 2.2.6 MAC Protocols Based on Time Scheduling . . . . . . . . . . . . 2.2.7 Comparison of MAC Protocols with Omnidirectional and Directional Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . ix
11 11 16 18 19 20 21 23
2.2.8 3.
Multihop Maximum Distance Probability Distribution in One Dimensional Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1 3.2 3.3
4.
4.3
Preliminary Discussion . . . . . . . . . . . . . . . . . . . . . . . . . Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Bayes’ Rule to Calculate PN|D (N |D) . . . . . . . . . . . . . 4.2.2 Mathematical Foundations for the Derivation of PN|D (N |D) 4.2.3 Derivation of PN|D (N |D) . . . . . . . . . . . . . . . . . . . Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . .
. . . . . .
35 37 37 38 43 44
Secure Probabilistic Location Verification in Randomly Deployed Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.1 5.2
5.3
5.4
6.
Definitions and the Network Architecture . . . . . . . . . . . . . . . . . 26 Multihop Maximum Euclidean Distance Distribution . . . . . . . . . . . 28 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Analysis of the Probability Mass Function of Hop Distance for a Given Euclidean Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.1 4.2
5.
Systems Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 24
Network Architecture and Assumptions . . . . . . . . . . . . . . . . . 5.1.1 Authentication of Verification Messages . . . . . . . . . . . . Probabilistic Tools To Verify Location . . . . . . . . . . . . . . . . . . 5.2.1 The CDF of the k-Hop Distance . . . . . . . . . . . . . . . . . 5.2.2 The PMF of the Number of Hops K . . . . . . . . . . . . . . . 5.2.3 Relating Probabilities with Plausibility . . . . . . . . . . . . . Probabilistic Location Verification . . . . . . . . . . . . . . . . . . . . 5.3.1 The Basic Probabilistic Location Verification (PLV) Algorithm 5.3.2 Performance of the Basic PLV Algorithm . . . . . . . . . . . . Security Analysis and PLV Improvements . . . . . . . . . . . . . . . . 5.4.1 Disreputation through Impersonation . . . . . . . . . . . . . . 5.4.2 Denial of Service through Payload Alterations . . . . . . . . . 5.4.3 Denial of Service through Hop Count Alterations . . . . . . . . 5.4.4 Denial of Service through Packet Replay . . . . . . . . . . . . 5.4.5 Wormhole Attacks . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
52 54 54 55 56 58 61 61 62 66 66 67 69 72 73
Multihop Distance Probability Distribution in Two Dimensional Sensor Networks 75 6.1 6.2 6.3
Definition of Maximum Multihop Euclidean Distance . . . . . . . . . . 77 The Probability Distribution of Maximum Multihop Euclidean Distance . 78 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 x
6.3.1 6.3.2
6.4
7.
. . . . . . . Sequence of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 82 . . . . . . . .
84 85 95 99 100 100 101 102
Smart Antenna-Based MAC (SAMAC) Protocol . . . . . . . . . . . . . . . . . 105 7.1 7.2 7.3 7.4 7.5 7.6 7.7
7.8
8.
Maximum Multihop Distance . . . . . . . . . . . Maximum Multihop Distance Approximated as a Single Hop Maximum Distances . . . . . . . . . 6.3.3 Analysis of Single Hop Maximum Distance . . . 6.3.4 Analysis of Multihop Maximum Distance . . . . . 6.3.5 Approximation Accuracy for Different Angles α . Numerical Results . . . . . . . . . . . . . . . . . . . . . 6.4.1 Mean and Standard Deviation of ri . . . . . . . . 6.4.2 Mean and Standard Deviation of dN . . . . . . . 6.4.3 Approximation of the pdf of dN . . . . . . . . . .
Properties of SAMAC . . . . . . . . . . . . . . . . . . . Hardware Platform and Assumptions . . . . . . . . . . . Neighborhood Generation and Collection at Cluster Head Conflict Relations . . . . . . . . . . . . . . . . . . . . . Group Formation . . . . . . . . . . . . . . . . . . . . . . Schedule Computation . . . . . . . . . . . . . . . . . . . MAC Protocol Details . . . . . . . . . . . . . . . . . . . 7.7.1 Two Modes of Operation . . . . . . . . . . . . . 7.7.2 SAMAC Time Slot Structure . . . . . . . . . . . 7.7.3 Communication Events . . . . . . . . . . . . . . 7.7.4 SAMAC Internal Queues . . . . . . . . . . . . . 7.7.5 SAMAC States . . . . . . . . . . . . . . . . . . . Simulation Study . . . . . . . . . . . . . . . . . . . . . . 7.8.1 Performance Evaluation . . . . . . . . . . . . . . 7.8.2 Target Tracking Scenario . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
107 109 110 111 112 115 120 125 126 128 130 130 136 137 142
Concluding Remarks and Future Work . . . . . . . . . . . . . . . . . . . . . . 144 8.1
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Analytical Work on WSN Distance Distributions . . . 8.1.2 Improvement of the PLV Algorithm . . . . . . . . . . 8.1.3 The pmf of Hop Distance in Two Dimensional WSNs 8.1.4 SAMAC Protocol Future Directions . . . . . . . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
146 146 147 147 148
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
xi
LIST OF FIGURES
Figure
Page
1.1
Directional antenna vs. omnidirectional antenna . . . . . . . . . . . . . . .
3.1
Illustration of single-hop-distances ri and furthest points Pi . . . . . . . . . 27
3.2
Comparison of the multihop distance distribution with Gaussian distribution 28
3.3
Kurtosis of experimental dN . R = 100m, λ = 0.05 nodes/m
4.1
Definitions of Pi , di , ri , and redundant hop . . . . . . . . . . . . . . . . . 36
4.2
Proof of Lemma 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3
Comparison between approximated and experimental PN|D (P |D). . . . . . 45
4.4
Effect of node density on multihop distance pdf curves . . . . . . . . . . . 47
4.5
Experimental and approximated PN|D (N |D), D: randomly selected. . . . . 47
5.1
Multihop propagation between nodes S and D . . . . . . . . . . . . . . . . 51
5.2
Proposed WSN architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.3
Plausibility of a node’s claimed location for different number of verifiers . . 59
5.4
Receiver Operating Curve (ROC) . . . . . . . . . . . . . . . . . . . . . . . 64
5.5
Effect of node density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.6
Effect of minimum verifier separation . . . . . . . . . . . . . . . . . . . . 67
xii
4
. . . . . . . 29
5.7
DoS attacks with payload alterations . . . . . . . . . . . . . . . . . . . . . 68
5.8
Effect of hop count reset attacks . . . . . . . . . . . . . . . . . . . . . . . 70
5.9
Resilience against hop count increment attacks . . . . . . . . . . . . . . . 72
6.1
Multihop propagation with sectored antennas between nodes S and D . . . 76
6.2
Iterative definition of maximum multihop Euclidean distance. . . . . . . . . 77
6.3
Distribution estimations using 1D Model with Gaussian pdf and ML estimation with Gamma pdf, σ = 0.001 nodes/m2 . . . . . . . . . . . . . . . . 79
6.4
Angular range model and model-related approximation . . . . . . . . . . . 82
6.5
Choice of next node in angular range . . . . . . . . . . . . . . . . . . . . . 83
6.6
Average upper bound of model-based error, R = 100m . . . . . . . . . . . 84
6.7
Multihop distance formation . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.8
Analysis of first hop maximum distance . . . . . . . . . . . . . . . . . . . 87
6.9
Analysis of intermediate hop maximum distance . . . . . . . . . . . . . . . 88
6.10 Calculation of equivalent radius req . . . . . . . . . . . . . . . . . . . . . . 89 6.11 Calculation of the area of the vacant region Vi−1 . . . . . . . . . . . . . . . 92 6.12 Calculation of E[dN ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.13 Average percent error in approximation of E[dN ] and σdN . . . . . . . . . 99 6.14 Approximation of ri and σri . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.15 Approximation of E[dN ] and σdN . . . . . . . . . . . . . . . . . . . . . . . 102 6.16 Approximation of pdN (dN ) for low and high density . . . . . . . . . . . . 103 6.17 Root mean square error of 1D and 2D models . . . . . . . . . . . . . . . . 104
xiii
7.1
Superframe in SAMAC protocol . . . . . . . . . . . . . . . . . . . . . . . 108
7.2
Conflict types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.3
Group formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.4
Sample scheduling result . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.5
Time slot assignment and sector numbers . . . . . . . . . . . . . . . . . . 124
7.6
Time slot structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.7
Early sleeping mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.8
Go to SLEEPING state after MAX AWAKE TIME . . . . . . . . . . . . . 127
7.9
Pausing backoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.10 SAMAC internal queues . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7.11 State diagram of SAMAC . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.12 Grid network architecture used in simulations . . . . . . . . . . . . . . . . 137 7.13 Comparison of SAMAC and 802.11 average performance characteristics . . 139 7.14 Comparison of SAMAC and 802.11 per-source node average end-to-end delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.15 Effect of time slot in SAMAC with 50 source nodes . . . . . . . . . . . . . 141 7.16 Information propagation speed vs. target object speed and sensing range . . 143
xiv
LIST OF TABLES
Table
Page
7.1
Definitions in Time-Slot Assignment Algorithm . . . . . . . . . . . . . . . 123
7.2
Schedule information of a node . . . . . . . . . . . . . . . . . . . . . . . . 124
7.3
SAMAC configuration parameters . . . . . . . . . . . . . . . . . . . . . . 136
xv
CHAPTER 1
INTRODUCTION
Due to the recent technological advances in hardware design and wireless communication capabilities, it is now possible to manufacture small, inexpensive and low-power sensor devices. Although wireless sensor nodes have limited amount of computational capability, a network of sensors can be used in various applications such as environment and habitat monitoring, military surveillance, structural health monitoring, seismic detection, underwater sensing, etc. Such networks are called Wireless Sensor Networks (WSN) which provide easy deployment without any requirement for infrastructure support. In addition to the various advantages of WSNs, the design of these networks involve addressing various challenges, such as unattended operation requiring self-organization, ad hoc deployment, limited amount of energy resource, and network dynamics such as mobility and node failures. Such challenges affect communication protocols designed for sensor networks. In particular, efficient and robust MAC protocols as well as routing schemes are required to meet the stringent requirements of WSNs such as minimization of end-to-end delay and packet drop ratio. Especially for applications that transport critically important data, timely and correct data delivery should be provided by WSN protocols.
1
Due to the large number of sensors deployed in a WSN and the cooperative nature of WSN applications, data delivery is performed over multiple hops. Hence, one popular interest in routing schemes is multihop routing with emphasis on capacity assessments and data delivery characteristics. In particular, propagation of sensory information over multihop paths is highly dependent on the distance of such paths and the propagation capacity of individual hops. Among these two, the multihop path length between two sensor nodes is directly related with the number of hops and the length of a single hop determined by the sensor communication range. On the other hand, the transmissions in individual hops are largely affected by the physical medium characteristics and the specifications of the employed medium access control protocol. Therefore, an analysis of the information propagation capability in a WSN involves the study of both the multihop distance properties and the medium access control mechanism of the network. Most of the current literature on multihop communication in WSNs involves transmissions and receptions using omnidirectional antennas. Specifically, state-of-the-art medium access control methods in the wireless medium are essentially based on contention schemes with omnidirectional antennas. However, directional antennas with their capability of directing the communication beams towards desired directions can prove to be quite useful in multihop sensor communication. For instance, when employed in sensor nodes, the extended range of directional antennas reduces the hop distance between two network locations [40]. This in turn lessens the multihop delay as well as the energy consumption of multiple consecutive packet transmissions on a multihop path. Furthermore, by concentrating the transmission beam towards a certain direction, a sensor node can effectively eliminate the interference from other directions. Apart from interference reduction, the
2
major merit of directional transmissions in medium access control is the spatial reuse property which enables multiple communications to exist in a neighborhood, a property not achievable by omnidirectional contention mechanisms [42]. Hence, the use of directional antennas in WSNs proposes various advantages compared to their omnidirectional counterparts [16]. In order to exploit the benefits of directional transmission in WSNs, the routing and medium access capabilities of directional antennas ought to be explored in detail. Regarding the routing improvement offered by these antennas, significant attention should be paid to their larger transmission ranges compared to omnidirectional ranges as illustrated in Figure 1.1. The directional antenna has a single main lobe extending towards a certain direction and a number of small side lobes around the sensor node. The communication range and power are concentrated towards this direction with a certain beam width, while omnidirectional range is smaller with no directionality. By omitting the negligible side lobes, the main lobe of the directional antenna can be estimated by an ideal sectored antenna which is basically an angular slice centered around the sensor node. Using this model, the range and the transmission capability of a directional beam can be studied analytically. It can be observed that the major variable that measures the sectored antenna range is the communication radius R of its transmission pattern. However, although communication ranges directly affect the transmission lengths, the distance that can be covered in a single hop transmission is measured by the distance between two neighbor nodes which is upper bounded by the sensor communication range. Furthermore, the distance between two neighbor sensors is a random variable due to the spatially random sensor locations. Hence, although communication range is the upper bound of a single hop distance, the actual possible maximum distance covered in a hop is determined by parameters such as node 3
Sectored Antenna Main lobe Sidelobes
Direction of transmission
α Sensor
R
Omnidirectional Range
Figure 1.1: Directional antenna vs. omnidirectional antenna
density and antenna communication range, and it can be evaluated by probabilistic methods. Moreover, multihop path lengths are random variables that can be investigated using the analytical evaluation of single hop lengths. This leads to an analytical modeling of the routing capability of multihop packet transmissions, especially for directional antennas that favor data dissemination in designated directions. Hence, a study of the maximum multihop path distance distribution is highly beneficial in evaluating the information dissemination capability of WSNs with directional antennas. The analytical evaluation of the distribution of the maximum multihop Euclidean distance is the first major task addressed in this thesis. The multihop maximum distance distributions provide sufficient information about the distances that can be reached with multihop directional paths and hence the multihop information propagation capability of
4
directional transmissions. In the analysis, the directional antenna patterns are studied using the model given by Figure 1.1 with an emphasis on the multihop characteristics of consecutive directional transmissions. The analysis is provided for both one dimensional networks [41] and two dimensional networks. Although the analysis of one dimensional network distance distributions is the basis of the two dimensional analysis, two dimensional WSNs demonstrate a more complex structure, which mandates different techniques to be applied. In addition to the study of multihop maximum distance distributions of directional propagations, the medium access control (MAC) protocol utilized by the WSN determines the network’s data delivery performance. Due to the difference between the transmission patterns of directional and omnidirectional antennas, the MAC characteristics of these two types of antennas differ [34]. In particular, effective MAC protocols are required to enhance network performance by exploiting the advantages of directional antennas. In the current literature, there are a number studies on directional antenna use in ad hoc networks, such as [17], [7], [18] and [6]. However, there are a few publications on directional antennas in WSNs [31], [3]. The power limitation of sensor nodes play the fundamental role in making a distinction between WSNs and ad hoc networks. Hence, sensor network MAC protocols should efficiently allocate network energy resources and minimize energy consumption without interrupting critical data delivery applications and degrading network performance. Furthermore, such protocols are required to address the two well-known issues of directional medium access in wireless environments, namely the Directional Hidden Terminal Problem [7] and Deafness [13]. In this thesis, the information propagation capacity of wireless sensor networks using directional antennas is investigated. There are two major contributions of this thesis. These 5
are the evaluation of maximum multihop distance distribution of directional packet propagations, and the design of a wireless sensor network architecture with directional antennas. Analytical methods and related formulas are provided to study the maximum multihop distance distribution. Furthermore, distance distributions for both linear and planar WSNs are modeled by probability density functions whose parameters can be calculated analytically using the provided expressions. With the support of maximum multihop distance distributions, it is possible to model delay and distance estimation models for WSN applications. One such application presented in this thesis is the verification of node locations according to advertised inter-sensor distances, which is a WSN security mechanism. The second contribution of this thesis is the Smart Antenna-Based MAC (SAMAC) protocol specifically designed for WSNs with sectored antennas. Detailed protocol description as well as performance evaluation results are presented. The following parts of the thesis are organized as follows. First, the current literature on the distance distributions in WSNs and the directional antenna based MAC protocols for WSNs and ad hoc networks is reviewed in Section 2. Second, in Chapter 3, the summary of [41], which is the analysis of the distribution of multihop maximum Euclidean distance in one dimensional WSNs is presented. Then, the derivation of the probability mass function of hop distance that corresponds to a given Euclidean distance in one dimensional networks is explained in Chapter 4. Chapter 5 introduces a WSN location verification mechanisms, PLV, which uses the results of the analysis presented in Chapter 3. The analysis of the multihop maximum Euclidean distance in two dimensional WSNs is presented in Chapter 6. The Gamma pdf model is explained and the derivations to calculate the required model parameters are provided in detail. The SAMAC protocol, which is designed
6
for medium access control in WSNs with sectored antennas is introduced in Chapter 7. Finally, Chapter 8 provides the concluding remarks and future work of the thesis.
7
CHAPTER 2
RELATED WORK
2.1
Distance Distributions in Wireless Sensor Networks
Estimation methods to provide information on the distribution of the Euclidean distance between nodes in wireless sensor networks are considered as versatile tools for performance modeling and protocol parameter tuning. Hence, estimation of inter-sensor distances is of profound importance for many WSN applications. The maximum Euclidean distance that can be covered in a multihop path in WSNs with random node locations is related with the information propagation capability of the network. Furthermore, it is a practical metric for application areas, such as estimation of coverage areas, minimum transmission delays, and minimum number of hops. However, the current literature on the analysis of this metric is limited. There are a number of studies that estimate the distance of a single hop to determine multihop distance estimates in the current literature. Distances to designated anchor nodes are estimated in [27] and [33]. In these studies, optimization algorithms which require increased computational cost and higher number of message exchanges are utilized. In [33], the Hop-TERRAIN algorithm determines the number of hops from a node to each of the anchor nodes in the network. The hop counts are then multiplied by the average 8
hop distance and the range between the nodes and the anchor sensors are estimated. Using the anchor location information and the calculated distances, triangulation algorithms provide estimated sensor locations. However, these methods are sensitive to the accuracy of the initial position estimates as well as the magnitude of errors in distance estimates. Furthermore, the fraction of anchor nodes affects the estimation accuracy. In [22] Nagpal et al. use distances to designated anchor positions to roughly estimate the locations of sensors. The maximum communication range of a sensor is substituted for the expected single hop distances leading to errors in distance estimations. The errors can be attributed to the fact that sensor communication range is only the upper bound of the distances between randomly located sensors. Random node positions necessitate an analytical evaluation of the Euclidean distances. In the current literature, there are some analytical methods that address the distribution estimation problem using probabilistic methods [21, 8]. The probability distribution of a single hop distance between two randomly located neighbor sensors is studied in [21]. On the other hand, [8] has a different perspective and investigates the remaining distance to a destination node in each hop of multihop greedy forwarding. In addition to estimation of Euclidean distances, hop distance estimation is a popular topic of interest in the current literature [2], [4]. [2] derives the connectivity probability in one or two hops and estimates the analytical bounds on connectivity in multiple hops. Using the connectivity results, analytical bounds of the expected hop distance are derived and supported by experimental results. Similarly, in [4], iterations based on the connectivity in one or two hops are used to analytically compute the expected number of relay nodes between two randomly chosen sensors. Experimental investigation of the distribution of hop distance and its expected value are provided in [40]. Beamforming antennas are shown 9
to reduce the hop distance in medium and large networks compared to omnidirectional antennas. The first study on the maximum Euclidean distance is [5]. In [5], the distribution of the maximum single hop distance is analytically derived for linear networks. The distribution of maximum multihop Euclidean distance in linear networks is analyzed in [41]. The results of this study are used in [44] to develop a Bayesian decision mechanism to determine the number of hops for a given Euclidean distance. However, the definition and calculation of multihop path distances in a planar network is considerably complex compared to a linear network. Hence, the applicability of the results in [41] is limited to linear networks and can provide rough approximations for planar network distance distributions. In this thesis, two contributions to the problem of maximum distance distribution estimation are provided. First, the derivations of the approximation results in [41] are used to derive the probability mass function of the distribution of hop distance for a given Euclidean distance in linear networks. In order to clarify the presentation, results of [41] are briefly explained before presenting the pmf derivations and the evaluation of the obtained pmf results through comparisons with experimental hop distance distribution data. Second, a method for modeling the maximum Euclidean distance in planar networks is provided. Although Gaussian pdf provides an accurate distribution model for linear networks [41], in this thesis, it is quantitatively shown that the Gaussian pdf model of [41] cannot represent planar network distances. Hence, an effective method to approximate the multihop distances with negligibly small errors is presented. It is illustrated that the multihop maximum distance distribution is accurately defined by a transformation of the well-known Gamma distribution. Analytical expressions for the expected value and standard deviation
10
of the Euclidean multihop distance are derived and the parameters of the Gamma distribution are calculated. Furthermore, the accuracy of the Gamma-approximated distribution is demonstrated through comparisons with experimental results.
2.2
Medium Access Control Protocols in Wireless Ad hoc and Sensor Networks with Directional Antennas
In this section, the current literature on the use of directional antennas (DA) in the design of MAC protocols for wireless ad hoc and sensor networks is explored. Most of the current literature is focused on wireless ad hoc networks while WSN architectures are considered only in a few papers. The papers with high citations in the current literature are outlined in more detail while some other methods are briefly reviewed or mentioned. Specific papers addressing various aspects of DA use are briefly explained under different categories. A more comprehensive survey on MAC protocols with directional antennas can be found in [39].
2.2.1 CSMA/CA-Based MAC Protocols Most of the studies in the current literature involve mechanisms similar to IEEE 802.11 medium access control with RTS/CTS control packets. These studies commonly focus on how the control packets should be transmitted, i.e. directionally, or omnidirectionally. Furthermore, methods to address MAC-related problems in ad hoc networks with directional antennas are presented. In [17], DMAC protocol is proposed to have better medium access performance with DAs compared to omnidirectional antennas for wireless ad hoc networks. There are multiple directional antennas at all nodes and each DA has a range of 90 ◦ . With the use of 11
different DAs for different transmission directions, the omnidirectional range of 360 ◦ is covered. The traditional RTS/CTS/DATA/ACK sequence of IEEE 802.11 is applied. Simultaneous reception of multiple packets at a single node is handled as a packet collision case. Furthermore, it is assumed that simultaneous transmissions to different directions are not allowed from the same node. An omnidirectional transmission is achieved by sending a packet by all DAs of a sensor sequentially. However, this requires the availability of all DAs simultaneously. On the other hand, unicast packets are sent on a single DA. Since the choice of the particular DA used to send a unicast packet depends on the direction of the destination, DMAC assumes that nodes know their locations and the locations of their neighbors. In DMAC, a node blocks its DAs that receive control packets whose destinations are not the node itself. Blocking refers to deferring channel access until the network allocation vector (NAV) advertised by the control packet expires. While some DAs may be blocked due to ongoing transmissions, the remaining DAs can still be used for transmissions. Two different schemes are proposed for DMAC as follows: Scheme 1. In the Basic DMAC scheme, RTS packets are sent in one direction (DRTS) while CTS packets are sent on all directions (OCTS). However, there is a possibility of directional hidden terminal problem. Scheme 2. Different from the Basic DMAC, if all antennas are available, then omnidirectional RTS (ORTS) is used. Otherwise, DRTS is sent using a selected DA. DMAC is mentioned as conservative in the current literature since it prioritizes omnidirectional transmissions of control packets. Omnidirectional communication trades off
12
spatial reuse capability for avoiding deafness, however the deafness problem is still encountered in DMAC. To reduce the effects of deafness, DMAC utilizes Directional WaitTo-Send (DWTS) packets. Furthermore, collisions are possible between RTS/DATA and ACK packets. In [24], Nasipuri et al. propose a medium access scheme similar to IEEE 802.11. The basic difference is the use of directional antennas for transmitting DATA and ACK packets. In each node, multiple directional antennas are directed towards different angles to cover the whole 360 ◦ range. A single antenna is set “active” while others are kept “inactive” according to a particular destination. RTS/CTS packets are transmitted omnidirectionally to find out neighbor destinations. For a node to be able to send a packet, the total received signal strength T RSS should be below a threshold value ST . Furthermore, there should be at least a LON GIF S period of time before starting a transmission. If the T RSS level goes below ST , then the node waits another LON GIF S after the first one finishes, after which it enters a random back-off before being able to transmit. The channel should be idle at all these times. The sender node has a CTS timeout counter and all nodes with no packets to send listen to the channel and set a timer OTH-RTS after correctly receiving an RTS. This is similar to the NAV logic in IEEE 802.11. In [7], MMAC (Multihop MAC) scheme is proposed, with the RTS/CTS/ACK/DATA sequence of IEEE 802.11. Nodes in MMAC both use an omnidirectional antenna and a directional antenna which can be steered towards the desired direction. During a time, a node is either in directional mode or in omnidirectional mode. “Transceiver NAV profiles” of neighbors indicate the power level and direction to be used for transmitting packets to them. When a node wants to initiate a communication with a neighbor node, the node
13
checks the NAV profile of this neighbor node (kept in NAV table) and chooses the direction of antenna accordingly. Furthermore, the sender node needs to check if the directional transmission ranges coincides with other communications. If no overlap is detected, then the node decides that it is safe to transmit, otherwise it initiates a back-off procedure as in traditional IEEE 802.11. MMAC exploits the advantage of higher transmission ranges in DAs and can send RTS packets directly over longer ranges. All nodes hearing the directional RTS set their NAVs and defer from channel access. Apart from the directional RTS packets, the concept of a multihop-RTS is proposed in MMAC. Hence, a second RTS is sent on a multihop path which is assumed to be determined by a module in a higher protocol layer. The receiver of an RTS replies with a directional CTS (DCTS). In [36], the DVCS MAC scheme for DAs in ad hoc networks is proposed. DVCS proposes Angle of Arrival AOA caching, Beam Locking and Directional NAV (DNAV). Directions towards destinations are stored in AoA caches and beams are locked between a pair of nodes during data transmission to improve reception power. DNAVs include a timer, a direction information, and a beam width value. Transmission to a direction is performed if no DNAVs cover that direction. Since beam width of each DNAV is configurable, omnidirectional and directional antennas are inter-operable in the same network. Hence, DVCS is argued to provide an optional enhancement to any existing MAC protocol without altering protocol configurations. Furthermore, power control at transmitters are proposed to limit the range extension effect of DAs that may cause increased interference. In [18], nodes are equipped with multiple DAs to cover the whole sensor communication range. RTS packets, which contain the duration of the intended four-way handshake, are transmitted directionally on all sectors of a node by sequentially scanning the sectors. The CTS, DATA, and ACK packets are also directionally transmitted. Furthermore, 14
neighbor locations are kept in a location table. An entry in the table contains the own ID, neighbor ID, own beam number, and neighbor beam number information. In every packet, the beam number that the packet is being sent is also included so that other nodes can update their location tables. The received beam numbers are checked by other nodes that are out of the communication events. Such nodes defer from using their individual beams until the channel is idle if a match in beam numbers that may interfere with the ongoing communication is detected. In [10], it is aimed to balance the trade-off between omnidirectional and directional reservations and to resolve the collision types inherent to ad hoc networks using DAs. It is argued that hybrid schemes that use omnidirectional and directional antennas in fact suffer from this tradeoff and either lose spatial reuse capability or encounter deafness problems. Switched beam antennas with predefined, fixed, and highly directed beams are deployed in nodes. RTS/CTS frames are sent on all beams aggressively. Furthermore, the beam number intended for DATA/ACK transmission is included in RTS and CTS frames. RTS/CTS packets are also sent over unblocked beams on a second channel to reduce collisions from inactive users that attempt to start a new communication. Furthermore, RTS and CTS packets are buffered and sent as soon as the current DATA/ACK of a previous dialog is finished. Then, the original communication can be resumed. This is proposed to deal with collisions from active users. In [32], the focus is on CSMA/CA based adaptive antennas which provide significant gains over the omnidirectional antennas in rural-area multihop networks. The selection of a low carrier detection threshold is shown to increase the throughput. Two beam-selection policies are studied and the best strategy is found to be provided by a directional beam. Up to 72% throughput improvement is achieved using 60 ◦ beamwidth antennas. The use of 15
narrower beam reduces the average packet delay. Moreover, directional RTS transmission is observed to generate less interference. In [29], enhancements to ad hoc network capacity using advanced beamforming antennas is investigated. Two types of channel access models, namely “Aggressive Collision Avoidance Model” (a node is never blocked upon receiving an RTS/CTS) and “Conservative Collision Avoidance Model” (a node is always blocked when it receives an RTS/CTS) are introduced. The effectiveness of a range of enhancements such as link power control, use of two channels for medium access, and directional neighbor discovery are studied. Furthermore, the connectivity and latency reduction possible with longer range links provided by directional antennas are investigated. Sophisticated beamforms such as steered beams are used. Moreover, a comprehensive antenna model with multiple antenna patterns, sidelobe modeling, and use of transceiver gains on bit-error-rate calculations are provided.
2.2.2 The Deafness and Directional Hidden Terminal Problems The two mostly encountered problems of directional antenna-based MAC, i.e. the Deafness and Directional Hidden Terminal Problems, are addressed in some studies. These can be summarized as follows. In [6], the deafness problem is addressed with the proposed protocol, Tone DMAC. In Tone DMAC, a node performs directional communication using DRTS/DCTS. After sending the DRTS/DCTS, an out-of-band tone is sent omnidirectionally to inform all neighbors about the communication. On detecting a tone, neighbors can deduce that the cause of any previous failures was deafness but not congestion. Such nodes can cancel their back-off timers and choose a smaller back-off value for retransmission. This decreases packet drops and transmission failures. Since tones cannot be demodulated but can only be detected, the
16
receivers can identify the sender of the tones using a hash function that maps tones to node identities. When two nodes have the same signature, they can be differentiated using the direction of tone arrival. Furthermore, the nodes that are in backoff periods change their antenna to omnidirectional mode so that they can listen to signals from other nodes which attempt to reach them. Smart antennas are expected to enhance scalability in ad hoc networks. [20] describes the evaluations of three directional MAC protocols, DMAC, MMAC, and SWAMP, as well as the IEEE 802.11 in a multi-hop transmission environment. These evaluations address the directional hidden terminal problem. In [20], three MAC level solutions are proposed based on NAV indicators, i.e. HCTS, BRTS, and RCTS, which inform on-going communications to a directional hidden terminal and set a network allocation vector to prevent collisions. In [42], it is argued that the collision avoidance methods may largely decrement the performance of the network if silencing of neighboring nodes causes a loss of connectivity between large parts of the network. Hence, [42] proposes the use of purely directional antennas and shows that the overall delay and throughput performance is enhanced compared to omnidirectional collision avoidance-based schemes. In [13], different factors which contribute to deafness in directional antennas are studied and its significant impact on network performance is observed. Two schemes are proposed to overcome deafness scenarios which are transparent to the underlying directional MAC protocol in use. Furthermore, it is argued that IEEE 802.11 short retry limit (SRL) needs a special handling in directional environment because of the presence of deafness. A detailed performance evaluation of the schemes with different directional MAC protocols running over switched beam antennas is presented. 17
2.2.3 Power Consumption in Directional Antenna-Based MAC Protocols Reduction of power consumption is crucial in wireless networks, especially for wireless sensor networks powered by limited battery resources. Directional antennas are proposed to have less power consumption with the help of reduced control packets and the range extension property. Power consumption reduction with directional antennas is addressed for ad hoc networks in some papers as summarized in the following. In [11], the potential use of adaptive antenna arrays in networks using protocols based on IEEE 802.11 DCF is considered. In addition to the different allocation vectors proposed, i.e. SHORTN AV and N AV , three types of power schemes are defined, namely “No Power Control”, “Global Power Control(GPC)”, and “Local Power Control(LPC)”. Although the third scheme is more complex than the other two, it provides the best performance in terms of network capacity enhancement. In [23], each node is equipped with an array of non-overlapping sectorized antennas covering all angles. No separate hardware is used for node location detection. RTS packets are sent in all directions, but RTS is immediately sent over clear sectors directionally without waiting for blocked sectors to get cleared. This helps save power, although little, compared to omnidirectional transmission. Furthermore, the angle of arrival (AOA) of packets from neighbors are kept in an AOA table so that subsequent RTS transmissions can first try the corresponding sector found by the cached AOA. This helps reduce power consumption since otherwise many unnecessary RTS transmissions over all sectors are required. In addition to these mechanisms, in [23], the destination of an RTS packet measures the signal power and calculates the difference between the received power and the SIR threshold for correct reception. This difference is notified to the sender via the subsequent CTS packet, 18
so that the sender can adjust its power to be slightly higher than the required level. This ensures minimal power consumption, however this incremental difference should be precisely determined. A low difference value runs the risk of packet failure due to unexpected interference, whereas a high value is equivalent to wastage of power. The scheme is tested for four cases: omnidirectional RTS and CTS, omnidirectional CTS-directional RTS, directional RTS and CTS, and addition of AOA caches. Directional antenna usage is shown to demonstrate significant power savings.
2.2.4 Mobility and User-Identification in Ad hoc Networks with Directional Antennas In [38], the problem of mobile user identification in the neighborhood of an access point(AP) is addressed. The protocol involves two rounds for user identification. In the first step, after users are located the most recent location information of node locations are kept in AP cache. These recent information pieces can later be used to start searching nodes in reasonable starting sectors rather than searching the whole area one by one. In the second step, the mobility issue for non-identified users is handled with a second round of scanning. This can be performed with one of four provided methods depending on the localization scheme used. Furthermore, employing multiple transceivers simultaneously reduces the required time to locate users. Each transceiver is assumed to operate in a different frequency. Users are assumed to receive in all frequency bands and transceivers are assumed to be ideally synchronized. Furthermore, users receiving a polling message are synchronized with the access point. Each transceiver scans half of the area for all users, then the areas are exchanged.
19
2.2.5 Directional Antenna-Based MAC Protocols in Sensor Networks Although the vast majority of the literature on directional antenna MAC protocols is based on ad hoc networks, wireless sensor networks are considered in a few studies. These are presented in the following. In [31], it is proposed that with the use of directional antennas, significant energy savings can be achieved in a wireless sensor network. Furthermore, it is argued that the proposed MAC scheme does not have the deafness and hidden terminal problems since it is based on a time-scheduling based medium access. The protocol consists two phases for sensor communication lifetime as follows. Phase 1. During Phase 1, sensors determine their neighborhood relationships and also determine the senders and the receivers of the data traffic. Then, neighborhood relationships are exchanged between neighbor sensors. Nodes receive priority levels according to their number of nodes. A location table is maintained in each node which includes the priority information and the sender-receiver relationships. The time schedules are negotiated among the neighbors according to the priority levels. Phase 2. During the second phase, nodes send/receive data with directional antennas. Sensors are deployed with 6 directional antennas with a sector angle of 60 ◦ and the MAC protocol switches to the active antenna. Another study is [3] which is an extension of the D-MAC protocol [30]. In [3], a theoretical model of MAC contention between sensors is provided and analyzed when sensors are equipped with directional antennas. Extensions to the protocol, such as HoL Unblocking, are made for implementation related issues for the use of low cost hardware in sensor
20
networks. Furthermore, Rendezvous times are introduced to alleviate the problem of high power bootstrapping packets, i.e. RTS packets for later communication events.
2.2.6 MAC Protocols Based on Time Scheduling Apart from the contention based mechanisms similar to 802.11, time scheduling methods are utilized to provide scalable and reliable medium access control for directional antennas. These methods argue for the avoidance of the directional antenna MAC problems with the allocated schedules. Some studies in the current literature are briefly explained as follows. In [1], a distributed channel access scheduling protocol, called Receiver-Oriented Multiple Access (ROMA), for ad hoc networks with directional antennas is proposed. Each node is equipped with MMBA type antennas with three main lobes and negligibly small side lobes. Each antenna can form multiple beams and commence several simultaneous communication sessions. ROMA, unlike other on-demand schemes, determines a number of links for activation in every time slot using two hop neighborhood information. Since channel access scheduling in ad hoc networks is shown to be NP complete, ROMA heuristically shows that it performs better than the UxDMA unified framework which involves time, frequency, and code division multiple access. UxDMA suffers from collecting the complete topology information of the network and distributing the corresponding schedules. ROMA on the other hand, fully utilizes the multiple-beam forming capability of MBAA antennas. At each time slot, the antenna of a node i is either in the transmission mode or reception mode. Each node i maintains the angular profiles of its one-hop neighbors for antenna beam orientation purposes. Placing node i at the center of a circle, groups of neighboring nodes
21
are created according to their polar orientation with respect to node i. Furthermore, every node is required to promptly propagate its one-hop neighbor information to all of its onehop neighbors whenever the attributes (link weight, group number) of a neighbor change. Time synchronization of all nodes is assumed. Nodes and links are assigned priorities based on their identifies and the current time slot. Given an up-to-date information about the twohop neighborhood of a node and link bandwidth allocations, ROMA decides whether a node i is a receiver or a transmitter. In [34], a unified representation of all smart antenna technologies is provided. Under the class of smart antennas, switched beam, fully adaptive array antennas (steerable), and MIMO links are considered. The effects of smart antenna properties such as range extension, higher data rate support for equivalent bit error rate performance, and spatial reuse are presented in detail in the perspective of physical layer considerations such as signal strength, SNR, communication pattern, interference suppression, and transmission power and gain. The properties of the three different classes of smart antennas are provided and their effects on medium access control protocols are summarized. The problem addressed in [34] is providing a fair medium access to contending wireless nodes in an ad hoc network while maximizing the utility of the network subject to transmission constraints of smart antennas. To accomplish the scheduling of potentially contending subgraphs of the network are determined by a “flow contention graph”. The edges in the graph are assigned weights according to the strength of interference between the corresponding links. Using the flow contention graph, another graph called the “resource constraint graph” is generated. This graph includes “resource servers” which are associated with the contention regions with certain amounts of resources derived from the flow contention graph. A centralized algorithm is provided for scheduling the links so that 22
channel contention is reduced. The algorithm runs in each time slot and divides nodes into two categories using a coloring algorithm. Then, resources are allocated to individual links according to their assigned rankings. In a later study [35], the presented scheme is extended and distributed resource allocation and scheduling algorithms are provided for each type of smart antennas. Performance results are obtained considering different parameters. As for the impact of scattering, adaptive beamforming is found to provide the best performance, while switched beams suffer from multipath unlike adaptive arrays and MIMO links. Furthermore, it is observed that increasing the number of elements increases the number of active neighbors for range extension. On the other hand, increasing the load increases the number of active links, however performance is bounded by the number of links that can be accommodated in a contention region. Moreover, performance improvements are more when gains are used towards rate increase as compared to range extension since range extension reduces spatial reuse capability despite the reduction in path lengths.
2.2.7 Comparison of MAC Protocols with Omnidirectional and Directional Antennas In [16], omnidirectional antenna-based MAC protocols MACA, MACAW, FAMA, and DBTMA are compared with their directional antenna-based versions. Each node in the directional protocols is equipped with a directional antenna consisting of N antenna elements which are deployed into non-overlapping fixed sectors. Each of these sectors spans an angle of
36O N
degrees. To send a packet to a unicast destination, the packet is transmitted on a
single sector, whereas broadcast packets are transmitted on all sectors. Signals are sensed in all sectors and the physical layer is capable of recognizing the sector with the maximum gain. A single sector, which is chosen by the physical layer according to reception power 23
levels, collects packets during reception. Based on the simulation results, it is argued that directional antennas are able to eliminate the hidden node problem and increase the spatial reuse capability.
2.2.8 Systems Solutions In [30], a systems solution, UDAAN, based on combination of directional and omnidirectional antenna capability is proposed. Mechanisms such as a directional powercontrolled MAC, neighbor discovery with beamforming, link characterization for directional antennas, proactive routing and forwarding are provided. Adaptive control of steered or switched antennas with n fixed directional antennas and one omnidirectional antenna are provided for each node. Three different types of antenna models (beamforms) are used: N-F (No Beamforming), (T-BF) Transmit Beamforming, and TR-NF (Transmit or Receive Beamforming). The medium access layer is named as D-MAC which is a variant of the single channel CSMA/CA approach. Avoiding collisions using complex protocol features are not practiced. In fact, collisions are controlled by the protocol using judicious back-off schemes to achieve high throughput in practice. The back-off intervals and the method of back-off depends on specific types of events, such as “No CTS”, “No ACK”, “Busy Channel”, etc. Furthermore, the behavior of D-MAC nodes are determined by protocol states, such as “Natural-Idle” and “Forced Idle”. Moreover, D-MAC, uses four different types of packet transfer modes, namely “Only DATA”, “RTS-DATA”, “DATA-ACK”, or “RTS-CTS-DATAACK”. All packets include the transmitter position information, so that the receiver can immediately steer to that direction. Virtual carrier sensing in D-MAC is performed by directional network allocation vectors (D-NAV). D-NAV includes the time period of deferral,
24
direction of antenna, and power level. The power level is the allowed power above which interference will occur.
25
CHAPTER 3
MULTIHOP MAXIMUM DISTANCE PROBABILITY DISTRIBUTION IN ONE DIMENSIONAL SENSOR NETWORKS
In this Chapter, results pertaining to maximum multihop Euclidean distance distribution in linear networks presented in [41] are summarized. Furthermore, the approximation results in [41] are briefly explained. These approximation results for the distribution characteristics of multihop Euclidean distance provide an efficient model using the well-known Gaussian pdf. Furthermore, since theoretical expressions of multihop distance expressions are computationally costly, the approximations outline a scalable method for calculating multihop distance distribution parameters regardless of the number of hops. The results of this chapter are used in Chapter 4 to approximate the probability mass function of the hop distance for a known Euclidean distance and in Chapter 5 for a location verification-based WSN security application.
3.1
Definitions and the Network Architecture
The analysis in this chapter considers linear networks with a uniform distribution of sensor locations with density λ. Sensor nodes have a fixed and equal communication range of R. No specific MAC protocol is assumed, however sensors are assumed to receive every packet arriving within their communication ranges. Moreover, effects of node mobility, 26
P1
P2
P3
P4
P5
P6
P7
P8
re1
r1 R
re2
r2 R
re3
r3
r4 R
re4 r5
re5
R R
r6 R
re6 r7
re7
R
Figure 3.1: Illustration of single-hop-distances ri and furthest points Pi
node failure, and existence of obstacles in the topology are not considered in the analysis. The following definitions are used throughout this chapter: Definition 1. Single hop distance (r): The maximum Euclidean distance of a single hop upper bounded by the communication range R. For hop i, ri is used. Definition 2. Multi hop distance (d): The maximum multihop Euclidean distance. dN is P used for N hops, and for linear networks dN = i = 1N ri holds. Definition 3. Pi : The furthest point that can be reached in hop i. ri is equal to the distance between Pi and Pi−1 . Definition 4. Vacant Segment Length: rei−1 : The distance between the furthest point Pi of i and the location which is R away from the furthest distance Pi−1 of hop i − 1 in the same direction on the line. Figure 3.1 demonstrates the multihop distance as a sequence of single hop distances.
27
Comparison of the Multi−hop−distance Distribution and the Gaussian Distribution, λ= 0.1, R=100m 0.1
0.09 Multi−hop−distance
0.08
Gaussian 0.07
1
probability
0.06
0.05 2
0.04
3 0.03
4
5
6
7
0.02
8
9
10
0.01
0
0
100
200
300
400
500 distance
600
700
800
900
1000
Figure 3.2: Comparison of the multihop distance distribution with Gaussian distribution
3.2
Multihop Maximum Euclidean Distance Distribution
The distribution of the multihop maximum Euclidean distance dN is illustrated in Figure 3.2. This figure demonstrates experimentally obtained distribution fdN (dN ) curves for hop numbers up to N = 10 and provides comparison with Gaussian pdf curves with the same mean and standard deviation values for each value of N . The similarity between the Gaussian pdf and the fdN (dN ) is clearly observed, which leads to the following conjecture.
Conjecture 1. Due to the strong similarity between the Gaussian pdf and the experimental distribution of dN , the distribution of dN approximately follows a Gaussian distribution. Although Figure 3.2 qualitatively shows a high resemblance to the Gaussian pdf, Central Limit Theorem cannot prove this similarity due to the statistical dependence between consecutive single hop distances in multihop distance dN . Hence, a quantitative statistical measure called kurtosis is introduced in [41] to investigate this similarity. Kurtosis is a 28
measure of the peakedness of a probability distribution. For a random variable x, kurtosis is given by: kurt (x) =
E[(x − x)4 ] 2
E[(x − x)2 ]
− 3.
(3.1)
Kurtosis of a High Number of Hops 6
5
Kurtosis
4
3
2
1
0
0
10
20
30
40
50 hops
60
70
80
90
100
Figure 3.3: Kurtosis of experimental dN . R = 100m, λ = 0.05 nodes/m
Figure 3.3 demonstrates the decreasing kurtosis values of the multihop maximum distance distribution for increasing hop distance values N . This supports Conjecture 1 and suggests that a Gaussian pdf with known mean and standard deviation values can model fdN (dN ) since the Gaussian pdf can be defined uniquely by these two values. However, these statistics of dN should be calculated analytically so that the determined pdf can be used in WSN applications and also manipulated to derive other network parameters of interest, such as estimated multihop delay, distribution of sensor locations, etc.
29
The theoretical expressions of the expected value E[dN ] and standard deviation σdN values derived [41] as follows. Z
R
Z
R−re1
E[dN ] = 0
... Z σd2 N
0
R−reN −1 0
dN λe−λreN 1 − e−λR−reN −1
−λre2
λe λe−λre1 dre ...dre2 dre1 1 − e−λR−re1 1 − e−λR N R
Z
R−re1
= 0
Z ...
0
Z ...
R−reN −1 0
(3.2)
2
(dN − dN ) λe−λreN 1 − e−λR−reN −1
λe−λre1 λe−λre2 dre ...dre2 dre1 , ... 1 − e−λR−re1 1 − e−λR N
(3.3)
where E[dN ] = dN . These expressions are computationally costly and not scalable with increasing number of hops. Hence, the next section outlines the approximations of E[dN ] and σdN . Furthermore, analytical computation of the kurtosis of dN is provided.
3.3
Analysis
The approximations of E[dN ] and σdN are based on approximations of single hop distance mean and standard deviation values. The single hop maximum distance expected value E[ri ] = r can be calculated using the following implicit formula, which is derived using the pdf fri (ri ) provided in [5]. The details of the derivation of this result can be found in [41].
µ
λr ln 1 − λR − λr − 1
¶ = λr
(3.4)
Since σr2 = σr2e holds, the variance of σr2 can be calculated by: σr2 = σr2e = E[r2e ] − re 2 = E[r2e ] − (R − r)2
30
(3.5)
In Equation 3.5, E[re 2 ] is found by: E[re 2 ] =
−r2 e−λr − λ2 re−λr + 1 − e−λr
2 λ2
−
2 −λr e λ2
. (3.6)
The single hop statistic are used for approximating multihop distance distribution statistics with the help of Assumption 1. Assumption 1. Assumption Single hop distances ri for hops i = 1, 2, 3, . . . are identically distributed but not independent. For linear networks, the multihop maximum distance is the sum of the individual maximum single hop distance values as given by: " N # X E[dN ] = E ri = N r.
(3.7)
i=1
Similarly, the standard deviation σdN can be found by: Ã !2 N h i X 2 E (dN − dN ) = E ri − N 2 r2
(3.8)
i=1
i hP 2 computed by the following recursive relation. where f2 (N ) ≡ E ( N r ) 1 i f2 (N ) = f2 (N − 1) + 2(N − 1)r2 + E[r2 ] f2 (2) = 2E[r2 ] + 2r2
31
(3.9)
To compute the Gaussianity of dN , its kurtosis is to be determined. The expression to calculate the kurtosis of the multi hop distance dN is given by Equation 3.10. [41] kurt(d) =
P PN PN 3 4 E[( N 1 ri ) ] − 4( 1 r¯i )E[( 1 ri ) ] = PN 2 PN PN P 2 E[( 1 ri ) ] − 2E[( 1 ri )]( 1 r¯i ) + ( N 1 r¯i ) P PN 3 PN 2 2 r¯i ) E[( N 1 ri ) ] − 4( 1 r¯i ) E[( 1 ri )] + PN 2 PN PN PN 2 E[( 1 ri ) ] − 2E[( 1 ri )]( 1 r¯i ) + ( 1 r¯i ) 6(
PN 1
P 4 ( N 1 r¯i ) + P PN PN PN 2 2 E[( N 1 ri ) ] − 2E[( 1 ri )]( 1 r¯i ) + ( 1 r¯i ) (3.10) where the following recursive relations are required. f2 (N ) = f2 (N − 1) + 2(N − 1)r2 + E[r2 ] f3 (N ) = f3 (N − 1) + 3f2 (N − 1)r +3(N − 1)rE[r2 ] + E[r3 ] f4 (N ) = f4 (N − 1) + 4f3 (N − 1)r +6f2 (N − 1)E[r2 ] +4(N − 1)rE[r3 ] + E[r4 ].
(3.11)
f2 (2) = 2E[r2 ] + 2r2 f3 (2) = 2E[r3 ] + 6E[r2 ]r 2
f4 (2) = 2E[r4 ] + 6E[r2 ] + 8E[r3 ]r
32
(3.12)
Furthermore, the expressions of the third moment E[r3 ] and fourth moment E[re 4 ] of r in Equation 3.12 are calculated by Equation 3.13. E[r3 ] = R3 − 3R2 (R − E[r]) + 3RE[re 2 ] − E[re 3 ] E[r4 ] = R4 − 4R3 (R − E[r]) + 6R2 E[re 2 ] −4RE[re 3 ] + E[re 4 ]
(3.13)
where E[re 3 ] and E[re 4 ] can be found using Assumption 1 applied to the results of Equations 3.14 and 3.15 as provided below. ¢ e−λ(R−rei−1 ) ¡ −(R − rei−1 )3 −λ(R−rei−1 ) 1−e e−λ(R−rei−1 ) 3 − (R − rei−1 )2 −λ(R−rei−1 ) λ 1−e ¶ µ e−λ(R−rei−1 ) 6 6 − (R − rei−1 ) + 3 λ 1 − e−λ(R−rei−1 ) λ2 6 ´ + ³ λ3 1 − e−λ(R−rei−1 )
E[rei 3 ] =
E[rei 4 ] =
¢ e−λ(R−rei−1 ) ¡ −(R − rei−1 )4 −λ(R−rei−1 ) 1−e e−λ(R−rei−1 ) 4 (R − rei−1 )3 − −λ(R−rei−1 ) λ 1−e µ ¶ 12 24 e−λ(R−rei−1 ) 2 (R − rei−1 ) + 4 − λ 1 − e−λ(R−rei−1 ) λ2 µ ¶ 1 24 24 + − (R − rei−1 ) 1 − e−λ(R−rei−1 ) λ4 λ3
(3.14)
(3.15)
Furthermore, E[re 2 ] used by Equations 3.13 and 3.13 is derived as in Equation 3.16. [41] E[re 2 ] =
−r2 e−λr − λ2 re−λr + 1 − e−λr
2 λ2
−
2 −λr e λ2
. (3.16)
33
CHAPTER 4
ANALYSIS OF THE PROBABILITY MASS FUNCTION OF HOP DISTANCE FOR A GIVEN EUCLIDEAN DISTANCE
Apart from the distance that is covered in multiple directional transmissions, the information dissemination capability of sectored antennas is related with the necessary number of hops to deliver sensory data between two locations. In other words, the hop distance between two sensors in a WSN should be determined to analytically estimate performance parameters of sectored antennas, such as end-to-end delay and transmission power consumption. However, when sensor nodes are randomly located in the network, hop distance is not deterministic, but a random variable, which is dependent on the communication range of sensor nodes and the node density of the network. Therefore, the hop distance between two sensors that are a certain Euclidean distance apart from each other is randomly distributed with a certain probability mass function. This pmf of the hop distance can be studied using the pdf of the maximum Euclidean distance, as presented for one dimensional networks in this chapter. In this chapter, the pmf PN|D (N |D) of hop distance N corresponding to a given Euclidean distance D is estimated in a one-dimensional sensor network. The results of [41] as summarized in Chapter 4 provide the pdf of the maximum Euclidean distance dN covered in N hops. Using these results, the pmf of the hop distance can be determined, however 34
the analysis requires analytical derivations. In this chapter, instead of the multihop distance dN as used in Chapter 4 for a given hop distance, the known Euclidean distance without any information of the hop distance N is referred as D. Hence, the aim is to determine the distribution of N for a known D value.
4.1
Preliminary Discussion
Before proceeding with the derivation of PN|D (N |D), some definitions given in previous sections need to be re-emphasized and some additional ones should be provided. In Figure 4.1(a), the source node S broadcasts a packet in a one-dimensional sensor network. Multiple nodes can receive the packet at the same number of hops. Such nodes have the same hop distance to S. For a particular hop distance i, let the set of nodes that are i hops away from S be denoted as Si . Among the sensors in Si , one sensor node, Pi has the maximum distance to S. The distance of Pi to S is di , and the single-hop-distance (the distance between nodes Pi−1 and Pi ) of hop i is ri , as defined in Section 2. Hence, di is defined as the maximum distance covered in i hops. For instance, d4 = d4 in Figure 4.1(a) is the maximum hop distance to source node S among all nodes in set S4 . In Figure 4.1(b), set S4 consists of nodes X, Y, and P4 . The multihop distance d4 is the distance of P4 to node S. On the other hand, the distance values DX and DY of nodes X and Y to S are less than d4 . Therefore, these nodes do not contribute to the multihop distance d4 covered in 4 hops. In fact, a multihop distance, as defined in Section 2, is possible by hopping through nodes Pi , i = 1, 2, 3, . . ., which provide the furthest singlehop-distance in each hop. Hence, the single hops from P3 to X and from P3 to Y are “redundant” in forming the multihop distance d4 , d5 , . . . , etc. Such single hops are called “redundant hops”.
35
d3 r1 S
r4
r3
r2
P1
P2
P3
P4
R R R R
(a)
r1
S
r3
r2
P1
P3 X
P2
r5
r4
Y P4
A
d4 Dx DY (b) Figure 4.1: Definitions of Pi , di , ri , and redundant hop
36
P5
To find the hop distance between a node A and source S in Figure 4.1(b), the single-hopdistance values r1 , r2 , r3 , . . . are taken into account. Hence, P1 , P2 , P3 , . . . are the nodes of the multihop path from S to A. The last hop from P4 to A in Figure 4.1(b), does not provide the maximum distance in hop 5, since node P5 is more distant to P4 compared to the distance between nodes A and P4 . In general, the last hop distance does not have to be maximized since the selected node, such as node A in Figure 4.1(b), does not have to be one of the nodes Pi , i = 1, 2, 3, . . .
4.2
Analysis
4.2.1 Bayes’ Rule to Calculate PN|D (N |D) Using Bayes’ Rule, PN |D (N |D) can be stated as follows: PN |D (N |D) =
PD|N (D|N )P (N ) . ∞ X PD|N (D|i)P (i)
(4.1)
i=1
In Equation 4.1, PD|i (D|i) is the probability of reaching distance D in i hops and P (i) is the probability of the hop distance i. Note that hop distance i = 0 is not included in the sum at the denominator of Equation 4.1 since this is equivalent to loss of connectivity. P (i) is the probability of the hop distance i and is equal to the ratio of the expected number of nodes that have a hop distance i to the total number of nodes in the network. Hence, using the definition of maximal distance di in Section 3, P (i) can be found by: P (i) =
Expected number of nodes found on [di−1 , di−1 +R] . Total number of nodes
(4.2)
Since sensor nodes are uniformly distributed with density λ and sensor nodes have equal communication range R, the expected number of nodes that can be found on any distance interval of length R is a function of R and λ, and is independent of the location of 37
the interval. Hence, the numerator of Equation 4.2 is the same for all i = 1, 2, 3, . . . and P (i) is uniformly distributed with respect to hop distance i. Therefore, Equation 4.1 can be simplified to obtain Equation 4.3 PN|D (N |D) =
PD|N (D|N ) ∞ X
.
(4.3)
PD|N (D|i)
i=1
The term PD|i (D|i) in Equation 4.3 is the probability of reaching distance D for the given hop distance i. The denominator in Equation 4.3 includes all positive integer values of hop distance i. Note that PD|N (D|N ) is different than the pdf of the maximum distance covered in N hops which is approximated as following a Gaussian distribution as shown in Chapter 3. However, this sum includes redundant terms and can be reduced using Lemma 1 as will be presented shortly.
4.2.2 Mathematical Foundations for the Derivation of PN|D (N |D) In this section, some mathematical axioms and lemmas that are required for deriving PN|D (N |D) are provided. All lemmas apply to one-dimensional sensor networks with random sensor locations. The following definitions are used throughout the section. • D: The given Euclidean distance for which PN|D (N |D) is to be determined. • R: Sensor communication range. • S: Source node • Si : Set of all nodes that are at a hop distance i to S. • Pi : The furthest node to S in Si .
38
• di : (Multihop distance) Maximum distance covered in i hops. (also equal to the distance of Pi to S) • ri : (Single hop distance) Maximum distance covered in the ith hop. • mi : Minimum distance covered in i hops. Lemma 1. N is upper bounded by an integer Nmax and lower bounded by an integer Nmin § ¨ ¥D¦ such that Nmin = D ≤ N ≤ N = 2 + 1. max R R Proof. Proof of Lemma 1 For a single-hop-distance ri , ξ < ri < R with 0 < ξ ¿ 1 is true by definition. The multihop distance is minimized without having any redundant hops if R < ri +ri+1 = R+ξ holds for all consecutive single-hop-distance pairs. The minimum multihop distance is then equal to the sum r1 + r2 + r3 + r4 + . . . = ξ + R + ξ + R + . . .. Hence, the multi-hop ¥ ¦ distance for a given hop distance M is lower bounded by M2 R. On the other hand, if all single-hop-distance values are chosen to be ri = R, then maximum distance is covered and is equal to M R. Therefore, the multihop distance for M hops is bounded as: ¹
º M X M R≤ ri ≤ M R. 2 i=1
(4.4)
For a given multihop distance D, the following holds for at least one integer N : ¹
Since N is an integer and
D R
º N R ≤ D ≤ NR 2 ¹ º D N ≤ ≤ N. 2 R
(4.5) (4.6)
≤ N , the minimum number of hops Nmin that covers
distance D is:
»
Nmin
¼ D = ≤ N. R 39
(4.7)
Similarly, since N is an integer and
¥N ¦
≤
2
D , R
the maximum number of hops Nmax
that covers distance D satisfies: ¹
Nmax 2
º
¹
º D = . R
(4.8)
Hence: ¹
º ¹ º D Nmax D ≤ +1 < R 2 R ¹ º ¹ º D D ≤ Nmax < 2 + 2. 2 R R Equation 4.10 is satisfied by Nmax = 2
¥D¦ R
and Nmax = 2
(4.9) (4.10) ¥D¦ R
+ 1. The latter choice
gives a larger N . Hence, N is lower bounded by an integer Nmin and upper bounded by an integer Nmax as :
»
¼ ¹ º D D ≤N≤2 + 1, R R
(4.11)
which concludes the proof of Lemma 1. According to Lemma 1 and Equation 4.11, PN|D (N |D) given by Equation 4.3 reduces to: PN|D (N |D) =
where
§D¨ R
≤N ≤2
¥D¦ R
PD|N (D|N ) , 2b c+1 X PD|i (D|i) D i=d R e D R
(4.12)
+ 1 and R is the sensor communication range.
Computation of PN|D (N |D) with Equation 4.12 requires the computation of the term PD|i (D|i), where i ² {1, 2, 3, ...}. PD|i (D|i) stands for the probability of reaching D at a given hop distance i, as defined before. It must be noted that PD|i (D|i) is not equal to fdi (di ) which is the probability of reaching a maximum distance of di at a given hop distance i. However, PD|i (D|i) can be derived using fdi (di ) and Lemma 3 as will be provided 40
shortly. Since the proof of Lemma 3 requires Lemma 2, first, Lemma 2 is provided as follows. Lemma 2. If a sensor node A in SN has a distance D to source node S, then D − R ≤ dN−1 < D. Lemma 2 states that if a node A has a Euclidean distance D and a hop distance N from the source node S, then PN −1 must be located within one communication range of A towards S. However, this is a necessary but not sufficient condition for node A to have a hop distance of N to S and Lemma 3 provides the sufficient conditions. The following is the proof of Lemma 2. Proof. Proof of Lemma 2 Assume dN−1 < D − R. Then, dN−1 + R < D. Since dN−1 < dN ≤ dN−1 + R, dN < D must hold. However, this implies that the hop distance of node A to S is larger than N . Hence, dN−1 ≥ D − R by contradiction. Secondly, assume dN−1 > D. Since mN > dN−1 , mN > D holds with this assumption. However, this implies that A is not in SN . Hence, for A to be in SN , dN−1 < D must hold. Using Lemma 2, Lemma 3 can be presented and proved as follows: Lemma 3. A node A at a distance D to the source node S has a hop distance N from S, if D − R ≤ dN−1 < D and if dj < D − R for all j < N − 1. Lemma 3 simply states that for a node A, which is a distance D away from the source node S, to be in the set SN , there are two necessary and sufficient conditions. The first condition is that node PN −1 must be located within one communication range of A towards 41
D dN−1 D−R S
PN−1 R
A R
(a) D dN−1 D−R S
Pj
PN−1
A
R R
dj
(b)
Figure 4.2: Proof of Lemma 3
S. In other words, D − R ≤ dN−1 < D. The second condition is that all the previous maximal points Pj before N − 1 with j < N − 1 must be located at more than one communication range distance to A towards S. Hence, 0 < dj < D − R. Proof. Proof of Lemma 3 According to Lemma 2, D − R ≤ dN−1 < D if node A has a hop distance N to source node S. This is shown in Figure 4.2(a). However, the reverse statement is not necessarily true. By definition, dj < dN−1 for all j < N − 1. However, if D − R ≤ dj < dN −1 holds true for any j < N − 1, then node A is in the communication range of Pj , since 42
dj < D ≤ dj + R, as shown in Figure 4.2(b). This requires node A to have a hop distance j + 1 to S, but not N . Furthermore, PN −1 is now in the communication range of Pj , which forces PN −1 to be in Sj+1 . However, this is a contradiction since if j < N − 2, then point PN −1 becomes a previous furthest point Pj+1 . Moreover, if j = N − 2, then PN −1 is either node A, which is further away, or some other node even further than node A within the communication range of Pj . Hence, dj < D − R for all j < N − 1 must be true in addition to the requirement that D − R ≤ dN−1 < D.
4.2.3 Derivation of PN|D (N |D) According to Lemma 3, the probability of reaching distance D at a given hop distance i is obtained as follows: PD|i (D|i) = Prob (D − R ≤ di−1 < D) i−2 Y . Prob (0 < dj < D − R)
(4.13)
j=1
Computation of Equation 4.13 requires the pdf of di , pdi (di ), for i ² {1, 2, 3, ...}. In previous sections, pdi (di ) is shown to be well estimated with a Gaussian distribution. The computation of pdi (di ) requires only the mean multihop distance, E[di ], and the standard deviation of the multihop distance, σdi , as shown in Equation 4.14. 1 pdi (di ) = √ e 2πσdi
−(di −E[di ])2 2σd 2 i
,
(4.14)
where E[di ] and σdi are found by Equations 3.7 and 3.8, respectively. Using the Gaussian pdf in Equation 4.14, Equation 4.13 can be written as: µZ
D
Prob (D in i hops) = D−R
¶ Y i−2 µZ pdi−1 (x)dx . j=1
D−R 0
¶ pdj (x)dx . (4.15)
43
Finally, Equation 4.15 is substituted in Equation 4.12 for individual values of hop distance i to compute PN|D (N |D) as follows: Z D N −2 Z Y ( ( pdN−1 (x)dx). PN|D (N |D) =
D−R
2d D e R
X
"Z (
i=d D Re
j=1 D
D−R
D−R
i−2 Z Y pdi−1 (x)dx). ( j=1
pdj (x)dx)
0
#.
D−R 0
(4.16)
pdj (x)dx)
The integral terms in the computation of PN|D (N |D) in Equation 4.16 can be substituted by equivalent “error functions” since the integrants are Gaussian pdfs. The following two definitions are used to simplify Equation 4.16 ¶ µ ¶ µ D − R − E[di ] D − E[di ] √ √ Y1 (i) = erf − erf σdi 2 σdi 2 ¶ ¶ µ µ D − R − E[di ] E[di ] √ √ Y2 (i) = erf + erf σdi 2 σdi 2
(4.17) (4.18)
Equation 4.19 below is the final form of the conditional probability mass function PN|D (N |D) using Equations 4.17 and 4.18. Y1 (N − 1) PN|D (N |D) =
N −2 Y j=1
Y2 (j)
!. 2b c+1 Ã i−2 X Y Y1 (i − 1) Y2 (j) D j=1 i=d R e D R
(4.19)
The computation of PN|D (N |D) in Equation 4.19 is simple with the use of error functions. The parameters of Equation 4.19 are the given sensor communication range R, multihop distance D, and the values E[di ] and σdi , i ² 1, 2, 3, ..., which are computed by Equations 3.7 and 3.8.
4.3
Numerical Results
The pmf PN|D (N |D) of hop distance N for a given Euclidean distance D is calculated by Equation 4.19 in Section 4.2.3. In this section, the comparison of experimental and 44
approximation results obtained for PN|D (N |D) are provided. Furthermore, the effect of node density and the choice of the distance D on PN|D (N |D) are studied.
Approximated vs Experimental PN|D(N|D) for σ = 0.1 nodes/m
(N|D) for σ = 0.05 nodes/m
Approximated vs Experimental P
N|D
1
0.9
0.9
0.8 N=5
0.7
0.8
N=6
N=6 N=5 N=6
0.7
N=5 0.6
N=5
N=5
N=5
N=5 0.6
0.5
pmf
pmf
N=6 0.5
0.4
N=5
N=5 0.3 N=4
0.4
N=6 0.3
0.2
N=6
0.2
N=6
N=6
0.1
N=5
0.1
0
0 D=367m
D=387m
D=427m
D=407m
D=447m
Approximation
D=430m
D=410m
D=450m
D=470m Approximation
Experimental
(a) λ = 0.05 nodes/m.
D=490m Experimental
(b) λ = 0.1 nodes/m. Approximated vs Experimental PN|D(N|D) for σ = 0.2 nodes/m
1
0.9 N=5
N=5
0.8
N=6 N=5
0.7 N=6
pmf
0.6
0.5
0.4 N=6 0.3
0.2 N=5 0.1
0 D=435m
D=455m
D=475m
D=495m Approximation
D=515m Experimental
(c) λ = 0.2 nodes/m.
Figure 4.3: Comparison between approximated and experimental PN|D (P |D).
The comparison between the approximated and experimental pmfs PN|D (N |D) is shown in Figure 4.3. In this figure, the horizontal axis represents distance D. In each plot, there are five values of distance D. The third distance value is equal to the maximum distance 45
of the fifth hop D = E[d5 ] and the samples of D are chosen with increments of 20m. The choice of the fifth hop is completely random. The pmf of hop distance N is represented with a corresponding bar plot over each distance value in Figure 4.3. As it can be observed, the change in D affects the pmf of N . Furthermore, when D is changed additional N values with a non-zero probability can emerge while some others can disappear. For instance, in Figure 4.3(a), hop number N = 4 exists for D = 367m while it disappears for D = 427m. Moreover, hop number N = 6 is negligibly small for D = 367m while it becomes the dominant component of the pmf when D = 447m. In fact, Figures 4.3(a), 4.3(b), and 4.3(c) illustrate the transition from a pmf with hop number N = 5 being the dominantly large component to a pmf with hop number N = 6 being the largest component for node densities of λ = 0.05 nodes/m, λ = 0.1 nodes/m, and λ = 0.2 nodes/m, respectively. Furthermore, the probability of N = 5 in Figure 4.3(a) first increases and then decreases with increasing distance D and the rising values of the probability of N = 6 can be observed. If the pmf is shown for a larger range of distance D, it is observed that this behavior of the probability of N = 5 is observed for all values of N . Figure 4.3 shows that the largest difference between the experimental and the approximation results is observed at the third distance values in each plot. In fact, these distance values are found at locations where the largest difference between the Gaussian pdf approximation and the multihop distance pdf occurs. Such locations can be observed around the peak of the pdf curves in Figure 4.4. These locations designate the expected furthest points of each hop, hence the expected starting point of the next hop. Therefore, it is not surprising to see that these distances also correspond to the starting point of the above mentioned transition in the pmf of hop distance in Figure 4.3.
46
Multi−hop−distance distribution p (d ) curves for σ = 0.1 nodes/m
Multi−hop−distance distribution p (d ) curves for σ = 0.05 nodes/m d
N
d
N
N
Multi−hop−distance distribution p (d ) curves for σ = 0.2 nodes/m
N
d
N
0.05
0.09
0.2
0.045
0.08
0.18
0.04
N
0.16
0.07
0.035
0.14 0.06
0.03
0.12 pdf
pdf
pdf
0.05 0.025
0.1
0.04 0.02
0.08 0.03
0.015
0.06 0.02
0.01
0
0.04
0.01
0.005
0
100
200
300 400 Distance (m)
500
600
700
0
(a) λ = 0.05 nodes/m.
0.02
0
100
200
300 400 Distance (m)
500
600
700
0
0
(b) λ = 0.1 nodes/m.
100
200
300 400 Distance (m)
500
600
700
(c) λ = 0.2 nodes/m.
Figure 4.4: Effect of node density on multihop distance pdf curves σ = 0.1 nodes/m, D = 170 m 1
0.6 0.4
0.6 0.4 0.2
0
0
0
0.8
0.8
0.8
0.6 0.4 0.2
1 2 3 4 5 6 7 8 N σ = 0.2 nodes/m, D = 443 m 1
PN|D(N|D)
1 2 3 4 5 6 7 8 N σ = 0.1 nodes/m, D = 443 m 1
PN|D(N|D)
0.6 0.4 0.2
0.6 0.4 0.2
0
0
0
0.8
0.8
0.8
PN|D(N|D)
0.6 0.4 0.2 0
1 2 3 4 5 6 7 8 9 N σ = 0.1 nodes/m, D = 612 m 1
1 2 3 4 5 6 7 8 9 101112 N
0.6 0.4 0.2 0
1 2 3 4 5 6 7 8 9 N σ = 0.2 nodes/m, D = 612 m 1
PN|D(N|D)
(N|D)
N|D
P (N|D)
0.4 0.2
1 2 3 4 5 6 7 8 9 N σ = 0.05 nodes/m, D = 612 m 1
N|D
0.6
0.8
0.2 1 2 3 4 5 6 7 8 N σ = 0.05 nodes/m, D = 443 m 1
P
0.8
σ = 0.2 nodes/m, D = 170 m 1
PN|D(N|D)
PN|D(N|D)
0.8
P
N|D
(N|D)
σ = 0.05 nodes/m, D = 170 m 1
1 2 3 4 5 6 7 8 9 101112 N
0.6 0.4 0.2 0
1 2 3 4 5 6 7 8 9 101112 N
Analytical
Experimental
Figure 4.5: Experimental and approximated PN|D (N |D), D: randomly selected.
47
The effect of node density on multihop distance distributions is illustrated in Figure 4.4. As observed in this figure, individual multihop distance distribution curves corresponding to different hop numbers become separated from each other with increasing node density. The separation of distance pdf curves suggest that as the node density is increased, the hop distance N corresponding to a given Euclidean distance D becomes more deterministic. In other words, increasing the node density is expected to cause the pmf PN|D (N |D) to get closer to unity at a single value of N . This effect of node density on pmf can also be observed in Figure 4.3. When node density is increased, the pmf of N becomes more deterministic and has one dominantly large component for individual values of distance D as observed in Figure 4.3(c) with λ = 0.2 nodes/m except D = 475m where hop distances of N = 5 and N = 6 are observed simultaneously. The effect of node density on PN|D (N |D) is specifically shown in Figure 4.5 for three randomly selected values of distance D. Two observations can be made in this figure. Firstly, when the node density is increased, a dominantly large component of the pmf emerges, which makes PN|D (N |D) more deterministic. Secondly, as the node density increases, the probability given to small hop distance values increases while the probability of larger hop distance values decreases. Here, it must be noted that the range of possible hop distance values N for a given distance D is calculated by Equation 4.11. For instance, in Figure 4.5 when D = 443 and λ = 0.05 nodes/m, the probability of N = 6 is larger than the probability of N = 5. However, when λ = 0.1 nodes/m, probability of N = 5 is much larger than that of N = 6 and is almost 1 when λ = 0.2 nodes/m. This can be explained as follows. The multihop distance, hence the covered distance corresponding an individual hop distance N , increases with increasing node density. Therefore, smaller
48
values of N have increasing probability of covering a given distance D. This in turn causes low values of N to have increasing weights in PN|D (N |D).
49
CHAPTER 5
SECURE PROBABILISTIC LOCATION VERIFICATION IN RANDOMLY DEPLOYED WIRELESS SENSOR NETWORKS
In this chapter, a probabilistic approach to location verification in dense sensor networks, Probabilistic Location Verification (PLV) algorithm, is introduced. The proposed security mechanism is based on the results of Chapter 3 and leverages the relation between the hop distance and Euclidean distance between a source and a destination sensor in a spatially random WSN. In particular, the Gaussian pdf model provided in Chapter 3 is utilized to verify geographic locations of nodes based on advertised hop distances in received packets from the nodes. To achieve this, a simple transformation from one-dimensional node density to two dimensional node density is used. Then, the sensor positions of a two dimensional WSN are mapped to one dimensional network locations within a narrow band between particular source and destination nodes. Hence, a corridor is formed between sensor nodes to model the two dimensional multihop paths using a one dimensional network topology. This is shown in Figure 5.1. In Figure 5.1(a), sensors of the multihop path are searched within thin single hop rectangular areas in contrast to the angular slices of the sectored antenna propagation shown in Figure 5.1(b). In fact, since the propagation within the corridor shown in Figure 5.1(a) searches next nodes of the multihop path inside rectangular ranges, this model is an approximation for two dimensional information propagation. 50
S
r1
r2
r3
r4
r5
D
(a) Corridor S
D
(b) Sectored antenna
Figure 5.1: Multihop propagation between nodes S and D
However, it is quite simple to analyze and use in practice. Hence, this chapter is based on propagation over a thin corridor/band between two sensor locations. Note that, for a more accurate representation of the directional propagation, the sectored antenna communication patterns should be considered as in Figure 5.1(b), which requires an analytical study of the multihop distances. Such an analysis is provided in Chapter 6. It should be noted that this transformation is sufficiently simple, as shown in this section, to meet the requirements of the location verification application presented in this chapter. This simple transformation makes the results of Chapter 3 compatible with two dimensional networks. However, for more accurate estimation of the relation between hop distance and Euclidean distance in two dimensional WSNs, a more complicated analysis is required due to the geometric complexity of these networks with randomly located nodes. This analysis is provided in Chapter 6 and considers the angular transmission ranges of individual sectored antennas in each hop. The location verification task of a WSN is achieved by a small number of verifier nodes deployed in the WSN and the observations of these verifier nodes are combined to determine the plausibility of the location claims. The plausibility of a location claim refers to the 51
level of confidence that the claimed location results in the observed number of hops from the claimant source to all verifiers and it is represented by a real number between zero and one. The determined plausibility of a claim is simply compared against a threshold to validate or invalidate the claimed location by the verifier nodes. Furthermore, since plausibility has a non-binary nature, multiple levels of trust can be used in the claimed location.
5.1
Network Architecture and Assumptions
The sensor network architecture considered in this chapter is shown in Figure 5.2. The wireless sensors are deployed randomly in the network with a known density, which covers a number of scenarios ranging from battlefield surveillance to observation of hazardous environments. The deployed sensor network is of large scale and sensor locations follow a random Poisson point process, resulting in uniform node deployment. Each sensor node i determines its position (xi , yi ) in a two-dimensional Euclidean coordinate system through a (non-secure) localization method such as presented in [26, 15, 12]. It is assumed that all sensors have the same communication range and transmit at the same signal strength. It is worth noting that the communication range may change in an actual deployment even if the transmit power of all sensors is the same. However, the probabilistic estimation of distances used in this thesis allows for graceful degradation in case of non-uniform communication range estimations. Furthermore, it is also assumed that there are no big gaps in the sensor deployment and no big obstacles are present that disturb the uniform distribution assumption. In case such obstacles exist, the performance of the proposed methods in this chapter decrease. Note that a similar case is discussed in Section 5.4.2 and Figure 5.7 as related to denial of service attack mitigation.
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Figure 5.2: Proposed WSN architecture
As shown in Figure 5.2, the presence of a small number of verifier nodes is assumed. Verifier nodes have the responsibility of verifying the location of the sensor nodes. Although the positions of the verifiers can be random, they must not be closely located to ensure accurate and independent observations. Furthermore, the verifiers know their locations. Location verification is performed either periodically to establish the trustworthiness of a specific node and its reported position, or aperiodically to verify the positional origin of a critical message. Each verifier is assumed to have sufficient computational ability to calculate its own likelihood function based on the packets received from a particular node as well as the overall plausibility value for a claim. The communication between verifiers is assumed to be reliable, and protected by encryption. For the purposes of this analysis, it is assumed that the verifiers are secure and cannot be compromised. Also, as shown in Figure 5.2, the presence of a small number of malicious nodes is assumed. It is assumed that the malicious nodes possess the same properties as regular
53
sensor nodes, i.e., the same processing power and the same communication hardware. In other words, a malicious node is assumed to be an equivalent version of a compromised sensor node.
5.1.1 Authentication of Verification Messages It is assumed that the sensors are able to use two levels of authentication: one using symmetric keys, and another using asymmetric keys. The symmetric key is used to associate the given verification request with a sensor node identity. Every sensor node keeps a key that is used to encrypt the verification request. The key is then used at the verifier to decrypt the request and to map the request to a sensor node ID. Although a unique key for each node is desirable, the large number of sensor nodes makes the unique assignment unfeasible. Thus, a limited number of keys are randomly assigned to the sensor nodes before deployment, and the ID-key associations are stored in the verifiers. The use of the mapping between the keys and the sensor node IDs is described in detail in Section 5.4. An asymmetric key is used by each node to help infer the hop count traversed from the length of the received verification packet. A low complexity asymmetric key system is assumed, such as TinyPK [43], where all sensors share the private key to encrypt data, but which they cannot use to decrypt. The public key is maintained only in the verifiers, which is used to decrypt the request packets. The inference of the hop count from the packet size is also described in detail in Section 5.4.
5.2
Probabilistic Tools To Verify Location
The main idea behind the proposed mechanism is to leverage the statistical relationships between the number of hops in a sensor network and the Euclidean distance that is covered. The so-called hop-distance relationship has first been investigated in [41] for linear sensor 54
networks and are presented in Chapter 3 of this thesis. The extensions to two-dimensional networks are presented in Chapter 6.
5.2.1 The CDF of the k-Hop Distance The analysis in [41], which is summarized in Chapter 3, shows that the distance dk covered in k hops in a linear network of node density λ and communication range R has a pdf that can successfully be approximated with a Gaussian distribution with the same average and standard deviation. To make the results of Chapter 3 compatible to one dimensional networks, a “band” of width
R 2
along the line connecting two points in the WSN is consid-
ered, where the nodes can be assumed to be in a linear formation. Hence, the projected line density λ is calculated as λ = λ0 R2 , where λ0 is the two-dimensional density of the network. Based on this approximation, the average hop length r¯ can be computed by solving the implicit Equation 5.1: 1 − e−λ¯r (1 + λ¯ r) R − r¯ = . −λ¯ r λ(1 − e )
(5.1)
Then, the expected value r¯k ≡ E[dk ] of the k-hop distance dk is computed simply by multiplying r¯ by k: r¯k ≡ E[dk ] = k · r¯.
(5.2)
The computation of the variance of the k-hop distance σk2 follows an iterative formula: σk2 = f2 (k) − k 2 r¯2 , where
(5.3)
f2 (k) = f2 (k − 1) + 2(k − 1)¯ r2 + E[r2 ],
(5.4)
f2 (2) = 2E[r2 ] + 2¯ r2 ,
(5.5)
E[r2 ] = −R2 + 2R¯ r + E[re2 ], and ¢ ¡ 2 2 2 −λ¯ r −λ¯ r −λ¯ r −¯ r e − r ¯ e + 1 − e 2 λ λ , E[re2 ] = 1 − e−λ¯r
(5.6)
55
(5.7)
where re is defined as re ≡ R − r for the first hop. With these statistical measures, the cdf of the k-hop distance dk can be approximated as follows: Z
d
P r{dk < d | K = k} = −∞
1 √
σk 2π
−
e
(δ−¯ r k )2 2σ 2 k
· µ ¶¸ 1 d − r¯k √ dδ = 1 + erf , 2 σk 2
(5.8)
where K is the random variable representing the number of hops taken, and r¯k and σk are as defined in Equations 5.2 and 5.3. Obviously, a packet cannot traverse more than k · R in any direction in k hops, and the approximation needs to be upper-bounded in range. Note that the width of the band to calculate λ can be varied according to the density. The additional analysis has shown that a band width of
R 2
leads to a successful linear network
approximation for two dimensional densities as low as 3 · 10−2 nodes/m2 .
5.2.2 The PMF of the Number of Hops K Consider the case where a node i broadcasts its location (xi , yi ) in a packet that is flooded in the network. Assuming that the packet is received in kv∗ hops by a verifier node v located at (xv , yv ), the aim is to know the probability that a packet originating at (xi , yi ) traverses k hops to be received by v at (xv , yv ). The conditional CDF given in Equation 5.8 can be used to calculate the probability that a message is relayed in k hops to traverse a p distance of d = (xv − xi )2 + (yv − yi )2 . For this purpose, an error margin ² is defined and used to compute finite probabilities for the hop distances. Bayes’ Theorem is applied on Equation 5.8 to compute the PMF of the hop number K conditioned on the distance d: P r{K = k | d − ² < dk ≤ d + ²} P r{d − ² < dk ≤ d + ² | K = k} · P r{K = k} P r{d − ² < dk ≤ d + ²} h ³ ´ ³ ´i d+²−¯ d−²−¯ 1 √rk − erf √rk erf P r{K = k} 2 σk 2 σk 2 . = P r{d − ² < dk ≤ d + ²}
=
56
(5.9)
In Equation 5.9, the two unconditional probabilities must be computed based on the location of the verifier (xv , yv ), the shape of the sensor field A, the node density λ (and hence, λ0 ), and the average hop distance r¯. The unconditional probability P r{d − ² < dk ≤ d + ²} is simply the ratio of the number of nodes in a ring of radius d and thickness 2² around the verifier node v to the total number of nodes. If v is at least d + ² away from all edges of the sensor field, this probability can be computed as follows: P r{d − ² < dk ≤ d + ²} =
λ0 π ((d + ²)2 − (d − ²)2 ) , N
(5.10)
where N is the total number of nodes in the sensor field. Obviously, if the ring around the verifier node v is not completely contained in the sensor field, the numerator of the fraction should be computed such that only the segments of the ring contained in the sensor field are accounted for. Similarly, if the verifier node v is at the origin of a sensor field A, then the probability that a node is k hops away from v is computed as follows: ((k + 1)2 − k 2 ) · π¯ r2 §r¨ P r{K = k} = R R , rdrdθ (θ,r)∈A r¯
(5.11)
where r¯ is given in Equation 5.1, and (θ, r) corresponds to the polar coordinates of a location inside the sensor field A. Note that the unconditional probability of Equation 5.11 is independent of the density of the network. For finite size sensor networks, these quantities can be calculated before deployment numerically, considering the intersection of the rings around the verifier nodes and the sensor field. Moreover, P r{K = k | d − ² < dk ≤ d + ²} values can also be computed offline for all values of k and small increments of d and then stored as tables in verifier nodes. The online computation burden of the verifiers can be minimized by using these tabulated values.
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5.2.3 Relating Probabilities with Plausibility After the verifier node v receives the location information (xi , yi ) of node i, v can compute the conditional probability mass function P r{K = k|d − ² < dk ≤ d + ²} for the number of hops needed to cover the distance d. This, along with the actual hop distance covered kv∗ , is used to determine how much a verifier can contribute to the overall decision process. Assume that a verifier v computes the distance d from a source claiming to be at (xi , yi ) based on the information contained in a broadcast packet. In addition, assume that the non-zero probabilities of the PMF of Equation 5.9 are {0.2, 0.3, 0.4, 0.1} for hop counts {4, 5, 6, 7}, respectively. The most likely number of hops the packet must have taken is 6 according to the PMF calculation. However, if a packet reaches the verifier in k ∗ = 5 hops, the verifier should not declare the claimed location implausible. Furthermore, the relative position of the probability associated with k ∗ in the entire PMF should also be taken into account. To this end, the difference between the maximum value in the PMF and the probability associated with k ∗ is considered: The larger this difference becomes, the less one should trust the claimed location. On the other hand, if this difference is small, the verifier should not be alarmed regardless of the k ∗ value. Theoretically there are an infinite number of nonzero probabilities for this PMF. However, for the sake of simplicity, the cases that have a very small probability are ignored. Let Pvmax (d) be the maximum probability computed for any number of hops based on (xi , yi ) and v’s location: Pvmax (d) = max P r{K = n|d − ² < dk ≤ d + ²}, n∈N
58
(5.12)
(a) One Verifier
(b) Two Verifiers
(c) Two Verifiers
(d) Two Verifiers
Figure 5.3: Plausibility of a node’s claimed location for different number of verifiers
59
where N is the set of natural numbers. A probability slack function Sv (d, kv∗ ) is defined, which is the difference between the maximum probability the verifier v can provide and the probability of the source being kv∗ hops away. This function is given by: Sv (d, kv∗ ) = Pvmax − P r{K = kv∗ |d − ² < dk ≤ d + ²}. Scaling Sv (d, kv∗ ) by Pvmax (d), i.e.,
Sv (d,kv∗ ) , Pvmax (d)
(5.13)
one obtains the distrust in the claimed location
based on the observed number of hops. An important observation at this point should be made regarding the distrust levels of individual verifiers. Consider two verifiers that calculate PMFs, one resulting in a very “peaked” distribution (say, {0.3, 0.6, 0.1}), and the other in a more uniform distribution (say, {0.1, 0.2, 0.2, 0.2, 0.2, 0.1}). Let the first verifier compute a distrust value of 0.6−0.3 0.6
= 0.5, and the other verifier compute
0.2−0.1 0.2
= 0.5. Intuitively, one can claim that
the second verifier can only make a very uncertain decision because of the shape of the distribution. On the other hand, the first verifier has a “stronger” opinion, be it supporting or against the acceptance of the claimed location. Hence, the second verifier’s input should be weighed less than the input of the first verifier. Pvmax (d) is proposed as a measure of the confidence in a verifier’s opinion. Although there exist many other ways to express the level of confidence, such as using a function of the PMF variance, weighing the distrust levels with Pvmax (d) both provides a good measure (as observed through simulations) and simplifies the plausibility calculations. If there are V verifiers participating in the verification process, then the overall plausibility Pi of node i’s location claim can be computed as: PV Pi = 1 −
j=1
Pjmax −P r{K=kj∗ |d−² 0 do 14: np ← P arent(T argetGroup) 15: prev ← T reeP arent(np) 16: T argetGroup ← Group whose parent is prev 17: if T argetGroup already scheduled then 18: break 19: end if 20: N extColor ← Color 21: loop 22: increment N extColor 23: if N extColor > M axColor then 24: N extColor ← 1 25: end if 26: if N extColor == Color then 27: break 28: end if 29: conf lict ← DetermineConf lict(T argetGroup) 30: if conf lict == F ALSE then 31: Schedules(T argetGroup) ← N extColor 32: Color ← N extColor 33: break 34: end if 35: end loop 36: if T argetGroup already scheduled then 37: Increment M axColor 38: N extColor ← M axColor 39: Schedules(T argetGroup) ← M axColor 40: Color ← N extColor 41: end if 42: end while 43: end while 121
Algorithm 4 AssignColor(T argetGroup) 1: Color ← 1 2: loop 3: conf lict ← F ALSE 4: for all Group j do 5: if DetermineConf lict(T argetGroup) then 6: conf lict ← T RU E 7: end if 8: end for 9: if conf lict == T RU E then 10: increment Color 11: else 12: break 13: end if 14: end loop 15: Schedules(T argetGroup) ← Color 16: if Color > M axColor then 17: M axColor ← Color 18: end if 19: return Color
Algorithm 5 DetermineConf lict(T argetGroup, Conf licts) 1: if Conf licts(T argetGroup) == T RU E AND T argetGroup! = j AND Schedules(j) == 2: 3: 4: 5:
Color then return T RU E else return F ALSE end if
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Parameters Definition Distances(i) Hop distance of Group i to root P arent(i) Parent node of Group i in Shortest Path Tree to root T reeP arent(a) Parent node of node a in Shortest Path Tree to root
Table 7.1: Definitions in Time-Slot Assignment Algorithm
After computing the time schedules, the cluster head node distributes the schedule information to its cluster by flooding a SCHEDULE packet. The SCHEDULE packet includes the information about the active time slot assignments of the cluster nodes. At the beginning of the network operation, nodes wait to receive the SCHEDULE packet. Upon the reception of the SCHEDULE packet, nodes extract their schedule information and start to operate in the set of modes defined by the SAMAC protocol. After processing the SCHEDULE packet, each node forwards the packet on its sectors except the one that it received the SCHEDULE packet from, so that eventually every node in the cluster receives the schedule information. Sensor that do not receive the SCHEDULE packet cannot engage in the SAMAC protocol and data transfers in the cluster. Such connectivity issues are related with neighborhood relations and the network topology, hence they are out of the scope the SAMAC protocol. After receiving the SCHEDULE packet, in each time slot, sensor nodes either turn off their antennas to save power or keep their antennas on to engage in communication events. When its antennas are off, a sensor is in SLEEPING mode. Otherwise, the node is active and can be at any of the protocol-defined states. The decision to be in SLEEPING mode is made by the sensor’s time schedule received from the SCHEDULE packet. An example schedule information of a node A is shown in Table 7.2. In this table, the superframe 123
Active True True True False
Time Slot 0 1 2 3
Active Sector 2 1 3 X
Table 7.2: Schedule information of a node
consists of 4 time slots. For instance, in slot 3, node A is not active, hence in SLEEPING mode, with no specified sector number. According to its schedule, when a sensor is active, it can communicate on only one of its sectors at a given time slot. For instance, in Table 7.2, node A can communicate with its neighbors on its 3rd sector in time slot 2. Hence, A can transmit packets to the channel and pass the received packets to its protocol stack on sector 3 in time slot 2. However, it cannot transmit packets on any other sector. Furthermore, packets received from other sectors are buffered in the physical layer and are not passed to SAMAC until SAMAC needs to process them. Figure 7.5(a) shows the time slot assignment and Figure 7.5(b) illustrates the sectors used in each active time slot. X represents that the node is not active in a time slot.
1
2
3
0
1
2
3
0
1
2
3
2
1
3
X
Superframe (a) Time slot assignments
1
3
X
2
1
3
X
Superframe (b) Active Sector Numbers, X: not active
Figure 7.5: Time slot assignment and sector numbers
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7.7.1 Two Modes of Operation According to SAMAC, a sensor node can be in one of the two operation modes described as follows. 1. BASIC mode: At the beginning of network operation, sensor nodes are in BASIC mode. In BASIC mode, a node does not have any schedule information and there is no differentiation between its sectors. The purpose of the BASIC mode is the distribution of the schedule information within the cluster. The schedule information is distributed via flooding. The flooding in our sectored-antenna system is accomplished by transmitting the schedule information over all sectors sequentially. Each sectored transmission follows basic CSMA guidelines for each sector, including backing off when the channel is sensed busy. The reception of information is performed in an emulated form as the adopted transceiver design allows for omnidirectional reception 7.2. In BASIC mode, nodes wait to receive a SCHEDULE frame, and only SCHEDULE frames are processed. Hence, if SAMAC receives a frame other than a SCHEDULE frame, that frame is discarded. Upon reception of the SCHEDULE frame, a sensor extracts its schedule information, forwards the frame to its neighbors, initializes its configuration, and goes to ADVANCE mode. The cluster head goes to ADVANCE mode immediately after broadcasting the SCHEDULE frame generated by the schedule computations. 2. ADVANCE mode: SAMAC protocol operation is performed when nodes are in ADVANCE mode. In this mode of operation, nodes are in one of the SAMAC states. Protocol events are handled according to current state of a node. 125
In the following parts of the protocol description, the protocol functionality in a single time slot is presented. The next section describes the SAMAC time slot structure.
7.7.2 SAMAC Time Slot Structure The time slot structure in SAMAC is shown in Figure 7.6. At the start of each time slot, nodes check their schedule information to determine whether they are active in that time slot or not. If a node is active in a time slot, then it can participate in a communication event. This can be a data transmission (TX) or data reception (RX). There is a certain amount of time called MIN AWAKE TIME at the beginning of each time slot allocated to determine if there is a communication with another node to be handled. If the node has no data to be sent and there is no data reception during this MIN AWAKE TIME time period, then the node decides to go to SLEEPING state, as shown in Figure 7.7(a). In this state, all antennas are turned off to save power. Hence, there are no interactions with the channel until the node turns on its antennas. On the other hand, if there is a communication event (TX/RX), then this event is handled immediately.
SLOT START
SLOT END
MIN_AWAKE_TIME
MAX_AWAKE_TIME
Figure 7.6: Time slot structure
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MAX_AWAKE_TIME
MAX_AWAKE_TIME
MIN_AWAKE_TIME
MIN_AWAKE_TIME
MIN_AWAKE_TIME
SLEEPING
SLEEPING TX/RX START
SLOT START
SLOT END
TX/RX END
SLOT START
(a) Go to sleep after first MIN AWAKE TIME
SLOT END
(b) Go to sleep after one transmission
Figure 7.7: Early sleeping mechanism
At the end of each communication (TX/RX) period, nodes wait for another period of time equal to MIN AWAKE TIME to determine if there is a new transmission/reception that needs to be performed. During each of these time periods, the node is in IDLE state. If there is no traffic for MIN AWAKE TIME, the node goes to SLEEPING state immediately, as shown in Figure 7.7(b), otherwise the traffic is handled.
MAX_AWAKE_TIME
MIN_AWAKE_TIME
MIN_AWAKE_TIME
MIN_AWAKE_TIME
TX/RX START
SLOT START
TX/RX START TX/RX END
TX/RX START TX/RX END
TX/RX END
SLOT END
Figure 7.8: Go to SLEEPING state after MAX AWAKE TIME
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In Figure 7.6, MAX AWAKE TIME defines the maximum time period that a node can be active in a time slot. After MAX AWAKE TIME from the slot start time, the node goes to SLEEPING mode regardless of its state as shown in Figure 7.8. MAX AWAKE TIME is a configuration parameter and represents the duty cycle in ADVANCE mode. As long as there are communication events to be handled, if MAX AWAKE TIME is equal to the total time slot duration, then the node spends no time in SLEEPING mode, which corresponds to 100% duty cycle. However, due to the battery power limitation, SAMAC allocates a certain amount of time equal to (Total Time Slot Duration - MAX AWAKE TIME) before the end of each time slot for nodes to be in SLEEPING mode and turn off their antennas.
7.7.3 Communication Events Communication events can be either data transmissions or receptions. During the IDLE state, if a node receives a packet from the physical layer, then SAMAC goes to RECEIVING state to handle processing of the packet. However, if the node has a packet to be transmitted, then the communication channel should be reserved with a four-way RTS/CTS/DATA/ACK handshake with the receiver node. Before sending an RTS packet to initiate this process, the node needs to backoff from channel access for a certain amount of time. Hence, packet transmissions start with a BACKOFF state. During the BACKOFF state, if the node senses the channel to be free during the whole backoff period, then the transmission of an RTS packet can be started. However, if the channel becomes busy before the backoff period is over, then the node pauses its backoff and saves the remaining backoff time period, as shown in Figure 7.9(a). In this case, the nodes goes to WAIT FOR NAV state and defers from channel access until the ongoing transmission in its neighborhood on the current sector ends. After the channel is sensed
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MAX_AWAKE_TIME MAX_AWAKE_TIME MIN_AWAKE_TIME
MIN_AWAKE_TIME
MIN_AWAKE_TIME
Channel busy BACKOFF START
BACKOFF START
END OF ACK BACKOFF END / RTS START
BACKOFF START
SLOT END
TX/RX END
TX/RX START
NAV
MIN_AWAKE_TIME
TX/RX START
BACKOFF START
TX/RX END
Go to Sleep
BACKOFF START
SLOT START
SLOT START
(a) Pause backoff due to busy channel
SLOT END
(b) Pause backoff due to sleep
Figure 7.9: Pausing backoff
idle again, the node retries to initiate the communication by going into BACKOFF state and uses the remaining time period from the previous backoff. Note that a node can also go to SLEEPING mode while in BACKOFF state at the MAX AWAKE TIME instance as illustrated in Figure 7.9(b). In this case, the remaining backoff value is saved to be used in the same time slot of the next superframe. SAMAC has a separate backoff value for each active slot time. For instance, when a node has a remaining backoff time at the end of time slot 1, then this value will be used in time slot 1 of the next superframe. This is required since the communication activities in different sectors of a node can be different. Hence, SAMAC utilizes the conventional backoff procedures, with RTS/CTS/DATA/ACK frame sequence in individual time slots and saves its backoff states to be used in the same time slots of the next superframe. Since each time slot is associated with a different sector of the node, SAMAC effectively differentiates between different traffics in different sectors.
129
SAMAC treats upstream and downstream frames differently in its backoff procedure. Since upstream traffic propagates from sensors to the cluster head and carries urgent data, the backoff window used for transmitting upstream RTS frames is smaller than the backoff window of downstream traffic. After each failure of channel reservation due to an incomplete backoff period, the backoff window is incremented linearly until it reaches an upper limit. During the RTS/CTS/DATA/ACK frame exchange between a sender and a receiver, nodes use the conventional states, such as WAIT FOR CTS, WAIT FOR DATA, and WAIT FOR ACK. For instance, a node that transmits an RTS frame waits for a CTS frame from its neighbor and goes to WAIT FOR CTS state to handle the incoming CTS frame.
7.7.4 SAMAC Internal Queues Messages received from the network layer are stored in the internal SAMAC queues. There is a separate queue for each time slot in SAMAC. For instance, a packet that is received from the network layer in time slot 0 is inserted to the queue with index 0. Packet insertions are performed at the tail of the queue and packets are popped from the head of the queue. If a packet cannot be transmitted in a time slot and the retransmission limit is not exceeded, then that packet is pushed to the top of the queue and is treated in the next superframe. Figure 7.10 illustrates the internal SAMAC queues.
7.7.5 SAMAC States In ADVANCE mode, SAMAC protocol can be in one of the following states in a node. • IDLE: In this state, the node is ready for initiating or responding to a new communication event. A node goes to the IDLE state right after the start of a slot time provided
130
NETWORK LAYER
Time Slots:
0
1
Queue N−1
Queue 1
Queue 0
Push to back
N−1
Pop from head SAMAC Push to head
Figure 7.10: SAMAC internal queues
that it has no packets to send. If no packets are received or there are no packets to be sent within a MIN AWAKE TIME period, then the node goes to the SLEEPING state directly. Upon completion of a successful communication, the node goes to the IDLE state as well. • SLEEPING: This state turns off the antennas of the nodes to save battery power. SLEEPING state is enforced by SAMAC at MAX AWAKE TIME after the beginning of each active slot. Furthermore, the node goes to SLEEPING state if there are no communication events during a MIN AWAKE TIME time period in IDLE state. In SLEEPING state, SAMAC does not make any communication with its neighbors and does not accept incoming packets from the physical layer and the network layer.
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• BACKOFF: A node is in BACKOFF state at the start of each RTS frame transmission attempt. When a node is in BACKOFF state, it should sense no activity in the channel for a dynamically adjusted backoff period. This backoff period is determined by the node’s contention window. The contention window increases linearly in SAMAC before each retransmission of an RTS frame. SAMAC has a separate backoff period for each of its time slots in a superframe. When activity is detected before the backoff expires, the remaining backoff period of a particular time slot is carried over to the same time slot in the next superframe. • WAIT FOR DIFS and WAIT FOR SIFS:Before going to the BACKOFF state, which is intended for a new transmission attempt, a node waits for at least a DIFS period and is in the WAIT FOR DIFS state. Furthermore, the transmission of the control frames in the RTS/CTS/DATA/ACK exchanges are preceded by a smaller time period SIFS during which the node is in the WAIT FOR SIFS state. These two states are similar to IEEE 802.11 states for the corresponding waiting periods DIFS and SIFS. • Waiting States: SAMAC has 4 waiting states apart from WAIT FOR DIFS and WAIT FOR SIFS. These states are WAIT FOR CTS, WAIT FOR DATA, WAIT FOR ACK, and WAIT FOR NAV. The first three states are used to handle incoming frames in a communication event. A node is in the state WAIT FOR NAV if it detects an activity in the channel during the BACKOFF state and it should defer from channel access. • Transmission States: SAMAC has 4 transmission states depending on the type of frame that is most recently sent to the channel. These states are TX RTS, TX CTS, 132
TX ACK, and TX DATA. Transmission states are encountered in the ADVANCE mode during a communication event. SAMAC state transition diagram provided in Figure 7.11 summarizes the operation of SAMAC protocol. The state WAIT FOR SIFS is omitted in Figure 7.11 to simplify the presentation of the protocol life cycle. The numbers near the transition lines represents brief explanations of events that cause the transitions given by the following.
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1. Go to sleep. If no communication event in MIN AWAKE TIME or after a time period of MAX AWAKE TIME from the beginning of a time slot. 2. If there is a packet to be sent in current time slot’s MAC queue. 133
3. Wake up. Occurs upon reception of physical layer notification at the beginning of an active slot. 4. If backoff timer expires and there is no packet to send. 5. If there is no sufficient time for RTS/CTS/DATA/ACK in this time slot. Current packet is inserted back to the top of the current time slot’s MAC queue. 6. At the MAX AWAKE TIME instance, the node should go to sleep. Backoff states are saved for next superframe. 7. Backoff timer expires and there is sufficient time for RTS/CTS/DATA/ACK sequence. 8. Node was backing off, but channel has become busy. 9. RTS transmission is over and the node is ready to accept a CTS frame. 10. CTS is received correctly and the node is transmitting DATA. 11. No CTS is received, CTS timer expired, and short retry limit not exceeded. 12. NAV expired, channel is now idle, and there is a packet to be sent. 13. Physical layer status goes to IDLE and there is a packet to send. 14. DATA is transmitted and the node is now ready to accept the ACK frame. 15. ACK is received and there is no more packet to be sent. 16. ACK is not received, ACK timer expired, but long retry limit is not exceeded. 17. ACK is not received, ACK timer expired, and long retry limit is exceeded.
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18. DIFS timer expires and there is non-zero remaining backoff time period for this time slot. 19. DIFS period is over, the channel is idle, and there is a remaining backoff time for this time slot. 20. Physical layer status goes to IDLE, but there is no packet to send.
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7.8
Simulation Study
In this section, the performance analysis of the SAMAC protocol is provided. The analysis includes comparison of the SAMAC protocol on sectored antennas with the 802.11 protocol running on omnidirectional antennas. The implementation of SAMAC and the simulations are performed using the Qualnet Simulator [37]. Table 7.3 shows the definitions and values of the configuration parameters of SAMAC.
Parameter SLOT DURATION MIN AWAKE TIME MAX AWAKE TIME CW MIN UPSTREAM CW MAX UPSTREAM CW MIN DOWNSTREAM CW MAX DOWNSTREAM RETRANSMISSION UPSTREAM RETRANSMISSION DOWNSTREAM BACKOFF SLOT
Definition Duration of a time slot Minimum awake time Maximum awake time Minimum contention window for upstream frames Maximum contention window for upstream frames Minimum contention window for downstream frames Maximum contention window for downstream frames Retransmission limit of upstream frames Retransmission limit of downstream frames Length of a single contention window of size 1
Value 20 * msec 0.2 * SLOT DURATION 0.98 * SLOT DURATION 3 10 20 40 7 7 20 * MICRO SECOND
Table 7.3: SAMAC configuration parameters
The network architecture used in the simulations consists of 64 nodes with a transmission range of 22m placed on a grid topology with 20m of separation between neighbor locations as shown in Figure 7.12. The sensor nodes are equipped with 4 sectored antennas and transmit frames of constant payload size of 40 bytes. Nodes are represented with circles surrounded by 4 sectors and node index numbers are shown beside the nodes. Links in this figure illustrate the generated schedules with corresponding time slot numbers. The
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cluster head node is at the lower left corner with index 1. The cluster head is deliberately placed here to test longer hop distances to the cluster head.
7.8.1 Performance Evaluation The performance of the SAMAC protocol as compared with 802.11 for varying data generation rates 1 through 7 packets/second is illustrated in Figure 7.13. In this figure, average values of end-to-end delay, data throughput, and data delivery ratio are investigated. Figure 7.13(a) shows the end-to-end delay of packet delivery. This figure demonstrates the exponential increase in the delay amount with 802.11 as the packet generation rate 137
is increased from 1 packets/sec to 7 packets/sec. Although the delay encountered by 802.11 is less or comparable to the SAMAC delay results, 802.11 delay exceeds the delay of SAMAC exponentially after 4 packets/second. The end-to-end delay of SAMAC is observed to be dependent on the choice of the SLOT DURATION parameter, which is the length of a time slot. Three different time slot lengths are evaluated, i.e. 10ms, 20ms, and 40ms. Less delay is obtained as SLOT DURATION is decreased to 10ms. Furthermore, the amount of delay in SAMAC is constant regardless of the packet generation ratio for all three time slots used in the simulations. On the other hand, 802.11 demonstrates a fluctuation and an exponential incline. In Figure 7.13(b), the average throughput values of SAMAC and 802.11 are compared. For all three time slot values of SAMAC, data throughput linearly increases as the data generation rate is increased from 1 packets/sec to 7 packets/sec. On the other hand, the throughput of 802.11 is observed to be comparably less than SAMAC and becomes nearly constant around 800 bits/sec. Figure 7.13(c) demonstrates the data delivery ratio characteristics of SAMAC and 802.11. SAMAC is observed to create no packet drops with a delivery ratio of 1, whereas 802.11 has a diminishing delivery ratio as the data generation rate is increased. This behavior can be attributed to the high contention in the wireless medium and failures after retransmission limit is exceeded in 802.11 which effectively silences all potential communication in large omnidirectional neighborhoods at the start of each communication. On the other hand, with time scheduling provided by SAMAC packets and with the spatial reuse property of directional transmission, simultaneous non-interfering communication events can take place in the same neighborhood which leads to a high data delivery ratio and throughput as shown in Figures 7.13(b) and 7.13(c) . 138
Comparison of Average End−to−End Delay
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Figure 7.14 demonstrates the per-source end-to-end delay of SAMAC and 802.11. The x-axis shows the indices of nodes that are data traffic generators the y-axis represents the end-to-end delay in seconds. In Figure 7.14(a), the packet generation ratio is 1 packets/sec. It can be observed that 802.11 has less per node delay. However, for a larger packet generation ratio of 7 packets/sec, as shown in Figure 7.14(b), 802.11 has considerably large end-to-end delays in the order of 20 seconds due to the high contention in the medium. Nodes 11, 17, 18, and 25 are observed to have similar end-to-end delays with SAMAC since they are very close to the cluster head. However, since these nodes reserve the channel near the cluster head during most of the simulation time, packets generated by other nodes have high end-to-end delay values and data delivery highly depends on traffic flows at different time instances. Hence, Figure 7.14 clearly illustrates the overwhelming performance of SAMAC compared to 802.11 for increasing data rates.
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Histogram of Per Source Node Average E2E Delay with with50 Source Nodes
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The effect of time slot length on SAMAC performance is observed for 50 source nodes in Figure 7.15 using histograms of the distribution of the per-node service time and per source node average end-to-end delay. Figure 7.15(a) demonstrates the per node service time histogram and Figure 7.15(b) shows the histogram of per source node end-to-end delay. In this figure, it can be observed that as the slot duration is decreased the service time and the end-to-end delay are also reduced. Furthermore, the distribution is more peaky and concentrated to a smaller range of values for lower slot durations. This suggests a more deterministic behavior for smaller time slots compared to larger slot durations. The results in Figures 7.13(a), 7.14, and 7.15 clearly suggest using a small time slot in SAMAC protocol to reduce the end-to-end delay and service time. However, using a smaller time slot has an important tradeoff. The energy savings are determined by the parameters MIN AWAKE TIME and MAX AWAKE TIME in a time slot and should be fixed as protocol parameters. For fixed MIN AWAKE TIME values that should be adapted
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independent of the slot time, the percentage of the time the node will stay awake will be large for small slot sizes. Especially in lightly loaded systems with sporadic traffic bursts, which is the case for most sensor networks, staying awake longer reduces the network life time. Therefore, larger slot sizes are advantageous from energy efficiency perspective. Another factor that calls for larger slot sizes is the contention issue. For cases where the scheduling group sizes are large, contention is required to coordinate the channel access. For all but most lightly loaded systems, several contention rounds are necessary to flush out packets pending to be sent to the next hop. Smaller slot sizes mean that contentions will be cut short and there will be backlogs to be delayed to the next time slots. Therefore, larger slot sizes have a positive effect on the delay performance from contention perspective. These considerations suggest that there should be an optimum size allocation for the slot time as a function of delay and energy consumption, which is a topic of future work.
7.8.2 Target Tracking Scenario The SAMAC protocol is tested for a target detection application on the grid network architecture shown in Figure 7.12. An object moves with a track determined by the Random Waypoint Model. The speed of this moving target is configurable and chosen to have a value in the range from 0.5 m/sec to 9 m/sec. When sensor nodes detect the presence of the target within their sensing ranges, they generate a data packet and send it to the cluster head. Nodes sense their ranges every second of the simulation time to monitor the neighborhood for an intruder. Different values of the sensor sensing range are used to demonstrate its effect on SAMAC node tracking performance which is measured by the Information Propagation Speed (IPS) given by:
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A large IPS value is desired for timely detection of moving targets. The simulation results for the target tracking capability of SAMAC are shown in Figure 7.16. Sensing ranges of 25m, 30m, 35m, and 40m are utilized for various object speeds. It is observed that as the object speed increases, the tracking ability is degraded as expected. Furthermore, better tracking ability is obtained for a smaller sensing range. This can be attributed to the higher data generation rate with a larger sensing range since source nodes have an increased probability of detecting the moving target when they use an increased range.
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CHAPTER 8
CONCLUDING REMARKS AND FUTURE WORK
In this thesis, the information propagation capacity of Wireless Sensor Networks (WSN) is investigated from two perspectives. First, the distribution of the maximum distance that can be covered on a multihop path is investigated for both one dimensional and two dimensional networks. Secondly, a MAC protocol specifically designed for wireless sensor networks equipped with sectored antennas, called SAMAC is described. With regards to the range extension capability of directional antennas, further distances can be covered as opposed to omnidirectional transmissions. To investigate this capability and to determine the maximum coverage achieved by multihop directional transmissions, the relation between the hop distance and the maximum Euclidean distance that can be taken in a given number of hops is studied. The prior study on maximum distance distributions in one dimensional networks [41] illustrate that Gaussian pdf can be used to model these distributions. In this thesis, the results of this study are summarized and are used in a WSN security application based on sensor location verification (PLV). To achieve this, one dimensional network findings and the Gaussian pdf model representing the multihop distance distributions are applied to two dimensional (2D) networks through a simple mapping. Although the requirements of the PLV application are met with these approximations, for applications such as delay and distance estimations, a new mechanism that 144
provides highly accurate distance distribution estimations for two dimensional networks is proposed. With the proposed mechanism, the maximum multihop Euclidean distance distribution is successfully modeled by the well-known Gamma pdf whose parameters can be approximated quite accurately. Apart from the proposed Gamma pdf model of two dimensional distributions, the probability mass function of the hop distance corresponding to known Euclidean distance values is approximated using the results of [41]. The performance results demonstrate that the proposed analytical method successfully models the pmf, hence it can be applied to WSN applications that require hop distance distribution as a prior information for network operation. The second contribution of this thesis is the Smart Antenna-Based MAC (SAMAC) protocol specifically designed for WSNs with sectored antennas. Detailed protocol description as well as performance evaluation results are presented. With the scheduling and time slot assignment mechanisms of SAMAC, high contention sources in the wireless medium are effectively eliminated. Furthermore, simple channel contention methods are employed to reduce the more rare cases of packet collisions. SAMAC is shown to demonstrate reliable data delivery, high data throughput and less end-to-end delay as compared to IEEE 802.11 using omnidirectional antennas. Furthermore, SAMAC is proposed for data delivery applications such as disaster recovery and military surveillance that require timely and correct delivery of critically important data. With the sensor sleep schedules provided by SAMAC, efficient use of limited battery resources is achieved, which is a strict requirement of energy-limited WSNs.
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8.1
Future Work
The topics of future study directions of this thesis can be summarized in two parts: The first part includes the tasks to be accomplished to apply the results of the analytical work on the relation between hop distance and maximum Euclidean multihop distance achieved by directional antennas in WSNs. As for the second part of the future work, the SAMAC protocol needs to be improved by adding more robustness and completeness to the protocol functionality besides possible optimization tasks.
8.1.1 Analytical Work on WSN Distance Distributions The analytical study on WSN distance distributions provide simple and generally applicable results. The future work of this study is presented as follows. Multihop Propagation Delay and Energy Consumption Estimation The probability mass function (pmf) of the one dimensional hop distance for a given Euclidean distance is presented in Chapter 4. This pmf is based on the Gaussian pdf model of the one dimensional maximum Euclidean distance distribution [41]. In [44], the model is used by a Bayesian decision mechanism to determine the number of hops between two network locations at a known Euclidean distance. Decision boundaries are defined instead of providing an analytical expression of the pmf, which leads to discrete levels of hop distance estimations. The results of [44] clearly demonstrate staircase graphs for the approximation of network parameters such as delay and power consumption. On the other hand, Chapter 4 of this thesis provides a detailed derivation of the pmf expression, which enables a more
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precise representation of the hop distance distribution. Therefore, estimation of the multihop propagation delay and total energy consumption can be achieved more precisely using the pmf of hop distance, which constitutes one of the future work topics of this thesis.
8.1.2 Improvement of the PLV Algorithm The location verification algorithm, PLV, introduced in Chapter 5 manipulates the approximations provided in Chapter 3 for one dimensional networks. The algorithm is based on the estimation of the hop distance using the Gaussian pdf model and a simple mapping from one dimensional networks to two dimensional networks. Although the results demonstrate that sufficient accuracy in decisions, the algorithm can be improved in two ways: First, the PLV algorithm uses Bayes’ Theorem to determine the pmf of hops distance. Chapter 4 explains additional analytical steps that needs to be performed to obtain a more precise pmf approximation. As a future research topic, these results can be incorporated into PLV to observe the resulting performance improvement. Second, PLV utilizes the results of [41] which are derived for one dimensional WSNs. However, Chapter 6 provides a more accurate model with the Gamma pdf and can be applied to the location verification application to improve the WSN security performance. Hence, with this more accurate representation of the maximum multihop Euclidean distance in two dimensional networks, the PLV application can be improved with enhanced location and hop distance estimation accuracy.
8.1.3 The pmf of Hop Distance in Two Dimensional WSNs Chapter 4 results are derived using the Gaussian pdf model. As a future work, the Gamma pdf model presented in Chapter 6 can be used to determine an approximation to the probability mass function of hop distance in two dimensional networks. However, 147
Chapter 4 benefits from the simplicity of a one dimensional network topology, such that the previous hops in a multihop propagation are guaranteed to be located on a line. In case of two dimensional networks, the extension of the Bayes’ Theorem should consider the possible locations of previous hops in areas defined by directional transmissions, which requires a more complex analysis compared to Chapter 4. Furthermore, additional geometric approximations are required for this analysis. Since, the pdf results presented in Chapter 6 more accurately represent the distance distributions in two dimensional networks, the pmf estimation accuracy can be improved by the Gamma pdf model introduced in Chapter 6. This in turn can better demonstrate the reduction of hop distance as a result of the extended range of directional antennas instead of the circular range of omnidirectional antennas.
8.1.4 SAMAC Protocol Future Directions The operation of SAMAC protocol, as described in Chapter 7, can be improved and extended. First, SAMAC depends on correct and complete neighborhood information. The current work assumes that this information is provided by a separate location service in a higher protocol stack and provided to SAMAC. However, in a real-world implementation of SAMAC, sensor nodes should determine their neighbors and propagate this information to the cluster head. Second, the optimization algorithm employed by SAMAC can be improved using additional stages and/or optimizing the ranking criteria of individual groups selected for time slot assignment. Finally, the current protocol description does not include recovery from failures. These issues to be addressed in future work are briefly explained as follows.
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Topology Discovery Algorithm The topology discovery algorithm of SAMAC needs to be developed, so that nodes discover and then propagate the neighborhood information to the cluster head. The key in this effort is to develop an efficient neighbor discovery methodology. Existing methods rely on exchange of Hello packets, which is suitable for omnidirectional antennas. However, in WSNs with directional antennas, discovery of directional neighborhood requires the concurrent activation of sectors, which reduces the probability of establishing the connection in a limited period of time. The transceiver design adopted by SAMAC allows buffered information processing in non-active sectors. In other words, although a sector may not be active, information received from that sector can later be recovered. Hence, this feature can be used for neighbor discovery including the interface information. An issue that needs careful consideration is that the discovery procedure indeed should locate all potential neighbors. In case a neighbor is not discovered, it can inadvertently interfere with the communication of a group. Although SAMAC can handle such unexpected cases, the performance is inevitably reduced. Therefore, finding all possible neighbors has a profound impact on the overall performance of the protocol. Another point of consideration is the assignment of weights to link qualities. Binary connectivity information is not quite useful if the link quality degrades the system operation. Hence, the neighbor discovery procedure should be capable of assigning weights to links. A traditional approach to this problem is to gather long term statistics about an interface, however, there may be insufficient periods of time to complete such operations. Therefore, efficient and fast algorithms to assess the link quality on links should be developed.
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Finally, the delivery of neighborhood information to the cluster heads is to be addressed. Since the schedule information, hence the time slots are not established at this stage of SAMAC, the communication needs to continue without any present schedules. A potential remedy to this issue is the use of contention-based simple protocols to deliver messages to the cluster head. The selection and potential simplification of such protocols also need special consideration. Optimization of Scheduling Algorithm The schedule generation procedure of SAMAC considers a sink tree composed of links of equal weights rooted at the cluster head. Using the link quality information, better paths can be included in the sink tree potentially unreliable links can be eliminated. Furthermore, paths that provide the required end-to-end bandwidth or reliability criteria can be established. Currently, the scheduling algorithm is based on a coloring heuristic that assumes uniform distribution of nodes and i.i.d. packet generation distributions. However, neither the location nor the potential load of the nodes are equal in a WSN environment. Therefore, it is imperative to consider the load carried in the subtrees in schedule computations. Furthermore, group weights can be considered so that groups with high data load can be split into groups sharing the same parent, which reduces per slot contention. Although this approach may potentially lengthen the super frame size, it would yield a better delay performance. The coloring procedure also requires further attention such that the assignment of time slots can start from the group containing the cluster head, or the group closest to the cluster head with no assignments, moving towards the leaf group. Furthermore, local color switching methods could be used to improve/optimize the delay performance across the network rather than for a single leaf group. 150
Recovery Algorithm Recovery from node failures is an important safety feature of any real-time and missioncritical system. In this cluster-based system, the operation heavily rely on the correct operation of all nodes as redundancies are eliminated to improve system performance. In case of node failures, the effects can propagate to more than the immediate neighbors of a node: When a node fails, the subtree in the downstream direction loses its connection with the cluster head. In most cases, alternative routes would exist, though their use would be eliminated to reduce contention and to improve delay performance of the system. If such a failure occurs, root nodes of the disconnected subtrees can indicate loss of connection via emergency messages. The emergency messages would be broadcast over all sectors at high repetition frequency to reach potential parents. Since the transceiver design allows the buffering of information received at inactive sectors, potential parents would be aware of such situations even though some of their sectors may never be used under a regular operation scenario. Then, local augmentation and schedule update procedures can be initiated. If such changes cannot be handled locally, then the cluster head may regenerate a new schedule based on a new neighborhood information. Dedicated time slots for maintenance is another method that can be employed in a later design of SAMAC. These time slots would be activated rather infrequently to ensure a lower overhead. This approach would allow the use of simpler transceiver designs and the additional maintenance time slots can be used for re-synchronization, neighborhood confirmation, and discovery of any unexpected changes not related to node failures. However, with this approach of additional maintenance slots, failures cannot be instantly recovered. Finally, the failure event of the cluster head requires a special treatment. First, the failure of the cluster head should be notified to all cluster members in a timely manner. 151
Then, the orphan cluster should be merged with other neighboring clusters. One method to achieve this is to merge the entire cluster with a neighboring one. Another option would be to partition the cluster and affiliate nodes to neighboring clusters according to their geographical locations and connections. For this purpose, the intervention of neighboring clusters’ head is required. Furthermore, necessary signal generation and exchange procedures should be developed.
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