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Recently, the wireless sensor networks are a hot research topic. Wireless sensor networks include many small-size and power-saving devices, normally used for sensing data and exchange information. In the wireless sensor network, a device called a node does not need a control system to control all transmission. It forms a network by itself and transmits information to remote destinations through multihop.

The wireless sensor networks have some characteristics, such as limited energy consumption, high-density deployment, the implementation of low-cost, and so on.

Based on the above reasons, wireless sensor network has widely be used in many applications, such as emergency applications, environmental monitoring, object detection, data collection in battlefield and monitoring system at home.

In a distributed system, time synchronization mechanism is a very important topic in wireless sensor network for the following reasons. First, they need a standard time in order to coordinate and communicate to each other. Second, the nodes must wake up and sleep at the same time for power-saving reason, so they need synchronization. Third, some scheduling algorithms such as TDMA need time synchronization, because they need to know the exact time slide to communicate information to each other. For these reasons, we must have an effective mechanism for time synchronization in order to facilitate the practical application.

There are so many people trying to develop the wireless sensor network for an underwater environment. The wireless sensor network in the underwater there are many applications, such as environmental monitoring, ocean current observation,

energy exploration…etc. These applications need time synchronization as well. The biggest difference is the transmission medium between land and underwater. There is a long propagation delay in the underwater, because the transmission medium is the acoustic wave. The speed of the acoustic wave is nearly 5 order of magnitude slower than radio on the land. The existing time synchronization schemes have a characteristic on the land, that the propagation delay is short. Therefore, we can ignore this propagation time for the time synchronization on the land. Nevertheless, the result will cause a great error, if we use the same method to finish the time synchronization in the underwater.

In the land, the most widely used scheme is NTP[1] for time synchronization in internet in wired environment. This scheme used the traditional way to achieve time synchronization. The traditional time synchronization is that two nodes transmit a packet to each other, respectively. The nodes record the transmit time and the receive time, then they can calculate the time offset for each other. It is not appropriate to the wireless sensor networks because of the non-determinism problem. The non-determinism is that the time difference between the time of the packet be construct and the time of the packet be send. In wireless sensor networks, RBS[3]

proposed a scheme that can eliminate the non-determinism problem in the sender side.

This method was based on the relative time difference of reference message packets arrived in each wireless sensor node. Therefore, we can get precisely time synchronization in the wireless sensor networks. In [4], they used the tree structure to achieve the time synchronization in wireless sensor networks. In [5], they greatly reduce the packet number than RBS in order to prolong the lifetime of the sensor node.

The above schemes, all of them can use its methods to finish the time synchronization in single-hop. But, they usually were based on a principle that a reference node start

the procedure of the time synchronization in its transmit range. After that, a node which is picked up in this area redo the procedure in its transmit range until all nodes finish the time synchronization. Although this procedure can complete the time synchronization in multihop, they have some drawbacks. First, it needs to spend long time to finish the time synchronization in multihop, especially in large scale wireless sensor network. Second, each node has some time error because of the clock drift.

Which means that the node which far away the reference node at very beginning will get more time difference than others. Therefore, we need a scheme that can reduce the hop counts in certain way.

We proposed a modified time synchronization in single-hop from RBS[3], coupled with the concept of small world. This method can greatly reduce the problem that we mentioned before. The small world phenomenon has two characteristics. The average path length (hop count) is low between the nodes in the network, and the cluster coefficient is high in the network. Small world is a phenomenon that discussed how each individual in the real world has relationships to other people. [7] performed a series of mail delivery experiments in 1967. By given receiver’s information, each individual who received this mail forwarded it to the next person according to receiver’s information such as address, career or race. In this experiment, Milgram found that an average of five and six intermediate delivers before the final receiver gets the mail. This work first quantified the famous concept of “six degrees separation” between any individual on earth. In [9][10], they further found that the cluster coefficient is good in the regular graph, but the average path length is very long. We just need to re-wired some links with the node in long-distance result in the average path length greatly reduces between the nodes. The kind of the links called shortcut. This kind of the network called a small world network.

The time synchronization in the wireless sensor network, nodes usually communicate information to each other by radio waves. In the view of small world, the link between nodes can be regarded the link as the relation between the nodes.

Original idea is that how we can create a small world phenomenon in wireless sensor networks. At this moment, some nodes must have a long-distance transmission capacity that can send the packet to the node in long-distance. This called shortcut in small world. We use the directional antenna to communicate the node in long-distance to form the small world phenomenon in the large scale wireless sensor network.

The scheme we proposed is as follows: First, we randomly pick up a node that called reference node. This node broadcasts a reference packet to the neighbors within its transmission range. The nodes which receiving this reference packet can use the technique of the time difference to estimate the time offset between itself and the time server. Second, the nodes that finished the time synchronization in this area start a new round to its neighbors that did not finish the time synchronization. And, some nodes that finished the time synchronization use the directional antenna to communicate the node in long-distance to finish the time synchronization. Third, the nodes that finished the time synchronization become a time server to repeat the step 1 and 2 until the all nodes complete time synchronization. In step 2, we use the transmission model from [8]. Each node connects another node in long-distance with random way. The result shows that we can greatly decrease the hop count in the wireless sensor network.

In the underwater, [16] proposed a method that finishes the time synchronization by time-stamping the packet in the MAC layer. In [17], the author found that the

overhead is high in the previous method. The previous method will cause excessive power-consumption. The author uses mathematical analysis to find the main error source: to decrease the number of the packets in order to prolong the life cycle of the sensor node. In previous works, in order to finish time synchronization, the authors all stamp the time information in MAC layer to decrease the time error from the non-determinism time. Although, these methods can finish the time synchronization in underwater, but there is a drawback as below: we have to modify the MAC layer.

Before we deploy the wireless sensor network, in order to achieve the purpose of the time synchronization, we need to modify the MAC layer. Let the packet can be stamped the time information in MAC layer before the packet be sent.

The method we proposed is as follows. First, we use the Underwater Positioning System (UPS) [15] to locate the position of each node. Second, we use the technique of the time difference to estimate the time offset between each node and the time server in order to finish the time synchronization. The biggest characteristic is that we can finish the time synchronization in the application layer without any modification in other layers.

The results show that the mechanism we proposed can greatly decrease the convergence time for the time synchronization in the large-scale wireless sensor networks. We use the directional antenna to form small world phenomenon in the wireless sensor network. Each node reduces the hop count between itself and the time server in the wireless sensor networks. In other words, the time error will be relatively lower between the nodes. In the underwater, the simulation shows that the accuracy level of the time synchronization is

μ

s and the time synchronization we proposed can finish the procedure in the application layer without any modification in other

layers.

The organization of this thesis is as follows: We discuss what is the traditional time synchronization mechanism, the problems in the traditional time synchronization mechanism, and the previous works in section 2. In section 3, we will explain the concept of small world phenomenon. In section 4, we describe that the time synchronization we proposed in more detail, including the time synchronization in the land and the time synchronization in the underwater. In section 5, we present the simulation results and analysis.

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