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Hierarchical and Nonhierarchical Three-Dimensional Underwater Wireless Sensor Networks

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Hierarchical and Nonhierarchical Three-Dimensional Underwater Wireless Sensor Networks Hierarchical and Nonhierarchical Three-Dimensional Underwater Wireless Sensor Networks S. M. Nazrul Alam Zygmunt J. Haas Department of Computer Science School of Electrical and Computer Engineering Cornell University, Ithaca, NY, USA Cornell University, Ithaca, NY, USA Email: [email protected] Email: [email protected] where sensors are deployed on earth surface and Abstract: In some underwater sensor networks, where the height of the network is smaller than the sensor nodes may be deployed at various depths of transmission radius of a node, can usually be an ocean making those networks three- modeled as two-dimensional (2D) networks. dimensional (3D). While most terrestrial sensor However, in many underwater sensor networks, networks can usually be modeled as two nodes may be placed at different depths of an dimensional (2D) networks, these underwater ocean and thus these networks must be modeled as sensor networks must be modeled as 3D networks. three-dimensional (3D) networks [1]. In many This leads to new research challenges in the area cases, network architecture and topology directly of network architecture and topology. In this depend on the physical dimensionality of the paper, we present two different network network and so results from 2D terrestrial sensor architectures for 3D underwater sensor networks. networks can not be used in 3D underwater sensor The first one is a hierarchical architecture that uses networks. In this paper, we try to address this a relatively small number of robust backbone issue and propose two approaches to build a 3D nodes to create the network where a large number underwater sensor network. The first one is a of inexpensive sensors communicate with their hierarchical network architecture where the nearest backbone nodes, and packets from a network is maintained by a small number of robust backbone node to the sink is routed through other and powerful backbone nodes. Actual sensing is backbone nodes. This hierarchical approach done by large number of inexpensive and failure allows creating a network of smaller number of prone sensor nodes. Once the sensing information expensive backbone nodes while keeping the reaches any backbone node, the information is mobile sensors simple and inexpensive. Along routed to the sink through other backbone nodes. with network topology, we also study energy Then we investigate frequency reuse issues for efficiency and frequency reuse issues for such 3D such 3D networks including variations due to networks. The second approach is a acoustic communication. We also study energy nonhierarchical architecture which assumes that efficiency of different hierarchical network all nodes are identical and randomly deployed. It topologies. The second approach creates a partitions the whole 3D network space into nonhierarchical network using one type of nodes. identical cells and keeps one node active in each This scenario is applicable where a large number cell such that sensing coverage and connectivity of nodes are randomly and uniformly deployed in are maintained while limiting the energy the network space. We exploit redundancy to consumed. We also study closeness to optimality improve network lifetime by partitioning the 3D of our proposed scheme. network space into identical cells such that only 1. INTRODUCTION one node remains active in each cell and full coverage and connectivity is maintained. We then Two major differences between terrestrial sensor extend our work for k-coverage, where any point networks and underwater sensor networks are in the network has to be within the sensing range network dimensionality (i.e., 3D instead of 2D) of at least k-nodes. We also provide comparison and communication medium (i.e., acoustic instead between our proposed scheme and the scheme of radio). Terrestrial wireless sensor networks, where an oracle can decide where to place the nodes (i.e., the optimal scheme ). Our scheme has [14] [17]. Cube is the only space-filling regular better performance for higher values of k. For polyhedron [12]. Triangular prism, hexagonal example, our study shows that our scheme can prism, cube, truncated octahedron [22] [27], and provide 4-coverage with probability 0.9971 with gyrobifastigium [15] are the only five convex twice the nodes needed by the optimal scheme. polyhedrons with regular faces that have space- filling property. The rhombic dodecahedron, The rest of the paper is organized as follows. elongated dodecahedron, and squashed Related works are described in Section 2. Section dodecahedron are also space-fillers. 3 presents the proposed hierarchical network architecture as well as frequency reuse issues and Kelvin’s conjecture [25] has been used in [2] to energy efficiency issues for 3D networks. Section show that if 3D network space is divided into 4 describes the proposed nonhierarchical network truncated octahedron cells such that the radius of approach and shows its closeness to optimality. each cell is equal to the sensing range of each Discussions on routing issues and possible future node, and a node is placed at the center of each research directions are described in Section 5. The cell, then this placement strategy requires paper is concluded in Section 6. minimum number of nodes. Kelvin’s conjecture was generally accepted a true for than a century 2. RELATED WORKS [28], but a counter example was found in 1993 Recent interest in three-dimensional underwater when it is shown that a space-filling structure sensor networks have generated a lot of research consisting of six 14-sided polyhedrons and two endeavors in 3D networking [20] [21] [8] [19] 12-sided polyhedrons with irregular faces of equal [9] [11]. volume has 0.3% less surface area than truncated octahedron [26]. But it is still unknown if Coverage and connectivity issues of 3D networks Kelvin’s conjecture is true for identical cells. have been explored in [2] and the solution Anyway, in a different context it has been shown provided in that paper works when the ratio of that body-centered cubic (BCC) lattice has the communication and sensing range is at least smallest mean squared error of any lattice 1.7889. This result has been generalized for any quantizer in three dimensions [5], which validates ratio of communication and sensing range in [3]. the results of [2]. In this paper, we use these results as a basis to determine where to place backbone nodes in our The aim of our nonhierarchical network hierarchical network. architecture is mainly to conserve energy by keeping a subset of the nodes active in a dense Frequency reuse for underwater acoustic sensor network to perform all necessary functions while networks have been investigated in [23] [24]. putting the rest of the nodes into sleep. This is a However, that work assumes that the network is very common approach in terrestrial sensor two-dimensional. In this paper, we extend that networks [29] [7] [31] [30] [6]. One important work work for a 3D scenario. Frequency planning in 3D in this context is geographic adaptive fidelity for radio network has been investigated in [10]. (GAP) [29] which only works for 2D network. Since some of the the analysis in this paper uses Our nonhierarchical architecture solves that the concepts of polyhedron, space-filling problem for 3D networks. It has been shown that polyhedron, Kelvin’s conjecture, and Voronoi GAP is quite inefficient in terms of number of tessellation, now we provide very brief references nodes being kept active. However, in this paper on them. Details on these concepts are available in we show that the efficiency of our 3D solution is [2]. A polyhedron is a three-dimensional shape higher than the efficiency of GAP in 2D. that consists of finite number of polygonal faces. A space-filling polyhedron is a polyhedron that 3. HIERARCHICAL NETWORK tessellates a 3D space. It is hard to show that a ARCHITECTURE polyhedron has space-filling property. For In this section, we describe a hierarchical 3D example, Aristotle himself made a mistake when network architecture that has two different types claimed that the tetrahedron fills space [4] and that of nodes – more powerful and robust backbone mistake remained unnoticed until the 16th century nodes, and less powerful and failure prone sensor 2 nodes. The network is built and maintained by the algorithm. One major criticism of this backbone nodes such that a backbone node can assumption is that GPS does not work communicate with the network sink over a multi- underwater and we do not have any robust hop path using other backbone nodes as routers. positioning mechanism for underwater Sensing is done by inexpensive sensors that move network yet. However, this assumption along ocean current and send the sensing ensures that our solution provides the lower information to the nearest backbone node. Each bound of the number of nodes needed to backbone node is equipped with a localization achieve full coverage and connectivity. component while mobile sensors are oblivious of Research in underwater localization is gaining their locations. There are several challenges to momentum [8] and it is possible that robust build such a network. Since the backbone nodes underwater positioning mechanism will be are expensive, we want to minimize the number of available in near future. backbone nodes while ensuring the mobile sensors can have a backbone node within an acceptable 3.1 Network Topology distance (i.e., maintaining coverage ) and also a In this subsection, we investigate the problem of backbone node can directly communicate with its finding a placement strategy that deploys neighboring backbone nodes (i.e., maintaining minimum number of backbone nodes in our connectivity ). It is also important to make sure that hierarchical network such that any mobile sensor interference at backbone nodes and at mobile can directly communicate with at least one sensors is limited. backbone node and any backbone node can Assumptions directly communicate with any other backbone node , possibly over a multi-hop path, through the • Homogeneous sphere-based communication: network created by the backbone nodes.
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