Coverage and connectivity in three-dimensional networks with random node deployment

Abstract

The increasing interest in using sensor networks in applications for underwater surveillance and oceanic studies underscores the importance of solving the coverage and connectivity issues in 3D wireless sensor networks (WSN). In particular, the problem of supporting full coverage, while ensuring full network connectivity is a fundamental one for such applications. Unfortunately, designing a 3D network is significantly more difficult, as compared to designing a 2D network. Previously, it has been shown that dividing a 3D space into identical truncated octahedral cells of radius equal to the sensing range and placing a sensor at the center of each cell, provides full coverage with minimum number of nodes [2]. But this requires the ability to deploy and maintain sensor nodes at such particular locations. In many environments, this is very difficult, if not impossible, to do. In this paper, we investigate the coverage and connectivity issues for such 3D networks, especially underwater networks, while assuming random and uncontrollable node locations. Since node location can be random, redundant nodes have to be deployed to achieve 100% sensing coverage. However, at any particular time, not all nodes are needed to achieve full sensing coverage. As a result, a subset of the nodes can be dynamically chosen to remain active at a time to achieve sensing coverage based on their location at that time. One approach to achieve this goal in a distributed and scalable way is to partition the 3D network volume into virtual regions or cells, and to keep one node active in each cell. Our results indicate that using cells created by truncated octahedral tessellation of 3D volume minimizes the number of active nodes. This scheme is fully distributed, and so it is highly scalable. By adjusting the radius of each cell, this scheme can be used to achieve k-coverage, where every point inside a network has to be within the sensing range of k different sensor nodes. We analyze and compare the performance of these schemes for both 2D and 3D networks. While for 1-coverage, the 3D scheme is less efficient than the 2D scheme, the performance of 3D scheme improves significantly as compared to 2D scheme for k-coverage, for values of k is larger than 1. As a result, such a distributed and scalable scheme can be more useful in 3D networks than in 2D networks. Although this paper targets in particular 3D underwater networks, much of our results are applicable to other 3D networks, such as for airborne applications, space exploration, and storm tracking.