Connectivity, coverage and power consumption in large-scale wireless sensor networks

Wireless sensor networks (WSNs) are typically constituted by a large number of connected sensors (nodes), generally distributed at random on a given surface area. In such large-scale networks, the desired global system performance is achieved by gathering local information and decisions collected from each individual node. There exist three fundamental global issues on WSNs that we consider here, namely, full network connectivity, high coverage of the sensing area and reduced power consumption, thus improving on the network lifetime. Full connectivity can be obtained either by increasing the transmission range, at the expense of consuming higher transmission power, or by increasing the number of sensors, i.e. by increasing network costs. Both of them are closely related to global network lifetime, in the sense that the higher the power consumption or the more the number of active sensors present, the shorter the network lifetime (Wang et al., 2007) [1]. Here, we are interested in the minimal number of active nodes required for keeping the network functioning, while the problem of redundancy, i.e. having additional nodes kept in a sleeping mode for a certain period of time, can be implemented afterwards based on the present ‘minimal’ results. So the main question is, how can one design large-scale random networks in order to have both global connectivity and minimum number of active nodes reducing the total energy consumption? Although these questions have been addressed often in the past, a definite, simple predicting algorithm for achieving these goals does not exist so far. In this paper, we aim to discuss such a scheme and confront it with extensive simulations of random networks generated numerically. Specifically, we study the minimum number of nodes required to achieve full network connectivity, and present an analytical formula for estimating it. The results are in very good agreement with the numerical simulations as a function of transmission range. We also discuss results on how to further diminish network energy consumption by switching off some of the active nodes at random by keeping the connectivity of the whole network. The present results are expected to be useful for the design of more efficient WSNs.