A study on the weak barrier coverage problem in wireless sensor networks

Anti-intrusion is a typical application of wireless sensor networks (WSNs). It usually requires sensor nodes to be deployed in a long belt region. The coverage problem in this kind of applications is often referred to as barrier coverage, which is classified into weak barrier coverage and strong barrier coverage. A belt region is called weakly k-barrier covered (k ⩾ 1) if an intruder traveling along any orthogonal crossing path can be detected by at least k sensors. For sensor deployment in a belt service region, an interesting and important question is “How many sensor nodes should be deployed to achieve weak k-barrier coverage with a given probability?” In this paper, we study the weak k-barrier coverage problem and attempt to answer this question by analyzing the probability of weak k-barrier coverage. We derive a lower bound for the probability of weak k-barrier coverage with and without considering the border effect, respectively. Moreover, we propose a simple but effective algorithm for accurately determining whether a deployed belt region is weakly k-barrier covered, and if not, what percentage of the region is not weakly k-barrier covered. Simulation results show that the derived lower bound is very close to the actual probability of weak k-barrier coverage, especially when k is small, and the border effect has a big impact on the probability of weak k-barrier coverage.