On the Coverage and Detectability of Large-scale Wireless Sensor Networks

Advances in sensor and communication technologies have made it possible to manufacture small sensors with sensing, processing, and wireless communication capabilities in a costeffective fashion. A sensor network can be formed by deploying specialized sensors in the region of interest to perform certain sensing and networking tasks. Application scenarios of wireless sensor networks include battlefield surveillance, environment monitoring, and etc. Many of the above application scenarios involve a large number of sensors deployed in a vast geographical area. Coverage and detectability are two fundamental measures of the performance of a sensor network. In general, sensing coverage represents how well an area is monitored by sensors; and detectability represents the capability that a sensor network detects an object that moves through the network. Formal definitions of the coverage and detectability will be introduced shortly. Characterizations of these two measures present important implications to protocol design and performance of sensor networks. While most of previous related work on the sensor network coverage and detectability focuses on protocol design [1][2][3][4][5], the goal of our work is to define and characterize the coverage and detectability, and examine the implications of the results. To represent the coverage and detectability of a sensor network, we define the following quantities. Area coverage ( fa): the fraction of the geographical area that is in the sensing area of one or more sensors. The sensing area of a sensor is the area within which the sensor can provide a valid sensing measurement. This is usually represented by a circle centered at the sensor with a radius of the sensor’s sensing range. Node coverage fraction ( fn): the fraction of sensors whose sensing areas are fully covered by collections of other sensors. This quantity represents the redundancy level of sensors from a coverage perspective. It has a direct effect on the performance of energy-efficient protocols which turn off redundant sensors while preserving area coverage [1]. Detectability (pd): the probability that no path exists for an object to penetrate a large-scale sensor network from left to right or from top to bottom without being detected. An object is detected by a sensor if it enters the sensing area of the sensor. We consider the worst-case scenario for sensor networks and assume that an object can take arbitrary paths.