Analysis of the redundancy in coverage of a heterogeneous wireless sensor network

A heterogeneous wireless sensor network (WSN) consists of sensors with unequal ranges of sensing and/or communication. In a dense WSN, a part of the region covered by a sensor may also be covered redundantly by a neighbouring sensor. In this paper, we analyse the redundancy in the coverage of a heterogeneous WSN and define the redundancy degree of a sensor. We follow a probabilistic approach to derive the expected redundancy degree of a sensor with a given number of sensors of each type in the neighbourhood. We demonstrate the accuracy of the analysis, and study the impact of the number of sensors of different types on the expected redundancy degree with numerical and simulation results. We also demonstrate an application of the redundancy analysis in the design of a heterogeneous WSN. We propose an algorithm to determine the minimum number of sensors of different types required to satisfy the desired coverage ratio and simultaneously minimise the cost of the network.