Quantifying Connectivity of Grid-based Wireless Sensor Networks under Practical Errors

Grid-based deployments of Wireless Sensor Networks (WSNs) are widely used in a multiplicity of applications. However, practical factors such as communication irregularity and placement uncertainty have to be considered for more efficient deployments. In this paper, we examine connectivity properties of the 3D grid-based deployment when sensor placements are subject to random errors around their corresponding grid locations and hindrances to wireless communication channels exist. A generic approach is proposed to evaluate the average connectivity of the deployed network. This generic approach is independent of the grid-shape, random error distributions, and the environment wireless channel characteristics. The average connectivity is computed numerically and verified via extensive simulations. Based on the numerical results, quantified effects of positioning errors and grid edge length on the average connectivity are demonstrated. Furthermore, we discuss several ways of achieving efficient grid-based deployment planning for connectivity, and illustrate these approaches through numerical examples.