Coverage Hole Detection and Healing to Enhance Coverage and Connectivity in 3D Spaces for WSNs: A Mathematical Analysis

The coverage and connectivity are the two imperative performance metrics for the growth of wireless sensor networks (WSNs) with sprouting technologies. In order to maintain these metrics, the issue of finding and healing of coverage hole is closely related to these two facts and plays a vital role in the performance improvement of the network. Many works in the past explored for 2D-WSNs, but now the time has come to investigate this matter for 3D-WSNs to reach the new heights of research and technology. In this paper, different scenarios with respect to the deployment of sensor nodes or network topology with the presence of different shaped coverage holes are discussed. Not only this, to heal these perceived holes introduction of sensor nodes having sensing radius different from initial deployed sensors has been suggested which in turn outlines the development of heterogeneous sensor networks, a keen issue with respect to technology development. This deployment of sensors to constitute heterogeneous sensor networks also influences the overall network cost in terms of cost reduction with an optimum coverage level. A mathematical analysis to give a relationship between the radii of former and later deployed sensor nodes is presented in the form of theorem. At the end, the results and discussion in order to achieve a specified level of coverage with respect to different packing patterns based on the mathematical analysis are provided. Also, some future directions to guide the researchers are discussed in this paper.