Regular Node Deployment for k-Coverage in m-Connected Wireless Networks

k-coverage is an important issue in many applications of m-connected wireless networks, such as localization of objects, mobile robotics, and tourism industry, where k >= 1 and m >= 1. From the cost perspective, it is often very important to maintain the desired level of coverage and connectivity with a minimum number of nodes. In this paper, we address the problem of optimal deployment in term of the number of nodes required to achieve k-coverage in m-connected wireless networks under different values of k, m, coverage range, communication range, and area of the irregular field of interest (FoI). We divide the FoI into regular patterns and estimate the optimal distance between nodes and pattern for k-coverage in m-connected wireless networks. Next, we estimate the minimum number of nodes and their locations required for the coverage and connectivity. We validate the analysis and demonstrate the impact of k, m, coverage and communication ranges, and the FoI on the number of nodes using numerical, simulation, and prototype results.