An Analysis of K-Connectivity in Shadowing and Nakagami Fading Wireless Multi-Hop Networks

In this paper, we develop kappa-connectivity in wireless multi-hop networks in the presence of both the log-normal shadowing and Nakagami-m fading. The formula are generally applicable in a variety of realistic physical situations. Based on the results, we are able to find the critical node density to satisfy node kappa-connectivity almost with probability 1. In addition, kappa-connectivity shows significant difference with distinct channel conditions, which necessitates a generic result. The result is useful for the design of a wireless multi-hop network in practice.