The Critical Range in Clustered Ad Hoc Networks: An Analysis for Gaussian Distributed Nodes

Connectivity is one of the essential properties of wireless networks. Although it is influenced by many environmental factors, it exhibits a strong and fundamental dependence on the distances between the nodes. Therefore, the connectivity of wireless networks from distance perspective has been a subject of constant interest for the research community. However, despite the fact that the assumption of uniformly distributed nodes is highly unrealistic for commercial wireless networks, analytical work on the connectivity of non-uniform node distributions is almost non-existent. In many real cases wireless nodes may be placed in a way such that they form clusters. In this letter we consider a set of clustered nodes distributed according to a symmetric Gaussian distribution and we present an approximate estimation of the probability density function of the critical range of the cluster. This is, to the best of our knowledge, the first estimation of the critical range for a clustered distribution.