Connectivity Probability of Interference-Limited Linear Multi-Hop Ad-Hoc Networks
Dali Hu, Jingxian Wu, Pingzhi Fan · 2016
In this paper, we study the connectivity probability of linear multi-hop ad hoc networks operating in an interference-limited environment. The nodes in the network are assumed to form a Poisson point process (PPP), and they generate mutual interference during communications. A node communicates to other nodes in the network by using its intermediate neighbors as relays. The average node density plays a crucial role on the communication quality. A higher node density means shorter transmission distance for each hop, but also a stronger interference from surrounding nodes. We characterize this tradeoff relationship by deriving the analytical probability that all nodes in a finite section of the network are connected, that is, the signal-to-interference ratios (SIRs) of all adjacent node pairs in the finite network section are no less than a threshold. The connectivity probability is expressed as an explicit closed-form function of various system parameters, such as average node density, the length of the network section, pathlosss exponent, and the SIR threshold. It is shown through theoretical analysis that the connectivity probability is a quasi-concave function of the node density, and the optimum node density that can maximize the connectivity probability is identified.