Analysis of k-Hop Connectivity Probability in 2-D Wireless Networks with Infrastructure Support

Wireless multi-hop networks with infrastructure support have been actively studied to solve the scalability problem in large scale vehicular and sensor networks that the end-to-end throughput and other performance metrics decrease sharply with the increase in the number of nodes in the network. In the infrastructure-based networks, wireless nodes are allowed to access the base stations either directly or via a multi-hop path. In order to provide meaningful services, it is often desirable to limit the number of hops in the wireless multi-hop path. In this paper, we study a 2-D wireless network where users are Poissonly distributed in a square area and base stations are placed at the four corners of the square area as a typical component of a larger network where users are randomly distributed and base stations are regularly deployed. We obtain analytically the exact and approximate k-hop connectivity probability for k = 2, i.e. the probability that all users can access to at least one base station in at most two hops, under a generic channel model. The results are verified by simulations and can be used in network planning, design and resource management.